Pion-Pion Decay Distributions for π⁻p → π⁺π⁻n at 100 and 175 GeV/c Citation Stampke, Stuart Reh (1982) Pion-Pion Decay Distributions for π⁻p → π⁺π⁻n at 100 and 175 GeV/c. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/bfmr-3581. https://resolver.caltech.edu/CaltechTHESIS:05172018-112232901 Abstract We report measurements of the reaction π - p → π + π - n at 100 and 175 GeV/c using a large wire chamber spectrometer at Fermilab. Production of ρ 0 , f 0 , and g 0 resonances was observed. Cross sections for π - p → π + π - n in the ρ 0 mass region are given. Decay angle distributions for ππ masses from .55 to 3.5 GeV/c 2 are presented. Moment analyses of the decay distributions are made as a function of ππ mass from .55 to 2.4 GeV/c 2 . Contours of ππ decay distribution dips are given in s ππ and t ππ . Comparisons with several lower energy experiments are made. Detailed discussions of the apparatus, trigger, and analysis procedures are given. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Fox, Geoffrey C. Thesis Committee: Fox, Geoffrey C. (chair) Frautschi, Steven C. Barnes, Charles A. Gomez, Ricardo Pine, Jerome Defense Date: 4 May 1982 Funders: Funding Agency Grant Number Department of Energy (DOE) UNSPECIFIED Record Number: CaltechTHESIS:05172018-112232901 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:05172018-112232901 DOI: 10.7907/bfmr-3581 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 10911 Collection: CaltechTHESIS Deposited By: Mel Ray Deposited On: 02 Jul 2018 23:40 Last Modified: 24 Apr 2025 22:17 Thesis Files Preview PDF - Final Version See Usage Policy. 133MB Repository Staff Only: item control page

Pion-Pion Decay Distributions for rr-p 41T+1T-n at 100 and 175 GeV le Thesis by Stuart Reh Stampke In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1982 (Submitted May 4, 1982) -ii- To Marian -iii- That voice was damned familiar. "Majistral is going to the John Bull," said the pope. "We can catch up V'¥ith him later." y. p. 441, Thomas Pynchon -iv- Acknowledgements This thesis is rather long . I have also taken too long as a student, a period filled with peaks of interest and joy as well as valleys of difficulty. Before closing it, I want to thank the many collegues and friends who helped me through it. For my parents, George and Grace Stampke, my brother Don, my sisters Paula, Sue, and Kathy, their children, and my departed uncle AL for their love and for their quiet and important support while I pursued a crazy goal, my greatest love and gratitude. It is a pleasure to thank my advisor, Geoffrey Fox, for his many insights, his comments and encouragement, his help in the completion of this thesis, and especially for allowing me the freedom to deal with a difficult period three years ago. I am grateful to Jerry Pine for being my advisor in my early years here, for letting me work on this experiment, and for refusing to let me quit . It is difficult to find the words to thank Clara and Ricardo Gomez. My love for them is deep. Ricardo tried to teach me some difficult lessons, both professionally and personally. Some I learned, some not. And finally during a crisis, they opened their home to me . Geoffrey, Ricardo, and Jerry: for your support, your counseling, your help, your criticisms, the friendship, and for just plain putting up with me, I thank you. I thank my collaborators on El 10 and E260. Together we built a major spectrometer and performed two interesting experiments with it. I credit our successes to them: C. Bromberg, J. Dickey, G. C. Fox, R. Gomez, W. Kropac, C. Malone, and J. Pine from Cal Tech; V. Ashford, H. Haggerty and E. Malamud from Fermilab; R. Abrams. R. Delzenero, H. Goldberg, F . Lopez, S. Margulies, D. Mcleod and J. Solomon from UICC; A. Dzierba, F. Fredericksen. R. Heinz, J. Krider, H. Martin, and D. Petersen from Indiana University; and E. Lorenz, M. Medinnis, and P. Schlein from UCLA. -vThe list must include Carl Malone. While working at Cal Tech he built much of hardware I was responsible for, and he built well. Carl also spent as much time in the trenches as many in the above list. For their technical skill in building equipment as well as their friendship I thank Jozef Ungerer, Svend Sondergaard, Hans Grau, Dan Sell, Joe Lyvers and Dean Davey. For contributing precious time and effort in preparation for our winter 1978 run I thank Bob Walker, and Alan Barnes. Several undergraduates were also essential to this experiment. G. Ray Beausoleil, W. Danchi, and C. Footman all made significant contributions to our analysis. I want especially to thank Louise Sartain, Roma Gaines, June Bressler, and Nancy Durland not only for their secretarial skill and dedication, but for their friendship. Student life at Cal Tech would have been unbearable without them, and without an understanding counselor. For me this was Lee Daniels of the Athenaeum. Special thanks to my "co-conspirators", Rich Delzenero of UICC, Frank Fredericksen of Indiana, and Kar Yung of Cal Tech. We worked closely and productively together. This was especially true of Frank and I, even though half a continent usually separated us. I thank Bob Blair and George Zweig for many varied and interesting hours of conversation on Physics and other things. For· literally opening the door to High Energy Physics for me, I thank Frank Sciulli, Steve Frautschi, and Jerry Pine. For getting me into Physics in the first place, I thank Duane Doty, Ryoichi Seki, and especially Robert Romagnoli of CSUN. Nine years as a graduate student is a long time. Without the friendship of my collegues, and friendships both inside and outside Cal Tech, I might have never lasted it. Ruth Hitchcock, Alix Martin, and Jim Lowry in Bloomington Indiana befriended me at a crucial moment. My love for them is undiminished by time or distance. -viLynn Anderson, Rosemary Baltrusaitis, Alan Barnes, Mark Bartelt, Tere Blair, Alena Bobb, Eugene Brooks, Wyatt Brown, Linda Contos, Rajan Gupta, Cindy and Shawn Hennegan, Rosemary Kennet, Jai Sam Kirn, Steve Knapp, Bill Kropac, Ken McCue, Frank Merritt, Frank Nagy, Beth Nordholt, John Osborne , Becky Rothenberg, Bonnie Strand, Lon Schlundt, Steve Sherman, Eric Siskind, Claude Stevenson, Cathy Van In.gen, Norman Wilson, and the Siskind Memorial Friday Lunch Bunch are honored and respected for their help and their friendship. I thank the technicians of the Meson Lab and the Target group at Fermilab for their technical support. The analysis for this thesis used the Fermilab Cyber computers. That system was a joy to use . This thesis was "typed" on the Cal Tech High Energy Physics VAX computer using the word processing and typesetting program "troff" under the UNIX operating system. Lastly, I want to thank the United States Department of Energy . They paid for all this. I hope the coming years will see the investments in me made by them and by Cal Tech pay off. -vii- Abstract We report measurements of the reaction rr-p ~ rr+rr-n at 100 and 175 GeV /c using a large wire chamber spectrometer at Fermilab. Production of p 0 , f 0 , and g 0 resonances was observed. Cross sections for rr-p ~ rr+rr-n in the p 0 mass region are given. Decay angle distributions for rrrr masses from .55 to 3 .5 GeY /c 2 are presented. Moment analyses of the decay distributions are made as a function of rrrr mass from .55 to 2.4 GeV /c 2 . Contours of rrrr decay distribution dips are given in smr and tmr. Comparisons with several lower energy experiments are made. Detailed discussions of the apparatus, trigger, and analysis procedures are given. -viii- Table of Contents page Acknowledgements iv Abstract vii Chapter I. Chapter II. Introduction 1.1 Perspective 1.2 El 10 1.3 Almost Raw Data Apparatus 2.1 Overview 2.2 M6 West 2.2.1 Beam Cerenkov Counters, Beam Composition 2.3 The MPS 2.3.1 Beam and Interaction Counters 2.3.2 Target 2.3.3 Target House, Forward Photon Detectors 2. 3. 4 Magnet 2.3.5 Spark Chambers 2. 3. 6 Proportional Chambers 2.3 . 7 Shift Registers 2.3.8 Cerenkov Counters Cl and C2 2.4 Triggers 2.5 Beam Momentum, Resolution 1 15 -ix- Chapter ill. Event Reconstruction and Scaler Analysis 3.1 Introduction 3.2 TEARS 3.3 Event Selection 55 3.3.1 Run Rejection, Data Set 3. 4 Chapter N. Sc al er Analysis Data Corrections 4.1 Weights 4.2 Veto Failure Background 4.3 Neutron Vetos 4.4 BCD Delta Rays 4.5 A-Station Trigger Correction 4.6 Target Region Delta Rays 4.7 Interaction and Decay Losses 4.8 Chamber Efficiency Correction 4.9 Background Rejection by Cl and C2 76 4. 10 Beam Corrections 4.11 Weight Summary Chapter V. Acceptance, Cross Section, Moments 5.1 Acceptance 5.1.1 Acceptance Weights 5.2 General Correction Formalism 5.2.1 Moments 106 -x5.3 Cross Section Results 5.4 The rm Mass Spectrum 5.5 Moments versus Mass 5.5.1 A PW.A Test Chapter VI. 5.6 Moments versus tpn 5.7 da · dt D.is t n 'b u t ions Decay Distributions 6.1 Scatter Plots 8.2 Resonance Region 6.3 High Mass, Low tpn Fits 6. 4 Tran.sf ormation to t r.rr 147 6.4.1 High Mass Exponential Slope Appendix A 6.5 Dips 6.6 Review Kinematics, OPE, PMA 182 A.1 Kinematics A.1.1 tTm A.2 One Pion Exchange A.3 Appendix B PY~ Trigger Electronics 196 -xiAppendix C AppendixD TEARS C.1 Overview B.2 Straight Line Fits C.3 Matching and Match Cleanups C.4 Beam Processing C.5 Targtrk C.6 Vt rig C.7 Kinks Corrections D.l Introduction D.2 Veto House Correction 207 223 D.2.1 Measurement D.2.2 Backgroun.d Subtraction D.2 .3 tJ.0 Smearing D.2.4 BB Failure D.3 Neutron Vetos D.4 BCD Delta Rays D.5 Target Region Delta Rays D.6 · Chamber Efficiency Measurements References 237 -1- Chapter I Introduction 1.1 Perspective Studies of the reaction ( 1.1) have been an important part of the high energy physics agenda since the first observations [St61, Er61, Pi61] of p mesons were published in 1960 and 196 1. These occurred not long after such resonances were predicted [Dr58, Fr59] to explain nucleon electromagnetic form factors. Interest in reaction ( 1.1) has largely focused on the creation and decay of the final state rm system as a map of the forces between pion pairs, and between pions and nucleons . At beam energies above a few GeV, one can view the reaction as a "quasi two body" reaction, in which either the final state pions are associated ·with each other, or one of them is associated with the recoiling neutron. If we draw one particle exchange diagrams for reaction (1.1), as in figure 1-1, these interpretations yield 1-la and 1-lb. Our experiment favors 1-la over 1-lb mainly by its design, which limits the rr± - neutron acceptance to high masses. The rm effective mass spectrum for reaction 1.1 observed in previous experiments, for example [Bo64, Hy68, Ro73, Gr74, Co78, and Wi78], is dominated by the prominent p 0 (770) and f 0 ( 1270) resonances. To a lesser extent, the g 0 ( 1700) state . was also visible. The (.,.) 0 (783) meson has a small branching fraction to rr+rr-. and its presence in reaction ( 1.1) is felt mainly through electromagnetic interference effects with the dominant p 0 . A continuum of effective masses is also present, and fine scale features of the mass spectrum, when coupled with analyses of the rrrr decay angle distribution have revealed evidence for other states not appearing readily in effective mass spectra. Reported states decaying to rrrr include [PDGBO] -2- .,,.- .,,.- .,,.+f 0 p n Figure 1-1. One particle exchange diagrams for reaction (1. 1) (a) Ti7:' interaction at the upper vertex, which may or may not be resonant . (b) iiN interaction at the lower vertex. Either vertex may or may :::ot be resonant. (a) is kinematically favored by the spectrometer over (b) . Resonant interactions at both vertices are backgrounds suppressed by the trigger. the s•(980) , c(1300), f(1515), p'( 1600), and h(2040). Of these, the h 0 comes closest to having a visible effect on simple mass plots. The rm decay distribution and the mass spectrum also show non-resonant effects from the Tiii ir:te::-ac tion. Sharp drops in mass spectra have been interpreted as caused by zeros in the 1irr interaction amplitude entering into kinematically allowed regions. The first s~ch drop occurs at about 1 GeV /c 2 effective pion mass and the amplitude zero inte rp retation probably competes with explanations based on the inelastic thres2old for 1m4 KK and the existence of the S •. The first p meson observations were interpreted as evidence for el astic '.iIT scattering, with the "target" pion being a virtual particle emitted by the !'2.uc leon. Although no real pion targets exist, rm scattering has remained a fairly important and interesting area of strong interaction studies. Data extrapolation procedures beginning with the work of Goebel [Go58] and Chew and Low [Ch59], have allowed reasonable determinations of the mr scattering parameters from a number of reaclions. The mr system found in reaction (1.1) is thus surprisingly complex, and high statistics data are needed to observe all, or most of the above mentioned features . -3- Reaction ( 1.1) is representative of a tremendous number of exclusive (all final state particles determined or detected) reactions studied in the last twenty years. Most of these studies were made at beam momenta less than about 20 GeV le on interactions characterized by relatively low, -lGeV/ c 2 < t ~ 0, momentu..rn transfer between target and recoil systems. A wonderful and varied hadron spectroscopy and the dynamics seen in low t experiments have both enriched and help to trouble high energy physics. The sheer number and variety of mesons, along vrit h a like proliferation of baryon states, helped show that most observable p~ticles "':: ere not, as once hoped, fundamental, while at the same time providi:ri...g the imtial \~ e r i ~~cc..: ~ cn of the quark model and unitary symmetry classification schemes. A "peripheral" reaction [Ja65], ( 1.1) is characterized by a dominance of small momentum transfers from the proton to the neutron at beam energies above a few GeV. Over half the examples of reaction ( 1.1) in this experiment v.-ere found at It I <. 15 (GeV /c) 2 . Such collisions are relatively soft, and can be viewed as resulting from the longest range form of strong interactions. In this, one begins to co~ider the second main focus in studies of reaction (1.1), the strong interactions between pions and nucleons. At low t, coupling constants are too large to permit straightforward perturbation analyses of the interactions involved. Quantitative an.d specific theoretical predictions about the behavior of the strong force (its explicit dependence on observable variables) in this region have come onJy with concerted effort. Phenomenological analyses, which have blended fairly general principles with reasonable models, have also been fruitful, leading one to believe that many of their results should be derivable from whatever final theory evolves. However, although the successes have been considerable, and important features of the strong force have been quantified, the dynamics of low t interactior1s have been difficult to interpret theoretically. -4- Modern origins of the peripheral model for low t interactions are found in the work Chew, Low and GoebeL and that of Drell [Dr60]. The simplest peripheral model is just one pion exchange (OPE), in which the exchange of figure 1-la is a virtual pion. However, although rr exchange dominates many reactions, simple OPE is too simple a description for ( 1.1) and any other reaction allowing rr exchange. A number of features of the data are simply inconsistent with OPE and other effects must be present. The simplest models for these are absorbed rr excli...ange models, such as the Williams or "Poor Man's Absorption" (PMA) model [Wi70, Fo71a, Fo7 ~ b, Wa73, and Oc73]. In PMA, one has a simple analytic model for the effects of absorption on basic rr exchange. PMA appears to be the simplest model that can describe the general features of reaction ( 1.1) in the low ( < .15( Ge VI c ) 2 ) t region . .The agreement ·with data has been rather good [Oc73, Wi78], and rather detailed studies are needed to see the limitations of the model. Although the significance of its success is still unclear, the model has been surprisingly resilient. Appendix A includes a brief review of OPE and PMA, and defines the kinematic symbols used in this thesis. PMA generally ignores the effects of other allowed exchanges. A more reasonable approach would be to invoke the principles of Regge theory, in which not virtual particles, but poles in the complex angular momentum plane associated with them represent forces. For reaction ( 1.1) other exchanges both allowed and found required by low energy data include Alo A2 Regge poles and cuts associated with the rr and A poles [Ki73, Ki77]. At this level of complexity, Regge models of rr-p 4p 0n are in excellent agreement with data up to 63 GeV le [Ki77, Al78]. Despite early difficulties, Regge theory has been found a reasonable, although complicated, framework for describing low and intermediate t hadronic interactions. This is a regime in which the more fundamental form of strong interactions, the color force of QCD [Fi78], currently runs into computational problems because -5- of large coupling constants and nonperturbative binding effects. In this context, the many complications needed for a Regge model of relatively "simple" reactions such asp production are not unreasonable. Although no longer on the frontier of high energy physics, e};..'Periments on peripheral interactions, such as reaction ( 1.1), still have a place. They can add to our spectroscopic knowledge, and continue to map the strong force in an old, but still difficult region. Any allegedly true theory applicable to strong interactions must be able to quantitatively predict the dynamics seen by such an ez,.-periment . This report, will hopefully add to the data set for such tests. Our e:x'})eriment is the highest energy counter experiment to study reaction ( 1.1). 1.2 EllO The experiment described in this report, Fer;nilab El lOA, grew out of three proposals (numbers 35, 51, and 54) submitted to the then National Accelerator Laboratory for peripheral physics experiments with large aperture, spark chamber spectrometers located in hadron beams. The initial El 10 proposal [Pi71] projected a systematic physics program covering s and t dependences of a series of quasitwo-body peripheral interactions, new resonance searches, and rm and Krr scattering measurements, all at beam energies up to 80· GeV. At the time it was proposed, 1971, the studies of El 10 were of topical interest. There was also a desire for a large, general purpose spectrometer facility at Fermilab. An am.ended proposal, 1 lOA [Pi72], was submitted in May 1972, and approved shortly thereafter. Some changes to the proposed spectrometer were made, the physics program was somewhat extended, and beam energies up to 200 GeV were projected. At that time, the EllO collaboration consisted of experimenters from Cal Tech, Fermilab, Indiana University (IU), the University of Illinois Chicago Circle (UICC), and the University of California Los Angeles (UCLA) . -6In 1973, during the early construction of the El 10 spectrometer, a second proposal. E260 [Pi73], was submitted by the EllO collaboration for an investigation of high Pt phenomena, including the production of hadron jets. E260 would use the EllO spectrometer and take data first since much of the El 10 instrumentation would not be needed. Only some large calorimeters, not in the EllO proposal, would have to be added. The group's efforts then centered on E260, which took Beryllium target data in January 1976, and Hydrogen target data during the surn.rner of the same year. The UCLA participation in the collaboration ended \vith E260, c.ithough they refurbished our Cerenkov counters between experiments. As the data taking for E260 was being completed in Septe:nber 1976, a few tests were made to evaluate the basic El 10 trigger method, which used multhvire proportional chambers as hodoscopes to count charged particles. By this time, El 10 represented fairly "old fashioned" physics, and Fermilab requested that the physics goals for EHOA be redefined in terms of a limited survey of peripheral interactions and resonance searches at 100 and 200 GeV. The result vras a pr'.)posal to survey the following reactions simultaneously: rr-p -') rr+rr-n with emphasis on p 0 rr-p 4 J<Jrr+rr-x, and rr-p-') J<°](DX. production, high mass mr scattering, rr-p -') J(O K-p, K-p -') J<Jrr-p, A few background reactions would also be recorded. The main data would be taken at 100 and 200 GeV, with some at 17 and 50 GeV. The 17 GeV point was desired for a comparison with results [Gr74-] of the Cern Munich collaboration. Spectrometer modifications, section 2.1, were largely completed by January 1977, and an engineering test run was made in February. Our first major physics run (Run I) took place in May and June of 1977, with most data taken at 100 GeV, and some at 20 and 50 GeV. Twenty, rather than 17 GeV was used after design studies indicated that a fixed spectrometer geometry was preferred for using the lower energies to understand backgrounds expected in rrrrn at 100 GeV, and 20 GeV -7- was the best compromise of resolution and acceptance for our low energy point. An extremely preliminary analysis of the spring '77 data [St78] indicated overwhelming background and resolution problems for mm at 200 GeV. In response to this, we lowered the beam energy to 175 GeV and additional ph0ton detectors were added at the downstream end of the spectrometer. One of these detectors was a high resolution photon calorimeter originally used for Fermilab El~ l [BaBO]. Its installation at the MPS had already been planned as a parasitic test run for a proposal to study c..i 0 ->rr+rr-rr 0 , P523 [Dz76a]. The other was a "lead ·wall", backed by scintillator and covering the major part of the forward aperture. Both of these detectors were behind our second Cerenkov counter, C2 (figure 2-2), a,."ld both \·.-2~e used, along with repositioned E260 calorimeters, as off line (not as part of the trigger) vetos. With these changes, we made a second major run (Run II) in the winter and spring of 1978. Most of the data for this run was taken at 175 Ge V, ·with some at 20, 50, and 100 GeV for calibration purposes. Table 1.1 gives our o--,."'erall event totals for the two runs excluding alignment and special calibration data. With the completion of the Run II, analysis of both runs began. Track findiri..g was done at both Fermilab and at Lawrence Berkeley Laboratory by the Indiana and Cal Tech groups. This effort was plagued with several false starts, requiriri..g two repetitions of the tracking analysis on Run I data. This wasn't completed until December 1979 for Run I. and shortly thereafter for Run II. which was held back until the problems in the earlier set were resolved. Although some preliminary studies of our mrn data were made during this time, final background and physics work on the rrrrn reaction didn't begin until this stage was completed. Fir...al tracking and physics analyses were made on the Fermilab Cyber 175 computers. A division of labor was made for the physics analysis of our various triggers. VICC had the /(Jl<.°X, and high mass rm scattering triggers. A thesis [De82] has been written on the K°"R° X data. Cal Tech and Indiana shared the "low mass" mm -8- Table 1.1 Total Events by Run (Thousands) Pseam Run I Run II 20 GeVlc 63 61 50 GeVlc 164 122 100 GeV le 1058 404 175 GeV le 0 1680 trigger, called "rrrmr"· Initial studies of the J(<Jrrp trigger were ::r:.c..:ie at Cal Tech, and Indiana is now pursuing its final analysis. Cal Tech analyzed the K°rrrrX data, and our E110 publications to date were based the Run I data from this trigger. These were a conference report [Di80] and paper [Br80], on the reactions rr-p -'> K° K±rr+X and rr-p ~ K° K+ K- X at 100 GeVI c. Observations of the D ( ~ 265) and E( 1420) mesons were reported in KKrr channels and possible er.....~an.ceraents 'Were found in the KKK channel. The analysis of reaction ( 1.1) from the rrrrnr trigger (see section 2.4) involved particularly close collaboration between Cal Tech and Indiana. Two theses, tbis one and one by Frank Fredericksen of Indiana [Fr82J, have resulted. Both reports use 100 and 175 GeV le data from runs 1 and II respectively, although the emphasis in the two theses differs. (The 100 GeV le data from Run II was compromised by a series of problems with the spectrometer.) The data analysis for both energies was, With two important exceptions, essentially identical. These were differences in the forward particle identification i;vith our Cerenkov counters, and the use of the forward photon detectors in the 175 GeV analysis. This thesis concentrates on decay distributions for reaction (1.1) and attempts .a limited rrrr scattering study from the data. Topics in Fredericksen's thesis, arid -9not here, are effective pion trajectories from the rrrrnr data and rr+rr-rr0 spectra from the P523 tests. Both theses include spherical harmonic moment distributions at the two energies, and a major goal for both was obtaining the cross section for reaction ( 1.1) in the p 0 mass region. Vfe will make qualitative comparisons between our results and those of several lower energy experiments, [Gr74, Co78, and Al78]. The emphasis in hardware and analysis documentation also differs between the theses. The docwnentation here, especially nwnerical correction factors, applies to the Run I spectrometer and analysis. Differences between run.s are noted when significant, and the forward photon detection will be briefly described. Fredericksen emphasizes the Run II spectrometer and analysis. 1. 3 Almost Raw Data A simple analysis of our data (after particle tracking) reveals its broad outline, and it is perhaps worthwhile to give a quick look at some uncorrected distributions to complete this introduction. The rrrmr trigger selected the topology of two charged particles coming from the target and traveling forward through the magnet by counting the number of particles seen in several proportional chambers between the target and dmmstream face of the magnet. Veto c0Ui.1ters surrounding the target and masking off the magnet upstream face suppressed events with extra charged particles, and events with photons coming from the target at large angles. The trigger was not designed to detect the recoil neutron. It v.,-as identified in later analysis by missing mass cuts. Also, the trigger didn't select the types of particles involved, either forward or beam. The selection was left to analyses of Cerenkov counters in the beam and spectrometer. Overall. this experiment recorded about a million events in Run I at 100 GeV. Of these, about 280,000 events were from the rrrrnr trigger, and roughly 10500 satisfied our requirements to be called mm. events. Rough numbers for 175 GeV were 1.7 - 10 600. 500: >Q,) 400. ~ 0 I() ' n 300. Is I.fl I l, I I I 'E Q,) > w 200. I 1 • j4 \:] 100. 0. 0. 1. 2. 3. m.'"'. GeV lc2 Figure 1-2. Uncorrected 1irr mass spectra at ~CQ GeV (so lid :~3~:5ra:::_) and 175 GeV (dashed histogram). These are fin.al event sc..:7"~ples v,;-';.~ll. It I < . 15 (GeV /c) 2 . million total triggers, 490000 events from the rrrrnr trigger, a.n.d about 9900 Ti:m events . (Both of these final samples include backgrounds of order 10%.) Figure l -2 shows rm mass spectra at 100 and 175 GeV from the final event samples. Peaks for the p 0 and f 0 are clear, but not so the g 0 . The g 0 "peak" barely tops a large background at 100 GeV and is even less significant at 175 GeV. The 175 GeV acceptance is better at rJ.gher masses relative to the p 0 region than the 100 GeV acceptarice , and figure 1-2 reflects this. The small final mm event counts will need ez.."Plan.ation, and Chapter III gives the details for Run I. One reason was a lack of active forward photon vetos. Most of our data clearly had unvetoed high energy tr°'s , as evidenced by total observed energies much less than the beam energy, figure 1-4. About half the recorded rmnr data actually had only two forward particles, and figure 1-3 shows the rm mass spectrum for those events. In the upper curve v; e make no missing mass selection, while the lower hatched area includes a rough - 11 - 5000 100 GeV 1r1r nT , unwei;l'lted > 4000 Q,) ~ 0 3000 I() .......... "' 'E ~ 2000 l.J.J 1000 0 0~-1~~~:2L:~1.~0~~~1~.5~~~2.4o:-z2~~z:%:l:d ..,,...,,. mass, GeV/c 2 Figure 1-3. Uncorrected 1111 mass spectra without (upper :;ur1."e) c..::-.1.d ".<~ '.:1 (lower curve) a neutron missing mass cut. ;.Jo Cerenkov cut was ;::::,ad.e for this figure, all particles vvere asswned to be pions, and not cut \ras used. 1600 100 1400 Gev 1r1T n1 , unwei~h ted N >a.> 1200 ~ 1000 c"' ~ 800 > l.J.J 600 400 200 -10 0 10 M~ 2 20 , GeV 2 30 40 Figure 1-4. 3.Ussing mass (squared) spectrum for the 11rrnr trigger. Large values are roughly twice the missing energy. (See equation A.4b) - 12 neutron missing mass cut. In both curves, prominent peaks at the p 0 and f 0 masses are seen. Also present in the upper curve is a bump at about 500 Y~eV. Th.at bump corresponds to essentially uncorrelated rr+rr- pairs and is not a resonant effect. Such pairs can result from particle decays involving one or more undetected and unvetoed rr0 , such as the c.v 0 4rr+rr-rr° decay, or from having one charged pion associated with the nucleon system (figure 1-lb) . In our spectrometer the former eA.rplanation is more likely as the difference between the cur. ~es . of figure 1-3 represents events with substantial missing energy. This is illllstrated by figure 1-4, which is a missing mass (squared) spectrum for reaction (1. 1) . The large peak in this figure corresponds to neutrons and goes to negative Mx 2 because of our resolution. The continuum in this figure indicates considerable energy lost to neutral particles other than a final state neutron. The most likely can.didates for these are one or more rr0 's associated either with the rr+rr- system or the recoil nucleon system, or both. The continuum runs to the kinematic limit of about 200 GeV2 in figure 1-4, and also penetrates under the neutron peak, giving a background of about 10% to the mrn signal. The lack of a 500 Me V bump in figure 1-2 is evidence that the rrrr system we study here corresponds to peripheral rrrr interactions as in figure 1-la, and not uncorrelated junk or nucleon resonances as in figure 1-1 b. Important to this argument is ·a reasonably poor acceptance for pions coming from low mass N• and 6. decays, which is zero for pion - neutron masses less than about 2.5 GeV /c 2 . Figure 1-5 illustrates this, sho°V\'ing rr+ n masses plotted against rrrr masses from rrrm events at 100 Ge V. The rm masses were found by forcing the missing mass on successful events to be the neutron mass. The distribution of events within the envelope reflects rrrr decay angle distributions given in chapter Vl What is of interest here is the envelope, which maps the limits of our rr -n acceptance. Only rr+n masses are shown in the figure. Resonances in the rr-n channel require exotic - 13 - 14 -- - 12 . .. 10 C\l C,) ........ > Q,) ""' 8 ~ + I: ~ 6 4 100 GeV 2 0 0 1 2 3 4 m1r11.. GeV lc 2 Figure 1-5. Scatter plot of rr+ - neutron mass ~.-e~s;_:_s dashed line follows the limit seen for rr-n masses. 71+;"j- :::ass. The (charge ±2) exchanges and none were seen. The rr-n mass limits followed those seen in figure 1-5 for rr+n masses, although the distribution was, naturally, roughly inverted. Figures 1-6 and 1-7 contain data for our models of the backgro12..rid lL.>J.der the neutron peak in figure 1-4. These figures show the rm mass and missing mass squared spectra for data from our rrrrX background trigger. ThJs trigger had the same charged particle topology requirements as did mmr. but the veto counters surrounding the target were not included in the trigger. In figure 1-7 vre also see a prominent peak with low missing masses and a continuum. However, the peak is shifted and distorted from that expected for neutrons. It corresponds to domin.a:it production of N• and D. resonant states of various masses. - 14 - 1000 100 GeV TT TT X , u nweifi1hted > Q) ~ 0 I() 'c 500 (/) Q) > w 0.5 1.0 1.5 2.0 2.5 2 1T1T mass, GeV/c Figure 1-6. mr mass spectrum from the ITITX trigger, no missing mass cut. 300 100 GeV TfTf X , unweifi1hted 250 C\J > 200 Q) (.9 ......... (/) c 150 Q) > w 100 50 0 -10 0 10 20 2 30 40 Mx2, GeV Figure 1-7. Missing mass spectrum for the 1T1TX trigger. Compare to figure 1-4. - 15 Chapter II Apparatus 2.1 Overview The E110 spectrometer, also known as the Fermilab Multiparticle Spectrometer (MPS), was located at the end of the M6 West secondary beam of the Meson Laboratory. The MPS was designed to measure forward going charged particle systems from low to high multiplicities. Descriptions of the beam and spectrometer have been given elsewhere [BrBO, Dz77, MeBO, YuBO] mainly for our previous experiment, E260. Here, we document the beam and MPS as they existed for the Spring 1977 run of El 10. Changes and additions for Run II -will be noted. Fredericksen's thesis [Fr82] should be consulted for a complete review of the spectrometer in that run. Spectrometer modifications for El 10 included changing to a trigger based on multiplicity measurements by our proportional chambers and adding a photon veto system upstream of the magnet. We also increased the upstream lever arm (target to MPS magnet) from "" 2.6 m. in E260 to "" 5 m. for EllO. The geometry downstream of the magnet was largely the same as E260 with only few proportional chambers moved about. The spark chambers ·· and their pulsing system were upgraded to allow longer delays from beam arrival to chamber pulsing, and shorter dead (recovery) time settings. Finally, magnet side lining proportional chambers and a bank of neutron counters were added, neither of which is used in this analysis. - 162.2 M6 West One of six independent Meson lab beam lines, M6 [Dz77, Ay77] was a high resolution, medium intensity beam, figure 2-1. It transported particles produced when protons extracted from the main ring of the Fermilab synchrotron struck an 8. 00 inch long by .04 inch square beryllium target about 1850 feet upstream of the .\~PS. During this experiment, the Ferm.ilab accelerator ran at a maximum (during extraction) energy of 400 GeV, with a cycle time of 10 to 12 seconds. The slow spill used for El 10 lasted about 1.1 seconds. The beam had an r.f. stn:.cture, ~...-tth "' 1 ns beam bearing buckets every 18.8 ns. Beam counts at the ~::PS -;rnre typ~cally 500,000 particles per spill. At these intensities, less than 1% of tl-:e :n.:.d~e~s were populated, and the fraction of those with two or more particles in a bucket vras measured at less than 1%. Using timing signals provided by the laboratory, we gated off the extreme ends of a beam pulse to avoid taking data ·when the beam intensity was unstable on a time scale of order tens of milliseconds. These stgn.als were also used to alert our on line computer to the arrival of the bea....m. A pile up rejection system (and other features of the trigger electronics, section 2.4 and Appendix B), reduced the effective beam to typically 300,000 particles per pulse. M6 is shared between three branches, "East," "West," and "Far IYest,'' only one of i;vhich could run at a time. The part common to all three bre..nches hc.d three stages, each roughly 150 m. long, designed as "point-to-parallel-to-point imaging systems" [Ay77]. The M6-West branch had a fourth stage with final focus r_ear the MPS target. The first stage of the beam, at a production angle of 3 mr to the primary proton beam provided sign and momentum selection. Fixed collimators near the production target restricted M6 to a solid angle of 1.34 µ,st . F-stop collimators after septum dipoles provided the main intensity control for the beam, and main bending magnets in the parallel section maximized momentum dispersion. This stage ends - 17- EXTRACTED PROTONS ~RODUCTION MG-WEST, MAJOR ELEMENTS (VERNIER DIPOLES AND SEXTUPOLES EXCLUDED) V H MOMENTUM ~ T~iET~ ~: ~ - MI O' SI SEPTUM MAIN BEND BENDS _ g~ MOMENTU M B DISPERSED ~ IN X 550 1 SECOND FOCUS ~ 21 ~ PRUSS 550 H STOP~-~ v ~ FIRST FOCUS 1 THIRD S2 c ~~~~£~H~f+HI 1:~1 cf> 980 \ 1 s: BDIF l~D~~c~i~~~g~ 1500 I RECOMBINATION BENDS .------ H E396 ~ FOURTH FOCUS 11~E' =-~=+moo~-,~1.~: ~ 1500 1 L - - - __ J (He BAG) 1 1850 \_ MPS 1 BA (MWPC) v Il DIPOLE ~ D COL~IMATOR g3B~~~V R QUADRUPOLES (VERT (HORIZ. H= HORfZ FOCUS) FOCUS) V=VERTICAL I I I t I PROFILE MONITOR SCINTILLATOR COUNTER Figure 2-1. MS West beam. First three stages are common to MS East and Far West. Beam envelope is schematic. E396 was an experiment, and removed its equipment from the beam when E110 took data. - 18 - with a momentum dispersed (in x) focus with dispersion of 2.48 inches/%, (D.xl ( ~). Collimators at the first focus set the beam momentum spread. They p were set to~ .80 inches for 50, 100, and 175 GeV/c data and 1.00 inches at 20 GeV/ c. Field lenses at the first and second foci constrained trajectories of the momentum dispersed particles, and recombination bends in the third stage removed this dispersion at the third focus. The second stage included the first of two threshold Cerenkov counters ("PRUSS") and, at the second focus, profile monitors and scintillator counters, a pattern repeated at each focus except the first. The third stage had a long parallel section in which two differential Cerenkov counters, "BDIFF" [An76] and "DISC" [Be72], were located. The second threshold counter, "C0" [Ay74], was upstream of this parallel section. The fourth stage merely transported the beam to the MPS with the fourth, and final, focus near our target. Beam magnet settings were computer controlled with a console located in our counting room. The beam was aimed through the target entrance \vindow (figure 25} by centering it on a halo anti-counter, Sc, section 2.3.1. Particle transmission from the second focus to the MPS was typically 65%, and of this, about 85% passed through the hole in Sc and was counted as "beam". 2.2.1 Beam Cerenkov Counters, Beam Composition Four gas Cerenkov counters, Table 2.1, tagged beam particle types and measured beam composition. The table also gives the nominal counter settings. PRUSS and Co were quite stable counters. DISC (built at CERN for the M6 beam line) was angle sensitive and required constant monitoring and frequent readjustment. especially after long beam down times or retuning the beam for any reason. BDIFF was a little less sensitive, but readjustment after each beam down time was also necessary. To maximize the kaon tagging efficiency, we required only a coincidence of - 19 - Name PRUSS Co BDIFF DISC Table 2. la Beam Cerenkov Counters Number & Type Type Z(*) Length of Phototubes (ft) 2-RCA 31000M Threshold 911 96 1-RCA 31000M 60 Threshold 1079 3-Phillips 56 DUVP 45 Differential 1245 8-RCA 31000M Differential 1322 19 Max. Gas Pressure 1 atm 5 atm 15 atm 20 atm • Distance from production target to counter center Table 2. lb Nominal Settings 175 GeV 100 GeV 50 GeV Co PRUSS BDIFF DISC rr rr rr rr 1T 20 GeV e e p p I\ rr K- K- p off rr Table 2.2 100 GeV /c Beam Composition and Counter Efficiencies Raw Beam Fraction (%) Tagged Beam Fraction (%) rr92.92 ± .002 91.47 ± .07 5.19 ± .05 3.96 ± .0013 3.34 ± .04 3.12 ± .0011 - rr K- p Co 98.44 ± .01 11.22 ± .28 3.49 ± .26 Efficiencies (%) BDIFF PRUSS .17 ± .001 86.41 ± .01 .08 ± .04 2.54 ± .15 91.99 ± .04 .47±.11 DISC .44 ± .001 92.69 ±. 03 .03 ± .03 any six of the eight DISC phototubes (Table 2.1). DISC pion and proton efficiencies remained acceptably low. Beam Cerenkov counter data included "tag bits", section 2.3. 7, and scaler totals. The scalers required only a beam coincidence and hence recorded the number of times each counter fired for all beam particles. Tag bits were recorded - 20 only with events, giving the pattern of counters that fired on a given event. To determine the beam composition and counter efficiencies, the Indiana group used a program [Be79a] adapted from E260. Using the Cerenkov scaler totals, the total beam scaler count, and accumulated Cerenkov counter tag bit patterns, the program determined counter efficiencies for each particle type, rr, K, and p, particle fractions for unbiased beam, and similar fractions for "tagged" beam. Vnbiased beam was the flux actually incident on the MPS, while "tagged" beam was recorded on events, and therefore distorted by relative cross sections for triggering. The tagged fractions were trigger dependent, but not the unbiased fractions (checked by comparing fits for rrrrnr and J<Drrp triggers). The fit results of Table 2.2 used only the rrrrnr trigger. Initially, fits were made for individual runs, but the statistical errors were large. Global fits, using only runs in which all the Cerenkov counters were at their nominal settings, were then made, Table 2.2. Since considerable run to run scatter was observed in the initial fits, we consider all particle fractions ur1certaiR to .5%. Within this uncertainty, the unbiased fractions are consistent with those expected for our beam, (the expected ·p fraction was 2.8%). The raw rr fractions of Table 2.2 include some muon and electron contamination. This was measured at 100 GeV as a fraction of the rr flux by placing a module of the E260 calorimeters in the beam and triggering on the beam. From a sample of 1250 tagged pions, the muon fraction was found to be µ = (3.2 ± . 6)% of the rr flux, and the electron fraction was found to be consistent with 0 ( 1 event) . Figure 2-2. El 10 Spectrometer, plan view, Run I configuration. For Run II, the major changes were addition of photon detectors, the "Lead Wall" and the El 11 photon calorimeter behind C2. Also a pwc, BBWV, was added at the 2x2 location, and the V3 counters and electron calorimeters were moved slightly. >- 0 -I ,. E Cl> +- Cl> "- (/) -I VO VI uI I He 2 V3 Z, meters 3 4 5 Figure 2-3. Front end region of the MPS for Run I. side view. The vertical aperture was determined by V3 in both runs. 0 --T-----,----' ,. I'. . __ \ 'I I l ' DEDX V2 ~ I• ~acuum Jacket nd H2 flask FRONT END SIDE VIEW MAY 1977 6 o;oxDy I N l\J - 23 - 2.3 The MPS The MPS as used for the spring '77 run (Run I) of El 10 is sho'Nn in figures 2-2 and 2-3. Upstream beam proportional chambers (BA), and a bank of r:eutron counters along side Vl are omitted. The main features of the spectrometer ~rnre a 12~00 inch long liquid hydrogen target surrounded by a photon/cha.:--ged r::.::.rt:cL2 veto system, a large superconducting analyzing magnet, multiwire proportional tracking chambers upstream of the magnet, proportional a.rid spark tre.cking chambers downstream of the magnet, two large multicelled atmospS.er:c _;;~·ess~e gas Cerenkov counters, various scintillation counters and a triggering systera wt-ii.ch used multiplicity signals from several of the proportional cha..rnbers. A PDP-11/45 computer running the MULTI on line system (as modified a.rid maintained for the MPS by the Indiana group) [Dz76b ], collected the data, -;,'.Tote it to magnetic tape, and provided simple diagnostics for monitoring the eA-periment. After each event, shift register (tag bit and pwc) and spark chamber (:\~TD scc.ler) data were read in through direct memory access (DNL.\) units, an.d photcLlbe (CA.MAC ADC) data were read in through a BD0-11 branch driver. CAY_-\C scalers were read before and after each beam pulse. Event and scaler data were iriJ tially stored on disk as a buffer, and then written on tape as time allowed, mainly betvreen pulses. A single data tape could hold about 10,000 events. Diagnostic functions were performed as time allowed, and included event displays of the spark and proportional chambers (1tvithout track finding), b..i:stograms of requested quantities, and end run summaries. The summaries were printed and written to tape after each run. A set of visual scalers were used as a backup for the C~\1AC scalers, readings being recorded by hand after each run. The coordinate system used for E 110 had z along the nominal. or surveyed, beam line (spectrometer centerline), y vertical, and x horizontal. The origin was taken directly above a survey bench mark near the downstream end of Vl . - 24 - 14000 12000 10000 bl 2 particle cl 3 particle 31rp al I particle 'ITP elastic 400 I) ~ 0Q. (/) .. .~ 0 300 Q. c ,.., Q. 6000 200 Q,) > UJ 1000 ~ cu ~ 8000 N c 500 .,,..,,.nr 500 4000 100 2000 oo!--.....iii........111L.c:::=::~:iii......;~====-c..--...;;;;:::t::===--..-....;;.;;;;::;::::::2 100 150 200 250 300 Pulse Height Figure 2-4. DEDX response for 1 to 3 particles. Data came from i:u.dicat.ed triggers; only events of the desired topology were included. Arrcw· points to the ADC pedestal. 2.3.1 Beam and Interaction Counters Beam and interaction definitions for the trigger electronics and scalers 1·:e:e made by five plastic scintillator counters, figure 2-2. Our beam was defbed by a small three counter telescope, Sa, Sb, and Sc, located at z,..., -2 .3 rn . Sa and Sb were thin 1" square counters (Sa= l/8" thick, Sb= 1/16" thick). Sc was 2" square, 1/4" thick and had a 1 /2" (x) by 1I4" (y) hole. Sc rejected particles that missed the ho le. Interactions were detected by either pulse height in a thin counter, "DEDX", near the target, or by the absence of a signal in a veto counter, "2x2", dovmstream of the F station (both in coincidence wtth a beam particle) . The DEDX counter 8" x 6" x 1/16" (x,y,z) covered the exit of Vl and was viewed by two phototubes \-Vhose signals were added before discrimination and recording by ADC's. Figure 2-4 shows the DEDX response to 1. 2, and 3 particles. A two particle signal was used to indicate an interaction. The 2x2 counter was 2" square, 1I4" thick, and viewed by a - 25 - single phototube (through a long light pipe to keep the phototube below the spectrometer fiducial volume).. The phototube was attached to a motorized "table" which allowed easy adjustment of the counter location in x and y. The 2x2 counter was aligned with the beam whenever the beam was retuned or the MPS magnet polarity reversed. For 175 GeV data, the 2x2 counter was replaced by a 1" square counter to preserve our minimum Pt bias. 2.3.2 Target Our liquid hydrogen target, figure 2-5, had a 12.0" long (room temperature) by 1.0" diameter flask made of .005" mylar, except for an upstream end made of Vespel with a .015" thick entrance window. The flask was supported by its fill and vent pipes which ran parallel to and below and above the beam, respectively. The flask, VvTapped with 10 layers of .00025" aluminized mylar "super-insulation", covered -.567 < z < -.262 meters. Temperature sensitive resistors monitored the liquid level (full I empty) of the flask. The hydrogen density is assumed to be the standard boiling point value of 0.0708 gm/ cm 2 with 1% error because the true pressure, temperature and bubble density are unknown. The vacuum jacket shape and fill/vent pipe locations were dictated by the target location within V1. Proper aiming of the beam between the pipes was essential. The pipes were searched for by vertical and then horizontal beam sweeps across them, recording increases in reaction rates when they were hit. The midpoint between the pipes was determined in terms of the beam at the BB and A stations, and the beam counters, especially Sc, were then aligned with respect to this location to about ± 1 mm uncertainty. - 26 - PMT ..... Scintillator Lead ·-.......... Aluminum-t- Foam Vent"'---=--------------------------------=-------.. Bea~ i II/ ,,_:_.........,._i:zs::::ll:lc:c(:i::s::z:::::==-=:zz::cza==Ta-=r: aag=-=et=====s:=z:a:::c:=)c:z::b;rn I 0 I I I IOcm 12 13 18 0 Figure 2-5. Side and front views of Vl. Details of the target, vacuum jacket and counter orientation (surveyed at 11.5°) are also shown. Signal cables for the {3 proportional chamber exit the front of Vl. Numbered segments refer to tag bits for Vl and {3 . The {3 and Vl segments overlapped. In the trigger, a hit in any {J segment turned off the two Vl segments behind it. IOcm - 27 - 1200 Full Target 1000 E ~ 800 ell 'E ~600 w 400 200 -:8 -.6 -.4 zv -.2 , meters .2 0 60 Target "Empty" DEDX E ~ 40 VcCUllTI j!? Jacket ~ w 20 I I 0 -.8 -.6 -.4 -:2 0 .2 Z11 , meters Figure 2-6. Vertex Distribution for the rrrmr trigger. 2-6a st::;ws ta~get full data for events -written to PST's, (upper distribution) and for events satisfying essentially our full set of cuts (lower distribution). (The vertex cut shown is obsolete, but representative.) The lower figure is target "empty" data. F1ask ends, the vacuum jacket, and nearby detectors are visible. The small ( 1.0") diameter of the target flask was part of an effort to eni.11.ance the detection of recoil protons from rrp ~ K° J\p and similar reactions . This effort also included a two inch diameter foam-mylar-glue low mass \-acuum jacket .12 gm/ cm 2 thick normal to the target ( "'3 x 10-3 radiation ler1gths). For struc- tural reasons, the downstream end of the jacket was a 1 /2 inch thick foam plug glued to the mylar end, about 3 x 10-3 radiation lengths thick. Upstream of the target flask, the jacket was a 1 /8" thick, 2" diameter aluminum cylinder. The beam - 28 - entrance window was .005" mylar, about half a meter upstream of the target flask. Figure 2-6 shows the vertex distribution for rrrrnr events. The vacuum jacket end cap is clearly resolved from the hydrogen flask. The shape of the vertex distribution results from a high rate of delta ray vetos, as discussed in section 4.8. 2.3.3 Target House, Forward Photon Detection Surrounding the target and masking off all but the forward aperture tb...rough the magnet was a set of lead and plastic scintillator shower counters, VO, Vl, V2 a..11d V3, and a cylindrical pwc, {3 , figures 2-5 and 2-7. For rr- p 4 1i+1i-n, they were used to veto a large background of events with charged and/or neutral particles ct:tside the magnet aperture. The cylindrical {3 chamber, with 192 anode wires at a radius of 8.~8 cm vetoed charged recoils. Interleaved pairs of wires were read out to the shift register giving 96 channels. A current division system using special amplifiers and CA_\L.\C ADC's was included (to resolve which wire of a pair was struck) but was not needed for mm, where f3 was used only as a veto. Groups of four consecutive shift register channels (8 wires) were fed to the trigger electronics for the veto. The sensitive length of the anodes was about 23.3 inches extending from z ;:::i -.670 m. to z = -.076 m. The cathodes were solid, the inner being thin and the outer being a . l inch thick cylinder which provided the structural support for the chamber. The main photon veto, Vl or the "Barrel," was cylindrical, figure 2-5, housing 24 counters and their 2" diameter RCA 6655 phototubes in a sealed nitrogen atmosphere (for target safety). Each counter had six 28" long, .25" thick fingers interleaved between lead cylinders of varying thickness. The fingers were radially tapered to insure close packing and were wrapped in optically graded alurninized mylar [Wa72] in a reasonably successful attempt to equalize light output along the finger length. Lead layer thicknesses were (from inner to outer) .135" (effective), - 29- VO V2 -----~)( Figure 2-7. Jaw counters . VO was upstream of the target and Vl was dmmstream, just after the A station. V3 was near the magnet. .135", .135", .260", .260", and .385". The inner layer was actually a thin lead layer pressed onto a brass cylinder. The outer can of Vl was a half inch thick aluminum cylinder. The counter thresholds were set to "' 1 MeV, and gains were monitored with weak Bi 207 sources glued to the light pipe ends directly in front of air gaps to the phototubes. A .003" mylar gas barrier covered the Vl exit. The vetoes VO, V2 and V3, figure 2-7, collectively called the "Jaw" vetoes, had a total of 12 flat 14x25 inch counters. (Two counters in V2 were only 14Xl8 inches .) - 30 - Each was a layered sandwich of 6 lead and 6 scintillator sheets (both .25" thick) in a thin walled (.125") aluminum box. RCA 8055 phototubes (5" dia. cathode) were used. VO, upstream of the target, had a 1" diameter hole to allow for beam passage. V2 had four counters and a fixed aperture. V3, six counters, had an adjustable aperture, but this was kept fixed (along with the V3 location) during the entire run. In Run I. this aperture was set to mask off the magnet pole tips ru"'ld rays traced to the magnet sides at its midpoint. For Run II, V3 was moved upstream of its Rua I location somewhat, and the aperture adjusted. The vertical ar1gular aperture ~·,~as only slightly reduced, but the horizontal aperture for Run II masked off the entire magnet, including the downstream end. Jaw counter thresholds were set to 1 /6 of the single muon pulse height . For this, beam stops relatively close to the ~IPS were closed to create a halo of muons about the beam line. In Run I. shortly after the 50 GeV and first set of 100 GeV runs were made, one barrel counter, (B-8), failed with a short in the phototube base. Because of the danger of damaging other equipment, especially the target and ~ chamber, a group decision was made to not repair the counter, and we completed the run, including most of the 100 GeV data and all of the 20 GeV data, with only 23 barrel counters. A sL.J.gle barrel counter strike trigger, rmB was added to evaluate the backgrour1d. As it turned out, this trigger was crucial for a neutron veto correction, but the loss of BB had no noticeable effect on the veto house failure rate. BB was repaired prior to Run II, and we had no further problems with the counter. Between V2 and V3, we had a helium bag, figure 2-3, covering the K° decay region of the Vee triggers. Its purpose was to reduce diffractive (3rr) backgrounds in the J(O rrp trigger. The electron modules and one hadron module (LlH) of the E260 calorimeters, figure 2-2, [see Ha75b] were maintained with increased phototube gains as a possible off line photon veto. The other hadron calorimeter modules were left - 31 uninstrumented. At one point, the 11 electron and hadron modules were moved into the beam on curve through runs to measure muon and electron beam contamination, Section 2.2.1. Otherwise, the calorimeters were kept clear of the C2 entrance window, figure 2-2. This resulted in about half of each calorimeter being masked by the magnet flux return. We ultimately chose to not use the electron calorimeters. as off line vetoes in the Run I data. However, preliminary studies indicated a reasonable sensitivity down to surprisingly low photon energies, and that if combined with a veto covering the rear of C2, we would have a viable off line veto setup for Run II. Also prompted by an extremely poor missing mass resolution at 175 GeV, a "lead wall" was added behind C2. The V3 aperture was reduced and the electron calorimeters were moved closer the beam. Also, the E 111 photon detector [Ba80 and references therein] was installed behind C2 (mainly as a test for proposal P523, see chapter I). These adjustments gave us an off line 4rr veto coverage. The lead wall covering the exit of C2 was roughly rectangular with dimensions 100" (x) by 80" (y). A single .75 inch layer of lead was backed by 20 horizontal scinWlator counters (8.5" by 50" each) with 2 inch phototubes. Phototube signals were sent only to the ADC's. Since only one layer of scintillator was used, there was no active charged particle - photon discrimination and the lead wall could not be used as an active veto. The El 11 photon calorimeter was located just do¥m.stream of the lead wall. This calorimeter was a high resolution hodoscope with seventy 1. 05 centimeter wide counters in x and seventy in y. Each counter had eight fingers along the beam direction interspersed between 6.4 mm thick lead layers, and the fingers from the opposite view counters. Since this calorimeter was to be used in P523 tests for rrO measurements, a hole matching the photon calorimeter size was left in the lead Wall. The hole was actually about 140 cm in the x view, and had a movable lead cover to maintain veto coverage when the photon calorimeter was moved. This - 32 occurred whenever we changed magnet polarities in Run II. The El 11 counter was positioned along the MPS centerline with a slight offset in x so that the bent beam just missed the counter. Data from the photon calorimeter were read into ADC's adapted from El 11 [BaBO], and buffered to the main on line computer ¥>-ith an LSI11 micro computer and DMA access. Details of this are in Fredericksen's thesis along with the photon calorimeter analysis algorithms . . 2.3.4 Magnet The MPS analyzing magnet, figure 2-2, was a superconducting dipole \\ith the flux return outside its large cryostat. Roughly a 48D48 dipole, the x-y aperture at the pole tips was 122 cm. (x) by 61 cm. (y). However, the distance between the upstream and downstream flux returns, was about 2.5 meters. For this experiment we ran at full field, I mag = ± 180 amperes gi1,.ing f B ·dl :::: 25 kG-m for an effective Pz kick of PK= . 7510±.0015Ge VI c . The main field was sufficiently uniform and fringe fields small enough that we could use a square field approximation for momentum analysis. However, the fringe field.s C.:d affect the y view pattern recognition, and vertical focusing corrections were applied in that view. A field map [Ha75, Ma78b], was used as input to these corrections, an.d for the acceptance calculations. During data taking, the field was monitored by recording the current before each run and at four hour intervals. Run by run A"° mass plots (from K°1mX data) verified both the magnet stability and. the field map. 2.3.5 Spark Chambers Eight spark chambers were grouped behind the magnet in two stations, E and F, four chambers per station, figure 2-2. Except for a size difference, the E and F chambers were essentially identical in construction. An aluminum frame supported four plan.es of .005 inch aluminum wires at 32/inch. These were glued to G-10 - 33 - ty effect of two alternating u-planes u-wires, 5. 7° slant .-- ~ n I I I I I I x-wires vertical~ + - - dead region -, r-...... I I I I I I I I ~ I I I :\ I~ L- I ~ I I I x-wire coverage I -I Figure 2-8. Spark chamber x-u plane. The u-cutoff -:;ms in all cha.i.rn1.:Jers, but was important only at the F station in Run II, where it set the fid'J.cial volume limit, section 3 .3. boards attached to the frames . Active areas were -2.4 m. (x) x 1. 2 m. (y) for U:e E-chambers and -3.6 m. (x) x l .B m. (y) for the F-chambers. Each chamber measured x, u and y coordinates with two spark gaps, x-u a:.~d y-y, the u wires being inclined at an angle of ±5.7° with respect to the x-wires, (four planes each way). As the chamber frames were rectangular, the slant u wires clipped off the edges of the x -views a bit as shown i.n figure 2-8, reducing the reg i:ms where the x wires were fully sensitive to about 2.2 meters (Ex) and 3.2 meters (Fx). No plugs or intentional dead spots were installed in the chambers. The spark chamber gas, a mixture of 90% neon, 10% helium, and a trace of ethanol, was filtered through liquid nitrogen cooled traps and recirculated. Spark chamber readout was by magnetostrictive wands ·with pickups and preamplifiers at each end, for a total of 48 signals. After discrimination each signal Was digitized in time with a SLAC designed [Be72b] MTD scalar system running at 20 - 34- Chamber Elx u y E2x u y E3x u y E4x u y Table 2.3 . Spark Chamber Efficiencies Whole Chamber Average Statistical Errors are all in Range .001 to .003 Imag=-180 Imag=+lBO Chamber Imag=-180 .910 .926 .913 Flx .938 .939 .944 u .930 y .828 .926 .939 .930 F2x .680 .921 .772 .903 u y .909 .675 .910 .881 .918 .909 F3x .819 .916 .897 u .918 .629 y .887 .877 F4x .892 .881 .890 .896 u .902 .940 y .926 .940 Imag=+l80 .912 .904 .795 .625 .832 .7?4 .868 .838 .578 .823 .896 .939 MHz. Up to 15 sparks per channel could be digitized "\vi.th a .25 mm least count error; however, the position resolutions for each plane (after averaging the tv.co pickups) was only "".7 mm. for the E-chambers and "'1.0 mm. for the F-cb.a n:bers . Some saturation may have been present in either the pickup or main amplifiers, as evidenced by some residuals being slightly shifted with particle position. High voltage pulses were produced by discharging coiled coaxial charge lines through thyratrons retired from use at SLAC. Each chamber had one such pulser, the eight pulsers being driven in parallel by a prepulser of similar design. Spark chamber dead times were initially set to 30 ms at the beginning of Run 1, and improved to 20 ms about one third of the way through the data taking. During Run II, 10 ms dead times were quickly reached. The chambers had both pulsed, an.d d.c. clearing fields. Track memory times for the chambers were ~2µs. Spark chamber efficiencies were ,...,.903 for the best chambers, Table 2. 3 and Appendix D, but problems existed near the beam and some of the chamber edges. Track angles were large near the chamber edges and wand or amplifier problems might explain the efficiency loss. Near the beam, efficiencies were also poor and . - 35 sparks from "old" beam tracks could often be seen. Beam envelopes from curve through data are "pinched" slightly at the E-station, evidence that good and "old" sparks in the beam region were subject to merging. This probably contributed to the efficiency loss of some of the spark chambers near the beam. Hm·.Tever, the poor efficiency regions were somewhat larger than the beam, probably meaning that spark formation and/or signal pickups also had problems. 2.3.6 Proportional Chambers Sixteen mulUwire proportional chambers (pwc's), with a total of 29 anode readout planes provided tracking data for the beam and secondary cha:"ged pc:ticles in front of the MPS magnet and supported the spark chamber tracki0..g behind the magnet. Their properties are summarized in Table 2.4. Some of the p-;Nc's ~rnre also used as hodoscopes to count particles for the trigger, section 2.4. Construction techniques depended on the chamber. The B, D a...71.d F' cb.cambers, had aluminum box frames, the BA, BB and A chambers had G-10 fre.mes pressed into a sandwich by either G-10 (BA) or aluminum (BB.A) outer frames . The cylindrical f3 chamber was supported by its outer cathode, a .125" thick aluminum cylinder, and the magnet lining r chambers were basically an aluminum, foam an.d G-10 sand~\ich. Not all of the anode wires in some chambers (Bx, By, Dy, Dy', and Dx') were instrumented; but those that were covered the necessary apertures, so that except for a handful of dead channels, there were no holes in the pwc coverage. The BA and BB stations gave the beam trajectory at the target. The BA station at z = -20.11 m had two chambers each with x and y readouts. The BB station at z = -2.57 m was one chamber with x, u (45°), and y readouts. The A, B, and C stations tracked particles upstream of the magnet. The A sta- tion had six anode planes in two chambers, the first containing Axl, Ax2 (staggered), Ayl and Ay2. The second had slant (±45°) planes Au, Av. The B and C - 36 - Table 2.4 Proportional Chamber Parameters Type Planes Anodes<ii) Anode Cathode A-C gap Anode Cathode spacing spacing Dia.{b) Dia.Cc) mm mm mm µ µ Gas 4 64 2. 000 solid 6.9 20 solid 3 32 .977 solid 3.25 10 solid 6 256 .977 .977 2.79 10 50 BIC 5 512(g) 1.954 1.06 6.86 20 lOO D/F'x 5 320 4.618 1.599 9.53 50 100 F'y 2 130 6.350 1.599 9.53 50 100 {3 1 192 1.837(h.) solid 4.06 20 solid Magic r 2 336 5.20 solid 8.0 20 solid r .r • 1,J.agw BA notes: (a) total wires per plane including uninstrumented wires; (b) gold plated tungsten; . ( c) Wire cathodes: Be Cu alloy . solid cathodes either AltLTninized mylar (BB, {3 inner) or Aluminum ({3 outer, r); (d) 80% Ar . 20% C02 ; (e) Uagic Gas= 20% Isobutane, 4% Methylal, .5% Freon 13B1, balance Argon; (f) Axl and Ax2 share a cathode plane, so do Ayl and Ay2; (g) 512 for x view, y view had 320 ,~,ires; (h) degrees. stations had five planes, Bx', Bx, By, Cx, and Cy in three chambers. (Bx' was the odd man.) Bx', Bx and By were upstream of the magnet, while Cx and Cy were actually inside the magnet, just -within the flux return (figure .2-3). Lining the magnet sides were two chambers rR and rL designed with current I division electronics, that detected particles too soft to pass completely th.rough the tnagnet. Very early in Run I. rL failed with a broken wire. For the same reasons as With the BB counter, we decided not to repair the rL until after the run. These chambers were used in a "high mass" mrn trigger only, not the rrrmr trigger discussed here. - 37- Table 2.5 Proportional Chamber Efficiencies Whole Chamber Average Chamber Chamber .985 Cx Ax1 .898 .980 .960 Cy Ax2 Dy' Ayl .893 .947 .997 Ay2 .963 Dx Au Av Bx' .941 .918 .951 Dy F'y' F'y Bx By .987 .981 Dx' (F'xl) F''x(F'x2) .991 .950 .984 .867 .953 Of the pwc's downstream of the magnet, only the D chambers, Dy, Dx and Dy', covered the aperture of the experiment. The four F' chambers, bet:'."een the Fspark chambers and the C2 Cerenkov counter, supported beam region track finding, where the better time resolution of the pwc's was used to help distinguish good from "old" tracks in the spark chambers. The y chambers, F'yl and F'y2, were between the F spark chambers and 2x2 counter. The x chambers F'xl, F'x2 (also referred to as Dx' and F"x for historical reasons) were hung from the front end of C2. Whole chamber efficiency averages are given in Table 2.5, and position dependent efficiencies are plotted in Appendix D. 2. 3. 7 Shift Registers The pwc readout system used preamplifiers located on each charnber (one preamp per wire) feeding a central 5921 element shift register through 200 ns long 50 0 coaxial cables (RG174). Most of the preamps (including all those used in the trigger) were built by our group with a simple single transistor design as in figure 2-9. The preamps were grouped 32 to a card with the transistors in 5 RCA-CA3081 - 38 - PWC PREAMP and SHIFT REGISTER RESET SHIFTREG DCHIN Vth 120 +12V IN I AQN ~uJ ~ ~ CLOCK J, L_ VI I I I I I I 200ns 75 up to 5 channels/chip PREAMP At chamber 32 channels/card SHIFTREGISTER 0 n mezzanine 32 channels/card OCHOUT AIOUT SHIFTREG OUT Figure 2-9. Shift register and pwc preamp. The signals SHIFTREG I:\r a~d OUT carried coordinate information, and the signals AIIN and AlOUT carried fast analog multiplicity information used for the El 10 topological trigger. chips. Except for the A-chambers, each preamp card fed a single sbift register module. For the 1 mm wire spacing in the A-station, we read out alternate Nires on 1 ·both sides of the chamber and sorted the signals in four ended cables. The BA, Dy' and Dx' chambers used an older, more complicated preamp driving ribbon cables. The {3 and r chambers used special amplifiers located near the chamber which included analog outputs for current division analysis. The shift register modules, figure 2-9, also built by our group, amplified. discriminated and, when in coincidence with a load pulse from the trigger - 39 - electronics, Appendix B, loaded the signals into the shift register. Upon loading, these signals were passed on to an analogue daisy chain in the same module. The daisy chain output current (AI OUT) was proportional to the number of "hits" , or distinct groups of wires on a chamber that "fired". Reasonably fast multiplicity measurements, these outputs were the essence of our multiplicity trigger. In effect, the proportional chambers acted as thin hodoscopes. A "hit" was any nwnber of consecutive wires that fired . A single nonfir ing wire was sufficient to separate two hits. About 5% of the time soft delta rays w:::i:..:.~d cc.'...J.~e two (or more) neighboring ·wires to fire in response to a particle. Becau.se of t~e daisy chain design, the multiplicity logic was sensitive to only the nw.uber of bts, and not the total number of firing wires. This considerably lessened, but did not eliminate our sensitivity to delta rays in the pwc' s. Only chambers used for the multiplicity trigger had their daisy chains fed to the multiplicity electronics. If an interaction did not lead to spark chamber pulsing, the shift reg ister, if loaded, was cleared with a fast reset pulse to await the next load . If a trigger occurred, shift register inputs were "clamped" during spark chamber pulsing to avoid spurious loads, and further shift register load pulses were suppressed while its contents were clocked into the on line computer via DYl.A access . The data recorded were the "·w idth" and trailing "edge" of each group of firing wires, where ''\.vidth" is the number less one of wires that fired in a group. In addition to the pwc information, the shift register contained 144 "tag b ~ ts" _(288 addresses). These recorded the condition (fire/not fire) of a large number of counters including the beam Cerenkov counters, the upstream photon veto counters (V1 to V3), and f3 chamber veto outputs; as well as recording which of our several pretriggers and triggers was responsible for the event. - 40 - 2.3.8 Cerenkov Counters Cl and C2 Two large rnulticelled atmospheric pressure gas Cerenkov counters, C1 and C2 (figure 2-2), were used for secondary particle identification. A rather complete description of these counters is in Medinnis ' thesis [MeBO]. Cl, between the E and F stations, was air filled with an index of refraction n-1 =2 .9 x 10- 4 . It had a radiator length of 4 m and an active area of 3.3 x 1.5 m 2 . The counter had two rows of 11 mirrors each ( 4 x 1.5 rn 2 ) at z = 1 ~ .5 m; however, for this experiment only the inner 18 mirrors were instrumented. The mirrors were Mg F 2 coated aluminized mylar backed by 3 cm urethane foam. Each mirror was viewed by a 5" phototube (either RCA 4522 or RCA 8854) ·with light collection by an. ellipsoidal cone . The entrance window was 250µ mylar followed by two sheets of 100µ black polyethylene. The exit ·window was 500µ aluminum except near the beam where it was mylar and polyethylene as in the entrance window. (Opaque diaphragms used in E260 to isolate the inner sLx cells, were removed for El 10.) Table 2.6 Cl C2 Thresholds, GeV le particle Cl C2 1r 5.8 12. 7 20 .5 45.l K 40.0 85.7 p C2, behind the F station, was filled with a helium-air mixture with an index of ·refraction n - 1 = 6 x 10-5 , corresponding to about 90% helium and 10% air. This was checked every four hours by comparing gas samples taken from C2 against pure helium in a small laser interferometer. C2 had a radiator length of 8.4 m. and an active area of 4.0 x 2.1 m 2 at z = 23.6 m. It had 16 aluminized Lucite mirrors (.6 mm thick in two rows of B) with Mg F 2 overcoats. These directed light toward RCA 4522 phototubes via paraboloidal ("Winston") cones. The phototubes were protected - 41 - C1 1.0 i 0.8 p 0.6 0 .4 0.2 0 C2 1.0 E' 0.8 Po.~ 0.4 0.2 10 20 70 40 60 30 ~o MOMENTUM (GeV/cl E() 90 Figure 2-~0. Ideal Cerenkov light yields normalized to 1 (see 2;:.:.~~~8:1 2.1) as a function of momentum. In practice, pulse height an.al.ysis in t~iies­ hold regions was of limited use. from helium poisoning by quartz windows glued to the cones, a 1116" gap between -windows and photo cathodes, and continuous flu_shing of the gas \7olume a.bout the tubes with C02 . The C2 entrance and erit 1;.vmdows vrere similar to Cl. 's, alt~'.)~gh the exit window had no low mass region near the beam. Both counters were painted black on the inside to minimize reflections, and prior to E 110, the C2 mirrors vrere refurbished at UCL;\ and reinstalled by M. ~:edinnis. Cl and C2 outputs were capacitively coupled to the ADC's to eliminate a 60 ·cycle ripple, and loaded with an 85 ns gate. Pedestal slewing on high rate tubes was observed, but all attempts to eliminate it with or without the capacitors were unsuccessful. Table 2. 7 lists the {3 = 1 photoelectron yields <N> for Cl and C2 found [Da78], using mm data. Where possible, one counter was used to tag pions for the other, and corrections for finite particle momenta and K contamination of pedestals have - 42 been included. The momentum correction factor was (2.1) the relative yield of Cerenkov light as ·a function of {3 and is shown in figure 2-10, which also illustrates the counter thresholds (Table 2.6) . The results for cells 2 and 13 are admitted "guesses" [Da78]. Table 2.7 Mean Photoelectron Yields <N >, {3 Cl =1 C2 Cell* <N> Cell <N> Cell <N> Cell <N> 1 - 12 - 23 3 .0 31 2.7 2 5.0 13 5.0 24 4.0 32 2.9 3 6.5 14 3.9 25 5 .5 33 5.3 4 6.7 15 6.2 26 3.2 34 2.9 5 5.9 16 6.9 27 6.4 35 4.3 6 13.1 17 4.7 28 4.4 36 3.9 7 6.9 18 5.8 29 3.5 37 2.7 8 6.8 19 5.9 30 2.8 38 2.1 9 4.4 20 3.7 10 10.0 21 2.7 11 - 22 - •Cells 1, 11, 12 and 22 were not instrumented. - 43 2.4 Triggers The E 110 topological trigger was based on counting hits in several of the proportional chambers to assess the forward multiplicity. The {3 chamber, Barrel and Jaw counters were also used, as well as the DEDX and 2x2 counters. Apperldix B discusses in detail the trigger electronics, gives diagrams, and lists multiplicity requirements for all the triggers used. This section only revie¥.rs esse!:ltials in the context of the rmnr trigger. The trigger sequence began with the arrival and interaction of a bea.rr: par::cle at a time when the trigger electronics was "live", that is, not processi.ng a pre\ious trigger candidate or during data read in. Only particles satisfytng BEAM= Sa·Sb·Sc·BEA.UGATE (2 .2) were counted as "beam". An interaction was flagged by either GO signal from the 2x2 or a two particle signal in the DEDX counter (we use + for logical "or"). INTBM = /B2x2 + IBDEDX = (BEAM ·2x2) + ( BEAIJ · DEDX~ 2 ). (2.3a) (2.3b) If these conditions were satisfied during the trigger live time, the electronics then checked that we had only a single beam particle -within the pi:.vc time resolution about the beam particle in question, that no previous interactions had occurred Within the last microsecond, and that the photon veto counters were ready prior to the beam particle arrival. The above checks did not include the spark chambers. If a preset 20ms spark chamber dead time had not expired by the time the trigger electronics had declared a trigger based on the charged topology, the electronics were simply reset and started again. Thus not all triggers were recorded on tape. For normalization, we consider the recorded events a random sample of the actual triggers. With the interaction, the pwc shift registers were loaded, and their daisy - 44chain electronics provided multiplicity outputs which were analyzed for agreement with any of our several trigger topologies. If a topology requirement was satisfied, and if the spectrometer readiness checks were passed, we had a trigger. Multiplicity measurements used the Ax2, Ay2, Au, Bx, By, Cx, Cy, Dx, Dy. {3, rR and rL chambers, with the DEDX counter providing limited (by Landau fluctuat:ons) information for some triggers. Several groups of chambers, A, BCD, BC, BCD', f. an.d "special D" were defined to measure multiplicities at various locatior1.s by \-otirig among the chambers in each group. In the absence of delta rays, a charged pc.rticle from the target would provide a single hit in most of the chambers it passed through. K° 's decaying between the A and B stations were be detected by a chan.ge of two in the multiplicity between A and B. For a given chamber, the multiplicity measurement was made ·with "daisy chain receivers" (DCR's) and "Window Discriminator Units" (WTIU's) designed by our group, see figure B-4a in Appendix B. The DCR's shaped daisy chain outputs (AI OCT, see figure 2-9) from the shift registers, passing them along to the ·wuu· s. DCR outputs were proportional to the number of hits in the chamber feeding them. vmu·s contained several independent pairs of discriminators. Each pair tested preset minimum and maximum hit requirements and output a fixed pulse height if '::ioth were satisfied. The Ax = 2 requirement was a special case set up as at least 2 hi.ts and less than 3 hits. WDU outputs for the various planes in a given re;uirer::ent were linearly added and then discriminated in "Majority Logic Units", also designed by our group. These units gave a NIM standard output pulse if the total height of the input pulse was above a preset level. Thus, an A-station requirement of 2 hits in at least 2 of 3 planes was satisfied by any two of the WDU's for the A-station sending pulses to a Majority Logic unit set to require at least two pulse height units, figc-2 B-4a. The NlM pulses were fed to standard Lecroy fast coincidence units along with pulses from other units and the veto counters to form the trigger for a given - 45 topology, figure B-5. The stiffness of each trigger was determined by the goals for the reaction, its cross section compared to potential backgrounds, and our willingness to lose good events to suppress them. Some compromises (reflecting the survey nature of the experiment) were also made to adjust live times. Delta rays, chamber ir:efficien.cies, electronic noise and close tracks can all distort multiplicity measurements. For rrrrnr , the biggest worries were considered to be reactions involving recoil >;· ·s decaying to rr 0 n or rr-p , which called for photon vetoes; low-t 1ie scc:.~tets, ':·.-~...:.c::i called for use of the 2x2 veto; elastic scatters with accompanying delta rays ~n the pwc's; and three particle (diffractive) events with two particles e~~2s8~\~ed by several chambers. The last two effects caused us to set up particularly stiff fon . ~ad :::citipEcity requirements for rrrrnr. demanding exactly two particles at both A and BCD with only slight concessions for chamber efficiencies and delta rays, and expec:i:1g losses from these effects. Losses from close tracks merging in one v'..e'N 1·:c..s another price of the trigger. We required two of three A charnbers (A..x2, Ay2, Au) to have exactly two hits, "A(2)2/3", and five of the six BCD chambers (Bx, By, Cx, Cy, Dx and Dy) to have exactly two hits, "BCD(2)5/6". The other rmnr requirements were 2x2, {3=0, and all l2 Ja'N co:..:r.:.ters ::_~d. :2e 24 barrel counters have no hits, figure B-3 . A {3 chamber inhibit existed on :r_e '.)er- rel veto, but this was covered by the {J = 0 condition. The Barrel c.:::d Jav.r :·2::;_'2.~·e­ ment was called BRINBJAW = 0, to emphasize the {J inhibit which turned off the two barrel counters behind any of the 24 {J sections that registered a hit. The 1imir final trigger requirement was thus Trig = 2x2 · (BRINHJAW=O) · ({J=O) · (A(2)2/ 3) · (BCD(2)2/ 3). (2.4) - 46 - Our trigger selected only the topology of the event, not the types of the particles involved. Thus the rrrmr trigger included data from reactions such as K-p ~ K-rr+n, frp ~ prr+n, rr-p 4 K+I\n, and rr-p 4 ppn, as well as "junk" such as rre ~rre (at relatively hight), rr-p ~ rr-rr+rr0 n where the rr 0 can. come from either the upper or lower vertex (see figure D-1), and at a reduced level, some diffractive and delta ray induced events. Except for alignment (curve through) and test runs, we had ten t:iggers operating simultaneously. Five of these, rrrmr (the subject of t:--Js thesis), VU n. rrp, nVO rrrrX , nV'O nV'O- X , an d rrrrns ..J ,, . \( l l h i gh mass 11 1irrn ) were cons1. .... ereu1 major p hJ.y- sics" triggers. The other five, rrp (elastic), 3np, mrX, 1irmp ( rrrrn "paddle"), ar:d IB (interacting beam) were background or calibration triggers, and were ''prescaled" to preserve live time for the main triggers. As a result of a run plan change shortly after the Run I 50 GeV running, the rrp and 11rmp triggers were removed and prescale factors for the other background triggers were adjusted to permit more live time for the major triggers. Late in Run I. 1mB ( rm "Barrel", section 2.3 .3) vrb.ch required exactly one barrel counter hit, but was otherwise the same as rrrrnr, was added. In Run II we also had a rr-p ~rr0 n charge exchange trigger. 2.5 Beam Momentum. Resolution Ultimately, the source of all our various resolutions such as momentum, mass, t, missing mass, angle, and vertex, are the position measurement resolutions, loca- lions of the various tracking chambers, and the material in the spectrometer. A detailed event simulation can, in principle, determine all relevant resolution parameters. However, most were measurable directly from data, although in some cases, their dependences on variables such as mrm were not. Most variations, hmvever, can be estimated from relatively simple formulae. The main exceptions are the cosfJ; and <fJJ resolutions, and we used a simple simulator based on our acceptance Monte - 47 Carlo for them. The simulation was checked with measured resolutions, and results were consistent with measurements. We prefer to use measured munbers for our claims wherever possible. We group in this section our 100Ge VI c resolution results. Kinematic symbols are defined in Appendix A. Average track angular resolutions, in milliradians, are given in table 2 .8. Table 2.8 Average Track Angle Resolutions View a, mR Beam x Beam y After x .033 .034 .086 After y Before x Before y .097 .138 .155 In the table, before and after refer to upstream and dmmstrea.rn of the )LPS ;:ac.gnet. The momentum resolutions observed in curve through data at 20, 50, and 100 GeV are summarized by 6p/p = .OOlp v'.037 + 8.60/p 2 . (2.5) PK The multiple scatter term (8.6/p 2 ) is only noticeable at low momenta. Ignori~g it gives ~p Ip=. 00026p. This improvement over E260 (.0007p) came from increasing both the magnet PK and front end lever arm. The missing mass resolution was determined in a series of fits to the neutron missing mass spectrum. Neutron Mx 2 plots, such as figure 1-3, indicate an average resolution, aMz 2 , of about 2.5 (GeV /c 2) 2 at 100 GeV le beam momentum. The neutron peak after mrX subtraction is consistent with a Gaussian with event configuration dependent resolution. A quadratic expression using the variable - 48 - C\I 5----------4 (.!) 3 >Q,) (a) '> 4 Q,) (.!) i 2 I O_I 3 C\I C\I b 5------------......------- ~ 2 b I IOOGeV, Imag=-180 -0.5 O_I 0.5 0 x 100 GeV, !mag= +180 -0.5 0 x 0.5 10 o All Events, (fwhm / 2.35) • Minimum at x- (b) =0 I '/ I I I I I I I I I I I I I I I .1 I 10 20 I 50 100 200 P-,,._. GeV!c Figure 2-11. Neutron missing mass squared resolution. In (a) a/ha is plotted against x- at 100 GeV/c. Part (b) shows the beam momentum dependence or the minimum aJh2 and average resolutions. These averages ("all events") follow a P~cim dependence above 50 GeV le. - 49 - x- = ( E- - Eb I 2) I (Eb I 2) (2.6) where E- is the forward rr- lab energy, and Eb is the beam pion energy, adequately describes a11z2 • Background subtracted neutron missing mass distributions were fit to a Gaussian form in eight x- bins from -1 to +1. The resolution, as a function of x-, see figure 2-1 la, was then fit to a quadratic function with the result alh 2 = (1.49±.05) +(-.007±.10) (x-) +(2.67±.20) (x-) 2 (2-2:1/c 2 ) 2 . (2.7) at 100 GeV le. Within our statistics, we found no magnet polarity or real TiTi mass dependence of the Mx 2 resolution. (An apparent mfm effect reflects the x- dependence folded with changing decay rrrr angle distributions.) Figure 2-l :b shov;s the beam momentum dependence of aJh2· The fits · that produced figure 2-lla and equation 2.7 also gave the beam momentum measurement, and evaluated an alignment kink (sections 3.2 ai.1d C.7) between the upstream and downstream sides of the MPS magnet. Our best beam momentum. estimate (found by forcing the mean neutron mass to its accepted value of .93957 Ge VI c 2 ) is Pbeam = 100. 05 ± . 04 ± . 10 Ge V/ C. (2.8) The first error is the statistical fit error and the second one is the rms spread from a .8 inch momentum slit setting, section 2.2. We have about 5800 examples of rr-e- ~ rr-e- in the rrrrnr data. While an easily removed background (just a total charge test), this reaction was extremely useful for resolution measurements. Being an elastic scatter (off an atomic electron), the kinematics are well defined and give a maximum electron energy of 85 GeV for a 100 GeV le beam. For this reaction Cl and C2 are useless. This is dealt with by evaluating the rre mass for both possible particle assignments. The resulting rre - 50 - 1200 2 combinations select closest per eYent comb1not1on N ~ > 1000 Q,) (.!:) 8 800 0 -...: l/'I c 600 ~ w 400 200 0 0. 1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 TTe mass, GeV!c 0 .15 0.2 0.25 0.3 0 .35 0.4 0.45 0 .5 0.55 2 TTe mass, GeVlc 2 1200 ... 1000 > Q) ~ we e~ts misldent1f 1ed as ,.,. ,.,. 800- L[) N 'c 600 (/) Q) > w 400 - 200 ... 00 .~ 0.5 I 1.5 2 2.5 mTT TT, GeV!c2 Figure 2-12. Pion electron scattering data. The events in 2-:2b •,rere used for tpn resolution estimates. The same events when plotted as rrrr yield 212c . mass distribution is shown in figure 2-12a. A very nice rre peak is seen, along with a mush resulting from ·wrong assignments. For our purposes, simply selecting the combination closest to the nominal rre mass or -VS of the scatter, is acceptable, figure 2.12b. The width of the rre peak gives a forward mass resolution estimate of 11.3±.1 MeV /c 2 . This resolution is applicable to any forward system \vi.th total 0.6 - 51 - momentum. near 100 GeV /c, vertex in the hydrogen target, and opening angles similar to those of the rre reaction. Figure 2-12c shows the "mr" mass for the rre data, and indicates that this resolution maps to mr masses of about .47 GeV /c 2 . This compares favorably with the K° mass resolution of a(mf(O) = 16±1 UeV foun.d in our K° K±rr+- X analysis [BrBO]. The K° momenta averaged about 30 GeV, but they decayed between the A and B stations. Equation 2.5, the data in Table 2.8, and the approximate form m 12 = vAA 9 can be used to estimate the mass dependence of a(mmr). The form for m 12 assLillles massless decay products and a small lab opening angle e. but is adequate for the present purpose if we expect only to get dCJ(m )I dm from it. Taki~~ extreme cases for the effect of p 1 andp 2 , we have dam./dm = (4.1±.B)MeV/GeV. The large error covers nonlinearities expected in the resolution, and tying this onto the estimate at mmr = .47GeV, we have a(mmr) = (11.3±.1) + (4.1±.8)(m1"i - .47) (2 .9) where the resolution is in MeV /c 2 , and mITTT is in GeV /c 2 . Both the rre and K° masses give estimates of the systematic forward mass error. These estimates are 3~IeV and less than 1MeY respectively. Another important feature of the rre reaction is that since all final particles are observed (and the target electron was at rest), Pt =O, where Pt is the transverse momentum of the forward rre pair measured with respect to the bea."11. ?ion. ·we thus get a measurement of the Pt resolution, and hence the tpn resolution for rr-p ~ rr+rr-n. To good approximation, the Pt resolution is constant, and also to a good approximation (especially when the recoil neutron mass is poorly measured) we can estimate t' =tpn -tmin =-pl This form implies that at = 2 CJPt ...JJT'T, and that a, = 0 at t' =0. Including a small zero point error gives (2.10) - 52 - N .01 ~ >Q.> ~ b.. .001 0001L-~_._~_;__--~....-........J------------"-------.._..___.~~----- . .00001 .0001 .001 .01 t' (GeV!c/ .I Figure 2-13. tpn resolution estimate from equation 2.11. For spectrometers of our type, this form is well born out at e\'"en rr:cderate tpn [Gr74]. Both parameters of equation 2.10 are available in rre scattering if we take ap,=<P,>, and 0': 0 =<1tl>=<Pt2 >. These values are <Pt>= .0:8GeV/c and <Pt2 >=.00041(GeV/c) 2 so that our t resolution is (figure 2-13) <lt = Y1.7x10- 7 +1.30xl.0- 3 it' I (2.L) This equation applies at m 1m= .47GeV/c 2 , but O't increases less tha..'11. a factor of t 1:rn from m'"' =.5 to 2 GeV /c 2 . The Pt measurements also give an estimate of our sys- tematic Pt error resulting from alignment differences between the beam and MPS front end. The average Pt components were <Ptz> = -.00125 ± .002 GeV! c and <Ptr> =-.00218 ± .002 Ge VI c. These errors are negligible . (The x-y difference reflects mistakes in setting up the BAy and Ay ct1ambers. Both had two y planes Which were meant to be staggered but weren't. This was corrected for Run II. The x View planes were staggered.) - 53The above claims are consistent with results from a Monte Carlo study which used the track angle resolutions of Table 2.8. This study also gave us resolution estimates for costJ1 , and cp;, the Gottfried-Jackson frame rrrr decay angles . The costJ1 resolution depends slightly on mrm, falling from .03 to .01 between the p 0 mass and 2.5 GeV /c2 . The cp 1 resolution was seen to be independent of mass, but tpn dependent. At tpn =-.01 Ge 112, it was 7° and at tpn = -.10 it was 3°. At tpn = t r..ir.• the cp 1 resolution diverges since the neutron azimuth is indeterminate, bd ia/ dt is falling below tpn =-m;rr . The 7° estimate is an effective upper limit. Figure 2-14 plots the vertex resolution, <lz, against the 1irr mass. Tr.1.e observed mass dependence of az reflects changes in laboratory opening c.::.:;le distr:!::Jutions as the mass increases. The vertex errors in the figure are those reported by TEARS (section 3.2) with an additional factor of 1.5 applied. This factor was deterrri.ined in vertex distribution fits with a series of <lz cuts, figure 2- 15, and is good to ~0% of itself. This underestimate has been traced by Bromberg to a missing term in the vertex routines which had no effect beyond the error estimate. Our vertex routines have been compared against another fitter [De80] and found to be highly efficient and, within the adjusted errors, accurate. Because of the dependence seen in figure 2-14, no cut on <lz was used. The TEARS vertex routines are described L.11. Appendix C. - 54- 6.0 5.0 l ' 4.0 ~ u - 3.0 ~ b 2.0 1.0 0. 0. 2.0 1.0 3 .0 4.0 Figure 2-14. Vertex resolution versus rm mass at 100 GeV/c. The resolution scale includes the correction of figure 2-15. f3 .0 ~ 4 .0 u ...~ ...,) ........ '-" ~ ~ 2 .0 0. 0. 1.0 2 .0 3 .0 a z (TEARS), cm Figure 2-15. Vertex resolution scale adjustment. Even with the larger resolution estimate, vertex feed out losses (section 3.3) were negligible. - 55 - Chapter ill Event Reconstruction, Scaler Analysis 3.1 Introduction This chapter reviews our track finding analysis and the selections used to extract rr-p 4'f'l+rr-n events from the 1mnr trigger data. The data processing went through several levels, DST, CST, PST, &n.d CPR. ec..ch distinguished by the amount of data retained on each event, and the r.1.u.c:-~ber of events kept. DST's, or data summary tapes, were the result of a t~ack :iadir~ analysis on raw data with the program TEARS [Fo75]. DST's were actually :s:.o b;>i copies of 800 bpi raw data tapes with the track, momentum, an.d \-ertex results appended to each event. Although based on the program used for E260, E: :o TSARS had substantial differences from the E260 version. For El 10, TEARS was optimized for low multiplicity events and the algorithms for tracking upstrea.rn of the m0..gnet bear little resemblance to those used in E260. DST's served mairly as a way station, holding tracking results enroute to more manageable formats with which data h.andling and physics analyses were more efficient. About two hundred DST's were needed to hold the Run I data. From DST's, compressed summary tapes, or CST's, were created by rerr..ovtr_g all raw data records. Simplified format copies of the ADC, tag bit, and pwc sbift register were included, but all spark chamber data was removed. Only results for matched tracks, and only the results of one of two independent before magnet analysis systems was included. Flags on the CST's recorded chamber responses (hit/no hit) for each good track. The CST format was compatible ·with all the triggers, and even allowed us to repeat the front end tracking at one point ·with some improvements to TEARS, without needing to recreate DST's. - 56 - CST's were split by trigger. The selection required only that the appropriate trigger tag bit be on. Hence no events were lost because of multiple trigger bit firing. This was allowed by the triggers, some of which overlapped. For iirm, CST' s were used mainly for correction factor development, and performing Cerenkov counter analyses. Beyond the trigger splitting, no events were cut from the CST's. For Run I twenty 6250 bpi CST's were needed, five each for the three major triggers, and five more to hold the other triggers. PST's, or physics summary tapes, had a format specialized to the ~,;-,-o bod.y topology of mrn. Scaler and some tag bit data were the only remnants of raw data on the PST's. The PST track data covered only the two good vertex p?:tides, a..n.d only enough information was retained to make fiducial cuts, evaluate weights, and do kinematic analyses. At this level, we evaluated all event by event corrections, using factors developed '"'ith CST's, and performed our full kinematic event arlaiysis. In creating PST's from CST's, preliminary selections were made. Events falling loose topology cuts and some basic trigger tests were rejected. Further cuts were made in the PST analysis and both sets are discussed in section 3.3. PST's were compact enough, to maintained as Fermilab disk files, and not tapes. If only weighted distributions were needed, PST's would be sufficient. However, weights were reevaluated every time the PST was read. A format more suitable to decay distribution analysis (fits) was used in CPR's, or condensed physi::s records. CPR's, which were created from PST's, held only kinematic analysis results, (m:r:"i• tpn.. Mx 2 , rm rest frame decay angles, tmr, and umr), and all correction weights for each event. No track in.formation at all was written on CPR's, and only events passing all cuts used for PST analysis were written to CPR's. Both rrrmr and rrrrX trigger data were processed to the PST and CPR levels. - 57 3.2TEARS TEARS created DST's after performing our tracking and vertex analyses. For rrrm and other non-vee triggers, it made few judgements on the topologies of events beyond setting flags for successful operations such as vertex finding . Selection of go.ad events from the TEARS results was left to later (CST and PST) ar:alysis piograms. For vee triggers, such as K°rrp, the desired topology was an integral pc.rt of the formalism. Appendix C gives a more detailed review of TEARS t!:-:.aro.. gi•.-en below, and tables in it are referred to here. Track finding began downstream of the MPS magnet V;ith ind2pend2nt s~::"a.ig~t line fits in the xz and yz views. Minimum spark requirements, Tc..b~e C. ~. 1.:..-...:: ~-...:d.ed both overall and local group requirements . (An overall requiremen.t sparn1ed all chambers in a given view, for example the x view chambers downstrea;:n_ of the 2a.gnet. A group requirement covered only a subset of these, for example the Fx chambers.) Two passes were made in each view. In pass 1, sparks in the F-stc..t~::m were required; in pass 2, the F-station was ignored. Both because of havir~ t~·.To passes and having relatively loose requirements in pass 1, sLn.gle view cleanups we~e employed to remove redundant tracks (keeping the better of two tracks with essentially the same parameters). Next, the xz and yz tracks were matched, section C.3, using slant view spark chamber information and the requiremer-.:.ts of Te.ble C.2. ~fore cleanups followed to remove spurious matches. This was our cnly viev.r !!:.::.tch- ing operation, and the term "match" will refer only to the track pairs found in it. None of the downstream cleanups were 100% efficient. We preferred to have high efficiency for good track and match survival over high efficiency in spcrious track and match removals. The single track and match cleanups were designed to compare tracks for duplicates and pick the best of a pair. If a track or watch ~·.-as reasonably unique, it survived these tests. Since the front end (between the target and MPS magnet) tracking chambers were all proportional, their superior time - 58 resolution provided a strong "effective" cleanup when we sought upstream tracks corresponding to downstream matches. As a result, the appropriate measure of multiplicities is drawn from the front end results, not the downstream ones . Spurious matches typically had no corresponding front end tracks. Those that did were fairly rare and usually shared front end tracks with a good match. .After completing the dmvnstream analysis we deterrrJned the bea..rn trajectory, wbJch was needed in the front end algorithms. One unique beam t r ajectory ':~"as found per event. The procedure used was not a fit since ·we had ocly t':·:o b 2 2.~ sto.tions (BA and BB) about 19.5 meters apart. Instead, we used the beam p;';-~ c c.ta to locate the beam position at each station, and con.."1.ected these with str-aig:it 1:::2s . If hlts in either view at either station were ambiguous, the event vrns flagged. The beam position and error were then d.ravm from averages of the beam location a.rid beam spot \-\idth for the view and station in question. Although such suspect !:Jeam events were later cut from the data, this allowed a full analysis of them, and in t he rrmt case, they vrere found to be as good in all respects except for a poor tpn meas- urement as the good beam data. Multiple beam particles were not a problem, although they would, without the strobe kill, dominate the two body rrJinr trigger. The strobe kill electronics, Appendix A, removed nearly all double beam v.i t::in the resolving time of the beam pwc's, and removed all double beam where both particles were in the same rf bucket (at the cost of losing some effective flu..x, but the scalers accounted for that), and charge and momentum cuts removed any surviving remnants. Having a beam track, TEARS turned to the front end analysis ·with the immediate goal of finding all possible "links", or front end tracks that joined to the downstream matches. The next goal was to locate main and (depending on the t r igger) Vee vertices. A general feature of the front end analysis was that it sought only linking tracks. With only one exception, if a particle failed to pass through the magnet - 59 - aperture, its tracks were not found. All but one of the the triggers were designed for all particles to pass the magnet and extra charged particles were heavily suppressed by the topological trigger. (The exception was the "high mass" 1irm trigger in which a single slow particle (nominally a 1T+) was intended to strike the inside magnet wall in one of the r chambers. For that trigger, the slow particle tracking was meant to be done in a DST analysis separate from the one described here. We will not detail those operations.) The front end analysis was performed twice on every event u.sing :;~e sys:s::1s ''Vtrig" and "Targtrk", optimized for topologies with and \vithout seccn.dili7 'v-er:ic:es (vees) respectively. Vtrig will be discussed in Appendix C. Both sets of resdts -:-.-ere written to DST's, but for CST's and beyond we specialized to the results of the system appropriate to a given trigger. On CST's, only Vtrig results were v.-:-i:te11 for the vee triggers, K°rrp, A'°mrX, and K° K° X. Targtrk results were used for all ct~er triggers unless Targtrk failed. In that case vtrig results were substituted as a backup. (This later proved unnecessary; all rrrrn events failing Targtrk re2or:struction also failed Vtrig .) The front end analysis of interest to mm was not Vtrig, but Targtrk. In this system, only main vertex particles were sought. No fits to a specific hypothesis were made; all possible vertex particles were found. The tracking requirements for Targtrk are given in Table C.3. In this table, only real sparks are included. An important feature of the front end algorithms was the use of information from the beam and matches to support the front end tracking. Since we rJ.ad a K° decay volume free of chambers, figure 2-3, and the A station was close to the target, the BC lever arm was not sufficient to always resolve the correct hit from t1·10 close A-station hits. Additional information was needed. This was provided by e:&i.rapolations of the matches to the magnet center and (in y only) to a point inside the decay volume, and of the beam track to the target. The y-view match extrapolation - 60 used a vertical focusing correction but the x view extrapolation only needed a square field approximation. All extrapolations were assigned inflated errors, arid were included in initial track fits. With the exception of the x-view mid magnet point, these extrapolated points were then removed from tracks in a refit. Refit tracks were then used to find momenta and charges using a square field approximation. The beam extrapolation was especially important in selecting the correct A.station hits for a track. In the fits, the beam provided a vertex "spark" , cJ.t:::o u.gh vertex was unkno-wn. Since a 'iVTong vertex spark could lead to a bad selection at the A-station, Targtrk was structured as a loop over three possible vertex s~arks along the extrapolated beam and sizable errors were assigned. After all front end tracks had been found by Targtrk for each of the three choices and a vertex had been found for at least one (and usually aU three), the best set of Targtrk results was selected as the one that made best use of the A-station information. Secondary criteria 1Nere the number of vertex tracks and the vertex x2 . The vertex fits were iterative x2 fits in both the xz and yz \iews to a corri_r!1on zv . Forward track deletion was allowed independently in either view. For Targtrk, and for the main vtrig vertex, beam tracks were included and could not be deleted. Targtrk used one final cleanup, called Sclean. Sclean selected only the best match of any pair having two different y view tracks matching to the same x \iew track. Since the slant spark chambers were virtually x chambers (stereo a..t"J..gle of .o nly ±5.7°), multiple x view tracks matching to the same y view track were allowed by Sclean Next, Sclean sought to remove "old" or out of time beam region tracks by requiring F' pwc hits on any matched track within ±5 cm of the 2x2 counter. There were two such chambers in each view and one hit in each view was required, amounting to two additional tracking requirements. In Run II, a BA type proportional chamber (called BBWV) was located with the 2x2 counter at a 45° slant. Hits - 61 - in this chamber were included in the match spark counting, and were also used in Sclean. A hit in BBWV on a track was enough for Sc lean to approve a match. For Targtrk, Sclean was used only after all tracks were found and the best vertex determined. In this case, Sclean (which was -wTitten for Vtrig) v."as an add on to flush spurious matches, especially in the beam region, that linked to the same fr on.t end tracks used by good particles. The Sclean processing in this case ~'." as on any match with a Targtrk link to the front end. The sequence ''vertex then Sdean" '>.-as considered reasonable since spurious matches always used the se..ce ~ro~1t e:-.;.d track as a good match so that the vertex fits were not much biased by the spillicus matches. The average tracking efficiency exceeded 99% on good (real) pc:rticles, but as discussed in section 4.8, the appropriate tracking efficiency inclu.des the effect of the trigger requirements and includes both particles in a conf:gcration dependent calculation. Without Sclean, Targtrk was only about 90% efLc:ent with respect to feed up problems in the vertex multiplicity. With Sclean, the feed up effects were less than 1.4%, while feed down losses were less than .3%. Particle momenta were evaluated in TEARS using a square field approxirnation. The xz plane component of the momentum is (3 .1) where PK= .7510 GeV le is the magnet's Pt kick and eb I ea, are the xz plane angles before and after the magnet, respectively. The full momentum of the particle is then found as (3 .2) where S:;; and S11 are the before magnet slopes. Unfortunately, the momenta measured by TEARS have a systematic shift characteristic of a kink of 6 e = .084 ± . 007 milliradians between the upstream and downstream (of the MPS magnet) chamber - 62 alignments. The kink had no noticeable effect on the tracking and li!'.1.king efficiencies. Monte Carlo studies have shown that this momentum error vras not the result of the square field approximation, and that the square field approximation has no noticeable effect on the resolution. We accounted for the kink by a first order momentum correction at the PST level, P =Pm ( l+oe; €1) (3 .3) where P is the true momentum, Pm the measured momentum, €J t~e b e::d .::.:--~gt e and oe the kink. Appendix C includes a discussion of the kink and. t:--1e e1,-:::li..:.c.:.i0n of 6e. 3. 3 Event Selection Despite stiff multiplicity requirements for the 11rmr trigger, sec::.io:1 2.4. most of the recorded data was not 11-p ~ rr+11-n. A large number of background reac tions either had or could mimic the required two body signal. Examples of these inclt.:de 11-p-+ rr-rr+ffln, J\p-+ K-rr+n, rr-p-+ I\ J(f"n, ftp-+ prr+n, and rr-e - ~ 11-e - (rre scattering, or extremely stiff delta rays). To extract our sample of i'iTiTl events (with reasonably small and correctable backgrounds), a series of cuts listed in Table 3.2 and discussed here was made. In addition to insisting on the expected topology, charge, and particle species, some cuts insured that the i::tended trigger was actually satisfied and were designed to facilitate corrections . Our basic topology cut required that two oppositely charged particles (total forward charge zero) come from a vertex found by Targtrk. Only Sclean. approved particles were included in this accounting, and the total charge test came after the vertex particles were counted. (One cut we did not make was requiring exac tly t•::o matches. Studies found no differences in event distributions made with this, and those with our usual cut beyond an expected reduction of event totals of ab out .;Q/6 . - 63 - Most two body charge zero events had large missing masses, indicating considerable energy going into neutral particles (mainly rr0·s ). A loose total forward momentum cut (75 to 125 GeV for the 100 GeV beam) was made in creating PST's, but for the final analysis, recoil neutrons were identified by a missin.g mass calculation requiring (3 . ~) where (3.5) The P;. are 4 vectors of the forward rr- and rr+ , the target proton Cn ), and the beam pion. For equation 3.4, a(!Jx 2 ) is evaluated according to equatio.c.s 2.6 a.c.d 2.7. As shown by figure 4-3 , virtually all 100 GeV events passing this cut fall between the limits -5<Mx 2 <7Ge v2. The Mx 2 cut left us with a backgroun.d of about 10% from events with unvetoed rr°'s. These background events, indistingu.is~a.ble from good rrrm events are accounted for by a background subtraction, section 4.2 and Appendix D, in the cross section measurement, but are left intact in decay distribution plots. Cerenkov analyses were needed to remove 'ftp ~ p rr+n , K-p ~ K-rr+n, and rr-p ~ K-K+p or jipn backgrounds. For the first two, we required that the beam Cerenkov counters tag the beam as a pion according to rr = ( C0 +PRUSS)· BDIFF ·DISC (3.6) when all counters were set. The tag was adjusted appropriately when one of the counters wasn't ready. For the pion induced backgrounds, Cl and C2 identified the forward particles whenever their momenta allowed. (The qualification is discussed in section 4.9 along with the details of the C1-C2 analysis.) - 64 - z 2.022 3.042 3.96 4.47 4.98 5 .70 6.30 11.5 12.43 z 1.943 1.689 3.042 3.96 4 .47 4 .98 5.70 6.30 11.5 12.43 12.43 Table 3. la Run I Apertures (meters) Name X limits Y limits V3xy ±.3 ±.12 ±.17 Hx7 Pole tip upstream ±.55 Mid magnet ±.55 Pole tip dovmstre am ±.55 1:agnet exit ±.55 ±.28 ±.311 ±.73 ±1.10 Dx7 Cl F4xy Table 3.1b Run II Apertures (meters) Name X limits Y limits V3x ±.225 V3y ±.0921 By ±.17 Pole tip upstream ±.55 Mid magnet ±.55 Pole tip downstream ±.55 Magnet exit ±.55 ±.28 Dy ±.311 Cl ±.73 F4x +1 .60 F4x -1.66 In order that acceptance calculations be well defined, fiducial cuts, Table 3.1, were made. These outer aperture cuts required that particles land well inside the F station. For Run I data, we selected the F-x cut to avoid a region of rapidly falling reconstruction efficiency on one side of the spectrometer. This was unnecessary for Run II, spark chamber improvements having been made for that run. We also required both particles to miss a 28x28 mm box (at Pbeam ~ lOOGe V) centered on the 2x2 counter. At 175 GeV, this cut used a 14.7 mm box surrounding the lxl counter. - 65 - Table 3.2 100 GeVI c Event Cuts Cut Percentage of Data Rejected PST Creation Vertex Found Two Particle Loose Momentum Cut Charge Zero A(2)2/3 Multiplicity BCD(2)516 Multiplicity BCD Hits on Tracks .5 4?...., , 56. 32. .143 .2 1.1 PST Analysis (CPR creation) Beam Pwc Beam Cerenkov Apertures ( 10%) Pass 1 Vertex z 4.4 7.3 15. 1.9 24. ~6.y 7.0 Bx radius Veto House (VO to V3) < .1 Mx 2.4 2 45. Cl C2 Reconstruction A- station 11. < .1 < .1 Cuts are listed sequentially. Percentages apply at the time the cut was made. The "vertex z" cut is a rough average two different cuts, see teic..i.. Final A-station cut requires tracks resolved in at least 2 planes of 3. "Apertures" includes outer and 2x2 cuts only. The last strictly fiducial cut was a requirement on the vertex z-coordinate. (No cuts were needed in the x and y views.) We actually used two different cuts, both designed to eliminate net feed out losses caused by a finite vertex resolution, section 2.5. For normalization, a cut inside the target flask requiring - 66 -.51m ~ zv ~ -.30m was made to give a well defined target length. For data distri- bution analyses, we cut outside the flask, requiring -.65m ~zv ~ -.23m. In this case, the downstream cut is about halfway between the target flask a...r1d the vacuwn jacket. These cuts were studied with a Monte Carlo, and the resulting feed out losses were found negligible. (The vertex cut number in Table 3. 2 is actually for a cut about midway between the two just given. For these, the a.1Tl.our1ts of de.ta rejected by the vertex cuts are 41% (tight cut) and 14% (loose cut) .) Trigger inefficiencies for close tracks motivated another "fiducLal" cut, nc..:::.e ly one at the Bx station requiring ~~5.85mm and D.y~6.S6rnm, where W:c an.d t:.y are track separations. These values require that the two pions be sep~c.ted by at least 3 wires in all BCD trigger chambers except, possibly, the Dx chamber, v1here crossing tracks were allowed. These cuts ·were set after looking at the co.L.csecuti--.-e struck 'Wire distributions to remove any need to account explicitly :or eve:--. . ts lost by soft delta rays causing tracks to merge (section D.4). Another separation cut required that the radial distance between the t;;ro tracks at Bx be mmr~ 500!JeV/ c 2 . greater than 13 mm. This rejected little data above It followed the ~ D.y cut which imposed an effective radius of 9.1 mm. The A station trigger efficiency was quite poor for events in -.;~.-hich the two forward particles were resolved in only one or none of the three A station trigger planes, Table 4.4.1 . This rarely occurred above rm masses of 500 JfeV/ c 2 . Although few events at any mass were involved, their correction weights were large. This motivated the above radius cut, and a cut requiring that the forward particles be resolved in at least two of the A station trigger planes. A few low mass events surVived these redundant cuts. There wasn't enough low mass data for acceptance corrections below about 550 MeV /c 2 , and except for some weighted mass distributions and scatter plots, we generally ignored it. - 67 - A major block of cuts was designed to ease trigger efficiency corrections. (The B station separation cuts could also be included in this class). We used a software trigger following the hardware to insure that the rrrrnr trigger was indeed satisfied. These cuts were that the {3 chamber have no hits, that the photon vetoes (VO through V3) all be quiet, that the A station have exaetly two hits in at least tvro of the three trigger planes, and that there be exactly two hits in at least five of the six BCD trigger planes. In addition, a more detailed cut was imposed for the BCD chambers. The BCD hardware requirement interacted with the recon~:.ruction efficiency and was also quite sensitive to delta ray vetoes. The trigger requirements were significantly stiffer than the tracking requirements if we assume all hits 1.vere actually on tracks, even allovving one bad chamber. To provide for compatibility between the BCD delta ray and reconstruction efficiency corrections (sections 4.4 and 4.8), we required that the two forward tracks both have hits on them in at least five of the six BCD chambers, and if both tracks satisfied this in oriJy five chambers, those had to be the same five. If one chamber was flagged as bad in the hardware trigger cut, then it was the only one allowed to fail this test. If the x view tracks crossed in the Dx chamber, then Dx was the only bad chamber allowed. We only used events for which the two good tracks were pass 1, section 3.2. Pass 2 tracks hitting the F-station occurred at a rate consistent with interactions, and wide angle Pass· 2 data had terrible reconstruction efficiencies . The track pass type selection was made after the charge and multiplicity cuts. A reconstruction efficiency cut at 50% was also made. Given the fiducial and pass cuts, failures of this cut were rare. Vfhen using event by event weights for acceptance, we used a 10% cut to avoid divergences. This cut was not used in decay distribution fits. To insure a good measurement of the beam track, we required a good measurement of the beam coordinate at both stations (BA, BB) and in both views . This cut rejected any events using the average beam spot for any view. - 68 In the 175 GeV le data, additional cuts to remove events with photons detected in any of the El 11 photon detector, lead wall, or electron calorimeters were made, [Fr82]. Counter elements along charged particle tracks and their neighbors were excluded from the cut. In the lead wall, and also the calorimeters, pulse heights from the remaining counters were added and the event was rejected if the total exceeded half the minimum ionizing pulse height. For the E 111 photon detector, pulse height signals from charged tracks were removed. Photons v;ere then identified by peaks seen in both (x and y) views, and if any were seen the e\·ent W2.S rejected. These forward photon cuts were tuned to optimize photon reje:::tion cs.;.d maintain acceptable charged particle efficiencies. They reduced backgrounds at 175 GeV/c to the 100 GeV/c level. 3.3.1 Run Selection, Data Set Important for the cross section analysis (as well as general data analysis) ·was the identification and exclusion of bad runs. ~fost bad runs vrnre knovm from our logs. These runs were compromised by conditions such as lack of beam or C1 C2 Cerenkov counter data, short run trigger electronics failures, and/or critical tracking and trigger chamber failures. These problem runs correlated ·well ·with large fluctuations in run by run diagnostic scaler ratio plots, especially plots of an, equation 3.10. Various other plots were also used, including a cross section evaluated using weights for all corrections, including acceptance. A few additional bad runs were flagged in these diagnostic plots and verified by our records. Most of the bad runs found in these reviews were excluded from both our scaler and decay distribution analyses. Only a couple of runs, for which the STROBE scaler was . unplugged were included in an expanded data set for distribution fitting only. This operation reduced our data set by about 15%, from 280000 rrrrnr events to 240000 events. Table 3.3 summarizes the 100 GeV data set fate from raw CST's to - 69 Table 3.3 Run I. 100 GeV /c Data Set Total Recorded rrrrnT Good Runs Only On PST (good runs) Events 277924 239419 38997 CPR•, Tight Vertex, total Itpn I < .15 (GeV /c) 2 p 0 (.60<mmr<.94 GeV/c2) 7425 5099 1422 CPR•, Loose Vertex, total Itpn I < . 15 ( GeVI c )2 p 0 (.60<mmr<.94 GeV /c 2) 10577 7250 2105 • Cuts for CPR's are cumulative. the final samples of nrrnr events used for our various results. For our normalization, we divided the data into positive ( +) and negative (-) magnet current groups. With this division a problem spanning the entire Run I data set emerged. The "triglog" cross sections an. see Table 3.4, depended on the magnet polarity. After considerable effort, we concluded that this did not represent a left right bias in the spectrometer for good mm data. It seems that the trigger simply allowed more garbage in the trigger at one polarity than the other. The data cuts are "polarity blind", and after the full analysis, the cross sections were, within errors, consistent. While the source of the polarity problem has never been isolated, we believe it to be due to a number of small asymmetries in the spectrometer, none of which were large enough to cause the problem alone. Examples would be small misalignments of the 2x2 counter, possible fringe field magnetic effects on the V3 phototubes, and a paddle near the extreme edge of the Cx chamber that was left out of the trigger. Although outside of the fiducial volume, this paddle would flag no delta ray vetoes, while its symmetric partner could. This problem was found and fixed before Run II, and V3 was located farther from the magnet in that run. The polarity problem was absent from that run. While not proving the above - 70- speculations correct, the lack of a problem in the Run II data showed that a small average lab beam angle (~1/ 2mr), and a half inch offset of the magnet with respect to the beam were not the culprits. At 175 GeV le, the number of mrnr triggers was over 50% more than the Run I, 100 GeV le total. This was more than balanced, however, by increased backgrounds, mainly the high Mx 2 ("fast rr0 ") background. The 175 GeV le good run set included 481000 rrrrnr events, and yielded only 8408 events in the final sample. (About 75% of this was used in the 175 GeV le cross section analysis [Fr82].) For decay distributions only, this was augmented by 1487 events (out of 75000 triggers) from a revised mrnp trigger, giving a total of 9895 events. This additional data resulted from a desire to check the A station performance by removing it completely from the mm trigger. Late in Run II, we redesigned the 11'7rnp trigger (from the one described in Appendix B) and essentially replaced rrrrnr by it. The rrrrnr trigger was then heavily prescaled while rrrrnp was not. To compensate for removing the A station from the trigger, we included stiff DEDX counter requirements both below and above the two particle peak. Other requirements were the same as for rrrrnr. The resulting events were free of A station biases, and no corrections for them were needed. There were Landau fluctuation (in DEDX pulse height) losses, but for decay distributions, this did not matter. The revised rrrrnp trigger overlapped rrrrnr significantly, so for runs with the revision, we use the dominant rrrrnp and ignore a much smaller sample of rrrrnr. - 71 - 3. 5 Scaler Analysis To obtain an absolute cross section, a, for n-p ~ n+n-n within specified mass and tpn cuts, we need an estimate, P, of the events produced by a total pion flux, B, incident on a target containing Nr protons/cm2 . Then a is given by - p (3.7) a - NrB. The produced event estimate, P, is obtained from the corrected fraction of recorded triggers surviving all cuts: P = TRIGLOG ~: . (3.8) TRIGLOG is a scaler total giving the number of times the mrnr trigger was satisfied. The number, Nr, is the number of nnnr events written on tape, and Ne, is the corrected number of events surviving the analysis. The ratio TRIGLOG I Nr is roughly a spark chamber dead time correction, as not all triggers lead to spark chamber pulsing, section 2.4. (In chapters 5 and 6, we will refer to Ne as a produced event total. This is admittedly at odds with (3.8) unless TRIGLOG = Nr. That condition was met in the Run .II data, but in Run I. these numbers differed by a few percent. The term is convenient.) Ne depends on specific cuts, such as mass and .tpn. which we apply to the final data, but not on the biases of the spectrometer. Our cross section analysis naturally splits into two pieces, the evaluation of Ne , and everything else. Ne is obtained by applying our full set of event dependent and acceptance corrections to the observed event sample. The other factors group themselves into an exercise in scaler analysis yielding a number, a 1. This section Will concentrate on expanding equations 3.7 and 3.8 into the terms we used, then defining and evaluating a 1 . Section 5.3 will complete the cross section analysis and present results. - 72The pion flux, Bis obtained from the scalers EFFBM, PRETRIG, STROBE, and the beam pion fraction, f w• B =f nf EFFBM (STROBE/ PRETRIG). ct (3.9) EFFBM scaled the "effective" beam flux onto the MPS, section 2.4.1. EFFBM was not s~aled during evaluation of a trigger candidate by the electronics, or while the on line computer read in the data from an event. However, the name is slightly misleading since this scaler was. located before the strobe kill electronics which, as discussed in section 2.4.1, could kill off trigger candidates for reasons dealing with spectrometer readiness. This amounted to a deliberate, but unbiased, rejection of part of the beam flux. The ratio STROBE I PRETRIG gives this reduction. The factor f n is evaluated as Irr=!~ ( 1-µ) where/~ (3.10) is the "unbiased" pion fraction found from the beam Cerenkov analysis, section 2.2.1. The factor (1-µ) accounts for a muon (and electron) contamination included inf i. Beam decays and interactions between the beam counters and the upstream end of the target flask are accounted for by f ct. It is useful to group equations 3.7 to 3.10 together to give TRIGLOG · PRETRJG a= [ NrffTfct·EFFBM·STROBE J Ne Nr (3.10a) (3.10b) The term aTL is, roughly, the cross section for the rrrrnr trigger to occur. We say "roughly" only because the target factor, Nr. applies to a fiducial cut and not to all the matter seen by the beam. Equation (3.10) is more applicable to this experiment than (3. 7). It eA.'J)oses a real distinction between the trigger, which includes - 73- mainly garbage, and the physics we extract from recorded good events. The terms not included in uTL are necessary to convert it to a "physics" cross section. Another and important effect of using UTL is that it can be evaluated on a more restricted set of runs than used for making event distributions. In that case, Ne! Nr represents the (corrected) fraction of recorded events that survive our analysis, and both terms in this ratio are from all runs analyzed for event distributions. Also useful is the "cross section per event", u 1, given by the second half of (3.10b): (3.11) By virtue of the 1/ Nr term, the cross section per event depends on the run set used to evaluate it. However, it is independent of all corrections and any 1m mass or tpn cuts used. Both an and u 1 depend on the target fiducial cut through the factor Nr. Our cross section evaluation used both aTL and a 1 at various stages; however, the goal of the scaler analysis was a1 . Our decay distribution fits treat the positive and negative magnet data on an equal basis. For this reason, and to reduce errors, we used the following procedure for ui. Table 3.4. Large mass cut cross sections, a+ and u- were obtained for positive and negative magnet polarities. Amass cut of .5 to 2.7 GeV/c 2 , and a -.15 (GeV /c) 2 < tpn < 0 cut was also applied. A target fiducial cut of - .51 < Zv < .30m was used. Event by event weights for all corrections, including acceptance, were applied, Ne = L; w. The liquid hydrogen density was taken as 0.0708 gm/ cm 3 evmts [PDGBO], with a 1% uncertainty, giving an inverse density of 1/ Nr = 11.25x105 µb. a+ and u- were then evaluated as (3.12) - 74- Although the •n. values for the polarities were quite different, the agreement between u+ and u- was within errors. To eliminate the remaining asymmetry, at least to first order, u+ and u- were averaged arithmetically, u= (3.13) Equation 3.13 is our reason for introducing an Ne estimate at this level. We used acceptance weights as a first order correction to account for 2x2 counter location _v ariations in a low statistics situation, where our decay distribution fits might have trouble. The cross section per event was then obtained by dividing by the total .weight used for u+ and u-, (3.14) These calculations used essentially the entire set of good runs. Only a few good runs were excluded here (for lack of some scaler data) and included in the general decay distribution analysis. The Run I. 100 GeV /c scaler analysis data is given in Table 3.4. Only statistical errors are given in the table. The a+ and a- values agree, within statistics. Applying equation 3.13 gives a polarity averaged a= 4.25 ± .08µ,b. And we have a1 = .2160 ± .005nb . This value is used for our p 0 cross section, which used the tight target cut. A parallel analysis was made by Fredericksen for the Run II data, [Fr82]. The tight vertex cut cost us ~ 30% of the good mrn data, and the tpn cut was also significant, but the statistics were still sufficient. The true target flask length 1'as poorly knOlfll. and the tight fiducial cut avoided a difficult to determine feed-in feed-out correction. Simple Monte Carlo studies showed that the tight target fiducial cut had negligible net data feed _out and was insensitive to the true flask length. - 75 - Table 3.4 100 GeV le Scaler Analysis Imag = +180 2681 6.3689x 109 5.7180 x10 9 Imag = -180 2179 5.2352x109 4.7005x10 9 6.4700 X10 8 9. 9481 x 108 5.08 19 X10 8 8.2026x 108 123930 2:w:1: 178453 54.0±.0024 141673 10995.64 47.9± .0028 964 14 8679.85 a± 4.19±.106µb 4 .31 ~ . 121 µb Quantity Events EFFBM B STROBE PRETRIG TRIG LOG an Nr Table 3.4b Special Data Cuts for Above Target -.51 < Zv < -.30 m Mass .5 < mmr < 2. 7 GeV /c 2 tpn -.15 < t;m. < 0 (Ge VI c ) 2 10% Min. Acceptance To recover sufficient statistics for general decay distribution fits, we opened up the vertex cut to -.65 to -.23m, actually outside the target. This cut was also insensitive to net feed out problems, and virtually all the data within it can justifiably be considered as actually coming from inside the target, see figure 2-6. From equation 3.11, a 1 must be adjusted for the expanded cut. Since we don't ~mow the full target Nr. we scale a 1 by the increase in weighted data. (The result is consistent with Nr for a 12.0" target.) The expanded data set had 7215 events for the same mass and tim cuts with a total weight of 2:w = 29 150 events, giving af = .1458 ± .0032 nb (3.15) The 175 GeV/c analog of equation 3.15 is af = .0471nb . These values apply to the moment and decay distributions of Chapters V and VI. - 76 - ChapterN Data Corrections 4.1 Weights About half of the mrn events allowed by the spectrometer dead tine and acceptance were lost through a number of m e8hanisms. Also, backgroun.ds of order 10% persist in the final data sample. We review our event by eve!l.t corrections in this chapter. Appendix D goes into the details of the evaluation of a n:.:..::J.ber of tt.e corrections discussed here . The major correction not discussed here is our acceptance, section 5.1, which has zeros in significant places. Global c8:-:'s8ticr_s, ~ot applied on an event by event basis were discussed with the scaler analysis, section 3.4. For this analysis, most non-acceptance corrections are accounted for by weights applied to each rrrmr event in our final sample. The major e xception is a background subtraction for veto house failures. Except for particle decay, interaction and geometric acceptance, all of the correction factors were fou..'t1.d through analyses of rrrmr and/or various background triggers, especially rrrrX and curve throughs. If the chance an accepted event survives a series of independent losses is P, then the number of observed events, N0 , can be used to estimate the accepted event count, (the number we would have without losses), NA, by (4.1) The weight, w, is just l/P. Equation 4.1 applies equally well to differential distributions as to total event counts. Because most of the losses depend on laboratory variables not visible in plots such as mass distributions, the w in equation 4.1 is an average weight. More - 77 - directly, we can evaluate the weight appropriate to each event and use (4.2) For each event, j, w; is found as a product of weights for each individual loss: wi =ITi wJ =TIi lip}. (4.3) The p} are the chances that event j survived the effect i. The counting error in a weighted distribution is estimated by a= vr;;;;;-. We have taken care to ?..!.1.alyze the data and evaluate the corrections, w;., to maintain independence of the corrections. Cases where mechanisms are coupled, such as chamber efficiencies in our pwc based trigger and track finding, were evaluated together. If some of the wi are "large". then it is probable that several thifl...gs, any of which could cause a loss, could all "go wrong" on an event. However, each pi is the probability a problem did not happen, and Tipi correctly calculates the chai.1ce nothing went wrong. Large weights in general are not desirable, but if all or at least a large fraction of the events have comparable weights, the situation is livable. In our case, the weight is built up from a number of weights most of which are about 1.1 or less. The largest weight is almost always the p>-chamber delta ray correction which ranges from about 1.18 to 1.40. Still, unusually large ·weights are to be avoided as they distort distributions. Results are more reliable if the occasional high weight event is excluded from a distribution without further correction, [Ea71]. Our high weight cut is applied on individual corrections, which under some circumstances can become large. The most notable case of this is our reconstruclion correction for which we cut at a reconstruction efficiency of .5, or a weight of 2. In addition to weighting for losses, we include weights for backgrounds not removed by the beam and C1C2 Cerenkov analyses. Both these analyses remove the - 78 - greater part of their backgrounds but an estimable amount persists. In this case the weight is interpreted as the fraction of events that have the correct particle species. Veto house inefficiencies can be defined, and evaluated with the help of the rrrrX trigger. Under some circumstances. that data can then be used in a background subtraction. We begin with the veto house problem. 4.2 Veto Failure Background Other than a finite acceptance, the most obvious problem vvith our data is a background of order 103 at 100 GeV/c under the neutron in the missing mass ~quared (!Jx 2) spectrum of figure 4-1. Figure 4-2 illustrates the probable sotll"ces of the background. At Mx 2 values near the neutron, N~ and 6. resonance production dominates. Missing particle kinematics are mainly set by the missing energy The rmX trigger, whose only significant difference from rrrrnr 1rns its lack of a veto house requirement, was used to estimate the background. The veto inefficiency, or "failure rate", including both instrumental and geometric effects, was measured by taking the ratio of known veto failures in rrrrnr 'With the total 11rrX event rate as a flinction of Mx 2 . The known failures were just rrrrnr events ·with .~Jx 2 above the neutron peak. None of these were examples of rr+rr-n. Includiri...g corrections to the rrrrX total for prescaling and delta rays, the failure rate, F, in a given Mx 2 bin is given by (Events in rrrrnr)·o F= ---------:--(Events in rrrrX)· P (4.4) where P is the mrX prescale factor, and c5 is the average p-chamber delta ray correction (mrX was not subject to delta ray vetos). Data at 50 and 20 GeV/c were crucial in obtaining the failure rate under the neutron Mx 2 peak at 100 GeV le. Indeed, 100 GeV /c data only to verified the consistency of the analysis. What we - 79 - 5000 1T1Tnr C\I > 1T1TX .•.•••....... <.9 4000 1T1TX weighted for subtraction Q.) 'en c Q.) ~ 3000 - ""O Q.) -& 2000 ·a; ~ 1000 0 10 Mx 2 ' 20 GeV 2 30 40 Figure 4-1. 100 GeV le Ux 2 spectrum for mmr and fully weighted mrX spectrum. By construction, the veto weight gives cancellation at high missing masses. (Deviations result from averaging inefficiencies measured at 20, 50 and 100 GeV le.) Under the neutron peak, the shape is rr:.airiJy determined by measured failure rates at 20 and 50 GeV le, and has a small model dependent~( 1236) corr!ponent. needed was the failure rate under the neutron peak, which was, by definition, unobtainable at 100 GeV. The need for using 50 and 20 GeV le data ·was the only reason we kept a fixed front end geometry for all energies (at the cost of reduced acceptances at the lower energies). Failure rates as a function of Mx 2 were found at each beam momentum and magnet polarity. These sets were then averaged as a function of Mx 2 after determining that they were all consistent. For our background subtraction, mrX events passing the same missing mass cut as the rr7mr data were then given the additional Weight, Wv = -P·F. Figure 4-3 shows our final Fas a function of Mx 2 . The very first - 80- .,,..,,.p '' ...... \ 'n 1ro Figure 4-2. Major background sources. The major source of background under the neutron peak is!::,. and N• resonances, although a tail of c.}O production is also present. At high Ux 2 values, mesons decaying to 71+rr- and one or more rfl should dominate, with lower vertex processes yieldLig rrc's also present and significant. Charged decays of N•'s are allowed because of the finite efficiency of the {3 chamber. bin applies only to the !::,.( 1236) mass region, as discussed in Appendix D. The jump at the !::,. presents a problem in actually applying this correction. We have dealt 'ivith it by smearing that bin according to our Mx 2 resolution, and applying an effective F built from the smeared!::,. bin and the relatively flat other values. For the smearing, one needs an estimate of the amount of !::,.(1236) relative to the rest of the rr71X spectrum. The !::,.( 1236) fraction and the overall background levels depend on mmr, but measured failure rates were independent of the 7171 mass. Details of the model and evaluation of F are given in Appendix D. Figure 4-4a, shows the mrX Mx 2 spectrum at 100 GeV le after correction for losses. After removing a small amount of mrn data from the mrX sample, it can be Weighted for veto house inefficiencies and prescale factors and subtracted from the rrmtT data. Figure 4-4b, shows the resulting background Mx 2 distribution and figure 4-5, is the subtracted 71rrn Mx 2 distribution. One problem that, rather surprisingly, didn't affect the veto failure rate was the failure of the BB counter, one of the 24 counters in the cylindrical Barrel veto, - 81 - 14 All momenta combined 12 ~ 0 .. ....c 10 C1> 0::: 8 Q) . .... :::> 6 I c ± ± ++±+ ----t+f+++f + I I l.J... 4 T + 2 -+ ,+ A- ~ -Y , -=+"=--.:::. Q.,___________________________________________________ _ 0 10 20 30 2 2 Mx , GeV 40 Figure 4-3. Measured veto house inefficiency. Data at 20, 50, and :c 1 GeV /c vrere combined for this figure. The curve, from a one pass srr:co~~­ ing, was not used for corrections. Chapter 1. The rates were consistent before and after the failure. As discussed in Appendix D, this follows from the fact tb...at an increase in failure rate would only be for the special class of vetos detected by a single photon interaction in the 3e2'rel. This is a small class, and the BB failure would only change that partial inefficiency by 4% of itself. Most of the mrX events were not mm events, but our trigger design did allow some mm. events in the rmX data. These were mainly neutron vetos, ,8-chamber delta ray vetos, and some events also passing the rrrmr trigger. The total of such good mm data in the mrX trigger is small, both as a fraction, and as an absolute number since the mrX trigger was heavily prescaled. These were removed from the - 82 - 6000 5000 .,,. .,,. x , a 11 we i g ht s b u t Failure Rate (a ) :\I > (1) (.!) - ' 4000 (/) c ~ 3000 w "'C E 2000 O' (1) 3: 1000 Otb.....t!:..!~---'--------'-------_._------__..------___. -10 0 10 2 20 Mx, GeV 1000 (b) 2 30 40 rrrr x weighted for subtraction C\J > (1) 800 ~ (/) c > (1) 600 w - "'C (1) ..c. 400 O' . (i) ~ 200 01-..~:..!---..l..--------'--------'-------.,........t.----~---10 0 10 20 40 30 2 Mx , GeV 2 Figure 4-4. mrX Distributions. 2-4a shows the 1mX Mx 2 spectrum with all Weights except the veto failure rate. This is included in 2-4b. The data of 2-4b are included, to scale, in figure 2-L - 83 - 5000 1nrn C\J > 4000 7T7TnT with 1T1T x background subtraction <l.) <..9 .......... -- (/) c 3000 <l.) > w -0 -- <l.) 2000 ..c O'> <l.) s 1000 0 -10 0 10 2 Mx 20 2 30 40 GeV Figure 4-5. Subtracted mm Mx 2 spectrum. mrX data before weighting to avoid subtracting good events, and to avoid double counting (i;vith a minus sign) the neutron veto and .B-chamber delta ray effects. The veto failure background subtraction was mainly needed for our p0 cross section measurement and our tpn distributions. The effect of the background on our decay distribution fits was minimal. We have chosen to not do the subtraction for those fits. The background was greatest at the p and decreased 1vith increasing rrrr mass. The above formalism can be applied to both our 100 and 175 GeV/c data. In the latter case, the "veto house" definition is extended to include the forward photon vetoes (electron calorimeters, lead wall, and El 11 photon calorimeter, section 2.3.3). After the additional off line veto cuts are made at 175 GeV le, section 3.3, - 84- . the veto failure background, as a fraction of the neutron peak, is comparable to that seen at 100 GeV le. In this case, however, corrections for good event losses due to the photon cuts must also be made. The loss was found by using rrrrB trigger data from Run II. Ux 2 and recoil neutron angle cuts, were used to get a clean sample of rr-p ~ rr+rr-n events. The forward photon detector response to these events set a good data loss of 12.5% [Fr82]. 4.3 Neutron Vetoes Neutrons interacting in the Barrel (labeled V1 in figures 2-2 and 2-5) veto c..bout 10% of our iiim data. The correction for this loss \'.~as fou...--:d in a study of the ;;:.B background trigger. The main feature of this trigger was a requirement that one and only one of the counters in Vl fire. Othervvise the requirements for mr B were the same as for Tirrnr. We checked this equality by turnir,.g off the B=l requirement for a run, and noted that the trigger was identical to rrrmr. The most striking feature of this trigger was a strong recoil neutron signal, identifiable through !Jx 2 and ~-;p cuts, where (4.5) is the difference between predicted and observed Barrel hits. Figure 4-6, shows a 100 GeV/c 6.;p plot for the Ux 2 cut -5<llx 2 <2.5 (GeV/c 2 ) 2 . This peak is cer-.:.tered on t::.cp = -1.2°, indicating a small error in the surveyed Barrel counter azimuth. (The surveyed orientation was 11.5° between the x-axis and the B-1 counter center, figure 2-5.) The neutron detection efficiency, Env, was found from ratios of rrrrB and mmr data. The two triggers are complementary, one having a veto on detected neutrons and the other not. N• backgrounds under the neutron differed slightly, but other . corrections are the same, and in principle they cancel. The background - 85 - 90 100 GeV/c 80 70 60 (j) ..,...._ ~ 50 > w 40 30 20 10 0 60 120 180 6¢ ,degrees Figure 4-6. Recoil neutron signal. Both the flat background level and peak vvidth depend on Data. are url':'teighted, and no tpn cut vras used : or this plot. v-r;;;;,. subtraction for rrrr B was internal, using the ~cp distribution, while the rrii'Ttr background subtraction used mrX data. Figure 4-7, shows the Env distributions. Owing to limited running time with rrrrB, the errors are rather large. The neutron efficiency measurement is discussed in section D.3. Our fits demanded a flat ...J=.t dependence above threshold, so we averaged the above threshold rate to get (statistical error only) - 86 - 18 t 0~ ~ 12 0 0:: > 0 Q) t 6 0 o.o 0.2 0.4 0.6 0.8 J-f, GeV/c 1.0 1.2 1.4 Figure 4-7. Neutron Veto rate, Env. 0. Env = I V=f < .08 GeV/ c .0981±.005 V=f ~ .08 GeV/c (4.6) For the early runs, before BB failed, Env is scaled up by a factor of 24/23. The neutron veto weight for rrrrnT is just wnv = 'Wnv = 1 _ ~nv and has the values 1.00 .../-=£ <.08 1.109 ± . 006 ± . 022 .../-=£ > .08, late runs 1.114 ± .007 ± .023 -..r-::E > .08, early runs (4.7) where the first error is statistical, and the second systematic. Early and late refer to before and after BB railed. - 87 - The systematic error in Wnv represents a 20% error for Env. Neutrons can rescatter and register in a second Barrel counter, or nuclear reaction fragments might register in a second counter. Such "double" neutron vetos were excluded by the mrB trigger. Unfortunately, the signal for them is similar to that for some D. 0 decays, and we have been unable to distinguish at any reasonable level between these sources for the two Barrel hit signal. The 20% error estimate is about midway between a D.0 dominated two barrel hit signal and a naive estimate of (Env) 2 . 4.4 BCD Delta Rays The only trigger correction for the B, C, and D chambers that may be treated in isolation is the delta ray correction. Chamber efficiency losses must be done in the trackfinding correction, section 4.8, as the same hits are used for both triggering and track finding. Close track losses are best treated as an acceptance effect after close track cuts. section 3.3, are made. The BCD trigger cuts, section 3. 3, remove any events "saved" by delta rays. The high BCD chamber efficiencies insure that relatively few recorded events are lost by these cuts. For this correction, we deal only with delta rays separated from tracks by one or more "quiet" wires. Delta rays unresolved from the track that created them were treated by adjusting the close track cuts. AB far as the trigger was concerned, "delta ray" includes not only real delta rays (penetrating electrons recoiling from a fast particle - atomic electron collision), but also random chamber noise coincident with events, and recoil protons from low Pt elastic scatters that occurred in the BCD region and were detected by a chamber. It is not useful to bother distinguishing these other mechanisms from true delta rays . - 88- Table 4.1 BCD Delta Ray Weights 6ok w =1.1244 ± .011 7 ± .0124 5ok chamber weight Bx 1.386 ± .012 ± .039 By 1.420 ± .013 ± .042 Cx 1.432 ± .013 ± .043 Cy 1.428 ± .013 ± .043 Dx 1.400 ± .012 ± .040 Dy 1.383 ± .012 ± .038 The BCD delta ray correction relies heavily on the stiff mrn topological trigger requirements to conveniently deal with correlations between chambers. Only the cases of 0, 1, and "many" chambers seeing delta rays need to be distinguished. We do have to consider two types of trigger condition. Cases where all six chambers (Bx, By, Cx, Cy, Dx, and Dy) have hits on both tracks, "6ok", and cases where one chamber fails to have a hit on one or both tracks, "5ok", need different corrections. Delta rays are more serious in the latter case, as a delta ray seen by just one of the five "good" chambers would cause a veto. In the 6ok case, at least two chambers must see delta rays to cause a veto. The development of the BCD delta ray correction, along with a discussion of the effect of delta rays unresolved from tracks, is given in Appendix D. Table 4.1 gives the correction weights. The errors are statistical then systematic. - 89 - 4.5 A-Station Trigger Correction The A-station trigger correction was developed by D. Petersen and F. Fredericksen of Indiana. The correction accounts for both inefficiencies and "noise" (mainly delta rays ) in the three A-station trigger planes. The point of view is that all events satisfying the hardware trigger, A(2)2/S, are acceptable regardless of where the hits came from. Noise is allowed to save events that would not pass trigger tests on the strength of hits on tracks alone. This is looser than the approach we use at the BCD stations. Having a 2 planes out of S trigger requirement, with one a slant plane, there is no "absolute" trigger suppression if tracks are unresolved in one view. The angular coverage of a wire pair at A is greater than at BCD. If tracks are very close, we do have problems with the trigger, but if the tracks are resolved at Bx, and not Axy, we have a significant, but not disastrous suppression. Data losses from a separation cut for particles unresolved in only one A-station plane would be excessive, owing to the relatively large solid angle covered by an Astation wire pair. We thus choose to not make such a cut, and to weight for inefficiencies in the trigger for single unresolved views at A. It follows that we don't make acceptance corrections for forbidden regions as in the BCD region. This approach does pull the A-station trigger requirements out of the track finding efficiency calculation of section 4.8, but errors resulting from this split are second order and minimized by not requiring that hits on the tracks themselves satisfy the trigger. The correction accounts for a multitude of trigger sins. We label cases of 0, 1, . 2, or S planes with resolved tracks as Ook, lok, 2ok, and Sok. The assignment of cases has nothing in principle to do with the bits on tracks, just whether the tracks are separated in the various views. The Sok case can be both saved or killed off by chamber noise (the latter being more likely.) If all planes have hits on both tracks, - 90- noise in two planes kills the event, but noise in one plane is no problem. If one plane misses a hit on a track. then noise in that plane cannot hurt. Indeed, one noise hit will make the plane satisfy the trigger again. But, unless that plane has exactly one noise hit, then noise in either of the other two planes will cause a trigger failure. In the 2ok case, where the tracks are unresolved in one plane, a single noise hit in the unresolved plane will help, but noise hits in the other two planes will only hurt unless accompanied by missing hits ("on" tracks). The lok ·and Dok cases simply require noise hits in order to trigger. The correction depends on -which plane(s) actually have unresolved tracks. A number of tools were used to obtain this correction [Pe78, PeBDb, and Fr82]. These included curve through and 3rrp data, a Monte Carlo simulation, and data from the revised mmp trigger described in section 3.3.1. The curve through data gave the response, especially noise response, of the A-station chambers to a single track. The 3rrp data allowed a measurement .of two particle cases (with one extra track's worth of noise) when the hits on one of the tracks were "erased". At this stage, iterative (to account for correlations) hand calculations could be used to evaluate the trigger efficiencies, but Fredericksen found that the correlations involved were better dealt with by using the data as input to a Monte Carlo simulation of the A-station response. Finally, the mrnp data gave a direct measure, since the A station was not even in the trigger. Table 4.2 lists the efficiencies found for Run I and the trigger condition A(2) 2/3. Event weights are just one over the efficiency. An error of .D4 is assigned to the efficiencies. Although the analysis determined efficiences for all cases, only the 3ok and 2ok cases are used in mrn analysis, and the average weight on events is <wA> = 1.16 . Few events were found in the lok and Dok classes, and cutting them out is relatively unbiased. (All but two such events were removed by other cuts, namely the B station radial separation and Ax ~y cuts.) - 91 Table 4.2 A-Station Trigger Efficiencies Class Unresolved plane(s) Efficiency 3ok 2ok none x y u x+y * x+u * y+u * x+y+u * .888 .809 .766 .739 .104 .090 .075 .104 lok Ook • not used 4.6 Target Region Delta Rays The last delta ray correction concerns the cylindrical (3 chamber. A delta ray detected by it will veto an event, and about 30% of accepted ·mrn events are vetoed there. This veto rate shows a strong vertex location (z) dependence; it is the main effect producing the uncorrected vertex distribution shape of figure 2-6. The vertex dependence results from a variation of total track length in the hydrogen target with vertex location. The beam and forward n- tracks add up to a single track over the full target length. The track length variations then come from the rr+ track. Delta ray vetos, both from the beam and forward particles is an absorption process . If the delta ray rate were small, the veto rate would be virtually a linear function of z-vertex. Correction weights for this loss were found using data from curve through runs, in which the {3 chamber recorded hits passively, and a simple model. The model assumes that the rate of delta ray production and detection by (3 is constant in z. A constant term is provided for delta rays produced in the vacuum jacket end cap. For each particle we find the probability that it passed through its part of the - 92 target without producing detected delta rays. The curve through measurements found a rate of .533/meter that a single track in hydrogen would create one or more detected delta ray. The chance that a particle passes through the end cap without releasing any detected delta rays was .989. Combining terms for the beam, forward n- in the target, and for the two forward particles in the vacuum jacket, a constant of .8313 results. The chance that an event survives a delta ray veto is then (4.8) Each observed event is then given the weight w6 = 11 Ps. Further details are given in Appendix D. 4. 7 Interaction and Decay Losses Hadroni.c interactions of the secondary particles in the target or spectrometer material result in both trigger losses and event reconstruction "failures". Correction weights for this were found using appropriate path lengths, rr±p cross sections for the target, and the n± absorption length of the spectrometer through the Fstation. Cross sections and absorption lengths used parameterizations from the review article of Giacomelli, [Gi76]. These agree well with data down to "' 2 GeV /c, the low momentum cutoff of the spectrometer. Beam attenuation in the target by hadronic processes has the same form as secondary interactions with only the path length changed. Because beam flux loss depends on the vertex, we combined it with the sec~ndary losses. The average hadronic loss weight, including both beam and secondary losses was <w1 >=1.11. D. Petersen studied losses expected from rr-+µv decays and found that in most cases the µ is deflected from the rr path by an amount sufficient to cause a reconstruction failure. The correction weight for this is - 93- _ e Wet - where c r Lm1T(-1-+ ~ cT Pi P;; (4.9) =780 cm, and Lis the distance over which a reconstruction failure would result. We use L = 9m, the average decay weight being <wet>= 1.016. 4.8 Chamber Efficiency Correction The reconstruction system described in section 3.2 and Appendix C, along with our topological cut (two good vertex particles with total charge zero) has been found highly efficient. Limited statistics event scans found the efficiency to be over 90% and dominated by chamber efficiencies. Failed two body events (in which both particles passed the magnet aperture) observed in these scans occurred at a rate consistent with expectations from decays and interactions. The observed reconstruction success rate in the scans depended on the event configuration, mainly through the location of particles at the F-station. The most prominent effect was a beam region problem resulting from both reduced spark efficiencies and from old beam tracks. The latter was a problem only in scans made without the Sclean track cleanup. At the level of statistics in the scans (a couple hundred events), no problems with our matching or match cleanups were found with Sclean in the system. A high statistics search for match problems was conducted on CST's with the help of the DEDX counter. We found that the feed down of two body events to single body events was at a rate less than .3%, and that the feed up to higher multiplicities was less than 1.43. These estimates are from event totals where we second guessed the topology and tried to construct "good" events (two body, total charge zero, and Mx 2 within our cuts) out of available tracks, either by addition in the case of single particle events, or by deletion in the case of multiplicities greater than two. Normalization of the rates was by the good two body set seen in the same study. The number of "saved" events was quite small. and mass or other dependences could - 94not be determined reliably. We include no correction for them but do use the above numbers as systematic errors. Feed up from true single particle events to two particles was also quite small, less than .3%. This latter number was taken from the two particle DEDX distribution of figure 2-4, and includes all the 1r7mT events with pulse heights less than 70. Such events also include timing errors for the DEDX counter electronics; in which case our DEDX cut has lost some good events at a level less than .3%. This is also included in our systematics. The DEDX study implies that virtually all the events rejected by the two particle cut, a substantial 42% (see Table 3.2), were indeed junk. To correct for reconstruction and trigger losses due to our finite chamber efficiencies, we use a brute force calculation by C. Footman of Cal Tech. This calculation indicates an average loss of about 3.4%, but more significantly, it accounts for configuration dependent losses by using measured chamber efficiencies as a function of position. For Run I. this calculation indicated severe losses for events with particles beyond x ~ +1.lm at the F-station. Because of that, we chose a more restricted fiducial volume than we would have on the basis of chamber sizes alone. This problem was resolved for Run TI, and a larger F-station fiducial cut was used for the 175 GeV /c data. Given measured chamber efficiencies (see Appendix D), the chamber efficiency correction calcul~tes the chance that both particles had at least enough hits along their paths to satisfy the various track finding, view matching, and BCD trigger requirements. The track finding requirements are listed in Appendix C, and the BCD trigger requirements are given in section 2.4. The efficiency correction gives a weight, w = 11 E. The calculation is equivalent to grinding through the binomial expression ( 4.10) - 95 where the sum is over all possible patterns of hits and misses that satisfy the various requirements. The Pi are individual chamber efficiencies and vary with position as well as chamber. Note that we do not calculate the chance of having the actual recorded pattern of hits and misses on an event. What we want is the chance of success, which includes all possible patterns that meet or exceed the requirements. We follow the intent of the above expression, but with two tracks, 44 chambers, and 24 requirements to satisfy for track finding, and the BCD trigger requirement (the A-station trigger correction used Indiana method, section 4.6), a straightaway naive ·calculation would be prohibitive. The actual calculation realizes that the tracks are independent as far as the tracking is concerned. It also takes advantage of our group requirement structure and the separate track finding stages (x-after, y-after, match after, x-before, and y-before) to save several orders of magnitude in computer time. The calculation loops over the particles in an event. For each particle position dependent chamber efficiencies are evaluated for all chambers. The track finding (including trigger effect) success probability for the particle is then found. For reasons discussed below (the BCD trigger), seven "partial probabilities" are found, the first six corresponding to patterns of all hits except for a miss in one particular BCD chamber, and the seventh for no BCD misses at all. The concept of partial probability permeates the calculation, usually referring to the probability for a group of chambers, independent of other groups, to have any pattern of hits and misses yielding a given total hit count. Partial probabilities for individual groups are found separately. The probability for each allowed (by minimum hit requirements) multiplicity within the group is saved, indexed by the multiplicity. For each view, we then find overall partial probabilities for each allowed (by minimum hit requirements for the view) multiplicity by taking the product of the various group partial probabilities when the sum of the group hit counts - 96- in the view is the desired multiplicity. The total probability for a view is the sum of its overall partial probabilities (now indexed by overall hit count). "Finally", the total probability for a track is the product of the individual view probabilities, corrected for a few hit patterns that didn't easily fit into the loops used. The use of partial probabilities was designed to avoid double counting of efficiencies and to speed the calculation. It was crucial for making the calculation with anything resembling reasonable computer times. ''Finally" was in quotes because of the BCD trigger. We allow only one of the six trigger chambers to miss a track. When considering two tracks, misses on both must be confined to a single chamber. Without this restriction, tbe efficiency for an event would simply be the product of two single particle probabilities: E = P 1P 2 . With this restriction, we can include only single track patterns that have either no BCD misses, one miss for both tracks, or both tracks having a miss in the same chamber. Letting i = 1, .. ,6 indicate which chamber (Bx, ... ,Dy) misses a hit (all oth- ers having a hit) and i = 7 indicate no misses, the single track routines calculate probabilities Pf through P~ for each particle k. For a two particle event, the Pf combine as E = P1P~ + P{EPi + PftPl + tPi Pl i=l i=I i=l 2 1 ( 4.11) to give the reconstruction and (BCD) trigger efficiency. 4. 9 Background Rejection by Cl and C2 The rejection of _Kt" K- n and 'jifrn final states by the Cerenkov counters Cl and C2 used likelihood calculations developed by W. Danchi for this experiment. These are described in detail in references [Da78]. In brief, the light seen by Cl and C2 is compared to the light expected under a given mass hypothesis for the final state particles. Geometric and momentum dependent effects such as light sharing - 97 - 100 90 ..... 80 70 ~ 60 l?.. 50 :::> Q) I ~ CL 40 30 20 .. 10 0 -10 0 10 20 30 40 50 60 70 ~L Figure 4-8. Likelihood difference Lfm - LKK versus P n-· 'PP combinations are included with KK in this plot. among cells and the p dependence of light production above threshold (figure 2-10) are included. The hypothesis with the largest likelihood, or probability. to produce the observed light is the one preferred by the Cerenkov counters. Our actual cuts, given below, basically follow this. Advantages of the likelihood method are that it allows natural a:c.d conver..ient evaluation of cases where two particles strike the same cell (light added) or cases Where a particle's light is shared among more than one cell, and it gives some selection power (from pulse heights) in kaon threshold regions . The method is fooled, as is a simple on/off method. by simple inefficiencies in a cell, delta rays near a - 98 - 1.0r----r---r--,---r---r----___,-------- .. 0.9 "' 0.8 ......0_ _.__8..J...o_...L...___,100 0 ·7o~---~20=--_...__~4-'-=o-~-6 P0 9CJ, GeV/c I. 0 .----.---.--.--..,------..-----.,..-------...---- 0.8 0.6 0.40::-------::.L2o=--__J_---:4~0-...L---6..J.O~....J_-8,LO_ _,L____,I00 Pneg, Gev/c Figure 4-9. Cl C2 efficiencies for mr and KK combinations, from [PeBOa] mirror giving light, K->µv decays, and has no sensitivity e..t all if c-::.e >:: ?~i- ~ ,._~e ~ 3 below the Cl rr threshold and the other is near :oo GeV le. In using the likelihood method, Danchi found that the preferred ·way ~8 ~- ;, 1<:e a choice and display the Cl C2 response was to use the difference of the logarithm of the likelihoods of a pair of hypotheses. Figure 4-8 shows this difference, M vs . Pneg for our 100 GeV /c mm data, along with the cuts used. Three problem regions are seen. We lose all discrimination when one particle is at or below the Cl rr threshold. The counters have no preference and !1L = 0 is returned. The other particle is well - 99 - 1.10 CERENKOV TAG WEIGHT 1.05 0.95 0.90 0 20 40 60 Pneg ,GeV/c 80 100 Figure 4-10. Vieight for the Cl C2 rrrr tag. Dashed curve is the value actually applied. The data curve is from ec;_uation ~ . ~3 , the efficie~cies i:i = ~ g­ ure 4-9, and observed 1mnr events . above all thresholds . The 50 GeV le region, where both particles are above the C2 K thresh::>ld is also a pr::>blem. Here we have only the pulse heights for a s2~2::~ 2 ~. and low asymptotic photoelectron levels make life hard. The banded structure of the plot reflects a net of zero to four selections in favor of 1irr over KK. The band at D.L < 0 is KK preferred, the bands at ~L > Cl 2-:"8 one to four (last off scale) net votes for rrrr . The /:J,,L contribution from cells that cannot choose is ~ 0, and the band widths are from photon counting statistics. The contribution to l:!.L for a given particle - counter combination is zero if the particle missed the counter completely. If one particle - counter combination favors KK and the other three favor rrrr, then the net number of votes is 2 for rrrr and 6L~55 (see figure 4-8 ) .would result. A mistake, e.g., KK misidentified as rrrr , will often look like solid rrrr selections. The scale of the plot or distance between bands, is set - 100 - 020 tt t t z 0 I- 0.15 u <t 0:: ~ ~ ~ 0.10 z 0 z 0.05 / / 0 / / / / ++ /++++ t / 10 20 Pmin 30 ,Gev/c 40 50 Figure 4--:1. ~on mr fraction. Data points use the Cl C2 tag. Dashed line follows equation 4.14. arbitrarily by an assumed probability of e - 20 for below threshold kaons to make light. (This is an unreasonably small nUc'Tiber if one considers delta rays and K decays, but the line Vvidths are also affected by the scale and no bias results.) Because the 100 GeV /c beam momentum was not well matched to the thresholds in Cl and C2, the Indiana group undertook a study [Pe80a] to develop a statistical background subtraction. The study was never finished, but efficiency measurements were obtained. Usi:ng these, we have found event by event tagging acceptable for most rr- momenta. In regions where rm losses are < 5%, likelihood based tags are reasonable. A weight based on Prrun (slowest particle momentum) is used elsewhere. - 101 he likelihood cuts used are (L = log of likelihood) None -1 /J.L = L(mr) - L(KK) = -3 -1 None p Mg < 12 Ge vI c 12 < P neg < 46 Ge VI c 46 < P 1169 < 54 GeV/ c ( 4. 12) 54 < Pneg < 88 GeV/ c 88 Ge VI c < Pwag Active tagging is used from 12 to 88 GeV le. The cut change between ~6 an.d 54 GeV le is to minimize TiTi losses in the C2 K- turn on region. The efficiencies for our Tn these, charged kaons and pions could be selected without Cl or C2. Si:r-~le pa:-ti- cle efficiencies were found, and then combined in a way compatible with the likelihood formalism to produce the efficiency plots of figure 4-9, which are tv.;a particle efficiencies, indexed by Pneg . The hole in the KK efficiency near 50 GeV le reflects the cut shift to a'.roid rrrr losses. The rrrr loss in the cut region is -53 while the KK contamination of the tagged sample is <:'. 83 . For the taggi:ng region, we apply a weight for mr losses and KK feed-in of W = _1_[1_(1-eKK)f KK e1i1T f ( 4.13) tag where f tag is the fraction of events tagged as rrrr, f KK is the fraction tagged as KK, and ei: is the efficiency to properly tag type i. The weight is a function of Pneg only (largely because f KK· e and f tag were parametrized in that variable only). Figure 4-10 shows the weight in 1 GeV le bins . Efficiencies used for the figure have been smoothed, but not the rrrr and KK fractions. We apply a simple crude smoothing (dashed curve) for the weights actually used, and consider them uncertains to ±.01 or roughly half the difference from 1. - 102 In the nontagging region, we follow the Indiana group and use a simple extrapolation of the f KK distribution of figure 4-11, in terms of Pmm . essentially Pr.2g folded about 50 GeV le: w = 1 - (.056-.0043(Pmm-13)). ( 4.14) We have checked that the b..L cut shift near 50 GeVlc, and the transitions from tagging to non-tagging at P min= l2GeV I c L"tltroduce no d.iscontin'J.i.Les into the ('veighted) Prun distributions. We might also add that the p0 decay kinematics insure that very few p 0n events are outside the tagging region, e\-er: :::.t extr-em.e cos9J. Events outside the tagging region are found mainly at higher iiii masses. The average 100 GeVlc C1C2 weight is 1.00, meaning that iiIT losses are almost exactly matched by KK contamination. At 175 GeV le, tagging by Cl and C2 was much less effective . Although limited tagging regions were available, more emphasis on weights for contamination -: m s needed. Details of the 175 GeV le analysis are given in Fredericksen's thesis [Fr82]. 4.10 Beam Corrections Corrections for both our beam pwc cut and Cerenkov co~'"lter taggiog a.re needed. In the former case, we excluded otherwise good events because of ~'Tlbigu­ ous data in one or more of the beam pwc measurements. The cut events r~d a poorly determined beam trajectory. hence a poor t measurement. As described in Appendix C, we could, and did, analyze the bad beam events fully in order to determine that this loss was independent of the fonvard event configuration, a2d tr.:.3.t a suspect t measurement was their only problem. The correction for this loss merely Weights each event for an overall fractional loss of 4.4%. The resulting ~'<"eight is w == 1.046, with a statistical error of .002. - 103 The beam Cerenkov counter analysis was more involved. At 50 and 100 GeV le, our nominal (all counters set) rr tag was rr = (C0 +PRUSS)·DISC·BDJFF ( 4. 15) Events not passing this tag were removed from the data sample. The pion efficiency for this tag was high, (:>99 %), and K-, p contaminations were insignificant. Although the beam flux has been corrected for the pion fraction, we need also correct for the efficiency and contaminations resulting from the beam tagging requirement. The correction weight accounts for both pion losses a.LJ.d the ccntai.'Ilinations, and is given by (either of) equations 4-16, ~,.... ) ( L... .:.Oa (4.:6b) where ei is the efficiency for the tag pattern (equation 1) for particle type i, a.~d fi is the tagged beam fraction for i. The first form shows the roles of inefficiency and contamination in the weight, but w is found on both sides. Form (4-16b) is the one actually used. The weight equation (4-16b) does not depend on the tag pattern used, but the efficiencies, ei do. For the tag (4-15), ( 4.17) Where the 100 GeV le Ei are the efficiencies found in Table 2-2. Most of our data runs had all beam Cerenkov counters up and working. For those runs, the above tag, (4-15) is applicable. However, a painfully significant number of runs (about 20% of our data) were made with one or more beam Cerenkov counters not ready, and we cannot afford to exclude them. These were - 104- typically runs made after several hours of beam or accelerator down time, and we took data with one or two of the counters not quite ready. The differential counters BDIFF and then DISC were usually the last ones "tuned". For such runs, we exclude the unprepared counter(s) from the tag, and adjust the expression for Ei accordingly. In such cases pion losses can be large (when, for example, C0 is not set), or contaminations up to half a percent (DISC not set). The average beam weight was <w> = 1.017. 4.11 Tleight Summary Studies of our vertex resolution, section 2.5, fou.n.d that no correct:on (\vitxn a 1% error) was needed for either of our vertex cuts. Our missing mass cut, equation 3.4, required a small correction. Accounting for events in a Gaussian tail beyond 2.5 standard deviations gave constant weight of 1.034. Corrections for pion the fraction of our beam flux were made in the scaler analysis of section 3.4. The average weight was roughly independent of rrrr mass, figure 4-12 . Over all masses, it was 2.39 at 100 GeV le and 2.56 at 175 GeV le. Table 4.3 lists 100 GeV le weight averages for ltpn I~ .15, and . 64~m~.9 GeVlc 2 , and the 175 GeVlc forward photon veto weight. Observed ranges and systematic error estimates are i~cluded. The latter were obtained from statistical errors in weight measurements, and systematic error estimates in those measurements. The errors are combined in q".Jadrature for our cross section, section 5. 3. - 105 - Table 4.3 100 GeV le Average Weights High Correction Low <w> A-station BCD Delta Ray f3 Delta Ray Neutron Veto Beam Pwc H::J.dronic Interact Cl C2 Reconstruction Vertex cut Mx2 cut Beam Cerenkov 1.16 1.16 1.30 1.10 1.05 1.11 1.002 1.034 1.00 1.013 1.017 Forvrard y Veto (175 GeV/c only) 1.125 1.12 1.12 1.20 1.00 1.05 i.09 .94 1.00 1.35 .995 1.:6 Error .02 .02 .013 .024 .002 .01 .005 .01 .01 .01 .005 1.43 1.41 1.11 1.05 1.14 1.06 l.~8 .0:5 5. 100 GeV /c 4. 3 ... /"- 3 v 2 .• ~+++ttl-1 11+1111 I I I I t I --t 1. . . . . 0. 0. 1. 2. 3. 4. mmr. GeV /c 2 Figure 4-12. Average weight as a function of mr mass at 100 GeV le. Error bars are statistical only. - 106 - CHAPI'ERV Acceptance. Cross Section. Moments 5.1 Acceptance Losses from finite geometric acceptance and the mechanJsms discussed in Chapter N distort the data for rr-p ~rr+rr-n into the distributions we actually observe. The acceptance is the most important correction if we seek to recover "produced" distributions from our data. This section reviews our accep t ar:.ce calculation. A comprehensive acceptance correction is intimately connected «.,-ith decay distribution fits . Section 5.2 gives the formalism used for the fits and ir..dicates the role of the acceptance in them. The outer edges of the tracking chambers and the magnet aperture L.11pose a set of limits within which particles must pass in order to be detected. :\eA.'t, the 2x2 beam veto presents a small "hole" which particles must miss. In addition, our BCD trigger requirements are sufficiently rigid that if particles are unresolved at the B station in either view, the trigger losses are almost total. The most reliable way to deal with this was to impose separation ("!J.x !::.y") cuts on the data at the Bx station and include the effect in our acceptance. Each observed event is viewed as a member of a class having the same kinematic variables in the rrrr rest frame, (5 .1 ) or an equivalent set. In (5.1) mrm is the rr+rr- effective mass, tpn is the squared four momentum transfer from the proton to recoil neutron, cosFJ; is cosine of the Gottfried - Jackson frame [Ja64] polar angle, and C{)J is the azimuthal angle in the same frame, see Appendix A. Averaging over target proton and recoil neutron spins, for a given beam energy, these variables completely specify a rr-p ~ rr+ rr-n - 107 - event in the 1T1T rest frame. To complete the event description one needs a set of laboratory variables, for example, (5 .2) The lab azimuth, cp L, can be taken as either the recoil neutron or the rrrr azimuth with respect to the beam (they differ by rr). PLab is the beam particle mo:r.. ent urn , xyzv are vertex coordinates , and FJ;, cp B are beam angles with respect to the !v:PS z- axis . ~ FJs, cpB, cpd form a set of Euler angles. The geometric acceptance is the fraction of events for which all required particles fall ''ithin the fiducial volume of the spectrometer. Table 3.1 gave these limits. If all variables, kinematic and laboratory, are specified, the acceptance is 0 or 1 only. If an average over some variables is made, the acceptance becomes a continuous function of the others and has limits of 0 and 1. Our acceptance was found in the Gottfried Jackson frame with a 1~onte Carlo event simulation built around an event rotation technique develsped by the Indiana group , ~Ma78a , St82]. The ~onte Carlo was run at 1T1T mass intervals of 50 !.: ev / c 2 from 550 to 2000 }leV /c 2 , and larger mass intervals up to 4000 },~ eY /c 2 . At each mass, grids of ~O cosFJ; bins and 18 'PJ bins covering the intervals - 1 <cos9; C and -rr<cpJ <rr were created at each of 14 tpn values from tpn = tmin to tpn = -1.0 (GeV/c) 2 . The tpn values were ltpn I= -tmin , .01. .025, .05, .075, .l OO, .125, .: 5, .2, .3, .4, .5, .8, and 1.0 (GeV /c) 2 . Events were generated in the x-z plane ('PL =0) using the z-axis as the "beam" . Cos eJ and cp; were randomized within each bin. Next, the vertex coordinates (Xu. Yv. and zv) and the beam angles (FJB, cps) were randomized . The xv, Yv · and beam angle distributions were drawn from observed data, but the zv distribution was taken as flat over the length of the target. Explicit beam and secondary particle absorption corrections are made to the data. The 2x2 was centered on the - 108 projection of a beam particle with average beam angles passing through the average vertex. The lab azimuth, CfJ L, was not randomized. The Indiana event rotation accounted for this. For each generated event, an acceptance equal to the fraction of rotated (in Cf r) events to pass all apertures was found . The net acceptance for a bin in mmr, cos8;, and C{JJ, was the average (including zeros) of all Monte Carlo event acceptances for that bin. Not needing to rotate in Cf L reduced significantly the required statistics, but randomizing in the other laboratory variables was needed to track their effects. The number of events generated depended on the observed event distributions and knov.n acceptance zeros. The bin sizes were small enough that flat decay angle distributions within a bin could be used. Positive and negative magnet acceptances were sufficiently similar and the actual data sample low enough that ·we could allow ourselves to make one grid applicable to both polarities. As a first order average for polarities, the magnet polarity itself was randomized, the relative amount of positive and negative polarity events generated being equal to the recorded C.ata ratio. The Indiana calculation is not a literal event rotation, and particles are not tracked in it. Instead, the calculation exploits the follo-wing observations . Even though particles receive a considerable Pz kick by the magnet, v.•hen viewed in transverse momentum (p,) space, the limits of acceptance for the 2x2 and outer apertures are, to an excellent approximation, rectangles. When an event is rotated, each forw-ard particle follows a circle inp, space . The angle between the Pt vectors, and their magnitudes are completely determined by the variables xx and PraJJ . In the absence of vees, events rotate about the beam as rigid bodies. For a given vertex location, the Pt limits are well defined, indeed linear functions of the particle's momentum at all but the lowest momenta. While separate Pt limits apply to the 2x2 - 109 - and to the outer apertures, the many chamber edge limits are reduced to one set of two limits in Pz and two in Py. More significantly, since no literal event rotation is required, particles do not have to be retracked through the magnet at each new azimuth There is no worry that not enough examples of the azimuth were sampled since literally all azimuths are done at once. The acceptance for a two particle event is calculated by first evaluating accepted arcs of rotation for the two particles with respect to the outer fiducial limits (the "MPS" limits). and setting the net accepted arcs as those for which both particles are allowed. The arcs are stored as a set of angles for end points , and careful accounting maintains the correlation between particles in a "rotated" event. The effect of the 2x2 is found by finding arcs forbidden by it and removing them from the accepted MPS arcs. Although the /J.x b.y effect does not naturally lend its elf to rotations in Pt space, it was possible to incorporate it into the arc formalism with proper correlations with the other effects. The A-station radial separation cut, section 3.3, was azimuthally symmetric . Events failing it had no good arcs at all. The acceptance is the net angular coverage of the final allo•Ned arcs . The Pt limits used in the MPS and 2x2 calculations were drawn from previously evaluated tables of acceptance limits versus momentum. These tables vrnre made by tracking simulated particles through the spectrometer and searching for momentum space acceptance limits . In the simulation, all tracks were generated from a single "vertex" located at the target center, and the 2x2 counter was located by a "beam" track along the z-axis before the magnet and at the nominal beam momentum. The magnet field map [Ha75,Ma78b] was used to track particles through the magnet. In the two particle acceptance calculation, limits for actual momenta were evaluated by linear interpolation between the nearest values given in the tables. The (small) effects of the actual vertex and 2x2 locations. and the real beam angle were accounted for by first order corrections to the limit values. - 110 -.o7S- t.., ... (a) -.200 ... (h) (c) Figure 5- 1. (a) 100 GeV/c acceptanc.e at mrrrr = 1.25 and several tpn values . Nine slices in cp; are shown, the nearest one at -1"80°, and the farthest at +l80° . Each cp; slice shovvn is an average of two neighboring slices in the grid. The horizontal axis is coseJ. (b, c) Arcs for MPS and 2x2 apertures, arbitrary scale . Dashed arcs are forbidden. For the 2x2, the upper drawing is in position space, all other arcs are in Pt space. A rigid body rotation keeps !::irp constant . Correlation calculations are shown for MPS arcs only (hatched arc is .net accepted). - 111 - .• 4. 0 . . - - - - - - - - - - - - - - , , • J 3.5 t (a) I e '" ii! 3.0 (b) t:,y, cm • 611 11112 -·-... ---.---...· m? N CJ -.......;. ..,. ..., 2.5 .n U\• ;:> LSD (ll m.11 c..'.I Cf.) Dri. 2.0 en ctl _, s I= l= ----; 1. 5 r..: -.: ~~ 1.0 - ~ ~ ~ •-RJ •5 • ··~ .,.. •21 •"2Z2• 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1. "Acceptance" Figure 5-2. (a) "Acceptance" for the BCD !::.x ~y cut at 100 GeV l e. The points are observed events, and the spread at each mass reflects decay distributions. Effects of the 2x2 and "MPS" apertures are not included in this figure. The BCD loss sets the upper limit on our accepta.r1ce at each mass. (b) Arcs for BCD effect, mmr Ri .65 GeV /c 2 and PLab = 100 GeV le. The Monte Carlo was checked by comparison with results from a more traditional Monte Carlo in which tracks were traced through the MPS. All lab variables, including rpL, were randomized, and all fiducial cuts were applied . No difference in the results were seen. Examples of the acceptance at 100 GeV/c are given in figures 5-1 and 5-2. In figure 5-1, examples of the grid at the / 0 are shown. The forward (coseJ~l) hole is the most serious, since the rrrr decay distribution is peaked there at low tpn and almost all masses. The 175 GeV le acceptance is similar, although the fall offs are - 112 smoother. Figure 5-2 shows the effect of the 6-x D.y cut on our acceptance. 5.1.1 Acceptance Weights In addition to use in our Monte Carlo, the Pt space rotation can be used to provide an event by event acceptance weight. Although such weights cannot correct for forbidden conligurations, the correction is reasonable in regions with no absolute acceptance zeros. Used in this way, we find many observed high (~ 2 GeV /c 2 ) 1irr mass events have acceptance of order 10 to 20/o. Tr.tis implies acceptance weights up to 10, by far our largest. To avoid divergences, a 10% acceptance c~t is applied when acceptance weights are applied. 5. 2 General Correction Formalism The formalism discussed in this section follows the one used by Grayer et al . • [Gr?~]. with modifications appropriate to our experiment. The acceptance modifies the differential distribution of produced events to create an "accepted" distribution, !1,, given by (5.3) where xK are kinematic variables as in equation 5.1 . lp is normalized so that (5.4) where Ne is the fully corrected event count in equation 3.8. The acceptance A (xK) is an average over the laboratory variables, xL. IA can also be given in terms of the observed event distribution, lobs . Correct- ing for the losses and contaminations discussed in Chapter N. with a weight, w, we have - 113 (5.5) The forms (5.3) and (5.5) allow us to obtain Ip. If the acceptance is nonzero, they can be solved for Ip. This is the method of acceptance weights, section 5.1.1. To extrapolate lp through acceptance zeros, one needs a good model for the reaction, or at least an expansion in a reasonably complete set of functions . That is, we express Ip as a function, F(xK,ci ), where the ~ci ~ are parameters to be determined. A well chosen F will provide useful information on the structure of the reaction, as well as provide a reasonable extrapolation. To apply these ideas, we bin the accepted distributions of equations (5.3) and (5.5) to give and (5.7) for a bin, k, in xK . N 0 is the number of observed events in the bL.11 (see equation 4.2). To estimate the ci, we used x2 minimization. The fits minimized the sum (5 .8) with u1e given by [Gr74] (5 .9) The average (over observed events) weight, <w1e>. and the average square, <w1e2 >, in - 114 - (5.8) do not vary significantly with cose; or cp;. and mr mass variations are slight above 600 MeV/c 2 . We have actually used ai = <w>aff If;; I. where <w>eff is an average over all masses of <w 2 > I <w > ~ 1. 01 <w >. Our fits are fairly insensitive to the value of <w >ef 1 . The claimed errors were affected more than the p~ameters. Using lf 1e I helped to stabilize the fits when a number of bins were empty, and also helped to satisfy the physical constraint lp ~ 0. A few violations were found in moment fits, but these corresponded to empty bins and were generally slight. In practice, we fit on only a subset of the xK. The fits were then repeated in successive bins of the remaining variables . Our decay distribution fits have only the decay angles explicit in F . In this case, the bins , k, are .601e = .6costJ; .6:;1 . Equation (5.6) then becomes, f1e = J A(cose1 .st 1 ) F(cose1 ,cp 1 ,ci)d01e (5. ~O) k Prompted by our small data sample, we took advantage of the expected symmetry about (/); = 0 (section 5.3) , folded the data, and fit only 0 ~ 'f J ~ 11 . The acceptances at rJ and -:p; were averaged, and the right hand side of (5. l. O) was multiplied by 2. The bin size in our moment fits (section 5.3) matched the acceptance grid, .6cos9;.6rf; = (.05 ~; ), so A(xK) was pulled out of the integral. Thus for our actual fits, (5 .10) was replaced by f1e = 2~jF(cose,,cp;,ci)d0.1e . ( 5. 11) k ~ was set by averaging the acceptance grids according to our mass and tpn distri- butions. The small data sample also caused us to use relatively large bins in variables not explicit in a given fit. Having f;; in <J;;, equation (5 .9), makes the x2 problem nonlinear, although linearization can be recovered near a minimum. To deal with this efficiently, most - 115 - of our x 2 fits used an iterative linear fit written by F. Fredericksen [Fr82]. On the first iteration aJc = max( <w >ef1 , Jinw) was used to initialize the fit. On all later iterations, equation 5.9 was used. Convergence was rapid; only three iterations were needed in most fits. Llnearization of the x2 problem carried the benefit that the full error matrix, and hence parameter errors , followed immediately from the matrices invoh"ed. Errors for the ci were given by the error matrix diagonal elements and were defined such that changing any ci to ci ±ac, shifts x2 by 1. A drawback of the fit was that physical constraints, such as lp ~ 0, were not naturally incorporated. For the lJlOment fits, (next section) we did not include this constraint. For the "high mass" fits of section 6.3, we included it only in a clumsy manner. The iterative fit was tested on Monte Carlo data created by running events of knovrn mass and moments (taken from [Gr74] and [Al78]) through our spectrometer simulation. The results from these tests were consistent v-rith the input moments down to statistical levels comparable to our data. The iterative fitter had stability troubles if the net weight in a number of bins was negative. Such cases resulted from statistical fluctuations when event by event mrX subtraction (v-,rith negative weights defined as in section 4.2) was used. For the p0 cross section, there was enough mrX data to fit it separately and then subtract the 1mX produced event total from the mrnr results . However, for the mass depen- · dence of the moments, this was impractical. We can either appeal to the general similarity of the rrrrX decay distributions to those of rrrrnr and leave the backgrou..'1.d in, or we can use negative weights for rrrrX and set bin contents to zero when negative counts are seen. We have chosen to leave the background in. - 116 5. 2.1 Moments Any reasonable function of polar angles, e and cp, can be expanded in a series of spherical harmonic functions, JT(cos 9,cp). [Ma70]. For particle decays, the expansion coefficients contain information on the spin of the initial state [Gr74], arid can be used as input to an amplitude analysis. The Gottfried-Jackson ands-channel helicity systems both have the y-axis normal to the production plane. Parity conservation implies that for such systems, lp(9,rp) = lp(9,-cp), [Ja6Qa]. This implies that only the real parts of the JT 's and only m ~ 0 are needed, so the harmonic expansion we use is lp(mrrri'tpn. Jl) =I; t tf Re JT(O) (5. :2) L m=O where 0 =(cos9,ip) and mrnax =l . The tf' are real fun.ctions of ?r,,."" and tpn, b~t are assumed constant in each mass and tpn bin fit. The normalization condition (5 .4-) is (5. 13) Normalized spherical harmonic moments, given by 1 <ReYf> =Np tftf' f Ip(O)ReYf(O)dO = ~ ( ;)- . ..:. 4) - are frequently used. The use of only Re YI' requires the term tl'f, where t2 ~r~ 0 = !h. = 1 a...'1d The normalized moments tend to remove the mass dependences of resonant amplitudes and display more clearly the relative importa.11ce of the various moments than unnormalized moments do. If only a finite number of moments are present, or at least significant, the series in equation 5. 7 may be truncated at some l = lmzx and m = mmax ~ l. At Ti1T masses below about 2 GeV /c 2 , TTTi angular distributions are well described by such a series. At higher masses, the usefulness of moment expansions becomes limited, - 117 - mainly because of the uncertainties in fitting large numbers of moments (see section 5.5) ,,.,ith limited data sets. Spin information in the moments is contained in the indices L and m . The highest L moment generated by a state of angular momentum l is L = 2l, which should project out more pure l intensity than moments with L < 2l. Odd L moments contain information on interference between neighboring even L moments. The index m combines information on the nucleon helicity flip an.d the spin of the exchan.ge involved. If just rr exchange vvithout absorptive effects were present, only m = 0 would be needed. In this case, the Cf'J distributions would be flat [Tr62]. Spin 1 exchange yields moments with m = 0, 1. and 2. In the Vmlia...rns model (P1·:A.), see [Wa73], moments Vvith m = 1 measure interference bet\".:-een pure rr exchange and absorptive corrections to it, and furthermore, m = 2 moments are forbidden [ Oc73], Pure ii exchange is mainly nucleon helicity nan-flip in the Gottfried-Jackson frame, while spin 1 exchanges are dominately helicity flip . The mome:it distribution thus reflects not only the spin of the decaying system, but the spins of the exchanges that formed the rrrr final state. 5.3 Cross Section Results Before considering the general decay distribution results, we complete our normalization. The pc region of the mass spectrum is known to be d8minated by the spin 1 p 0 resonance, but a small s-wave background is also present, as well as interference effects Vvith D-waves. In addition, effects of p-~ interference have been observed in high statistics experiments at high tpn. This relatively low mass region is thus rather complex. Even separating the resonant intensity from the swave background is a nontrivial. model dependent affair. For these reasons, we chose to follow Grayer et al. and quote only the cross section for the same mass and tpn cuts used at 17.2 GeV le, [Gr74]. - 118 The mass interval is .60 ~ m1T1T ~ .94 GeV lc 2 and the tpn interval is ! tpn I ~ .15 (GeV lc) 2 . Data from the rrrmT and rmX triggers were fit separately with moments having Lrnax. = 2 and mma:x = 1. The mrX veto failure weights, section 4.2, were set positive for these fits . The background correction was made by subt:acting the 1mX produced event count from the rrrmr produced event count. No scaler analysis was done on the rrrrX data . The veto failure weight was designed to scale the TiTiX data for a direct subtraction from rrrmr. Five mass bins, .60-.70, .70- .77, .77-.84, and .84-.94 GeV lc 2 , were used, for the fits, and their results added. A single tpn bin was used. These bins were selected to maintain reasonable statistics for both the rrrmr and rrrrX fits. The tight target cut, - .51 ~ Zv ~ -.30m, Vvith a cross section per event of a 1 = .216nb at 100 GeV le was applied. Data from both magnet polarities were combined for these fits. Our p0 region cross section result is aP 0 = ( .934 ± .040 ± .053) µb , (5 . ~5) where the first error is statistical, and the second systematic. Table 5 .: sum"'"rnarizes the fit results . We emphasize that what we call the "p 0 " cross section is actually and Itpn l ~ .15 (GeV lc) 2 . We note that the TiTiX background at the p 0 is about 13% of the rrrmr signal . This is a worst case. The background as a fraction of rrrmr falls ·with mass to negligible amounts above 2 GeV lc 2 . (Figure 1-2 indirectly implies this.) Our cross section at 175 GeV le for the same mass and tpn cuts was evaluated by Fredericksen, [Fr82]. His result is ap 0 = (.229 ± .012 ± .o:o) µb. Our :oo and 175 GeV le cross sections along with the low energy result of Gr?~ are given in figure 5-3. PMA includes a basic 1/ Pt2at, dependence for the cross section, and this is often Used as a benchmark for the p 0 n cross section. The line in figure 5-3 passes - 119 - Table 5.1 100 GeV le p0 cross section Trigger Events Ne rrrrnr 1414 4972.3 ± 140.5 rrrrX 416 647 .5 ± 58.2 1T1m 4324.8 ± 152.1 a1 .216 ± .008 nb a= Ne a 1 .934 ± .066 µb through the 17.2 GeV le point and falls as 11 Pt~. Low energy p 0 cross section measurements have shown a persistent lack of consistency in method for background subtraction and mass and tpr. interval selection. Also, t min effects are significant at beam momenta belmv- about :o GeV/c . Compilations of low energy p 0n cross sections find dependences in the 1/ PJ.l 9 =·c9 [Br72] to 1/ PlaiJC?±.o4 [ Gi72] range. Since we use the same mass and tpn cuts, we feel that the Gr74 point is the only published low energy cross section directly comparable to our values. The 100 Ge VI c point is within errors of the line in figure 5-3, but the 175 Ge VI c point is significantly lower. Taking our two points together, we find that the cross section falls off more quickly, not slower, than 1 I Pl~ . In terms of PMA, the extra drop off of the p 0 n cross section requires a steepening of the d r;/ dtpn distribution. This can be obtained by having larger exponential slopes for the collimating factors of PWiA at the higher energies. The high precision results of Wicklund et al. [Wi78] require just such an effect. We note that our tpn distribution fits, though not - 120 - 100. Gr74 10. 1. This Experiment .1 10. 100. 1000. P/Ab, GeV le Figure 5-3. Cross section results for the p mass band and i tpn I < .1 5 (GeV /c)2. Also shovm. is the Cern Munich 17.2 GeV le result, [ Gr74-]. The line follows :V Pk and passes through the low energy point. - 121 reliable, do show such an increase in the exponential slopes, and are roughly at values expected by e:xi.rapolating the trends of Wi78. In more basic terms, if 1i exchange is still dominant at our energies. and the effective rr trajectory. a(t), is negative, then the s 20 - 2 dependence of the cross section exceeds 1 I PJw (s ~ 2mrrPtab ). An effective tpn averaged a of about -.06 is sufficient to bring both our values within errors of a straight line through the 17.2 GeV le point. In the sections that follow, we relax the target vertex cut from the one used above to - .65 ~ zv ~ -.23 m. Although outside the flask, virtually all the da t a passing this cut came from interactions in the hydrogen, and as for the tight cut, feed - in, feed - out losses are negligible . We scale the cross section per ever.i.t for the expanded cut, yielding .1 46 nb at 100 GeV le and .047 nb at 175 GeV le . An error of 10% should be assumed for these numbers, mainly because the 1irrX backgrou.,_1d ·has been left in. 5.4 The rrrr Mass Spectrum As discussed in Chapter I. the uncorrected rrrr mass spectrum shows promi.n.ent p 0 and f 0 peaks, as well as a weak g 0 and a high mass continuum. Figures 5-~ab show rrrr mass spectra from our moment fits (next section) at 100 and 175 GeV l c . A Itpn I ~ .15( Ge VI c ) 2 cut was used, and mm.ex= 1 was imposed. The lower curve in each figure is the uncorrected final event sample in 50 MeV le bins. In these figures, the p 0 andf 0 are clear. The g 0 is a weak presence, especially at 175 GeV le, but it seems real. At the mass spectrum level. the h 0 is a lost cause in both uncorrected and corrected distributions . We note that Corden et al. [Co78] needed an amplitude analysis to pull out comincing g 0 and h 0 signals. Only a mere hint of the g 0 was visible in their corrected mass spectrum, and the h 0 was invisible at that level. Having not done an amplitude analysis, we will not be able to make any claims for the h 0 , but will refer to the 2 GeVlc 2 region as the h 0 region, and - 122 - t 2000. ~ .,J c:QJ ~ t+ t 0 ....... en Itpn I < .15 t 1500. ::e '° 100 GeV le tt t 1000. \t+t t t 500. o. ttt +t+++ 1. 2. 3. m.W?r. GeV /c 2 Figure 5-4a 100 GeV l e TiTi mass spectrum for Itpn I < . 15 (GeV l c) 2 . Points "ith error bars are produced event totals from moment fits vvith L'm.e.X = 8 and mmax= 1. The hjstogram is the uncorrected event total in 50 ~~ e V / c bins from figure 1-2. note features of the data there. Above the g 0 , we observe a slowly increasing distribution at 175 GeV/ c, and a flat distribution at 100 GeV l e. With fe·w exceptions, the individual bins are not statistically incompatible . The better high mass statistics and acceptance at ~ 75 GeV le imply that figure 5-4b is a better estimate of the mass spectrum above mrrrr ~ 1. 9 than figure 5-4a. However, as noted in the next section, we expect that moment fits generally underestimate the high mass distributions. The high mass decay distribution seems more compatible >;vith an exponential (in cos9,;) th.an a sum of harmonic moments. This inspired another set of fits, described in section 6.3, which first fit just the CfJ dependence in slices of cose;. The cp; fits were to the form ! 0 + I 1 cos:p 1 . Since - 123 - ltpn I < .15 tt tt > ~ ~ 0 175 GeV le t 1200. BOO . t t \ t\+++++ tt t t LC ........ en -.) c: ~ t +++ ~ 400 . +t+ 0. 0. 1. 2. 3. m.'"'. GeV /c 2 Figure 5-4b 175 GeVl c iiii mass spectrum for Jtpn I < . 15 (GeY/ c) 2 . Point s "\Vith error bars are produced event totals from moment fits ''ith Lr...e:x 8 and mnax=l . The histogram is the uncorrected event total in 50 1:ev le b ~ns from figure 1-2. = TT J-1Tcos~dc; = 0, only the Io term appears in the cos9J projection, an.d this term was used in a second set of fits . At low rrrr masses, we fit I 0 to a sum of Legendre polynomials, and at masses above 1. 9 we fit only the forward peak to an ei\.- ponential. This method makes more demands on the data than a moment fit, and e..t low masses ~00 MeV le mass bins were used . The mass spectra from these fits are shovm. in figures 5-5ab . We observe that the high mass spectra run a bit above the moment results, although the 100 GeV le results weren't "helped" that much. These fits run slightly below the moment results at the p 0 , but the disagreement is not as bad as it appears in the figures. Rebinning the moment fit results, we find that the "rp fits" are just over one standard deviation low at the p 0 , and are in complete agreement With moments in the f 0 and g 0 regions. We feel that the moment results are more - 124 - 2000. • 1500. • • 1000. 100 GeV le 500. Itpn I < .15 0 O. L___.o£.~---L~--_._-----1.~-==~~~----J o. 1. 2. m.tm, GeV /c 3. 2 Figure 5-5a 100 GeV/c rrrr mass spectrum for Jtpn ! < .15 (GeY/ c) 2 . Poids \\ith error bars are produced event totals from fits described in section 6.3. The fits were in 100 MeV /c 2 bins at low masses, but we plot the results as events /50 li•:ev for comparison to the moment fits (open circles). The vertical scale is the same as in figure 5-4a. Error bars for the moment fit results were excluded here for clarity. reliable whenever a moment sum (equation 5.12) can be used. For our data , this means moment results are preferred below~ 1. 9 GeV/ c 2 . Above about 2.0 to 2.2 GeV /c 2 , the cp fit method is preferred if we accept an exponential forwar d peak. Figures 5-5ab are consistent V\'ith high statistics results of the ACCJ\':OR collaboration at 63 GeV le [Da79], which were obtained by similar methods. The exponential cos9; dependence claim is much more compelling for their data than ours . Their data also give an indication of what we might expect to see at the g 0 . With our data set, statistical errors would almost wash their g 0 out of the mass spectrum. - 125 - 175 GeV le • 1200. lt,.n I < .15 + •• t + .\ t·~· . BOO. 0 • t • 400 . +.+.++++ . ~ 0 0. 1. 2. 3. Figure 5-5b 175 GeV le iiii mass spectrun1 for I tpn I < .15 (GeY/c) 2 . Points with error bars are produced event totals from moment fits described in section 6.3. The open circles are the produced event totals of figure 5-4-b. Error bars were excluded here for clarity. Our mass distributions at high masses run a bit above those of Co78 at 15 GeV le, but their data stops at 2.2 GeV lc 2 . Our mass spectra seem at odds Vvith the results of Robertson et al . at 25 GeVlc, a low statistics bubble chamber e:x"Periment. Figures 5-6ab are mass plots for a .15 < l tpn I < 1.0 (GeV /c) 2 cut. In this case, only moment fits were used for the acceptance correction. 100 MeV /c 2 mass bins were used, Lmax values stopped at 6, and moax was 2. These selections were motivated by the low event counts at high tpn. The p 0 and f 0 are prominent again. A reasonable g 0 is seen (this time its better at 175 GeV /c). We note that the high mass region does not increase with mass. This may be due to the Lmax used in the high tpn fits. The high tpn acceptance is relatively better, when compared to decay - 126 distributions, than at low tpn, but the raw event totals were much lower. The plots given so far are too coarse to show a number of fine scale features reported by Grayer et al at 17.2 GeV le. These features are shoulders on the high side of the p 0 and f 0 peaks at ~980 and 1460 MeV /c 2 , respectively, and effects from p-c.> interference at large tpn. We searched for these in fine binned, weighted mass plots, but our small data set washed out any effects with fluctuations. In particular, we can neither confirm nor deny the presence of p-c.; interference in our data. Effects related to the shoulders are seen in the moment results, c.....11d we turn to them now. - 127 2000. - + .. 100 GeV le Itim I > .15 1500. - + ~ ~ 0 0._.. ., ....... ~ 1000 . ... Cl ... ! 500 .... + ... o. I 0. + ++ + ++ + ++ +++ ++ + I t I 1. m.'"', GeV /c 1200 . ... + + >QI 2 800 . ... I 2. 3. 2 175 GeV le It,an I > .10 0 0 - + ++ ....... en d ! + + ++ 400 . ... + + o. I o. I 1. + ++++++ I I 2. I 3. m. ... GeV/c 2 Figure 5-6. High tpn mass spectra at 100 and 175 GeV le . . 15 < Itpn I < 1.0 (GeV /c) 2 . - 128 5. 5 Moments versus Mass Data up to rrrr masses of 2.4 GeV /c 2 were fit in the Gottfreid - Jackson frame to the form (5.12). Figures 5-7 to 5-10 show <Re}'17'> and tf' = f;f'Np<Re}'11'> at 100 and 175 GeV le as a function of mass for Itpn I < .15 (GeV /c) 2 . Because of our small data sample, a single tpn bin was used for these fits, and the smallest mass bin was 50 MeV /c 2 . Lmu values given in Table 5.2 were used, as well as mmax = 1. Higher moments than those used were found consistent vvith zero in preliminary fits and excluding the high moments improved the fits. ("Threshold" means the first bin fit, usually 550 hl:eV/c 2.) Figure 5-11a shows 100 GeV/c <Yf> results from preliminary fits -with l tpn I <.15 (GeV /c) 2 . figure 5-11b sho1,ys L 10 results from another preliminary fit on the sa."11.e tpn =9 aild interval. In both cases, the moments are, Vvitb.in our statistics, consistent Vvith zero, and were excluded in later fits. In the high L case, we interpret this not as meaning the absence of the moments from the produced distributions, but rather that our small data set is unable to eA.-tract such moments. We're better off constraining them to zero to reduce the number of parameters in the fits. L~ 0 1 2 3 4 Table 5.2 Moment Constraints Mass Lma:g, Threshold Threshold Threshold 700 MeV 900 MeV 5 6 7 8 ~9 Mass 1300 1:eV 1300 1'~eV 1700 MeV 1700 JleV unused In some regions, especially the 175 GeV le p 0 , the moments are not well determined. Errors and fluctuations are large. Our results are "fragile" in the sense that including extra moments or going to much smaller mass bins can cause the fits to go ,berserk. Patently unacceptable results can be obtained if some caution is not - 129 used. This was our primary motive for allowing only moments that were either well established in lower energy experiments or were required by our data. Our low statistics, compared to the complex and often rapid dependence of the mm reaction on all kinematic variables, is the primary reason for our troubles. Our confidence in the results rests on reasonable x2 per degree of freedom values, and also on . the agreement between fit results and weighted data in good acceptance regions . With these caveats, we consider some of the features seen in figures 5-7 to 5-10, and compare our results to lower energy results. Our mass dependence results for 100 and 175 GeV le seem consistent ¥rith each other. and generally similar to low energy results at 17.2 GeYlc [Gr74], an.d 15 GeY le [Co78]. Above the g 0 mass, we are more consistent -with the 15 GeY le results than those at 17.2 GeV le. The data in figures 5-7 and 5-8 (N <1T>) show few surprises. The p and f signals are present in moments expected for their known spins. In the preliminary fits, no peaks were seen for these states in moments higher than L = 2l, where l is the spin of the resonance ( 1 for the p and 2 for the f ). The shoulders and rapid falls on the high sides of the p0 and f 0 reported by Gr74 (at ~ 1 and 1.4 GeV lc 2 ) seem present in our data. Perversely, the p 0 shoulder is best seen in the 100 GeV/c L=O, m=O plot, and the / 0 shoulder is seen only in the : 75 GeV le L=2, m=O data . The g 0 seems to be present, but puzzli:ng. As '\\ith the p 0 and f 0 , the g 0 mass region has bumps, admittedly small, in low order moments . However, in the crucial L = 6 moments, the g 0 is again perverse. At lOO GeV le, we see fluctuations consistent with the g 0 . At 175 GeV le, the L = 6, m =0 moment does not have the desired bump. The absence might be bla.rned on statistical fluctuations. but is nontheless disappointing. - 130 - N<YP> 400 . 200. 0. ,.wL--~--~.._~----~ - 0. 100 GeV le 2N <Y{ > -100 . -200. t ~ N<Y~> ft tt+++ + .... +t t 200 . t + + t+#~ t 400 . 200 . +.t ++++ 0. '---~~·--~~~---~~ G. - 100 . 2N < Yj > -100 . -200 . -300 . ~ -200. ...____.__ __.___ __.___...__. 0. 1. 2. m.tm. GeV /c 2 -400 I 0. I 1. 2. 2.5 m.'"', GeV /c 2 Figure 5-7a Unnormalized moments at 100 Gev/c . N < Y8> was plotted in figures 5-4ab . A Itpn ! < .15 GeV le cut was used for these fits . 2.5 - 131 400. r----c~---,-~--,.-~----- 200. 0. 100 GeV le 0. 100. 2N <Yi> -100. t +++ 0 t tl++ 200 0 2N <Y-) > +t 0. -100. 100. 0 0. -100 0 ++-+- 2N < Ys > -100. -200 . "'------'-_..._ o. _..__-..i...._ 1. _J 2. m.'"'. GeV /c 2 Figure 5-7b. See previous caption 0. 1. m.'"', GeV Ice 2. 2.5 25 ,-~-----=-~132 175 GeY le 400. 200. N<Yf> 200 . 0. 0. ++++ N<Yf> "T//+f _ _Jlf/!!..;.!..../_f+f., 0. r----·----~ 2N <YJ > 0. 200. 2N <Y{ > -100. 0. 200 . 0. 0. 0. -100. 100. 0. 200. 0. 2N <Yg > -100. 0. 2N <Yd> -100 . 0. 1. 2. 2 .5 2N <Y-) > m.'"', GeV 1c2 2N <Y~ > Figure 5-8. 175 GeV I c unnormalized moments · See t ext . 1. m.'"', GeV /c2 2. 2 5 - 133 - The 175 GeV I c data may contain hints of the h 0 . Fluctuations of the type one would e:xpect are present in a number of moments, even the L = 8 moments. However, our binning is quite large at the h 0 mass. and a one bin fluctuation does not make a resonance. The fact that it is seen in a number of moments can also be explained as propagating fluctuations in the fit. This caution might also be applied in the 100 GeV/c 9° signal. No obvious h 0 signal seems present in the 100 GeVlc moments. We note that the m = 0 and 1 moments are largely of opposite sign, a condition consistent VYith PKA. and the more sophisticated Regge modeis for ii1Tn. Also, \\ith the exception of the 100 GeV le L = 8 moments, all the moments we have plotted in 'figures 5-7 and 8 are solidly non zero at all masses above 1. 6 to 2 GeV I c 2 . The noted exception may very well have been a case like the L = 9 and 10 moments . That is, our data is not good enough to sense its presence. Figures 5-9 and 5-10 give our normalized moments for the two beam momenta. Since produced event counts are removed from the averages, these moments are directly comparable v.ith those at 15 and 17 GeV le. We note that the rapid drops already discussed become more prominent in the normalized moments. For the most part, we appear quite consistent Viith the lower energy results . Some of the caveats of the proceeding paragraphs still apply, but the broad agreement, span- ning an order of magnitude in beam momentum from the other experiments to ours, speaks strongly for the stability of the mm reaction. - 134 - - .40 +.+ <YP> 100 GeV/c + .20 t·~+ 0. l- .10 0. 2<Y{> .~ f .201 < y 2> 0. ~ +++-+- +++ <Y£> .20 + t 0 ++*+-+ -.10 .40 -.20 + +.......-+- 2 < Yj > .10 ...++++-+/+++++ 0 +.r+t+ t +-+-•++ l 0 t t +++ -.10 t+ -.20 t tt#f ~t4t +++++ -.10 +·i +t + -.20 0. 1. t 2<Yd 2. 0. 2. 1. m.Jm, GeV /c 2 2.5 mmt: GeV /c2 Figure 5-9a . :oo GeV / c non71alized r:;.o;.nents for ; tpn : < . ~5 (GeY / c) 2. 2.5 1..., - ,------,----,.----r------ 00 .L .40 100 GeV /c .20 .20 0. .10 2<YJ > -.10 .05 -.20 .20 2 <Y~ > -.05 -.20 - .10 .05 <Yfi> 2 <. Y~ > -.10 -.20 -.05 .10 2 <Yd> -.05 -.20 0. J - -.10 0. m.7m. GeVI c2 2 <Y~ > -.10 1. -.20 0. 1. m.tm. GeV /c2 2. 2.5 Figure 5-9b . 2. 2 .5 - 136 - .40 <YP> .20 0 175GeV/c 0. +-++-1-.10 2<Y11 > -<Y£ > .20 .....++~+ ++ ~+ + t ++ +/+++ 0. t 0. -.10 -.20 1'++- - t ¥t¥ Jtt +t+++ f+* t +\ *2<Yd > ,,,.... + - + ++ ++ <Yg> +/t .20 0 .10 2<Yj > 0 -.10 -.20 0. 1. 2. 2 .5 m.'"', GeV I c2 Figure 5-10a . 175 GeV/c normalized moments for Jtpn \ < . 15 (GeY 1 c) 2 r----,----,----r------13 7 .40 175GeV/c .20 0 .20 .10 -.10 2<Yi > - -.20 .20 + ++-+- 0. - .05 0 0 2<Y-} > ++++ -.05 .10 .10 -.10 + .05 2 <Y~ > +++ 0. .20 .05 ,., .10 0. 0. t +++ 2<Y6 > -.05 .~0 t 0. -.10 0. -.10 1. m..n. GeV /c 2 -.20 0. 2. 1. m"'", GeV /c 2 2.5 Figure 5-10b . 2. 25 - 138 - At masses near 2.0 GeV lc 2 , results, especially Y 6 , are in accord with the 15 GeV le results of Corden et al., and in disagreement with those of Grayer et al . at 17 GeV le. We believe that this reflects acceptance limitations in the latter experiment at masses above the g 0 . Both our, and the 15 GeV le e:A-periment had relatively good acceptance at high masses, while the 17 GeV le experiment lost all forward peaking in their high mass raw data. Certainly, our data sample is tiny when compared to the 17 GeV le data set. We believe we are viable at the higher masses only because our acceptance allows a substantial part of the forward peak . However, we note that our <Yr> moments are only about half those of Corden et al. Since the L = 9 and 10 moments were consistent with zero in our data and not theirs , this may reflect a gradual degradation in the moments \\ith L . At "" masses above about 2.2 GeV /c 2 , our fits to }'f's become inadequate . Even \\ith only m =0, and 1 large numbers of moments are needed to describe a sharp forward (cose;~:) peak and little or no backward peak. (See the distributions of section 6.2) The high frequencies (in cos(JJ ) of the highest mome nt s are not ,.,-ell followed by our low statistics data. One might reasonably expect the needed spin content in the moment fits to parallel the Chew - Frautschi plot for the p trajectory. This has worked at masses up to the g 0 . Extrapolating figure 17-9 of Perl ~ Pe7~] to m,,:. = 2 Ge\' l c 2 , we find a spin of ~ 4, implying an Lr::ie:x value of 8. Also, the spin =8 break do•xn at 2.0 Ge\' /c 2 . The 15 GeV le data of Carden et al. [Co78] show that the L = B content rises like the (mass) 2 . By this criterion, fits with Lr::i.ex mm; R: moment becomes significant in the 1.7 to 1. 8 GeV lc 2 region, and that L = 10 opens up by mrrrr ~ 2 GeV / c 2 . Thus the p trajectory argument places only a lower bou.."ld on the needed moments. We expect that the low order L :I: 0 moments are not unduly distorted by these failings, but that forward peaks will not be properly followed and produced event totals will be uriderestimated. - 139 .l 2<Yl> ·-~ ·. l 2<Y6> 0 .05 ---++++++++±!"+/+++ + <Yfo> 0 20 1.0 ·.] 30 0 mmT· GeV /c 2 -DO 0 1.0 20 m'"'. GeV 1c T 30 ++ l t .~ 2 0 (a~ • DO t · .10 0. 1. 2 g,. , GeV1c 1 (b) Figure 5-11. Constrained moments. Figure 5- 11a shows low tpn m = 2 moments, and 5-1 lb shows low tpn moments with L = 9 and :o. These moments are consistent with zero and were constrained to zero in our final fits. 5.5.1 APMA Test Relations between m = 0 and 1 moments are evident in the distributions of figures 5-9 and 5-10. Most obvious are the consistently opposite signs. Ochs ~'ld Wagner [Oc73] found that PW.A predicts that the ratio -(m~-m;) TL= mmr °" <Yi> L (L+ 1) <Yf > 1 (5 . J.6) does not depend on L. They further noted that PL= rL(mrr,,)lr 1(mp) gives the mass dependence of the PMA absorption parameter Re CA- Using the 17.2 GeV le data of Grayer et al. they then found ReCA as a function of mm;· We repeat this operation 3 - 140 with our moment results . Figure 5-12 shows the 100 GeV le ratios. The curve in figure 5-12 is the ReCA result of Oc73 . We assume, as Ochs and Wagner did, that PL (mp) = Re CA (mp) = 1. As an attempt to avoid distortions from poorly determined moments, we used only moments where both the m = 0 and 1 moments were at least 1. 5 standard deviations from zero . . The agreement of these 100 GeV ratios Vvith Ochs and Wagner's results is satisfactory. The excess of L = 2 ratios below 900 M:eV lc 2 was also noted by Ochs and Wagner. They felt it was due to neglecting a density matrix term (p[f) in deriving equation 5.16 [Oc73]. At masses above 2 GeVlc 2 , ReCA seems roughly constant. This agrees with results of 'Shimada and Wagner [Sh80] who used 63 GeV l e data from the ACCMOR group to measure Re CA . Similar plots (not shown) at : 75 GeV le also find that PL is independent of L. However, the overall mag:litude of the 175 GeV le ratios is about t¥.i ce the curve and the 100 GeY le values. Vie belieYe that the problem is poorly determined p 0 moments at 175 GeV le (see figure 5-10a) . The ratio PL is quite sensitive to errors in the moments, and our 175 GeV le vc..lues at the p0 are not precise enough to use in this case . It would, perhaps, be more prudent to normalize the 175 GeV le ratios elsewhere along the Ochs and Wagner curve . We feel that equation 5. :i. 6 is verified by our data , but a measurement of Re CA has not been made . The 175 GeV troubles Vvith these ratios should not be held in conflict v.-ith PV.LA. . 1 - / , .i. "I .l. - • '·' ••• ••• ++++ • • .... -··· -1 ••• s.. a ••• a •l a.I I ••• ~ ~ l.. ••• L~3 L:'i 1.s ••• ·I. I -··. .. ·I ••• S. I ·l ••• s. I 1.1 ~ ' l.. l. I L=-5 L~ 6 t.t/++ ••• •. s -· .. -1 ••• I I I.I l.. -··· a ••• : •l D.....____ l. . .1- ,---L---, .&.... • •--.....l.'----1..J. . •- - _ ; Figure 5-:2. }loment ratios PL at 100 GeV/c . All ratios are normalized by settingp 1(775 MeV/c 2 ) = 1. - 142 - 5. 6 Moments versus tpn To obtain the tpn dependence of the moments, we have fit several large mass bins. centered on the p 0 , J 0 • and a large mass bin from 1.6 to 2. ~ GeY /c 2 . The Lr:iex values were set according to Table 5.2 and the highest mass in each fit. For all of these fits, mr.:IB:K. = 2. Figure 5-13 shows our p 0 region results. Below -v=t;;, R: .40, only m =0 and m =1 moments are significant. Above that value. m =2 becomes nonzero. Around this value, the other moments also change dramatically. The low and high tpn values of these moments are in fair agreement v..-ith lov1~er energy results. [Gr74 and Al78], but a slight shrinkage is noticeable in this transition between o~ data and the low energy data. This qualitative feature is predicted by the Regge model of Kimel and Owens [Ki77], which includes 1i, A1 , and A2 exchanges, and cut contributions for the 1i and Ai. To illustrate the shrinkage, figure 5->~ shows the zero crossing point of the < Y~ > moment. In this plot, we have included 17.2 and 63 GeV le points taken from [A.178]. We note that the effect slows at our energies. In the lo·w tpn region, absorbed tion well at lower energies. 1T exchange has also described the rrrm reac- lndeed, P1lA has been highly successful. Other exchanges, specifically Ai and A2 exchanges, are clearly present, but they do not become dominant ur1til the "high" tpn region. Since P1,:_A. contains no other exchanges arid no moments Vvith m~2. the shrinkage in tpn is not preocted by it. The transition point does, however, give us a limit on the region where Pl,,::_,\ can be tested and applied ¥1ith few reservations. - 143 - 175 GeV le 100 GeV le .64 < mmr < .90 GeV /c2 .64 < mmr < .90 GeV /e 2 .20 .20 ++++-1..L 0 o~ • !O < Y10 > TT++ + . 10 !~ Jt-++t-+t-++t 2 <y l> <YP> 1 1 -.10 2<Y/> .20 .20 . 10 .10 ++++ 0 i------------:------------~ +++ - . 10 - )0 - .20 -.10 ++++_...,_ -.10 2<Y~ > -.20 ++ 0 . fF-tr""'1~+-=------------------l ++ + - 2C -+- ' -.20 2<Y~> - .4C ++ -.40 0 C2 04 06 ~, Ge\"/c 0 .8 1.0 0 0.2 0.4 0 .6 ~,Ge\'/c 0.8 1.0 - 144 - 0.6 t) ....... > Q) ~ 0.4 ~ 0.2 0 0 0 I 0. 100. 200. PLab, GeV le Figure 5-1 4. "Sb...rinkage" of the p0 <Y~ > versus tpn zero c;:-css i;:-'"g pci ~t from 17 to : 75 GeV le . See text. d a Di s tr"b 5 .7 d:t 1 u t·ions Figures 5< 5ab display :oo GeV le ~~ distributions for mass ba."'lds centered en the p 0 , f 0 • and also the : .6 to 2. l GeY /c 2 bin. Both moment fit results, e.n.d acceptance weighted data appear in the plots . The acceptance weights chronically underestimate the data at lmv tpn, but give a reasonable showing at higher values, allov.ing us to continue the plots beyond our last fits . Figure 5- : 5a is plo:.ted with -tpn to show a transition between the low and "high" tpn regions near -tpn ::t .1 5. da at t h e p o, but it is striking in the 1600 to 2: 00 The effect is not too clear in d:t MeV /c 2 area . Above and below the transition, the slopes appear roughly exponential, especially at the higher masses . Also, a very slight turnover is seen below It I ~ m;,. - 145 - 1o4 .,tit ........ <o ........... .64 < m 11 r. < 90 Ge\" l c 2 10 4 4--+- 10 3 + ...........,.,_ +~ "J., lOl' + •... ~ 10, ".: I 0 .0 4 10 2 fft-+- ++ "t: J 0'"l l - ~ ".: 103 ..0 t lftt- t- +fft +tr + 60 < m""G:\2 :: ] () c-;__ ::...- ++++ " .... "t:l 104 -++i'"tl\(r~ 17 < m"" < l.3" Ge\· ; c 2 + ..... =5 +-+--+- =5 " t:: "'tl +-tt;t+ =+ ++++++ ++++ -+-++ l 01 +-+ l 6 0 < mr.r- < 2 10 Gr \ 1 c 2 ~ Jo' 0 () 2 0 4 0 G 0 8 11+ 1r -tpri . (G e\ . c)2 (a) (b ) I 02 0 OJ 02 C": v=t;". \, p \ /(" fig~e 5<5. :co Ge\;-/ c de;/ dt dis~ribu.tio:is. b (a), ~~e '>-e:.-~ica.~ sc·c..:2 is oflse:t sligh~ly ~o positiYe tpn only ~or clc.rily . X::-i d.c.~c.. '·"-ere mec..s~,s -: -,<~h tpn > nu . Jrd rb" e'-P '=' ,. . _,. , ~-.de J-- ,.._ lo-,\ ; i··e .. ·"'· C.du 1. t pn re~1·on e:, . 04 c - 146 - .64 < m7m < .90 GeV /c 2 0.8 . 0.2 t +t t + + ++I+ + ++1+ -+ + ++I+ +++ I ++ t 0 0 0 , 02 0.3 0.4 0.5 -tpr-~ , (GeYI c) 2 Figure 5-16. 100 GeV le p 0 region rmX/ mm ratio. This is better seen in figure 5-15b, which expands the low tpn. region by using --J=r;;;;, as the horizontal axis. The turnover is expected in rr exchange dominated reactions "\\ith neutron recoils . The small tpn region does not go to zero, in agreement 11.ith the PKA model and disagreement Vvith simple OPE. This is also a feature of the Regge models of Kimel et al. We included weighted data in figure 5-15b as a check on the moment fits . Although weights underestimate d a/ dtpn. and the underestimate is tpn dependent, the effect is slow compared to the bin size. The forward dip is not a strong feature of the low rrrr mass data and some care (a rr1tX background subtraction) was needed to observe it. Figure 5-16 plots the ratio of mrX data over 1mnr. The peak at low lpn. is enough to wash out the pc dip. The dips at the higher masses are stronger and rrrrX subtraction, though used, was not needed to observe them . /:;; resonance recoils , unlike neutron recoils, do not have a low tpn dip. Hence our background peaks somewhat at low tpn relative to mrn. The problem is worse at the p than at higher masses because the back- grounds are larger. -147- CHAPTERVI Decay Distributions 8.1 Scatter Plots In this chapter we present rr+Tr- decay angular distributions in the Gottfried Jackson frame for Tr-p -+Tr+Tr-n. We also consider tmr distributions. and draw a few limited conclusions about mr scattering. We begin with a pair of 100 GeV le scatter plots in cose; versus TrTr mass. Figure 6-1 is at low tpn. To reduce the point density, this plot uses a restrictive Itpn I <.08 (GeV /c) 2 cut. Our forward acceptance zero is present at all masses. Though heavily populated at all cos8;. inspection reveals that the p 0 density is reduced near coseJ Ri -.4. The f 0 band shows three distinct clusters of events. The g 0 region seems undistinguished in the forward direction, but contains a significant cluster of events near cose; Ri -.7. Above the g 0 , the backward or cose; Ri -1 region quickly dies while a strong forward peak is established. The forward peak survives until our acceptance zero cuts it off completely. No mass band above the g 0 is notable for local increases in the event density. Figure 6-2 shows the cosfJ; versus mass distribution for Itpn I > .15 (GeV /c) 2 . At high masses, we still see forward peaking, structure at the g 0 mass is less distinct, the f 0 has only two broad clusters at extreme cose; values, and finally, the p 0 region shows clear clustering towards the middle, not the ends of the plot . The forward acceptance zero is much less evident in figure 6-2. The presence of clusters of events in these figures implies dips between them. One can easily visualize a number of possible contours for the dips that "connect" the various mass values. We will map the low tpn dips in section 6.4. - 148 - 1.0 •·,. ,_, :·: ~···· . ,,.' ... . .. •• • • .... :i·.. .. ... • _... . .!""lo.I...~.: • • r" • •.. I ~ •• ..... ..-·'. ... . .• •• • .. . .! I .. . .. . 0. r . .·. .. .. .. ·. • -1.0 0. 1.0 2.0 3.0 Figure 6-1 . 100 GeV le scatter plot of cose; versus mmT for Itpn I < .08 (GeV /c) 2 . (An isolated small point corresponds to a single observed event. The point size corresponds to both the relative weight, including acceptance, of an event, and to the event density. This applies to all scatter plots of this chapter.) 4.0 - 149 - 1.0 .. · " ' ' .t •,, ... .;..-•At.._ . •,_:. . ...•. 41rC••c•, •.:.:...: .. :-.: .-,:;i,,.._t, ~ ...,~."t.:-r-,, ~r·.-.,:;-1t, ~~ -,.. , t ~ • ,. •••• • • - ~. ·-· • ••• • e # • • · ' .... .-· • ~::."''""'·~ ..... • ..t~· ':. l'-' ' . ~I •,.;.•• • ••.... :· • '·'• • • e • '. • e \~ ~ • """ ... .. I •· ·~•i'"!' ,·.,.• 1 • ...o ..··S • ·~ , r ~· '1 ~· ••• ...• • • ~~· ••• ':9·:- ••• ·: 4'' • , •· I 0 • -~-·· • • • • • •• •.J.. I ,- •• • • • . .. "·. ...• "'~1·'1 • ~· ~\! :'':"- • • ~ ••• •••• ""... : .$~•. ;·:· '· •• •, •• '·'•i•. '.r:. . •· .. ., ~ ;,1... . • ". •· >71~·,: /°. ::.~:~,~~: :· :. :.· ~• • :\ ! '•' \,fl' 4IJ I I • •• t . . .. •.· I .,.. -. .. ·-. .. . .S ,_ " • ' ••• • .~· ~· ~~ 4' • , ~ ' : : • t tt 't t '• : !I~~, •; ·::~~ °'!j.:.;. ·~ :~ /. : . -· ~ .. ·. 0. .· t ... - . . -... . . .. ... :- .' : ., . .·. . .... , . . . . . .· .. ,•..."' .........,.,.. ·:·-'.. . . ...... . -· . . ,. r•1.·, I t ~ £• \ ... • • • ·~:. •w. \ 7 "' -a• a, .• • • • • • • • • .. . .. .. ...... .. .. ••r •• • • ' .. . ·. " ' .. • •• • •I • • J." .• •. I " •. --~·,.. ·- -··". tit •• . • • • • .. •• • •• . ·-.. • • t • • I.-:' •., • • • ~ • .-.i I • • • e f • ~·• • '~ ••• t • t I ~ r ~.....:. • - · • ··~, '\. • 'I • • • ,., ··: . .".t, . e W • &,; ~···-· ••• ~: .. : ~:·:· 1· ·:. • •• t 1 ;~~ l-• I • •• •• •• • • ~~ ' z:9 ' I ~ ••• ._ • t .._ • '~·~~{·.'i· ~ ~. •. :·.~(. t' ..,,., ...·' ;• ."• •.... ,., .. . •..; :1!·. ·. '.·. J·... -~ ' ~. '.,j..1. •• • •••' • .... •• ••• ••• ,,..~ :. ·~.·..i.\. ·.: • .,· ····,.-· .1,., ........ . ,.,.f~' M~ l._o ''• ··~··.~ .'~ .~··~,·g".'·~ . ~.....•"'·~""'"'·· . ·...... •.:,.... •. .. .. ... .•.•.•)·•'f' .. . ,. ....... , ......:r.'.... .·.. . .... .... '· ,.., .. # ;"'• :'• •,' •,I ': • • ' oo \ t ~: -1.0 0. • J·~· ·~ .... 1.0 2.0 mTTTT' 3.0 GeV /c 2 figure 6-2 . .JOO GeV le scatter pJol 0f cosf)J versus m.1Tr. for (G::N /c)2 l tpn ! > .~ 5 4.0 - 1506.2 Resonance Region In this section we consider decay distributions for the p 0 , / 0 • g 0 , and h 0 mass bands. The same sequence of plots is given for each mass band. We include scatter plots ( 100 GeV I c only) and projections (both energies) in coseJ and cp; of the rm decay distributions. The projections show fully weighted data as points with error bars. Smooth curves on the projections are moment fit results and represent produced distributions. The weighted data follows the fit result in cose; fairly well in good acceptance regions, but falls away from it in acceptance zeros. The acceptance zeros at low tpn are mainly in the peaks of the produced distributions. As figure 5-1 illustrates, they also tend to be broad in cp;, and the forward zeros are centered on cp; ~ 0. The effect of all this on cp; projections is to make weighted data appear systematically below the produced distribution curve. Another effect is to make weighted data at low tpn suggest that m = 2 moments are significant when they are negligible. Histograms without error bars on each projection are uncorrected distributions of the final event sample. For each mass band, both low (I tpn I < .15) and high (.15 < Itpn I <1.0 (GeV /c) 2) plots are presented. The information content of this section is contained in moment coefficients, but decay distribution displays allow one to see more clearly their implications. Figures 6-3 and 6-4 show this sequence for a p 0 mass band of 690 to 840 MeV /c 2 , or about ±.5r about the p0 mass of .770 GeV /c 2 , with r = 158 MeV /c 2 [PDGBO]. In figure 6-3, a single broad minimum passing through cose; ~ -.4 and cp; The lack of events near cose1 =0 is seen. =+ 1 in figure 6-3 reflects the forward acceptance zero. The minimum position depends on both these variables. Projecting the data onto cose;, we see a considerable forward-backward asymmetry resulting from interference between the S-wave background and the resonant P-wave p, [Eg74]. The interference term, yp is proportional to cose;. s.. "' - 'd Q) bD J... QJ QJ 17) 0 co I 0 co ..-! a • ....... I : • • •I" • ••• I I'. • . ..... • .: • •, - .. # .'•~ • . " · ·. . . . ' . . , :"• '• • ' I 4'y' ' .. • : • •• \ ... ., t • • • • •• ,• • ..... ....... •• • ... ''· .;. ·, . . . .: coseJ 0. • •.... •• "'· I.,, I • . •' ~ ,,,, 1. ...• •• • . .•. .' ..,._._ •• •••• ' "' Figure 6-3. p 0 decay distribulions at 100 (row including the scatterplot) and 175 GeV le (lower row). For this figure, Itpn I < .15 (GeV /c) 2 . -1. ~. ·~ : .:•f' ~ ,~,. ': ..'J •'"'' .. • : ·: • :. • : .:-:..1' ..·,,,•........... • ~ •.,_~ ·~ • ., .. • ··:.. ........ ~. • .... I. ... , f• • • -~. • .:"" 'l~· •.. : • o ' . ,. . .: ' .:••••••• .. ~.....·':"·. . ., ... ... , ....,~'•}Ir:........ •• • .. I•• .: .. o ' , ,~., '. • I . . .•:. . . .•, . .:: .,. ~·c.. "~~-·:,:::·., ~.j... . -· I • . 1! •• • • • • • • ,,. • _.. e,.... ·•••·:·,; .. :· .... :. ............ .,~ •.• ~.,.... • ·' • ' · a; , • ' •• • ' ... • .. .. ; t: ' ..............~ ............ t-·........... : :. .• '\:, • ~· ••• '!-· ••• ·;., .. .. • . ..· .~" :' .. ~ ,.,,.· . . ~·:'l',.._ ' •• ~ : • .. :. ;~··rY'}:: I·!.· vr. •... . ' • .. • . •.., • ,-... ,,,.. ~ .•..:\of\ ·~~~" ~·• .·... " ... , . ... ... '" ... .• ·~• ...••,·;:~· . .:.!Lr.·~····' .. • • • ••• ,\~ '''?..· tT'll " i ."• • -..,1 ' ~· •/,, •>~ •:r,.: • ,,,,,·,····.··~.\. • • .... 10. 100. 1000. -1. -1. 20. I 100. 1000. I I I cose, 0. cos91 0. I I I I 1. 1. ':=t 0. -180. 100. 200. 300. 0. -180. 100. 200. 300. 400 . f/JJ, degrees 0. f/JJ, degrees 0. 180. 180. I f---'o CJ1 ,_. Q) Q) . • • : · :· # • • •• : ... • . -1. ·, ··: .. • I • • :• '• • .. •., • 0. • ••• • cosfJ; • • ...... ;I. • • ; • " "• •' • • (' (• - I •'• ,,.. .... "' , . , •• ' • • 1 ' • • ............... './' ....... "'- •: •• "': . ' 1. Figure 6-4. p 0 decay distributions at 100 (row including the scatterplot) and 175 GeV le (lower row). For this figure, Itpn I > .15 (GeV /c) 2 . M . . <·.:. : .:.. ~ .~ . .: .:.: ;. . ' . ..... ;·:; . :.··..,..,,·:: :.::\ .,.. : !~ • ··....~~' •. • ·~~r· ~··..,.: "• .. •"'• . . ' :• .' ... . . :.•.. ...·.•. ..,,.. .,.... . ·... rn .\, . .'• ...... .... ~· r I.:, :r,'.••' -.,,••1:: •;. •., ~ fbO 0 . . . :. ·.~. : ·. .. ... .·. ... .. .. "d .: . ·:. :. ..:..::. .~.~.•. ;:·; ~~~; '·: . :· .~.:"": : ' •• •·., .•·. •)" ,. : ' •.,.,,~ •·· ~= ~ •••'·•, ..••,•"'r•\ i•''•• •• . s.. " ' I/'•' . . : .. : ..: :"'-- : .,, '.:-:. .-~. ,. ~· ..;.:·.. .· .....~ ~ : .. ~···· .. 0'° . • : : ,.: ... · ., .. :· ,. ...... ,.. . '... ~. •.. ... ...•.... ..... ..• . co 0 0. 100. 200. 300. 0. -1. f -1. 100. 200. 300 . cose; 0. cos{}J 0. 1. 1. -180. o. 100. 200. -180. 0. 100 . 200. 300 . 'l'J, degrees 0. 'I' J • degrees 0. 180. 180. I I ro CJ1 1-4 - 153 Tl' Because J-ncos(mrp)d<p = 0 for m '¢ 0, only moments with m = 0 appear in cosB; projections. Projections in rp; are a bit more involved, and not often shown. The curves in our <p; views are numerical integrals of the moments on cos9;, but several patterns are worth reviewing . First, gonality of Legendre polynomials). Form f YfdcosB; =O unless L = 0 (ortho- = 1, only odd L moments survive in the rp; view. In general, the only m #- 0 moments seen in the rp; view have even values of L + m. This follows from observing PL(x) is even (odd} in x if L is even (odd), and that }T(x,rp) is (d/d.x)m.PL(x)cos(mrp) times numbers. AB a corollary, moment terms with m -:F- 0 and L + m odd are not seen in either projection, both variables must be used to extract such terms. The rp; projection of the p 0 at low tpn clearly shows the cosrp dependence of a significant m = 1 contribution. The p 0 high lpn plots of figure 6-4 are a radical change from those in figure 6-3. In the cose1 view, we have lost the forward and backward peaks . Replacing them is a near perfect sin2 B; with only small constant and cose1 terms. The cp; distribution now has two peaks centered at <p; = ±90°· The shape is mainly cos2rp 1 with a comparable constant term and a small cosrp 1 term. The double rp; peak is characteristic of m =2 moments. Indeed, recalling figure 5-13 we see that the moment con- tent of the p mass band has changed completely. At high tpn. the only nonzero moments are a ~ that has changed sign, a now nonzero Y~, . and a (constant) Y8 0( Ne that "keeps" the distribution positive. The decay angle distribution reflects not only the spin of the decaying state, but also its production. In the absence of interference effects, Lichtenberg [Li65] notes that a spin 1 p decaying to two pions has /(9;) not flipped, and I(e1 ) 0( 0( cos 2 9; if the nucleon spin is sin2 B; = 1-cos 2 B; if the nucleon spin is flipped. In the Jackson frame, rr exchange is non flip, but spin 1 exchanges are spin flip [Wi7B]. Swave mr scattering just gives a flat term, and interference effects can bring in other s. ~ - tlD Q) "C Q) Q) J.., en 0 -1. •. • • • . •. • •' : • • • •' ' :· ,• : I • • . • • • .·~.. : .• . • .. ., •• .,.._(·~ _.:~•.r;~ •• ' .•,t;(, •., , 1.:-. ,.... • • ,:· • • • 1'•" ,• . • - 1i .. ...... ..c. ,,_ 0. • __ r • • • • ~ -···. . I' cos61 1• • •• • I - •I •• t • .. 1. . . .• . · - ~ ; :~ ~~ ,~;.. ' , •••I • •• ·' f'j. :• •. .• •• . ... · . , ;.••. r. "\1'· • -.: • •• • • • • • :.< •'. . ...• :•• , .• • •..•':11. ....... . . . . . :"' ~ .~.,..,,, .. .· .. ... .. ··. ·.·•' _.ir,, -. ' •• . ..::. ....:'".~·: .... \.~. . :..... . ~ :,~::>~ .· .. :•. .\~~ : , • f .•·• . \ : '\ :. ... •A ... f1• \ V I . . ... ."..:·.... : .... ·. . :. . . . ·:.... . . . : ... ·, -~. -a., .. , ,,~.. •• ·- < .• . , • . • . • . .• . ,,,.,. Figure 8-5. / 0 decay distributions at 100 (row including the scatterplol) and 175 GeV le (lower row). F'or this figure, Itpn I < .15 (GeV /c) 2 . T"""l I co d 0 ~ co 10. 100. 1000. 10. 100. 1000. -1. -1. cose, 0. cos61 0. 1. 1. -180. 0. 100. 200. -180. 0. 100. 200. 300. '/)J, degrees 0. 'PJ, degrees 0. 180. 180. ~ ~ CJ1 s.. " - "C ~ s... <L> <1> 111 0 • • • • • • • • • : ... t..• .. ....... . \, .... . .... . \ • ... cos(}; I • I 1. .. \:I \ ••• .• • ~~ •• .. . . ..... ~ . . !'-• . . ~· •• "! . .. ..... .. . .: . .. .... ·. .. & •• # ...."·..•. . ,· •. : .· . . . ·. . .. .._ ~·.. ... 0. . .. . ~ t ··...... :. . . . . I Figure 6-6. / 0 decay distributions at 100 (row including the scatterplot) and 175 GeV le (lower row) . For this figure, Itpn I > .15 (GeV /c) 2 . I ..-I g 0 ._ .•. .. ....... ~· . . . ~-. . l..,•..: i: .•·.• •. • '•. :• • •. :,. . . •. • .. •'t.......•I:. .,t.c•.••., ~ t. 10. 100. 10. . 100 . -1. -1. coseJ 0. coslJ1 0. 1. 1. I ~ ~ -180. 0. 40. BO. 120. 160. -180. 0. 50. 100. 150. 200. I 0. I rp;, degrees I t it rp1 , degrees 0. 180. 180. I 01 01 I-A - 156 (especially linear in cos9J) terms. Evidently, the high tpn region of the p 0 is dominantly spin flip with relatively little interference, while the low tpn, region is mainly non flip and has considerable interference. The / 0 mass region, 1180 to 1360 MeV /c 2 , is shown in figures ·6-5 and 6-6. The acceptance holes of figure 5-1 are clearly visible in the low lpn scatter plot of figure 6-5. Multiple dips are seen in the low tpn cos9; projection, and there is only a small forward backward asymmetry. Eguchi et al. [Eg74] attribute this to the relative absence of interfering 7T7T amplitudes. We note that the change bet\\-een the low and · high tpn cos9; distributions, while significant, is not the total reversal seen at the p 0 . The double dip of the low tpn plots has become just a single dip in figure 6-6. An m = 2 double peak in 'l'J is quite prominent at high tpn. Figures 6-7 through 6-10 repeat this exercise for g 0 and h 0 mass bands of 1590 to : 790 and 1900 to 2060 MeV /c 2 respectively. The g 0 displays a large forv.- ard backward asymmetry, but does muster a backward peak. The backward pee.k at the h 0 is required by our fits although we have no data in the last h 0 bin. The cha:n.ges from low to high tpn become less pronounced as the mass increases from the p to the h 0 . In particular, m = 1 moments return beginning at or above the / 0 , and m = 2 moments fall with mass. Except for the dramatic Y~ sign reversal at the p 0 , the m = 0 and 1 moments retain their low tpn signs, (once m = ~ recovers), e.~d the generally negative m = 2 moments eventually die off. The low tpn costJ; distributions have changed dramatically as the mass increased from the p to the h 0 region. The forward peak sharpens, the backward peak at first sharpens but then essentially disappears in the high masses, more dips enter, and the dips seem to move around with mass. We note in passing that at low tpn and intermediate masses (f 0 and g 0 ), the CfJ distributions seem to flatten out and become more consistent with the TreimanYang condition for 1T exchange dominance, namely a flat cp distribution [Tr62]. This - 157 - is illusory. The rr-p ~ rr+rr-n reaction fails the test almost everywhere . The reduction in the rp; dependence of the integrated (in cos FJ;) distributions results from a cancellation of strong (f J dependences of both signs. The signs and magnitudes of the cp; dependences couple to the slopes of the cose; distributiop.s . This is a prediction of PKA.., and is seen in our data when we make cosFJ; slices. The Treiman-Yang test failure for mrn should be immediate upon considering what an m ~ l moment means, but it is amusing to note that the only places flat cp; distributions are found are in dips of the cosFJ; distributions, and these have been shown to correspond to zeros in the /iii scattering amplitude [Pe73]. rn s.. ~ ..,, 'd Q) bll Q) ~ Q) I o • : • • • : : ·:. •• ·•.!:• ~ ;·· ' :.. •• • •• • • : :: • • • o .. •• :• :' .. , , :-.. , , , • .. ":'.!II,-, . . ..-·' • .•\"-}'>.;..:• • • . -1. " : • : ' • • •• • ' • " ' • • • : : . • • • • • : - • .... • I • • • ..• ~ cos61 0. 1. ,,, ••• J ... • _!1 --·· •· ,. • ... ' : . \• . : '._. .... ~-:: ·: . . ·: .=:: :..: • • \-• • •: • • .• • ::• • I .......... • : ' •• •• .. • ••• ....... • .: J, •• : ··~ .... , ••• · ., .. ,... . • • • • 0 ~: ': i '':.:':.::.~.:-.- · · " ~ : :.;. }£°"' . . . . .. .. . .....""~ .. •l· . .· : .... . . .. : ·~. '.:· .. ............ .•" ... .... .·. .. . .. .·....."f"~...::f"j""'',,1"1 .. .. . .. . • ··••- ...":lt •• ' . . ..,. ... ..... : • .-.~ .. . .. . ...... . Figure 6-7. g 0 decay distributions at 100 (row including the scatterplol) and 175 .GeV le (lower row). For this figure, Itpn I < .15 (GeV /c) 2 . I ~ • 0 co 0 ~ d co 10. 100. 1000. 10. 100. 1000. -1. -1. cosfJJ 0. cosfJ; 0. 1. 1. 180. -180. rp;, degrees 0. 180. 0.--...~..___.___,_--L~.L..--'--J 50. 100. 150. 200. f/JJ, degrees 0. ++r +++ trtltt t -180. 0. 100. 200. 300. I OJ CJ1 ....... t:). ....- 't1 Q) J.,.. bl) Q) Q) 11> .. '. -1. r . I .. I . . .· : .. . .. . ' f t. I 0. I • • ti ' I I \ • ' ... 4 I 1. .. ' ... .. ·. ...·." I•._•• ..·..•. .. . .... . ~ .... . ...\·.:.... . . • • c .. :. COS6J . • • . .. Figure 6-8. g 0 decay distributions at 100 (row including the scatterplot) and 175 GeV le (lower row). For this figure, Itpn I > .15 (GeV /c) 2 . I 0 co rl 0 r-i 0 co 1. 10. 100. 1. 10. 100. -1. -1. coseJ 0. cosf)J 0. 1. 1. C-1 -180. 0. 40. 80. -180. 0, 40. 80 . 120. I 0. I I f/'J, degrees 0. 'Pl, degrees 1513' I 180. I 180. I co CJ1 ,_,. s. ..... - 'O QJ bO QJ QJ J... fl) 0 ,. . -1. ' ' ~ .. 0. •. •• • • ...... ... .· . . ·'. .. cos61 .. - .. ··.. • .. ... . .:· -·.. . . .. • . \' . I " 1. ... ,.~, •. > • ....-• : . :#JS ·. ".:~ ' .. . .·. .:. .."·. " fl' ..·...·:.: :t~ .~ Itpn I < .15 (GeV /c) 2 . Figure 6-9. h 0 decay distributions at 100 (row including the scatterplot) and 175 GeV /c (lower row). For lhis figure, co 0 0 ....-i co 1. 10. 100. -1. -1. 1000. 10. 100. 1000 . cos61 0. cos61 0. 1. 1. t -180. 0. 100. 200. 300. -180. 0. - 100. 200. 300. 'PJ. degrees 0. '{JJ, degrees 0. 180. 180. I f--' 0 m rn &. ....- re Q) J... OD Q) Q) 0 • • l- I- .... t- .... a . a 0. 1 • • cos9; • I • 11 1. •.a. ~ ·.-:i :·~. • ' • . • . . ·• a.. _____ I ... ....., .... Figure 6-10. h 0 decay distributions at 100 (row including the scalterpJot) and 175 GeV le (lower row) . For this figure, Itpn I > .15 (GeV /c) 2 . 7 -1. CD o 0 ...-i a:> 1. 10. 100. 1. 10. 100 . -1. -1. cosfJ; 0. cos9; 0. 1. 1. -180. 0, L&.J 40. BO. -180. 0. - 20. 40. 60 . BO. I I 0. I - I f/JJ. degrees I 'l'J, degrees 0. C I 180. 180. .......... m I !--" - 162 6. 3 High Mass. Low tpn Fits At rrrr masses above R:J2 Ge VI c 2 , our cose; plots bear a strong resemblance to diffractive scattering distributions. These distributions show a strong forward (cose; ~ 1) peak, little or no backward peak. and a single dip next to the forward peak. The dip moves toward cose; = 1 as the 1T1T mass increases, but seems to disappear near mmr = 2. 7, becoming (at best) a break in the distribution. The resemblance to diffraction is enhanced if we plot the data in t 7iii rather than coseJ, section 6.4. In this case, the dip, and later break, is roughly fixed at t'ITTT ~ -1 . The high mass forward peak appears roughly exponential in either coseJ or t 1Tii · The rrrrnr trigger was not optimized for high masses, and we clearly suffer from forward acceptance problems and low statistics. The high mass region is in somewhat better shape at 175 than at 100 GeV le. However, due to acceptance differences both data sets must be fit separately. This mass region is of considerable interest when viewed as a case of diffractive 1i7T scattering, and. ·we e:Ktend our . analysis as far as possible. (The methods described below are quite data intensive . We have not attempted them at all at high tpn .) The ACCMOR group at CERN recently investigated 1m masses up to 4.0 GeV /c 2 at 63 GeV le with good high mass acceptance [Da79]. The fitting strategy here is motivated by their methods . As discussed in section 5.5, spherical harmonic fits are not generally well matched to the high mass region. However, figure 5-11a shows that moments Viith m = 2 are consistent with zero for Itpn ! <: .15 (Ge VI c ) 2 . With only m =0, and 1 moments present, the produced distribution at constant cose; follows the form, (6. l) In a cosFJJ projection, only I 0 survives . This allows us to make acceptance corrections at high masses without committing ourselves to a spherical harmonic fit . A - 163 physical constraint is JI 1 J ~ 10 . (Otherwise, da/ dO < 0 would occur.) We have used (6 .1) in (5.6) for a series of rp; dependence fits. Up to 20 cosEJ; slices of varying size at each mass were fit. The iterative linear fit of Chapter V was used . The <PJ range was folded as in the moment fits, and bins with an acceptance of less than .02 were excluded from the fit. If less than five of the nine CfJ bins had acceptances greater than .02, no fit at all was tried. The tpn cutoff for these fits was Itpn j < .15 to insure a minimal m = 2 presence . We fit only this one large tpn bin . The acceptance used in the fits was first averaged for mass and tpn inten~als according to weighted data. For cosB; bins larger than our grid, a second a\"erc.ge among the affected bins was then made according to the weighted data distributic:-i. Because of our relatively small data set, and the demands of a sharp forwal~ d peak, we needed fairly large mass bins in order to obtain even marginal statistics in each mass bin. The cose.l bin size selection was constrained near cos eJ =: by the steep forward peak. and our eventual need to fit / 0 in cos9; (see below). "on the o~h er hand, our small data set required the largest bins we could bear . A nun1ber of sets were · tried at each mass, in addition to trying different size mass bins before our final bin selections were made. In the extreme forward direction, the 'PJ fits usually failed for poor acceptance. The highest coseJ bin was always rejected, and as the 1i1i mass increased , more high coseJ bins were added to the rejection list. We were not able to obtain I 1 in all the fits, but a reasonable I c could still be obtained in good acceptance, low statistics cases if 1 1 were "aba..."'1.doned", and we sought only I 0 . Jn some other bins, the two component fit gave II 1 ! > fo, sometimes by a wide margin. Physically, these cases clearly had I11 I < 10 , but the fits badly over estimated the I 1 component, which in turn distorted the I c result . To ignore the rp; dependence completely in such cases would unnecessarily increase the I 0 errors . For them, we set j! 1 j =Io by fitting fp =Io( 1 +s cosrp; ), wheres= ±1 . - 164 The sign of s was taken as the sign of I 1 found in the first pass fit. Unfortunately, these last tricks did not help the high coseJ problem. In the light of the above compromises, it might seem we're no better off than with moment fits. The improvement over moments is slight, but usefuL and allows us to push our acceptance corrections above masses where the moments fits fail. The acceptance correction with (6.1) required a second fit. In this, we fit the cose; dependence of ! 0 , and extrapolated the result to coseJ = 1. An exponential fit to the forward Io peak was used for masses above 1.9 GeV/c 2 . Tllis extended our results to about 2.6 GeV /c 2 at 100 GeV le and to about 3.0 Ge\' /c 2 at ~ 75 Ge\' le. Away from the forward peak, the high mass I 0 values were added to the htegral of the exponential to obtain the produced event count. Below 1.9 Ge\' /c 2 , ·we used a Legendre polynomial series 10 = 2: aL PL(cose) . (6.2) L (The aL are related to the tf of equation (5.12) by aL = Y7T(2L+ '.:.) tf.) Produced event results from these fits were given in figure 5-5 and comparisons to the moment results were made there. The I 0 results along with curves from these fits are shown in the next section. 6. 4 Tran.sf orm.ation tr;> t 1l'1T The main motive for doing the fits of section 6.2 was not just to e1.'tend our acceptance correction a few hundred MeV /c 2 , but also to provide input for a study of rm scattering at the highest masses possible in our data, and specifically to measure the diffractive slope of the forward peak. Additional objectives were to document the approximately fixed position of the lowest l t 1m I dip, and, possibly, to measure the high mass mr elastic scattering cross section. - 165 A number of problems have prevented the latter measurement. First, ·we do not have enough data to make a "traditional" Chew - Low pion pole extrapola:~on [Ch59] of, for example, the Colton-Malamud-Schlein type [Co71a, Co7~b], or ·with any of the common form factors. 1n our case, reliable accepta.."1.ce corrections for our small data set required much larger binning, especially in tpn, than was tolerable in these methods. We then appealed to P1ViA as a model for the "tc.rget' ' pion tpn dependence. In this case also, a number of ingredients were missing . First. the exponential slope B. of the P1tA. form factors is not yet reliably knov:n froru our data. Our fits so far for B (they have not been discussed) give values cf aboi.lt :o to 15 Gev-2 in da/ dtpn for our beam momenta. Figure 5-15a may also shmv a mass dependence to B, so extrapolating the low energy results of Wi78, ·which e..pply to the p0 , are not much use at the higher masses. Our need for a large tpn bin is aseJ.::1 our bane. We are unable to use differing tpn dependences of the absorptive arid /iii scattering terms to separate them. A formal solution of PK.\ is possible if B is knov.n, but without detailed fits using well determined 11 values , the separation (whether valid or not) is useless . Although a rm cross section is not reported, we can still make useful obse~-\~a­ tions about the decay distributions and determine an exponential slope. ·we 8eg~n by reconsidering the scatter plots that began this chapter. Figures 8-l 1 asd 6<2 are the analogues of figures 6-1 and 6-2, but now we use measured t,, 71 \-c.lues in place of cose;. The variable tm is the squared four momentum transfer from the beam pion to the forward rr- (see Appendix A). It can be mec.sured directly or approximated at low tpn by equation 6.3 (see below). For the scatte~ plots, v.-e use directly measured values of t mr· In figure 6-11, the high mass dip has indeed become roughly straight in -tmr at a value of roughly 1 (GeV /c) 2 . This dip runs into a concentration of events at the g 0 and it is not clear from the scatter plot whether it penetrates them, goes around them, or turns away from them. Another clear dip - 166 - is seen running along the backward kinematic boundary. Jn the scatter plot its path from mmr R:i 1 and -tTm ~1 up the edge is clearly seen. This much implies that the dip survives through the / 0 resonance. Whether it also passes tb..rough the p 0 or exits the kinernatically allowed regions at mmr ~ 1 and either -t r.1i =0 or -t m; ~ 1 is not clear from the plot. A third dip, running roughly parallel to the second, but farther into the plot is also seen, but in the scatter plot it may not be convincing. (lt is clear in the projections.) We next consider briefly the high tpn scatter plot of figure 6< 2. The !:Jo.c~'-v.-ard kinematic boundary is much fuzzier here because of the now l~ge rar.:.ge of t;pn values included. Only one dip is clearly obvious in this plot. 1t "sta:'ts" at -t "" ~ 0 and mmr R:j 1 and runs roughly parallel to the kinematic tmr limit. Other possible dips are evidently fairly weak, and not readily traced by this plot, but is seems clear that no dip can penetrate the p 0 mass region and stay kinematie:c2ly c..llov.-ed. In both these plots, most dips are found at roughly constant umr . The oe.jor exception is the high mass dip in figure 6-11 . Section 6.5 considers them in mc~e detail. Figures 6-13 (100 GeV le) and 6-14 (175 GeV le) present the I c results of the previous section. We again use -tTm instead of costJ; to represent the Gottfried Jackson polar angle. The former is more directly a dynamical variable than. cos DJ, but the reference frame remains the same. Since the t mt range expands c.s rc'4!:1ly m~. the high Itmr I cutoff is the last bin completely inside the physic al '. t "" , ~a..:.'!ge at the low end of the mass bin. At low tpn, the approximation tmr = -2q 2 -J 1 - cosFJ; (6.3) where q = .5vm;rr -4m; is the final state pion momentum in the ""rest frame is excellent. Equation 6.3 is exact at tpn = m; and corrections to it at small tpn < 0 are small enough to ignore. Bounds on trrrr are set by mrrrri the limits cosFJJ = ±1, and tpn, see Appendix A. - 167 - The vertical scales in these figures should be considered arbitrary. They are essentially the produced event scale for events binned in cose; bins of size .1. The transformation to t.,m has merely squeezed or stretched the horizontal axis . vYe should also caution that the decade scales in the plots vary from mass bin to mass bin. These plots track quite nicely the mmr evolution of the dips . In some cases, dips in one mass bin map to an inflection or break in the curve in the next , but the effect is still traceable. At the lower masses, no dips are fixed in trm· However, beginning at m1T1T ~ 1.7 GeV/c 2 , the low tmr dip is clearly established at~ -1 . Furthermore, even though it is seen to fade into a break at masses a~ove about 2.6 GeV /c 2 , the break is at the same location. The points in figures 6-13 and 6-14 are the 10 results of our CfJ fits . The curves are fits to the Legendre polynomial series of equation 6.2 (mmT~ 1. 9 GeY/ c 2 ) or to aI1 e~xponential in the forward, -tmr ~ 0 region (mmr~ 1.9 GeV/c 2 ) . E}:ponen.t ials are not statistically compelling in our data, but we believe polyno rrJ. al fits at high masses in principle underestimate the forward peak . Reasons for this have been discussed in Chapter V. We remark that exponentials are preferred in the high statistics ACCMOR group's 63 GeV le data. - 168 - 4 • • • •• 1 • •• • '· ... 3 •' .• • " . ... .• I .. ... . • .. 'I • : I• • • t .,.... ' • . ··. ·.•... ... ;:···~··. ·. C\l ). () ., •• - . ... . . •• .. , ........ ·..... •, .. . . .... •·: f " ..... .... •·:a:,· • r , .. , ,.\: \·.-. ...• • ~ .:,::··: . • ... ' • .......... > ·' .: .. Cl) lJ • • •• •• •... ' ., l ·-:. rl· • • :1 ~: ..., . .. .. .. . . .. 2 ~ ~ ~ 1 0 0 1 2 3 4 Figure 6-11 . 100 GeV le scatter plot of -trm versus mmr for ! tpn I < .08 (GeY/c) 2 . The backward kinematic of coseJ -1 maps to the 1i"ii ma~s dependent limit seen, and the limit coseJ = + l maps to trm = 0. = - 169 - 4 • • • •• • • • ••• I •• 3 .....• ·' . '"• . • • . • • ... C\2 () .. ......... > Cl) CJ ' 2 • • • . • t:: t:: • ' .. . '" ... .. .·. • '; ' . .· .. . '• , I' . . .· .• ~. •.! ··: .·. .. ~ .. .. 1 0 0 1 2 3 4 Figure 6-12. 100 GeV le scatter plot of -tmr versus m 1m for l tpn I > .15 (GeV /c) 2 . Since no upper limit was placed on Itpn l, the backvrnrd kinematic limit for -tmr is not sharply defined for this plot. - 170 - 112 N ....... ....... c.> C\i I C\i 8 C\i I ~ ~ t+ +.: . ~ !: . i ~ ..~ ~ - ~ ...... ., > t!J I'll ++ ++ ~ ...... \1 I ~ ++ .-. ++ ... C) ....... > + +++ ~ (I? N c.> ~ I .. .. l ~ . ~ ~ ~ 0 ........ > Q) l? 0 0 .-; D cu c.; > ~ - crS j r"'" C\i t 8 r"'" C\i lt:l C\i ~ t\l I > I t C,) ....... l- > 8 t lt:l C\i ++ ... . . . L. .. . . . . . . . ~ ~ ~ ~ (I? C\i t!J . -t I'll -t- ... 1\ ~ .. ~ ~ " f-• I ~ Figure 6-13. 100 GeV le decay distributions int,." for i tpn I < .15 (GeV /c) 2 . The points are 10 values and the curves are from fits described in section 6.2 . ...... >., ++ I ~ +:;:::. \ ~ C) ....... ++- ft ~ CQ f ....... ~ ~ -: ~ ~ 0.. ro c: ::s s:: ::s0 () 0J I f-" Ol ro ~ (JQ " ti "2 I- t .. 1 ... I- f t Y+\J -T_. 2 GeV 2 , ~ I \ ur · '\f I / II I ~ IW t .~~~ 1 r .~~~..I u• II .~~ m" 1 ' 1 1.4 - 1.5 GeV /c2 Pitl I 1.5 - 1.6 GeV /c2 "ltf t t.6 - 1.7 GeV /c2 2 I 1.1 - 1.2 GeV /c 2 1.2 - 1.3 G<!V /c2 1.3 - 1.4 G<?V /c2 T i .I '111\11'~ lo! II r JW ., [ 1~ ~ . .~~j t J -T,.,.. 2 J GeV 2 .80 - .90 GeV /c2 .90 - 1.0 GeV /c 2 1.0 - 1.1 GeV /ce ll:t .., tll ., 4 t ~ rY I 2 -T..,,. 100 GeV /c I 1 GeV2 I I .60 - .70 GeV /c2 .70- .80 GeV /c2 I~ - 172 - ++ CV () ' > a Q) ("? C\i I C'.i ' ~ - ++ ~ t 1- al al() t\i ~ • ..:...+--- - C.) t+ ...... ~ a "'N >Cl ~ t!J .,....; ++ . I r-: t+ N f-= I -+---+- + . N : fl "'N > " t!J N~ I . I ~ 2 Figure 6-i4 . 175 GeV le decay distributions in t1i1i for I tpn \ < . : 5 (GeV /c) . The points are ! 0 values and the curves are from fits described in section 6.2. p.. ; ~ c g f) ...j'.. '_. I (J) ~ (1) C?tl ~ J 1D 11 - k t- I 'f . ,., ll .~ ~\ I 11 _ I 11 .. 1 -T... 2 GeV J 2 1.4 - 1.5 GeV Ice ti J n __ I .I~ ~ ) .l I ti ,,.., trt2 .••'L l\ .. l l'l' m' le•.~ 1.5 - 1.6 GeV /c 2 1J!J I II I. I I 11 I I !'\Tl ttl 1.6 - 1.7 GeV , -T.... GeV 2 2 1.1 - 1.2 GeV /c2 1.2 - 1.3 GeV Ice 1.3 - 1.4 GeV /c2 I u' "' ·- r1M ~.ii 1 JW ",l t -T1111 , 2 J GeV2 .80 - .90 GeV /c 2 .90 - 1.0 GeV /c2 1.0 - 1.1 GeV /ce 1rt2 ,.a 11• 4 I • ~1 r ,:..; ~ 2 -T_. GeV2 175 GeV /c 1 J .60 - .70 GeV!c2 .70 - .00 GeV /c 2 4 I GJ -J. ,_. 10 8 6 4 N ,,,,., I -. CJ ...... > Q) 8 _... '-' m6 4 2 6 ACCHD! 63 G•V/c 0 1.5 2 2.5 m1T1T' 3 3.5 4 GeV/c2 Figure 6-15. Exponential slopes (in tmr) for the high mass forwarc pe :=.ks of figures 6-13 and 6-14. Also plotted are slopes found by the ACD~ OR group for the rrrr scattering intensity [Da79]. The errors claimed by Da79 are comparable to the symbol size. 6.4.1 High Mass Exponential Slope Figure 6-15 shows the exponential slopes from our high mass fits, along 1~ith values found by the ACCMOR group. We have excluded the highest 100 GeV l e mass band and the two highest at 175 GeV le as unreliable. Reasonable fits were obtained in the other mass bands . Our results are reasonably consistent vvit.h the ACC~,:OR values. We both have roughly the same B values. and both experiments see a fall in B with mr mass. Our values appear to fall faster than theirs and are systematically lower. However, they were able to analyze their data much more fully, including a - 175pole extrapolation using PMA [Da79]. In our data, we found that our slopes increased (as did errors) when we made smaller tpn cuts and dropped a bit when we expanded the cut. This leads us to believe that we probably underestimate the pole extrapolated slopes. (The slopes of figure 6-15, and not pole extrapolated values, are appropriate for acceptance corrections.) We do see that our slopes are, within errors, independent of P/.a.b. Such behavior is expected if off shell mr scattering is a meaningful process. Note that the slopes of figure 6-15 are in terms of t 1Tn· Plotted in this way a significant factor of q 2 is removed from slopes in terms of coseJ. Despite a slight antishrinkage, the relatively constant slope in tmr is characteristic of diffraction. 6.5 Dips Virtually every polar angle (cose;. tmr) distribution given so far has one or more dips in it. A number of authors, Odorico [Od71, Od72ab], Pennington [Pe73]. and Eguchi et. al. [Eg74] have all stressed the importance of amplitude zeros in any global understanding of rrn scattering. Pennington emphasized that nn amplitude zeros are closely related to the dips seen in the decay distributions. The apparently smooth evolution of our dips makes such an interpretation attractive. Taking observed quantities as the real part of the dynamic variables, dip locations track the real parts of the amplitude zeros. The depth of the dip is related to the imaginary part of the amplitude in the case of observed data. Alternately, the depth is related to the imaginary part of the zero, which is not observed and can only be obtained by amplitude fits. The presence of backgrounds may move the dips relative to the nn zeros, but if these are small, we can get a reasonable map of the real parts of zeros by following the dips in our distributions. The net mr scattering amplitude is almost surely a complicated sum of different amplitudes, and if dips in decay distributions track anything, it is zeros or minima in the net amplitude. - 176- Pennington warns that following dips in da/ dO is not by any means general enough for a full understanding of the 7r7r amplitude zeros. The exercise still seems a useful first approximation for observing the dominant patterns. Figure 6-16 shows our patterns. In this figure, smT = m~ and -tmr are used as the dynamic variables. lines of constant umr are parallel to the diagonal cose1 = -1 line. The kinematic boundaries are this line and the -t mr = 0 axis. The dots ( · ) were obtained from projections of our 100 GeV le moment results since 50 MeV lc 2 binning was available. The points labeled "I" were from the same source. The dots locate clear dips, while the I's locate breaks in the cose; projection of the fit results. Since the points in figure 6-16 were obtained by hand, errors for the I's (in tmr) are large, and some of them, especially the ones clustered at s = 1. may not be real. The arrows locate mass bins where the 100 GeV le moment distribution was falling as cose1 =1 or cosB; =-1 was approached. The open circles are dips and breaks taken from high mass 100 GeV le slices of figure 6-13, and the x's are 175 GeV le data from figure 6-14. From figures 6-13 and 6-14 we can continue the map of the leading dip but have essentially no information on the others. We see at least three families of dips (breaks are included), labeled A - D. B - C, and E - F, in the figure. The patterns are sufficiently striking that some discussion in terms of models seems appropriate. For this, we assume that our dips follow rrrr amplitude zeros, and -will try to understand the observed patterns in terms of either of two dominating amplitude structures. Without detailed fits. the following discussion must be considered somewhat speculative. An appealing dynamic origin for zeros is found in the Lovelace - Veneziano model which has the amplitude structure r(1-as)r(1-at) ( t ) = ------vs ' r(1-~-a,) (6.4) where CXz = a~+aJ·x. In equation 6.4, s, t, and u, are smt, tmT, and u11'1T. For real - 177 - F 12 x II 10 x 0 N i >~ '9 ,, x 7 ..., <C)'S ox o" " J:: F U> 6 • 5 0 • . ct( 3 t l 1 c l 2 .. .. B A 0 2 3 ~ 5 6 7 8 10 - t '11T J Ge V' F'igure G-16 . Pattern of decay distribution dips seen in our data . Symbols are.; explait1C: d ir"- Lhr_· Le~:t. - 178 - pion targets and rrrr _. rrrr, Smr + Umr + tmr = 4m: . (6 .5) Forbidden double poles in the numerator of (6.4) are killed off by the denominator [Ve68]. This process creates zeros away from the double poles, and their dependence on smr, tmr, or Umr depends on the condition (6.5) and the ai. Assuming constant a:i leads to zeros at constant Umr· Small deviations from this may be related to finite resonance widths or variations in a. 0 , and a 1 . Large deviations are presumably effects not contained in (6.4). Odorico noted that the zero associated with the p-p double pole enters the kinematically allowed region at m1i1T ~ 1 GeV /c 2 . He argued that this was the dominant reason for rapid drops in event distributions and moments at this mass. This explanation of the effect was contrary to assertions that the drops just reflected the coincidence with the 1iii ~ KK kine:natic threshold. Odorico supported his position by finding similar effects in other reactions where the KR threshold is not a factor, but the Veneziano amplitude is active [Od72b]. The dip series B - Eis consistent with this first Odorico zero. Equation 6.4 contains one extra fixed umT but non double pole killing zero, the Adler zero, which passes through the point smr = tmr =Umr =0. The KK threshold does lead to a wig- gle in the Adler zero [Pe73], and this is reflected in our dip patterns . In figure 6- : 6, the Adler zero corresponds to the dip series A - D. At rrrr masses above the resonance region, where the decay distributions resemble diffraction scattering, a more convenient way to consider l'(s ,t) is e:x-plicitly in terms of exchange models. In this case, the amplitude is the sum of amplitudes for allowed exchanges including p, f, and Porneron. Such models could lead to fixed t 1m dips although their actual location would reflect the full amplitude and no single part. In figure 6-16, the dip series C - Fis consistent with a fixed t rrrr dip at smr values above about 3.5. -179- Our low smr pattern of dips is in reasonable accord with the zero patterns given in Pe73 and Eg74, and our identifications were based on these sources . Our dips agree with Pennington in sending the Adler zero (line A - D) outside the kinemat ic boundary in the backward (cos9; = -1) rather than forward (coseJ = + 1) direction. Our dip shows a sharp wiggle nears= 1. Pennington remarks that such behavior is expected for a smoothly varying P-wave and rapidly varying S-wave, and is characteristic of the KK threshold. The gross behavior of this dip is rougt.J.y along constant U 1m though. The B - E series of dips also follow roughly cor.lstant (though deviations are larger) u11'n and evidently leave the plot at about s mr= 1. The third line ( C - F) of points is a series of breaks near ttm = 0. These and the c.rrows near s7T1i = 2 seem consistent with constant umr behavior. We see no dips tha'(, could be eas ily identified with higher mass double poles, for example the f -f, f -g, ac.d p-g do'Jble poles . If present, these presumably have large imaginary parts CI.ld. vie are not sensitive to them . We see two entries to the plot from the left; one (point B) at s I.ii ~ 1, c.:-id another (point C) at smr Rj 2. (The two arrows here are in neighboring mass bins .) The first has been identified by Odorico and others with the p-p double pole killing zero . The second exits the physical region nearest the the p-f dou8 le pole intersection [Eg74]. We note (as did Odorico [Od72b]) that the entry of fr.Js zero c oincides with the rapid changes in moments at mmr ~ 1.4. (The c.gree:::ent here is better than at 1 GeV /c 2 .) In this case, unlike the first Odorico zero, no convenient threshold is available to compete with the explanation. This observation in turn lends support for the presence of the Odorico mechanism at 1 GeY/ c2 . The B - E and C - F series of clips approach each other at s mt = 3, and we might consider whether or not the actual pattern is C - E, and B - F, or something completely different. The rest of this section is speculation on this question. The fixed u1m hypothesis implies that the zeros do not cross, and analyses of lower energy -180 data [Eg74] indicate no zero crossing. On the other hand. a sharp turn of the C - F · series is difficult to understand from (6.4) with constant or even near consteu.'rlt o.i . We might speculate that C - Fis not one zero but two, consisting of an Odorico zero and a fixed tTrn zero not included in the amplitude (6 .4). The Odorico zero would continue on at roughly constant umr but gather an imaginary part sufficient to obscure it in our low statistics data. (This seems inconsistent with low energy data.) Similarly, the fixed tmr zero would continue down in s1r1T, and while not pc.1tcularly strong at low masses, be capable of distorting the patterns associc..:ed v;i'.:.h other zeros. We note that in the region of -tmr ~ 1 both the Adler and first OG.o i'"i ~o zeros deviate and run parallel to a fixed tmr path for several mass bins each. Since the "constant" umr zeros clearly have distortions of up to ±.5 (GeV /c) 2 • ·we might admit such a possibility for any "fixed" tmr zero and allow it to move c.. b:t clcser to ttrn = 0 at the lowest masses, crossing the s1r1T =O axis at about -t nn = . 5. This slight bending increases the number of points along this dip significantly at lov; mc.sses and may explain some of the distortions seen in the first two "fixed u 1m" zeros . It would also add an alternative mechanism for the Adler zero wiggle. One final benefit might be to indicate how p exchange. whose trajectory crosses ze:o at t ~ - .6, contributes to a high mass dip which is closer to tmr = -1. These speculc.tions imply that exchange diagrams play a significant part in the low mass region. At any ra.te, while gross patterns can be "understood" from simple applications of so~e models an amplitude analysis is called for, but resolving ambiguities in sue~.!. an ar1alysis requires high statistics data. It will be interesting to see what the ACC\:OR colla- boration might say about the zero patterns. - 181 6.6 Review In the previous chapters we have described our measurements of, and results on the n-p 41f+Tr-n reaction. We have presented the cross section in the p 0 region, Gottfried - Jackson frame spherical harmonic moments for the mm reaction as a function of rrTr mass and as a function of tpn at the p 0 , decay distributions in cosfJ; rp; and tmr, and the high mass diffractive slope for the forward mr peak. (Fredericksen's thesis also includes effective pion trajectories at the p 0 .) We have confirmed the ACCMOR group observation of the fixed tmr dip at high 1m masses, and considered its mass dependence into the resonance region. Our low mass dip patterns are consistent with low energy results. Our basic conclusion from all this is that reaction ( 1.1) is highly stable . That is, the gross features and many fine ones too, haven't changed much in the PW> interval of ~ 15 to 175 GeV le. The cross sections at 100 and 175 GeV le are in rough accord with simple extrapolations from lower energies. The slowing of the shrinkage in <Y8 > might be considered a change from low energy trends, but a calculation of the Kimel and Owens model [Ki77] is needed. The high mass fixed trm dip was probably visible in some of the low energy experiments, but the ACCMOR group. was the first to publish its observation [Da79]. The analysis reported here has been more a survey of reaction ( 1.1) than a detailed study of one topic . For this thesis . the survey approach was adopted in the hopes of finding either significant changes in the reaction or demonstrating a general "stability'' with Pia.0 . For the most part, we found the latter. - 182 - APPENDIX A Kinematics. OPE. PMA A.1 Kinematics A brief review of kinematics for n- __. n+n-n and some notation definition are useful. Needed approximations are also given. We then discuss one pion exchange and the Poor Man's Absorption model (PMA) . PMA has been used as a method for isolating 1T exchange; that is, as a model for the "target" in rrrr scattering [Da79]. Our ability to use PMA is limited by our small data sample. Our track finding analysis provided measurements of charges and momentum . vectors (P), for the beam and the forward charged particles. Mass identification was provided by our Cerenkov counters once the momenta were found. The beam pion will be denoted by the subscript b, the target proton by p, the forward pions by f and/or charges, and the recoil neutron by n. The total forward system (rr+ + n-) will use f with no sign. Laboratory frame four vectors P = (px ·Py ,pz ,E) satisfying m2 = p2 =E2-p2 (A.1) are known, where m denotes the rest mass. These, along with the charges and a lab four vector for the target proton, Pp = (0,0,0,~). are our kinematic data. We use units with the limiting velocity c = 1 throughout. The total forward four momentum is P1 = P/ + Pj. and the total energy is E1 = Ej + Ej. Mandelstam invariants for rr-p ~rr+rr-n are (A.2a) (A.2b) and (A.2c) - 183 with (A.3) P} = m} is the Jr+rr- effective mass. In a pattern used throughout the thesis, we use tpn to distinguish (Pp-Pn) 2 from tmr = (Pb-P/) 2 . The recoil neutron is undetected. We determine that the unseen system was a recoil neutron by evaluating the squared missing mass, (A.4a) or (A.4b) and requiring, within the limits of our resolution, that Mx 2 = rn;. Equation (A.4a) was used for the missing mass calculation. At momenta above 30 GeV /c, our missing mass resolution, figure 2-11, causes the neutron Mx 2 peak to include negative values. Mx is not useful and Mx 2 is the proper variable. (A.4a) is also as good as we can do for Mx 2 . The missing mass necessarily involves differences between two large and poorly measured numbers, essentially E0 and E1 , and there are just no clever tricks to use for Mx 2 with an unmeasured recoil system. Our Mx 2 resolution is essentially the E1 resolution. The contribution from the error in Eb from the finite momentum slit width is negligible on an event by event basis. The effective rest mass, m1T1T• of the forward pions is given by m~ = (Pj + Pi) 2 (A.5) The mr mass measurement using (A.5) is as good as we need get. The mrr = 0 approximation. mmr =0 VP~ Pi~ is not useful, except to illustrate that the mmr resolution is set by both the lab momenta of the pions and the lab opening angle, e. -184- In practice, this form distorts the mass spectrum noticeably. The mass resolution can be improved slightly if we force Mx 2 = ~ by adjusting the forward momenta according to their resolutions. None of our other measurements were noticeably improved by this trick (actually attempted to improve on fPJ , defined below) and we abandoned it. Assuming we have isolated neutron recoil events (with only a small background), we can easily improve on the tpn measurement, (A.2b) . A more reliable and accurate estimate of tpn is (A.6) where pl is the magnitude of the transverse component of P1 measured with respect to the beam. The kinematic limit tmin, which for neutron recoils is (A.7) with Eb the lab beam energy, is negligible at our energies for most purposes . Monte Carlo studies have found equation (A.6) to be an unbiased estimate of tpn at all values except the smallest. A.2b sends a substantial number of events to positive (and unphysical) lpn. Equation (A.6) depends crucially on the recoil neutron assumption. At large missing masses, far from the neutron peak, one would have to appeal to (A.2b). Decay angle distributions in the forward 1T1T rest frame carry a great deal of information about the produced states and their production mechanisms . Tvvo planes are naturally defined. The production plane contains the beam, target proton and recoil neutron. The decay plane contains the forward pions and the beam. To work in the 1T1T rest frame, we apply a Lorentz boost of magnitude and direction -P; to measured particles. The 1T1T decay angles are commonly defined in terms of the 'Tr- direction with respect to one of two coordinate systems . In both, the y-a.Xis - 185 - Tr- Figure A-1. Lab and Gottfried Jackson frame momentum vectors. cpJ is assumed zero. is defined as normal to the production plane, (A.8) where the particle name denotes its rrrr rest frame momentum. The choice of z-axis distinguishes the two coordinate systems. In the Gottfried - Jackson (J) frame [Ja64], the z-axis is along the 1T1T rest frame beam vector: (A.9) In the "s-channel helicity frame" (H), the z-axis is directed antiparallel to the 1T1T rest frame recoil neutron, --n z=-lnl This choice seems conventional. ln both systems, x = fj xz, and the polar angle FJ is - 186 - p / / / / x Figure A-2. Gottfried - Jackson frame momentum vectors illustrating 9; and 'PJ. Production and decay planes are also shown. rr~ = rr--. The boosted proton momentum vector, P is equal and opposite to the laboratory rr+rr- momentum vector. defined as the angle between the rr- and z-axis. The azimuthal angle, cp, is defined as the angle between the x-axis and the plane containing the z-axis and ri-. Tue decay angles are then evaluated by a simple vector decomposition with respect to the a.x.es. Our resolutions for these angles were found insensitive to the calculation method, and the choice of which forward pion (fast or slow, rr+ or rr-) we use. The transformation between the two systems is a rotation about the y-axis. In this thesis, we use only the Gottfried - Jackson frame. Figures A-1 and A-2 illustrate the Gottfried - Jackson angles, eJ and cp;. - 187- In rough terms, the Gottfried - Jackson frame emphasizes the spin exchanged between the beam - forward and target - recoil systems, while the H-frame emphasizes the role of the target and recoil spin. Although the transformation angle between the systems is small at small t,,,., amplitudes in the H-frame that are dominately nucleon spin flip are mainly non fiip in the J-frame. ln the Gottfried Jackson frame, pion (spin 0) exchange is non-flip and A meson (spin 1) exchanges are nucleon flip [Wi78]. A.1.1 t 'tr1T At .,high•' masses, tmr seems a more natural variable to use than cos9;. The form tmr which is exact at tpn = =-2q 2 (1-cos6;) (A.10) m; is commonly used. In the above, q = .5Vm~ -4m~ is the final state pion momentum in the mr rest frame. We note here that one can define directly observable Mandelstam variables, s7m, tmr, and umr, even though tpn = P} < 0, where PE is the p-n four momentum transfer. These are given by (see figure A-3) =(P11 +Pg )2 (A.11a) tmr =(Pb - Pj) 2 = (Pj - Pg ) 2 (A.11b) smr = ( Pj + Pj) 2 'U1i1T =(Pl - Pb )2 = ( Pf - Pg ) 2 I (A.11c) and satisfy Smr + tmT + Umr = 3m; +tpn . (A.12) The definitions (A.11) seem quite natural. Equation (A. l la) is just mrm = -vs;;;. The - 188 - 1T f 0 + ....-----· 1T'f + n Figure A-3 . Mandelstam variables for 1T1T scattering. mmr .10 N ,,......._· = 2.0 GeV /c 2 .08 c.> ........_ >C) u .06 - ~ .04 I .02 0 0 .5 1.0 2.0 3.0 4.0 -tmr, (GeV /c) 2 Figure A-4. Fixed 1T1T mass dependence of -K for several tpn values . -189 - limit at coseJ = -1 ----- ___ {_ _____________ - .10 N ,-... C) .08 ....... > .06 Q) '-' ~ .04 I .02 0 1.5 2.0 2.5 3 .0 Figure A-5. Mass dependence of-Kat tpn = -.08 for trrrr = -1 and -3. values calculated through them, however, clearly apply to an off shell target of mass2 =tpn. (A.12) shows that upon extrapolating to the pion pole, tpn =m;, not all of smr. trm, and~ remain fixed . An estimate of the small errors (at low tpn) in equation A.10 follows from A.11 and A.12. Assuming fixed s mr and tpn, we obtain tmr = -2q 2 ( 1-coseJ )+ K (A.13) =2{3q 2 cosG; -mmro. (A.14) where K =(m: -t,. )/ (2mmr) and p =Vl + o(o+mmr)/ q -1. We note K < 0 for physical tpn, K = 0 at~ =m:, and K _. 0 as tmr _. 0. Figures A-4 and A-5 illustrate typical 6 2 K values. In A-4 we plot -K vs tmr for various tpn values and mm,= 2 GeV /c 2 . In A-5 we fix tpn at -.08, and plot -K vs m1T1T for two values of tfm. Also, if we fix both tpn - 190 - and trm (or cosBJ ), we find K is almost independent of m7T7T · K is strictly independent of Plab . Equation A.10 is good enough for our purposes. We note that our acceptartce grid is in terms of coseJ, not tmr. At low tpn and at low tmr K is negligible, and our bin sizes are relatively large . The place where K would be largest, coseJ R: -1 is affected more by the q 2 factor in (A.10) changing over a mass bin than by K. In some cases (scatter plots) we have used tmr from (A.11b). For our high mass fits and dip maps. we have used (A.10) to transform results obtained in terms of cos9; . A. 2 One Pion Exchange The one pion exchange model is among the oldest descriptions of the strong force. Indeed, its roots are the work of Yukawa [Yu35], in which the existence of the pion was postulated to explain the short range of the nuclear force. The importance of pions as the dominant quanta of soft collisions follows from their being the lightest observable strongly interacting particles. More modern origins of the model. applying it to high energy reactions, are the work of Goebel [Go58], Chew and Low [Ch59], and Drell [Dr60]. Goebel, Chew and Low also opened the related field of ?Trr scattering . The strong force at "large" distances of order 1 fm, is such that single exchanges are not a good approximation of the force , but they remain important first order terms. Figure A-6 is an OPE diagram for rr-p ~ p 0n with p 0 4 rr+?T-. The one pion exchange differential cross section is [Ma76] (g 2/ 4?T)(-tpn) daU/ ---e(tmin-tpn). (A.15) dcoseJ (tpn -m;) 2 The e function expresses the t min cutoff of equation A.7, qcm is the center of mass momentum of the beam rr- proton system, s is given by equation A.2a, and q 7m is - 191 - Figure A-6. OPE Feynman diagram for p 0 production. the 1T+1T- breakup momentum (see equation A.10). The term da~!,f I dcos9; includes any resonant amplitudes from the upper vertex. We observe that this form has no cp; dependence on the right hand side. Following from the pion spin being zero. this gives the Treiman - Yang test for 1T exchange dominance: \PJ distributions are flat . The next essential point is that the -tpn factor in the numerator, which comes from nucleon vertex terms, implies d a/ dipn = 0 at tpn = 0 . Neither prediction is born out in mrn. Distributions in cp; are not flat. The cross section does not go to zero as lpn--+ O. although the observed cross section does have a forward dip in d a/ dtpn. below tpn Rl m; . Also . d a/ dtpn has a much steeper tpn dependence than implied by OPE. These and other failings have been taken not as evidence that pion exchange doesn't occur, but that the strong force contains other significant effects . One pion exchange alone is not viable. but pion exchange must be an important factor in any situation where the strong force is present, quantum numbers allow it, and collisions are not so violent that finer scale structures (quarks) are evident. - 192 Simply introducing form factors to collimate da/ dtpn doesn't do anything for the r/)J dependence, and neither does simple Reggeization of the rr exchange . Hov'.7- ever, more sophisticated Regge models [Ki73, Ki77], which explicitly include rr, A 1 , A2 poles and cuts as exchanges are in quantitative agreement with rr-p ~p 0 n data at energies up to 63 GeV le. The Kimel et al. models are quite involved and have been tested only at the p 0 . Absorbed rr exchange models for mrn have also had some suecess, although they are mainly useful in situations where other exchanges can be ignored or lumped together as part of the absorption mechanism. Since we have referred to one such model frequently, we spend some time describing it. 7.3 PM.A The Williams, or "Poor Man's Absorption" (P:W.LA) model, [Wi70, Fo71a], as extended by Wagner, Ochs, and Shimada [Wa73, Oc73, ShBO] provides a useful framework for discussing our data. The simplest absorption model to remedy the gross defects of simple OPE, PW.A has been rather successful at lower energies in describing rr-exchange dominated reactions in the low Itpn I region. The tpn dependence in PMA is governed by a pion propagator, absorption, and by angular momentum conservation [Wi78]. Although recent results [Wi78] have sho¥m the limitations of the model, the qualitative success of PMA is impressive. Although PMA is usually formulated in terms of s-channel helicity frame partial wave amplitudes, it is more useful for us to use forms based on production amplitudes in the Gottfried-Jackson frame . Ochs and Wagner [Oc73] e}qxess the full P1IA amplitude in the Gottfried Jackson frame as _JJ_{ Y-f;;; Fo - CA mmr Fi exp ( . Fo. - 4 2 7r tpn -mn 2 2 mmr -mn -U:XC/)J ) -ae a } T (mmr 2 ) ,eJ J I (A.16) where we have specialized to the case of rr-p --> rr+rr-n. T is the 7T1i elastic scattering amplitude, and has no explicit tpn dependence. The rr+pn coupling constant is - 193 - g 2 /4rr=29.2. tpn. Fn=Fn(mmr.tpn) are collimating form factors with Fn=1 at =m:. CA is an absorption parameter. Absorption is expressed by this and the form factors. The index a. = ±1 gives the s-channel helicity frame nucleon spin flip, and the factor m1T1T I (m~-m;) ~ 1/mmr results from a rotation from the s- channel helicity frame to the Gottfried Jackson frame. Absorption correctiorIB are most naturally introduced in the s-channel helicity frame, even though the Gottfried Jackson frame may be more convenient for later work Assuming both schannel nucleon flip dominance and small tpn, Ochs and Wagner find that the mrn cross section has the form (A.17a) where l l cA 12 2 - tpn 2 IT 12 + I m1T1T F2 aT 12 I' o = (m;-tpn)2 Fo (m;rr-m;)2 1 8€J; , (A.17b) J I .1 = ~ (m1T2 -tpn ) F F R 0 1 e cA ( mmr - a T 12 m 12m -mn2) 8€JJ 1 1 I (A.17c) The factor q = .5Vm!r -4m; is the final state pion momentum in the mr rest frame. PMA does not specify the rrrr elastic amplitude T. That is, it is not a 1T1T scattering model. Rather, it is a model for the tpn dependence of the "target" pion and its major background. Jn PMA, the background is determined solely by the absorption of elementary one pion exchange and angular momentum conservation. The original Williams model, [Wi70], effectively assumed CA = 1. Estabrooks and Martin [Es72] showed that, at the p 0 mass CA has a small imaginary part. Ochs and Wagner [Oc73] then determined Re CA from the Cern Munich 17.2 GeY 1i1Tn data. They found that Re CA depends on m1T1T• dropping from (an assumed) 1 at - 194 mnn< .9 GeV/c 2 to R=l.4 at mmr=l.9 GeV/c 2 . Accepting CA as a mass dependent parameter resolved the major problem with PM.A. and extended its useful region from just the p to all mr masses. The low Itpn I nature of PMA is emphasized by equations (A.17), which admit no moments <Yr> with m > 1 [Oc73]. This is certainly not the case for Itpn I~ .15 (GeV /c) 2 . Both this, and lower energy experiments see significant m = 2 moments at larger Itpn I values. Both A1 and A 2 exchanges have been found necessary in rr-p ~ p 0n, largely with the help of a high statistics polarized target experiment [Be79b, Be79c, Ki73]. A Regge model [Ki77] including these exchanges as well as rr exchange has been found in quantitative agreement with the tpn dependence of <YI'> moments for the p 0 at 63 GeV, [Al78]. At fixed mmr, the A-exchanges are predicted to become more important with increasing PlaJJ, but at any given Ptah, less important with increasing mmr. Associating m =2 moments ·with significant A exchanges, our results imply that they are mainly important near the p mass, and are apparently a minor feature at mmr '.:>1.5 (see figures 6-3 to 6-10). In this light, we assume that PMA is an acceptable framework for describing our low tpn data. PMA does successfully predict a non vanishing d a/ dtpn as tpn -i. 0, and the presence of significant m = 1 moments at low It;m I. At low energies, a prediction [ Oc73] that the ratio <Yf> "1L(L+1) < yt> -mmr (A.18) does not depend on L has been verified. (The ratio does depend on Re CA.) Section 5.5.1 repeats this test. The collimating form factors Fn are not specified by PMA, but are usually taken 5B (t to be exponentials of the form e · n pn -m 2 ) 11' , and often the En are taken to be equal. The exponential form for Fn seems well established at low energies, however, - 195 - Wicklund et al. [Wi78] established differences in Bn for P1t..\ amplitudes applying to specific partial waves at the p 0 . They also observed PLa.0 dependences which extrapolate to~ 9 to 11 at our energies, depending on partial wave amplitude. Consider- ing our relatively small data set, it seems reasonable to assume (A.19) with B around 10 to 15. - 196 AppendixB Trigger Electronics An overview of the trigger electronics is given in figure B-1. This system was designed by R. Gomez and J. Pine. Essential differences between E110 and E260 were the multiplicity and veto counter electronics used by E110, and deletion of the E260 calorimeter electronics. The general structure had three stages. First a pretrigger flagged an interacting beam particle. Then, if the pretrigger survived various tests for spectrometer readiness or double beam, it "strobed" the multiplicity outputs of several of the pwc's and veto counters to determine if we had a "trigger". We considered a trigger to occur at this point whether or not the spark chambers could fire. The third stage involved the spark chamber firing electronics and fast reset inhibit. If the spark chambers fired, various latches held the trigger electronics and scalers idle until the event was read into the on line computer. They would then resume normal operation, but the spark chambers would not fire until a preset recharging (dead) time had elapsed. The events actually recorded on magnetic tape are viewed as a random sample of the triggers we had. The trigger system was built to take advantage of the 18 ns rf. structure of the Fermilab beam and the relatively low intensities required for this experiment. Fast logic pulses were typically about 5 to 10 ns wide. The fast electronics were NIM standard Lecroy and EG&G modules, with Latches, OR's and AND's being Lecroy 364 or 365 units set to appropriate levels. The multiplicity logic was built by our group. Assuming the spectrometer was ready to accept a trigger, and we were within the "' 1 second long BEAMGATE (derived from beam start/stop pulses provided by the lab), the trigger sequence began with the arrival of a beam particle, BEAM =Sa · Sb · Sc · BEAMGATE which suffered a (loosely defined) interaction, (B.1) - 197 MPS TRIGGER ELECTRONICS - OVERVIEW PRE TRIG LATCH no STROBE KILL) MSTRST SHIFT REG RESET LAM 2 (3 INTBM 2X2-----1 BRINHJAW - - - a MULTIPLICITY ELECT SHRG D.C .......---. DC RECEIVER WINDOW DISCS MAJORITY LOGIC Figure B-1. E: 10 trigger electroilics oveniew, see text. JNTBJ.1 = IB2x2 + JBDEDX = (BEAil · 2x2) + (BElJJ · DEDX ~ 2) :::' ?) (.i--.- as sho\•,-n in figure B-2a. Tne IXTB~,: signal set the pretr-igger latch \';~hich sent a clipped. li::J.e she.~ed signal, SHRGLO_!:J), to load the shift register. Settin.g of the PRET:RlG LA.TCE ~tcp~e::l accu...rnulation of effective beam, EFFB~L U!'ltil a master reset pi.:l.se, 1~STR~T. re::d the latch. An output of the PRETRIG LA.TCH was shaped, split, and sent off to the reset logic, strobe kill generation, and trigger logic areas. Unless a spark chs..:r1jer trigger occurred, the pulse sent to the reset logic created a 1~STRST pulse to clear the PRETRIG LATCH. The pulse sent to the trigger logic had to survive a "STROBE KJLL" to reach it. (At 20 GeV, a large electron and muon background prompted us - 198 - BEAM AND INTBM a) BMGATE So Sb IB2X2 (TO TRIGGERS) Sc INTBM (TO PRETRIG) LATCH STROBE KILLS KILL LATCH So PRETRG SHRT STROBE KILL BB ~4 BRL JAW PRETRG SHRT -,__ LJ"'"" VETO KILL MSTRST DEDX LATE SH RT --=-....r:-=------t PRETRG - - - l LONG (200ns)1-...1""" b) DE DX LO'""'"No..;:;.G~~--1 (200ns) L--..J PRETRG .._,SHRT DEDX - - - - - 1 2'.3 EARLY INT Figure B-2. Bea_'tTI. counter and Strobe Kill electror.Jcs. to use C0 as an on line veto at the strobe kill. The STROB:S scaler the:-i recc:"~e~ the effective beam used in cross sections.) The strobe kill electronics, figure B-2b, were provided to ins'..l!'e the.t the spectrometer was in a relatively clean state prior to an event and to veto po:ential triggers by multiple beam particles. A second bea..u. particle arriving necr iE L::J.e to the pretriggering particle, either before or after it but "\\ithin the resohing time of the proportional chambers, could easily satisfy the two body trigger electror.J.cs. Early and late particles in a ± 200 ns window were flagged by the DEDX counter and - 199 resulted in the EARLY and LATE kill pulses. Another test for multiple particles was to use the output of the BBX, Y and U chamber daisy chains and require BEX+ BEY+ BBU =BB~ 3 . That is, kill on BB~ 4. Finally, a kill for two particles in a single rf bucket was provided by the Sa counter, with a discriminator set just below the two particle peak. In the spring '77 data, we threw away more single particles through Landau fluctuation than actual double buckets. The Sa2X kill rate was "' 7% while the real double beam rate was <'. 1%. (For the winter '78 run, we added an Sb2X discriminator and required Sa2X · Sb2X for the beam counter kill. The <'. 1% number was taken from the winter '78 data with the SaSb coincidence required.) We also required that the photon vetoes, Barrel and Jaws, be below threshold at least one bucket before the pretrigger event. This was mainly important for the Barrel which could suffer large, slowly decaying pulses, from halo strikes. A failure to be below threshold before the pretrigger event caused a VETO KILL. The timing for creating all the fast kill pulses (all the above except BB) was set so that the pretrigger pulse would not kill itself. The STROBE KILL pulse was then STROBEKILL = 2XKILL · EARLY KILL · LATE KILL · VETO KILL (B.3) 2XKILL = (Sa 2X) · (BB'?_4) (B.4) where In Run Il, the 2XKILL also included an Sb 2X signal to reduce Landau fluctuation losses. The STROBE KILL was latched until reset by a MSTRST pulse. If set, the output of this latch intercepted and vetoed the pretrigger pulse on its way to the trigger strobe of figure B-1. Surviving pretriggers were known as STROBEs. A bit over halfway through Run I (at run 281), a previous interaction kill was added to the strobe kill in response to 'old' events too often superimposed on good - 200 - events. This E~~LY INTER.\CTION kill was generated by a pile up gate v1ith 112 µs output duration fed by a DEDX ~ 3 signal. As fo~ the other kills, the timi:::1g i:--::..s such that the pretrigger event ·wouldn't kill itself, but any interaction Vvithin 112 µs before the event would ki.11 the strobe pulse. VETO LOGIC f3 24 f3 I f3 2 BRLINH(5-8l BRL I NH (9-12)____,__ BRL INH(l3-16) BRLINH(l6-20l 8RLINH(21-24 __. f3 3 f3 4 BRLINHJAW Jaw I Jaw 2 Jow3--0-J BR L JAW (TO ,____~STROBE KIL L) Jawl2 Figure B-3. Photon veto electro:n.ics . Note the..t the Lead y~ ~: E:.:'°'.;.d. c''"b:;~' photon detectors doY·.T1strea.m o~ the magnet ·were not in the t:."igE;er. The STROBE KILL (EARLY E'JT kill) did not r.:u:.ke decisions based. 0:--1 the fc~\"-c.~d topology of the event under consideration; it looked either upstream of the target (multiple beam) or at the readiness of the spectrometer prior to the event . Thus, - 201- in terms of the reactions of interest, the strobe kill was an unbiased rejection of pretriggers. Th.at, in turn, is equivalent to throwing away the effective beam accumulated in order to generate the pretrigger. Over a large number of pretriggers, this fractional loss of effective beam is proportional to the scaler ratio STROBE/PRETRJG, and we correct the EFFBM scaler by this ratio in cross section calculations. Veto counters, depending on the trigger, were used to reject events on their own merit. and not for reasons of beam condition or spectrometer readiness . Their electronics is shown in figure B-3. The Barrel and Jaw inputs are phototube pulses, the {3 chamber signals came from special outputs of its current division amplifiers and were 8-wire groups located to cover the division between two barrel staves. The veto output BRINHJAW was an "or" of the Jaw counters and {3 inhibited Barrel counters. The f3 inhibit was included for the main proton recoil reaction, K°rrp, which needed veto coverage, but did not want protons penetrating the Barrel to cause vetoes. For 1r1rnr. the {3 inhibit on the veto. in turn. required that we use f3 =0 in the trigger explicitly. This {3 =0 signal was derived from the shift register daisy chain, figure B-4b, (which had a lower effective threshold than the (3 chamber inhibit). The f3 chamber inhibit pulses. and each output of the Barrel and Jaw counters, all had tag bits. Examples of the multiplicity logic are shown in figure B-4 for the A station and p chamber. The BB and r chambers followed the (3 chamber example, and the many BCD combinations were similar to the A station setup. The shift register multiplicity (daisy chain) outputs were analog signals proportional to the number of hits in a chamber (AJOUT, see figure 2-9 in section 2.3.7). The daisy chain receivers matched impedances and had output lines to the window discriminators and to our ADC' s. Each window discriminator module had one input feeding four window discriminators. Each discriminator had two independent digital settings from one - 202 - MULTIPLICITY DAISY CHAIN WINDOW RECEIVERS AX2 SHREG LOGIC (A-chambers) a) MAJORITY LOGIC DISCRIMINATORS 0,1 A(0, 1)3/3 l 2 A(2) 213 ~I A(~I) 1/2 DC A(2!2) 1/2 AY2 SHRE DC b) ~-MULTIPLICITY DC RECEIVER SHAPER LECROY 621 1 SH~E~/3~ DC1,,~ L.:.J AU SHREG DC PHA Figure B-4. Multiplicity electronics (examples). to eight and was designed so that a low limit of eight or a high limit of seven turned off that limit. The digital outputs were high impedance and paired so that chains of discriminator outputs could be set up. The majority logic units were similar to the window discriminators except that only lower limit settings were available. Thus the majority test was based on the sum of the window discriminator outputs. The A(2)2/3 pulse was then formed by at least two of the three ("2/3") A chamber window discriminators claiming two "(2)" hits in the daisy chain. The window discriminators and majority logic units were not gated. This was a . relatively slow part of the electronics, pulses were long to cover pwc rise and fall - 203- lr7rnT TRIGGER A (2)2/3 BCD(2)5/6 {3~ I IB2X2 BRINHJAW TO 7r7rnT SCALER STROBE TRIGLOG OR (no prescoler for Tr7rnT) OTHER TRIGLOGS Figure B-5. Final trigger selection for rrrmr. times, the rise time of shift register daisy chains, and timing differences resulting from particle flight times between chambers. Signals were a bit noisy, and at high multiplicities subject to late changes of mind about the hit counts by the shift registers. However, the system was fairly reliable at multiplicities ,. . , 2 or less. The trigger coincidence is shown in figure B-5 for the rrrrnr trigger. It was formed by an "AND" of A(2)2/3 and BCD(2)5/6 from the majority logic units, ~1 (that is, {3 = 0) from the {3 multiplicity electronics, and the IB2X2 (interacting beam 2X2) pulses. A pulse in the BRINHJAW line could veto the whole mess. If these conditions were satisfied, and the strobe pulse existed (has not been killed), then the 'TT'rrnr trigger was formed. Whether or not the spark chambers fired, we consider that the experiment has triggered at this point. The number of these triggers was scaled and used in the arRIGLOG calculation for mm . Table B-1 lists the requirements for the Run I triggers. Some of them, mrX, rmB, 3rrP , and the curve through (CT) were used to develop correction fac- tors for the rrrrnr data. In the table, "W" is the range, or "window," of hits allowed for the chambers of a group, and ML is the majority level required of the group. V - 204- TABLE 2-8 Trigger Requirements Trigger DEDX 2x2 v {3 A w IB DEDX(a) ~3 m 2x2(a) Yes Yes 1fP 3np mrn1 mrnp mrB ~1 ~3 <2.7 mrX mrnH K°np K°mrX K"X°X BCD ML W ML Yes Yes Yes Yes ~2 1 0 2 2 0 2 2 Yes ~1 Yes Yes Yes ~3 ~1 Yes Yes C.T. (Curve Through) Require only: 2-4 2 2 5 2 zCb) 2 3 3 3 2Cct) 4 3 3-5 0 zCd) ~3 5 2 2 2 2 ~1 O, l ~1 (c) 2 2-4 r 5 2 1,2 1,2 3 1 5 0-3 5 0-4 0 Brl=1 0 Jaw=O 1 3 3 3 2 5 2 3 BCD' Special D w ML W ML ~2 2 1 2 2 2 ~1 1 1 5 BEAM · 2x2 Notes: (a) IBDEDX and IB2X2 are or'ed to form single IB, (b) Band C chambers only, (c) {3 or a Barrel hit required, (d) x and y planes only. refers to BRINHJAW = 0, 2x2 is INTBM 2x2 . The various triggers were OR'ed in a daisy chain to form the TRIGLOGOR pulse which was also scaled. The prescale unit ( divide by N) of figure B-1 was not in the electronics for 1T7mr or the other major triggers. Its purpose was to reduce the nmnber of spark chamber triggers for the background reactions by giving a nonzero output only every Nth input pulse, N being set by s¥¥itches on the unit. The prescale units were connected as shown for all background triggers except rrrrB , which did not need one, IE and rrp elastic. These last two used the spark chamber trigger pulse, SCTRG of figure B-1, as input to the prescale unit. - 205Unless the spark chambers were ready to fire, the TRIGLOGOR output was inhibited by the spark chamber dead time latch, SCTRG LATCH. In this case, the PRETRIG and STROBE KILL latches were reset by a fast reset pulse derived from a suitably delayed PRETRIG pulse, and the whole multiplicity electronics started up again with the next interacting beam after the clears. If the spark chambers were ready, the TRlGLOGOR signal initiated the spark chamber firing and dead time electronics and set the trigger latch, TRJGLATCH. The output of this latch intercepted the PRETRIG pulse and halted the fast resets. With a spark chamber trigger, all latches using the MSTRST reset remained latched, until the on line computer completed its data acquisition and sent a PDP-11 CLEAR pulse to generate a MSTRST. The PHALD pulse from the TRIG LATCH was shaped near the ADC's and used for ADC load gates. The output of the SCTRGLATCH was clipped and fanned out to the spark chamber prepulser (to fire the chambers), the spark chamber dead time generator (a pair of EG&G - GG202 gate generators in series), and a gate generator to create a pwc "clamp". This clamp prevented electronic noise from the spark chambers from unloading the shift registers. The SCTRGLATCH was reset by a pulse from the dead time generators. Most Run I data taking on multitri.gger runs was with a 20 ms spark chamber dead time, although this was 30 ms for early runs (through the 50 GeV data taking). The dead time was set to 50 ms for curve through "alignment" runs. Run II multitrigger running was mainly with a 10 ms dead time (which was comparabl~ to the computer read in time) . A number of Carnac and visual scalers provided essential normalization data as well as monitoring functions. The EFFBM, PRETRJG, STROBE, and TRIGLOG scalers were used for normalization. each trigger having its own TRIGLOG scaler. In addition, scalers for BEAM, INTBEAM, TRlGLOGOR. and SCTRG monitored the electronics. SCTRG was nominally equal to the number of events written on tape, differences - 206 occurring only in cases of tape or computer errors. Such errors were random, and do not affect our cross section results. Early in our data taking, an inefficiency of a few percent was noticed in some of the trigger tag bits. section 2.3. 7. This resulted in events on tape whose trigger couldn't be identified. Although this did not affect our cross section analysis (see section 3.4), the loss of events traceable to a given trigger was undesirable, and a second set of tag bits was added with more liberal loading gates. - 207Appendix C TEARS C.1 Overview TEARS [Fo75, Br79] performed our tracking and vertex analysis, tackling the time consuming pattern recognition job of track finding from chamber data. For mm and other non-vee triggers, it made no judgements on events beyond setting flags for successful operations such as the vertex finding. Selection of good events from the TEARS results was left to later analysis programs. For vee triggers, such as K°rrp, the desired topology was an integral part of the formalism. The tracking began downstream of the MPS magnet with independent xz and yz view fits and a view matching operation, sections C.2 and C.3. Next, a beam particle trajectory was found, section C.4, and then the front end (between the target and magnet) analysis began, sections C.5 and C.6 . The immediate front end goal was to find "links" for the matches, meaning front end tracks that joined to the matched tracks at the magnet and find their momenta. The next goal was to locate main and vee (depending on the trigger) vertices. Distributed throughout these analyses were several "cleanup" operations designed to remove most spurious tracks and matches and yet remain highly efficient for real particles. The front end a!lalysis was performed twice on every event using the systems ''Vtrig" and "Targtrk", optimized for topologies with and without secondary vertices (vees) respectively. Both sets of results were written to DST's, but for CST's and beyond we specialized to the results of the system appropriate to a given trigger. On CST's, the Vtrig results were written for the vee triggers, K°rrp, K°rrrrX. and K°K°X. Targtrk results were used for all other triggers unless Targtrk failed . In that case Vtrig results were substituted as a backup. Sections C.2 through C.6 give details for the various analysis steps. - 208 - C.2 Straight Line Fits Our tracking both before and after the magnet sought straight lines separately in the xz and yz views. For simplicity, we discuss this for the after magnet tracking here and note front end differences in sections C.5 and C.6. The straight line tracks were found by the routine Onevul. which directed the pattern recognition, spark deletion for>!' minization, and single view cleanups, and the routine "Fitlin", which did the actual x2 fits. The pattern recognition began with spark searches. If there were enough sparks within a 1 cm "road" connecting a spark near the magnet (in the El or a D chamber) to one in or behind the F2 chamber to satisfy the minimum spark ("minspk") requirements a ")(- fit would be attempted. At most one spark (the closest to the road center) per chamber could be included in a road, and both overall and all group minspk requirements had to be satisfied, see Table C. l. A road was rejected if the spark requirements weren't met, or if its defining sparks were already part of a track satisfying X= x2 1 (total sparks-2) ~ 2.5 =Xo· I fit to a straight line was made on the sparks within it. If the resulting xwas less than xo. the track was passed to the single view If a road was successful, a cleanup. If not, high >f sparks were successively deleted and a refit performed until either x< Xo or all minspk requirements were reached. In the latter case, we required x~x 1 = 5.0 in order to keep the track. In these fits, the spark resolution of each E chamber was taken as .7mm, and the resolution of each F spark chamber was set at LOmm, values consistent with residual widths observed in chamber alignment studies (see Fr82). For proportional chambers, the resolution was nd/ ...JI2,where d was the wire spacing, n the number of consecutive wires firing, and 1/ ...JI2 the standard error of a square, unit width distribution. To avoid biasing against crossing tracks or high multiplicities expected on some triggers, sparks were never "erased" when tracks containing them were found. - 209- Table C.1 After Magnet Track Requirements View Pass x 1 x x x 1 1 1 y 1 y y y 1 Chambers E1,E2,E3,E4,F1.F2, F3,F4,Dx.Dx',F''x Dx,E1 ,E2,E3,E4 F1.F2,F3,F4 F2,F3,F4,Dx' ,F"x Mins pk 6 3 1 Group x overall E!Dx group 1 Fx group Z-end 6 y-overall 3 E ! Dy group 1 1 E1,E2,E3,E4,F1,F2,F3, F4,Dy.Dy' ,F'y,F' 'y Dy.Dy' ,E1,E2,E3,E4 F1,F2,F3,F4 F2,F3,F4,F'y,F' 'y 1 Fy group z end 2 2 2 Dx, E 1, E2, E3, E4 E3,E4 Dx,El 4 1 1 overall Z-end * Z-beg * Dy' ,Dy,El,E2,E3,E4 Dy',Dy,El E3,E4 4 y 2 2 2 1 1 overall Z-beg Z-end x n.a. y n.a. Dx' ,F"x F'y,F"y 1 1 Sclean-x Sclean-y x x x y y 1 After magnet tracking requirements. Requirements marked with a ... ,, are redundant. Sclean requirements apply only to tracks within ± 5cm of beam. The above procedure often found duplicate tracks, and a single view cleanup was used to identify and resolve such cases. This procedure compared a "just found" track with all previously found tracks in its view, first to detect an "identical" pair, and then to select the better one and reject the other. Given two tracks, - 210 - a count of the number of chambers in which they used different sparks was made. If that difference exceeded 5 (out of 11 x or 12 y chambers), the tracks were passed to the next test. If the difference was 5, both tracks had to have x~ Xo in order to be passed. Otherwise, the tracks were declared identical and the poorer one was rejected. The next test compared slopes and positions at the track midpoints, (z .~9.5m). To be considered distinct, either the slopes had to differ by at least .01, or the positions had to be at least 3 cm apart. If two tracks were declared identical, the poorer one was rejected. The decision of which track of an identical pair to retain was made as follows. If one track had x<xo and the second had xo<x<x 1 • then the first track was kept. If both tracks had x <x0 • or both had Xi <x <x 1 • then the track using the most sparks was kept, and if the spark counts were the same, then the track with the smaller xwas kept. We had a storage limit of 10 tracks per view. As a guard against the possibility that inferior and/or spurious tracks might fill up the storage before all good tracks were found, the tracks were ordered in quality, first by spark count, and then by 5(. Whenever the limit of 10 was reached, a new track candidate would be first checked to see if it was worse than the last track in the list. If so, it was rejected immediately, and if not, it was passed to the cleanup procedure described above. If it passed, then the previous worst track was removed to make room. For each view, the after magnet tracking was done in two passes. In pass 1, all tracks were required to have F chamber sparks. In pass 2, the F chambers were completely ignored in an effort to find tracks that missed them. (In pass 2, the road defining chambers were adjusted appropriately.) No explicit fiducial cuts were placed on either pass, except for a weak magnet aperture check, so pass 2 tracks pointing to the F station were possible, and were found. Although essential in the y view, good pass 2 x view tracks are expected to miss the F station (unless the particle was absorbed by an interaction). The single view cleanup was relied upon to - 211 - eliminate pass 2 tracks that were merely fragments of pass 1 tracks. Since almost every pass 1 track would have an analogue pass 2 track before the cleanup and extremely few x view pass 2 tracks are seen to hit the F station, the single view cleanup is seen to be quite efficient. A few such tracks survive, but the number is consistent with the expected rate of decays and interactions. We have found that if these tracks do find matches, they typically match to "old" beam tracks. C.3 Matching and Match Cleanups In our only formal act of xy view matching, the slant (u,v) spark chambers were used to identify matches, or xy track pairs that specified particle paths. We shall use the term "match" to mean only xy matches after the magnet. In searching for matches, all xy track pairs were considered. Given such a pair, projections to the slant chambers were made, and a search for sparks within 1 cm of the projections was conducted. At most one spark per chamber (the closest to the projection) was considered, and to be included in an initial match spark list, it had to have a x2 contribution less than 2.5. If the list of such sparks did not satisfy the match minspk requirements (Table C.2) the match was rejected. If the match survived this test, Xm = ')f I spark was calculated and minimized by removing the high x2 sparks until either Xm <5 or the minspk requirements were met. The match was rejected if minspk was reached and Xm >5. Surviving matches were ranked first by the number of match sparks and then by Xm up to a total of 25 matches. If that total was met, a new match had to be better than previous matches in order to be kept, in which case the worst was deleted. Next several cleanup operations were conducted. These were developed from early Monte Carlo studies and experience with E260 and E110 including event display scans. The basic cleanup compared the lists of match sparks of every pair of matches involving the same x view track. Given such a pair, the match with the - 212 Table C.2 XY Match Requirements Chambers Minspk Group El ,E2,E3,E4,F1 ,F2,F3,F4 3 overall• E 1,E3,F3,F4 -5.7° group 1 E2,E4,F1,F2 +5.7° group 1 • Overall requirements reduced to 2 for matches involving pass 2 tracks that miss the F-station. higher Xm was removed if its list of sparks was a subset of the other's . The next cleanup, Sclean, did not literally remove matches, but only flagged them as good or bad. Also, Sclean did not operate immediately after the matching, but waited until after some of the front end processing was done . It was run separately for the Vlrig and Targtrk systems, and it only looked at matches knovfl1 to link through the magnet to the front end. Sclean assumed initially that all x view tracks were real, but that only the best xy match involving a given x track was true. Here, "best" used the match ordering described above. All other matches involving the x track were flagged as redundant. Matches involving a given y track but different x tracks were allowed for several reasons. First, the uv stereo angle implied a good x resolution, but not y. Also, the y aperture was smaller and y tracks were virtually unbent by the magnet. Good tracks merging in the y view were thus considered fairly likely. Sclean also included a beam region test, using the better pwc time resolution to remove "old" beam region tracks that might link along with good beam region tracks . Matches projecting to within a 10 cm square around the 2x2 counter were required to have at least one hit in each view in the F' pwc's in order to be judged good . (In our 20 GeV le data, the bent beam missed one of the F'x chambers completely and went through a dead spot in the other, so this test was revised for this momentum to require two F'y hits and ignore the F'x chambers. For the winter '78 run, we added a slant BA type pwc that moved with the 2x2 and only a single BA hit - 213 was required to pass the test. Failing that the basic F'xy test was reverted to. The slant BA chamber was also used in the track matching.) For Vtrig. Sclean tested only matches known to link to the B and C stations. and only Sclean approved matches were admitted to the full Vtrig analysis. This was done to reduce the number of hypotheses fit by Vtrig. In the Targtrk analysis, Sclean was used only after the vertex was found, and it operated only on matches linking front end tracks found by Targtrk. In this case, Sclean was used to address a problem of multiplicity feed up that was observed in event displays, and was one of the reasons we reprocessed CST' s. The above discussion ignored differences between pass 1 and pass 2 tracks. Except for a reduction of the overall match spark requirement by one when a track missed the F station, there was none. Mixed pass matches were largely eliminated by the basic requirements. and the various cleanups. Those that survived were found to be almost always bad or associated with decays and interactions and were removed by later event structure cuts. The only valid mixed pass cases involved pass 2 x view tracks that passed through the dead edges of the Fx chambers (figure 2-8) but live Fy regions. Pass 2 only matches that were aimed directly at the F station occurred at a rate consistent with decays and interactions. Ultimately, we chose our fiducial volume, decay and interaction corrections so that the analysis used only pass 1 tracks. Events with pass 2 or mixed pass matches were cut from the data. Our cleanup philosophy was not to be completely efficient at removing spurious matches or tracks. To do so would increase inefficiencies to an unreasonable level. Rather, we sought to remove enough of them to make our final event selection cuts unambiguous and efficient. We relied on the good time resolution of the front end chambers to insure that most bad matches wouldn't link to the front end. Sclean was added to the Targtrk analysis because the bad matches that did link used the - 214 - same front end tracks as a good match, and so would increase the apparent vertex multiplicity, affecting one of our basic cuts. Event scans indicated that Sclean analysis was our best tool for selecting the best match when two used the same front end tracks. C.4 Beam Processing A good beam track was essential, both for efficient vertex finding and for a good t measurement. Having only two stations "' 19.5 m apart made track fitting useless. So we used instead a procedure [St78b] that always produced a single beam trajectory for each event, with flags and errors to indicate its quality. Multiple beam particles weren't a problem as the strobe kill suppressed them, and the mm topology cuts removed whatever survived. The beam trajectory was obtained by connecting pairs of points locating the beam at the BA and BB stations with a straight line. Its error matrix was calculated formally from the errors assigned to the points . On most events, all BA (2x and 2y) and BB ( lx, ly, and 1u) planes had single hits, making the point selection obvious. Also, the proper hits could be identified in most cases of delta rays or chamber noise by comparing the various chambers at each station. For example, if BAx2 had two hits and BAxl had just one, the BAx2 hit closest to the single BAxl hit was selected, and these two were used in forming the BAx point as if both planes had just one hit. 1f BAx2 had no hits and BAx 1 had one, then the point used BAxl only. At BB, if one plane, say BBy had two hits while the BBx and BBu had just one, we could use their data to select the proper y view hit. Indeed, if BBy had no hits at all, the other planes could be used to construct a BBy point if they each had one hit. We attempted to "save" the data in a plane only if it had 0 or 2 hits (single hits were fine) and only if the other needed plane(s) had exactly one hit. All other cases - 215 - were considered too unreliable to save. The evaluation and saving operations were carried out independently at BAx, BAy, and BB. Use of the slant plane at BB mixed the x and y views when a plane needed saving. At BB. if the x or y view had a single hit but the other view needed saving and could not be, the view with a single hit was still considered good. If a point was declared unreliable, we assigned a position and error obtained from the average beam spot and its width as a beam particle was a priori known to be in the beam spot. The large error minimized the impact of a poorly known beam on the reconstruction, especially the vertex. For the same reason, point errors were increased if the data used to define it were found inconsistent. Explicit quality flags were set for the x and y views indicating whether or not the data at each station was perfect, saved, or unreliable according to the hit counting described above. The flags were originally meant to identify cases of double beam events. But for mm. forward topology cuts completely eliminated double beam cases and we found that the flags were a measure of the chamber response to a single beam particle. To insure a good tpn measurement in mm we cut out any events that had any unreliable plane. The events lost by this cut were an unbiased fraction of the recorded events, and the large errors of the beam track in such cases prevented a loss of reconstruction efficiency, so a correction weight derived from just the ratio of cut to total events could be applied. C.5 Targtrk Targtrk was our front end analysis system for non-vee topologies such as rrrrn, and the physics studies reported here used only events successfully analyzed by it. Targtrk sought before magnet tracks coming from our target and linking to the matches. It fit for only a main vertex, and made no judgements about the number of vertex particles. The linking requirement was absolute. Targtrk found no tracks - 216 - for particles without matches. The number and locations of the front end chambers were not sufficient for reliable unassisted pattern recognition. Because of our ~ decay region, the BC lever arm was not long enough to provide sufficient discrimination between near Astation hits. This remained true even if information from the matches was used. We needed assistance from beam track information and a vertical focusing correction in addition to match data to provide reliable front end pattern recognition. This was done by creating "pseudo" sparks in several artificial chambers created by the program. One such chamber was near the target, using the beam to define its spark. one was at the magnet midpoint, z=4.4 7 m and using match extrapolations to set the spark, and in the y view only, a chamber was defined at z = 1.60rn, again using a match extrapolation. Table C.3 Tracking Requirements -- Targtrk View Chambers Minspk Group y y y Ayl. Ay2 By.Cy Ay1,Ay2, By, Cy 1 1 2 Ay group By group Overall x x x Axl ,Ax2,Au,Av,Bx' ,Bx. Cx Ax1 ,Ax2,Au,Av Bx',Bx,Cx 4 2 1 Overall Ax group BCx group The pseudo sparks at the target and magnet midpoint were used to define a 1.5 cm road for (nearest) spark searches. If the number of real sparks did not meet or exceed the rninspk requirements of Table C.3, the road was rejected. All pseudo sparks were used in initial fits and could not be removed to reduce the track x (as defined in section C.2). Real sparks could be, and if necessary were, removed to reduce x below 3.0. If all minspk requirements were reached before x passed this - 217 limit, the track was rejected. For acceptable tracks, the beam and z = 1.60m pseudo sparks were then removed and the track was refit with the remaining sparks . The beam pseudo spark was especially important in selecting correct A station sparks. The selection was fairly sensitive; a poor beam spark choice, or a bad beam track could easily mess it up. As a result much work was invested in our beam alignment and analysis (section C.4), and Targtrk was structured as a loop over three candidate beam sparks each at a different z. To maintain good efficiency at our target, these z values were -.60, -.30, and 0.00 m, each with an error of Uz = .25m . They bracketed our target and the last was near our DEDX counter. The coordinate of the beam spark was taken as the beam track extrapolation, and its error, a0 , was initially the projected track error or lmm, whichever was larger. Once the slope, b, of a road was set, this error was increased to a = va6 + (b az ) 2 The complete Targtrk analysis was repeated for each beam spark selection, (and all tracks and vertices found were indexed by it). This consisted of projecting matched tracks through the magnet to form pseudo sparks at z = 4.47 m (mid magnet) and z = 1.60 (y view only) . Y view projections used a Winds method [Co77] calculation to account for vertical focusing effects which were found significant at low momenta(<: 5 GeV le). Y view pseudo spark errors were set to 5 mm at mid magnet and 5 cm at 1.60 m. The x view projection to the magnet mid point had a curvature correction, and a 3mm error added in quadrature with an estimate derived from the after magnet error matrix. Both the vertical focusing and curvature corrections used preliminary momentum estimates derived from the after magnet track and the front end road being set up. The y view was done first with at most one front end track, or "link", being found for each match. Next, x view tracks were sought for those matches having y view links . The y link for a match was used to project the Au and Av sparks to the x - 218 - view with they track error being combined with the chamber error. Au and Av were not explicitly required to be on a track since the Ax group minspk was only 2 for 4 chambers, but they did help to flush bad matches lucky enough to link in y. When an x view track was found, its momentum was found with a square field calculation, section 3. 2. Once the tracking for all three beam spark choices was completed. a vertex was sought for each set of tracks found with simultaneous x and y view fits to a common zv. The beam track was required to be on all vertices, but forward tracks in either view could be deleted to reduce the vertex')(-. Particles were flagged as to ·whether or not they were in the vertex in one. both. or neither view. The successful vertices (just one per beam spark) were compared in turn, and the be st one was flagged. A vertex whose tracks missed more A station sparks than the previous one was "rejected". That being equal, the vertex using fewer xy track pairs was "rejected". These tests being passed, the vertex with the lower ")(- was preferred. All Targtrk results from the three beam spark choices were written to DST's (to allow for studies), but only the tracks and vertex for the best choice were written to CST's. The A station spark counting test was the most sensitive. A bad vertex usually resulted from a poor A station spark assignment. An incorrect track would usually share sparks with a good track. miss its proper sparks, and thereby increase the unused spark counts. Noise and delta ray sparks would rarely affect the count of missed sparks. Targtrk was judged successful if any vertex was found, regardless of the number of particles in it. If no vertex was found at all, Vtrig results were written to the CST as a backup. Sclean was not used by Targtrk. Bad matches that linked to the front end in both views always shared tracks with good matches, and there by did not distort the analysis. However, this sharing did lead up to a feed up problem for the multiplicity tests. To deal with this, Sclean was used to flag bad linking - 219 - matches after Targtrk was done . C.6 vtrig Although we did not use Vtrig results in the analysis reported here, it was used for the vee triggers and Vtrig results were written for Targtrk failures. Part of our confidence in Targtrk rests with the observation that no Targtrk "failures" succeeded in vtrig . Vtrig fit front end tracks and vertices to the specific topology characteristic of a given trigger. For 1T1m that was two charged particles from the main vertex . For a vee trigger, such as K°rrp, this was the nominal number of vees and nominal number of main vertex charged particles. Vees were made only of oppositely charged particle pairs known to link through the magnet using only the Band C stations for front end tracking . All such pairs were potential vees. Successful vees passed a z-vertex cut, zv > .1m, and had four tracks (two for each particle) in the vertex . Having vees, main vertex hypotheses were tried. (Since no vees are needed in mrn, Vtrig started with the main vertex for it.) The number of main vertex hypotheses was set by the number of vee candidates, the number of charged tracks, and the desired charged main vertex multiplicity. 1f more than one main vertex hypothesis succeeded (and each contained a specific vee choice), the best one was selected depending mainly on the total tracks (including neutral "tracks" from the vee) from both x and y views in the main vertex, and then on the vertex >!' if need be. To reduce the number of hypotheses tested, Vtrig included the Sclean match cleanup. (Sclean was originally designed for Vtrig .) For Vtrig, this ran only on matches that linked to the BC stations, and only Sclean approved matches were admitted to the full Vtrig analysis. - 220 C.7 Kinks Our square field momentum calculation with a Pt kick of . 7510 has proven extremely good. Monte Carlo studies comparing this approximation to an integration of our field map found square field errors completely negligible compared to our momentum resolution. Unfortunately, there is a catch resulting from alignment errors. The momenta measured by TEARS have a systematic shift characteristic of a kink of .084 ± .007 milliradians between the upstream and downstream (of the MPS magnet) chamber alignments. The kink had no noticeable effect on our tracking and linking efficiencies. The above studies have shown that this kink is not an effect of the square field approximation. It is less than our angular resolutions (Table 2.8), so it could easily have been missed by the alignment runs (given their statistics), which used 37ip data with the magnet simply turned off, and straight line fits through the full MPS from the A to F' stations. The alignment fits did not include any parameters for residual fields. The kink is qualitatively of the same order as the expected bend from residual fields (,..., 15 gauss with unquoted errors) at zero current observed in our field map measurements. Although small, the kink is a systematic effect easily seen in our missing mass spectra. lts effect is to shift measured momenta up or down depending on the bend angle which, in turn, depends on the charge of a particle and the magnet polarity. The effect of the kink is adequately parameterized as p = pm ( 1+0 e; e) (C .1) where P is the true momentum, Pm the measured momentum, e the bend angle and oe the kink. This correction was applied at the PST and CST levels on individual particles to allow for evaluation of oe with our full data sample. The effect of using uncorrected momenta on our missing mass is shown in figure C-1, which plots Mx 2 at 100 GeV /c as a function of - 221 %- =(e- - Eo I 2) I ( E0 I 2) (C.2) where e- is the 11"- energy and Eb is the beam energy. These shifts are appreciable when compared to our missing mass resolution, figure 2-11 . The data for these plots was the mean Mx 2 resulting from fits to a Gaussian for the neutron missing mass peak after a mrX background subtraction (and without a kink correction) . A straight line adequately follows the x- dependence. The shift in Mx 2 upon a magnet polarity change, (C.3) shown in figure C-2a is approximately (C .4) where Px is the magnet Pt kick. Iterative fits using equation C.4 to predict 69 result in our value of .084 mR. Figure C-2b shows our final f).Mx 2 result and figure C-3 shows the individual polarity Mz 2 distributions with the kink correction. The small residual slope is unexplained. It is small enough to be caw:;ed by either the approximation 3.1, our our square field assumption. In either case, it can be ignored, the shifts it represents being much smaller than our Mx 2 resolution. - 222 - 4-------------------- 88=0 4-----------.----.r--or--....-lmog =+ 180 (\J 3 ~ 2 (!) 3 ~ 2 (\J (.!) .. C' )( .. I 0 {;' )( 0 ~ -I -2-1 I ~ -I -0.5 0 x- -2-1 0.5 -0.5 0 x-· 0.5 Figure C-1. Missing mass2 .calculated without kink correction factor. 8----~------------6 100 GeV, 88=0 2.Q--..--...--------1.5 1.0 N (!) ~ 4 2 (\J.. 0 N .. (\J > ~ )(. -2 <1 -4 -6 0.5 .... o~~- +-fl...-.~'f-t-~~ ~ -0.5 ~ ~I 100 GeV, 88=8.4 x10-5 <1 -1.0 -0.5 0 x- -1.5 -2.QI 0.5 -0.5 0 x- 0.5 Figure C-2. D.Mx 2 before (a) and after '(b) kink correction. 4-----------------.,-..--(\J 3 !mag =-180 4-----------.----.--.--.....-~ 3 ~ 2 (!) N > 2 Q,) (.!) A Imag = +180 .. 1...-~..,..............,_+--~~ (\J)( 0 ~-I -0.5 0 x- 0.5 I -2-1 88= 8.4x10- 5 -0.5 0 x- 0.5 Figure C-3. Mx 2 after kink correction . No correction was upplied for re:sidual slope. -223AppendixD ColTections D.1 Introduction In this appendix we expand on the development of some of the more significant non-acceptance corrections. In some cases, unusual methods were used and they merit a review. Since the development of our A-station [Fr82] and C1C2 [Da78] methods are given elsewhere and our discussion for them in Chapter N was reasonably complete, they are not discussed here. Although some repetition exists, this appendix assumes corresponding sections of Chapter IV are read in parallel. D.2 Veto House Correction Because of inherent instrumental inefficiencies and one large hole (the forward magnet aperture) in the veto house, there is a considerable ( "' 10%) background under the neutron in a 1T1mr missing mass squared (Mx 2 ) plot at 100 GeV, figure 1-4. The background is smaller at 20 and 50 GeV, mainly due to better Mx 2 resolutions at the lower momenta. We need the veto house ({J, VO, Vl, V2, V3) to suppress a tremendous background. see figure 4-4, of events with extra (unseen) 7r0 's and charged recoils . Without it, the topological trigger would take virtually only background data, and our limited Mx 2 resolution would fail to isolate the relatively small fraction of mrn events. In a one particle exchange picture, figure D-1. extra 11'° 's can come from either vertex (or both vertices). Lower vertex ,,-O's would be from recoiling N• (and fj) resonances, while upper vertex 1r° 's would be decay products of mesons such as the ~0 • Because upper vertex n° 's are typically "fast" and result in large Mx 2 values, most of the background under the neutron comes from lower vertex processes. Another upper vertex background characteristic is that the 1T+1T- mass is shifted - 224- .,,.,,.p Figure D-1. One particle exchange model for rrO backgrounds. Resonant amplitudes at both vertices are shown for brevity. Upper vertex can be almost any nonstrange meson giving one or more n<>·s and a pair. The G>o is just the lightest such state. ,,.+,,.- down from the parent mass; and is concentrated at mr masses at or below the p, see figure 1-3. On the other hand, the rr+-rr- mass spectrum for events with extra rr°'s associated only with the lower vertex, is quite similar to the spectrum from rr+.,,.-n. The topological trigger stops most upper vertex charged particle backgrounds. Charged decays of N•·s are vetoed by the p chamber, and Vl if the (3 chamber fails to fire. Hadrons routinely penetrate and are detected by Vl. Indeed, of the charged particles seen by {3 and not Vl, all seem to be delta rays. Charged recoil products that miss Vl and strike the A-station would violate the topological trigger. Part of the experiment design was set by our desire to measure veto failure backgrounds and, if possible, subtract them. We had a prescaled background trigger, rrrrX. with no veto house requirements at all. and we kept the front end geometry fixed to facilitate measurements which combine all our momentum settings. All veto failures were (up to prescalin.g) contained in the 1mX trigger. The background in 1T1rnr is the non 1rrrn part of rrrrX times the veto "failure rate", defined below. Veto failing backgrounds a.re assumed to have the same n+rr- -225distributions as found in 1mX. That is, no special configurations of the n+rr- are selected as veto failures from among the nnX sample. Our studies indicate that this is a reasonable assumption. The background "observed" in mrn results from the production of background states and subsequent failures to detect the extra (excluding forward n+n-) decay products. The veto "failure rate", F, is defined as the fraction of the background for which the veto counters fail to detect the extra particles. F depends on the flux of extra decay products in direction and energy, the veto counter geometry and counter efficiencies. Background decay kinematics are dominated by available energies, and when discussing only the extra particles such as 1T° 's, this is roughly half of Mx 2 : (D.1) where t is the momentum transfer to the recoil neutron or N•. Averaging over many (background) events, the decay product flux at any direction, and hence the failure rate, depend mainly on Mx 2 . This even extends to upper vertex backgrounds. To a good approximation, no other dependence for F is needed, and the measured failure rates show little, if any, mmr or Pt effects. At any momentum setting, we can exclude all the background resolved from the neutron by a simple Mx 2 cut. But unresolved background can't be measured at that momentum setting. Without reference to other momentum settings, we could only use simple extrapolations and fits which run the danger of not being able to extract a reasonably correct background shape under the neutron. (Simple extrapolations were used for a preliminary study [St78], and for the neutron veto correction in sections 4.4 and D.3.) - 226By keeping the front end geometry fixed, measurements of the failure rate at any Mx 2 value from any beam momentum setting will apply to the other settings. Once we know the failure rates, we can use the Mx 2 spectrum from mrX to estimate the background in mm. Thus, 50 and 20 GeV le measurements of F and the 100 GeVle Mx 2 distribution from mrX can be used to "predict" the veto failure background at 100 GeV le. Failure rate measurements at 100 GeV /c do not directly help because we can measure F only at Mx 2 values away from the neutron peak. However, the main check on this method is agreement between failure rates seen at the different beam momenta in Mx 2 regions where the measurements overlap. D.2.1 Failure Rate Measurement The mrX trigger was essentially rrmir without the veto house requirement. There was a weak "special D" requirement for 1mX (1 or 2 hits in both Dx and Dy), but the only effect of this was a slight delta ray (at D) suppression and our method compensates for this by construction. The failure rates were measured by plotting Mx 2 distributions for both rrrmr and mrX data on CST's. The same trigger and topology cuts were used for both types excepting no veto cuts were made in 1mX data. In each Mx 2 bin (at least 3a.uz2 from the neutron peak) the failure rate, F, was evaluated as: (Events in 1r'TT'nr F= __,_ ____________ __,_)·o __ (Fluents in rrrrX}· P (D.2) where Pis the mrX prescaling factor(=. 5 at 20 GeV /c, 40 at 50 GeV le and either 40 (early runs) or 80 (late runs) at 100 GeV /c). 6 is an average (3 chamber delta ray correction for rrnnr. leaving it out would underestimate F. The mrX trigger was not subject to (:J chamber delta ray vetos or corrections. We needed to use both types of triggers. as the number of 1r1mT events in the 1r1TX sample was too small to be useful. The prescale factor P was then necessary, as only 1/ P of the rmX events .. 227- 14 - 20 GeV/c --- 12 .. ~10-- .. --------- CL> c B- ,,,, ,- --- 0:: 2~ ++++ .:to --+-ff I 0 I I I I 10 20 30 40 Mx 2 , GeV 2 -- 14 - 50 GeV/c 12~ ~ 10-- CL> & B0 LL. 4- 2I I I I 10 20 30 40 Mx 2 , GeV 2 Figure D-2a. Failure rate measurements at 20 and 50 GeV le. allowed by the spark chamber dead time were recorded. For the measurements, we split the data into sets distinguished by beam momentum and prescale factors. To be consistent with A-station cuts, we re- stricted the study to mmr values > 500 MeV. Pt and mmT dependencies were searched for with no significant effects seen. Mx 2 overlap regions between the -228- 14 ~ 100 GeV/c Early runs 12 - fl. 10 - .,- J,# t -· 0 8 - a:: 4- 2 0 i--------- 7 I I I I I 0 10 20 30 40 14 - - Mx2 , GeV2 100 GeV/c 12 ~ *~4 Late runs 10- ct> 0 8 a:: ct> s64 - 0 I I I 0 10 40 Figure D-2b. Failure rate measurements at 100 GeV /c. Early and late 100 GeV /c run sets differ in both prescale factor and BB status (broken in late set). various beam momenta were reviewed and found consistent. We then combined the failure rates by averaging the observed values whenever data sets overlapped. The combined result is shown in figure 4-3. Here we show individual sets in figures D-2. The lowest Mx 2 value (''6.0 bin") in the combined and 20 GeV plots represents a - 229- 30 ,., .... I ...•~ 20 > "" 10 5 0 1.0 2.0 Mi (GeV/~} 2 3.0 ~.o Figure D-3 20 GeV le mrX Mx 2 spectrum. Hatched area satisfied rrrmr trigger requirements. Other histograms are all events (uppermost, including both dashed and solid lines) and the remaining after mmr tags were removed. problem at the /:J.0 and will be discussed shortly. The smooth curves of figures 4-3 and D-2 are single pass smoothings of the combined set from the plotting program. They exclude the /:J. 0 bin and are for comparison purposes only. The first two bins of the combined plot (-1 to +1 and +1 to 3 Gev2) are actually the /:J. 0 bin ( 1.20 to 2 Gev2) and 2 to 3 Gev2 bins from 20 GeV/c. The other bins are all 2 GeV2, a size motivated by the 100 GeV /c Mx 2 resolution, and carried into the 50 and 20 GeV /c analyses for lack of data at the lower momenta. At 20 GeV /c we can just barely resolve the ti0 from the neutron, as in figure D3, a plot of 1mX data only, and we cannot resolve the 6° from higher mass N•'s. Although the statistics are rotten, the 6° appears shifted down a bit from a nominal peak value of ..... 1.52 Ge~ (=(1.232) 2 ). This is a predicted effect [Ja64], but it doesn't help our resolution any. For veto failure rate measurements, we define the "6°" (at 20 GeV /c) as all non mm data between 1.2 and 2.0 Ge~. This is slightly - 230inside the neutron cut of .45 to 1.35 Ge ve. so we subtracted an estimate of the good neutron content in the mm.r data for the neutron tail between 1.2 and 1.35 Gev2 in the failure rate measurement. This attempt to get into the neutron peak was only done at 20 GeV /c, and only because the ll0 failure rate is a problem and the n -~ separation is poor. On the failure rate plots, the ll0 bin sticks up like a sore thumb. Otherwise, the failure rate behavior is roughly as expected from early Monte Carlo studies, although at a higher value than the studies predicted. The failure rate (excepting the ~0 ) is fairly flat below -B Gev2 with a rise above that value from geometric effects. N• decay products (11"') tend to go forward as the N• mass increases. That the failure rate flattens out at extremely high Mx 2 apparently indicates most events with upper vertex rr° 's also have N• recoils. The veto house is not expected to be effective for cleanly produced (.,.)0 n states. Fortunately, the rise in veto failure rates occurs above the neutron Mx 2 cut, even at 100 GeV /c. D.2.2 Background Subtraction To subtract the veto failure background from our 1T'1mr data, we chose to subtract weighted mrX events directly. This was done to preserve correlations between the variables Mmr, cosfJ;, rp; and t; 1TTrX distributions being a bit different than those seen in mrnr . . Multivariable arrays with reasonable granularity would require more bins than data. We first extract background events from the 'ITTrX data by removing all events that could be real mrn. Within the neutron Mz 2 cut only, we remove all events that satisfied the 'Tt"Tmr trigger, all neutron veto events, and all (3 chamber delta ray vetoes. This avoids double counting good events and the neutron and (3 chamber veto corrections. Delta rays in the (1 chamber were identified by hits in (3 and no hits in any other veto counter. We checked that this cut was as pure in mrn as the - 231 frmtT trigger. Neutron veto events were identified by having a single barrel stave struck with no other veto counter firing. The struck veto counter had to be within a Pt dependent b.rp (hit-recoil) cut of 2.5a about the average f;.rp peak seen in the neutron veto measurement, section 4.3. The f;.rp cut is Pt dependent, and no single barrel strikes were removed below Pt = .OB GeV /c, the neutron veto threshold. A few background events are lost by these cuts, but that loss is extremely small. Given these removals, we made PST's of the mrX data with a flag set to distinguish them from 1T1TnT PST's. The background processing was done in the same job as the rrmtr data. All corrections and cuts were done in the same manner as for 11'1T7lr except that neutron veto and p chamber delta ray weights were excluded, veto counter cuts were not done, and we applied an additional term to the rrrrX weight. The extra weight was w,, = -PF where P was the prescale factor and F the failure rate. F is Mx 2 dependent. Within the rrmt Mx 2 cut, we must combine a smeared /::,.0 failure rate with a flat everything else. Although only a small part of 1T1TX, the !:J.0 accounts for a significant part of the veto failures. Outside the neutron cut, we used the combined measurements directly for the Mx 2 plots of section 4.2. D.2.3 6° &nearing To smear the /:J.0 in the failure rates, we view the background at any Mx 2 value, as composed of a /::,.0 part of fraction f ll and everything else, a fraction ( 1-f tJ.). Missing mass resolution is the sole reason for ll0 smearing. We know that l:l0 events have a poor failure rate but cannot tell which events are actually f). 0 's. The net failure rate as a function of Mx 2 is then (D.3) where F 1 is the fiat part of the failure rate ( = average of all bins within the neutron .Mz 2 cut other than the /l0 ) and F 2 is the 6° failure rate. A smearing function - 232- S(Mx 2). is applied to the !l0 failure rate. I A = f ~ S(Mx 2 ). where f ~ is the number derived below. S(Mx 2> is a simple Gaussian smear of a square distribution from 1.2 to 2.0 Gev2 (the 20 GeV 6.0 cut) with unit area: S(Mz2):: /6 lert{ 2;~f ]-sr/[M:~·2]] (D.4) where a is the appropriate missing mass resolution. This procedure is needed only at 50 and 100 GeV/c. At 20 GeV/c, /A= 1, and F(Mz2) = F 2. Only a few 6° decays penetrate the neutron peak. We had to resort to some modeling to get/ A at 50 and 100 GeV le. There are simply no measurements of 1T•rr-ll0 or p 0 ll0 at very high energies. Existing measurements, which are also not compatible with our cuts, go only up to - 20 GeV le, and one 200 GeV I~ bubble chamber experiment [Bi74] gives only an Bµb upper limit to p 0 1:!0 {95/o C.L., no events). To get I A• we start with I A = mrX mr.6 = mr6 x mm . mrn rrrrX {D.5) We can use our data to get rr1m,/ rrrrX, and this provides the only rrrr mass dependence used in F(Mz 2 ). Plots of this ratio are given in figure D-4 along with the linear fit actually used for I A (mmr in Ge VI c 2) : 1rmt -X 1r1T =.0457 + .0328 mmr (D.6) For rmW mm., we note that both reactions a.re dominated by n exchange and so assume that they have the same 1nr mass dependence. The reactions have different t dependences and tmin values. We assume that the Pbeam dependences of da/ dt are the same. Th.us we are assuming that - 233.6--~~~~~~~~~~~~..--,....-~~~,.-- ' I I 100 GeV/c I I .5- I I I I -~ .4- I - I ·--·-- I I I I .2- +1ttt .I - ---ttfx-·-t+ 0 I 0 L-~~f-~t-r t -- -- T± ~ ~-*f+ ± I I + I I I I I 2 2 m,,w , GeV I c I 3 I 4 Figure D-4. Ratio of events Trrrnr/TrrrX with neutron Mx 2 cut. Data from CST's, dashed points not used in the fit. 1m6° mm = ~= a(p 6°) 0 p n 0 a(p 0 n) ' (D.7) and we can use data to get the ratio at 20 GeV le and then extrapolate it to higher Pbflam values by integrating over the du/ dt forms. Using 1'i1'iX data, we find (statist- ical error only) at 20 GeV/c. (D.8) Given our arbitrary upper cut of 2.0 Ge V2 for the 6°, this is a reasonable value. In this ratio, we included non neutron events in the p0 6° set even when Mx 2 was below 1.2 GeV2. Events identified as (3 chamber delta rays or neutron vetoes were included in the p0 n set. For the beam momentum extrapolation of u(p0 A)/ a(p 0 n), we take du/ dt forms inspired by the poor man's absorption model for n exchange [Fo71b]: - 234- (D. 9a) ~l -tebt le (D.9b) dtl,on = p" (t -m; )2 where numerical constants are grouped into k, p is the beam momentum; a ...,z and b =4 are assumed the same for both reactions. The b value was inspired by fits by Kimel and Owens [Ki77] to the p~ reaction. Their n exchange terms have effectively -vb "' 2 (the correction is insensitive to b). Letting tm.in h(p) =f - In (p) =f et>t (t-m.;)2 dt (D.10a) and -tebt t lilin (t-m;)2 dt (D.lOb) u(p 0 6°) I ltJP) In(20) a(p 0 n} (D.11) 20 -w we have h(20) In (p) · The I b and In integrals can be evaluated in terms of exponential integral functions E 1 and E 2 , which have been tabulated [Ab64]. (D.12a) The p dependence is in t min· We find In (20)/ In (p) = 1.000 at all p, the 20 GeV t min - 235- for p 0 n being already well below m:, and the (-t) in du/ d.t suppresses low t cross sections. The /:,.0 terms contain significant effects. For the sake of simplicity, we used a single t min value, evaluated at ml = 1.5 Ge ve. and obtain the following values (statistical error only): Table D.1 Model Results p, GeV/c fmm(pOt:,.O) 11/<P )I JA(20) a(p 06°); a(p 0 n) 20 -1.02 x10-2 1.000 1.70 ± .20 50 -3.93 x10-s 1.347 2.29 ± .27 100 -1.39 x10-s 1.503 2.56 ± .30 Since we claim no mr mass dependence observed in F(Mx 2 ), and yet use one for the 6°, we should note that the A0 is a relatively small fraction of mrX at 50 and 100 GeV I c, and that it is unresolved from the neutron at these momenta. Thus we can't hope to see a mass dependence from the ~l' in the failure rates . D.2.4 BB Failure Part way through Run I, after the 50 GeV runs but well before the 20 GeV runs, one barrel counter, BB (figure 2-5), failed. We decided not to repair it, and instead enabled an unprescaled background trigger at 100 GeV, 1mB, which was originally planned for 20 GeV neutron veto studies. Running this trigger at 100 GeV turned out to be crucial for neutron veto measurements, but it has not been mentioned yet in relation to veto failures. At 100 Gev the mrB trigger was intended to estimate the number of veto failures from the loss of one barrel counter. But, rather perversely, the best estimate of the effect of the loss comes from our 20 GeV data. The loss of a single counter does not affect the veto efficiency for cases where at least - 236two of the barrel staves would normally fire, or a barrel stave and a jaw counter or the P chamber fires. However, we expect an efficiency drop of...., 4% for single barrel strike vetoes, a value comparable to our /::, 0 failure rate. However, the data indicate that the missing barrel stave is not our problem. Most vetoes involve at least two veto counters firing. Further, the 20 GeV missing mass distributions of figure D-7 lead us to believe that most single barrel vetos probably involve 6° decays, and they can be used to estimate the /::, 0 failure rate contribution from the loss of BB. There are about 10 6° events in the neutron /::,,rp cut between 1.2 and 2.0 Gev2, and 62 events outside the Arp cut below 2.0 Gev2 for a total of 72 6° events with a single barrel bit. This implies ...., 1/ 23 x 72 =3 events would have had a hit in the dead counter. There were about 900 p0 b.0 events in the same running (181 p 0 /::,, 0 events recorded in mrX times the prescale factor of 5). Thus the /::, 0 failure rate coming from the dead counter is -3/900 = .3%, much less than the observed rate . We conclude that the high failure rate at the 6° is from an inherent inefficiency for low recoil masses, which correspond to the softest photons seen by the Barrel. D.3 Neutron Vetos The mr B trigger discussed in the proceeding section was most useful for measuring our neutron veto rate. As shown in figure 4-6, this trigger displays a strong neutron peak in the variable l:!.rp = 'P/o't'1AX1.rfi. -rpBarnl· Mx2 cuts are needed _to cleanly extract the neutron signal from these data, but it was generally cleaner than that of the mrnr trigger after these cuts were made. We found the neutron veto rate (neutron detection efficiency) by parallel analyses of 'frrrB and nrrnr data. Only runs for which the mrB trigger was active were used. The same topology, m.mr (> 600 MeV), and Mx 2 cuts were used for both triggers. No Cl C2 cuts were made, all forward particles being assumed pions. A - 237soo----.----..----..----.-----------------------T~---. Mx' for ,,,,.n Topological Dote 500 N ~ <.!:>400 It) .....: r/'J ~ 300 > w 200 100 9a -4 0 4 8 12 Ml, GeV 16 20 24 28 2 Figure D-5. Mx 2 spectrum for mrnr data used in neutron veto study. Shown are Mx 2 cuts used, and the rough background estimate used. conservative Mx 2 cut of -5 < Mx 2 < 2.5 Gev2 was used at 100 GeV, as shown in figure D-5, to reduce background subtraction burdens. Figure D-6 shows a preliminary background subtraction study for nTrB with a fixed ( ± 22.5°) ~<p cut. A similar plot, figure D-7, made with 20 GeV data. shows that most of the large 6rp background is single photon hits from ~ decays. 0 The ~ (approximated as IPt I ) dependence of the neutron veto rate was found after a study of the peak in figure 4-4 as a function of V-f. We found that the 6rp resolution depended on ...r=f and that the neutron detection efficiency had a threshold of ...r=E - .OB GeV/c. The btrp resolution at 100 GeV is shown in figure D-8, which used three different sets of large -..r=£ bins in an attempt to flush out statistical fiuctuations, and have enough data to allow fitting. btrp distributions (not shown) for these bins were fit to a Gaussian with a fiat background. The mean, width, and height of the peak, and the background level were all free parameters. The fits break down for bins below -...r=£ below -.1 Gev2, an effect that could be due to either - 238 - 120 Tri! Missing Mass No A.p Cut ~ ....e Missi119 Mass Squared BO Events Outside A.p Cut 60 . ~ <..::> I(') -..: ..,, 'E Q) > LLJ 40 • 0 • B 12 Mx', Gev' 16 20 24 o 28 • e 12 16 20 24 20 Mx', Gev' ~ Mass Squared Appro• . Backgr0!'1d Subtroct TTB TTB • Mrssinll Mass Squared ~ Events Inside l::.f> Cut .. 60 ~ [tn l::.f> Cut - ~X0utside 60 <..::> I(') ....: ..,, <..::> c I(') ....: ..,, Q) > c w 40 ~ w 40 20 20 -4 0 4 B 12 Mx', GttJ' 16 20 24 28 -e -4 0 • 8 12 t6 20 24 Ml, Gev' Figure D-6. Preliminary fixed flrp cut study on 100 GeV /c mrB data. Note that the uncut and cut failing distributions are shifted to higher Mx 2 . 28 - 239Mx 1 ,,,,9 M,,,,>.6 One barrel hit 1 a) Mx , no llf> Cut 12 8 cl Ml llf> Outside ±22.5° Cut 12 8 Mx', Gev' Figure D-7. 6~ study at 20 GeV /c. Events outside the ~rp cut are clearly dominated by the 6(1236) resonance. resolution or a threshold. We favor a threshold because we see one in 20 GeV data, figure D-9, where the resolution is better' and the effect coincides with a predicted neutron threshold for the Barrel [Pi74]. The neutron detection efficiency was found from the ratio of V-f distributions in rrrrB and mmr. The smooth curve of figure D-8 was used to set 3a ( fjcp) cuts as a function of V=t in rrrrB. The background outside the cuts was flat, and was used to subtract the single photon background from the n~utron veto signal. We also did a background subtraction for the Trrrnr data. For that, we used a ~ distribution from the rrrrX trigger scaled to the event total in the hatched region of figure D-5. Both the rrrrX and single photon backgrounds were peaked at smaller V-f values that rrrrnr or flrp cut rrrrB distributions. Since neither 7rrrnr or mrB were prescaled, the neutron detection efficiency, defined as the ratio of detected neutrons to total neutrons. is found as - 24048 a) 4 44 (/) Q) ~ 01 40 2 Q) "'O 36 32 (/) -4 Q.) ~ 28 01 Q) "'O ~ -s.. 0 24 .2 .6 .4 8 J-t b b) 20 16 12 8 _ _ _ _ _ Limit from 4 0 o counter size .2 .4 .6 .8 1.0 Ft, GeV/c Figure D-8. Recoil neutron azimuth resolution at 100 GeV le (b). Points were found in three sets of fits to a Gaussian plus flat background. Smooth line is the dependence used in Env measurement. This was not used for the study of figure D-6, but was used for our Env measurement. Also shown (a) is the error in surveyed counter orientation. B Erw= N+B (D.13) where B is the number of detected neutrons from mrB and N is the number of rrrrnr events. Equation D.13 assumes background subtractions have been made. The two triggers are complementary, one having a veto on neutrons and the other not. A side effect was differing backgrounds under the neutron, but having subtracted these, the other corrections are the same, and they cancel out in D.13. Thus this equation represents the fraction of mm events that suffered neutron interactions in the barrel, and hence the loss of such events from the 1T1T'Ttf trigger. - 241- 6 20 GeV/ c 12 o) c"' 8 C1> > w 4 .........._____, Ql--t-l-l~--'.l..-'IJ....1.1.LJL_.i.~-4-i.LJ+l--+-U.-+""-1...._ 8 b) -160 -120 -eo -40 o 40 ao 120 160 ~cp, degrees 0~ .. Q) 0 er 10 0 Q) > 0 o.o 0.2 0.4 0.6 0.8 1.0 1.2 1.4 J-f, GeV!c Figure D-9. 20 GeV /c !!lrp distributions for events inside (a) and outside (b) neutron Mx 2 cut. (c) shows 20 GeV /c Env values . Figure 4-7 shows Env at 100 GeV le. And our results are given in section 4.3. D.4 BCD Delta Rays We now discuss the development of the BCD delta ray correction. This correction was designed to account for delta ray losses in our tight BCD trigger requirement for rrmir. and was tailored for consistency with the reconstruction efficiency correction. That correction includes effects for the chamber efficiencies in the trigger and track finding. Our BCD software trigger cuts were set to cleanly - 242separate the problems of the delta ray and chamber efficiency corrections. The formalism discussed below was built around a measurement of the needed parameters from curve through data. that being the only trigger free of BCD requirements and, hence. our only trigger that allowed a bias free measurement of the delta ray rates. The BCD delta ray formalism makes use of the stiff BCD trigger requirement to deal in a simple way with correlations between chambers. We include as "correlations .. chance pairs of delta rays created by one particle and seen in different chambers, as well as "true" correlations caused by penetrating single delta rays. Delta rays coming from different particles are not viewed as correlations. We need not distinguish between one delta ray seen by a chamber and several delta rays seen by that chamber. For a single particle, we need only use the following classes of events: a) no chamber sees any delta rays, b) exactly one chamber sees a delta ray signal, and c) delta ray signals are seen by two or more chambers. Class b) splits into six subclasses, one for each chamber. For Trmt events, small but finite, chamber inefficiencies in the BCD chambers require that we distinguish between cases where all chambers satisfy the (software) trigger requirement of a hit on each of the two particles (6ok), and cases where one chamber fails this requirement (5ok}. Trigger cuts insure that there are only two such classes we ne~d to deal with. In the 6ok case, we can have (any number of) delta rays detected by one of the six chambers. A veto would require delta rays to be detected by at least two chambers. In the 5ok case, a delta ray signal seen by any of the five good chambers would cause a veto as one chamber is already bad. We express the delta ray corrections for the 5ok and 6ok cases of mm in terms of parameters found for the several single track cases defined above. Consider first the 6ok case. Let P~o be the chance that the k'th particle made no delta rays at all, P°" be the chance that this particle created delta ray signals in -243- Table D.2 BCD Single Track Parameters Pc = .8212 ± .0039 Pi = .1291 ± .0034 Pm = .0497 ± .0022 chamber i Pi Poi Bx 1 .0280 ± .0017 .1507 ± .0036 By 2 .0179 ± .0014 .1608 ± .0037 Cx 3 .0145 ± .0012 .1642 ± .0038 Cy 4 .0156 ± .0013 .1632 ± .0038 Dx 5 .0241 ± .0016 .1547 ± .0037 Dy 6 .0289 ± .0016 .1498 ± .0036 (statistical errors only) two or more chambers, and Pa the chance that it made a delta ray signal in only the i'th chamber. We assume that P1:o, P11;m. andpki are all independent of track location within a chamber and that these values are unaffected by the presence of other particle(s). We define P1: 1 as the chance that exactly one chamber had a delta ray signal, not worrying about which chamber it was: P1:1 = ~ki (D.14) i For a -single particle we have (D.15) For two particles, we have just the product of single particle expressions. -244(D.16) Only those terms in D.16 involving P• or PiiP2J i-.t; can lead to vetos. Calling Pnu the chance no veto occurs. we rearrange D.16 using D.14- and D.15 to get two expres- sions for Pnv : (D.l 7a) (D.17b) Invoking the above assumption (P~ = Pfi for particles j and k). these become (D.lBa) Pm.J = P8 +2PoP1 +l:Pi2 (D.1Bb) i lions D.18 may be used to express Pnv , and their equality was a check on the measured numbers. Pnv is used to get an event weight: We= 1/ Pnv (D.19) The less frequent 5ok case is easier to express. If any chamber other than the one failing to have hits on both tracks has a delta ray, the event would be killed. Define Poi to be the chance per particle of seeing delta ray(s) in any chamber other than the i'th chamber. Th.en, since either particle can make the offending delta ray signal, the correction weight is W:s1=1/(1-poi) 2 (D.20) There is one such factor for each of the six BCD chambers. Delta rays seen in chamber i (the one missing its hit) do not cause vetos and do not enter into D.20. -245- Delta Roy Rotes Po , ~ Po .20 .90 .85 ! t .BO Pi, ~ ! t ti t t f ! .15 t t t t I I I t tI .05 0 .75 '( I .10 t f I I I P,. .08 .06 .04 t ti Hif I ~, f .02 0 151 Figure D-10. BCD delta ray rate parameters P 0 , P 1, and Pm for the various curve through runs. These runs were combined for the values in Table D.2. With the above formalism, we needed only thirteen parameters to evaluate the BCD delta ray weights. As mentioned above, we used curve through data for the parameters. This single particle trigger is the only one in El 10 without BCD chamber trigger requirements and a reasonable topology; it required only BEAM·2X2 as its trigger. Of the fourteen curve through runs made in the spring '77 running, only three runs were excluded from the study. During one the Cx chamber was dead-disabled by water dripping from the magnet; and two were muon contamination runs in which a calorimeter module was placed in the beam. That compromised the track clean up procedures used. The data were analyzed with cuts insuring that only one beam particle was present without imposing any conditions on the BCD chambers, and allowing for delta rays to reach the spark chambers and be found as tracks. Multiple beam - 24-6 - Delta Ray Rates, .3 pf .3 P.o: B• •2 fI .I ! rt ftlft t -f .3 p~: •04 .04 .02 .06 .2 .2 t f t f f t i i l !i .I .3 p~ : p~: Dx .04 ff ! t f t! f i I .02 t us lK l50 151 115 !17 !13 RUN M3 m 5't 0 ........................................-........,.._ ~2 c• w 1M l50 a1 115 NI !13 »• w !43 JU o. .2 .2 .I .I w 150 Ill tt5 l~I m sza m HT RUN '43 Uf RUN Figure D-11. BCD delta ray parameters p.;, and p 0i versus curve through run and for the various chambers. particles in the same r.f. bucket, or just within the resolving time of the propertional chambers could look like delta rays and distort the measurement, so care to eliminate them was needed. Any event that seemed to have extra particles involved was rejected. The runs were studied separately to see if any were pathological (none were), and were then combined to produce the results. All beam momenta were included as their results appear consistent and no beam momentum dependence should be expected in this delta ray effect. Chamber sagging from beam intensity could have been an effect, but no significant beam intensity effects were seen (unlike the Beta chamber correction), probably because the BCD chambers -247were normal to the beam. and delta rays are a reasonable distance from tracks. Out of 22287 events in the curve through runs. 9639 passed all the cuts and were used in the analysis. Delta rays were counted as the total hits in a chamber less the number of hits on the good track. This removed miscounts that could arise from inefficiencies. The values for the various P's were taken from a histogram of the number of chambers having delta rays in each event. The p's came from plots of the appropriate count of delta rays in each event. Figure D-10 gives the run dependence of the P's, while figure D-11 gives the run dependences of each of the p;, and Poi, respectively. Table D.2 gives the values of the parameters for the combined data set, and table 4.1 gives the resulting weights. The curve through data allow us to test the validity of the assumptions made; that delta ray rates are independent of track location and are not affected by the presence of a second track. These were checked with plots of the distance, D, between a track and the delta rays it created (in the coordinate measured.) Distributions in D were taken for each chamber in 5 mm bins in the range -.3m~D~ . 3m. The distributions had a central peak of half width about 5 centimeters. and long, substantial tails. (Special fine resolution plots verified that the delta rays were never actually on the tracks.) The peaks came mainly from single plane delta rays (the kind that made p.J, while the tails were mainly from multi plane delta rays. To get an overestimate of the chance that a delta ray would land on top of a second track, we found the ratio of the contents of the most populated bin to the total entries in the plot, correcting for actual wire separations. The largest values were about 8.% for single plane delta rays, and 5.% for multi plane delta rays. These ratios are the chance that a delta ray would be masked by a track if it went through the worst bin The chance that a track was at the wrong place at the wrong time is itself only a few percent. Thus, delta ray-track overlaps appear rare. - 248- These distributions also gave an indication of the potential position dependence of the delta ray weights. 'Ibe worst case is a track near the edge of a chamber. Tb.en. the rates for that chamber would drop by about half on that track. Using Dx as the example, we note that Dx participates in about 48% of the multiplane delta rays. For a track near the chamber edge, this fraction would drop to 24%. For this track, Pm drops to about 76% of its curve through value. In mm, tracks near a chamber edge are low momentum and accompanied by a stiff track near the beam line. Referring to equation D.17a, we see that Pnv is dominated by P 1m +P2m. A reduction of 24% in one of these values, results in a reduction of the veto rate by about 12%, and this is a worst case. Mainly for this, we assign a systematic error of 10% of the fractional part of the weight in table 4.1. Lastly, we have only discussed delta rays resolved from tracks. This means there was at least one "quiet" wire between the delta ray and the track. Delta rays unresolved from their creating track can cause event vetos by merging the hits from two close tracks . In a delta ray free world, one would choose a separation cut of about 1.5 wires to insure good trigger efficiency against merged tracks. Plots of the number of neighboring wires excited by a track indicated that a 1.5 wire cut was not enough, but that a three wire cut was adequate. Th.is cut applies to x-view separations as measured at the Bx station, and affects all the BCD chambers except Dx, where bending by the magnet can cause legitimate tracks to cross. In such a case, the trigger is viewed as 5ok, since the other five chambers must be perfect for the event to survive. - 249- D.5 Target Region Delta Rays As for the BCD delta ray correction, the target region, or p-chamber delta ray correction used curve through data to provide measurements for the veto rates. In the curve through runs, the (:J chamber recorded hits passively. A simple absorption model was then used to account for the strong z-vertex dependence of the veto rate in 1rmtr. A more complicated model. described later, was also tried, but abandoned. Curve through data give us the delta ray detection rate when a single particle passes through the entire target and the vacuum jacket end cap. All the spring '77 curve through runs were studied, as well as three of the winter '78 100 GeV runs. (The latter were used for target empty dat~ no target empty curve through runs were taken in the spring '77 session.) We measured the rate of f3 chamber hits after a series of fairly stiff cuts to insure a sample of events with single beam particles that had no hadronic interactions in the spectrometer. We required that the beam pwc's find a unique beam track (beam flags ~1), that TEARS find just one particle after the magnet, and that this particle link to the front end with measured momentum within ±10 ~of the beam momentum. We also required that the photon vetos (Jaws and especially the Barrel) be quiet. Delta rays do not penetrate into the Barrel, but hadrons do. The measurement was for the rate of any nonzero number of delta rays seen by the (3 chamber. Multiple delta rays were just as deadly to an event as single delta rays. We looked for an x dependence of the delta ray rate, where x is the horizontal location of the particle at the target center. The rate was consistent with flat. : The delta ray rate does depend on the beam intensity. This reflects a change in efficiency of the chamber as delta ray production rates are independent of beam intensity. For this work, we never actually measured the absolute efficiency of the fJ cha.m ber. All we need is the detection rate~ efficiency x delta ray flux at p. The -250I 20 ~ 2 x 20GeV/c il11-----+-. I - ~ 0 20 18 - D 50GeV/c 15- i '°o I e IOOGeV/c I tI R c a: I I .I at. a: ~ I J---..d fer IOO GeV ewera9e I IOOK I I I I I 2001< SOOK 4001< 500K aoDK Beam Intensity, particles/pulse T T I I I *I * J. ~ >0 0:: ! 2 'ii 14 0 12 T I JC I J. 10 100 l!>O 200 250 Run 500 350 Figure D-12. Delta ray rates at the fJ chamber. Data are from curve through runs and are plotted against beam intensity (a) and run number (b) . (J chamber delta ray rate dependence with beam intensity is shown in figure D-12a, which shows a reduction of about 20 to 25% in going from essentially no beam to 600K particles per pulse. This reduction in rate (hence also efficiency) seems to be from "sagging" of the chamber high voltage during beam pulses. Such sagging is more pronounced at higher beam intensities, and is believed to come from increased levels of beam halo and other radiation about the chamber. Beam halo is particularly destructive. A particle passing through the chamber parallel to its axis will deposit much more ionization in it than a particle coming from the target - 251would. Furthermore, much of the halo would have interacted in the first Jaw counter, V0 , to produce showers parallel to the p chamber. The 20 GeV point is an apparent exception to the intensity dependence claims. But there is evidence that we had much more halo than beam at 20 GeV. The BEAM rate was about 50K particles per pulse, while the rate into Sa· Sb was over five times this. A lot of particles missed the hole in Sc. The beam focus was much poorer at 20 GeV than at the other momenta, and it is reasonable to expect that there was considerable halo outside the beam counters. For these reasons, we use the measured delta ray rates at 20 GeV, rather that the value that the 100 GeV data would imply at 50K particles per pulse. The 50 GeV rate is consistent with the 100 GeV intensity dependence, and the curve through conditions at 50 GeV were comparable to the 1T7m conditions at 50 GeV. So we use the measured curve through value in the 50 GeV correction. The 100 GeV mm data were virtually all taken at beam intensities greater than 300K particles per pulse. Since the measured delta ray rate is seen to be constant above that level. we combined the data from the runs above 290K particles per pulse for the rates used here. No explicit beam intensity dependence was used in the correction weights beyond the beam momentum selection. The delta ray rate was plotted against run number, figure D-12b, to look for chamber deterioration; none was observed. The spring '77 curve through runs were all done with a full target. We also need target empty data to separate delta rays coming from the liquid hydrogen and from the vacuum jacket end cap. For this, we used three 100 GeV curve through runs from the winter '78 data set, two with target full and one with the target empty. With these we obtained a target empty rate expressed as a fraction of the target full rate of 6.90±1.93%. The curve through delta ray rates are given in table D.3. - 252- Table D.3 Curve Through Delta Ray Rates and Model Parameters Raw(%) LH2 (3) End Cap (3) p(lmeter) pca,p 100 GeV 16.12±.34 15.01±.46 1.11±.31 .533±.018 .989±.003 50GeV 17.91±.89 16.67±.96 1.24±.35 .598±.037 .988±.035 20GeV 11.42±.82 10.63±.85 .79±.23 .369±.031 .992±.002 The correction factor for a mm event was built wing a simple absorption model with its parameters derived from the curve through results. We assumed that the probability per unit length, p, for a track to create detected delta rays is constant along the length of the hydrogen target. We discuss how reasonable this is later. The probability Pf that a particle survives its passage through the entire target without making delta ray hits is : Pf =e -pL = 1-Rh. (D.21) where L=.3048m is the target length, and R"' is the measured delta ray rate from curve through data, as given in the LH 2 column of table D.3. The chance that a particle passes through the end cap without making delta ray hits is (D.22) where the Re values are given in table D.3 which also gives the p and pcap values. For a mm. event, the probabilities of survival for each particle in the hydrogen depend on its path length in the liquid: (D.23) (D.24) - 253- \ \' \ 30 \ \ \ 20 \ \ \ IO '< I ~a: cross section ' .......... ---• %-----~----2~--3~-.__--5~--6- K, MeV Figure D-12. Delta ray kinematics. Smooth curve is the recoil angle - energy dependence. Dashed curve is proportional to the cross section, vertical scale for it is arbitrary. Hatched limits show effects of target region material. Detected delta rays would be produced with energies ~ 2 MeV. where z 11 is the vertex, zv and zcl are the upstream and downstream ends of the hydrogen flask, L =zc1 -zu. Using this, and including a pca:p factor for each of the two forward particles the chance that an event survives a delta ray veto is, (D.25) at 100GeV/ c. Each observed event is then given the weight w6 = 1./ P8 . Delta ray production is simply ne elastic scattering. An estimate of the veto rate can therefore be calculated from general principles using formulae for the ne cross section, simple recoil kinematics, the range-energy relation for electrons, and - 254- 'ff. 80 .; ~ f 60 .E ~ 0 -~ 40 E ., a:: 20 upstream 2.o.so -o.~o -o.~ Z,m -o.40 -0.20 o Figure D-14. Position dependence of the veto chance 1-p. Heavy curve uses our estimate of the target region material. values for the fJ chamber efficiency and the arn.ount of material through which a delta ray must pass. This calculation has been made using our best estimate of the material in the target area and an efficiency value found during test run measurements of the 3rrp reaction. The asymptotic efficiency value was e Ri . 94, a value we expect is higher than the true value for 100 GeV running. The calculation ignored electron straggling, assumed a pencil beam through the target center (so no azimuthal integration was needed), and considered that any electron getting into the {3 chamber had chance e of being detected. Figure D-13 illustrates the recoil electron kinematics. The solid curve is the recoil angle with respect to the beam. The calculated lower limit Tmin of the electron energy imposed by the kinematics and range-energy relation is shown. This model does show that the probability p in equation D.21 is z dependent, an effect not in the simple model, because of a "high momentum., low recoil angle cutoff 0 -255- L4 1.3 - ~ elastic scatter model ~ ~ ~ 1.2 I.I ____.J.0_2-J i.o--_-=o-=.s--"""":_o~.-=-5--_-::!oL-.4:----_...1.o.-3 Zv, meters Figure D-15. Comparison between simple model (used for corrections) and the elastic scatter model. Both corrections are constrained by the measured curve through delta ray rate. For all practical purposes, they are equivalent. imposed on delta rays by the target and P chamber geometry. Figure D-14 shows the z dependence, normalized to 1 at zu, (the figure assumes an infinitely long flask). Using an efficiency of .94 and an estimated T min of 1.85 MeV the calculation predicted a 13.4% delta ray rate for the hydrogen flask, about 1.5% below the 100 GeV measurement. Fortunately, we don't need to pursue the elastic scatter calculation beyond this qualitative level. Such work would require using the 3np trigger to find beam intensity dependent efficiencies, a probable relaxing of the simplifying assumptions, and adjusting Tmm to agree with the curve through measurements, (with possible changes in it for beam intensity related threshold changes). We are saved because the simple absorption model with a constant p is good enough. Numerically, it is within 1% of the elastic scatter results when we set Tmin to conform to a crucial -256 .. constraint. The delta ray corrections for z =Zu and z =z 4 are fixed by the curve through measurem.ents regardless of the mod.el UJe choose. The results of this are . shown in figure D-15 for 100 GeV weights. The curve through based numbers can be checked with a small sample of real delta ray vetos contained in the mrX data, although there are too few such events to get a decent Zv measurement with 1mX. The rate agrees with the results of this section. D.6 Chamber Efficiency Measurements Position dependent chamber efficiencies were central to our tracking efficiency correction, section 4.9. Most chambers sag by varying amounts in the beam region. In the x-and some u-spark planes, the efficiencies fall off near the chamber edge. Also, the x-spark chambers have a geometric cutoff at there edges from the u-spark chambers (x and u share a common gap.) Finally the proportional chambers had a number of "dead" wires, from amplifier problems and/or discontinuous wires through their epoxy wire supports. In determining chamber efficiencies, one must know that a real track passed through a chamber in order to give it a valid reason to respond. It seems evident, therefore, that using found and reliable tracks is essential to the process. But this implies that the tracks used have already introduced a bias, both from the trigger and tracking requirements. A simple ratio of sparks (or pwc hits) on tracks to total tracks overestimates the chamber efficiency and a method to remove the biases must be developed. One (approximate) option would be to find tracks with reduced requirements, somehow remove new spurious tracks, and do the simple ratio, knowing that the biases are reduced. As a function of the ;'looseness" of the new requirements, one might be able to determine efficiencies as the limit at no requirements at all. We chose, instead, to remove our biases directly with the method described - 257- below, which did not need any second or third rounds of tracking with reduced requirements. Our efficiencies were found by analyzing tracks from the 3np trigger. This trigger was chosen because although it was heavily divided, it was quite clean and had a reasonably large amount of good track data, and a loose, more easily unbiased trigger than the other reactions. Indeed, there were more good 3rrp events than 1T'1T7l. events. One expects that chamber efficiencies depend only where a track went, not on the trigger or reaction Our efficiency results were verified by also studying rrp elastic data. The 311p CST's for the same runs used in mm analysis, were analyzed by first requiring a good three body event. A three particle vertex in the hydrogen target, total charge -1, and no particles striking the 2x2 were all required. All tracks considered were SCLEAN approved and TARGTRK analysis was required. We required that the total energy be less than 105 GeV, but permitted off energy (missing neutral particles) events to enhance the slow particle flux. A software trigger cut was made. Assured of using good tracks, the crucial step is removing the trigger and tracking biases. A chamber's response is taken as unbiased if th.at chamber is not needed to form the trigger of find the track. That is, if other chambers involved in a requirement provide enough hits to satisfy it, then a track will be found regardless of the response of the chamber in question. This is equivalent to the claim that if a track has exactly the minimum number of hits needed to satisfy a requirem~nt, then the chambers with the hits are all biased and only the chambers with no hits are unbiased. Further, if the minimum hit requirement is exceeded, even by just one hit, then all chambers are unbiased. This applies to each and every one of out requirements. -258- It is clear why we need to remove the biases. All observed tracks have met at least the minimum requirements. We wouldn't see a track if it didn't. Ignoring them would artificially inflate the efficiencies. By making topology cuts, we deal only with tracks we can reliably associate with real particles. Since the loose TEARS requirements allow many phony or "ghost" tracks to be found, even after cleanups, including them would cause efficiencies to be underestimated. We examined the satisfaction of trigger and tracking requirements by an event looking for chambers which must be thrown out because of requirements met only minimally. As most chambers are involved in more than one requirement, usually a small group or two and overall view, a chamber is removed only in the sense of using its hit (if present) for its own efficiency calculation. It is still available for satisfying requirements when other chambers are considered. A final criterion for eliminating a chamber is shared hits, from close tracks. Because the ionization in a chamber is doubled when two tracks pass the same location, the inefficiency is roughly squared. The shared hit test was only available for pwc's. Next, after a chamber fiducial check, the response of acceptable chambers is output in a series of scatter plots, half of which record the track position, and the other half recording the track location when a hit is present. Ratios of appropriate scatter plot slices were then used to make position dependent efficiency arrays. The bin size in the arrays is itself position dependent, giving fine binning near the beam and large bins away from the beam where statistics become marginal. The small bin size is .5 cm for spark chambers. and one wire spacing (rounded to the nearest millimeter) for the pwc's. One and two bin holes in the pwc's were checked to be sure they were from bad channels and not the binning. Two bin holes in a pwc reflect a poor wire at or near a bin edge. Plots of the efficiency arrays for positive magnet are shown in figures D-16 and D-17. The coordinates are in the lab, and the scale reflects the double bin size, being expanded in the beam region. Points - 259outside a chamber's fiducial volume are assigned zero efficiency, and average ' values ,denoted by "A" with no error bar, are assigned in cases of zero or extremely few events within the chamber itself. A local average was used near the x spark chamber edges because of their construction method, figure 2-8. The efficiency arrays were indexed only by the coordinate measured for storage reasons, (they have about ten thousand bins as it is). We thus assume that the efficiency is constant along a wire. This assumption works well when we make beam region (2x2) cuts. Beam region problems in the proportional chambers seem concentrated in the two dimensional beam spot. Wires passing through the beam spot behave "normally away from the spot. This constant efficiency assumption 11 runs into a problem at the edge of the x-spark chambers because the x wires share their gap with the u (slant) wires. Special procedures were developed to deal with this. but we later decided to exclude this region from the spectrometer fiducial volume. Separate arrays were created for each beam momentum and magnet polarity. Otherwise, the efficiencies are whole run averages. We checked that the reconstruction efficiencies are consistent over the run by doing the analysis initially on smaller sets of runs. A failure of an F spark chamber for a few late runs didn't even affect the results, attesting to the loose requirements of TEARS. We see poor reconstruction efficiencies only when most or all chambers in a requirement have rotten efficiencies where a track passes. - 280- -.25 0.0 .25 x 100 ..,. : - ---=..;;..!.gl _'i?t ~~...""'·~- - ._-.,.,.-.. A4"9' ., M ;. u ; ElU 50 .-4 u .... .... l&l .-4 0 -.25 u o.o .25 0.0 .25 100 ElY 50 0 -.25 Y , 100 aeters -ri-1tl't"'1"". .·,1w.-...~..........."i'i~-'..'1~-~·,--=- - 50 I E2X 0 -.25 0.0 .25 x 100 ~ .;, u r:: ~ ~ 50 E2U C) ........ ~ l&l 0 -.25 0.0 u .25 100 50 E2Y -.25 0.0 .25 Y, meters Figure D-16a. E-1 and E-2 Spark chamber efficiencies, 100 GeV le, lm.ag = +180 . Note: Beam regions are expandP.d in all chamber efficiency plots. Divisions along horizontal axes are equally spaced at indicated scale. 100 . ., . - 261 - -1-1~1,prw"~~::··t '"""'Y""---~·~~~.,~·,1t~r= 50 0 -,25 o.o ,25 x 100 .:. ::..iff11";11'ti~t1tti~~iti~ttii"..;~·~~titl'~·~.;,..,./_;...~~1;;~,~""~-'F. . . ---~· M .;. ....... ... u ~ ElU 50 u Ja:I 0 - , 25 0.0 u .25 100 so EJY -.25 0.0 .25 Y, meters 100 50 0 -.25 100 H >.u ~ ....u Cl 50 .... ..... o.o x .25 .• -~j-~~!11llli~~.'1'"VN1""'.,,.................-.,.._r...,.....-..i,'til1'i.'!!1!·1.:.· I E4U ..... Ja:I 0 -.25 o.u .25 u 100 50 E4Y -.25 0.0 .25 Y, aeters Figure D-16b. E-3 and E4 Spark chamber efficiencies, 100 GeV le, Ima.g = +180. - 262100 _1rn1 inlill!'iiitti'tqp;;l·--~-.....,,..,~...."'..,......1,-.·.,,,1,..-..............·~·~~.\1111im111- 50 1 1111~~ FlX I 0 -1.0 -.2S 0.0 .2S 1.0 .2S 1.0 x 100 H >.u c: .....II 50 u ......... ....lllJ 0 -1.0 -.2S o.o u 100 so 0.0 .2S Y, meters 100 -1.0 -.2S 0.0 .2S 1.0 x 100 H .;, u c: .....QI u ......... ....c.J 1'li#lli,W'11'1'r.1,~ti':,,.,...,....~::·1''1•·v~w''""1'1;i;i,,•1,•,·'~.~.·.,·.._.. .,. . . . . . . "'l1Wi\'~',~1r/\1 so I 0 -1.0 -.2S 0.0 .2S 1.0 u 100 so -.:lS 0.0 .2S Y, meters Figure D-16c. F-1 and F-2 Spark chamber efficiencies, 100 GeY Jc, lmcg = +180. - 263 100 so 0 o.o -.2S -1.0 .2S 1.0 x 100 H ;.. u c: "u · · l111'f1"°""~<";'~1~i....·'''"'~;~~.;~~••.;,'•'l1\~';;;.,;;;----.~."lsWl,- so ,3u · .4 t .... .... .4 (al 0 -.2S -1.0 .2S 0.0 1.0 u 100 so 0 o.o -.2S .2S T, aeters 100 so 0 -.2S -1.0 0.0 .2S 1.0 x 100 .;.. u c: . i~.l•P,Ji11.!f!Hl~~tfil"._,,........1tiiit+l1~'9;t.,.t..."'1 . • I . .~tl!'i'~'i, .. ~1111.. T"'1,•1' ""••l•'""~. .,,.... I~· r1·T i . H so ! . ', , "',1•; . ,~~,AA ~ A NU "u .4 .4 .... .... w 0 -.25 -1.0 .25 0.0 1.0 u 100 so R ~·r.--~""-M - ·rut _; .,,,.,,-.,,-..,..;"t"f",,,,,,,,,.~ ..... , .. ~l1111 ·-- F4 Y 0 -.2S o.o .25 Y, .eters Figure D-16d. F-3 and F-4 Spark chamber efficiencies, 100 GeV le, Imag = +180 . - 264100 AXl 50 -.024 100 ·--,...,,.......- 50 AYl H .;. CJ i.... u 0 .024 -.024 .024 0 x x 100 50 .._._ . -· · --1~--";,,;,.;;,,..i,.,,,,.._~._-_ AY2 ........ ....Ill 0 -.024 u .024 -.024 100 100 i; . :. AV 50 . t,. I ·t -.024 .024 0 y y 50 -.·.J.~ .......--.._.,.==I I AU .024 0 ,.,. . . _ -.024 0 . 024 U, meters V, meters 100 50 BXP 0 -.07 0 .07 x 100 H ~tr·-·"-·-·· · 1r1r~~ I - - . - ;.. .;.. () ti ....= u .... .... .... l&l 50 BX 0 -.Ol 0 .07 x 100 . .!,.,...... ~ ~- . .... ••- ..........- ,..,.......;!;• ! 50 BY 0 -.07 0 .07 Y, meters Figure D-17a. A and B station proportional chamber efficiencies, 100 GeV /c, lma.g = + 180. Note: Beam regions are expanded in all chamber emciency plots. Divisions along horizontal axes are equally spaced at indicated scale . - 265 - 100 .. _ ~.. . j , - .. . . . . ..- - " " ' · - - - - . . . . . - - so . .:. ------1o4i~ ,,I ex ' 0 -.07 0 .07 x 100 .......,_-.--.,,-.-....-----~­ ___,-\. ' so CY 0 -.07 0 .07 Y. ~ters Figure D-: 7b. 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