A Study of the Reactions π^±p → π^±π^+π^-π^op and π^±p → π^±π^+π^+π^-n at P_(lab) = 14 GeV/c Using a Triggered Hybrid Bubble Chamber

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Nagy, Frank Joseph (1980) A Study of the Reactions π^±p → π^±π^+π^-π^op and π^±p → π^±π^+π^+π^-n at P_(lab) = 14 GeV/c Using a Triggered Hybrid Bubble Chamber. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/q42m-vd27. https://resolver.caltech.edu/CaltechTHESIS:05192017-102645117

Abstract

We have studied the reactions π ^± p → π ^± π ⁺ π ^- π ^o p and π ^± π ⁺ π ⁺ π ^- n at a beam momentum of 14 GeV/c. A bubble chamber with a downstream wire spark chamber spectrometer was used to record the data. The bubble chamber camera was triggered by identifing inelastic events in an online computer using data from the downstream spectrometer. The film taken represents an exposure of about 80 events/microbarn for the π ⁺ data and 70 events/microbarn for the π ^- data.

We find these reactions to be very rich in subprocesses involving baryon and meson resonances. The invariant mass spectra are presented and estimates of the cross sections for the production of known baryon and meson resonances are given.

The reactions π ^± p → π ^± ω ^o p provided more evidence for the existence of an N ^* resonance with mass 1789±5 MeV and width 81±9 MeV which decays into ω ^o p. Using previously published data along with our results, we find that the production cross section of this N ^* is independent of s. Studies of the angular distributions raise questions about the validity of the spin-parity analyses of this N ^* done so far.

We have studied the processes π ^± p → π ^± η ^o p in the relatively unexplored region of low |t _ππ | and small η ^o p mass. We found that the π ⁺ η ^o p cross section is about twice the π ^- η ^o p cross section in this region. The η ^o p mass spectrum for the π ⁺ data shows an enhancement at about 1600 MeV while the π ^- data show no evidence of a peak in the η ^o p mass spectrum.

Item Type:

Thesis (Dissertation (Ph.D.))

Subject Keywords:

(Physics)

Degree Grantor:

California Institute of Technology

Division:

Physics, Mathematics and Astronomy

Major Option:

Physics

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Public (worldwide access)

Research Advisor(s):

Peck, Charles W.

Thesis Committee:

Unknown, Unknown

Defense Date:

20 December 1979

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Funding Agency	Grant Number
Department of Energy	UNSPECIFIED

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CaltechTHESIS:05192017-102645117

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https://resolver.caltech.edu/CaltechTHESIS:05192017-102645117

DOI:

10.7907/q42m-vd27

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No commercial reproduction, distribution, display or performance rights in this work are provided.

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10186

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CaltechTHESIS

Deposited By:

Benjamin Perez

Deposited On:

19 May 2017 20:58

Last Modified:

15 Jan 2025 00:58

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A Study of the Reactions rr ±p + rr ±rr +rr - rr 0 p and rr ±p + rr ±rr +rr +rr - n at plab = 14 GeV/c Using a Triggered Hybrid Bubble Chamber Thesis by Frank Joseph Nagy In Partial Fullfilment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1980 (Submitted December 20, 1979) -ii- "Any sufficiently advanced technology is indistinguishable from magic . " - Arthur C. Clarke "When the end of the world is near, spend the remaining time in a bar." - Jack L. Chalker from And the Devil Will Drag You Under -iiiAcknowledgements Foremost I must acknowledge the help and guidance of my thesis advisor, Dr. Charles W. Peck, whose leadership was crucial in performing this demanding experiment and whose encouragement helped to bring my thesis work to its completion. I also wish to thank my collabora- tors from the three institutions involved in this experiment: California Institute of Technology (Cal Tech), Lawrence Berkeley Laboratory (LBL), and Stanford Linear Accelerator Center (SLAC). Thanks must also be extended to the scanners and measurers of the bubble chamber data analysis staffs of these institutions and to the accelerator and bubble chamber operations crews of SLAC without whose efforts this experiment could not have been done. I would like to extend special thanks to the following physicists for their efforts on the experiment and their guidance during my stays at the various institutions: V. Davidson, A. Dzierba, A. Firestone, L. C. Rosenfeld, and A. Sheng of Cal Tech, R. Ely, D. Grether, and P. Oddone of LBL, and J. Ballam, J. T . Carroll, G. B. Chadwick, V. Chaloupka, D. Linglin, and K. C. Moffeit of SLAC. I also wish to thank G. C. Fox and R. D. Field of Cal Tech for their support and help. To my many friends at Cal Tech, I wish to extend my thanks for enriching my life. To a special group, my appreciation for their love and understanding. For "entertaining" me with their endless questions and problems concerning computers, I wish the terminal users the best of luck in the future (they will need it). I must also express my -iv- appreciation of the efforts of the Zeta plotter and the unnamed author of the PPLOT plotting program without whom this thesis could not be written. I also extend thanks to Louise Sartain for putting up with me for all these years. Finally, I want to thank the U. S. Department of Energy for their support of this research. -v- Abstract + ± + - 0 ± ± + + We have studied the reactions rr-p + rr rr rr rr p and rr p + rr rr rr rr n at a beam momentum of 14 GeV/c. A bubble chamber with a downstream wire spark chamber spectrometer was used to record the data. The bub- ble chamber camera was triggered by identifing inelastic events in an online computer using data from the downstream spectrometer. The film taken represents an exposure of about 80 events/microbarn for the rr + data and 70 events/microbarn for the rr data. We find these reactions to be very rich in subprocesses involving baryon and meson resonances. The invariant mass spectra are presented and estimates of the cross sections for the production of known baryon and meson resonances are given. ± 0 + The reactions TI-p + TI w p provided more evidence for the existence of an N* resonance with mass 1789±5 MeV and width 81±9 MeV which decays 0 into w p. Using previously published data along with our results, we find that the production cross section of this N* is independent of s. Studies of the angular distributions raise questions about the validity of the spin-parity analyses of this N* done so far. + ± 0 We have studied the processes rr-p + rr n p in the relatively unexplored region of low It Tirr I and small n° p mass. - + 0 We found that the TI n p 0 cross section is about twice the TI n p cross section in this region. 0 The n p mass spectrum for the rr 1600 MeV while the TI spectrum. + data shows an enhancement at about data show no evidence of a peak in the n°p mass -viContents Acknowledgements iii Abstract v Chapter I. Introduction 1. Diffraction Dissociation 1 2. This Experiment 2 3. Five-body Final States: np~nnnN 5 10 5. Summary of the Results 16 Chapter II. Experimental Method 1. Overview 19 2. Beam 19 3. Bubble Chamber 22 4. Spectrometer 23 5. Online Trigger and Data Collection Computer and Programs 29 Chapter III. Data Reduction 1. Overview 33 2. Spark Chamber Data 33 3. Bubble Chamber Data 40 4. Merging the Spark Chamber and Bubble Chamber Data 44 5. Kinematic Fitting 46 6. Fit Selection 49 Chapter IV. Cross Section Determination 1. Overview 56 -vii- 2. Elastics Normalization 57 3. Beam Contamination 63 4. Geometrical Acceptance Correction 66 5. Computer Trigger Efficiency Correction 70 6. Channel Corrections and Background Estimates 77 Chapter V. Results of the Five-body Channels 1. Overview 102 2. The da/dt N Distributions 109 3. Invariant Masses Involving the Fast Pion 113 4. Fast Invariant ~1asses Selected on a Fast p Meson 126 5. Invariant Masses Involving the Slow System Particles 133 6. Associated Fast Meson and Slow System Resonance Production 159 7. Double Slow Resonance Production and Sequential Decays 205 pt Chapter VI. Production of the n° and w0 Mesons 237 1. Introduction 2. 1T 3. 'TT ± ± 0 240 n p Final State 0 w p Final State 251 0 4. Angular Distributions of the w p System 273 a) Phenomenology of Angular Distributions 273 b) Observed Angular Distributions 282 0 5 . Discussion of thew p Resonance Spin-parity Analyses Appendix A. Fast Algorithm 324 330 -viii- Appendix B. TORTIS Track Finding and Spark Chamber Calibration 1. Track Finding 342 2. Calibration Test Quantities 347 3. Initial Calibration 350 4. Tracking the Calibration with Data Runs 351 Appendix C. Computer Trigger Efficiency Determination 355 List of References 360 -ixList of Tables Table I.l rr +p + rr +rrrrrrN cross sections 6 I.2 rr p + rr rrrrrrN cross sections 7 I. 3 Predicted maximum cross section estimates 9 I.4 + 0 + 0 rr +p + rr pw and rr +p + rr PT"l cross sections 11 I.5 rr p + rr pw I.6 Predicted w and ri I. 7 A compilation of the observations of the pw enhancement II.l Beam shape and momentum at bubble chamber 22 III.l Results of the data collection and reduction for each experiment 35 III.2 Estimate of the fraction of lC events assigned to the wrong channel 54 IV.l Lost picture fractions 61 IV.2 Elastics Normalization quantities 62 IV .3 Four prong exposures 62 IV.4 Beam fractions 64 IV.5 Lost and background event counts in lC 4-prong channels 80 IV.6 Normalizations and background fractions for the lC 4-prong channels 101 v .1 Cuts used to define the lC data sample 104 V.2 Observed channel cross sections 105 V.3 Results of the fits to da/dt v .4 Results of the fits to da/dt N pr 0 and rr p + rr p ri 0 0 0 cross section 12 12 cross sections rrrr 0 15 A exp (BI t rr rr I) 106 A exp(B l tpNl+ct~N) 110 -xTable V.5 Resonance masses and widths used in the fits 114 V.6 Major fast resonance production estimates 115 V.7 Additional fast resonance production estimates 116 V.8 Channel cross sections with fast resonance production removed 118 V.9 Background fractions and total events within fast p cuts 119 V.10 Estimated slow system resonance production V.ll Background fractions and total events within slow ti and p cuts 161 V.12 Estimated slow system resonance production for the fast p cuts 164-165 v .13 Estimated fast meson resonance production for slow system resonance cuts 186-187 V.14 Estimated slow system double resonance production 207 V.15 Estimated slow system resonance production with cascade decay 208 VI.l Fitted parameters for peak 240 VI.2 0 + - 0 Fitted parameters for w -YJT Tf Tf peak 253 VI.3 Fitted parameters for the w p peak VI.4 da/dt VI.5 c 0 11 -YJT + Tf 0 Tf 136-137 0 1 265 0 Tf Tf slopes for w p mass bands 1 values from l+c cos~ PP fits to the da/d~ 269 PP 293 distributions VI.6 Results of the l+a cos8 +a cos 2 e fits to the 1 PP 2 PP da/dcose distributions 294 Asymmetry of the da/dcos8 295 PP VI. 7 PP distributions -xiTable VI.8 a 2 values from fits of l+a cos 2 epn to the da/dcos6pn 2 distributions VI.9 Results of VI.10 w Gottfried-Jackson frame p l+c cos~ · +c cos2~ 1 2 pn distributions pn 0 00 fits to the da/d~ pn density matrix 305 306 307 element VI.11 a 2 values from l+a cos 2 enw fits to the da/dcosenw 2 309 distributions 0 VI.12 w helicity frame p VI.13 c 2 density matrix element 00 318 values from l+c cos2~nw fits to the da/d~nw 2 319 distributions VI.14 0 w helicity frame p _ VI.15 cose 1 1 PP versus cose density matrix element 319 0 nw correlation results for w peak 321 events VI.16 VI.17 cos6 cose PP PP versus cose 0 nw correlation results for w wings 322 events versus cos6 0 pn correlation results for w peak 323 events correlation pattern 326 327 A.l versus cos8 correlation fractions PP nw Definition of quantities in Appendix A B.l Constants correction formulae 353 B.2 R.M.S. run-to-run changes in the spark chamber constant354 constants (in inches) C.l m(p) coefficients 357 C.2 Elastic roll elastic mis-trigger fraction 359 VI.18 Predicted cos6 versus cos6 p pp _ nw for J =3/2 VI.19 Combined cos6 - + 340 -xiiList of Figures Fig. I.l Plots of the Tables I.l and I.2 cross sections 8 1.2 Plots of the Tables I.4 and I.5 cross sections 13 II.l Elevation view of the secondary beam line 21 II.2 Plan view of the bubble chamber and spectrometer 24 II .3 Schematic of the trigger, spark digitization, and computer input electronics 27 II.4 Flowchart of the online computer program 30 III.l Flowchart of the data reduction process 34 IV .1 Contour plot of s(p,cose) 69 IV.2 <Ef> versus recoil (N * ) mass 74 75 IV .3 Corrected and uncorrected n distributions IV.5 Kinematic fit confidence level distributions for the lC channels IV. 6a-d Missing-mass-squared (rnm 2 ) distributions (dN/dmm 2 ) 81-85 IV. 7a-d. dN/dmm2 for lC events with CL<5% 87-89 IV.8a-b dN/dmm 2 for lC events rejected by ionization 92-93 IV. 9a-b dN/dmm 2 for lC events with a rejected ambiguous lC fit 94-95 IV . lOa-d dN/dmm2 for lC events with an ambiguous lC fit 96-98 V.l General Feynman diagrams representing our data 103 v .2 dcr/dt for the lC reactions 108 V.3 dcr/dtpN for the lC reactions 111 1rn recoil mass 76 IV.4 78 -xiii- Fig. V.4 dcr/dt V .Sa-£ dN/dm for fast invariant masses V.6a-k dN/dm for fast invariant masses cut on pf or pf V. 7a-k dcr/dm for TIO channel slow system invariant masses 138-149 V .8a-h da/dm for n channel slow system invariant masses V. 9a-g dN/dm for TI PP for the 4C reactions 112 120-125 ± 0 0 128-132 150-158 channel slow system invariant masses 166-173 0 cut on pf V. lOa-f dN/dm for n channel slow system invariant masses 174-180 0 cut on pf V.lla-d dN/dm for TI 0 channel slow system invariant masses 181-185 + cut on pf -H- V.12a-j dN/dm for fast invariant masse? cut on 6 V.13a-£ dN/dm for fast invariant masses cut on slow p V.14a-n dN/dm for fast invariant masses cut on slow p V.15a-d dcr/dm for TI 0 0 ± 188-192 193-198 199-204 channel slow system invariant masses 209-213 cut on t::. V.16a-b or 6 -H- dcr/dm for n channel slow system invariant masses 214-216 cut on 6 V.17a-d da/dm for rr 0 channel slow system invariant masses 217-221 cut on slow p V.18a-d da/dm for n channel slow system invariant masses cut on slow p V.19a-d 0 dcr/dm for TIO 222-226 0 channel slow system invariant masses 227-231 cut on slow p+ V. 20a-d dcr/dm for rr 0 channel slow system invariant masses 232-236 cut on slow p -xivFig. ± 0 AZ+ exclusion cut VI.l dN/dm for Tifn VI.2 dcr/dm for VI.3 dcr/dm for n p mass VI.4 Feynman diagrams for n VI .5a-b Scatterplots of TI TI TI VI.6 dcr/dm for + - 0 mass in w0 region 252 VI. 7a-b • w0 pea k an d in • w0 wings • dN/d l\A f or events in 254-256 VI.8 dcr/dt VI.9 dcr/dm for w p mass 261 VI.10 + 0 0 Scatterplot of Tifw mass versus w p mass 262 VI. lla Scatterplot of TI p mass versus w p mass VI .llb Scatterplot of TI p mass versus TI TI TI p mass VI .12a-b dcr/dt for separate w p mass regions 266-268 VI.13 s dependence of N*-+w 0 p production cross section 270 VI.14 mass showing + - 0 mass in . 0 . n region TI TI TI 0 production TI TI TI for events in w peak + 0 + + - 0 0 0 Definition of w p Gottfried-Jackson frame and the (8 , versus w p mass VI.16b <Ym> versus TI +TI - TI o p mass VI .17a-b dcr/dcos8 VI .18a-b dcr/d<P VI .19a-b dcr/dcose 0 264 279 280 281 284 !l (wo !l for low masses for low masses PP 263 pn 0 pp 249-250 PP 0 PP 247 258-259 0 PP VI.15a 0 0 TITI 241-242 245 + - 0 mass versus TI +TI - TI 0 p mass TI TI 239 for high masses . ) wings 285 287-288 289-290 291-292 -xvFig. 0 VI.20 case VI. 2la-b do/dcos8 VI. 22a-b do/d¢ VI. 23a-b do/dcose VI. 24a-b do / d~pn for high masses VI.25 w Gottfried-Jackson frame p VI. 26a-b do/dcose VI.27a-b do/d¢ VI.28a-b do/dcos8 VI. 29a-b d o/ d ~ A.l Schematic of FAST track analysis algorithm PP asymmetry versus w p mass pn pn 297-298 for low masses 299-300 for low masses pn 301-302 for high masses 303-304 0 nw nw 296 nw 0 00 versus w p mass for low masses for low masses nw for high masses for high masses 308 310-311 312-313 314-315 316-317 341 -1- Chapter I Introduction 1. Diffractive Dissociation The major single component of the total cross section (~30%-50%) for hadron-hadron scattering is forward diffractive scattering. This type of scattering consists of two similar parts: elastic scattering and inelastic diffractive dissociation. Diffractive dissociation reac- tions are similar to elastic scattering except that one of the particles involved in the reaction is transformed into several final state particles. As was first pointed out by Good and Walker [1960], this process is analogous to the diffraction of polarized light by a polarizer in which the incoming internal state (polarization) is transformed into a new outgoing internal state. Hadronic diffraction has been extensively studied in many experiments (see the reviews by Leith [1975] for instance). In general, diffractive dissociation has properties similar to those of elastic scattering. Compared to other inelastic processes, both have very little energy dependence, are independent of the non-diffracting incoming particle (factorizable) , and are sharply forward-peaked [Leith 1975]. Theoretical ideas on diffractive dissociation stress this similarity; exchange of the Pomeron Regge pole is used to explain both elastic- scattering and inelastic diffractive dissociation. Other theoretical models, such as that of Drell, Hiida, and Deck [Drell and Hiida 1961 and Deck 1964], have been put forward to explain non-resonant --- -2diffractive dissociation in which the final state particles do not come from a diffractively produced excited state. Much experimental work has been invested in studying these non-resonant states as in the diffraction of beam pions into a low mass 3rr system, in particular the A and A effects. 1 3 At the same time, studies of the diffractive pro- duction of the A meson from beam pions have shown that excited states 2 can be diffractively produced. 2. This Experiment As mentioned above, pion dissociation has been very extensively studied in many experiments. Nucleon dissociation, unlike pion dis- sociation, has yet to be examined by any experiment with comparable statistics. Our experiment was conceived to provide a high statistics body of data on nucleon diffractive dissociation by pion beams. This experiment also had to cover most of the 4rr solid angle so that the particle angular distributions resulting from the fragmentation of the nucleon would be unbiased . The necessity of a laboratory frame 4rr detector can be gotten around by using a nucleon beam where the products of nucleon dissociation appear as a system of fast forward particles. Such an experiment still requires a large forward detector system to cover most of the 4rr solid angle in the beam nucleon rest frame. In addition there is the added complication of the veto sys- tem for the nucleon target to insure that only the beam particle dissociates. This veto system introduces further inefficiencies, partic- ularly in the region of low momentum transfer where the target recoil -3particles may not have enough momenta to reach the veto detectors due to energy loss in the target and its container. Finally, with a pion beam it is very easy to change·,from a particle to an anti-particle beam (n + to n ) to test factorization while antiproton targets do not exist. By using a liquid hydrogen bubble chamber as the target and detec- tor, nearly complete coverage of the laboratory 4n solid angle is passible . . However, a standard bubble chamber experiment designed to gather large numbers of events in the proton diffractive dissociation region would require an unmanageably large number of pictures, most of which would be of elastic scattering, pion diffraction, or non-diffractive events. The film processing load can be reduced to a workable size if only those events of interest are recorded by somehow triggering the bubble chamber. Since the bubble chamber must be made track- sensitive before each beam pulse (by sharply reducing the pressure, a process with a millisecond time scale) , this trigger must operate between the time of the beam pulse and the time (1-2 milliseconds later) when the camera flash lamps would normally be fired. Thus the trigger for the bubble chamber is of the camera flash lamps, not the bubble chamber expansion mechanism. Our experiment used as a trigger the requirement that the mass recoiling against a fast forward particle be within preset limits (the lower limit was just above the elastic peak). We detected and mea- sured the fast forward particle in a magnetic spectrometer just downstream of the bubble chamber. The trigger calculations were done by -4an online computer. Since a triggered bubble chamber does not take a picture with every beam pulse, a rapid cycling bubble chamber allows for a modest real event rate even if the trigger conditions are met for only a few percent of the pulses. The SLAG 40 inch rapid cycling bubble chamber (4-10 pps) was chosen for this experiment. This cham- ber also had a beam exit window through the magnetic flux return, a necessary condition for this experiment. of 14 GeV/c was used. A pion beam with a momentum At this momentum we had sufficient beam inten- sity to have about 10 beam tracks per pulse in the bubble chamber in a very small momentum bite (about ±0.3%). The experimental apparatus and data reduction procedures are discussed further in later chapters. More details of the experimental apparatus and the data reduction procedures (especially concerning hybridization) are to be found in the thesis of L. C. Rosenfeld [Rosenfeld 1977]. A discussion of diffractive dissociation in the reactions: ± TI p ± TI p ± TI p ~ ± 0 TI pTI ± + ~ TI TI n ~ TI TI TI p ± + - (la) (lb) (le) observed in this experiment has been published elsewhere [Chadwick 1978]. -53. Five-body Final States: rrp-+'!TrrrrrrN The 5-body final states produced by pion beams: ± ± + + - rr p ~ rr rr rr rr n are examined in this thesis. (2b) These reactions have been studied by several other bubble chamber experiments. Tables I.l and I.2 list several of these experiments giving the beam momenta and cross sections observed for these reactions. These final states have been found to be very rich with many sub-reactions involving one or more resonances. The extent to which diffractive dissociation contributes to these final states is unclear and buried beneath the contributions of many other processes. The cross sections given in Tables I.l and I.2 were fit with the form ap -n (p is the laboratory beam momentum) to obtain estimates of the cross sections at our beam momenta. These estimates of the total 5-body cross sections are given in Table I.3. The cross sections observed in our experiment are expected to be smaller than those in Table I.3 as some unknown fraction of the total cross section is excluded by the trigger condition. We can expect that our trigger will exclude all or part of those reactions in which the fastest pion is one of the decay products of a resonance. The arrangement of our apparatus is such that only very fast pions (with more than half the beam momentum) of the same charge as the beam can trigger the experiment. pions and oppositely charged pions are bent into the sides of the Slower -6- Table I.l + + rr p + rr rrrrTIN cross sections (J (µb) Reference pbeam (GeV/c) Aderholz 1965 4 Otter 1975 4 3430±690 Brown 1970 4.08 3780±360 970±100 Pols 1971 5 2880±40 850±20 Prentice 1971 5. 5 1940±190 Slattery 1967 7 2200±200 Wagner 1975 7.1 2160±90 Deutschmann 1964 8 2100±200 900±100 Aderholz 1968 8.04 1910±80 740±70 Kung 1969 8.5 2120±327 Kennedy 1978 10. 3 1654±100 Baltay 1978 15 1005±77 Ballam 1971 16 1280±170 Ballam 1967 16 Grassler 1974 16 1050±100 Hones 1974 18.5 1200±150 + TI p + ++-o TI TI rr rr p + rr p + +++- rr TI rr rr n 930±330 503±38 350±100 360±60 -7- Table I.2 TI - p + TI TITITIN cross sections pbeam (GeV/c) (J ( µb) - + - 0 1T p +rrTirrrr 0 TI Bandar 1964 4 2110±90 1100±60 Chung 1968 4.2 2180±110 1160±60 Miyashita 1970 6.7 1720±200 1170±100 Milgram 1970 6.9 1600±120 Cason 1970 8 1390±90 530±40 Biswas 1964 10.25 1770±350 1030±340 Caso 1967 11 1200±200 650±100 Kittel 1971 11 1240±110 680±50 Brandenburg 1970 13 840±80 Ballam 1971 16 1240±150 Ballam 1967 16 Kittel 1971 16 820±100 Cason 1973 18 . 5 860±70 Sisterson 1972 20 780±100 Reference h p - + + + rrrrrrrrn 650±100 450±50 -8- 10. 1T:1:p-+1T:1:7r+1r-1rop + rr+ x 1r~ ..0 8 1. .._. b 7r + rr+ x 1r ~ ,.Q 8 1. '-' b 0 .1 _______,...___.__.__._.............-_...__......___.__..._._._. . . . . 3 6 10 30 60 100 1 Pbeam (GeV/c) Figure I.l Plots of the cross sections listed in Tables I.l and I.2. The lines are from the ap-n fits used to interpolate to our beam momenta. -9apertures of the magnets. At least half of the events with a neutral 0 fast meson (such as a p ) will be lost due to decays in which the pion going forward has the opposite charge relative to the beam. since the software trigger places a recoiling against the fast pion, the Also, modest upper limit on the mass fraction decays lost will be greater than one half. of such resonance From an examination of the quasi-2-body and quasi-3-body cross sections measured in other experiments, we expect that this experiment will observe between 25% and 50% of the cross sections given in Table I.3. Table I. 3 Predicted maximum cross section estimates Final State CJ (µb) 1T +1T +1T - 1T 0 p 1290±70 - 1T +1T - 1T 0 p 980±130 1T +1T +1T +1T - n 460±100 1T - 1T +1T +1T - n 450±70 1T The previous works on the final states listed above have concentrated on meson resonances such as: + + + + + + 1T-p + g-(1680)p 1T-p + B-(1235)p 1T-p + Az(l310)p and quasi-2-body reactions including: (3a) (3b) (3c) -10- among others. TI +p + (4a) TI p (4b) In these works, the more detailed studies were in addi- tion to the measurements of semi-inclusive resonance production in these explicit final states (reactions (2a) and (2b)). Thus there is no body of data to which we can directly compare our results in detail for the S-body final states because reactions such as those given in (3) and (4) are mostly excluded by our geometrical and trigger acceptances. However, there are some quasi-3-bod y reactions that have been studied by other experiments in kinematic regions that overlap ours. 4. TI ± 0 + ± 0 + p +TI w p and TI p +TI n p The quasi-3-body reactions: TI TI + ± ± 0 p + TI W p p + TI (Sa) ± 0 n p (Sb) have been investigated in bubble chamber experiments as sub-reactions + - 0 0 of the final states in (2) by virtue of the TI TI TI decays of the w and n 0 mesons. Tables I.4 and I.5 list some of these experiments giving the beam momenta and observed cross sections for these reactions. The cross sections have been corrected for the unseen decay 0 modes of the w and n° mesons. cross sections were fitted by ap As in the previous section, these -n and the total reaction cross sec- tions at our beam momenta were estimated (see Table I . 6). However, -11Table I. 4 TI +p + TI +pw 0 and TI +p + TI +pn 0 cross sections a (µb) Reference pbeam (GeV/c) TI +p + TI +pw 0 TI +p + TI +pn 0 Otter 1975 4 901±222 Otter 1975 5 545±23 Prentice 1971 5.5 510±71 Otter 1975 8 245±22 Kennedy 1978 10.3 137±13 76±13 Baltay 1978 15 51.5±5.5 31±5 Bartke 1977 16 117±12 35±5 Otter 1975 16 70±7 Hones 1970 18.5 101::!:14 162±33 34±9 -12Table I.5 11" p -+ 11" pw 0 and rr p -+ 11" pn 0 cross sections <J pbeam (GeV/c) Reference 11" p -+ 11" pw 0 (µb) 11" p -+ 11" pn Bondar 1964 4 289±45 Chung 1968 4.2 206±28 Gordon 1975 6 482±47 Miyashita 1970 6.7 178±24 Armenise 1973 9.1 137±24 Biswas 1964 10.25 133±56 Caso 1967 11 78±33 85±42 Bartke 1977 16 82±11 17±5 Cason 1973 18.5 39±5 31±7 Sisterson 1972 20 48±10 Gordon 1975 22 31±8 89±30 19.5±6.6 Table I.6 0 Predicted w and n 0 cross section estimates Reaction Totalt <J (µb) Observable <J (µb) +pw 0 92±14 39±8 63±10 20±10 0 38±9 3±2 0 22±11 6±5 TI" rr pw + rr pn rr pn 0 (t corrected for unseen decays) 0 -13- 1Qr------r---,.--,-~.,.......,-------....-------- 7r±p41r±p c,; a 1 ·--~ i ...... b 0.1 .......-.100 ,.c . . *. . .*. .·- .f:.... . ... . . .... .. ' ~ .......... b 10 1 ...._~__...~-----'--.Jo.--"'-'-..-.~~--~.a...---..&.......i~........ 3 6 10 30 60 100 1 Pbeam (GeV/c) Figure I.2 Plots of the cross sections listed in Tables I.4 and I.5. are from ap-n fits used to interpolate to our beam momenta. The lines -14once again our experiment cannot observe the full kinematic range of reactions (5). Previous experiments have concentrated on investi- gations of the B meson (reactions (3b) via B±-+'Tl"±w 0 ) , the A meson 2 (reactions (3c) via A~-+'TT±n°), and the quasi-2-body reactions in (4). It is precisely these reactions that our trigger rejects in whole or part. Some data does exist [Baltay 1978, Caso 1967, Cason 1973, and Kennedy 1978] that allows us to make rough estimates of the cross sections we should observe for reactions (5). These estimates are also given in Table I.6 (in the "Observable" column, uncorrected for unseen decays). 0 w ~ 0 0 These estimates are made by subtracting the B±p and w ~++ or ± 0 cross sections from the total rr w p cross section and subtract- ing the A~p (A~+rr±n°) cross section from the total rr±n°p cross section (the error on the rr-n°p estimate is due to the scantiness of the data). Several experiments, including ours in preliminary results, have reported observation of a pw 0 enhancement at about 1800 MeV. All these experiments were bubble chamber experiments and their results are based on relatively few events (exposures on the order of a few events per microbarn). Table I.7. A collection of ~he observations are given in Preliminary results reported for our experiment [Davidson 1974 and Linglin 1974] are included for completeness. For many of the experiments (as noted in the table) the cross section of the enhancement was estimated by us from data and figures given in the reference. Given the observation of this pw 0 enhancement in several beams at many energies, this effect seems to be an N* which couples strongly to 0 pw . The narrow width seen for the enhancement seems to support this -15Table I.7 A compilation of the observations of the pw 0 enhancement Reference Beam pbeam (GeV/c) Atherton 1975 p 5.7 1810±15 87±20 Davidson 1974 TT 4.5 6 14.2b) 1820 120 Guyader 1971 p 13.1 1750±25 100±25 Juhala 1969 K 4.6-5 1780 Linglin 1974 TT 7 13.7b) 1800±15 110±20 7.2±2 6±1 3 7 1764±18 115±50 9.2±2 8.1±1.5 Milgram 1970 + TT Mass (MeV) Width ~MeV) a ~µb) a) 14±3c) 9±L9 10.6±2.7 5. 2±1. 2 16±4c) 9±3d) Chien 1976 K+ 6.8 15±5d) Colton 1970 p 6.6 18±5c,d) Davis 1972 K+ 12 2.5±0.8 Sisterson 1970 TT 20 8±2d) Theocharopoulos 1974 K 8.25 5±2d) Wohl 1978 K 14.3 3±2d) 0 d) + - 0 decay mode. a) cross section is for w -+TI TT TT b) preliminary results of this experiment. c) cross section is one half that quoted in or estimated from reference for comparison to rrp or Kp data. d) cross section estimated from data and figures in reference. -16view. This interpretation has been pointed out in other papers as well [Atherton 1975 and Milgram 1970]. Some experiments have attempted to explain the enhancement with a Double Regge Pole Model (DRPM) with varying degrees of success [Sisterson 1970, Milgram 1970, and Juhala 1969]. For the most part, however, this effect seems as well estab- lished as an N* as some of the other resonances listed in the Particle Data Tables [Particle Data Group 1978]. With our large statistics, we can investigate this effect in more depth, including more detailed 0 studies of the w p angular distributions than done previously. 5. Summary of the Results We present plots of the invariant mass distributions for the reactions: ± + - 0 ± TI p + TifTI TI TI p ± + + ± TI p + TifTI IT TI n (6a) (6b) + where the fast pion (Tif) was used to trigger the experiment. Our experiment separates these reactions into a fast pion with a momentum above 8 GeV/c and a slow system of three pions and a nucleon. The slow system particles have momenta below 1 GeV/c for the majority of the events. + The fast invariant masses (involving the TI ~) show strong p~ and pf peaks. These fast mesons are correlated to some extent with the production of resonances (6 or p) in the slow system. By subtract- ing the estimated contributions of the fast meson resonances, the resulting reduced channel cross sections are nearly independent of the -17sign of the beam as would be expected for diffractive dissociation. + - 0 The reduced rr rr rr p channel cross sections are approximately twice the rr +rr +rr - n channel cross sections. Examination of the slow system mass distributions reveals that they are very rich in resonance production. The 6++ and 6 - are par- + + - 0 ticularly strong with about one half of the rrfrr rr rr p channel events + - 0 ++ being from rrfrr rr 6 . Some double resonance production in the slow system is seen, in particular the reaction: rr ±p (7) has a fairly large signal. The quasi-3-body reactions (including (7), pf6rr, and pfpN) are very prolific while the quasi-2-body reactions are The most prominent quasi-2-body reactions are: relatively weak. rr +p -+ wf6 ++ (8a) rr +p -+ p f6 ++ (1890) (8b) 0 0 0 rr p -+ pfN(l688) (8c) + * rr p -+ rrfN (8d) ± A peak in the rr +rr +rr - n mass spectra at about 1700 MeV appears to be a new decay mode of a known N* . The decay scheme seems to be: (9) rr n --18- + - 0 A second peak, this one in the rr rr rr p mass spectra, was found to be the pw 0 resonance discussed in the previous section. This N* was found to have a mass of 1790±5 MeV and a very narrow width of 81±9 MeV (narrow relative to the known N* 's). Studies of the angular distribu- 0 tions of the w p system were made in an effort to determine the spinparity of the N* . Though our results are in good agreement with other experiments from which Lednicky [1975] found a JP of 3/2 0 for the w p resonance, the failure of some of the predictions using this result when compared to our data raises questions about the validity of the assumptions underlying the spin-parity analysis. We have also studied the n° production in the relatively unexplored kinematic region of low It rrrr I and small n°p mass. We found that the rr;n°p cross section was about twice the rr;n°p cross section in this kinematic region. We interpret this difference in the cross sections due to the change in the sign of the beam as evidence for the impor- ance of negative signature Regge trajectory exchange (such as the P) in this reaction at our energy. This interpretation can also explain 0 . the presence of a 1600 MeV pea k in t h e n p mass spectrum o f t h e rr + data while the rr data has no indications of such a peak. -19Chapter II Experimental Method 1. Overview In this experiment, we have merged a missing mass technique with a bubble chamber to study nucleon diffraction-like processes. A mag~-· netic spectrometer equipped with wire spark chambers was placed downstream of the bubble chamber to measure the momentum and angles of the pion scattered out of the beam. This measurement allowed an online computer program to calculate the missing mass of the nucleon system recoiling against this fast forward particle. We then used this online missing mass measurement to trigger the bubble chamber flash lamps in order to enhance the number of inelastic nucleon excitations observed on the film. The spectrometer information was also used in the offline data reduction to improve the measurement of the momentum of the fast forward particle. 2. Beam The experiment was done in beam line 14 of the Stanford Linear Accelerator Center. II.l. A schematic of the beam line is shown in Fig. A 19 GeV/c electron beam from the accelerator was targeted on a 1 radiation length beryllium target to produce the secondary pion beam at a 1° production angle. The pions produced in the target were transported to the bubble chamber (BC) by a series of bends in the vertical plane. The beam was brought· to a focus at two positions before reaching the BC. The first focus (Fl) provided preliminary -20momentum definition for the beam. The slits at Fl were preceeded by , 1.1 radiation lengths of lead to reduce the electron and positron beam fractions. Though the Fl slits were moveable, they were left in fixed positions during the data taking. We varied the secondary beam inten- sity by changing the intensity of the primary electron beam. The second focus (F2) came after the main vertical bend so that the collimator located there served as the momentum defining slit (fixed position and size). For both the rr + and rr - beams, the F2 slit was followed by a pair of scintillation counters (Bl and B2) that were primarily used in beam tuning and monitoring. During part of the rr + running we also had a scintillator (BO) and a set of proportional wire chambers (PWC's) before the momentum slit as aids in beam tuning. Immediately before the BC vacuum tank, we placed another scintillator (B3). The computer trigger software used B3 to prevent a BC picture from being taken if too many or no beam particles passed through B3. For the rr+ running, another set of PWC's were added upstream of B3. These two chambers were arranged with their wires at right angles and then rotated about the beam as a unit through an angle of 45° (see the discussion of the spectrometer's XY and UV coordinate systems below). This orientation was used because the beam had a very narrow horizontal width. These PWC's were used to define the beam profiles during tuning and were used for part of the rr+ data reduction to reduce the uncertainty in the beam particle's momentum vector. The nominal beam shape and momenta are given below in Table 11.1. 0 . 2 .08° I I20 5 m cm I m s Figure II.l c Legend: B scintilation counter C collimator v Cerenkov counter 0 dipole magnet F focus Q quadrupole magnet TC primary target {l r. l . Be wire) so . . ~F2, . lm Fe slit /, CHI Bl ~LO + Elevation view of the secondary beam line. This beam line was used to form the 14 GeV/c n- beam and transport it to the bubble chamber. All major bends were in the vertical plane. The horizontal trim magnets {00.5, 02.l, and 03.l) were normally off (zero bend). e- beam (19 GeV) ~ TC3l L_:_:.·~)!_ _ ~ , ' .., 1Fl, adj1 r.1. Pb filter . 1it C2 ' ... I I ...... N -22Table II .1 Beam shape at the bubble chamber Vertical FWHM 15 cm Horizontal FWHM 0.8 cm Azimuthal angular FW1IM 1.5 mrad Horizontal (dip) angular FWHM 2.2 mrad Beam momentum at the bubble chamber 1T 1T + p (GeV/c) a (MeV I c) 14.20 36 0.22% 13.72 55 0.40% 3. Bubble Chamber The SLAC 40" liquid hydrogen bubble chamber was used as the target for this experiment. The beam was brought to a horizontal focus and dispersed to an approximately parallel beam in the vartical plane as seen from the observed beam dimensions in Table II.l. The 40" bubble chamber can be run at a rate of 2 to 12 expansions per second; we took most of the at 8.6 pps. Tr beam data at 4 pps while much of the 1T + data was taken Although the bubble chamber can be expanded and made track sensitive at these rates, its camera can only take 2 pictures per second. The magnetic field of the 40" bubble chamber was set to bend the beam upwards in a vertical plane so the non-interacting beam particles and the fast forward scattered pion passed through the bubble chamber's vacuum tank exit window (8 inch diameter). The field value was set to -2326 kilogauss to bend a 14 GeV/c beam through about 6.6°. The exact field values were determined from the data by the standard method of measuring the apparent invariant mass of neutral vees. 0 For those vees + - that fit the hypothesis K -+'TT TI , the field scale was adjusted until the s + 0 TI TI invariant mass was centered on the K mass. The position dependent values of the field were determined from this scale value and a separately measured field map made by the SLAC technical staff. In addition to the main field map, we also used a map of the fringe field in HYBRID, the program used to connect the bubble chamber and spark chamber measurements. 4. Spectrometer Unscattered beam particles and fast forward scattered pions left the bubble chamber through the 8 inch (diameter) exit windown of the BC vacuum tank. This aperture limited the maximum angle acceptance of our magnetic spectrometer. The spectrometer consisted of four stations of magnetostrictive readout wire spark chambers, two either side of the magnet (see Fig. II.2). on The magnet was a 40D48 with an fBd£ of 28.56 Kg-m, thus bending a 14 GeV/c particle through an angle of 61.2 milliradians. The 15 inch vertical aperture of the magnet limited our low momentum acceptance because low momentum particles left the bubble chamber at larger vertical angles than the high momentum particles due to being bent more in the bubble chamber magnetic field. Thus low momentum particles that made it through the BC vacuum exit window generally hit the spectrometer magnet above its BEAM - I [XJ Figure II.2 _I t2 I 3 A3R /AJL t I I XY 5 ' 6 Camera t1 l 61. 2 mrad 1 m Stations I EJ---1---------------~------t" I XY 3 • " UV3,4 XYl, 2 ,~,AlR I /AlL UV 1, 2 BC iI [XJEJ[XJ tI><? BC Magnet Coils 40D48 Magnet Spectrometer Coard. System y[_Z I Plan view of the bubble chamber and spectrometer. XYl-10 and UVl-4 are the wire spark chambers. B3, AlR, AlL, A3R, and A3L are s~intillation counters. PWC is the beam proportional wire chambers used in the n experiment. Not shown are the bubble chamber vacuum tank or the iron flux return yokes of the magnets. B~ !. PWC Bubble Chamber BC & General Coard. System yLx -25aperture. The spectrometer magnet bent particles in the horizontal plane to facilitate physical construction of the final (wide angle) spark chamber station. Our spectrometer coordinate system was such that the Z direction was defined to be downstream Flong the beam, Y was in the vertical (opposite gravity) direction, and X was the horizontal direction such that the coordinate system was right handed. Each spark chamber sta- tion then consisted of at least two XY spark chambers. Each spark chamber contained two perpendicular magnetostrictive wands to provide a readout of the spark position in two dimensions. Stations 1 (nearest to the bubble chamber) and 3 (immediately downstream of the magnet) contained an extra pair of UV spark chambers. These UV chambers were rotated 45° about the Z-axis so the UV position measurements would allow the separation of the XY measurements of two or more tracks into their correct (X,Y) pairs. The final station (4) was really two pairs of chambers (or sub-stations, called 4R and 41 for right and left halves) situated side by side; this was done to allow measurement of widely bent (lower momentum) particles. All the chambers were similar. They consisted of two 1 meter by 1 meter areas of wire and nylon mesh (wires in one direction, nylon fibers in the other) separated by 1 cm. The wires of the two sides were oriented at right angles to one another to provide for the simultaneous XY (or UV) measurements. The wires in the mesh were separated by 0.5 mm, but by using two sets of chambers and the pulse-center finding circuitry in the electronic readout system, we were able to achieve -26a resolution of about 0.3 mm. The chambers were filled with 80% Ne/ 20% He gas at atmospheric pressure and the high voltage pulse was controlled by a triggered thyratron switch . The unscattered beam particles passed through the center of the spark chambers in stations 1, 2, and 3 and between the two halves (4R and 41) of station 4. The spark chambers were made inactive (dead) in the regions normally traversed by the beam, since otherwise one or more beam tracks would frequently appear in the spectrometer along with the trigger candidate track. For the XY chambers this was done by not providing high voltage on the HV plane in a narrow (in the X direction) stripe . For the UV chambers, a foam block was inserted between the HV and ground planes to prevent the formation of sparks in the beam region. These dead regions provided the lower limit to the scattering angles accepted in the spectrometer. To reduce multiple scattering effects, helium filled bags were placed between the stations (including inside the magnet gap). Stations 1 and 3 also included the Al and A3 trigger counters. These were plastic scintillator paddle counters, a pair at each station (an R or right and an L or left counter) with a gap between then to pass the beam. At each station, the scintillators covered the active area of the spark chambers at that station. The A counters were used to form the (single track) trigger by the coincidence of any pair with one counter at each station: RR AlR·A3R (la) -Z7- AlL .-- -· I ' .----' I I I I I L.~ I AlR _,..,.._ I Wa nd { F2 r n Discriminators l I I 91 I ~ I J One side of a spark chamber ~ I ~Fl '" SC Trigger ~ Spk (\ F2 aO • t UV Spk J ~ RL y J J SC Control I reset F2 l I I I 20 Mhz clock I 100 µsec Signal Router IFl I l ~ LR ., I A3R $$$$ II I Fl A3L I I J I J I t t Start Stop - .-- Scaler 1 J J I I J I I I I I I I t Pulse I t Reset kl= Scaler 2 Kt: Scaler 3 KJ: Scaler 4 Digitization Done Readin Complete Interrupt I J ~ 1) ..... Sigma-2 Interface .... L__J/ ..... Sigma-2 Memory Sigma-2 Processor Figure II. 3 Schematic of the triggering, electronics. spark digitization, and computer input Fl and F2 are fiducial pulses, and Spk is a spark pulse. -28RL = AlR•A3L (lb) LR = AlL·A3R (le) LL = AlL•A3L (ld) SCTRIG = RR + RL + LR + LL (2) This logic is also shown in the diagram in Fig. II.3. This fast trig- ger fired the spark chambers and initiated the digitizing of the spark positions. These and other signals were accumulated in a set of com- puter read scalers which were reset before each beam pulse (see Fig. II.3). After a delay of 300 ~sec to allow all the sparks to be digit- ized, the computer DMA (Direct :1emory Access) began to read the counter scalers (not shown in Fig. II.3) and SC (spark chamber) scalers into memory. When this operation was complete, the computer was interrupted and control transferred to the BC trigger program (called FAST). Each spark chamber wand included two fiducial wires that bounded the active area of the spark chamber (the fiducials were separated by 37 to 41 inches, depending on the particular chamber). The fiducial and spark signals were detected and amplified by a pre-amplifier built into the wand. The amplified signals were sent to the digitization/ scaler box for further amplification and digitization. The time bet- ween the first fiducial signal and up to 4 additional signals (either sparks or the second fiducial) were converted into counts of the 20 MHz internal clock and stored in the four scaler registers associated with each wand. The scaler system included an adjustable discriminator (so low level noise was ignored) and center-finding for each signal but the -29first. A separate unit provided the control for this system (reset, begin digitization, and begin readout). 5. Online Trigger and Data Collection Computer and Programs The data logging and bubble chamber trigger decision were done with an online computer. For this purpose we used a 16-bit Sigma-2 computer (made by Xerox Data Systems) equipped with 32K words of core and a foreground/background operating system. The foreground programs did the data logging, performed the calculations necessary to generate the bubble chamber trigger, and accumulated run statistics. The back- ground program was used for software developement or to run a more complete analysis on a fraction (about 10% in practice) of the data being taken by the foreground. The computer controlled the data col- lection and trigger electronics by generating pulses or logic . levels on a set of output lines. The two most important of these controlled the BC camera flash lamps and the beam gate respectively . The computer also read the BC roll and frame numbers and ready-condition signal from input lines. The BC roll and frame numbers were recorded on the spark chamber data tape so the BC and SC data for a particular event could be located and matched. By checking the BC status line, the computer could automatically pause data collecting (via its control of the beam gate) when the BC went offline for any reason. The experi- menter controlled the trigger conditions, began and ended data runs, and monitored the performance of the equipment with the computer . A special part of the foreground program monitored and displayed (on a -30- Check Bubble Chamber Conditions Exit: BC Not Ready Check Spark Chamber Conditions Exit: SC Not Ready Exit: Beam Timing Error Wait for SC Interrupt Call FAST (Triggering) Check Final Event Conditions Bad Event Good Event Assemble Event Data Record Accumulate Monitor Data Exit: Write Data Record Figure II. 4 Flow of control in the online trigger and data collection computer programs. -31set of Nixie tubes) the beam intensity in real time to allow the beam line operator to maintain a stable beam. The background program pro- vided us with histograms of relevant quantities which were used to monitor and re-calibrate constants used in the trigger program. Fig . 11.4 gives a flow chart sketching the control flow of the foreground program. The foreground program was initiated a few milli- seconds before each beam pulse to allow time for initialization. At this time the status of the equipment was checked to insure that the beam pulse could be used . Once the beam pulse had occurred and the spark chambers were fired , the readin-completion interrupt from the spark chamber electronics initiated the BC trigger program (FAST). Before examining the spark chamber data, FAST used the data in the counter scalers to check the following event conditions: (1) a beam gate did occur, (2) the beam counter B3 recorded the passage of between 1 and 12 particles, (3) and the spark chambers had been fired. In addition to these software conditions, FAST also imposed the mass cut of m0 <m <m where m0 and m were the lower artd upper limits on the ~ x u ~ u mass (mx) recoiling against the fast forward pion. were set to 1.1 and 3.8 GeV respectively. Typically mi and mu The lower limit eliminated the majority of elastic events and the upper limit removed a large fraction of the pion diffraction events. The approximations and track-finding algorithm used by FAST are discussed in more detail in Appendix A. FAST was required to make its decision within the bubble -32chamber flash lamp delay time (usually set to 2 milliseconds) . If FAST determined a picture was not required, the BC camera control was inhibited from taking a picture. After FAST was completed, the fore- ground program checked to see if the event data was to be recorded on magnetic tape. The event data was written whenever a picture was taken or, if no picture, when the software conditions listed above were met. Finally, the foreground program accumulated statistics (printed at the end of each run) used to monitor the performance of the spark and proportional chambers . As the background program we normally ran TORTIS which was the complete (both X and Y-view track finding and matching plus corrections) spark chamber analysis program. TORTIS is described in more detail in Chapter III on the data reduction methods. The TORTIS used on the Sigma-2 provided us with a sampling of our data as it was being collected. This was done by providing a facility for the foreground program to transfer an event data block directly to the background program. We used TORTIS to prepare histograms of various quantities to provide us with checks on the performance of the spectrometer and trigger software. We also used TORTIS to determine the calibration constants of the spectrometer and the shape and momentum of the beam (needed by FAST) . -33Chapter III Data Reduction 1. Overview After the data had been collected in the form of bubble chamber film and magnetic tape records of spark chamber data, there ensued the task of reducing the data to a useable form. This involved locating and measuring the events on the film, merging the spark chamber data with the bubble chamber data, and producing data summary tapes containing four momenta for the particles involved in each event. These final tapes were then used to prepare histograms of interesting quantities and as the data input to physics analysis programs. Fig. III.l gives a flow chart of the steps (including computer program names in all capital letters) involved in the data reduction process as detailed in this chapter. Table III.l gives the statistics of these experiments from the number of beam pulses through to the resulting numbers of events for specific final states resulting from the data reduction process. 2. Spark Chamber Data This experiment produced raw data in two forms: pictures of tracks in the bubble chamber and digitized spark chamber and counter data on magnetic tapes. This information had to be further analyzed and merged together into a single set of data before yielding information from which the desired physics results were extracted. For the spark cham- ber data, this further analysis was handled by a program called TORTIS. -34- Online Trigger Program BC Film Scanning TORT IS Measuring (Automatic and Manual) TVGP Calibration Constants Calibration Constants HYBRID SQUAW Ionization Scan DST Generation Program Figure III .1 Major processes and information flow in the reduction of data for analysis. Analysis Programs -35- Table III.l Results of the data collection and reduction for each experiment -'IT 'IT + Beam pulses 6.8 x 10 6 8.7 Spark Chamber triggers 2.9 x 10 6 2.9 x 10 6 SC triggers/beam pulse 0.422 0.333 BC picture triggers 3.7 BC pictures lost due to late trigger 1. 0 x 10 4 3.2 x 10 4 Fraction of pictures lost 2,62% 5.60% BC events 1.21 x 10 5 1.89 x 10 5 Elastic scatter events 4.4 Inelastic 2-prong events 4.5 x 10 4 3.3 x 10 4 4-prong events 36793 66894 17203 27102 p events 7542 10792 ++ 'TT 'TT n events 4234 4839 'IT 'IT 'IT ± ± ± p -+ 'TT p -+ 'TT p -+ 'TT ± + 'TT 'TT - p events ± + 'IT + 'TT 'IT 0 'IT x x 105 10 4 5,7 7.5 x x x 10 6 105 10 4 -36- TORTIS was actually used in three versions in this experiment. All three versions used the same spark processing and track finding algorithms; the only differences were in the auxiliary routines and the use of the program. One TORTIS was the background task in the experiment's online computer and was used for calibration and monitoring the performance of the equipment and software. Another TORTIS was built into the HYBRID (or MATCH at SLAC) program that merged the bubble chamber film measurements and the spark chamber measurements. HYBRID will be described more fully in a later section of this chapter. The third TORTIS was a stand-alone program on the CDC 7600 computer at LBL. This TORTIS was used to fine tune the spark chamber and beam calibration constants. These constants were then used in HYBRID (or MATCH) to calculate the parameters of the spark chamber track for each event . TORTIS accepted as input the raw spark chamber data for an event. This consisted of the digitized counts of a 20 MHz clock for the sparks and fiducials. Also included in the event data record were some computer generated numbers and counts from scintillation counters as auxiliary data. TORTIS first scanned the raw spark chamber data to remove obvious bad sparks and the fiducial counts. The fiducials were recognized and used to form a running average for each wand. Next, the spark values were converted from clock counts to positions in the spectrometer coordinate system. The averaged fiducials were used in this conversion since they measured the distance between the fixed fiducial wires in terms of time (as clock counts). After converting the spark data, TORTIS merged the data from the spark pairs at each -37station. This was done by searching for spark pairs (one in each chamber) whose positions differed by an amount less than a preset value. The average of these two positions was then used as the posi- tion of a single spark in the spark chamber station. Thus we ended up with a set of unique spark positions at each station and in each plane (X, Y, U, and V) at that station. Here also, the sparks from the two halves of station 4 were concatenated so station 4 could be logically treated as a single station. Track finding was done by finding projections of tracks in the X and Y-planes separately. In finding these projected tracks, TORTIS used the constraint that the track halves (before and after the magnet) must meet at the magnet center in both views, and that the Y-track had a very small bend angle in the magnet. No constraint could be made on the bend in the X-view since that bend is proportional to the momentum. However, a weak constraint that the X-track intersected the bubble chamber fiducial region was applied to eliminate track testing with extraneous sparks. The X and Y-track views were matched into single tracks by using the information from the UV spark chambers at stations 1 and 3. Each XY combination was used to predict the expected UV spark positions. If a spark was found in the correct position (within a preset cut) in either set of UV chambers, then that XY combination was taken to be a good matched track. In addition, if only a single XY combination existed (only 1 X-track and 1 Y-track), that track was also taken to be a good match provided that the X and Y-sparks in station 4 came from the same half of the station. The TORTIS track-finding -38algorithm is discussed in more detail in Appendix B. TORTIS also calculated a four or six component x2 statistic for each track. This x2 was useful in selecting the best track match from a set of ambiguous tracks (which had common sparks among them) and in determining the match x2 in HYBRID. The component~ of the x2 were: (1) DXM, the difference in the spectrometer X-plane at the magnet midplane between the projections of stations 1 and 2 sparks and the stations 3 and 4 sparks. (2) DT.1, the same as in (1) above, but now in the spectrometer Y-plane. (3) DUl and DVl, the differences in the positions of the spark in the UVl chambers (if any) and the position calculated from the XY measurements of the track. (4) DU3 and DV3, same as in (3) for the UV3 chambers. The last two components could appear independently depending upon the presence of sparks in the UV chambers, thus changing the number. of components in the x2 . in the n In particular, the UV3 chambers were not used run of the experiment. The distributions of these quantities (the components of the x2 ) had widths of approximately 1.5 mm (FWHM). The errors governing these widths (and used a priori in the x2 ) were the spark chamber setting errors (a ~ O.Jmm) and errors arising from multiple coulomb scattering (contribution about the same as the spark chamber setting error). Both TORTIS and FAST (the online trigger program) required a set of parameters which described the position and size of the spark cham- -39bers and described the beam. Some of these constants were determined by the design of the spectrometer and spark chambers, such as the spectrometer design momentum and bend angle and the actual spark chamber fiducial separations. The spark chamber fiducial separation was also measured by the digitization system in terms of 20 MHz clock counts. This time measurement was thus a direct measurement of the speed of sound in the magnetostrictive wands. Since the speed of sound was very sensitive to the temperature, a running average of the fidu- . cial time separation was kept. Thus the fiducial separation was an example of a parameter that varied with time but was treated as a constant for any one particular event. The beam parameters (momentum, angles, and shape) were also taken as constants that changed when the beam was retuned. Finally there were the spark chamber spatial posi- tion parameters that located the zero point of each chamber relative to the entire spectrometer. The Z-positions (along the beam) were fixed by the emplacement of the chambers. The transverse (X and Y) positions were initially measured by a survey, but the values actually used by TORTIS and FAST were slightly different (by a small fraction of an inch) from these survey values . The adjustments to the survey values were made by using TORTIS to calculate the new parameters using special runs in which we steered the beam into the active area of the spark chambers. TORTIS was also used to recalculate these constants for each data run to remove the effects of small random drifts in the values. The beam calibration runs also permitted us to determine the beam parameters we needed. The beam runs were repeated at several -40points during the course of the experiment and most particularly after the beam conditions were changed. The procedures used in these cali- brations are discussed in more detail in Appendix B. 3. Bubble Chamber Data In contrast to the spark chamber data, the bubble chamber results required much more processing to get them to the point at which they could be merged with the spark chamber results. The film processing was divided up among the three laboratories participating in this experiment. Cal Tech was responsible for 24% of the rr film, LBL for 76% of the rr and 22% of the rr+ film while SLAC did the remainder of the rr+ film. A portion of the SLAC rr+ film (19% of the total) was actually scanned and measured (first pass) at LBL with the remaining processing done at SLAC. A normal roll of film consisted of 1000 frames which contained about 400 events within the bubble chamber fiducial volume (only 350 for the rr film due to a different fiducial volume and the ignoring of some event types). The remainder of the frames contained events out- side the fiducial volume (in invisible hydrogen and the beam entrance and exit windows). In addition, each roll contained an approximately equal number of events in the fiducial volume which were not associated with the computer trigger and so had no track in the spectrometer. Human scanners were used to locate visible events (according to roll, frame, position on the film, and event type). At SLAC and Cal Tech, directed scans were done by using the tracks found by TORTIS to predict -41the location of the outgoing fast track on the film. At LBL, an unas- sisted scan was done with a special program used to filter out events that were not associated with spectrometer tracks. The events selected by the scanners were then measured. As with the scanning, different measurement schemes were pursued by each of the involved groups. All the Cal Tech data (including remeasures) were done on the automatic POLLY film measuring system [Allion 1969]. POLLY was operated by a PDP-10 computer with the human operator directing its operation and verifying its actions. One of the major functions of the operator was to manually guide POLLY when measuring tracks where confusion with other tracks or obstructions (i.e., flash lamp reflections, 8-ray spirals, etc.) made automatic measuring difficult. The SLAC spiral reader measured most of the SLAC film sample [Lloyd 1965]. The spiral reader is an automatic machine which does, however, allow the operator to manually measure otherwise difficult tracks. Special event classes (more than 4 prongs or a neutral or charged decay) and certain events judged to be hard to measure on the spiral reader were measured on the SLAC manual measuring machines. The remeasures were handled in the same style as the original measurement pass by dividing the load between the spiral reader and the manual machines. All the other measurement passes were done on the SLAC manual machines. At LBL, two measurement systems were also used. The film was first processed by a flying spot digitizer (FSD, also known as an HPD or Hough-Powell Device). The FSD is fully automatic with no provision for operator assistance and was controlled by the DAPR pro- -42gram running on an IBM 7094 computer [White 1968]. Those events that the FSD could not measure were measured on the COBWEB system [Albrecht 1968]. About 55% of the LBL TI film had to be measured on COBWEB. After improving the performance of the FSD by using the spark chamber data in the pattern recognition process, only 20% of the LBL TI+ film was measured on COBWEB. COBWEB consisted of several Frankenstein film plane digitizers being run in semi-automatic mode under the control of an IBM 7044 computer. The semi-automatic operator allowed the machine to follow tracks with the operator's help and to automatically digitize at intervals along the track. Basically, the computer control was used to speedup the measurement process. In addition to FSD failures, COBWEB also made all the second pass measurements. Although the three labs used cifferent measuring systems, their outputs were similar. The data for an event included identification information plus several (minimum of two) pairs of film plane digitizations for each track in each of three views. The data were used as input to the standard geometrical reconstruction program TVGP (for Three View Geometry Program) [Solmitz 1966]. TVGP has been used on many other bubble chamber experiments and is structured such that the parameters to describe a particular experiment appear as sets of constants. These constants describe such things as the optical path (from the liquid to the camera), characteristics of the measuring engine (optical characteristics and measuring error) and the bubble chamber operating conditions (magnetic field and liquid type and density). Some of these were set a priori, some (the optical constants) -43from measurements of the fiducials as recorded on the film (their spatial positions were known by surveying) , and some from measurements of particular events. The latter allowed the magnetic field to be 0 0 + - determined by measuring the K mass in neutral decays (K -+'Tr TI ) and the liquid hydrogen density to be gotten from measurements of the muon range in stopped pion decays (TI +~µ +v µ at rest, followed by µ +~ +v v e µ also at rest). With these constants providing needed parameters, TVGP produced .a five parameter description (with an associated SxS error matrix of the parameters) for each track of an event. This was done by using the film plane digitizations gotten from the measurement tape to calculate the particle's trajectory in three dimensions. The five parameters thus deduced are the polar (with respect to the camera axis) and azimuthal (about the camera axis) angles at the beginning and end of the track, and the track's initial curvature. However, due to energy loss by ionization of the liquid hydrogen, the particle's trajectory depends on its mass as well as its momentum, especially for lower momentum particles. Thus TVGP provides for a number of different mass interpretations to be made for each track. The mass interpretations we used for this experiment were TI+ and proton for positive tracks and TI for negative tracks. ± The SLAC data also included the interpreta- - tions K , p, and various strange particles for events with decays to include the small number of events coming from rarer reactions. The vast bulk of our data, however, only involved pion and proton tracks. -444. Merging the Spark Chamber and Bubble Chamber Data The measurement of the fast forward and beam tracks in the bubble chamber had large errors on their momenta (op/p ~ 5-10% for momenta above 8 GeV/c or so). The standard bubble chamber technique of beam averaging using the very well known central beam momentum ( op/p 0.5% < for our beam) was used to improve the measurements of the beam. A similar process which we called hybridization was done to the bubble chamber measurements of the fast forward track using the better momentum from the spark chamber measurements of the same track. Both these similar operations were carried out by ~he computer program HYBRID which we wrote for this experiment. HYBRID used the TVGP output tape and a spark chamber data tape as inputs, producing an output tape resembling a TVGP output tape but with averaged beam tracks and hybridized fast tracks. HYBRID proceeded by first using a portion of the TORTIS computer code to locate spectrometer tracks. The TVGP track banks were then searched for the highest momentum track of the same charge as the beam. The matching process then selected the best TORTIS track that was compatible with the bubble chamber measurement of the fast pion. matching involved a 9 or 11 component x2 . This The first 4 (or 6) compon- ents were those from the x2 for the TORTIS track (see Section III.2). The five new components measured the actual matching of the bubble chamber and spectrometer measurements: (1) Difference of the bubble chamber and spectrometer momentum measurements (FWHM ~ 1.5 GeV/c). -45- (2) Difference in the polar (or dip) angles at the end of the bubble chamber track (FWHM ~ 7.5 mrad). (3) Difference in the azimuthal angles, again at the end of the bubble chamber track (FWHM ~ 3.5 mrad). (4) Difference in the transverse coordinates (Y and Z) at the end of the bubble chamber track (Y FWHM ~ 2.5 mm and Z FWHH ~ 3.0 mm). The x2 also included the TVGP correlations (in the error matrix) for all but the position measurements. After a satisfactory match was found, HYBRID then merged the bubble chamber and spectrometer measurements to form the hybrid fast track measurements. This hybridization was done by taking a weighted average of the momenta (which was dominated by the spectrometer measurement due to its much smaller error) as the hybrid track momentum, using the bubble chamber azimuthal angle, and using the spectrometer polar (or dip) angle without averaging either angle. Details of the HYBRID program and its functioning may be found in L. C. Rosenfeld's thesis [Rosenfeld 1977]. -465. Kinematic Fitting The four-prong events of this experiment are mostly a result of the following five reactions: 7T ± ± 7T ± + - p + 7T f 7T p + 7T f 7T 7T ± + 7T p (1) 0 7T p (2) ± + + p + rr t'rr rr rr n ± ± + 7T p + 7T f 7T Tr p(MM) + + + ± Tr p + rr ;r ;r n (MM) ± (3) 7T (4) f (5) where (MM) stands for missing mass consisting of two or more neutral particles (i.e., Tr o both with n ~ 1). o n o n (rr) for reaction (4) or n(;r) for reaction (5), The leading pion is labeled as the fast pion (nf) that was responsible for triggering the experiment. After hybridiza- tion, the data tapes contained measurements of the momentum vectors of all the charged particles of these reactions. Using the principle of conservation of energy and momentum, the mass of the neutral system of reactions (2) through (5) can be calculated. Events were fitted to the reactions (1) through (3) using as constraining relations the four equations from conservation of energy and momentum (four-momentum): l E. initial 1. l l final E. l p. t. = final initial 1. (6a) 1. 1. (6b) -47These kinematic fits were carried out using the SQUAW computer program [Dahl 1968] which is a companion to TVGP. Since energy-momentum con- servation is used to constrain the kinematic fits, the resulting values (after the fit) of the energy and momenta of the particles of the event will exactly conserve energy and momentum. Reactions (2) and (3) involve a missing neutral particle whose four-momentum is not measured, but by assuming a mass for the particle, the kinematic fit determines the unknown momentum vector. Reactions (2) and (3) thus result in one constraint (lC) fits since the four energy-momentum equations must provide for the calculation of the three momentum components of the missing neutral particle. Similarly, reactions (4) and (5) produce zero constraint (OC) "fits" which are really the use of equations (6) to calculate the missing momentum and energy. This is because the missing neutral system (usually consisting of several neutral particles) has an unknown mass . In contrast, reaction (1) results in fully constrained (4C) fits since all the momentum vectors are measured and all the masses are known. Reactions (1), (2), and (4) may result in more than one fit per event. This can be due to the two slow positive particles being . 1 y. interpreted as rr +p or prr + respective Approximately 18% of the lC four-prong events that fit reaction (2) made the fit twice, the second fit having the mass interpretations (rr +p) of the slow positive tracks . interchanged (prr +). This was about the same fraction of OC events which had two "fits" to reaction (4). two fits with interchanged tracks. Only 4% of the 4C events had This fraction is small (compared -48to the lC and OC cases) because the fits with the wrong mass interpretations were frequently failed by SQUAW which resulted in only one good 4C fit per event. Also, not all events could have had two fits because the initial momentum and rate of energy loss were inconsistent for one mass interpretation of a track or one track was definitely known to be a proton (by being flagged as a stopping proton by the scanner). The ambiguous events (multiple fits) were reduced to a sin- gle fit as described in the next section. All fits to reactions (2) through (4) used the hybrid track for + the fast track (n-). f The 4C fits to reaction (1) were made as HYBRID fits using the hybrid track and as BCONLY fits for which only the bubble chamber measurement was used for the fast track. Thus both a HYBRID and a BCONLY 4C fit were attempted for each event. This was done primarily for the two-prong events to insure that all the elastic events were found. The elastic events on the film were ones that had leaked through the trigger and as such, the spark chamber measurement of the fast track may have been slightly wrong in some way (e.g., a secondary scattering when exiting from the bubble chamber). In fact, about 5% of the two-prong elastic events had just the BCONLY fit with less than 1% having only the HYBRID fit. For the 4C four-prong events, 7% of them made just the HYBRID fit and 4% just the BCONLY fit (the remainder made both types of fit). These numbers were a result of our selection of the bubble chamber fiducial volume. very near to the bubble chamber exit windows. We accepted events These events had very short (10 cm or so) fast tracks visible and so had very poor measure- -49ments of the fast particle momentum. This was of no consequence in the HYBRID fits since there the fast track momentum was essentially determined by the spark chamber measurement. As discussed earlier, the parameters describing the event (momenta and energies of the particles) exactly conserved energy and momentum after kinematic fitting. Since the fits were constrained by energy- momentum conservation, the errors in the parameters were considerably reduced by the kinematic fitting process (relative to the errors from before the fitting). experiment. Thus fitting improved the resolution of the Finally, the chi-square (x 2 ) statistic of the fit was useful in selecting between ambiguous fits for a single event as discussed in the following section. 6. Fit Selection Although kinematic fitting improved the resolution, it did not completely solve the problem of dividing the events into separate channels as given by reactions (1) to (5). Kinematic fitting did provide the x2 statistic which was useful in selecting among the ambiguous fits. In addition there was extra information to be gotten from the bubble chamber film. This information was the ionization, or bubble density, of the track. This quantity is nearly proportional to 1/6 2 and so the bubble densities associated with different mass interpretations for the same track go as the mass squared: (7) -50The bubble density on the film is also proportional to l/cosA where A is the dip angle between the track and the plane perpendicular to the camera axis of the bubble chamber. As the dip angle increases, the track is becoming more parallel to the camera axis so the camera is looking along the track to an increasing extent. Thus the apparent bubble density (as projected onto the film) increases with the dip angle. We used a program to prepare a list of events for which the ionization information was needed. For each slow positive track (two tracks for each four-prong event), the program calculated and printed the projected bubble densities for different mass interpretations. This was done for each view and in units of the bubble density of a minimum ionizing track for which the beam tracks provided a handy reference, thus considerably reducing the effects of the bubble chamber operating conditions. These lists were then given to human scanners who selected the correct mass interpretation having observed the apparent bubble density on the film. These selections were then fed into the DST program (see below) as the ionization data. For some of the SLAC TI+ data, these selections were done by programs using bubble density information collected automatically by the spiral reader. Not all the events were scanned for ionization information. Some events only made a single kinematic fit in SQUAW and so were unambiguous. Tracks with momenta above 1.2 GeV/c were skipped since the l/p 2 decrease of the bubble density overwhelms the increase due to the mass to the point such that the tracks always appear minimum ionizing. In -51addition, the scanners marked some events as undecidable because the tracks were obscured or had too high a dip angle. The TI film was particularly difficult to scan for the ionization as the film quality and bubble chamber operating conditions were not as optimal as those for the TI + film. In either case, the four-prong events were easier to scan than the two-prong events since the two slow positive tracks could be visually compared to decide which one was the denser in bubbles/cm. The ionization information plus the output tape from SQUAW containing both the measured and fitted track parameters were used by the DST generator program to produce data summary tapes (DST's). The DST's were then used by all the efficiency calculation and physics analysis programs. In addition to constructing the data record from a pre-specified map, the DST generator program also assigned each event to a particular channel by eliminating ambiguous fits. The algorithm adopted to remove ambiguous fits (leaving one "best" fit per event) used the information from the ionization scan and the kinematic fit x2 to effect its choice of the "best" fit. This process was not exact and therefore corrections to the cross sections were calculated by other means as discussed in the final section of Chapter IV. The general scheme of the selection algorithm was to use the ionization data to reject all fits with tracks whose mass interpretations were incompatible with the ionization results. As an exception to this rule, if all the 4C fits of an event were rejected by the ionization results, then the ionization information was ignored so that none of -52the 4C fits were rejected (i.e., the 4C fit information was considered to be more reliable than the ionization data for these events). happened for only 2.5% of the 4C events. This About 4% of the 4C events had multiple 4C fits from the TI +p/pTI + positive track ambiguity. The ionization data eliminated 3/4 (3% of all 4C events) of these ambiguities by rejecting all but one of the 4C fits. Similarly, 18% of the TIO lC events (reaction (2)) had more than one fit to the TI 0 reaction with 2/3 of these ambiguities (12% of the TIO events) being removed by the ionization. Of the events with lC fits (reactions (2) and (3)), 34% were ambiguous between the TI 0 and n fits, this being reduced to only a 17% ambiguity by the ionization data. If after using the ionization results an event was still ambiguous with several non-OC fits, then the "best" fit for that event was selected by choosing the fit with the lowest x2 value. This procedure cannot give a perfect separation of the channels since the x2 value gotten for a fit depends on the exact values of randomly distributed quantities. Thus if the chi-squares associated with ambiguous fits were nearly equal, random fluctuations ensured that the true fit sometimes had a x2 greater than that of the ambiguous false fit (and so was rejected). With a couple of assumptions and the information given above, an estimate (as an approximate upper limit) can be made of the fraction of the lC events that are misidentified (wrong fit selected). More precise estimates of the losses and backgrounds and the procedure used to obtain them are discussed in the final section of Chapter IV. At -53-· this point, we need to estimate the fraction of times that the ionization and chi-square fit selections pick the wrong fit for an event. We can take the fraction of times the ionization information causes the wrong fit to be selected (the error in the ionization) to be less than 30%, especially as the four-prong ionization scan was significantly easier to perform than that for the two-prongs. This number comes from looking at the scatterplots of the confidence levels of the chisquares for rejected (by the ionization) fits versus those of nonrejected fits. Similarly, from the scatterplots of the confidence levels for ambiguous fits, a maximum of about 20% of the chi-square selection events were in the region where the chi-squares overlap due to randomness. If we assume that in the overlap band that the worse case is for the two chi-squares to be independently and uniformly distributed so that in half of the overlap band cases the selection process picks the wrong fit, then the chi-square selection failed in about 10% of the events for which it was applied. Table III.2 summar- izes the effects of these selection errors as an approximate upper limit for the fraction of the events in the lC channels that are misidentified. -54Table III. 2 Estimate of the fraction of lC events assigned to the wrong channel Fraction of lC events in Ambiguous Resolved by ionization Resolved by chi-square Fraction misidentified channel : 0 with >l 1T fit 18% 12% 6% 5% with n fit 34% 17% 17% 8% n channel: 0 with rr fit 34% 17% 17% 8% 1T 0 So we see that the selection algorithm misidentifies approximately 10% of the events in a channel . This number represents an upper limit to the errors introduced by the selection process , but does not take into account losses to the OC channels or backgrounds made up of true OC events (with multiple neutrals) that made a passing lC fit. Also, about 10% of the lC events have had all their lC fits rejected by the ionization selection and so ended up in the OC channels. Estimates for the channel losses and backgrounds are given in Chapter IV. Finally, there is also about a 1% background in the rr four prongs associated with events from the reaction: (8) which were fit as such and separated from the SLAC rr + data. This is the largest four prong reaction that does not belong to the set of reactions (1) through (5). All other strange particle reactions will -55either involve a decay seen in the bubble chamber (and so relegated to a separate class of events) or be considerably below the 1% level. -56Chapter IV Cross Section Determination 1. Overview Suppose that in this experiment we observe N events for some + + ' reaction (TI-P ~ TI~X ~ TI~TITITIN) in some particular region of phase space. Each event has a weight, w., to correct for the effects of our limited 1 geometrical acceptance and inefficiencies in the computer trigger. We then calculate the observed cross section for this reaction with the formula: a = 1 f obs 1 e N l W,1 (1) i where e is the exposure in events per microbarn. The factor f b 0 in s this formula represents the fraction of the selected reaction which survives the cuts used to select the events. In many cases, f b 0 s will be one, but if in selecting the events a range of masses containing a resonance peak were selected by cuts, f obs would be the fraction of the resonance shape found between the mass cuts. The exposure fac- tor e includes corrections for several other effects that remove events from or add events to the set of events in a channel. Events were lost due to inefficiencies in the spark chambers (e.g., not making sparks) and due to selection cuts in the programs used to find tracks in the spark chambers and to match these tracks to their corresponding bubble chamber tracks. Non-pion contaminants in the beam add events which + must be removed before cross sections can be given for TI-p reactions. -57Events were lost due to bubble chamber pictures not being taken when the computer trigger program exceeded the flash lamp delay time. In selecting the events that make up a channel's data sample, some are lost and must be corrected for and similarly background events remaining in the data sample must also be corrected for. A large part of the remainder of this chapter discusses how these various corrections were made. 2. Elastics Normalization We have normalized our experiment by using published rrp elastic cross sections to calculate the exposure (e). During the experiment we took elastic trigger rolls for which the lower mass cut used in the computer trigger was set to zero so elastic scatter events were triggered upon. These elastic rolls (about 4% of the rr film and 5% of the rr+ film) provided us with an unbiased sample of elastic events from which an elastic rolls exposure was found by using the published rrp elastic cross sections. Since the four prongs were unaffected by this change in the trigger, the ratio of the number of four prongs in the total data sample (elastic and production trigger rolls) to the number of four prongs in the elastic trigger sample was used to scale the elastic rolls exposure to the exposure for the entire data sample. The formula used to calculate the exposure was: 1- £ 4~ e = s ch e' pix l- £ rr~ pix 1 rrp E cuts N -2U?. a rrp (2) -58where sch is the correction resulting from inefficiencies in the final selection of events for a particular channel's data sample. Section 6 of this chapter discusses sch in more detail and Table IV.8 presents the final values for e for the four channels of interest. At this point we will consider e' which is the four prong exposure uncorrected for channel selection effects. The published elastic cross section we are normalizing to is represented by the a rrp factor in equation (2). This was gotten by integrating published values for do/dt(rrp-+'!Tp) over the interval O.OS~JtJ::;D.3 (GeV/c) 2 . This t interval was chosen to remove effects of the geometric acceptance (e.g., loss of events at very low It!). N is the sum of weights for elastic events (in this rrp same t interval) from our elastic trigger rolls. The fraction of true elastic events that survive the cuts used to define an elastic event is given by srrp cuts This factor serves to correct e' for the small number of elastic events lost in selecting the elastic events. 4 Np tot is the number of four-prong events found on all the film and N:~ is the number of four prongs found on the elastic rolls; their ratio serves to scale N from elastic roll elastic events to all the elasrrp tic events that occurred during the experiment (including those elastic events excluded from the production film by the computer trigger). We have taken corrections for inefficiencies in making sparks, finding spark chamber (SC) tracks, and matching SC and bubble chamber tracks to be independent of the event type and computer trigger . rections then cancel and are left out of equation (2). These cor- The ratio of 4P rrp the beam contamination corrections, sbm/sbm' is also taken to be one. -59This correction is discussed in more detail in section 3 of this chapter. 04P and Q, TIP• are the fractions of four prong and . . Th e quantities ~ . pix pix elastic pictures lost because the computer trigger program processing time exceeded the flash lamp delay time. The factor Q, 4P • pix was taken to be equal to the fraction of all production (inelastic trigger) pictures lost, Q,p~od. pix The elastic loss fraction ( £TI~) was determined from the pix loss fractions for the production and elastic trigger rolls ( £ e~as). pix We assumed that the reason for a picture being lost was that extra sparks from a second event or a beam particle outside the normal beam area would cause the trigger program to use an excessive amount of time in the track finding due to the larger number of possible spark combinations. To see how changing the trigger conditions gave the different values found for Q,p~od and Q, e~as (see Table IV.l), consider pix pix the case in which two events occur and leave tracks in the spark chambers. Since elastic events are so prevalent in this experiment, the probability is very good that at least one of these events is an elastic event. If we are taking a production roll, the trigger program must find an inelastic event before deciding to take the picture and so may first find and reject the elastic e vent track and will use some fraction of the available time to do so. The same situation of an elastic event occurring with an inelastic event then has a smaller probability to lose a picture when an elastic trigger roll is being taken. The probability is smaller than the production case because the finding of either event's spark chamber track by the trigger pro- -60gram is sufficient to satisfy the trigger conditions. For inelastic events, the trigger program and conditions are identical for production and elastic rolls so we have assumed that the probability to lose an inelastic event picture is the same for both these cases. We have also assumed that the probability of losing an inelastic event picture was given by the production roll picture loss fraction (ip:od). pix elas . is approximately From Table IV.l we see that £ . pix one half of i p:od. pix This comes as a result of the small probability to lose an elastic event picture (as discussed above) and the larger number of elastic events on the elastic rolls. The probability of losing an elastic event picture ( iTI ~ ) WaS determined by: pix f where f (3) e is the fraction of elastic roll events that really were elas- e tic events . This fraction was found to be 70.1±0.7% when averaged over the two experiments (the individual experiment values agreed within their errors). Table IV.l gives the values of the quantities in equa- tion (3) along with the correction ratio of 4 (1- £ pix ~ )/(l- £TIpix ~ ) for equa- The errors in £TIP and the correction ratio are dominated by pix . Nnelas . 1 arge d ue to t h e sma 11 num b er o f e 1astic . t h e error in • wh'ic h is pix tion (2). rolls. However, the error introduced into the normalization by the lost picture correction is small since £TIP is a small number (compared pix to 1). -61Table IV.l Lost picture fractions 1T 1T + 2.62% 5.56% 1.88±0.12% 2.95±0.10% pix 1.56±0.17% 1.81±0.15% (l-t 4pix ~ )/(l-Q,1T~ ) pix 0.989±0.002 0. 963±0. 001 Q,p:od _ Q,4~ pix pix Q,e~as pix Q, 1T~ Table IV.2 lists the values of some of the quantities used in equation (2) [Davidson 1976]. The integrated elastics cross sections were evaluated from published data [Foley 1963 and 1969] for dcr/dt integrated over the required interval and interpolated to our beam momenta. The values obtained for cr "P are considered to have a 3% sys- tematic error [Foley 1963 and 1969] in addition to the quoted statistical error. During the 11 experiment, the upper trigger mass cut was set at 2 . 8 GeV until roll 125 after which it was raised to 3.8 GeV . h was use d throug h out the 7i + experiment . ). ( wh ic For this reason, only four prongs with N* masses between 1.3 and 2.7 GeV were used in deter. . N4P d 4P mining tot an Nel' Using the Table IV.2 values (and combining the two parts of the 11 + experiment to get a single number) we found the overall four-prong exposures quoted in Table IV.3. These exposures are the result of calculating e' and do not include the channel detection efficiency (sch). The errors quoted in Table IV.3 are purely statistical. Both experiments are considered to have systematic errors of approximately 5% which when combined with the 3% systematic error in cr 11p gives over- -62all systematic errors of about 6%. Table IV .2 Elastics normalization quantities SLAC 1T+. data LBL 1T + data 1. 015±0. 005 1.003±0 .005 1. 010±0. 005 2.17±0.05 2.19±0.05 2.19±0.05 4236±82 4082±81 1127±43 24985 20021 13716 632 708 229 data 1T l/€1Tp cuts cr (in mb) 1Tp N 1Tp N4P tot N4P el Table IV.3 Four prong exposures + 1T 1T e' (events/µb) 77. 7±3.9 85.7±3.8 percent error 5% 4.4 % systematic error 6% 6% -633. Beam Contaminatiun We must also correct the exposure for the events that come from the non-pion components of the beam. The hadronic beam fractions given in Table IV.4 were calculated from the data in the SLAC User's Handbook [Boyarski 1968] while the electron fractions came from the electron-to-pion ratio measured for the rr experiment. The muon fractions were estimated from rr and K decay over the length of the beam (14.88 meters). Table IV.4 Beam fractions Particle type rr ± rr + beam rr beam 90% 94% K-+ 5% 3% p or p 3% e µ ± ± The p fraction of the rr .4% <2% <2% beam and the e+ fraction of the rr + beam were ignored since they represented less than 0.1% of the beam. The muon fractions were calculated from rr and K decay but are given as upper limits only because an unknown fraction of these decay muons will escape from the beam phase space before the bubble chamber is reached. The fractions of positrons and direct muons in the beam were very small compared to the electrons since most of the electrons came from elastic or inelastic scattering of the primary electron beam from the produc- -64- tion target. In events of the type we are interested in, like elastic scattering or the reaction Tip-+TIX, with a beam momentum near 14 GeV/c, we cannot tell the difference between events caused by pious, kaons, or protons in the beam. The electrons and muons in the beam interact much less frequently than the hadrons and so contribute essentially no events. Because the kaons and protons contribute both reaction and elastic events, both the numerator and denominator of equation (1) must be corrected as indicated by the ratio s~!/s~~ in equation (2). If we combine and rewrite equations (1) and (2) with N b 0 s being the observed weight-sum (Lwi from equation (1)) and Nel the weight-sum for elastic events (same as N TIP (j obs = s (j in equation (2)), we have: Nabs TIP Nel ( 4) where the other factors have been absorbed into the scaling constant s. Then to get the "true" cross section for the reaction Tip-+TIX, we must subtract from Nobs and Nel the numbers of events due to the beam contaminant of particle type c: =s N0 b s -N c.X (j ;rp Nel -Ncp = (j obs 1-Nc X/N 0 b s 1-Ncp /N e l (5) where N X and N are the weight-sums for events from the contaminant c cp reaction (cp~cX) + and contaminant elastic scattering standing for K- (either beam) or p (TI + beam only). (cp~cp) with c Since the contami- nants are known to be a small fraction of the beam so that N0 b s >>N c X and N >>N (and taking N ~ N ), we have: e1 cp e1 TIP -65- l Gobs [ NcX ] - Nobs (6) Since the cross section for a scattering process is proportional to the number of scattered particles observed divided by the number of beam particles incident on the target, we can rewrite this as: G TTX where f c ~ 0 [ obs ex] [1 _ f Gc Gc J 1 _ f cG a b p (7) TTP o s is the fraction of the beam that consists of particle type c and we have used Gobs~ GTTX (to lowest order). Now, by ignoring small second order terms and defining the scale factor r by GcX/GTTX = r (ocp/ G ) , we get: TTP a,x ~a obs [1 - (r - 1) (8) Finally, by using factorization [Leith 1976] we can say that r is 1.0 with a 20% systematic error. 4P TT Thus we can set the ratio sbm/sbm to 1.0 and include the effect of the beam contamination in the systematic error. Thus the systematic errors due to the beam contaminations are: TT + beam: TT beam: 0.2(fKoKp+ f p Gpp )/G TTP 0.2£KGKp /a rrp = 0.2% 2.3% (9a) (9b) -66- 4. Geometrical Acceptance Correction By using a hydrogen bubble chamber as target and detector, we have essentially 100% detection efficiency over the entire 4TI solid angle for the slow tracks resulting from proton dissociation. However, we must correct for the geometrical biases in the detection of the fast forward pion resulting from the limited bubble chamber exit and spectrometer apertures. These biases occur because the geometry of the apertures precludes detection of all the events; in particular, only those events with a fast track at a given scattering angle (8) and momentum (p) and in a particular range (or set of ranges) of the azimuthal angle (¢) about the beam particle's direction are detected. Since the physics is independent of ¢, the number of events observed (as a function of p and 8) must be corrected for the number of unobserved events in the ¢ ranges blocked by the apertures. The limited geometrical acceptance is taken into account by weighting each event by the inverse of the probability for the detection of that event (the geometrical efficiency) . -+ -+ -+ The geomtrical efficiency, s(x,x' ,p), is in -+ -+ general a function of the vertex position (x), the beam angles (x'), -+ and the momentum vector of the fast particle (p). This efficiency was determined for each event by tracing the fast track through the BC exit and spectrometer for 128 equally spaced azimuthal angles and determining what fraction of these traced rays successfully pass through the spectrometer. cally integrating: This procedure thus corresponds to numeri- -67-+ +, 1 e:(x,x ,p,cose) = Z1T J21T e:(x,x' -+ -+ -+ ,p) d<jl 0 (10) The ray tracing was further enhanced to smooth out aperture edge effects by retracing (with multiple scattering taken into account) those fast track rays which passed near an aperture edge for an additional 5 tries. Thus each event was ray traced through the spectra- meter about 150 times. This gave sufficient statistical accuracy so that the error in the geometrical efficiency was ignored when calculating the error in a weight-sum. The ray tracing program was checked by comparing traced rays with observed rays. -+ -+I When processing the data to calculate e:(x,x ,p,cos 9) for each event, the traced and observed spark positions at stations 1 and 2 were compared and used to adjust the bubble chamber-to-spectrameter connection parameters. The agreement was better than 0 . 01 inches (the spark chamber setting error is approximately 0.017 inches). For some 4% of the events, the ray tracing program claimed that the actual ray of the fast track failed to pass through all the apertures. -+ -+ For some regions of (p,8), the efficiency e:(x,x' ,p,cos8) is zero -+ -+ for portions of the bubble chamber (x) or beam phase space (x'). Thus events that actually occur in these regions are not detected and we are formally in the position of dealing with the indeterminant quantity of 0 events divided by a 0 efficiency to correct the cross sections. This difficulty was overcome by averaging the efficiency over the ranges of -+x and -+x ' in · t h ese cases: -68- - -+ -+ -+ -+ -+ = f J s(x,x' ,p) n(x,x') d 3-+ x d 2-+ x' s(p,cos6) (11) -+ -+I x,x -+ -+ where n(x,x') is the normalized beam distribution which gives the frac-+ -+ tion of the beam particles which pass through the volume d 3 x at x in the bubble chamber with beam angles within the range ~' to ~ 1 +d2~ 1 • These integrals were done by use of a Monte Carlo program which gener-+ -+ ated events within the (x,x') space for a fixed (p,6). The resulting rays were traced through the spectrometer with the same ray tracing program described above. Besides allowing s(p,cos 6) to be calculated, -+ -+ this procedure also allowed the (p,8) region where s(x,x' ,p,cos6) is never zero to be found. This method had the disadvantage relative to the method discussed earlier (using the data itself to do the numerical -+ -+ integration) that the beam distributions in (x,x') must be known and adequately parameterized. As it turned out, most of the events lay within the region of the -+ -+ (p,6) plane for which s(x,x' ,p,cos 6 ) is always non-zero. For the four prongs, only 14% of the events were outside this region and thus have €(p,cos 6) used as their geometrical efficiency. -+ -+ The s(x,x' ,p,cos 6) non-zero region corresponds to approximately the area within the 0.3 contour line in Fig. IV.l. -69- -rr+ Experiment Geometric Acceptance - ............. _________ .,..._..,.,,,.. I I I I J I :gt J ·/ I / I I I / I I / --,,, .,, / ,,,. / 10- 3 1 2 3 N* (recoil) mass (GeV) Figure IV.l Contour plot of s(p,cose) as a function of the mass of the system recoiling against the fast forward pion (~ * mass) and the or the N momentum transfer from the beam to the fast pion (t 7T7T ). 4 -705. Computer Trigger Efficiency Correction We have also weighted each event by the inverse of its computer trigger efficiency. This efficiency reflects the loss of events by the three cuts made by the computer trigger program in selecting inelastic events for bubble chamber pictures: (1) the DEL3 cut which corresponds to a high recoil mass cut, (2) the RESID cut, which eliminates false spark chamber tracks, and (3) the HMF cut which removes the elastic events (low recoil mass) . The three quantities called DEL3, RESID, and XMF are given in Appendix A as d 3 (equations (8) and (10)), r (equation (31)), and d -ct(x -x ) 2 1 3 (equation (28)) respectively. 2 Similarly the three cuts made by the trigger program are given by equations (lla), (32), and (28) in Appendix A. The total computer trigger efficiency is the probability for an inelastic event to pass all three cuts: (12) The resulting computer trigger efficiency for the four prongs is dominated by sRESID since the four prong threshold is considerably above the lower mass cut at 1.1 GeV. There is a large effect from sDEL 3 begin- ning at 3.7 GeV (near the upper mass cut), but most of the interesting features of the data occur far below this region. Though the average of sf shows a very small linear dependence on the recoil mass (see Fig. IV.2), it mostly constitutes an overall constant correction to the four -71prong cross section on the order of a few percent. The computer trigger efficiency, like the geometrical efficiency, -+ is a function of the momentum vector of the fast track (p) as is to be expected since the computer trigger program calculates its test quantities from measurements of the fast particle. The computer trigger efficiency is dominated by statistical effects in the beam phase space (especially the beam energy), the spark chamber setting error (resolution), and multiple scattering of the fast particle. This efficiency is also dependent on the values of the program parameters used to describe the apparatus and determine the trigger cuts. The efficien- cies due to the individual RESID, DELJ, and HMF cuts were calculated by using the gaussian integrals: +ITRC 1 sRESID €'MM}' 1 ~ crD(p, 8) 1 ;2rr crM(p, 8) (13a) -ITRC /z; crR(p,8) €DEL3 = exp { -(r-r(p, 8 )) 2 /2cr~(p, 8 )} dr J ID MAX exp{-(m-d(p, 8 )) 2 / 2 cr~(p, 8 )} dm (13b) exp{-(m-~(p, 8 )) 2 /2cr~(p,8)} dm (13c) J -co +co J ID MIN ' where ITRC, IDMAX, and IDMIN are the values of the parameters used to define the cuts on RESID, DEL3, and MMF respectively. are called w d and d'. in Appendix A. r' 3max' min These parameters Monte Carlo studies were used to evaluate the dependence of the means and variances of the test quantities (e.g., ;(p,8) and crR(p, 8 ) in equation (13a)) on the -72- fast particle's momentum vector. edure is given in Appendix C. A detailed discussion of this pro-- With the test quantity means and vari- ances parameterized as functions of the fast particle's momentum vector, equations (12) and (13a-c) allowed us to calculate the computer trigger efficiency for each event. The upper trigger mass cut for the rr experiment was raised from 2.8 GeV to 3.8 GeV at roll 126 (of the BC film). used for the entire rr + experiment. trigger efficiency ( <sf> or <sf ast The 3.8 GeV cut was Shown in Fig. IV.2 is the average >) for 4C and lC four-prong events as a function of the N* mass for rolls below 126 and rolls above 126 separately. The two different upper mass cuts are clearly evident as rapid drops in <s > at 2.8 and 3.8 GeV. · fast Also evident is the weak linear dependence of sf on the N* mass for masses below the trigger cut. Fig. IV.3 shows <sfast> with the linear dependence on the N* mass removed. slin(~*) (slin(~*)) For masses below the trigger cut, <sf is a constant with the value 1.0. ast >/ The curve in Fig. IV.3 that goes from 1 at 2.7 GeV to 0 at 2.9 GeV is an estimate of the shape of sf (with the linear mass dependence removed) at the mass cut. The data points above 2.8 GeV for rolls below 126 are non-zero and have large error bars because <s fast > was calculated using the actual data which has very few events in the region. This estimate of sf was combined with the ratio of the number of events from rolls above 126 (and including roll 126) to the number of events from rolls below 126 to yield an extra weight function to correct for the "missing" events above the 2.8 GeV trigger mass cut. This ratio was found to be 2.7 -73by using the 4C and lC weighted events (weighted by the geomtrical acceptance and trigger efficiency). weight-sum for the events. By weighted events, we mean the Taking either 4C or lC events separately or using unweighted as opposed to weighted events did not give a significantly different value for the ratio. The resulting corrected N* mass distribution for the lC events is shown in Fig. IV.4 along with the uncorrected distribution for all rolls. The corrected dis- tribution now has the same overall shape as the distribution for rolls above or equal to 126. I I I I 0.0 upper mass cuts used in the n ( <E ........... Average trigger efficiency v w (/) I f experiment. 11:1 t1 1, t 1: : ·1 I t I II I t : I t t t I . ltt ::: t 11 1 1:1: I I : t I I I : I I : ! ~ : : 3 (GeV) I I I I I • t : It 1' 1: I I t I I I :::: ···::•:: : : : : :: : : I : : .. i !1 :::1 : : t t I t I 1,1, I I : : I I I : tf I : : 1 I : 1't I ! :1: :1 ltt ~I -I : 11 : : : : i::: 1 1 : : : : : : :::: : : I I 1: • t : I I I I I I I I t I : I I I I t I I I 1t I I : I t I : I I 1 I I I • t I t 111 "'1111 I . :::: I I : : : : ::: :1: t ~ I II I i I I ! t I ..I • I : I I I I I I I I I I I I .. . 4 ~ * (recoil system) mass for the two different Figure IV.2 N>f mass 2 >) as a function of the N '"'-... I~ 0 11 S "'~ 126 - -- •I I ltt t I • t I I I I ! : : ! : !: ! : : ! : II I 1, t •1:1 10 I t1 t 1,t I : I t I t e I I I I ~ 0.5 1 I 1 I 1 t I I .. : I L::": It ·:·: '1'1 ---·- ·--~~- I I I .. I I I I I : •1 • I R0 11 s . . ._ 126 I I t t I I I I t11 I I I • I .+l /\ 1.0 n-p4niN* N* -)7T+1T-p or rr+n-1T 0 p or n+n+1T-n I -...,J I .p.. -,..-- ,.-- I I 0.8 " 2.5 0.0 L-1........ L ... -.... I above 126. I . ~ ··-I t .••'' ' ••• • +.~. I I : • I I t I ......·•· .. ' ' '' •• '' ' '' '' ' I . • Figure IV.3 2.7 1J~ rnass 2.8 (GcV) 2.9 I .J I I •• I I I I I I I I I ' ·•· •• ' • +le I • I I I I ••• •• • 3.0 I I I I I ' I ...... Vl I I I ... * mass has been divided out of <Ef> which results in a flat curve for rolls 2.6 I I I I t • •' ••' • •' ' ·•· •••' •' •' ' -r· 0.00958rn - ..-_. ..............---t~-~.+! • . . .,. ..----r-·T- T--,.---,- 0.90996 I -1,...__~_ _J___,L . . -L-.L - --L-.--L......L- -!...-j_ __J_..J.__.J_~~ H.olls <126 - I~oils~~ 126 The line through the low roll data is an estimate of the decrease of Ef with mass at the cut. The linear dependence in the N \ w' 0.2 ~ - ~ /\.+..l 0.·1· ' .. r--4 •r-f ~ ~ 0.6 +' <V I + -. - ---r--r- r--.---r1 El~ 1.0 ~. ~~r:~ar term ,.--....._~~ 1.2 rr -· p·>?Tr--·N* '1) ~ 1 r1 •• •• 3 Figure IV.4 TI ~t·• • 1 • 11 :• . .. ~· '•"'' :: l1: L•l 0 - N* mass distribution. ro • 1 r•: :•:: r• .. •• 1: .. : : :::: ..: . ··~···i.:··· .: .: :... .:.: :r:•:• I "'L~. N* mass (GeV) 2 uncorrected corrected Effects of the correction weight function on the 0 :~ Pt 200 t\D .d J.-1 .,...> 't1 lO 400 Q) N cu ~~ ~ Vl .r:1_, > 600 800 1T-p-»7Ti·rr+rr-(nN) + (7rN) = 7r0 p or 1T+n 4 I I '-.I CJ\ -776. Channel Corrections and Background Estimates The procedure adopted to resolve questions of ambiguous fits (multiple kinematic fits for different channel hypotheses) for an event was to select a single fit to describe the event. event was assigned to one and only one channel. is not perfect. Thus each However, this process Some events that belong to a channel are not assigned to it and thus lost. In addition, a background of events lost from the other channels creeps into each channel. The number of events so lost or gained are estimated and used to calculate the correction to the cross section (shown in equation (2) as the factor Ech). Fig. IV.5 shows the confidence level distributions of the events in the four lC channels. The confidence level (CL) for an event is the probability of x2 values (for the kinematic fit) larger than the particular value observed for that event. The CL distribution is useful in that in a perfect world (errors assigned correctly and residuals distributed as gaussians) , it would be a constant distribution so that 5% of the events would have CL<5% and so forth. As is seen in Fig. IV.5, considerably more than 5% of the events have CL<5%. These extra events are from two sources, background events from other channels that were incorrectly identified and good events from the correct channel. There are more than 5% of the events of the channel in the CL<5% bin because the residual distributions contain more events in their tails than given by gaussian shapes. These excess tail events also show up as extra events in the CL bins immediately above 5%. The distributions above about 20% are very flat as is to be expected. Thus, after making -78- 2000 1000 0 7r+p4nt n+ TT+ 11"-n 1000 tll 500 +) ~ Cl.) 0 > ~ n-p 47Tf rr+n-nop 1000 500 0 7r-p41t'f 7T+ TT+ 11"-n 500 0 0.5 0.0 1.0 Fit Confidence Level (CL) Figure IV.5 Distributions of the kinematic fit confidence level (x 2 probability) for the four lC channels. The shaded region shows the events below the 5% CL cut along with the fractions of these events in the channel. -79the CL~% cut on the data, there remained the problem of estimating the number of background events remaining in the channel and of estimating the number of good events lost from the channel by the CL cut and the fit selection process. Once these numbers were known, the channel efficiency (sch) and the normalization constant (e from equation (2)) were calculated for each channel individually. The pertinent numbers of events are given in Table IV.5. The number of events comprising each channel's data sample is given in line 1 of the table. The distributions of the missing-mass-squared (mm 2 ) are shown in Figs. IV.6a-d. One feature of our experiment that can be seen from these figures is that the hybridization to improve the measurement of the fast track has dramatically improved our resolution in the neutral missing mass. The width of the TIO missing mass peak corresponds to a sigma of about 70 MeV which is less than one half of the n 0 peak sigma of many pure bubble chamber experiments at these energies [Baltay 1978, Cason 1970 and 1973, Hones 1970, Johnson 1976, and Kung 1969]. Similarly, then missing mass peak in our experiment shows a sigma of about 50 MeV which is also better resolution than that obtained in previous experiments [Cason 1970 and Johnson 1976]. Also shown on the plots are the values of the centroids of the peaks. The TI experiment was processed through TVGP with a slightly low value for the bubble chamber magnetic field so the peaks are 10 to 15 MeV below the correct values (the TI 0 or n mass squared) . to be observed in the invariant masses of the TI 0 instance, the w peak is about 5 MeV high). A similar shift is also experiment (for This shift was not cor- 14±6 440±34 0 29±11 721±65 865±96 4. Events lost to 4C channel 5. Events lost to OC channel 6. Total events lost from channel 7. Background events in channel with mm 2 >m 2 (from OC and lC channels) 0 9. Background events from lC channel with mm 2 <m 2 395±62 3867±69 865±96 8971±116 11. True number of events in channel 0 0 395±62 10. Total background events in channel 0 0 8. Background in channel from 4C's 0 0 0±15 3. Events lost to opposite lC channel 0±15 426±30 692±62 2. Estimate of good channel events removed with CL<5% n channel 3838 channel 9145 0 + experiment . 1. Events with CL~5% (channel data sample) rr 1r 0 335±59 317±81 6720±134 641±104 0 3668±83 371±64 0±15 36±20 515±53 836±84 324±65 65±17 152±26 0 50±15 50±24 0 400±48 634±76 3524 n channel experiment channel 6525 ·rr rr Lost and background event counts in lC 4-prong channels Table IV.4 I 00 0 I -81- Figures IV.6a-d Missing-mass-squared distributions for the selected (CL,;;;:5%) events of the four lC channels. The sha~ed distributions show the estimated background event distributions in each channel. approximate mm 2 values of the peak centroids. Also given are the ~ > <1) ci +l {/} Lee 0 -0.2 300 600 h • (a) b I I I I I I -0.1 1 I I I e e 1 I I I I I I I I I I I I I • • • 'ff • I I I I Figure IV.6a I I I I I I •••••••••••• 0.3 ts'...,..., ,,Jae H 1 0.4 e e e e I 2 ffipeak"'·Ol 768 I I' i 0.1 0.2 1To mm 2 (GeV2 ) I e I 0.0 1 I ?T+p--nrtp7T+ 7T- 7ro ( CL~5%) t;'~ 900 ....... , , I 00 I N ~ > v ~ ......, {/} ,,f (b) 0.0 0[ 100 200 300 IM' 1 0.5 +~ I Figure IV.6b 1.5 t~,Q..m.R!'A 1.0 n mm2 (GeV2 ) I m2 n IC •I 2 ffipeak"".88107 n+p 4 ntnn+n+n- (CLZ5%) _l 2.0 I ():) I w r:r.1 :> <L> ci +> tll e 0I -0.2 200 400 '7 (c) -0.1 ~=-It I ii I I I Iii Ii I ii ii I I iii I ii 2 1111 Figure IV.6c 0.1 0.2 1To mm 2 (GeV2 ) 0.0 ii t e 0.3 ._J, I f t e I'd t I 0.4 I iiiiiiiiiii mpeak"'·O 1540 iiiiii IYiJdXMB,rAXXXIXl'2tgJ~ 0 h ' d 'Ss'd I 600 ............ ,, 7T-P 4 1Tfpn+n-1TO (CLZ5%) I CXl .i:-1 -85- 0. C\l N t"J co LO cc. z ~ LO td ~ ~ LO • Q) ~ C\l Pi s 1\11 ~ ,,....... t) ..._.. "2 I \.!) > Cl) ...._..., ~ 0. + ~ + ~ Nd s~ l:: C\l E '"Cl '°>. H 8 ... (!) ~ 1..... ~ ;:l ()j) d t 0.. I . LO ~ 0 _________________ ..._... 0 0 C"'J 0 . 00 ~ µ.. -86rected for. The number of events lost from the channel by the confidence level cut (line 2 of Table IV.4) was estimated by using Figs. IV.7a-d. These plots show the missing-mass-squared distributions for the events with a confidence level below the 5% cut used to define the channel data samples. The shaded areas show the estimated distributions of good channel events removed by the CL cut. This estimation relied upon two assumptions about the missing mass distributions. The first assump- tion was that events belonging to the channel in question have a missing mass distribution that is symmetric about the mass of the channel's neutral particle. The second assumption is that events that do not belong to the channel have a very different missing mass distribution compared to that for the channel's events. Furthermore, these back- ground events should occur in localized regions and be non-symmetric. Thus in Figs. IV.7a-d, the shaded distributions for events with mm 2 above the neutral particle's mass squared (m 2 , indicated by the arrow) 0 is a reflection of the same distribution from below m2 . 0 This was done because the background events with mm 2 less than m2 are fewer in number 0 and are confined to a smaller region of the mm 2 distribution. In the case of the n° channel (Figs. IV.7a and IV.7c), the excess events peaking near zero are taken to be background leaking into the TI nel from the 4C channel. In the n channels, the TI chan- experiment was found to include some events with rnm 2 <m2 that appeared to be TI 0 0 0 events (Fig. IV.7d) while no evidence was found for any non-channel events -87- Figures IV.7a-d Missing-mass-squared distributions for the events removed from the four lC channels by the confidence level cut (CL <5% events). The shaded events show the estimates of the distributions of "true" channel events lost with the CL cut. -88 - 80 (a) 60 tn ,.._) ~ 40 > ~ 20 0 ~WWWV\/VVVV\/VVVV\A,NJ't -0.1 0.0 0.1 rr 0 mm 2 (GeV2 ) 0.2 n+p4ntnn+n+n- (CL<5%) 60-------------------------------_____... (b) tn 40 ,.._) ~ ~ 20 OL-A.~~~~~~~--l..~~~~~~ 0.0 0.5 n 1.0 mm 2 (GeV 2 ) Fi gu r es I V.7 a and b 1.5 -89- n-p4n[pn+n-~ 0 (CL<5%) 60~----__..,~----------------------- (c) 0 -0.1 WWWVVVVVV'..VVVVV.JV'VVVV'...,.,,-. 0.0 0.1 rr 0 mm 2 (GeV2 ) 0.2 n-p4n[nn+rr+rr- (CL<5%) 40 (d) 30 Ul _.,.,) fil 20 ::> ~ 10 OIC--UQ..-J~ULJt:W~~~~_.~~~.oAi.i~n..J 0.0 0.5 n mm 2 1.0 (GeV2 ) Figures IV.?c and d 1.5 -90with mm 2 <m2 in the TI+ data (Fig. IV.7b). 0 The errors associated with the estimates in line 2 of Table IV.4 were chosen to encompass the uncertainity in the outlined procedure, particularly with regards to the subtraction of background events with mm2<m 2 . 0 Returning to Figs. IV.6a-d, the shaded regions here show the estimated mm 2 distributions of the background events remaining in the channels. At the same time, the numbers of background events are given on lines 7 through 9 of Table IV.4 (line 10 is the sum of all the events from separate sources of background). The background events are mostly from the OC channel and possibly the other lC channel (e.g., from then channel as background in the TIO channel and vice versa). They have missing masses that lie above the neutral particle mass (for the most part) and are consistent with their distributions starting 0 near the multineutral threshold (TI TI nTI 0 at (m +m ) 2 for the n channel). n TI distribution for the TI 0 at 4m 2 for the TI O channel and TI In addition, the TI O channel mm 2 experiment (Fig. IV.6c) shows a considerable number of background events from the 4C channel (the small shaded peak at about 0 in the figure). These estimated distributions were made by explicit used of the assumptions stated above. It was assumed that most of the background events had mm 2 >m2 and that, except for an y 4C background, the events 0 with mm 2 <m 2 were relatively free of background. Symmetry was used to then subtract away all but the background events. This was done by 0 constructing a histogram in which events with rnm 2 >m 2 were accumulated 0 with a weight of +l (as in a normal histogram) and events with mm 2 <m 2 0 -91were accumulated with a weight of -1 and shifted to a new mm2 value given by: = 2m02 - (mm 2 ) (14) old Thus all the events appear to have mm 2 >m 2 in the histogram, but 0 slightly less than half have a negative weight. This accomplishes the desired purpose of reflecting the mm2<m 2 part of the distribution 0 about the centroid and subtracting it from the original mm2>m 2 part. 0 This was done on an event-by-event basis to suppress a false signal from a mismatch in the relative mm 2 positions of the steep side of the mass peak. Even so, large statistical fluctuations appeared at the leading edge of the mm 2 background distribution and were removed by a hand smoothing approximation. The error in the estimated number of background events is the square root of the number of events in the channel's data sample. This error represents an error of about 15% to 30% in the estimate of the background and is considered adequate to cover any systematic errors in the procedure used to make the background estimate. Finally, for the TI - experiment TI 0 channel data, the 4C background was arrived at by inverting the process and subtracting the upper portion (mm 2 >m 2 ) of the distribution from the lower portion. 0 The procedure outlined above was checked by hand-drawing a smooth symmetric curve through the mm 2 distribution and estimating the background from the excess above the curve (in the 4C and multineutral rnm 2 regions). Besides losing events by the CL cut, lC events were also lost by -92- Figures IV.Sa and b Missing-mass-squared distributions for events with lC fits rejected by the ionization selection (and so becoming events in the OC channels) . The shaded regions show the estimated distributions of lC events incorrectly rejected by the ionization selection. The small shaded peak in Fig. IV.Sa near a mm 2 of 0 represents 4C events that were incorrectly rejected by the ionization selection. -93- rr-p41rf P1T'+n-(mm) 60.---r~.,-,-.,~~,....,.......-------~__,~---~ n° events lost as rejected fits 0~~---...----~~_.__~----~~~~ -0.1 0.0 0.1 mm 2 GeV2 0.2 rr-p47r[rr+rr+rr-(mm) 30-------------------------n events lost as rejected fits (b) t/l 20 _.,j d Q.) :> ~ 10 Oi..i..-"'--.......,_._~--i..£..~__._--~UL-~.__~_._.u.._~ 0.0 0.5 1.0 mm 2 GeV2 Figures IV.8a and b 1.5 -94- Figures IV.9a and b Missing-mass-squared distributions for lC events with a second ambiguous lC fit that was rejected by the ionization selection (the mm 2 distribution shown is that for the rejected fits). The shaded regions show the estimated mm 2 distributions of the lC fits that were incorrectly rejected by the ionization selection. -95- 11"-p41T[n1T+rr+ rr- 60 .---.....~~--~r--o--.-~~--~..-------71' 0 events lost as rejected fits 0--------------------------------------0.1 0.0 0.1 0.2 rr 0 mm 2 GeV 2 n-p4rrf"prr+rr-rro 60.--..---.----------~-.----,..---,.-.--------.--. n events lost as rejected fits (b) tll -+-> d 40 <l.) ~ Pz;:I 20 o~.&...--JC-J:i.--Jc..c=.--L....--\....__...~~c.&-J..-~..L-~....Z::....~ 0.0 0.5 1.0 n mm 2 GeV2 Figures IV.9a and b 1.5 -96- Figures IV.lOa-d Missing-mass-squared distributions for lC events with a second ambiguous lC fit. The shaded regions show the estimated mm 2 distributions for lC fits that should have been chosen as the correct fit. -97- rr-p47r[nrr+rr+rr- n° Lost events as ambiguous fits 60---------------------------..__....--~ CLz5% 40 20 ~ ..+-> ~ 0 1-9-.p....+-....+-+.+-.+JlillA ........qM.+-+-t--+--f---+-+-+-+-+-+-+-+-+-t-+-1~ ~ CL<5% (b) 15 10 0 j.,..j.,...&.-.&..-"'--'-~~~Wi.J..gj~....i...-..._.__..-.L....1.~.....&....I___,__......._.__, 0.2 -0.1 0.0 0.1 rr 0 mm 2 Figures IV.lOa and b GeV2 -98- n-p--1-rr! prr+rr-rr 0 Lost n events as ambiguous fits 20Qr--r--r--r-----r-~-r--r--T--r--r--.--r--r---. (c) CLz5% 150 100 50 .en ..._) §~ 0 --------~~---~----- ~ (d) CL<5% 20 10 0 ,___..__~....__...____.___._____._.._...~. . . . . . . ~~~--'---~--' 0.0 0.5 1.0 1.5 n mm 2 GeV 2 Figures IV.lOc and d -99the procedures used to select the best fit and assign each event to a single channel. The ionization selection caused some lC events to be lost to the OC channels (Figs. IV.Sa and b) or selected the wrong lC fit from among a set of ambiguous fits (Figs. IV.9a-b and IV.lOa-d). The basic procedure used to estimate the number of events lost in these ways was to look at the rnm 2 distributions for various classes of events. The results of these estimates are given in lines 3, 4, and 5 of Table IV . 4. In all of these cases, the number of events was estimated by the excess events above a hand-drawn curve used to approximate the smooth mm 2 distribution fro~ t he correctly rejected fits. The errors assigned to these estimates also included the uncertainty in the choosing of the correct hand-drawn curve. Figs. IV.Sa and b show the mm 2 distributions for the lC fits of events for which the lC fits were rejected by the ionization selection so the events were assigned to a OC channel. Figs. IV.9a and b show the rnm 2 distributions for lC fits rejected by the ionization selection in favor of other lC fits (of the opposite channel). The estimates from these figures (Figs. IV.9a-b) provided a check on the estimates obtained from Figs. IV . lOa-d which show the mm 2 distributions for lC fits ambiguous to the lC fit used to assign the event to a channel. All of these figures (IV.Sa-IV.lOd) show mm 2 distributions for the TI experiment only as that experiment suffered much larger fit selection losses than the TI+ experiment. The results of estimating the losses from the channel data sample and the background remaining in the data are summarized in Table IV.5. Given there is the fraction of the data sample of each channel due to -100the background events (about 10% of each channel) and the fraction of the channel's events that were lost by the fit selection process and the CL cut (again about 10% for each channel) . The channel correction factor (Ech in equation (2)) was taken as 1 minus the channel loss fraction. The background estimate was not included in the correction factor so that the cross section for production of a resonance would be the corrected normalization divided into the number of events in the resonance. The background events left by the fit selection process were considered to not contribute to the resonance signals. Also given in Table IV.5 are the normalization factors (exposures) for each channel with the channel correction factor included. The estimated systematic errors given in Table IV.5 include the contributions from the beam contaminations. 10 .5±1.8% 12.8±1.5% .872±.015 67.5±3.6 5.3% 6.0% 9.8±1.6% 11.4±1.1% .886± .011 68.6±3.6 5.2% 6.0% 10. 3±0. 3% .897±.003 76.9±3.4 4.4% 6.4% 7.3±0.7% .927±.007 79.4±3.6 4.5% 6.4% 2. Lost events fraction 3. Channel correction (Ech) 4. Exposure (e in events/µb) 5. Percent error in normalization 6. Estimated systematic error n channel 10.3±1.6% n° channel experiment 9.5±1.0% n channel n 1. Background fraction n° channel . n+ experiment Normalizations and background fractions for the lC 4- prong channels Table IV.5 I ....... 0 ....... I -102Chapter V Results for the Five-body Channels 1. Overview The data to be presented in this chapter are from events of the lC four prong reactions: + + + - 0 1T p + 1Tf1T 1T 1T p (la) + + + - 1T +p + nfn n TI n - + - (lb) 0 1T p + 1Tf1T 1T 1T p (le) - + + - 1T p + nfn n TI n (ld) where one of the outgoing pions has been subscripted with an "f" to indicate that it is the fast poin that entered the spectrometer. The online measurement of the fast pion's trajectory was used to trigger the bubble chamber. The fast pion could not be confused with another pion of the same charge since the fast pion had to have at least half of the av ailable energy of the event to enter the spectrometer at all. This experiment's tri gger thus selected events of the t ype shown in Fig. V. la. However, these is some contribution from events with the production of fast meson resonances (Fi g . V. lb). The events with fast meson resonances represent a background in our experiment. Our obser - vations of processes like that in Fig. V.lb are heavil y biased by the trigger since not all of the decay s of the fast meson resonances will have triggered the experiment. As will be seen in this chapter, reac- tions (la) through (ld) are dominated by single and multiple resonance production, including fast meson resonance production. -103- (a) p p Figure V.l General Feynman diagrams used to represent processes occurring in the data. The major contribution is shown in (a) where the components of the N* (or slow) system may involve resonances among all or some of the particles. The N* system may also involve non-resonant sub-pro- cesses not specified here. The diagram in (b) illustrates production of a fast meson resonance (usually a p or f fast pion and a slower pion. 0 ) which decays into the The comments made about the N* system in (a) also apply t0 the rrrrN system at the lower vertex of diagram (b). -104The events used in the final analysis were required to have the mass~* invariant of the particles other than the Tif+ less than 3.7 GeV and an invariant momentum transfer from the beam to the fast pion (tTITI=(pµf-pµb) 2 ) greater than -0.6 (GeV/c) 2 . These cuts served to eliminate events with low acceptance (i.e., large weights). A few remaining events with weights greater than 20 left after the ~* t TI TI cuts were also removed. and Since these events represented only a few percent (3-5 %) of the sample and because we were unsure whether these events belonged in the sample, we did not correct the cross sections for their loss. In any case the resulting error was within our system- atic error and well within the combined statistical and systematic errors. The cuts used to define the lC data samples are summarized in Table V .1. Table V.l Cuts used to define the lC data sample CL:::: 5% Kinematic fit confidence level (CL) cut: Cut on invariant mass of slow system (TI +TI - TI 0 p or TI +TI +TI - n): Cut on momentum transfer from beam to fast Cut on event weights: ~*<3.7 GeV TI: It iTTI l< 0.6 (GeV/c) w . s:, 20 1. Table V.2 gives the final weight-sums and corrected cross sections for reactions (la) to (ld). These cross sections are the portion of the total cross section seen by this experiment and as seen in Table V.2 are only a quarter to a third of the total cross sections predicted -105for these reactions at our beam energies (see Table I.3) . However, these partial cross sections cannot be directly compared with other experiments as one third to one half of them are from the biased fast resonance production. In this chapter, we will estimate the contri- bution of the fast resonance production and subtract it from the observed cross sections to give cross sections for the diffractive process in Fig. V.la (see section 3 of this chapter). The cross sections in Table V.2 were calculated using the corrected channel exposure factors. discussed in Chapter IV (see Table IV.5). In addition, these cross sections were corrected for back- ground events left in the channel data samples (again see Chapter IV) and for the loss of events with low It (events with It Tr Tr Tr Tr I due to the acceptance cutoff I below 0.003 (GeV/c) 2 were completely lost). The errors of the cross sections in Table V.2 include the contributions from the channel normalization errors (see Table IV.5). The table also lists the fraction error in the cross section and the fraction of the predicted total cross section actually observed (see Table I. 3). Tabl e V. 2 Observed channel cross sections Channel Weight-sum cr (µ b) ( % error ) + + - 0 rrfrr rr rr p 27336±351 320±15(4.9 %) 2.76±0.26 % 24. 8±1. 8% Tr f Tr + + + Tr rr n 1146 7± 225 137± 7 (5 . 2%) 2.29±0.43% 29.8±6.7 % - + - 0 rrfrr rr rr p 19319±295 261±15(5.8%) 2 . 84±0.30 % 26.6±3.9 % - + + rr rr n 10597±222 145±9 ( 6 . 1%) 3.26±0.46% 32.2±5.4% Tr f Tr dcr /dt correction fraction of predicted cr tot -106The low It lTlT I corrections were gotten by fitting the data shown in Fig. V.2 with: dcr exp(Bt ~=A dt lTlT ) (2) in the range from 0.02 to 0.6 (GeV/c) 2 . given in Table V.3. The low It 1T1T The results of these fits are I correction was taken to be the dif- ference between the data and the fit for the lowest t lTlT bin (from 0.0 to 0.01 (GeV/c)2). Table v. 3 Results of the fits to dcr/dt 1T1T A exp(B It 1T1T [l_ . (mb/GeV 2 /c 2 ) -2 B ((GeV/c)) 1Tf1T 1T 1T p 1. 617±0. 037 -4.36±0.10 + + + - 0. 6 77±0. 024 -4.14±0.15 1T f 1T 1T 1T p 1. 322±0.036 -4.25±0.12 - + + - 0.832±0.031 -5.03±0.18 Channel + + - 0 1T f 1T 1T 1T n - + - 0 1T f 1T 1T 1T n A For most of the remainder of this chapter, we shall present invariant mass distributions for combinations of the particles in reactions (la)-(ld). We shall use this data to estimate the production of resonances in these -reactions by a method discussed in section 3 of this chapter. The estimates of fast meson resonance production (sec- tion 3) will be used, as mentioned earlier, to extract the cross sections of the diffractive parts of reactions (la)-(ld). By selecting fast p's we will see that there is only a small amount of A meson pro- -107duction in these reactions (section 4). We will see that the slow + system (rrrrrrN without rrf) is dominated by resonance production (section 5). By selecting on a 6 or p in the slow system or by selecting a fast p, section 6 will show that there is considerable quasi-2-body (see also section 3) and quasi-3-body reactions involving fast meson resonances and associated slow system resonances. The lack of a detailed model for the fast meson resonance production prevents us from correcting these estimates for the events lost due to our trigger (see section 3). However, in section 7 we will discuss double reson- ance production and cascade decays involving only slow system resonances and so unaffected by the lost of a part of a fast resonance decay distribution. As a general observation, we find that reactions (la)- (ld) are incredibly rich in resonance production as they are the final states of many quasi-2-body and quasi-3-body reactions. to this complexity, the do/dt tially pure exponentials. rrrr As a contrast distributions were seen to be essen- Similarly, the dcr/dtpN distributions also show rather simple behavior as discussed in the next section. -108- rr±p 41rf1r1T1TN 10 1 10- 1 1 o-2 lrr1T=(Pbm-Pf) 0.0 0.1 2 0.2 0.3 0.4 -ttr1T' ( GeV 0.5 0.6 2/ c 2) Figure V.2 Plot of do / dt 'TT'TT for the four lC reactions. The error bars include the errors quoted for the exposure factors (Chapter IV). The curves are the results of the fits to the data discussed in the text. -109- 2. The do/dt N Distributions Fig. V.3 shows do/dtpN where t pN is the invariant momentum trans- fer from the target proton to the outgoing nucleon (proton or neutron). Fits of the form: do = A exp(Bt + ct2 ) dt N pN pN pt to thjs data are shown in the figure. given in Table V.4 below. The results of the fits are These distributions should be contrasted with those given in Fig. V. 4 showing do/dt + + + - TI-p-+'TTfTI TI p . (3) pp for the 4C reactions Whereas the lC reactions (la) to (ld) have do/dtpN dis- tributions which are very nearly pure exponentials, the do/dt pp distri- butions for the four-body reactions show a marked change in slope at about -0.6 (GeV/c)2. The 4C events with It PP I below 0.6 (GeV/c) 2 have a preponderance of events from the reactions of the form: + A p (4) L whereas those above the break show a very strong peak at about 1700 MeV in the TI+TI-p mass indicative of copious N* resonance production. The lack of a steep forward slope in the lC do/dt N distributions and pt 2 a slope (of 1.5 to 2.0 (GeV/c)- ) comparable to that above 0.6 (GeV/c) 2 in the 4C do/dt pp distributions can be interpreted as a relative lack of heavy fast meson production in the lC four-prong data as compared -110- to the 4C four-prong data. This conjecture is supported by the fast invariant mass distributions discussed below. Table V.4 Results of fits to do /dtp N =A exp(BitpNI +Ct~~ A (mb/GeV 2 /c 2 ) 2 B ((GeV/c)- ) C ((GeV/c)- 4 ) p 0.481±0.023 -1. 59±0. 01 0.110±0.043 n 0. 171±0 . 00 7 -1. 236±0. 042 p 0.351±0.020 -1. 54±0 .12 0.163±0.050 n 0.235±0.018 -1. 77±0.17 0 . 175±0.075 Channel + + - 1Tf1T 1T 0 1T + + + - 1Tf1T 1T - + - 1Tf1T 1T 1T 0 1T - + + - 1Tf1T 1T 1T -111-1- -l- rr-p 47T f1T1r1T N 1rf...1.. rr · rr +rr - n ...L - ..1.. - ...L ..1.. 1TfTi'1r 1T 0 p 0,.. 0 - Trf rr. rr. rr n 2.0 2.5 Figure V.3 Plot of do/dtpN for the four lC reactions. errors quoted for the exposure factors. The error bars include the The lines are the curves resulting from fits to the data discussed in the text. -112- 11"±p 41T f±1r+ 1T-p I I I 2.0 2.5 Figure V.4 Plot o f da/ dt transfer t PP pp , . ± ±+f or tne reactions rr p-+'lTfn n p. The invariant momentum is from the target proton to the outgoing proton. -1133. Invariant Masses Involving the Fast Pion Figs. V.Sa thru i show the invariant mass distributions for masses of the fast pion + c~f) with one, two, or all three of the remain- ing pions in reactions (la)-(ld). 'Ibe distributions are given in terms of weighted events per bin where the contents of a bin are given by the sum of weights of the events within that bin. We have done this rather than present the distributions in terms of the cross section (do/dm) due to the difficulty of correcting for effects of the trigger on the angular distributions of the fast resonances. For instance, of the events with a fast resonance decaying into two pions, only those cases in which the fonvard (fast) pion has the same charge as the beam will trigger the apparatus and so be a part of the data sample. Thus an experimentally undetermined fraction of the fast meson resonance events are lost since we do not accept events over the full decay angular distribution. We have not attempted to correct for the unseen events using theoretical models because of their unreliability. The estimation of the amount of fast meson resonance production is thus the determination of a background in this experiment. This background is then subtracted from the observed channel cross sections (Table V.2) to yield estimates for the diffractive portion (Fig. V.la) of reactions (la)-(ld). We have extracted the resonance signals by fitting the data with a Breit-Wigner of mass~ and width dN dm = N r(m) rR and a polynomial background: \ + l a.m i i (5) l where the mass-dependent width function has the form (from Jackson -114(1964]): r(m) = r [g(m) R q(~) ) 2£+1 (6) The parameter £ is the decay angular momentum of the resonance and q(m) is t he magnitude of the momentum of the decay products (two-body decay) in the rest frame of the resonance. For these fits, the masses and widths of the resonances were fixed at the nominal values given by the Particle Data Tables [Particle Data Group 1978) and listed in Table V.5. The exceptions where we allowed the mass (rR) to vary in the fit are noted in the text. Table V.5 Resonance masses and widths used in the fits (MeV) IR (MeV) Q, p(770) 770 155 1 f(l270) 1270 180 2 g(l680) 1680 180 3 A (13 10) 2 1312 102 2 A (1640) 3 1640 300 2 6(1232) 1230 115 1 6 (1890) 1890 250 3 N( l470) 1470 200 1 N(l688) 1688 140 3 N(l700) 1700 150 0 Resonance ~R (~) and width -115The most prominent peaks visible in Figs. V.5a-i are t hose of the p(770) resonance in the TI~TIT mass di s tributions (Figs. V.5a and d) and + in the 'TTf 'TT 0 ± T in the 'TT f 'TT mass di s tribu t ions . f 0 0 mass distributions (Fig. V.5c). The f (1270) is also seen The results of the fits to the p and peaks are given in Table V.6 in terms of the sum of event weights and as a fraction of the total observed channel production. Note that the fast meson resonance produ c tion represents a backgroun d to the events for which this experiment was designed to study (Fig. V.la). Table V.6 Major fast resonance prod uc tion estimates Wei?ht-sums (channel fractions) Resonance 0 + + - + p -+TI f 'TT T - + - - + + - 'TT TI p _3f'TT 'TT 'TT p --3 f'TT 'TT + + +TI - n _3f'TT 'TT TI n 6722±412 (24. 6±1. 5%) 4209±300 ( 21. 8±1. 6%) 3331±248 (29.0±2.2%) 4663±312 (44.0±3.1%) 109 3±296 ( 4. 0±1. L~~) 324±221 ( 1. 7±1.1%) 183±165 (1.6±1.4%) 879±246 (8.3±2.3%) 3003±344 (11. 0±1. 3%) 1455±242 (7.5±1.3%) _'.f f 'TT 0 0 + + - 0 The 'TTf'TT TI TI p channels also show several other fastresonances with small er signals than those given in Table V.6. signal sizes are given in Table V.7. along with the p tion. 0 and f 0 0 The estimates of these + - estimate was obtained The g -+Tifrr values in the fit t o the TI;'TT- mass distribu- + The evidence fo r the g (1680) is the narrow peak seen in Fig. • V. 5 1K in t h e Tif'+TT +TI - TI 0 . 'b ution. . mass d istri The fit, which used r(m)=rR and allowed rR to vary found an anomalously small width of 40±25 MeV -116compared to the accepted value of 180±30 MeV [Particle Data Group 1978]. In addition, we only seem to see the g+ via a 4TI or TITIP decay mode and not in the pp, A TI, or WTI decay modes. 2 + + - 0 The enhancement in the TifTI TI TI mass at 1680 MeV is evident but of rather low statistics, but its interpretation as the g(l680) may not be correct given these anomalies. - + - 0 Finally, no corresponding signal of the g is seen in the TifTI rr TI mass distribution (Fig. V.5k). Table V.7 ± + - 0 Additional fast resonances in the rrfrr rr rr p channels Weight-sums (channel fractions) - + - + + - 0 _rrfrr TI TI p Resonance 915±223 (3.3±0.8%) ± 2 ± 0 f :: ± + - 0 A -+rr n g ->-TI f 1T 1T 0 _rrfrr rr rr p 'V 0 568±106 (2.1±0.4 %) 51±61 (0.26±0.32%) 131±24 (0.48±0.09 %) 56±18 (0.29±0.09 %) TI 398±156 (1.5±0.6 %) 'V 0 28±13 'V 0 co. 10±0. n5 ~0 0 ± :::;: 0 . The w -+n frr rr . ' signals were obtained oy fitting t.he mass spectra with a Breit-Wigner form with f(m)=rR and allowing~ and rR to vary. 0 The shape of the w peak is entirely due to our resolution in the ± :::;: 0 rr frr rr 0 + - mass; the fits gave widths (FWHX) of 43±11 NeV for the w -+'TTfTI rr 0 - + 0 peak and 62±66 MeV for the w +rrfiT rr peak. 0 The fast w events 0 -117for the 1T + data were found 'to be mostly a result of the reaction (309± 59 events out of 568±106 total): 1T +p (7) + from in which the trigger selected only those events with a forward 1Tf 0 the w decay. The corresponding rr reaction of: p 1T ( 8) is barel y visible in our experiment. The number of events of reaction (8) found by the fit is in fair agreement with the expected 0 number of 34±7 (by isospin the w 6° cross section is 1/9 that of the o++ w 6 final state cross section). small cluster of events at the n 0 o +-o Then -+'!Tfrr rr estimate is due to a mass (Fig. V.Sh) which seem to come 0 from the analogue of reaction (7) with an n° replacing the w . corresponding n° signal in the rr able. n 0 + The data is just too small to be observ' The existence of the Az-+'TT~n° is discussed in the section on the production in Chapter VI. + + - 0 - + + - The rrfrr rr rr p and rrfrr rr rr n channels show the largest percentage of fast resonance production. production of 6++ and ~ This is due in part to the associated resonances with enhanced cross sections (due -118t o isospin) relative to the 6 0 -1- and 6° that can be made in the other two channels in association with a fast meson resonance. The associ- ated production of fast meson and slow baryon or meson resonances will be discussed in a later section of this chapter. For now, we have subtracted the contributions of the fast resonance production to obtain cross section estimates for the diffractive process illustracted in Fig. V.la. These reduced cross sections with the fast meson resonance backgrounds removed are given in Table V.8. These cross sections include the same corrections as used for the observed channel cross sections given in Table V.2. The error on the cross sections includes the contribution from the normalization error. The predicted total cross section is once again that from Table I.3. Table V. 8 Channel cross sections with fast resonance production removed Channel Removed Weight-sum Removed Percentage Remaining a ( wb) (% error) Fraction of eredicted a + +1T - TT 0 p 12858±680 47.0±2.5% 173±12 (7.1%) 13. 4±1. 2% +++ TTf1T TT TT n 3514±298 30.6±2.6 % 95.8±6.4(6. 7%) 20.8±4.7 % TT f 1T 1T 1T p 6076±445 31. 5±2. 3% 181±12 (6.9%) 18.5±2.7% - + + 1T f 1T 1T rr n 5542±39 7 52.3±3.8% 71.6±7.7(10.7%) 15.9±3.0% 1T f 1T - + - 0 tot -119The distributions of invariant masses with the fast pion and the outgoing nucleon (p or n) are not shown. In these distributions most of the events are above 3 GeV with a fairly sharp cutoff between 4 and 5 GeV (depending on the particular invariant mass) . They show no structure as they smoothly rise to a peak at (or just below) the cut- off. Table V.9 Background fractions and total events within fast p cuts Total weight-sum within cut Cut on resonance 0 ± =i= p f -+'TT f TT ± ± 0 p (~-TI f TT + + - 0 . ; : iT iT 1T p Fraction of events in cut from background - + - 0 . ; : iT 1T 1T p + + - 0 ~lT 1T 1T p - + - 0 ~lT 1T 1T p 9167±215 5290±166 48 .5±1.6% 43.5±2.0% 7019±191 3826±134 70. 2±1. 8% 73.7±2.5% ++ + - ~n 1T n n 3708±138 - +1T +1T - n + +1T +1T - n - + + - n .;: 1T .;: 1T ~1T 5061±162 52.4±2.4% 37.7±2.2% 1T 1T -120- (data & fits) (data & fits) 7r±p~rrt1T+ 1T-rrop rr±p~rrf7T+7r+7r-n Prob(Xiit)z5% 2 2 -tntr{f) < 0.6 GeV /c (rr7rrrN) mass < 3.7 GeV Figures V.Sa- Q, Invariant mass distributions of masses with the fast pion and one or more other pions (rrfn, rrfrrn, and rrfnrrnrr masses). The distributions are shown in terms of weighted events as discussed in the text. The curves shown with some of the distributions are the results of fits to the distributions with one or more resonances and a polynomial background (see the text). For those distributions for the n channel reactions (Figs. V.Sd, e, and j) in which only a single rr + appears in the invari- + each event appears twice in the distriant mass (other than the nf), bution. -121- 2000 (a) The curves are fits to the p f 0 , and g 0 for rr+, and the p and f 0 0 , 0 for rr . 1000 0 (b) 600 J0~1 ~ I .... .-. ,. •.. , 00 ·~- U.-:•.: . : t } 300 ' : I ;+- LflJ~ ....... ... ·!· ' . 1•: : : · -~ .. . - ..'-. :; 1"' '•• 1•1 ~~ ·~ I ·~ .... I . !.! .,_. ' •• • ·- -!.!.!-' I - t' ••• t ' '-· .,. : I I 0 (c) 1000 + The curves are fits to p- 500 0 0~~-'--'-'--~--'--11.......L...~--'--~.......--'--2l.....L.~-J-~~-L-J3 1Tf7r mass Figures V.Sa-c (GeV) -122- 1500 (d) 1000 The curves are fits to p 0 and f 0 • 500 0 l() 0 (e) 1 nfl11J1i~ }ci rul~ u 600 ' 1 l l LI ~J ' : : :-· :,:_ ~! ~\h 400 .J:-•, r . . :;:_r' · ) ...:' i:-' ._: • . .r, ........·· :•... ,•~: l 200 I ···:: _,..1,.JL,, :• . ''• ,, ,. · ·~- ' ,•..,' I I rTI ' ~ii ... -· ~v~-·-:. l · ~:··: :·: . . • • ' . \ ~n ~~ ....,_ .. , ...... '•• . • : t. :-. ·-· !;i .., ' u . ' • a. ... .•, 1 1ff7r (t each t .-~ ·-· ' - 2 mass e~1ent Figures V.Sd-e (Ge\t) appears t1vice) 3 -123- 1000 500 ~~r1J ,..,1 ~ ,., .. { t1 I If 0 I LO I :·:: :;l' j I ..j.. ..j.. 1Tj 1T' 1T' I 1 ••, ·-•.!·-'1i 1 • I (g) 1 J I '~~~ I~ l'-J ;: '1n 500 l nLJl~1/i U' ,! . r I I ~. ~• '" ..,.J ~ _J~ ·1· 1Ti 1i 1f r . ', l, ..r)-" I : ,;. --i~~ t : : _,.Ji1 ,1'..; ...... ti : •• ! ., • ........ ! ! .. ,,..~ j .-i... ,:- .J :,•'•' •;·:~ ·, •.J.•,, ...;- ·1 ! t • t • • • • ~• I _.. !• • .•;·t• ,_, r t •• ••.J • I 0 I l ! •.. ,. 1T{1T-7To r 0 I I t .. • ~J '•' ) -y" f, t ~k~-- r 0 , •t. • t_..J t I If IJ n r4I. ! ..,_ ••• I I I I • 1~' I • f~ •'"'\ ~1 ·~-~ ·-.. ..--· ! : • !'! •• ,.' Jt ._. '-; I I :: j ' • I , I 4 ~•.,,.:.:i,Jl_I !, Ll'1 I ·-··- "I* U~ , :f1. j ' '• I , ' j'' 1,. j ~ "' !'"""i"" .-·I• 0 \, 1' .Jo 1r -1T+,,,,.O " 1 I i •' • I ' • 1 i '1 '1 II \ \ ',.1 I • •2 ':1, ,r ,. f~ \ ' · I · I i I • The curve is a fit t 0 t he wo only. I :_.J,' _.' ~ s:.:f '1 ', \ ("11} \ \ 41 ~ i t r- 1 500 r.'- • r t, i ! 1 ..,,., ~1Jli...ur,.n! I .!ilJ u : 1 ! u Lr'l v~ .~ :..J• , .-. ·t· ...•.~. I .: • t,. '"' t ' ' ;k, .: . - • , .·-· : ·i---1· 'n ' 0 If ::~::,-.~:~~ I~ •'o : Sf 1·. o: "'o "1.1"•' ' t.,. ... 1•, t:i It It•• ..... t ..;• • .. - . : j ,-.!··'- . . ., . . "·· _J r _._--'--L-~I ~1~111!~'~ ' ~"~'~~~~.l.-l-L~~~~· ~'. ~ ~: 0 O) , • :--~·-' ' .J, •• '. ·' 1·1· j :::. 7T(7r7T • t I t t ?.J 1 1 - mass Figures V.Sf-h . -~ 1 II I I 1 J 3 (Ge'/) I 1 -124-1- 400 ~I~ ~:~~;i I i rI300 I I l I ..J... I j I I I I I .-. :: 0 ~ :: I i I I , I i I l 1 i 1 ! :: i 'i : fl l ri t m' '-· l r ~ nl 1~ n :! I i' :1 '1u f I:.: i f"1 : r,. •• ' f 1 Q ~ l n I : ,: ' r). ,:f1'. ''. It I . ~ I t I ' t f ti t&} i :tJ.! : Li :··· : I 1 HJ I ' l r I••• t I , 1,.., ~ • • I t tl.JM'' ;~ ..,, ,t '. J ·~: M: : :~~ . •: 11 tL:. i~ ;· ~ f It I t t I I ti '· I 1 ,.. ' I s ,HJ ••• , t 'L-' , ··w· · tU··· . .. ~: :_: • 1 '.J •* •! i r 100 t- t ft In i I ~• ·~ I t i I ,. t '~-~:.~li I 11 I ; I 1 ·~' • •' ~ : ; · • . t ~ i::i 1-t' t ~ • ~ ! .. i : I ! ' t:i ::''~ .... u L : I • ~ t f I -~- Il I ~ i:J 1' '·1 '• '•j 1' I •I iJ 1' \. _ ,' • .I , I, •f Ii ·,' •t 4 • ' .,• • nlfb I 6 00 r -'l · ! Lil I r' •• .:too r I ' r ., .....--: ...i:· ~ J I ' !i .J I •,. 1 I-· ' ,I t• • ' t rtT1t4 -·I ~'I 1 · l •r; .ill. 11•1111'" ... l~·:. , t ( 1~ • • (J.) ~ r ..i !.. ~ '., rD ~·~ ~ ~ 1i';-1r+7r-t The curve is a fit to the A+ . 2 1i';1i'·n-t I• •l I· 'J !: ' -"',' ~~ ,I ~ . ' j t I~ ~-Pf I ~ ;• 1: ,,u ·1, ! ._.Ao I n I:•!:.. l ~IJ , ., ,: , ' U :: 14~ tft ' _,,, •• ' t:1 I µ : : - • ..t. t t , . iI 'r : ; .1 \ •• 1 ·' ~ : : : : :; ~ t :: : : : IJ '"' I t 0 i r' I ! 200 r 0 I 7r-1r+7T+ ~ 1.f) ..J... ...l.. n-p-,.rrrrr · rr · rr n t t • j t ! 1• ....••·::n·· . u' : ! ;t ~ r I I ,t _ _, --'1t t •I r 200 r-' rr o r_b-~~-d._·~1---~~~--··---'~·~--· -·~·-c.~·-~-.J-L..-1-J-_~_._~~~ 0 1 2 3 • (Ge\~) :rr::-?T mass f .J.. c~.re~ ~ a -D:>car·s \ ! each Figures V .Si-j ;.. ' "· . ,,~ 1 A Cl '\. . vll .-\,.,-v / -125- 1000 ~ (k) 500 l :,. f 'I ,. - ''' ,• ::: :: :-: •• I ,-, t • t 1• t ~ ... ....... ' •••, ,.! • : .: . . : !. ... .... ,if t ·ff' ' ·- ,._. : ·- j ,--·• :..•'r'': ,1' • ,,; ; ._.: : : :: : :: ' .. . :·: ',_ .. .,. ' .. ' ~ .- • f .. : I t ~ ... .....r-:·-:· . r-:" .~ . ::: I . ' Q F·~.J,-4-~~~~-+-l~l-+-lt-+-+-T-.;-+-+--lr~~-;-;r-+"o'~-~~Tf+-4 .. 1 I I rirl~ mu~l ~· • • r1 : l •1-t .: 'H n, I : :-r'I .. ;1: : :;~ i: 1 1 1 nl 7.LI I~H' 1 ~:-"': ;P.f' ' t' 1 ~I ::-~:::: ::.. : ~:: 1 I I• t : Ii :- , . ' 1 I u .J ~! :.u;, , , _.. t ' 1J ·- • '. I ·- ' IJ !•••' .. '• rt •J' • f : , a'. ...1;, t t I I ... l!~ I I I I I I ! ' I I I I I I I 3 7Tf7T'7rrr mass Figures V.Sk-9, I j_ ! 0 (Ge v·) -1264. Fast Invariant ~asses Selected on a Fast p Meson Figs. V.6a-k show the 3TI and 4rr fast invariant mass distributions for events that were required to have a fast p meson. This cut was ± ~ 0 ± 0 + defined by requiring the rrfrr mass (pf) or the rrfTI mass (pf) to be between 0.6 and 1.0 GeV. Since the fits were made with fixed mass and width for the p , the ratio of all the p signal to that portion within the cut is 1.46 for all the fast p cuts. Table V.9 lists the fraction of events within the p cuts that are expected to be from the backgrounds under the p peaks. The table also gives the total weight- sum of the events within the cut. + - 0 A small amount of A (1310) production is observed in the "f" rr 2 + + mass (Fig. V.6c) and in then channel rrfrr rr mass (Fig. V.6e) for events within the p~. Fits to these peaks gave signals of 179±174 events and 413±159 events respectively. The A in the n channel 2 + + - mass is also evident in the uncut distribution (Fig. V.Sj) for rrfrr rr which t he fit gave a signal of 400±177 events. This result seems to indicate that the n channel A is being observed solely through the 2 decay of the A to a fast p and a pion; the A ~p rr branching ratio is 2 2 about 70 % [Particle Data Group 1978]. + - The A in the rrf rr rr 2 0 mass is not seen in the uncut distribution (Fig. V.5h) due to its being a small signal on top of a large background. + - 0 mass shows a However, the "f" TI + cut large enhancement in the A (1100) and A (1310) regions for the pf 1 2 (Fig . V.6h) in which the A contribution is unresolvable and so not 2 estimated. The lack of A production in the lC four-prong channels can -127be contrasted to the large A production cross sections in the 4C four prongs. As discussed earlier, the 4C A production shows up as a for- ward peak in the da/dt + + - n£rr rr PP distributions in addition to peaks in the mass distributions. The A mesons in the 4C channels are pro- duced by diffractive dissociation of the beam pions off the target protons. In the case of the lC channels, the proton must also be diffracted to produce an extra pion and apparently the double diffraction amplitude is considerably smaller than the single diffraction amplitude. ++ - 0 The g+(l680) for which evidence was found in the uncut nfrr n rr 0 mass (Fig. V.Sk) also appears in that mass distribution for the p f and + pf cuts (Figs. V.6i and V.6k). appears abnormally narrow. In both of these cases, the g + again Also the size of the signal appears to be the same in all three cases making the exact interpretation of this peak very unclear. -128- (data & fits) (data & fits) 1T 1T±p~p?1T±1TOp rr±p ~ pyrr±7r+n 7r±p ~ Pf1r =t=7r 0 p P£0~1rf7rT 0 ...+- :%: ...+- -1.. 0 Pf ~rrrrr · p[~rr --- rr 1 Prob(X~t)2:5% < 0 .6 Ge V 2 / c 2 (rr7rrrN) mass < 3 .7 GeV -t1rtr{f) 0 -1- :;: definition: -+- ::;:: . mass < 1.0 GeV 0.6 ~ rrrrr 0 Pf~-rr[rr definition: 0.6 s 7Tf7To mass < 1.0 GeV Pf ~rrrrr· Figures V.6a - k Invariant mass distributions of masses with the fast pion and two or all three of the remaining pions for events in which the fast pion forms a p with one of these pions (see above). -129- ..,,..±p 4po1T:::'1TOP 'J f . .. (a) -1-00 fl,, 200 J.. M,.., ,...., n.ui'lu l. .. : I J:..::;_. &.' . ... ' 1;-1 •t I ...J l :••• I ~· m 1 1" ;- • u • • • •• : ·-. •. ..... : f IIt.! , l II ~ l il Ii ~I I • JI 'I f I ff •• ::...! : ,f-' .' - n 1 I n I 4 ·· 1 n u1I : .. u ' '"i J, •!.r •• ,_1 .,,...,\_ n, ,J' ... .......... '. u1...,... t 1 . -, ~ ' 1 i ,~ ... 1 •1'. PU~ . . . . . . . ' - 11~ .,...,.. - ' - , •J ·:O· !li.:I . 0 l() ~00 200 ( ... 0 ·-;;\) mass . Figures V.6a -c :rr::~ . t ; ;y ··'!~··· . -130- (d) 200 .·-.. ..·- •" ,' It t .. .•'. •" r• I It f l : •;_.: I :> Q) ~ ·~· 100 t t I !J 1 I 1' 0 ltt I ~1 l:11~1 ._: I I I 1 J :: : :: : : ::.... : ••:: 1.! ••' Ill tt :J- ·~! I I ' l() ......, :::••• :' ._, :-·! : ·--•.! '•. :'•' ._. 11 I I I I , .•• : .. : !: t I It ·h - ! I t ,I •,ti '" V'l ..+-) Q (l) ::> 0 7r;7r+7r-t 7r{7r+7r-t 0 '"d (l) + The curve is a fit to the A . 2 (e) 400 +.-) l""'I ........ . ~ I •i-1 :.. \!..) ;:: It It •• ti 11 ti .. 200 I I 1 •' ,;, ltf flt ("" '• I I 't t I I : I ·~: I I I ' 2 1 1T'f7r7T (t each 3 mass e~rent Figures V.6d-e (Ge 1/ ) appears twice) 4 -131- - n;n+'ITn;-n+1T- 200 (f) J% .~m ~ I fUJ~; · ~ ~-~' :J. 100 : ,... .r'.:::• :-:, , I , ..., •' .!··•::.,-'·;•• ::':.-' U •. !·~ ·~: • . ··~!· : ' ~· ,-, d-. ! :_;; -:' ~ • :...; ..... : ~ ,.. : f ... j •'' :u ,. :::·.. . . ._: ........; ··-. , •, 1 .. .. ,, I '.t '• I •• It 0 ~.........~~·~·H~-+-+-++++-~~+++-+-"l-T-lr-;-+++-H-"r-T-T-+-1-1··- (g) . .. i Figures V.6f-h -132- 500 p~rrrr0p p~~1T;rr=r 7rltr+7r-7To trf"7r+7r-7ro 400 300 200 100 ·-•• I •• -·• 0 200 (j) 100 0 ...• 400 300 200 (k) 100 2 7Tf7T7T7r 3 4 mass (GeV) Figures V .6i-k 5 -1335. Invariant Masses Involving the Slow System Particles + In the laboratory frame, the particles other than the rr£ in reactions (1) are relatively slow, having momenta usually substantially below 1 GeV/c while the fast pion has a momentum above 8 GeV/c or so. The slow invariant mass distributions for the rr 0 channel are given in Figs. V.7a-k and those for then channel are given in Figs. V.8a-h. The estimates for resonance production in the slow system are given in Table V.10. The errors in the cross sections given in the table include the errors in the normalization but not the general 6% systematic error (Chapter IV). The estimates listed in Table V.10 were made by fitting the mass distributions with the Breit-Wigner form and polynomial background used to fit the fast system masses (equation (5) in section 3). This procedure introduces a systematic error in the estimation of the resonance production due to the lack of a model for the background other than a polynomial shape. This system~ . atic error was estimated from the variations in the results from doing several fits to the data with different numbers of terms in the background polynomial. The size of the systematic error seems to be depen- dent upon the signal-to-noise ratio for the resonance and to the nearness of the resonance to the invariant mass threshold. meson resonances, then 0 0 and w Thus the fast peaks, and the slow p's have moderate systematic errors (in the range of 15 to 30%) as the background under these resonances is fairly well determined by the non-resonant parts of the invariant mass distribution both below and above the resonances. The systematic errors in the baryonic resonance estimates are very -134large (ranging from 25% to over 100%) due to the uncertainty in the shape of the background. The estimates for the 6++, the 6 , and the four-body invariant mass (TITITIN) resonances are mode moderate due mostly to the larger signal-to-noise ratios as compared to the other baryon resonances. The figures and the table of resonance cross sections show that the slow system invariant masses are rich with many resonances being produced. the TI + The largest signals are for the 6 ++ and 6 resonances. In data, about one half of the channel cross section is invested in the 6++ production while in the TI data the 6 about 35% of the channel cross section. 0 ++ only accounts for The 6++ in the TI+ data can be + produced in conjunction with a fast pf or pf while in the TI a pf can be made. data only The question of associated fast and slow resonance production will be considered in more detail in the next section . For now we will make the observation that the occurrence of a fast resonance in the lC channels enhances the likelihood of a resonance in the slow system. The data. 0 n 0 and w production is also a very striking aspect of our This is due to the narrowness of the peaks (widths due to our -135resolution) and the small backgrounds under these peaks. chapter will discuss the The next n° and w0 production in more detail. There 0 we will also present evidence for a resonance which decays into w p. 0 The N(l790) listed in Table V.10 and seen in Fig. V.7k in the TI+TI-TI p 0 invariant mass is consistent with being entirely due to the w p resonance. The TI +TI +TI - n invariant mass (Fig. v.8h) also shows a small peak of about equal strength in both the TI + and TI data. The peak is at about 1700 MeV and was fit with a mass of that value and a width of 150 MeV. As will be seen in a later section, this peak appears to be entirely a + - 6 - decay. TI TI Evidence not presented in this thesis seems to indicate that the decay scheme being observed is: N(l700) ~ TI +N(l470) L (9) TI+6- L TI n This appears to be a new decay mode of a well known resonance. exact identification is unclear and awaits further work. The In particular studies of the angular distributions of the decay should allow us to select the correct identification among the candidates: N(l688)F N(l700)s 11 , and N(l700)D 13 [Particle Data Group 1978). 15 , + t:,. 2731±699 627±230 6.(1890)-+1[ +1T 0 p N(l790)-+n 1T Tr p -+n TI 1T + - 0 3089±199 + - 0 W n -+Tr n n 0 3938±540 200±31 0 + - 0 TI 0 p +rr - 5177±572 p +-+1[ +1T 0 0 2191±548 p + -+n 1T N(14 70) -+ir p 0 0 2.3±0.8% 10.0±2.6% 11.3±0.7% 0.7±0.1% 14.4±2.0% 18.9±2.1 8.0±2.0% 4).6±2.7% 151±738 N(14 70)-+·rr P 'V 12.6±1.4% 3454±373 -+'[[ 0 t:,. +·1r p 4.1±1.4% 46.7±1 . 8% Channel fraction 1127±381 12775±468 Weight-sum p 0 ++-+n +p t:,. Resonance _ _ _ _ _ _._Iff +·rr +TT - 1T 0 p 7.9±2.9 34.4±8.9 38.9±3.1 2.52±0.41 49.6±7.2 65.2±7.8 27.6±7.0 ~1.9±9.3 43.5±5.1 14.2±4.8 160.9±9.3 o (ub) - +TI - TI 0 p 0 0 494±199 'V 2518±192 91±23 3217±535 1976±597 2428±604 165 ±576 'V 2291±302 4143±343 6709±343 Weight-sum 2.6±1.0% 13.0±1.0% 0.5±0 .1% 16.7±2.8% 10.2±3.1% 12.6±3.1% q).9±3.0% 11.9±1.6% 21.5±1.8% 34.7±1.9% Channel fraction _ _ _ _ _ _ _1T_f1T Estimated slow system resonance production Tab le V.10 7.2±2.9 36.7±3.4 1. 33±0. 35 46.9±8.2 28.8±8.8 35.4±9.0 Q.4±8.4 33.4±4.7 60.4±5.9 97.8±7.1 o (ub) I I Cl\ w f--'" 938±400 4030±392 + n - +·Jr - n t:i + + - N(1700) -+ir TI TI n 385 ±77 '\, 0 + - N(1688 )+ rr ·rr n 3653±700 784±161 + -+ir TI + N(l470) -+1r 1r n 0 638±408 N(l688)-+TI +n p 1438±777 + N(l470) -+TI n +Jr + Weight-sum t:i Resonance Weight-sum 3.4±0.7% 6 .8±1.4% 31.9±6.1% 5.6±3.6% 12.5±6.8% 35.1±3.5% 8.2±3.5% 5.0±1.0 10.2±2.2 47.5±9.3 8.3±5.3 18.7±10.1 52.4 ±3.9 12.2±5.2 4.7±1.6% 3.7±0.8% 392±88 3.8±1.4% 26.4±6.6% 25.6±3.0% 31.0±3.3% 494±169 398±149 2795±695 '\, 0 '\, 0 2707±311 3281±344 Channel fraction ~µb) Channel fraction a - + + lffTI TI TI n + + + TifTI TI TI n Table V.10 (cont.) 5. 8±1. 3 7.3±2.5 5.9±4.2 41. 4±10. 5 40.1±5.1 48.6±5.7 a (µb) "I ~ w -138- 7r+p~rrtrr+rr-1T 0 p a 1T-p~7r£rr+rr-rr 0 p <> fits fits Prob(XEt)~5% 2 2 -t1r1T{f) < 0.6 GeV / c ( rr+ 1T-7Top) mass < 3.7 GeV Figures V. 7a-k Invariant mass distributions for the slow particles (other than the ± rrf) of the rr 0 channel. The distributions are given as da/dm and include curves from the resonance fits described in the text. 15 '- 'U b "d ......, 1.0 0 5 E 10 3 ,.n' ......,, N 0 ~ q) ~ .....-.20 25 0: vf:' I : I II ' I' :: ~'· I I ; ~. !/1} . 1.5 ++ . (GcV) The curves are fits to the ~ . Figure V.7a n+p rnass 2.0 rr±p 0 rrfrr+rr-rrop 2.5 a 1ft o 7rr .j.. (a) 3.0 I ....., '°I w 0 "O ' , b .. 'U El ~ ',.n' .,, N 15 ....___~ 1.5 0 The curves are fits to the A • Figure V.7b - 7T-p rnass {GcV) rr ±:p-,. rr f=TI +rr- -1Top a 1rt <> 1ft + (b) I t-' I 0 .j::-. / -141- r--r~r--....,....--,--..,....--,.--..,---.---..---...--.---...---.---.---~ Cf:) I o/ ol t:: r I ~ ;... I ~ r ..c: w (J !/') 0 .~ l Vi ;Ij C-1 ~~~ r-1 ~ """' i-f t- QJ t.:J ...__,. +~- L .,.._ +<J C) 0 ~ i.- 'I- ~ r--. > 0 w (/) w QJ ·ri lo-; '"-"' :l bi) -.-1 µ.., QJ ;.. C1:l (/) QJ > H :l (J Cl) ..c: r r I tQ t in ~ WU '.D p .. I b 'U ·- •' tf· ' I. If · I fl I • '\ t i '\ I v ' "' I 1'j'.}, • . ' ,f " 0 . ( GcV) .&..-.-. ' o' ', The curves are fits to the p Figure V.7d 7T+TI-- 1nass 1.0 ..____~_L ' f' I • , . I . {. 1ft a 7rr (> (d) u 1.5 2.0 ~"-"',i''ffl'47r~"!f.'T' •' .1, ·,h.fi't> ~~if# hHI,-\11-r li...'I o.;j ., 1 ' "" ut • 1," ! l • ', r./J. ' .. •.. !I ,ti~. _,:'lat,J_.l(i, lt '•"t·~"t. • ! '· ...·• "•..t I . I {\ ' • ..... :• '·, ' I .J :•: :• :i.!•., ~I ~ " .,, I' •'' ' I : : ,~~·-U~ {l\t1 , .. Tii"' :•lr '.'· 1;1~11 ·1 •• : 1• ~ • 'J !,.°I )I'· • • "«'1:1 ·I.I , I {,• , • '1' • I "'ri ' j t •• ., ' ll...~ t . r! 1 .-· l I 'tl~ . ..tl. .! flI lJ(~·i'j]\f ·.' {ift· ~/·1 \J l.i 11 I f.i~ I: I Jt] --...,-----r --·...,---....,-~- -·~-------- -,-- - --,----,.----.----,.--- --.--- - 0 L - L-- - ..1----'l..l.---..L 0.5 0.0 s ~d 5 3 ,1) (\J '· 0 ::?. 10 ~ .....,_ t. . . 15 1r:!:p- >1rtrr+1( ·1r 0 p I I N +:-- !--" 'U b •• 0.0 . i . f • l 0.5 ..... . I ' • \._ 1f+rr I! • . • i.J •'I : · ) ; I I I f , , fl t' ... .J'. '... t llltt.SS 1.0 + (GeV) , • i.l' W , I b 1 T· • M>. /. " 1.5 , v • I I 1 I I .! !'{ l;J.1 A.t..O;;. Q TLJ ·, ,y;_"~b ,_~1 +- 7Tr o 7rr <;- (e) <J 131_~ t 'l{I;! ¥U-u·o, LI+ I ):' ..I?.I I.!.., I I Ll &JJl01 ...-., ~-· • .:> 1 I UL'. ,. •. t t II ..... y-•, '( ll>I b 1 • - ~ -> v I ~·1t•ta'. I•; ,,. ;, m.·11 I Figure V.7e 0 i .- r -----..,.--..,.----,- _.___....L _ _ _.___ ____ _.__.-------L-..._._, J o ' 'r"~· l.1, I a •'::~·~o: 1· , :··::.1f\ 4 _ _ ._..£...--__-1--.. _ : The curves are fits to the p . _..1.. _ t ... • ,"l.,r"tt"' c i. • v'f • .. ·f· t l ftI ._•-. '• \ • f t I I • I I .,"' t I t I I .t ., t .;; ·.\ r ~ • .J1~ r1'.t' ' t I t • • l :·.' :~,:·':: \~ • ,.fl! "I I It I I l t • .,j t""Jt u.l I I f: t ~ I :~. :;:1 .. , I. Q L __,,__ __..___ii..____,__ __...L___ 8 td 5 ._ 3 ,n ! l •.'J v/11'": •1 • •.f.•i Ji 1' ! Ir· 1~m vt_ ~1r(f :·rt·" W'~ I~ 1 10 1, 1l.1fr !i: 1. --·,.-- --, - - ·r --···--.,..-·-.---r- --- r -.. ---·-,---- ·--r - - ---, --- --, - --- -,--.....,-·-- ..(\) a '-~,;S ...... '1) ,,,--... ~ 15 1(Lp-·>-1rt11··l·n--··-rr 0 p I w I p. t-' "U b _ ...~ e 3 ..0 '- (\J 0 0.0 0 . ,.,.• 10 ·- ""';f ~ ~ ~ 15 ____.___ ' - {) L-- - - --1- v - ---r·- -.--- I 0 .n..- I 1 1(·1r rno.ss (GeV) 1.0 Figure V.7f 0 L _ , -- ----.----...----.,....- I - ___ __._ - - -- ----'-----.-L-~ I ·rr:!;p -~ rrj:n+ 1f-·-rr0p ---.- ---,---.--·-- The curves are fits to the p • ---,.-I a n'r ... o 7rr I ..... I ~ ~ 0 ' P\j E ..(\} - I I "': " p· "' If·: vb •. ,1 " 1..J ' .1,",,1:' .,·f 1 +'.i·•:.·b1 ',I • • tfi .. i . -,·- 11 • l a 1fr " -rr, -4- (g) -...,.-- 2.0·s mm;. • . .. ~. (GeV) . -· ? 5 : : • . : : : 6: o: ) : • :: · ' :; b.: i 3.0 " : .'1 ' 1.:, :' (,: '' t "'• "'• ..'·•''• •o.,: •'.I ••:•t• , •·'. a . .b • 'J. . i :r '. . . ' .. " "" .• • ' .. • • • ..... " .. (,• . , !il,·'.i'' "1U1":f1'fa rr.ri\f• t,i1ir11l11tl"t1 "' ' • ' .. ,., " LI ..:111t· ., ::;": Figure V.7g rr•1r·p !' !rJ r r~1: t ~f!-:h «:':i 1flt 1 t1~ 1 :tt ! i H 1 f ! 1 I ····· T -· · -- -T-- · - ·- -,···· - ···- . -·- - · ·-, - · -· -r- ·---r- i ti.t.a1ttt1rt11r1lutt 1l µtt 11 1 Hf.11 1l1nL!.t 1 . J,J :1r )Jr,u 1i r1 1.1. i. . 8 r-··· ·····,...--·--.·- · ·- ·· r···--·- , - ·-· 1 - -· - · 1r±p-->1Ti :1f ·l·1r--·-1r 0 p I I Vl .p- I-' -146- ,,....._ 0 ,,--..... '"""' .. \!.) O'\ co .-4 '-' ,, .... + i.....; ....._, 'J"J vi '° ....... Cl 0 ......... ·" ..... + t\-< <J .c !"-. :> Cl.I .c w 0 w Cl.I ,._. w ;::! -rl bO "--! ·.-i µ., (1j .,., (/J Cl.I > ,._. ;::! (.) Cl.I .c E-< ~ C\~TI oz/qrl) C\2 urp '.op ' -14 7- ,,.-...., > <l) µ ::i .,..,t.D 0 0.. µ. I tj4 02/qrl) N mp/.op t== ~ 0 'U b '"---. "O El 310 ·- ' ·....___ N 20 1 I I 11 ' ' & ' ' '%i ii,' Figure V. 7j t •.,,j'. l'• ' ' ' " 'Q n° and w0 • Q. 2.0 • • ·- y. a 7rr - <> 7rr . n + . (j) O"f.•'r.11.W,t:r.1A·,t.u• ,~t~~~J.. fi'il?'f.'1\' . . 1.0 1.5 n+rr--rro mass {GeV) ' ' The curves are fits to the ~~ 11 0.5 1 ~ ' ·~·~':t;i I t ·.~ ! JlJ.J\~~ ·a~·:t a:~· . +~~~i!ut tt ~J .!Jfu..\ ; f:k1T1lj'l't• h1~11: t ' ll: rr I :!t\11~ I~ ~· rr±p4rrfn+rr-rr0 p I ():) +-- I ~ I 'O Q1 1.0 • b2 "'.. 3 8 'd .04 "'.. ro 0 ~ >5 Q.) ,--.. B 1 • 1.5 ·~r·,--- J I ' t 2.0 1 1 : • I , n. : '. • • , • •'I 9 ,Q rnass , • Figure V.7k TI+rr-rr0 p .. 1 I ~III I •· ~;.. I: ! {1 0 I I • • !·•ti tr~•·.1' ' 19)f • ;.. ! I pi , , • I • ' I I •! (GcV) 2.5 1 • I I •• , I "• ... , I l I , l 1•• I ' • UI '!I I I ~1. 0• • l . •• ' I , I ' I 3.0 l : • • • t I I o 7rr <> 1fr .... (k) I ~ I I II I: I I • I I I I ! J_ U : : '6'' I I I t I I I 3.5 t I ••• : l.1. .'i't . .. l lI u .!_ O u ' '' : l i:I : 111 ··t tt :o '• • •''' l t l l l I l IjI:I 1 I 1 11 . The curves are fits to the N+(l790). , hi ~ ' I i.J'' n' .~I ! . ' .L 1 11 rr±p~rrtrr+rr-n°p I \.0 I ..... .p. -150- ~ 7T+p~ntrr+7r+rr-n a n-p~rr£rr+n+rr-n 1T-r' fits fits Figures V.Sa -h Invariant mass distributions for the slow particles (other than the n~) of then channel. single rr + For those da/dm distributions in which only a appears in the invariant mass, each event appears twice in the distribution. -151- -6>- -~- -~J1 ·-R>- ··£o:_·~· LD -¢- • -...n-o.-. .;!)--~ ..-1 -¢--0-~ -~- ---')---~ ~= --.. -~-...:;.,s- > --m:-.....LJ .... ---a.-.-<'>-·-"-· ~·-- - -~ I' C) ~ ...._.., -=~- ~ --~4'- -~--a ---o~-- ~::: -- ·--¢- ~-:J ~o--- 0 -o- --~· --...:J--- t::: ····O--<-·- =;,-.-. + t:;: ---· 0 - - - 0 - ~ - -- -. - ----::::! - - ¢ . - -<>----e ···- ---a--- ---.O -··- ...:...-¢- ····C-··--<>····-0 ..... --¢·····Cl··:::-~--~ ···----t:--<>· -C··--<>·· · ·Ci •••• -~- ····-0 ----· 0 --<>-9--· ~ ---.::tS-~'!I>. - ----a-~- ---~ ~- J j tO ~ > ~ ,.., ~ + ~~::: ~- cO "'"4 -¢- .-:::-~:..~- cu co R -. -a~.:=w· -- --· - -0 · · -- ·--g~ v.: C\'2 02/qri) mp/.op ::l Oil -M µ.. ,, 9 ·- '-... b 'U ..... ~o El 0.0 0 I 3 3.n 6 ·- "-,, N 0 :JJ ...Cl) .....> .,,..._, 12 I I lit I I 0.5 I I 7T+7f- I I I I 1.0 mass (GcV) I I I . The curves are fits to the p Figure V.8b 0 • a 1rr ~ 1rt +. (b) 2.0 v,·nut10J-~:.G@t\'1}j':"g~{io I 1.5 (each event appears l'vrice) I rr±p 4 7rfrr+rr+rr-n I I I-' Vt N '{j b p -->1r{:1T·:-1T -1-rr ·· ·:r1 I ' The TI ' ii., . . .J (• ,' t _j,_ _ _ - -1 --- - • ~'\. I 11 l\~ ' i ' l t ~- , I .. . I I curve is a fit to ,. • ' .+ I I \,1' I ~ ! .<I.· ,' ~· 4 , ' 1 ' I .... . • 1 <.· •l , II '' ! • uppca.r:~ Lvdcc) l :V ~·v • "• 1 · ~ ~- ti t. c t the~+; the TI+ curve is a fit to the~+. N+(l470), and N+(l688). Figure V.8c (each eYcnt · ti..:·t") 1-r ·•..,,.-w..! .,:i' ',• u ,, _. , ,!,, ,. ltf 4 '·'-l _h'·' :• o & "1,'. v. -~1-1~:-!..l;:i1 \1•,.~ i; ;. 1' ! ' ' , I 1 , Y, ., , I f4;.;_~J, t J.'C( ,;. 1 ,• ~- ! .'lu:' (: t~ ..'. !.'· 1. I '1 '•' I <.,·'.J .. \·,. • . u Tir <> 11 t .+ (c) --~-- --· _.____ _L ____ ...__ _ -· ' - ---1--- - ~~-:_.L_"~~hS·'-''1v"\t:''bt-i?\.,'-1til\J~\.~:v_ 2.0 2.5 3.0 • I rr i· n tn ass ( Gc 1/ ) ) I :S· ·{"' ' tH. ! tl.111 J ,v ; .I ..I,:r.t·~I t,·. •• I • ~ ..~. , 1 ·~ 1 t·1 ·!fi i.'· ,) ''~ 'I t·' • •, ... L _ __ ._ ___ ··· ' -·-- • 1.5 I ' ' (? t I ! 1. l !'fl;~Tit : ,!. ~·I ll j •/' \~ :1~1·· l : • I . l. ' ' v 0 L j~ .__H _..__ _ : I J J I J ' ' "; I ,' ~' .•' ., .','f : I ·J : '1: . !:'.+; ; , : i • ' ~ 11:'1_\;:, : fi1 1·: Jl· . ~.1 ~ . u·." I . I I I "I ' l I-.·'· 1~-'·1 •' 1I(', · ·"l·'· T~"· ' r· .l ,· 1' ·1· '1 I]";I.f~ ..'''·.-,J ·-·- -.--·---r---· -- ·- .--- -·· ·-, - ·- .-- -·-r·--·-··--:·--···- . ------.- ----,..-·--·---.,---- -·-.-·--r--.-------,.---r-----r- 1.0 ·u ~ a .n :t ,_:; N C1 ~ · 10 '-J \1) .... ....... ,,--....... 15 1r:!: l w I I-' Vt -154- ,,,.-... > -~ ~-~ -~ I ..0.. ii ~ . !;/) 0 er. N d 8 ,... ...... ~ ' I -··~- .l.J ~ "'d . co :> <l) .l.J UJ .l.J ·r-1 4-< ~ ::l 00 <ll -,-l C1l ""' ~ (/) <ll > ~ ::l CJ -0- Q) --¢.-- . - · - - -c.g~- ...c: - *'- fc-f lO ~ . . __ _..___ _-'-~....._---'-_ __.__ _-..1._ __ ._ _- - ' - - - - ' - - - - - l o o~ (A 9 ?1 02/ q'Tf) mp/.Dp ...c: 0 ~- ...... <l) t,'j '-"" ~ ·- -i~ <J <:.) ..._.,-. - ~;."!;;..--¢---~- I -155- r--~"T"""-i---,.-,--~"T""""""T"--r--,..--.-...,-_,..--,,....,..,~,,...,.,,..,.,.,..=s,.....,..,~~ t>< ~ M ---0--· --·::9.:04- ----<>-- ·----c ·-·-· o %::..:: -----12 -¢- - ~ ·-----0------ ---<>~ --o--· ---a.-~-- --0-~~ El ~ -- ------i!I ---::~ -- a -:i !>--- ·~- . LO ----------<.>--<>--.:r- - -- ·:::~ - - 0 - - - - ----0--------0 ---~ ----o---:::3 ---- -- -0 - .. $' ---- -a ---~-- Ei ~ 0 ~-- (.!j .._,, ---- ~:i- -- o~--¢-- :J ~ - ------- c~ ----CJ---- ---o·---· ------0 -···-~~ ••• 0 N .,:, a ··::: ~-.~~ -----= ~-------o ---··· ---<>- . ...... ---:&~ --~ ---~.Q...._. --i.i-:l ~- + ~ + .., -----a----¢ ~-- ~ .. · -~-;3. ---o- ----c---~ ;··if·:.-· - ¢ = ti ----(>- -¢-o."ci;:: --•c-==-<>• · -cl· --<>- ~~·....1'"'1- <,i.- ~ I -~~I ..;g.. i -~M t'l") __...__.__..__...__.__..________..___~c:> oc:/qrl) N ~ ....... ..... ____ --~t----~ -- .._...._....__.__...._...._...._~_..__.. Vl ill ~ ...-4 mp/.op 0..-i al CX) > ...::::!al .,.,eo µ.. -1.5 2.5 Figure V.Sf rr+rr-n mass (GcV) (each oven t appcH:1 rs twice) 2.0 " 7rr a TI"r 3.0 ... (f) ~.-r-T--r--r--r--r--r---,---r-- rr:l:p-nrfrr+rr+rr--n Then+ curve is a fit to the N°(1470); then- curve is a fit to the N°(1470) and N°(1688), 0 1. 0 b'2 '"d ' -- pd f:1 i4·- " (\} 0 ~~ ;, 6 Q) ,-.... a I I-' °'I IJ1 -157- L,.. __ 0 L_..J.,.......__.j._.__ __ 1.0 "d 1 '\J ' , ..... b 3 afW? ..0 '· . 03 (\} ;~ Cl) ~ ,-...4· 1.5 -L..u;,. ' ~,{! \ ' j' , ' ~~ '. l . 1 " f' • L I 1 I ~: fj l I _.J- .., I t It 1 I I •• 1 t I I ---r--r • • •• ' I - • t I : t The curves are fits to the N+(l700). Figure V.8h 2.0 2.5 n··rrr+rr-n nu1ss (GcV) I I I" i::: :: : Q1 t : t : : I 1 *t I t t IJ I iL ! I I 6 n-, . -. t; ... ~ 1ft I I I : 3.0 ---L~-l _ ____._ : I LJ : • (11) .,. 3.5 • 11;1 t: l ~!~.: fnr· ·~-'' . . }t'H1· It ·~·ri: 11 : 1·? r : :ti•1: 11 l • f , [il . ' ··~ -...l---1--....!..-----L--. 1---- - .t..-.....L.- --1----- L----4---J.......- &. J. i.j ' j . I·~; ,~,f' ' : .q·'lt, .;• 1:11!1 · ·> ~··~~ , 1 , i ~~ '*~t f'i a._· ~Ti~•Jf.P': .:un•,1·:.1rh - y11 r t~ f )_" f t I IJl :·:rt ttbl tttl1!ll,!': .: i: I I dt 1 .il1U_ .:: 11.11~.:.: . .I· I • "r~·! L,· ;.~,·;:V.•I ;,,·! ·. . ·ti : ll+l t h, . I ~ •1 : I , 5 r --r--,--..·--·-i--·- r-·--r----, - --r-· · --·-,-----r--·.,...-- , --·-,-- -- r-----·T--r 1r±p-;.rrtrr+rr-1·rr-·n I I-' VI 00 I -1596. Associated Fast Meson and Slow System Resonance Production We have investigated the associated production of a fast meson resonance (p(770), f 0 (1270), or g(l680)) and a slow system resonance (usually 6(1232) or a slow p(770)). This associated production was found by examining scatterplots of two invariant masses where each event was a single dot. The associated production showed up as the overlap of the two bands (enhanced concentrations of events) of two resonances. We did not use the scatterplots to estimate ated resonance production. the associ- Instead we used the projected plots of the distribution in a single invariant mass primarily due to their ease of interpretation. These plots were made by selecting events in either a slow resonance (6 or p) or a fast p with a mass cut about the resonance peak. The same scheme was used to generate the plots in Figs. V.6 discussed in section 4 of this chapter. This procedure has the difficulty of dealing with events coming from the background under the resonance peak within the defining cut. As can be seen from Tables V.9 and V.11, 30% to 80% of the events within the defining cuts come from the contributions of these backgrounds. As will be seen in the plots, non-physical peaks are observed in some of those cases in which one of the particles forming the invariant mass upon which the defining cut is made also appears in the invariant mass being plotted (Fig. V.13a for example). The slow system invariant masses for cuts requiring fast p mesons are given in Figs. V.9a-g for the rr 0 channel with the p~ cut, in Figs. -160V.lOa-f for then channel with the p~ cut, and in Figs. V.lla-d for the n° channel again but now for the p~ cuts. We have fitted the resonance peaks in these distributions and listed the resulting estimates for their production in Table V.12 in terms of the weight-sums. Table V.12 also gives the fraction of the uncut resonance production (see Table V.10) contained within the cut (see "Resonance fraction" column). The column labeled "Fraction of cut events" in Table V.12 is the fraction of the events within the cut (see Table V.9) which were found to be in the fitted resonance. It is unknown how many o f the events in the fitted resonance are actually part of the resonance the cut selects rather than being events from the b a ckground under the resonance peak within the cut. The data may also be presented in the o bv erse manner b y cuttin g on the slow system masses and plotting the fast invariant masses. 6++ or 6 The cuts were defined by requiring the rr+p mass o r the n -n mass to be less than 1.36 GeV. The ratio of the total 6 signal to that portion below 1.36 GeV is 1.55. Similarly, the slow p cuts were defined by requiring the rrrr mass to be bet ween 0.64 and 0.84 GeV which gave a total resonance signal to in-cut signal ratio of 2.01. Table V.11 lists the fraction of events within the defining cuts that are due to the backgr o unds under the slow resonances. Table V. 11 also gives the total weight-sum of the events within each cut. -161Table V.11 Background fractions and total events within slow 6 and p cuts Total weight-sum within cut Cut on resonance Fraction of events in cut from background - + - 0 p 2!.f+7T +1T - 7T 0 p ~Tr 13251±234 8622±181 31.4±1.3% 44. 2±1. 7% p -+'IT TI 6526±179 4395±145 82.8±2.1% 71.6±2.4% + +7T 0 6907±178 4382±140 62.3±2.7% 77.3±2.7% 6438±167 4745±147 69.2±2.0% 66.7±2.4% 6 ++-+'IT +p + - 0 p -+'IT - p -+'IT 1T 0 + + - 0 ~Tr 1T 1T p + + + - 6 -+'IT 0 P -+-rr - + - ~Tr 7T 0 7T - + + - + + + - 1T TI p - + + - 2!.f" iT rr n 2!.f" " rr n n 5003±136 4948±140 40.3±2.1% 63.3±2.7% +Tr - 5207±153 5025±156 69.7±2.8% 75.5±2.9% 2'._f 7T 7T TI n ~iT The fast invariant mass distributions cut on the 6++ or 6 given in Figs. V.12a-j, those for the slow p 0 cuts (n + in Figs. V.13a-£, and those for the slow p- cuts (rr Figs. V.14a-n. 0 0 iT 11 n are and n channels) channel only) in The fit results providing estimates for the observed resonances are listed in Table V.13. This table is organized in a fashion similar to Table V.12 (see discussion above) except that the uncut resonance estimates are in Tables V.6 and V.7 and the total cut weight-sums are in Table V.11 Comparing the numbers in Tables V.12 and V.13, the effects of the uncertainty in the estimation of the resonance signal due to the background events within the defining cuts can be seen as a disagreement in the results found by the two obverse methods. As an example con- sider the results for the p~6++rro final state in the rr+ data (corrected -1620 for the resonance cuts): by cutting on the pf we have 5634±430 events while the 6-++ cut gives 4242±421 events for the same process. This discrepancy may be due to the background event s as they contribute 0 about 5 0% of the events in the pf cut and about 30% of the events in the 6 -++ cut. An unknown fraction of these background events under the peaks in the cuts then contribute to the resonance peaks observed in the cut invariant mass distrib u tions. Because of this difficulty, we present no estimates for resonance production in a diffractively produced slow system in analogy to our earlier estimation of the total channel cross section for diffractive production of the slow system (see Table V.8 in section 3 of this chapte r ). The difficulties discussed above do not change the conclusio n that there is substantial associated fast meson and slow system (either baryon o r meson) resonance production. For instance, a large fraction of the 6-++ signal appears to be produced along with a fast p (either neutral o r charged). the data. Similarly there are large ppN signals present in However, the quasi - 2-body processes seem not to be as prev- alent in the data as the quasi - 3-body processes such as prr6 or ppN . o-++ In section 3 we discussed the observation of the w 6 states in the rr + data. o -++. and n 6 final Tables V.12 and V.13 show evidence for the reactio n s: + rr p and: (lla) -163- 'IT (llb) p 0 0 2 3 There also appears to be some weak evidence for the A 6++ and A 6++ + final states in the 'IT data. + 0 6 (1890)-+TI 1T p f - + - - 0 p +1r TI 0 1205±309 799±288 2164±350 p++TI +'IT 0 ± :F 0 p ->-n 'IT f f f -~IT 688±163 - 6 -+1r p 0 3456±250 6++·rrr +p P +TI n - ± ± 0 pf +Tr f Tf ± ± 0 pf+1rf1r ± :i: p0 TI f f ± =F 0 p f-+1r f TI ± ± 0 p +Tf 'll 0 6 +11 p 378±274 6++Tf 0 p 0 ± =f pf +1r f TI 0 ± =i= pf+1Tf1f 3859±375 Weight-sum 6+++Tl +p Resonance 0 ± =i= pf+nfrr Cut on 44.1±16.0% 36.5±16.0% 41.8 ±8.2% 19.9±5.2% 27.1±2.2% 33.5±26.8% 30.2±3.1% 13.1±3.4% 11.4±4.1% 23.6±3.9% 9.8±2.3% 49.2±3.8% 4.1±3.0% 4 2 .1±4. 2% 605±219 24.9±10.9% 35.4±10.2% 10.5±7.1% 241±159 1139±26 7 26.3±2.8% 22.5±9.0% 1767±163 515±195 617±205 lti.9±5.1% Resonance fraction Weight-sum Resonance fraction Fraction of cut events - + - 0 0 TI f 'lf 1T 'IT p + + - 7ffTI lf Tf p Estimated slow szstem resonance eroduction for the fast p cuts Table V.12 15.8±5.8% 21. 5±5 .1% 6.3±4.2% 46.2±4.6% 9.7±3.7% 11. 7±3.9% Fraction of cut events I ,j:-- Q'\ I I-' , N(l688)-+TI +TI - n ± =i= 0 +'If - p - t-1r ± =f pf-+TifTI pf -+TI f TI 0 t:, ->-'Jr n t:, -+n n + + Resonance o pf-+nfTI o ± =f p -+"/f TI f f o ± =f Cut on 639±221 Weight-sum 68.1±37.4% 17.2±6.0% 320±180 1615±444 1130±211 64.8±42.7% 57.8±21.4% 41.7±9.2% Resonance fraction Weight-sum Resonance fraction Fraction of cut events ________ TI -f 'IT +TI +'If - n ________ ·ff f lf + +TI +'If - n Table V.12 (cont.) 6.3±3.6% 31.9±8.8% 22.3±4.2% Fraction of cut events Ln °'I I I-' -166- <> rr+p-)op~1T+1Top ,oY-)>1frrr- o 0 - 0 rr - P-)>PfTr 1i P Pf~7Trrr · 0 - .l- n+ fits ·------· 1T fits Pro b(xiit)z5% 1r2 I 2 - t trn{ f) < 0 . 6 Ge v I c (7r+-rr-7T 0 p) mass < 3.7 GeV .c· . .t • Pf0 -?"JTfrr-r-- d e11n1 t..l on: s: rr=frr=F mass < 1.0 Ge\T .J... 0.6 .... Figures V.9a-g Invariant mass distributions for the slow particles of the rr for events in the fast o 0 peak (see above). 0 channel ~t:4 -100 ~- ~200 ~ V: IE ' '11 I ' 1 .• .J L 'ii, J . . ••' : L • , . . 1 •:. •,. ' (J• [- l•U L.• ' l '• • _ L _ __ • -- L - · • Figure V.9a • '• o , The curve is a fit to the 6 • • ··. . • "'v' ++ . n· ts ~ Lrr-.: . m!~~ (Ge v) • •1, j , • ' 10 , . . . i I o 1fr <> 1fr + - (a) o - -· t!1 I • ~ i,._f . ~+· lff'*Jfrt~j " > 7 f . ' · ; ' ( t " f ~ Wt~~~_1~Q~~3 0 u1~ •1J ~· ' - ~ ~--~- · 2 5 I ---,---~ - --,- - ---,-- Pro ->rrf=TI:r= l! I I I I : ! " y1 L;,t_il dt Lt 1 !J•1 •:• . : J •, 1' :t, . l'i.o£'J '! •'\'\" tt.t,• ·•,.. -t.·,,/'j'J,\[;'_ . 1 t# t ~'Ii)! i;il,~, (!J~J~lrj' t [ ii;. ! 1}: ": ;,j': Ll; • t! 0 f :J,:, lf:k. I~ 1 / c1 (/) +..) II \ ~ ~ ~300 0 500 600 1T=l:p ->pprr±rrop ---,.---.-·-·----r------.--....---.--------.·-- --,- ·---r--·---,-- ----.- ---- ,-·-- r - I f--' I a..._. 0 ~ 100 ~ ci .,., '· C/l~ (\} 300 .. .~l: j :•f . •• ._ L_. __ ': ' • 1 ': ' vi ·~1 1 1 111 11 ~·~ I v I • ~·.~ ' . o 1fr ... <> 1fr • • I ..... 0 The curve is a f i.t to the t:. • I.' • • • • • L'---~· ~s ••• Figure V.9b 5 - -~-~ -~ • •• " .. .. • 11 '' -1; f. 'r·r . ,,,'I ' I ro I; I . . : .. ·: -: "• ·r:-"'''" '·· .. : ' I :•. J. 1,t,1• "' • • <r1•• <'•••": •: ;,,: 'd : ::..'.\\; i•;•:; •• ,c,9,..,','••. •"'t• ! •I• .:_,..__ '1," • • I //"'"'' • : • : • : ,., "• " • n . •I·; 'i>' :\• n; .,, s___=.L 3•Q • : <'i : " --2.n __,--2• 0 (Ge\') _J.._1___j_ .. • 7T p ma • • •H:•'1 • .<" 1 r r,:~-:~'~li,: u..r: t. ·;·'l"!. tf:r~ 111n t1 f 111 fl1 _ 4 - - , _ _ J ____ 1.rr'I: i I ---.--·-- 1f:f=p-).pPrr±rrOp Pro--> rrt1T=t= ---,----.-----r I ,1 d,1.l!rl till .. I - r· 00 °' I I I-' -169~...,....,_,....,..........,.....,__.........,_,.....,........,.._,_,,___........,_,,....,.....,_.,._,_...........,.........,_.....,.....,_.-.-.......... ~ ~ +<:I GJ .c .j...J 0 (.) . .j...J O'\ > Cl) .j...J -,.-! GJ ....... ::l 00 GJ ,.... .,..; i:... ,.... t1i Cl) GJ > ,.... ::l (.) GJ ..c t-< 0 0 C\l 02/s1u~A3: 0 0 ...... -170- 1 ' t t' i -.- f f ' I I '> i r ' I r r _., _ ___ .., ___ _,, _ _ ·-···· + a. ., =-· .-:- .-Q: :t. -;..-.,__ ~~ ,. r .J ~- ~ : - - ':-·· -.~;:~~:~·· - 0 'li . - ·-:~--_,...._, .....-~-: .... ":fl ~ ··'-' ·- - --1 -~, --,_ ~..:.----=~: __ _______ .. .:::·.:: ::::::::::::::..,. ,c :=--- ---·, _ __ ,___ ....: .::· --- ..., - -......- ____ _ -.... -· ---·., -_, --·- -·- ------·-, ---- -· ~ ...---......__ ...,__ r 0 ~-- 0 ;. ~: ~ .::::::_:-:·_:_:_~~;::;:~::-- - ,.... ·,-~--- : ---· --- '.>---=-~,---~::-~:::-_:::-=·-- --~-=-'-,>----- --:; : •--· - - --"'-.........~--· :··--· ---··::St··· -~ ·--· j _.., -- '--7=-.,2::~ '" I i I· I r 0 0 0 "Y' • .I 0 0 0 ':'\] C2 . t:o ---', ' .~,.. s~ ·- "-= ; -' ' ,., ~· .µ · ~ ~r..1 •...... ~ ~ ~.) C/l 0.0 1 lII lJ: ,', : : :v : ·lo'\! I : t C t } 1 \ j• f1 _! 1'1 I o : : ~a· .:1 f ; .l ,' : , I• t •·"" : ..., : f I ,u • t :'.J,-f,~-- : .; ·;~'1 •~ : .~.l'rl:Il :,. ' i : I:: : p fo _>rrl:n=t: • t • 1 L. - • ' I I • • I • , I 0.5 Figure V.9e llHtS S 1.0 t • t ' •. . (Ge\~) ' ' .. The curve is a fit to the p . 1('1r 0 ' ! , , : •• 1:i · __.1.....___ _ __ L __ __-L-. - . . .l.- • • . ..•• .L. • . . 4...... _ ..L _ __ _ i _ _ __ • •• t If'f ' I _t v; J ' ,-, __ l I t I 1.5 i. ...., ' "" ' 1::1'.,' '7··1· . ·'· -I vi ·r ! TI . I' ""1 IHI u~i ta}. .. . 11 "-r' • ;. rI,1 '/'·';).,.~J 1I :,i' '.:lj i,;J~,. ~ ~ 1 .1 j I 1.- : J + 'lft a 7rr I> (c) f I 2.0 , • ! . J . Y1:r:~~; .. . 1fl-)rf\.•r.,,. '( wL·~;·i:·-1 . /. .)·~.~1 •tt· ~-l- --~~ -· ;!:...'. ..l.L.-~~M • '(lYU· I I I ··-r- ·- - · - - ··- , - ·-· ·1- ·- ·--, - ·- - - r ··· ··---r ·-- ----..,----T-- - --.----r-- :/;/ii/ '('J:; \ .Jrf ! 1f 1 J I I i/: : . .:"'( '(: ;i.,{tl t. .iJ r If1.f1fl 1: ·v I I ,-- t1 11f i l I l I 1t1fr Hu 1iilf1 lll 1 :!~J· I I !rl HlI ! "1' :. 't':-.' J........ _____ J _ _ •• • 0 L . --- 100 'JOO ... 'N - . .... 0 ~ Q) ... ... ~ ~300 -100 - ··- ---,·- ·----r - . - ,-. - . --,-- ·- ··· ·.,- -- - 1(i:p- >pp1r:±:1r 0 p I-' "I I I-' ' ._:q 0 L____ .l .0 ;,: 100 n G) .+> ti) 0 C\l ...4 .... 4 •· ""~200 • ( f I JI I t d' t , '~} • • 1 • I t ' I • ~· ' f • - • I I 0 UHiSS If l • • : , ·, .~ 7 ' t f '! ' • ~ '\_ j t t ',~:t:: ' 1•• ++ If f t 1 f I : 1 ; It ~ ') ·- "-'. :) : • Ll • • 1.J ::. l •al• ••t t • f ' ~;f: t ' I 11• t I :. t.!;.J "(' I •• ' •'C il ·tt ,1, fl '·• t. t _., 1 t • Lt , 1 :• . . 1f;· n·t 3 .0 ___ J _ __ __ _"--2-----!---- ': ' • '/.i:.tJ ll ttl '• • • : f ] 1'.1 J·:·:• ur·· ,LIJ.:.. '":• :' • (1890). (GcV) the~ Figure V.9f 1r ·1r p 1 ') ,._, .0 I • i ' 1• 1 a ~ (f) ·-·· ·-------.---···- -.···-· ·--,-·- ·--···- ··· ·--.---,--- ---r-- .A--.. __i_ __ -L-- _ ___l.,. ____ ---4-----1- -----L.. f • ·, · ·l • It•• • The curve is a fit to 1.:).. ,i 1 ..i•• f ~- · 1 1 f, ~. ~,, • ' .• .·l· I ,,.~~ : • I' \·.. .v t A........t"'~ ___1l:...:'... .. ..L - .. .. .._ ___ __ .1.._. _ . ........... . - . ....,. • II r· ,i, ,.,.', .: II ·r.. ,.. .' ·, .:·I:::: I..:.t · ~·: . .',:·: : ::: : {,~: l f. •,!.'•: M IY.I • " . . I 111 l 1l rI ldi1 .., ... -· · ·1- ··· --. - lil ·-r··-··· ·· -r · . ·rr=l:p . >p~1r:t: .rr op Pt·o -> rrf=rr=i: - ···- ··- -,..·- · · . ! 11 nr ~i r }H~~,}J.1 i1°: 11t ; 11 it l l11 . ! fl } r1 Id. : i.: hi! J % rrrr~' .f:Jt: fl!\. IiL iit1 i; - iJ-r'r ::·i~:·:"' t! 'l. : :Py !.:~· · i'i:i, Iil1.;tl"'1 ttr·!ll··r· 1.il •• - ·-·-r· . --..- · - - ...- - ····-· L-. . ... . ,300 r ·-· ---. ·- . I I-' I N -..,J -17 3- ......-.. +-1 b.O {:: {:: .._..... Q a -----• ~a -¢ • · '3:.::ci---- ~~ ::~::: ---n----¢==:;;>--_-- -o::<:'.: •--¢.-- _--;;---¢ ---a ---- - ¢ - - .•.• c;. ••• ~ Cl~=- -~ ·--..i:J:--- -o- -<!>--€!-. - •• :~::: ~?-~ < ) - • • • ("!• • • ----~::: ---<>-- -¢--"·-~==e:--- ---o --... ---n ---<>---CJ - - • --¢- --¢----$.~---·..o: --6-- N . ··-0 --- ---6-- ···Cl ••• ---¢>---a--· · - ¢ - - -----c--- ---~ -~ :::&::. --<>---__ ¢ - - ··-0·-· ··0·· --..Q...g. ••••• ~.s! -..-..-..-.::::, ..•. ,......... > (!) ~-~-c-- ---42----- --¢ <)- -- t:) ..._., j~ s .,j.:?. -- ---¢--- --?---:-::~::: · ····Cl-··· --Q-- - 6 - - .. -~C4 • • • VJ t;-· •. --=;~---a - --- Vl ---c--- --0-· ---,':!··· --<)-- -~<>-... a.:.-o ·. . CJ •• --¢- -¢~- - --a··::P··· --Q__.:.:.·-C~--:0 -- 0 -~ J -~-::;;_C: :. -~l -<>-Cl-3~-:i--- --¢.--. --?--3-·· ~:J--· -----0-~- ----c-----1>--o- I I --~~- jt...f) ---a--- :a; 1~ ...;:~- I · -C·· :ti - ~~ --o-~ j I 0 0 0 C"J 0 ~ I i:d C\1 ··-..C·-·· --J.>--?-- 02/ S1trG~\3: ~ I ~ ~ OJ) O'\ > <ll ~ ::l OJ) o,-l i:.:.. -174- ~ 1T+p~pfn+11.+n c n-p~p~TI+rr- n P?-?rrt1Tp?-=>1r"£1r+ rr+ fits ···-···· rr fits Pro b(Xiit)?:5% -trrrr(f) < 0 .6 (7r+7T+rr-n) mass r'I· 0 .o GeV2 / ' c 2 ·< 3.7 Ge\r .c· · +, · Pr0 -"rrf. rr :::· d e11n1 t.1on: rrrrr· mass < 1.0 Ge\ ! ..J... ::: Figures V.lOa-f Invariant mass d i stributions for the slow particles of the n ch annel f or events wit h in t he fa st p 0 pe ak ( see a bove). ~ 100 Q} ~1 1--> ' (fl' 0 C\l ~ 300 : I •I I I I 1 I . , ,o I • u; o .. ... '• : O T- -- t 1 o o •fl uo .... L... O Io I lu• · ! : ~ 0 I ' n -L-- - -· .!.-.. . · •. Figure v . lOa • · ~~ ) - • D h 1 ·o,IY A .. !f,:rlu. : <>fl, 'SI.'. ·'"-"' _'J 1 , • 1,_.t :Y··I f1 •I · I . _!.1.-__ -'--- .. _J__ - · -"'----- . -~-10 7f '7f+ rna SS (Ge V 1 i Tl : . i' -~ a 1Tt - -1<> 1Tt (a) 2 . rl~ r lf. 1 i!J.~·r1 :fr! rh I;t,:1·hh l~. ~J¥6 :I· If1i ';ltl · " I ..• o· jil 111 · "' •- :lI 1.tl1 [;(iln 1I CJ,! ,Q 0 ' ' • ;· 1· ''•01 " ' ' ' •·. q •O• II .: ... : ...... .':..J... .•· .• .•1 .• .• '• '1 I n, , r, '• I • I I • n. 1 I '• ·O 1 lfi I .•• •1•, •I L . ... . . ~-.I.-0r... ~.. ~.:.> t :I -~--~ .. .: .: .: . t c) I I I . . . ---.---- -1 rr±p ->pprr+1f:::n Pf 0 -->rrf=n=F o I V1 I t-' ........ -176- i .......-.-.........,....,,..,....,....,.........,_,...?'""!"..,.....,....,,_.,.......,.....,__C> l....,....,....,...,....T""T"'-r-1'-r-.,....,....,....,~..,...,.. , • ,, , , , , ,1 ~ ,. N , r 0 .......... + ... !... f ,.a t.: ~ ........._.. ¢ -6-t .¢1 ~ 0 -~ .j ~~ :;~ -6.......;';l· -~ ~ H- --c.!'tl lO ::~·=.;_-1,...; .":,::~- i -:f".r-· I .f: I -- "11~~ j .. ..;:;~ I --::<P- -:.-f........... ~ ---.::: ...... - -----~ -·-~: --- ~:: -r-~ -->- ·-------:: .-~~::#-_.·-· -=:? >=:= ............. ,::....... ·'.>- ~I 0 -U :o ...j • I M -A:- - : i - - i . - - ·----o ....... ,.... + r +~ "°>- --- -o ----, --::>- !! ~t -¢.- ,,....,::t.:::.:. ·:.~~ ' -~ ---<>-- --~-- •*# ---_--;--·~·-··=· ·-----~..,..·'---- ~----~-· - - - - - - - : : ;. . . . . . . . . . . . . . . . t l ----0--______ ;5::~_;·..... ~-.;___ ______ :::::·:_:~~-::_-------->.=:_-:;_ -------:·-~---· ................ ;::·::.:~ :---~___:::._-:>==-'-,.......... --¢--- j ·--~~~~- ------.::.-- ·--- - - c > - ···---:-·----·+··-0 -·-·--·> - ; ---~- ..... .......... _:::-.98.::~... . -.; LD ::::::~:-..:·.-..-:. - 2=-,.).-:; - -·:-.---........ Q~..._3--- 0 ' .J ~~ ·····'"'' - --·~"--i.......;.·- -~~~--- ........ ~ f J ~1-·........................................_._1~,....._.........-............~·~'~·.........~.......................I~ _ I_. . . . . . . . . . . . . . . . . .. . . _ . .. . . . . . ... 0 0 ~:i a. .. J-:-;-J-- ·-r-:;,"'- er o:_.f 0.. , 0 j ·--- ·:.~ ti-41 Q.. l .' _j --~:1 ·~. - ----:r·-·· - -'>- o~ ~ -rl ··-::i-- -~ -~1 ----0·--· -<(>.::;.....; . - 0 0 C"') 0 0 N 021 s-;.n~ . .~3: 0 0 --i o0 ~~ ::-... (I.) Q +' (J') ~ (I.) > 100 400 r---i 1.5 ,_L._----'--. _ ._ L _ _ - - - ! - - _ _ j _ _ . _ I -,-- The curve is a -- - . . + o 1fr - <> 1ft f -- ·------r---r------r---- - - . - - r - - - . . . . - - - rr±p->pp1T+rr±n Pr 0 ->-rr[rr=t= I I '-J '-J I-' ... ' ' I 100 ~ I I• tf I 0 t .. i• 1.0 f.J+ .t ::.i 1 i " I 1 I t ' I I I ' I 1 I - I i19 l H 0I 1·5 I '. ' • . • • I • -~I2.0 Figure 'I ' ; ... 't . I - · v lOd _ '" '"~ 25 V) ' Q..... 1 . 'O ,.,. .0 I .•b The curv e is a fit to the 6 • I ·" , 1'; -~ rr- n mass (Ge "°t :u 6:9 •. ;: : • u•. ~ •: ,_; e:!!11 lj1 6 I It '(!: t,f1. ~l. " : '•i: \.: ' - I ~ I t ~1:-:.·:. : ·1 ;711 !: · I . · I I : 1 J 'fii, '' ! ~: 1i 1 Vft !t t: t ~Tr1,.•;f:Jrr1 1fH:tr Ji i.l6}ti.t~rr~ 1,'1-t:o· ,t,;.~ .,~J]Tf ~t~:r ".,,J;,1~,,. ~~~!i\Itik~NA4~ Tr,~1u.~·n.•. ___ ~f Q.) 1 , ~J I: \.. .: '. ,1ti;j~. (Ji. . *..) Vl -01200 '· , •: I I :,,, ••• ••''•• •' ... ~ 0 I I 11: •• • Q.) ~ 300 ~100 rr:i:p->pprr+ rr::l:n Pro _}1ff1T=r a 7rr + <> 1f'f I 00 I ....... ......_. -179- r---r---r---r---r---r---r---.,...--.,---r-.,---.,...-::-::r"::":::'T.:":::"'lt:~.~-~~~-~--:l::--..,.---i:~::::-,~::::-..., .i, 9 --- .. ::::::.,i.:.9-~ 0 0• . t"'j j :=· 1 ----------o ___·_-_-_·;;=;:-:a-~~;;.·!-- . " ·--------0::::::0::::--¢~~ ....;; ---~ _________;:-----o-~~:: ·-----···---C·---·-----·· LO ---<>--- j N• ~....,,...,.._. ····•:I •••• ----;;,}Q.-- " i ·:::::'?5::~ .~' -H"'"'"' ---.=-~~~;_:_:_:_:_:· ~.~ ~.~ .. ~ .. A I 0 -------1~ ··---~--------~ Ii ~ 1· ~ ··-· ·-:J-··---=.:..;-::::----o.··· ···-C·· =:::::c· ....";:::::: -----= ....... "P-1 Q.. --~- - - -.:>--C·· ·· ·····-·t-:- ----·· --·•-!) •• ·42 ~ ····--.:J------.)- - ···--·-:.:=.=:. :=· . .. _.... .-i H ..... ' <lJ 0 -¢-- r-1 ··=-:::~ 4-'~----...... ..;:::....... ~ ····=···· ----~::i ··-:: ......:............. _____.., _31t __ E::: ~ ••••• ;;i ~ I ~ o._ r "' --1:~~- ••• .;::: ••• -----¢-...- c.. ·•····- ..........~- :; .. .......:i •••••• """ A ---~ ~-- .-·: :-·?,; _. -) -=-~-•••*Ii.:? .. ··---<>-- ···-0 ::··~« ·':)·:.::.... -~ - -ti ···w··· -,~- \:: j I I ---~~-~:-...~ ~~ Itn -=~-1 rl --.::i-s- ' --<).--- -~ -::;-,r',i ":} -~ -:~::i .s, ~ ,__._..~_...__...__.__..._..__......._.___...__..__.________..__.L_.__,iC! 0 0 C\2 0 0 0 ~ -" ..:\~TI ...... 08, ' S~ U:d ...l.:fr 0 Ln o"l"""f -180- 0 I • :~ i J! j ! i 4 ! ..j ! lfj -I . 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Q) <--< -181- <> n +p-).pj1T+1T-p a 7r p~p£7r+1T-p 7T+ ·------· 1T fits fits Pro b(XEt)25% < 0.6 mass Ge\72 / c 2 < 3.7 GeV p;-.:;1T[n° definition: 0.6 ~ n[rr 0 mass < 1.0 Gev; Figures V. lla-d Invariant mass distributions f o r t h e slow particles of the rr + f o r events within the fast p- peaks (see above). 0 c hann el 111 I " ' I LI " I 1,f ;1 I - I 1 I -·· , .v 0 "1 "1l: I l. ., 2- j !J: /,; ! : •: • , , G. rnftss .. ...... . TL (Ge V) The curves are fits to the ~+t-. Figure V.lla n+p -A-.... . ...-L-....... > ' . L".. " 1.e.J r.. .... v • J - _ --- ·- L - --- ---'-- - · - '' •,, •: ..-;. . fl ' 'I I , ' r. · • !..., • :\~I~ 11 I ur~ !1 I i~f't-> I I ~yt' .Y/: :·, .,. "H . •.LJ..~tthl~ . !{4i .. '. ' " i i~.~ .. ~ : · · H YL·~t •• ~ .. 30 . "i .. l i ! i' ."~;1,L{l.\~:+f · : ' 1 1 i ' j t . +1,. :U1l.°>'l.~ ' . " '"'"''"'-''~'•>"imt:·1"··~··"''.f• " •"';. '~·z ~ . .-~-'"""~• 0 •.;~r.•_:'·, . ".....,. '·'"· '·. • •·.. ""' I ' ~.: : •·r·l ~ ,'f ~ ~,,: ,~~ I I r.~ I f--' 00 N f/.U. j }l -!- 1ft a 7rr ()> (a) I \ ---r----,-·. ----y- - ···· -...,-- - --· -- · ··· ···- ·- r - - ·- ,·- ·-- ....,-- · - -----.- -----,- --,----r··----.----.-- pf=->rrj=rr 0 1f \ t~ 1 ---,-.-- --,.·- -----·--r - 0 L_ !.__/·_____ 1.0- 100 &1200 ~1 pt1(1·rr·-·p I Cf) ~ J !f..., lj I 1 J rI 111. , 1 I 11. ., .. - -. -- - ·-..,-- " -l - - . ., .. 1, 1 I 1. ,. •- I • .1 . , I .. .,- . - -, - ·-----.-- ----1 1 ·J 11 <?r • V' ... I 11.. o 1r, -> 7fr , + (b) ··- ··· -··-----.------.,.-- - , - 'I.· 1·,1 1 ' I ' , • I, L • '- • l- . . • .. •'i . . . • • · r L> L. • ' .1:.t·1.,.i l,!:1:_1: , -ii •t •• . • i . L . 7 ••• ' ' : . I.. -· • 1 ' ( t ' " ,ti1 ~·• t he ~ o '> ') ,;,..f.J .._!:._• • · ..L..i .i .. '. ... . L . . . . . Tr) a• ..L Ct (, > " -. '. d• t .,'•'j,h , 0. c. L "->• : : - •") . "" ' ' I I " ,. •<' llltt:sJ ' .. ..• .L. o '•" L7 e v llb Figur . f p ' '•·o" ' ·• ', )' The curves are f 1'ts to · .1.... • I I. I f ·1 • • ,.,,, • • • • • • • · ·.·r : . ..... . . .. . j ' '. tl • , , . ! . ... ;.y• ,t . ,, .. • • • 1, ' ' ' ' ' , • ' •• t· ' ' . ... ... • ...... '. . ' I "I . "'ll !! ' ..J.!...... . , , " ·,·. , , , ' " "." . .. •• • : .,._,,. .\ • .. • : : .... : , •, 1 1 . 1 - 3•0 ti lf'q]~l-;j? !~~11,l1}ll i -·. 1t 1 .1 ,J~n,:.. . :;,~ ·f. !Jri .. 1.1I r~Hiu .1 " n1lJl ·.1~. 1 n ! 11J IIi11;:.:: h1·t..\. . :·: .'1 :! ~·1: .Jrf'·i, .' I·.(11u11r11111 I", ,-4- ~1-f . t·'· ~1 .. ' r \..!'a ·,.,., ·:· ''··1..... : : · -~ :· :· ._.,._,:, ,1L . l "'-.'" . . . ~ r, ~t ;. '~ L/.1,··r1 I':j(t,r-et· . '(.lt1r· tlJ~.1 d !,~,,1~~,r··!!f,~-t~~· - ~1 ~ ~ ·~~• Lt .' ~j 1 l II I -, - ... , .. ... --,- I,ll Il fIf'l ....... t1·q11, , Jt11 ·- .. ··- -··· · ..,.... l"~ • - 0 L ·1.0 r1 (t} .k 100 µ·· •t.) " (\} 0 ~100 1r=::p - >pt·ff·> 1( · p pj=- >-rr.f=-rr 0 I w I I-' 00 ~ V"' t· Qj d (/) ... J 0.0 0 100 '~ 200 0 .-4 l.,d (1) ~ 300 ·- -100 . J tf .' . : : . ... ,l !,I •'. l ·'•: ' • ··· • " ' : : •: • "· ;~; ;1 u J • I .·1f~ • 11 • b 'ol I I --. 1 o I . -'--- : I· • ' ·- 1 Figure V.llc r' ·O • "" • 0 ( Ge V) ( {' .. . • I -L-----1'.__ 1r+rr-- rnass ' ,;':!.i :: The curves are fits to the p • '('"''• . I i ~}~, ·.~~i.!/;..H% .he " I --.- . t'!11 !L H i I !. . ti L:t,... ::; .:: : .''-·<..c,,,.,.,.t ,.J! ll1 .: •n ..!l t oi..5 .'.11.t ....I:/'t6t ~ .:t.i.,"' '.'• ~· 1 .. 1. 0 · - ~-i__-'----~-L---0_L______,__-~--•5 •!or · : ; : ; •- : • : • u'<J' • JI lfflri I :.~1: ,~,. ,I.:.~ I 1 [J· : . ... :•;· 1o-o • 1'{;1 _._.:r.. ;.~'(···-<Cl : '~ -:-._ . I ~ : .,I/ ::li.:11" 1 Q ,11. l. '11f 111 " lt;i± 1liJ I I f.Wrt1j iYI,.I j .. 11t1l llfill., lt ! 1 . - -.---.--- ---,--- -,---.-----. ------.- ----.--- rr±p-->pf=rr+rr--·p p{-->rr{rr 0 q f ·MJ2 • 0 'b a 1fr <> 1ft + (c) I +-- CP ,_..I -185- r-r-r--.,.--r-.-,.---r-~-.--,-.....,..--.-~-r-,::::=;~==~~C> ~-a·--_'-;"" Cl""J ---¢----- -0 ----c;;i---- ___.¢.:.::£.· --- -0 ----->- - "0::2.::.:." -->~--:c: __ _ --a-- -.0.-- ~ a --- ---<)- ---=--·-·C ••• ---~?.:i ::_ j t><>-r::.·:P:.:: ~.:;--71 .. :::W-----<:> ,· --~·-----<>----~-~--·:..,=:,:·-: :::· -~-- ~ ¢ ----!> _,:::... _____ _ .....:i --- jN ~:>.:s"=-- ---c ·----=-, --· ¢> ---~ ~ - --=<>------<;>· ·-----:J·--':::1:..--- ----<>--- -- -::i--- ~~-=~-----c-- 11 --- ~----- :i --· ---·<>--···- -·-··---- --¢====::::~ :::.. ----::.-~--. ---. ..,:: •---- _,_.., ::--.:--- ~ ! ·--· --- i0 1 . ---::;:::::::_~_ · ·:::;.5·:~:: ---o----.. .,_, ... ---~ ··-- ::".'~--- ----»---·--··--· ---~ ·---::- ---<'>-------·-······· -.----.q-----. ,_..-~-------. J lj -,.,~::,- j' -~---..e--... ---::? -·' - ; 7 6 - - - ....._ .. - - • I !, i' ____,.- --t>---:..::- -.-_-_-__ --------~------- .:; -.:·-· i ---¢- - -'-'·-------·:'.!----· --·-::----- _:.;:.:..e· -----:>---. ----<>--<>----:::~; : :: ~-:> ~ lf:: :>-::;_·.:.. I r-1 ~"-·· I -----=-~ --::!-- ~ - ·->-:-=:~-. ~..r- •. I ~J • I --::-"'" . 'jj~ ~ 0 0 N 0 0_... 0 L{) rn ~ ~ .I,"'N :.-4 • ...;:i - - - - - · -->- ~ '-' -..... ,-! ~ 0 g -+1T 0 -!· +++TT +p ++-+'TT +p ++-+ir +p f'i f'i f'i 0 ± =i= f -+Tr 1T f ± =r0 g -+n _lf t ± =r: 0 p -+1r f n 0 ± =r- 0 2 f o ± =r o A3-+TT f TT Tf + + 0 ++-+1r+p +++ TT +P f'i f'i + +Tf 0 - Tf =F o =r- p -+·TT 'TT =r- =r o 0 p -+TT p -+1r 'Ir p -+Tr + +'IT 0 p -+Tr Tr p -+1T ± =r- 0 f 0 ± =r- 0 A3+([ f1T 1r 2 0 A +TT ·n 1r A -+n Tr Tr p -+1r ·rr 508±200 303±113 298±204 :;:.69±110 133±95 333±139 2L106±214 1243±173 ± 0 f ± =r: 0 p -+1T f 1T 0 p -+1r 1T -!- p -+TT f TT + - 430±140 1762±244 'TT 557±192 2737±257 Weight-sum ± 0 f ± =r- t ± =i= ± =r- f -+1r _Tr 0 p -+TT f'TT ++-+'If +p Resonance f'i Cut on ) 14.5±11.0% 30.5±15.2% 35.8±3.9% 41.4±7.5% 58. 7±10 .5% 47.0±19.1% 51.0±22.3% 40.7±4.6% Resonance fraction 1f f TT 'TT 1f + + - 0 7.4±2.9% 4.4±1.6% 2.2±1.5% ~0.5±0.8% 1.9±1.4% 4.8±2.0% 3!+. 8± 3. 2% 19.0±2.7% 13.0±1.8% 3. 2±1. 0% 4.1±1.4% 20. 2±1. 9% Fr ac tion of cut events 1054±140 619±129 1158±154 Weight-sum 11 p 25.0±3.8% 42.5±11.3% 79.6±17.0% Resonance fraction TTfTf TT - + - 0 Estimated fast meson resonance production for slow system resonance cuts Table V.13 22.2±3.0% lLi .1± 3. 0% 13.4±1.8% Fraction of cut events co I (J\ I f-' o ± "f A + 1r 11 ·rr 2 f +1f - 0 p 7.2±2.2% o ± :i= f -;-1r f rr +1[ - + 'If -l-'lf 429±169 2368±224 0 f p 0 11 -+'1r n 11 -+'IT n +Tr - Wei ght-sum p +1r 94.0 ±50.7% Fraction of cut events 447±144 376±116 Resonance fraction o ± =f f +rr rr f o ± :i= p -t 'JT fTf p +rr rr Weight-sum 2069 ±179 - Resonance ± =f - Cut on 1r 1r 1r rr n + + + - Ta ble V.13 (cont.) 48.8±23.6% 50.8±5.9% 50.9±21.7% 44.4±4.9% Resona nce fraction L - + + - rr,,rr 1r 1r n 8.5±3.1+% 47.1±4.7% 9.0±2.9% 41.8±3.8% Fraction of cut events I -.J I I-' co -188- rr+ (data & fits) (data & fits) rr±p--;rr[rr-1T 0li ++ Li++ ~rr+p n±p~-rrrrr+rr+ fl- Ll- --;rr-n Pro b(Xiit)~5% < 0.6 -tntr{f) (rr7rrrN) mass 2 2 GeV / c < 3.7 GeV iJ. ++ ~Ti+D definition: n·p mass < 1.36 Ge.\l !:.:.- ~rr-n definition: < 1.36 Ge\l 7r n mass ..I. ..L Figures V .12a-j Invariant mass distributions of masses with the fast pion and one or two of the remaining pions. . above cuts to be in the 6 channel). ++ The events have been selected by the peak (rr 0 channel) or the 6 - peak (n -189- 900 (a) 0 The curve is a fit to the p , 600 f 0 0 , and g . :-,.,.• 300 .:-: ..........., ,.......... ... -· . ., I I I I•• ("• 0 ' I (b) 0 l{) -100 200 0 r 600 The curves are fits to 400 200 00 I 2 1 7rr7T J. mass Figures V .12a-c (Ge'/) 3 -190.J... ..l4 ·' rr-p 47Tf1f ' 1T ~ ti .J... I (d) 400 ~ v '---! ,,.,. r -1 r 200 rr t 0 ~ II"'\ ·~ ,, '· r r r 0 r '/'; .;..:. ,....., ~ ,.\;..)' .. 1-"' ,... r •. ,--, r r 0 \j I v n I \ \,,.J ,., r ..v .. .J ....l ·d, _ _Ji l.J ,:..r-J I r -+~ ~ .. 1" I LJ rt:.c 200 •rl ~ I ' 0 t .. • !.;... .•• r "- .. r : .. ~ '"'1 ;4 .I. ,, !· 0,,v I ,.,..." ri.J ;- •'-' .. ~ ' ' -J i..: .. :·: '•I .. •'-~ I . J .--~'' ' ,,,. t1 1 ' I I If ·-· I tf t I I J I ' I ltl ...,, 'fl ...,LJ' '' .-. "" .. : ' . ltl 1.I I 'I ,, j •' ' . ·'· ........'' .."" ' " :_: '! .. , '' I '""l •'· ;-; ,-•I , .. , I ",,_' '• _;! ..""'' ' . l r I !I j r 0 :11as s "\ l ' 1. "!" \"7', r• ci ). v , ·, . \...JV , 1 - \l Figures V.12d-e -191 - 600 (f) A 400 I '":1: ........··..' "; ~-1;, .. :. . ...... 200 .: 0 ... ·-· .. _.... ·' '... •• .J•. • I n;n+1To (g) 1Tj1T-7To 400 j ;u ..· . j 200 1• I : \.t• I t I 0 I J n:1T-1To The curves a r e fits to 1T~1T+7TO 0 and A3. 300 200 f .., 10 I I It I '1st• :·-,.! : 100 ·',1,." .. ....., I :- • 'i• I .. 1 I 2 nrrrrr mass Figures V.12£ - h 3 (GeV) ., 1;.•t --~ltfll I 1• 1i I ' I !: •• : 11'•1 J~I f • I f I • -192- rr±p~rr!n+n+~- ~-4rr-n 200.-.-.--.--.-P-.-~-..---r--.-.-~~~---..-.--~..-.-.-...-.-~~ (i) ·-•••• 150 •• OI ii_i~~un,~~ l: -;:: ::l!::1.ill~· !. 100 ' • 1J''• r., , ·- • •• ,iJ -· • t I 0 l() n .: .•:, ·-. ·1·.. .'••. .' -:. ~- . .:.. ... .. .'••'••.,. ..'•'~! t ' I !'i • ~ I • • 50 I I . ' 1, "' •' ' 0 •' , ·rri: nm: r• 1 • o•ru:: '1 •JI: I 300 (j) ' • ' l I j I ~ :j:l/l .: : ·11 I~..rf.. ' ~:!.~ :~·: .. !: frltj . :;:i't! ::.• ' •• :: I : 200 · 1 f) : I ·:-- ' .J t .-. ··1'i: :: : :::·:,,.! n ::~,r ·:. l 1 -' '' ' l ' 3.l .. Id ! . : !i- !.i • 1 ' i. : riJ ' - • ]:Iu\t:~':• : • j I I 1 ,; ·~ ~ i~ l: . u ' ~~::' .. . 1Tf7r1r j u ~: .!;:,~ • ' --~ 1i - ~~_:U 1 - I'.! I r':! 1, - '1. ,4, R n r: 100 ~ LI l :11i 1:: . '1!ti -.-i.f.1~ :• . .. .-t...:;,~ 2 mass 3 (Ge 1/ ) (t each e~rent appears twice) Figures V .12i-j -193- n+ (data & fits) 1T (data & fits) 7r±p~7rfpotrop po-71f+1T- 1T ...~ p~1Tf-1-p Q7T ...l-. n p 0 -7>1T +1I"- Pro b(XEt)~5% 2 2 -tntr{f) < 0 .6 GeV /c (rr7rrrN) 0.64 mass < 3.7 GeV p 0 -71T+1T- definition: ~ rr+rr mass < 0.84 Ge'! Figures V .13a- 2. Invariant mass distributions of masses with the fast pion and one, two, or all three of t he remaining pions for events in the slow system p peak (see above) . 0 -194- Po~rr+rr- 7r±p->rif=po1Top 600~..-...--r--r---r-r--~~~-,--,--r-r~--.-.~-.--.-T-r-r-T-"""1 ri (a) 500 ~I 400 300 ~ ~ ~rtiJ ,!'U~trfn, . ........ , , . •. , 200 L r 100 0 ~~; ~ I , I ·-.! U : 1 • t I --: - .. ·~·-- ..:.. : , ·~.: (b) 0 LO I 1.Jl 1 fli\1 :~ ill ~I . ·~un ~ i 200 ImI II ..-, I t•: ·; .... -~ :.... •"' ~ I I r• :! I I I : l 100 ~ .,_.;i i-l ~ CJJ '1 1l u- 1 •• I I.. '1 I I I II : It ~- t 1 t It I I I ... ... - • I .. 11 1:• I t .... I I I : ~ I 1 I I : J I : f I II If ,_, I I I 1 t t•, ..t 0 •M r ( c) \l) ~ ,_ --: 1--+--+--f'o'-l-+-·-l-~-+-+-1-+-;-+-"t-+--+-.,..-;.-+--+-"i-+-+-+-'r-+--+-~ 300 f + fits to the p-. 200 r rr 100 ~ f 1 7rf7r 2 mass Figures V.13a-c (Ge\') 3 -195- (d) 600 The curve is a fit to the o0 and £ 0 • 400 0 l.() " riJ. ~....) ,,..; ~ 0 ;..:0 "'d 0 ,... '*_:) ~ ~ •!'"""! 0 !;:I""""'" 0 1 1Tf7T (t 2 mass (Ge\T) Pach e'.,..en.,.. ....,, , ... ; .... \.J appears ~ Fig u res V .1 3d-e 3 -196- 300 ~ '_'_' I~:~~~~ I I I I I I I I j I I I l I I I I I j I I I I I I I ..... rrf- rr +7f- 'r" 1 ( ) 200 100 ;;.> CD ~ 0 , 0 ,LO , .~ Cl 200 rl 0 l> 0 "d j 100 ~ +.:i r-1 ~ .,.... Q) !;;;.... ........ , (g) n~ rlf 0 ! . I IP UH1f . t • t""4 & TI I n ::n :! U11J1lU r: ri !t I! ~ !I,·: : .-, "I : : \;f\J l!1 :., t-' \... i 4 1 i : ,.. !~1 ... 1 I t :"tt I • • • 1 ~!! ~~ 1 : l 1' •I J !_,- ~:--' 0 ro-1 , I ..... Vl I t 1 f '-,:!!! .~ 1 I t "'\ 11 -· It 1, I t • I • • • t't : t I ~II ! i, L i J 1 11 ! -'::""""!!' • -:I l 1 - I ' I ' 7r;1T'-1To (h) 1T'{1T'+7ro 200 ~ 100 I :In Ii·~. I :n 1 I:~I~ ;J-1~:21 1 W: ln ~ 1 · i: 1 .•. n,JI I ~clJ ........ J in: 11 ~ i n_,.J1 w~il ~ ,q_ , : : :1 ~'TI II : j :!: ~ •:•: ~: .n : : 11 11 ; I I I I l '. ~ \ J ! I ·'· ' t I t .. ' ;: , ......~ : . •!• : ,J :: : • , •uI I t •• t •• ' I l i·~, ~ I I ' ! ti ', : :: It ... - •'- I, t• ••1;.t l•t • ~• If: \ !• I : j, : : : : ! if: :1: i; Ii 1, I I t I t •t :11,.t I~! I 1 ... l1 t .t I 1 1T(7rTr I l I ~ .. l• !i I t .t. • 1 r. I •• t , .. t .. t t l • I! t I •!: ! !! I :, .. U : lt:··~ ·· .-i: • : : ,-' ~ ! : ~'..l !.. •, •f t •t • ' , , • t : :"':: •• jl 00 n I ~ I I t 2 I I I I I I I I I \ 3 mass (Ge\/) Figures V .13f-h 1 ! ! I l i I I 1 ~ -197-1..!... 0 -rr-p41Tf1T ·p n .J.. (i) ....•• .... .. 200 I I I I f I ;:::-;l r:: : I 1 Ii I • m:li i . ·~ !n 1 > () ""-! ~ f rt r.~ :.: P.hlft·:·. : n·: ' l ~>~'l h., ~" .:r1 :•!ti I: ~m , 1 ~r -..- If' ' ~fl ~ ..J rl ,.. .. ,...~ . ... , ......, r-· '"d ·v""'' ·+~ r1 ~ ..... ~ ~ ·~ () !;;.~ ·@ ·w ~, : 1j'· • •!....'~ ,•,•l1 tt i •t •• 1 !1 •t 1• ' , -- • l • • t ,,,l • I I I ' ••• 'I' ', r' 0 vt-. f 100 I 1 r r I :: ill~ ~I Jnlr·-11 •' •'ni '! l tl l '- ! r I tI t ' . j· . .W !j-!J: 1 l i '.! ~ ·I :::· t 1 •'' t I I 1 . • ' . I , I• •• •• • I ,l ·~ :: 1 I : . ~v i . :: •f '• u ••••·•••• :.Jo I • :•: ,1 ,, 1 - I jl I••• : ~ .. I l . l •Ll ,. · :un I 11 ~ I I ! i· \1~:1 1:· .~ :-:1 ~ i 0 I " I I.. : i 1 i ! !l :J1: :: 1 ::~! l I . : II J · .. J • : : . ... f j r::' ·! ' , I I .... I : ~ f1 1 ' .. I : : : :1.J'LI!:i •t t j1 :~.. ~ ' I • (.J ·\ + I 1 J The curve is a fit to the A • 2 t --·-- .I ~ 300 I~ ~ ~ 200 r- r I J!' .! t }1 .. .., . ~ ' II ' 100 !'',_ I I I I I l, • ' ,_ 1 · ~··: ! ' ... 'I I ,j 11 I ' -! 2 mass each e·\'"en t appears 1Tf7r1T (t Figures V.13i-j .l. • "\ . . w1ce) -198- 300 I , I 0 I I I 0 I, 0 ,, 1 ~I nio rr u o - ·>-7T+1T1Tfn+n:no, n;n+n-n° r ... '! I- ~ j ! 1 r 1 200 ;- ..j r- ~ n r ~ ~ r ;.. :oo 0 i n ' j ..... l ~ r ! l"'I . .,., , -~ ;- .. t J I r 0 J r 0 -:.rr·-'- TI -- ~ ..! r- :2GO ~ r -' • • • ..,,1 f I .... '; ' ' . . ;' , J :- r ,... ... 1 ~ i 0 1 r 1 ' 0 rr '\ \.:rC Figures V.13k- 2., '-\ • j· -199- (data & fits) (data & fits) TI+ 1T 1T±p~1Tfp+1r-p p+ ~rr+-rro rr±p-?1Tfp-rr+p p- ~rr-rr 0 Pro b(Xiit):-2:5% -tnrr{f) (1T+n-tr 0p) 2 2 < 0.6 Ge\1 / c mass < 3.7 GeV definition: mass < 0.84 p=-?1T=n° 0.6L1 s: 1r=rr 0 Ge \7' Figures V.14a-n Invariant mass distributions of masses with the fast pion and one, two, or all three of the remaining pions for events within the slow system + p- peaks (see above). -200- 1r..._p 41T::"°1 'O ..L1f p ..l.. ...l.. I 600 {a) The curve is a fit to the o 400 f 0 0 , 0 , and g • 200 0 (b) ~ iuMrt~ [~ 200 'I : 100 t •"\. .. t f' : : ,U I . 1 : I: J1 t.:• r: : ::I I I•"•' • a ''1 1 ti t HI I I I ~ • : 11 ·+ '.~ . !l L:,.., J_n l ••• I .} I ~ : '• ! I '•i t I f I : 1,. I I' ~.. I~ I ""~ r-1 ........ ~ 0 t C) ~ .. 1 I .. I I 200 I r"J.ri. I . . ~: : 1·-·. '·'"'f . rr.~ ~: ' ......... I -.- '•t f (c) 'M .. t1 ·: : :I :.-I: :••-<•.•••-; • ' r.. , , j I j~ l., I : 1.. .1 . ,_, 1 . 1 I ,I ' I }-, l i U':;: ~I :: : .L... :': ··:. rru~ n I ~ 100 I I It - •' .:: I' .,.t • I' :.,.: !•., '•1 1.,..- I I : I•• I" I ;~ ; : •. • : I.... • a •tU • ,&.J, , t t •' t It I ~1 i Ll :r wµi I~ ,.,J • • I ...... , tI ' '1 I .... !~t ' . ' f.,,,., I 1 un II l ~ II 4f ~ ·--•. ::~: '·i.;! I 00 2 1 7Tf7T mass Figures V .14a -c (Ge\/) u. : • • 3 -201- 1r±p~1rf" p+rr p p+ ->rr+rr 0 300 ~,.........,-,-__,_..._,...~,....-.-..,......,.....,....,.....,.....,...,_,.._,._,..._.,.-.-"T_,......,.........,_.....,,.....,....,,_,_,,__,.......... 1T;1!'+1f1rj1T+1f- (d) 200 100 ::> (j) ~ ~ 0 0 l.(j '"d 0 o+...J rl ~ ~'J (f) •rl 100 1 7Tf7r1i 2 mass Figures V.14d-f 3 (Ge~\:') 4 -202- - -1,..,,.. ...t.. ...... "rr" . +o-tJ: 1!'---p-> 11 f /1 0 P- ->rr .rr, , j I t i rrf ~: 1 ........ ~ rrftr j o · I1 0 I 400 I The curve is a fit to the ~:1~1C.}w ·- . . : :~,~: .,:, :·i·~·~-~ ~-J I...[, I : '·' . ,r 0 0 LO ' ... , •. ' ' • ~ 1~L J r.1: ; 0 ~ c 1, i ~ '~1 {: ' :~ :1 \ I · I ; .I , I , ; " 1 ' ~ il 1 ,J ', ' I ' !,,-, ! ;, ..r I I~'n .. Q ~, 1 ~ } '''"~' J ' I 1';"l! . l n f '. ri,. I ;1 .-, i -]j ... ' ··~·~·-l.Jc·nUl ...,,, ~ .,. : 1 :--, , ,, . ., '· ' .,. !..I. '·h ,__, .... .. , :.,·· "'"' , . b '"'-" r ' j' .. ·:: ' . .... ,r r .. , i :· j 11'1'0 1J 7T'· Tr • . .J -! ~:'u' ~ . ' ··-· ,;" : : . -: I " ..... 1' ' ' 1 , I r' r 1 ' U '' .. :.._,'<•:· : ..::4) ~ I ;-:_: ' -· r \•; r [. r' I~!' ru : •·''·• ,I ~ ~ • nl n n1 n1 j :+iFL.J .. :11 r:-nlJ1..., ru ' I 1 ' -I4 I Ill :'" ' :4 : Lr'i .lJ I l ··~ I I i' .:cl, ·: w · :, '"·'·'· ,.·. · ·., : ... ':. ., ,·w ·' l . ·. rn i _mj. I . .' ,' : :•.• : .:: : ''< !J;I " ' r:i 1 ... : I o:• :l..h "' ,,,. cij ' 11• .,,,_ I"• "•;:: Ir; "iH"..I ,. .,, U .; 00 00 r .,,., ..... -. ~ ' ... . ·-· 'tJ ~ (h) rr ?.OO t· ? ' '·· ,,•: .... ,, .. rf .·n1J"c! 'r..:r 2w__, o or , £-'. , . 1\ ice\:) 7T.(?T r11ass ... v .14g-i Figures ' J ··1U-1 b ' ' " ·-¥!.. ' 3 -203t 1T=p->1Tf 7f p p 4 - -i-1T -· IT 0 ' 0 ' T 300 f •) d 200 ~ 1). d~~w r~ ~·'' ••' r-1,; ' ''• .11~:: di .. 1 :~~ l!~ : n: ~-r-JLi ': :~ ,.::!. : j~· .! ' .., ! H. ;n. ! ··. ••I~ ·~ '! ~ .fi'f: • 1 t.ll ' ! •f ..... ' 100 a I t ,. r:tl~ .•' • ll-t_ '''..t,. n 1; a~! ... '~ ' t t ..... ... _.,.J , .,] : "I t • ',' •'...... '' ••1,' ...i,It.,, I. I' l'-• I! ' • • •• , ' t ! ¥;:_: 1 l , , , ,.t Lf' • ·: I t I 0 ' •'• ··~.. •••,• ''t' ..... t u. 1 ..~ .r ; I '... • t r .of .. 1 ! i . •. 1 --~~-:- ~ r.dt. 'l L . 0 l{) . · 200 ...v . ..;.-.:. ....~ ......... CJ] ........ 0 ·!;;:,.- mass Figures V.14h-X. -204- 0 L() ' 7r f7T..7r7T J. n-iass Figures V .1 4 m-n (Ge\:) -2057. Double Slow Resonance Production and Sequential Decays Finally we present the slow invariant mass distributions cut on the requirement of a resonance in a subgroup of the particles in the invariant mass (resonance decays into another resonance) or in the particles not in the invariant mass (double slow resonance production). Note that these estimates are not plagued by backgrounds from fast meson resonance production as they involve only resonances within the slow system. The mass distributions cut on the 6 given in Figs. V.15a-d and V.16a -b respectively. V.18a-d show t h e mass distributions for the p and the n channel respectively. 0 -H- and the 6 are Figs. V.17a - d and cut for the TIO channel + The mass distributions for the p- cuts are in Figs. V.19a-d and V.20a-d. The estimates for double reson- ance production are given in Table V.14. The most prominent process observed is: ± (12) only a small fraction of which can be explained by the production of a fast A meson and a slow 6 -H- (see previo us section). Table V.15 lists the estimates for the production of slow resonances followed by their decay into another resonance (cascade decay). As discussed in section 5, the N(l700) observed in the TI +TI +TI - n mass is consistent with the cascade decay for the entire observed cross -206section: + N (1700) -+ + + - (12) n n 6 L The N(l790) also appears in the cut. TI '1T n +TI - TI 0 p mass distribution for the 6 ++ However, from studies of this resonance for the was found that the ;r n~w 0 p events, it +p mass peaks at about 1150 ~1eV and satisfies the 0 6++ cut for almost all the events in the w system does not form a 6 ++ peak even though the n+p p+Llo p+N(l470) + + p p 0 0 p p p 0 P N(l470) poll+ p-Ll++ 0 p p fl + p-Ll++ 0 fl++ Cut Resonances a (µb) Resonance fraction 7.0±2.1 16.1 ±5.1% 8.8±2.6 62.0±27.8% 9.4±3.5 74.5±38.6% n 1000±469 13.0±6.1 69.5 ±49.8% 723±269 ~~~~~~~~~-n-fn TI TI + + + - 3041±238 38.3±3.5 23.8±2.1% '\, 0 556±167 699±206 2184±357 27.5±4.7 55.5 ±11.8% Weight-sum ~~~~~~~~~~ 1T 1T 1[ 1f + + - 0 19.2±9.0% 13 . 9±5.2% 47.3±3.9% 8.0±2.4% 10.7 ±3.2% 16.2±2.7% Fraction of cut events a (µb) Resonance fraction p 8.7±2.1 30.2±8.0% 7.3±2.4 12.1±4.1% '\, 0 398±243 5.9±3.6 15.3±5.3% 1T1T1T1Til - + + - 1427±192 20.8±3.0 21.3±3.1% 246±254 ~3.1±3.2 691±159 501±164 1482±268 21.6±4.1 46.1±11.3% Weight-sum 1T 1T - + - 0 ~~~~~~~~~-1Tf1T Estimated slow system double resonance production Table V.14 7.9±4.8% 30.1±4.2% ~ .6±5 .8% 15.8±3.7% 11.4±3.8% 17.2±3.1% Fraction of cut events I N I '-' 0 + - N(1700)-+'rr +'ff +6 - 561±85 14±88 N(l688)-+p n 0 254±85 31±154 101±29% 7.3±1.2 ~o. 2±1. 3 146±37% 3.3±1.1 32.4 ±12.7% ~O.Li±2.0 792±161 10.3±2.2 TITI 'f fTin -----------!- N( 14 7 0) -+p 0 n N(l688) -+TI 6 + - N(l470)-+1r 6 ~4.4±5.6% + + + - 119±151 ~1.5±1.9 6(1890) -+p+p Resonance fraction 5.9±2.8 17.1±9.2% o (µb) 468±222 Weight-sum 6(1890)-+1! 0 6++ Resonance -+ products + - 0 __________ TI + f 1T 1T TI p 11. 2±1. 7% ~.o. 3±1. 7% 4.9±1.6% ~-D.6±3.1% 15.8±3.2% 6-;l . 7±2. 2% 3.5±1.6% Fraction of cut events o (µb) - + + - 351±88 412±128 5.2±1.3 89.5±30.1% 6.1±1.9 83.4±38.5% ~2±28% 6.9±2.2 94.3±44.2% 5.3±2.2 90.0±50.4% 46±108 ~.6±1.4 466±149 358±149 __________ TI f TI 1f 1f n '\, 0 Resonance fraction -f·rr +1r - 'ff 0 p 158±192 Q. 3±2. 8 Weight-sum __________ ·ff Estimated slow resonance production with cascade decay Table V.15 7 .1±1.8% 8.2±2.6% ~.9±2.1% 9.4±3.0% 7.2±3.0% ~l. 8±2. 2% Fraction of cut events I N I (X) 0 -209- <> 1T+p-71Tt Jf'-TIO Ll ++ /j_ ++->1T+p 0 rr-p~rr£n-7T 0 Li++ Ll++ ->7T+p TI+ -------· 1T fits fits Pro b(Xiit)25% < 0.6 GeV2 /' c 2 -t1Ttr{f) (rr+rr--rr 0p) mass < 3.7 Ge\r Li++ ~~rr+n .. definition: TI' P mass < 1.36 Ge\7 .J- Figures V.15a-d Invariant mass distributions for the slow particles of the ~o channel for events within the 6 ++ peak (see above). '"d b ' ......... 3 .n '-....," 0 (\} .... 6 il I t' 6 . • I 0.5 _j_ l 0 l 1. 0 _ j L-----L--- - mass (GcV) 1 __ The curve s are fi ts to the p- . Figure V. 15 a n-rr ..L..--- . 1.5 n±p->1ft1r-- not:>.++ D. ++ _>7r+p a 1rr -1<> 11"t (a) I N I I-' 0 -211- I j -l- • <:l -' ' -:! <l 0 l::: I f.: -H.,... ~ ..... j 0.. -H ~ ro mp; .op ) :l "'u b 1.0 0L ·d 2 3 8 . ,0 (\) 0 ,_I '-:J VJ ~ ;-.-..... t - " •: I l I: ,, 1! '. • : _, , ! : I I I1'. ' ' ' ' • l . : • f : • ' I ; • j l. '{ I , ' l "'I l I' ·1: .l,.v !>~ l · ,, I f • I · I I .• I1 ' I I: I l • .i , I , I . , I I f• • • •• : 1 j. Pl 1 . 1 11-1 N'V' I rru1ss 2.0 L ___ q . , ,., , • . rr " "' I: ; ' . ';: (Ge~/) 2.5 t __ ____ _/,... _____ .1....- ___.-J.._.__ __j____ .. r 1 i- 1.l t • ., 1 I 1 "' 7rr o 7rr ~ (c) _ I I <: I ., ,,,r I 3.0 • . , v_•J. - 1 .:.1~~-ro., . t , ,.,,· '' ,",', ;' ·r". '' r ,.._ v·J. " •l j J • I'~l j I I' 1,111I 1 ,.J, ._ ' '"',1 vI "'1j 1 I •' • • . vj 11 , .. , v 1 : ':' ':': f ...: : I ,,,·;", ...., . 1l fI::r•'; ,:YI IL 1 I Iv,J : · · .. ·r "'" t 1 ,s.t\!.,.r.1!.I.·a /, : • •: 1.-i._ ', j' · , /1 :· Ir~ ' ·· Figure V.15c 1r"t·1r0p ! - t 1 'I" . ·1· I I : l l: !• ' The curves are fits to the f'..++(1890). 1.5 -..? .·-...· .,! ! ; I' 'J 11 I ·l ! ! ll. ! l· 1 I ; •. : ~ - ~ . ' _l~J · 'l ·r--.: . 1 -~ i ·~ ,, ' ·; ! •' I ,• , , · · .. ' ·, ' 1 , i '° ..: ' . : : · ,, I I• : 1 1 I ! : . .. . ~; ,:. · /,;\~ Yi t . r~ . , 1 · 1 t t " I j ' • •fl ' L - - ____ .i......;. . - - L ._ ,__ _J..._ _ ___l._,_. _ _J _ __ _ __,_ ___ ~ _ _J_. __ _ _ _ ·-·· 1~ · \? ·~ ·. .t, . ·, . y ... '-' I I I.". (... 1 I <.,I ·1 .1. !*' :"'1:::., ~:~l. :::11 111 ... l ! ~; I l ' ' '' '• ' ' ' ' •,.. 1 ,, '' ' ' I\ l l ! ~ !lnr .,., I., I It l l:' !! l i .j 4, tJ t1 l. It J' v j I ,l l i I ll In I . Jv l I: 1;r 11+!"-':i I v 1T ::! :p ->1r 1r .. 7f 0 L\ ·i · ·l · .::.\ + + - >-11~ -l ·p 6 r -·-··--.- -- ·- .- -·---.-- - ·--.-··-·- ,·-- ·- ·-,-- · -----~-- -- --.-·- --··-.-- --·--,.--- -- ..,.- -··- --,··- ----,-----.,..---,--- • I I N I-' N -213- r I i r ,...., ' .~ t . ' J ~ r I ! "' J- T 1 >' -·<l . ' j ' ' -~ ' _J 0 l(~ Q ' C\2 '-"" '/J \t'C: c:S ,...+ r ~ ~ -~ Q ' ~ i::: ,._ - + t::: j i ~ i r r ~ ! N ..Jo o-,,, -4 oz,/qrl) mp /.on I • ""d LI) .-f :> 0 .w (/) (!) .w H ::i ·.-i bi) ·.-i µ.. 4-1 -214- ~ rr+p~1Tr'IT+1T+~- L1-~7r-n rr-p~7T£7T+7T+ Li- il- ~7r-r1 0 rr+ fits fits Pro b(Xiit)~·53 2 2 -tn1r{f) < 0. 6 Ge v. . ;' c (7r+1T+rr-n) mass < 3.7 GeV Figures V.16a - b Invariant mass distributions for the slow particles of the n channel for events within the 6 - peak (see above). '3 c~ L . ... . ... J.. CI . , , :.i 1.0 t \ I t. I I .l 1 ~: : I • ' ' : :, ( , t; : . ~ "rn: I !\' I i ,> i J.1:' 1 +!1J,1·1' ·1,··1: .1 J t .I: .:1"I' ti :1\:: .... :t • • l it t ~~ t ." I : I - I ~ f •1 • I I. t I I I I <> \ ,, I I , <1 , ..., , a 7fr °' ·rrt+· (a) . t • ' I. .+: 1 r, I ' ~· • t • .. ( I I i ·tt' I· ·11· ·1 l 1·r1 '• .... ._," .. ... ... • 1 L 9 0 ....... _,___ t ' I l ·30 ..J_ _-- ..L . .... ... _i___. _,____ __ ~- ~-? ~ ......f) ., . , • · : 1 r : t :,:,' '?+ti' t tt~!J;ti+~%. t ... 1..-._.. _ _.___ ... ( [' . . 1 t,...., "(\ r) l.t 1 I (each event appears twice) Figure V.16a The curves are fits to the N°(1470) and N°(1688). · b 1 .n ~ . J' .f ..J.... ..... .! I r 't l\ f t' r r•'J -- ~-.... · "-· · .. l .• .... ...&..... ... . _ . _ - - - ' -- .. .. --~--- .. .. -.L .. J · ; t' I' I ' ,; .: 1 1 "' II ! ! ,. 1I I ' . ;: f :. I 1'· : r; ::. .! :: t:'J· ! r r ·1·.1' .: n,_:.r:..: : i; 'li.1;1 i. ,, 1 :.\1:1vrr. t· i ' :II f: ,. ~:([,. 0 l I I 1.~ . 1 1 vL:. :i ·t ..l, 1.': . f11 : :·tt lfri, :l j :' .'I :; Ii". :. : '/.1/ fl' i:j":·v 1 · f1;, l . )c · ~YI l , I U j r .1 , ..')"'1 ;I~ J111...".,1. l' 1~l··"1'· ,,,,_. n. _: ) ' : .. "oI :,1.•, , rqv I J _ ~.J' u1 b "-• "d ~ ') L 1 "-1 3 ..n (\) ' 0 ~ ~ ¥'" ~· • ·1 t- -~ 4-. I f. t : I :·1 r,1 'I ! I I I 11.:l:p-·}1rt1( 1-·rr·!·.:..\ · · .:..\·· ·->rr--··r1 5 r·.-·----,- · --·-.· · ·---.------......- ..,... . ...... ..... ...- r ·- ·-·····.-----r----.,. . . -·-r-----. --- --1-·--r·-·--,.----.,.---, . I I \Jl ~ N I l - 1 .fi 1.0 0,0 L · ·u O.r:.,) b •cj -t rl 1..0 ...... ..) .n ....:, __, {'\) D ,. C:) ..... J L ... J . r·· '.) 0 •·- ..........,. ~ ~ j.-· r 2.5 -.... . L ..., . j_ , ·1 / ·_ •. '~ 'j 'I ·- -. -- 1..!. • :~) \: .L. ·L ~ ~ • - .. ., 1 . l. ' .! . I I ' - ·1 •. ' I . '.. -- ., . I I . "! ' ! IfI ". f I I I . I' i •• . I ' ' I. I f :I .,:,'' t 1 ;: ·.i: : -v I'' I J I' - ,' ' I '' I ~. ' .. . . --, t t . I . '\. -- - '. ' ' I I 1 I • • 1 1 ·1 .•......, I 't ;I I I I it ' I I f , I:-~ I • • I ~f 't ' ; f: i '"T • I ' t f ' I,' f I ' I ' I ·· -i ··.. · -r- i."·'\ --· - >·rr •' · n ...... I . . t f t ' I • ., - --- , , f • I • : I I I t ; ' I . : u -> 71 t 11 1 1 f l. Q() ~. L I. I ' - • . I.. I I I . I. : I' I :nr.1.ss !. 'I I : j 1· f I 1 •: I Figure V.16b Tr !·1r'i ·rr ·r l . 4. . I -' I t 1 I I : L I! ' I ' I : : f .1 t I ' I ' - ·,1 . • f I : : I I ' I • , • ·' ,' 11 / ' • ., I ' .. .. . I f t I : : I. • • ' • : t '.)' :! : f f . I I , , • • 1 t t. • L - i (. .J. ..... L- _ ..___ ~o l ). L . 0 I ".I I! '1 :: : Js t, I I"'· : ll ?.• •• ~~ •.J. ,) '-·· ....J.-. •I -- L.----.L.- l . . .. I :• l 1:• fl'v l: II.l"'l 1· r 11 11 tl; ''l· : ·~ r!y l·:·p,,.; 'i· !:J:'r: ,h1"i:: · .l :ii·>I Y: ~.! . I·' n :;.11 ·11 ft.u.:1 ·' I ' 'I f f re· ,v·) I ·, f I I I 0 r ...., • • ) t I The curves are fits to the N+(l700). ..L : "' ! t . . ; I.. '. , I•1 1 !1;~~~~'. d1t~; f' i ·: ':: ~~f-f~. : . t I ' I j I: 1r,+ (b) .. ----v--·---, .........,._.._ , --- ~ I l ' .t !''' ,!' 'i ' 1' .i ' ! \I • ..... , . {.. , 1 , . , : r . , , . ; , 1• • : • : • 1 I : ! :' 11 1 j ' ;': .1: 1t'.i.! : :! :,·'·.1 ::· ::l :·11: ·:I: I: : : I: ,'f', : J :. <1: .,,y,/{1!,, ,;1q1I: 1·:i ! : ·.1·~ r :1 1,,.::11:::: 1: ·::: : ' · ·;:: ·,· I ::111: 1-'X1 :· 1i: -11 ;, ,11 '1 ·.. ., •• :'1 !-> '"'" ' 'l ' •!'1.. .I. ·I · . • l··· ,·l1 :: ,I, , : :1 1; . · ... r:·r .· . i 11 'i·J·: : •.1. I ~1,,,11.:1·1 1 , 1 ; •• 1·1 !·11·• ,..:~'· ·' : •11 I l ' ' ' I' ( ' I " • I •' I . 111 •••1 ~ ! I'l I " ~ ,, ; •:.' ; 1. .i1:ii·t i :'l ·,: · !1 ' ·.~ i i 1Y1'I \ 1 !11:. , !:.1.'11'!"·1'/i 1· ':'1!.;·: .: ~1: l '1111· I r.~11 1 ' I • I :/ I ' ' I ' l "' I ' ., I I •v1I' r I I .! . •ff ·· "f ) . >·n· ·· ·-'7 1· · "'\' • I\ °'I I N f--' -217- .) rr+p~1Ttpo1Top po~;r+ rr c rr-p-->7rr ponop po-)rr+rr- fits fits p 0 -)JT +rr 0. 6·4: d ei..lillLlon: ~· . 1.. rnass < 0.84 Ge\T Figures V. l 7a-d Invariant mass distributions for the slow particles of the for events wit hin t he p 0 peak (see abo ve) . TI 0 channel E1 td ' (\} 0 1.0 0 4 . . 1 .o r-:. -r - ~~~~~~~ Figure V.17a 2.0 rr p rnass 0 . (Ge V) .. L - - L - ' J - The curves are fits to the 6+. - -...L.. .------,-- ---. ... ---,. rr±p--).1Tfporrop po-}1T+1T.-----,------.------, o Trr <> 1fr + (a) I N I-' CX> I 0 •· 'U t;· 1 -· '· .... '-.0 2 3 8 tj (\} 4.--. L ! ) 1.5 --- I I "'. . •': .. ,• 1b:·; ·:>/, i I '> !;, , :_ . l I ' !.L~1I~ft i, i a 1fr <> 7rr +- (b) . I I ' S I ' I O "I I ' " I I rnass (GcV) ' I ' I " O ' . I 2.5 ' .. 1 : fl> . .. ' I I IT~.lf l ~ ~ : J . ~ :..~ I ,• o· . "' ' I fJ I I , O • IQ " . ". l.. I ' I . I I ' I 3. 0 ' t y'.: jJ . V• : . :·ri': ] [i I . I !: :l · :a ·I :,r rl 11111 i; 1 i'!' f \ r:·+!·f 11f.l"t' lilti1.11i,.tf fti!J}t:tll lff 1'-tJ :o: .. Figure V.17b n+ rr-p I · ·- .L- 111!·: rtvl},Ii'lJ: :,: I . . 1 '~iL..... t~: tii 11~'- rt ,11i r? t I.. t 1r\',t11 r1 f'>l 1: · I ' fi !1,1d 1. 1 ' I -.,.-----.----.-......---.---..----.----.- 1r:±:p . ·>n(porrop po->7r+1T- ......---. I I N I-' l.O -220- ... ·~ 0 -221- I t::: .J_ 't ~ L o: c.. ~. I I 0 oJ 1 r ' I 0~ . ~~~J ~r ~ ..... I r ~i -H r ~ I I r r r i 'l;. i;n "Cl 1 t: . d r-i j ,...., > ....11.1 ::l °"'!::: ""' /;)/) Q 0 r--.. •.-l C\i it= +,_ ~ -222- 7r+p~ntporr+n Po-?rr+rro n-p->-rr£porr+n Po-?rr+rrrr+ fits 1T fits <> 0.64 -• mass < Figures V.18a-d Invariant mass distributions for the slow particles of the n channel for events within the p 0 peak (see above). 'd "b·-. 0 1.0 1 ~ 2 ·- .3 3 ·- ................... (\} 0 :-:.1 4 \l) :_:. ,.._ 5 ·- 6 'I t I 11\1: : : ! • I I I I •U· • J: . .1 J : • I t1. "•,: : t I I I 0 .. 1 r:.) mass (GcV) '> "-'· 0 Figure V.18a (each event appears twice) rr+n ~ I. D 1rt + <> 7rr (a) The TI+ curve is a fit to the A+ and N+(l470); the TI- curve is a fit to the A+. i~ rn·· I• ~. ·V.-r~··:jti, t I f •f •• f I • If 0 :1 : I I I t rr± P -> rr rr +Pon P o-r_,._rr.,--1_-1T_-.------.---.-----.----.--.....--~ I w I N N c 2 L 1 • • 1 : ' rr+rr n . ,1 • • 11{;t ~ • : .1 . •r • I I ' ~ I • ·.! t •• : :: ·:;trt..i' ·t"t~··.::f::l~}~·. : :'.::t·.~;· : . .• (J •• •' •tJ' 0: rs twice) . v) n1 ass (Ge - 2. o L Figure V.18b 2.o " : ... . b" : _: • "l• " I :. .. '• " . f. :: :I b, ! :' -L-_.____,,.l ... v. ~J:rf: f'J1·:ilT1~J*fi;~!'~tlt:~ I o 1fr <> 7Tr + (b) .. :·I: 1·II ?l: : flTll':l'll:: }t: 1~1 . Ji:t1 f· ::: :':'!tf H°ff Uil'. 1 . (each even t appea I • I ..... j.~ .'1 .'I ! .: : fr ~-: ' 1'I• . i :, :: /, . i;' !" I I i : : : \': ' .. ' . : " ·1trr·· :,\'tJ' .I °'1: 1j,.~ r" ijn· ;-"I i,11 • I• I .' '' (lo ~ rr±p--?1Ty=rr+pon po->rr-1-rr'-- 0 -- -.---------.--1--r--,---r--r--r--...----.---..--~---.---.---. ~~r. 1 ,5 . · ·- n \.>Q ) . . --,.- The TI+ curve is a fit to the N°(1470); the TI- curve is a fit to the N°(1470) and N°(1688). • 0 -· 10 . 'U 1 """ ·b 'd s .. 3 ..a ...... ... g3 , ~ Q,) ;> ,,.......4 o 1 I N N .i::-- ./ -225- l E:: lf.> J°j ~ [~ ._._. . . _·~-·. . _.·_~·._. ·.~''-'----~·~·. _.!_~1._. 1_~·--·~l~_._.._._,ic: oo __ (") N ~ oz/ qrl) mp/..o p - 226- . 0 M l l::: + t: A l 0 o. . 0 ~ c... . ......' . IJ":) N . . . 1..1' 0 .-I ...-! (A~n 02/ qrl) mn• I / .f)P 0 N l1' • I 0 0 O--' 0 . -227- ~ 1T+p~rrtp + n-p 0 7T - p+ ~1T+1To p '1T p p -?7f'7T 0 1T+ fits ········ 1T fits - p~rrf ..1.. .l. -- ' j Pro b(xiit):>5% -t?Ttr{f) (rr+n-7T 0p) 0.64 2 < 0 .'6 Ge V ,/ c 2 mass < 3.7 GeV p+ -77r+n° definition: ~ rr+n° mass < 0.84 Ge\: Figures V .19a -d Invariant mass distributions for the slow particles of the for events within the p + peak (see above) . n° channel 'd 'd ._ ' "-·. b 1 f:1 --~ .n 2 ·- '·~ ....N 0 ~ >3 (t) ,..,..._ 4 --~ 0 Figure V.19a 7f-P mass (GeV) 2.0 ___...~___...__ 0 i- Trr a 7rr Q I,...,. The TI+ curve is a fit to the A ; the TI- curve is a fit to the A and N°(1470). 1.5 ~~~~....__~....L...~_._-~__,_~___.._ n±p->rr{p +rr---P p + _>rr+ rr 0 I CX> I N N ...._ 'lJ b ~cs El lo......;,_} - ) 0- :1.0 1 ..r:. ...... '} ...., ·- [\ } L) ... ) ...... \l..) ~ . 't. } ~ ,. ' 1 r , l.. I. - 1- r -~ · --r - -- - · · · - .J.. • ~- '- !. 1.5 L I . I _, , • l ' I , I . 1 - .L . •• l•' •.1I.1: ' '' ,_ I' <) L0 - . L . . ... ~. Figure V. l 9b ,.r· i-1,.1)'. I • ..., > !.lHtS S -• · o : 1;. ' ... • :"..11,··· ,; l, ,. • I .-.j • 1,: ' I_ . y .. ' 't L \ r r· \.l l~\, ' r) I, L {' . . ' .~" ' ) " I ' '-'" ') I • ·1 '' I I . '( ·• .... 30 ' """ l CL• ... . ...'. ..., 1, J , . l, 1,$- I ' !,t: ;;,, ' ·• J LI i . i"j-'1 • . . , -• ) ir. ~ . . ~ ~. . ~t~ !. I ""'. ' . L;:: .... "" "I . .' ' > I · :'::,e .:!lf!1··1 ~11·· t:f4~tl:,1l:·:hT11H i f 1.~ ,: . 1 _ · • . ··r·I"··'./ f· 11:--1 · 't :·:. .: i:.... ., ., . :r :. i .. ; '> : : .. . . .,I}I. I · " 11 c•I". •:1.lI . '.•'1·1: ·.,~ ,. 'r.I rI! ,' .. . " " I ' ' : ,\ti . ' : ' " I. ' . . I " , , ,. :.:,: •• : ~. ., 'I ' . ,i.; : . ~· , ' •: ' • • The curve is a fit to the 6++(1890). , /." t''.J... ' ''.. ;" I: ' " " : .;. 1rr u 1rr v (b) ·- - r··· .. ····,-- --- ---, - - .... -r ·- -···-- r - - --........ · - ·- -.....,.--. • - u. ',1:·,;., ; :: \'· I:!: .: ~ 'i: i 11 -:·!. : '1"' r • I1 ' ,• iI, I I . • ,, j l .. . ;: : : r" . i: . : I .::' .; •'I : l 1··1-1· .•.. I / ' I. , ,,. "J ·· -· rf~ll1,' .' ' ,I ' ..,. . 1 hf l .:. I, i '. \f!1~1~ 1. :11 }l 1.! l, I .. . ~li I .III, 1/TrJ l! ·: n\°' I Ir ! 1j l:: !j II vi !l •I I -· -,-.... ._,... ··- --r···- ....,.,... --·- - · i·- ·. -- -, - - - -r· · - "'" 1 . . -rr=::I)->1rr o·: ·1'( ·n fJ-:- _>1r-1·rr 0 '°I I N N -230- ,,_..,.........,...,....,.............,,..,....,......."T-i-.,......."?"T-r-r...,...,.-.-.,.._.'?""T"'"!'""T........._...P""T'""....._._............ ~ N lO 0 ._._. . . . . . . . . . . . . . . . . . . . . . . . . . . . . _. . . . . . . . . .__._._. . . . .-.............._._.._._.__._._. . . . . . . . . . . . . o ....... oo C\l 02/qrl) mp/.op b 'd '-- .. 1.0 0t ~1 3 .n """--- . N 0 ~2 Q.) > ,,.-.. 3 t • 1 I 1.5 I I I D 0 1 1 ' II 1 • ' I 0 ·:,.a..,, 1 I . I I I I 2.5 I ,t : I rnass (GeV) I t Figure V.19d I J..1 tUI 1 • n+rr-rr p 2.0 Q .ff 6 ~ ~ ¢1i' . ·:.i J ~ 'i t\.J t } I : 1 ::• : I I t'a : : : ti t t I I II I : 1 I I 3.0 tI It II t t I 1 1 1 1 It ..... t 1'1'I : (I & I I ~I • j 3.5 . ll6"f"1lt 1:.• :• :::•••:_ Qt I : a 1rr <> Tri + (d) Ii i i !! 11 ~I .t .1. 111 : 1~1f:.1 ,~,~:: ·m o:.:.:UY.#jWi1' .: .·:a:.•·1r:• ..: ··: !:6:it· ·1·m:1· ¢:..tfP . ? . ~I ;X· I: : b: I.::!~}::: l? :rm. 'J91l:l''• 1 n±p 4 1Tfp+1l'-P p+ 41T+rro I N I I-' w -232- p- -~1T-1fo a 1T p-)>1Tfp-1T+p p- -~7T-TIO <> 1T+p~rrtp-1T+p fits fits Pro b(xiit)25% -trr7r{f) ·( (rr+n--n°p) 0. 6 mass Ge V 2 ; c 2 1 < 3.7 Ge 1/ definition: 0.6~± s: rr+n° mass <~ 0.8 . .1 Ge\; p- ->7r-1To Figures V.20a-d Invariant mass distributions for the slow particles of the n° channel for events within the p- peak (see above). ........... . .... N 0 8 1 I r 1 (GeV) p- -}rr-rr 0 The curves are fits to the 6++ Figure V.20a rr+p ~----L-- ' rr±p-->1r{p-rr+p a 1fr - (a) I N I w w I -234- 0 l \:: t:: ,...-.... > ..... ; <:) I ~ Q.,, ~ \/} 0... -' 0 J N ~ l I . cd Vl ..Cl 0 N s ... > Q) c.. -H~ c. 0 l=:: I 't- .+I l- " O.i -H ~ I l I [ ~~............'-l....o~L....l.....J'-J....l~~-J...J~_.__.~....1-..L~~...:....:.-l.-J.~~o N ..... 02/qrl) U.lp/.op o~ :i .,..,00 µ.. -235- LO --o- C\i •-i."':l ............ ~-1t::: l:: 0 .............. ¢ -<)- 0 (.) 0 N ~ " ~---;~---. . . :::;:.-, ~~:..-· --<!>- _.; ·--· ·---t~ ..:::=;-3=- •• :.:-o-•-_-"'>..~ 1,,,,.r••• -~ -_o,.!_A" ...... ~- ~ ~; -236- 0 . ~ 'D 0 N > r t l ~'--''--'......--"--"....l..-'--""'_._....__._......._.._,.._..._...__..__i.......1'--l.__..__.......__._.__,_-1,....._~~ N (At}f'i oz/q1i) ...... Ul"O /.op '" I 0'1"""1 -237Chapter VI Production of the n 0 0 and w Mesons 1. Introduction We can study the quasi - 3- body reactions involving the n 0 0 and w mesons: + rr p ± rr p + 0 ~ rrfn p ~ rrfw p + - by vir tue of the rr rr rr (la) ± 0 0 (lb) decays of these mesons. These reactions have been studied in other experiments (see Chapter I) which for the mos t part concentrated on studies of the B(l235), A (1310), and g(l680) 2 mesons which decay into rrn° (A ) or rrw 2 0 (B and g) or studies of the 0 quasi - 2-body reactions with a 6( 12 32) produced along with the n° or w meson. By probing t he diffractive dissociation re gion, our experiment has accumulated even t s in a relatively unexplored kinematic region for reactions (la) and (lb). Our experiment observes relatively small cross sec tions for reactions (la) as compar ed to those cross sections observed by o t her experiments . from A 2 However, few of t he n's we observe come decays while other experiments found the A 2 to account for a substantial portion of the n° production [Baltay 1978, Kennedy 1978, and Sisterson 1972]. Our trigger rejects most events from the conversion of a beam pion into an A meson. 2 + The rrfn 0 mass distribu- + tions show an A- peak (see Fig. VI.l ) which was removed by a cu t to 2 avoid the trigger - imposed biases. The remaining n° events come from nucleon diffractive dissociation processes, but we observe that the -238- + 0 - 0 cross section for nfn p is about twice the cross section for nfn p. This is a surprising result as the cross section for diffraction of 0 the proton into an n p system would be expected to be independent of the type of the beam particle. The data and a further discussion of this result are given in the next section of this chapter. 0 Our experiment also observed w reactions (lb). production in the quasi-3-body 0 Here again, as for the n , our data is limited to a kinematic region relatively unstudied by other experiments. The B 0 and g mesons and the w 6 final state have been extensively studied in many experiments (including those listed in Tables I.3 and I.4). We do have some events from t hese sources (except that t he B is not seen at all) as was discussed in Chapter V. However, in contrast to our 0 data whe re we have no overlap with o t he r pub lished results, w n0 produc- tion in our kinematic re gion has been studied by other experiments with rather sma ll statistics. These studies have been of the low mass 0 w p enhancement (see Chapter I, especially Tab le I.7 ) . Several exper0 iments (including ours) have attributed this enhancement to the w p decay of an N [see for example Atherton 19 75 and Mi l g ram 19 70 ]. We 0 have examined the angular distributions of the w p system but have not determined the spin-parity of the N in the final section of t his chapter. due to inconsist encies discussed -239- rr±p->7rf1J OP 10 .... b n·1 ,' '' J J '' ' • • I J ~ 1 l.J • : l I l I.. j r I l l.U uI i 0 1.0 1.5 ?Q '""-". ?;_,,. b- 3.0 rrf"n° mass Figure VI.l ± Plot of the nfn text) . to + 0 + - mass spectra for rr rr r. 0 masses wit hin the n Events below 1.6 GeV were excluded from the A2 decays. ~ 0 0 cu t (see analysis as due h n o events .ave h ± o mass a b ove 3 . 0 GeV. Mos t ot- t.e a rrfn -240+ 0 2. Tifn p Final State We have observed reactions (la) as part of the final states: ± + - ± 0 (2) TI p-+ TifTI IT TI p + - by virtue of the rr rr TI 0 decay mode of the + - the do/dm distributions for the rr rr rr 0 n0 meson. Fig. VI.2 shows mass in the region of t he n0 . The curves in the figure are the result of fitting a Breit-Wigner resonance shape (with f(m)=rR) and a quadratic background to the data. Although the width of then 0 peak is due to our resolution (see below), + - 0 mass (rather t han the existence of a spectrum of errors in th e rr TI rr a single fixed value) modulates a gauss ian i nto a Breit-Wigner shape. The results of the fits are given in Table VI.l below. Table VI.l + - 0 Fitted parameters for n +TI rr TI rr 0 peak + Mass (MeV) 548.3±1.2 554. 6±1. 9 Fixed width (FW1-lH, MeV) 12. 5 12.5 Events in peak 200±31 91±23 Observed cross section (µb) 2.52±0.41 1. 33±0. 35 Corrected a ( µb) (for unseen decays) 10. 7± 1. 8 5.6±1.5 Fraction of estimated 28±8% 25±14% 0 o(rr p-+Ti n p) (Table I.6) -241- Figure VI. 2 + - Plot of do/dm for the TI TI TI 0 invariant mass in the region of the 11 The curves show the results of the fit to the 11 the text. 0 0 peak as described in The dotted curve shows the background distribution result- ing from the fit. ........... _ (a) ..,,,. .;.. n17 O I Ii _:..J { r!° V ? ;; ') _; , 3 9 11 -·- ;..., , V ..._. - • - 1 (J, ;J 0.8 0.6 rF ~ ,._.._, 0 ·1 r ::> .~ (J) ~ r r [ n ·) L v . :....i : ~i \...") ~ fI ~ 0.0 I l"'a 0 II I '; (b) 7T;p7J 0 a 11 =1.33±.34 µb / ''\ q v . ._, I ;- ' .. ;1' .~ v r> G ;- i ; .r '' r .. I.. v . -- ~ /""\ ::-.,, 'v. ' po../ J :- I (\ l"I n ( . I'°', ·-:.: 0 U .r ·. • vv ,~ .,· · I 1 ...l... , .r'"'."' - -- ..,.: (' ·...; l I I .,.~ .l :. - Figure VI. 2 --":) . . , c C: , ~ ~} ''t -- \ :\ ..... "1 n \ti ·; ~ ... ....... ' -243The mass of the n0 from the rr + experiment is in good a g reement with the accepted value of 548.8(±0.6) MeV [Particle Data Group 1978], and that from the rr experiment is high due to a slightly incorrect value used for the bubble chamber magnetic field while processing the rr data (see also Chapter I V) . 0 w This same shift is also evident in the results (see below) bu t does not ot herwise affect our results. fixed widths of the + - in the rr TI rr 0 mass. The n0 are from our r eso lution of 12 to 15 MeV (FWHH) A fixed wid th wa s used as the lo w statistics and narrow peak make the widt h poo rl y determined by t he fit. The results from varying t he width in the fi t are 12.5±3.4 MeV for the rr+ and 9. 1 ±4.2 MeV fo r ~he TI peak. The cross section is give n in the table as fitted and also corrected for the no -¥IT +rr - TI 0 branching r atio (23.6±0 . 6% [Partic le Data Group 1978]) . The er ror on t he corrected n 0 cross section is domi- nated by the error in the fitted cross section and includes the errors on the normalization factor and in t he branching ratio . ± Immediatel y 0 apparent is the factor of two in t he rrfn p cross section for the change in the charge of the beam. We have examined the TI in the fit selection process. 0 data for an excessive loss of n events No evidence was found for losses large enough to account for the c ross section differen ce . We also examined the missing-mass-squared spectra of the two prong reactions: ± + rr p ~ rrfp + (anything neutral) (all OC an d rr 0 t wo prong events) for n 0 (3) peaks fr om reaction (la) with -244the n° decayin g into neutral particles. We found small peaks at m2 n whose sizes were consistent with the signals from reaction (2) and the factor of about 3 from the ratio of the all neutral and ing fractions. + - TI TI TI 0 branch- Though reaction (3) has more n° events than reaction (2), the l arge background under then 0 missing mass peak and the b r oadening of this peak due to the low missing mass resolution (compared t o the + - TI TI TI 0 peak) make this data serve as a check only a_nd unusable in our analysis. ference in the TI + and TI Altogether, we found no evidence for a dif n 0 cross sections due to a technical problem rather than the physics underlying the n° production. 0 Fig . VI.3 shows the n p mass spectra from the t wo experiments. The n 0 is defined by cuts in the TI + TI rr 0 mass : 530 through 570 MeV for the rr + experiment and 535 throu gh 575 for the TI experiment. cut was shifted by 5 MeV since the central value of the n about 5 MeV high. events within the n 0 n°p mass above about 2 GeV. TI the n 0 0 0 decay. mass on l y eliminated eve n ts with an The histograms in Fig. IV.Ja are for events to e ither side of the n° peak. rr peak was cut except fo r the eve nts from an A.2 +'IT n + 0 + - TI The spectra shown in Fig . VI.3a are for all the The A2 cu t at 1. 6 GeV in the rr ~ n [ TI 0 The The n° wings are defined by the mass region of 420 to 600 MeV except for that ?Ortion wi th in peak cuts given above. These histograms hav e been normalized to t he number of events in the background under the from the fits to the TI + - 0 rr rr 0 n peaks as gotten mass spectra discussed earlier. 0 The n p mass spectra in Fig. VI.3b have these background distributions sub tracted and show no significant changes from those in Fig. VI.3 a. -245-1- ....L. rr~p->rrfTr .J_ · 7T - Tr 0 p 0.6.--,-,.-~~~~-r-i-r~~-r-T~i~j~•in~1~ · 1~~~0~(~~~~~·1~~~~)~.~ Q 1Tt a rr{ 0.4 . '!]o mngs nt 7T% ·~ a :r/ (no rr; 7i'r I !·~ -:>· • • 11 • . 1.5 ? ·O .,..J, 2.5 1J 0 p rriass ~3.0 \'G-e ."". . . ,; " J Figure VI. 3 Plots of the n0 p mass spectra for the rr + and rr experiments. The upper plot (a) is for all events within the n° peak cuts (see text). For the lower plot (b), the background distributions from events under the n 0 have been subtracted (see text). -246- + - Figs. VI.5 are scatterplots of the TI TI TI 0 + - 0 mass (each event corresponds to a single dot). While the n clearly seen for the TI + data (Fig. VI.Sa), the n° band is barel y noticeable in the TI events in the n 0 data. The rr 0 mass versus the TI TI TI p band is + data also shows a clustering of 0 0 band near an n p mass of 1600 MeV where the n p mass spectrum shows a peak (Figs. VI.J). The da/dt iTTI distributions for the 0 n events were fit with the functional form Aebt giving values for the slope (b) of 6.06±0.97 (GeV/c) -2 for the TI + data and 6.78±1.58 (GeV/c) -2 for the rr - data. These slopes are significantly lar g er than those found for the overall + -1- 0 - TI[rr'rr rr p data (Chapter V) and are consistent wit h ge neral observa- tions of the t-dependence of ~ * production. The Feynman diagrams in Fig. VI.4 illustrate two processes that could contribute to the observed difference in the TI sections for n° production. + and n cross The use of Regge exchange terminology provides a f ramework for discussion, but not an explicit explanation of the difference. The interference between different Regge exchanges from the top vertex could account for the cross section difference. As a simple example, let us Pomeron and p exchange parts. from rr + ton (i.e. term is changed. examine an amplitude made up of both When the charge of the beam is changed from particle to antiparticle), the sign of the p This leads to a form for the cross section ~f: .;~ + 2Re (Pp ) (4) where the Pomeron (P) and p interference term accounts for the differ- -247.l- rr- (a) ..lo 1!'[ •• i• P1P1··· • CJO I :R I p p (b) . I !·' ;·p , ... : J..) I I I .t w .0 p Figure VI.4 Feynman diagrams illustrating possible processes involved in our observed n° production, including double ~egge exchange (a) and t h e production of an N* that couples to 1° p (b). -248ence in the rr + and rr cross sections. The sign of the interference term in equation (4) as being the same as the sign of the beam was arbitrary and suggested by the data with the assumption that Re(Pp * ) is greater than zero. 0 The n p mass spectrum (Figs. VI.3) for the rr + experiment shows a peak center ed at about 1600 MeV with a wid th of about 100 MeV (FWHM). The rr mass spectrum is suggestive of a slight dip of marginal statis - . tical significance at the same po s ition as the peak in t he rr + 0 - + spectrum. 0 About 2/3 of the difference in the rrfn p and rrfn p cross sections . b e l ow 18G comes f rom t 'ne · n o p mass reg ion . e V. The peak in one mass distri bu tion and t he marginal dip in t he other are consi s tent wi t h the simple model discussed above. Here the N exci tat ion illustrated by the Feynman diagram in Fig. VI . 4b may have both Pomeron and p exchange (or some other negative signature trajector y in place of the p) con tributions wh ich inter fe re. As discussed before , this could enhance the rr + cross section and decrease the rr cross section givin g rise to a peak in the one mass spec tra and a dip in the other. There is a 0 well known N wi th a lar ge n p branching ratio [Particle Data Group 1978 J. 0 The N(l535) decays about 65 % of t he time to n p, but it has too low a mass to be completely consistent with its interpretation as 0 1 • the cause of the n p peaK in the rr + da ta. ± 0 In conclusion, our results on the rrfn p final states have shown that the rr + cross section is lar g er than the rr cross section. A s ig- nificant part of this difference is due to a peak at 1600 MeV in the 0 n p mass distribution of the rr + data and a l ack of such a peak in the -249- 1.0 • 0 • • •• .• ....• • • • • • • .. .. •. • • . • • .. •• : • • •• •••• • .. • • • • • • • •• • • • . • ·.1. . . .. • .. •• . .• ·' ., • . ..... • • • ~ I t:: 0.6 + f:: •! • • I • • • • •• • •• • • ••• • • -- • • • • , - • • • • • • • 0.4 1.4 2.2 mass (GeV) 2.6 Figure VI . Sa Scatterplot showi n g t h e correlations bet ween the and the 1T + TT 0 TT p invariant mass for the TT + + + - p-+:! f ;T 1T iT +ii - 7T 0 0 TT invariant mass p channel. - 250- ........, •... ..... • • .• . •... ... ··r1,•" ..t.•··-· .... • .... ........ .,. • >" •• • • • \ : .., .. ..·..- .... .. ,,.... ........ .·,. . ., , .•_....,_,.,.,.,_4-. :• ,·.•• ',... .• ... . . . . .. -·-··.,,......,. .., \•• ;. .•....• • ...•: ..~ .... . \\... .a".·-.·.··.-.·JO. 1.0 • •• ., .. ·~:i.t~· ~ • • • • • •.I"~· ~ t)- •. •• • ~.... ~· '.I: •.• -~,· ;. , , •• .i :i"~ • .. ....,~ •lit"" .._. ..... ~,,..., .... (. ••• r~~ •• •• ~-,••Z. ., ~ ••• : .'If • • ~• • • • "' •• t~ :~ • • • .. • •, _. • • • J. .v ; ••• \. • • ,., ....•••• • • "'· • ~ I •••• -o" • • • .._ •• • ••• • ·~,~. • ~.. ~-.~ ..... ..,.. 'I". • 0 ~ . ~~ • • ,., • ~ I ...,. • It • • .. " .: ·~-: •~JI "\ <>o~ <'(': ••#• •• S •• ........,r•.pt!! .~. ,,.,.. ~ .,,. ~ •• 1.; ~. • • •• .. .. 11>~1i_·t.\~l~....~·~,~1~p.,::.J:-.y· .. ·<? ···' •• : ""' ""' ·-;: . .. . ., ·. . . .. ··.t " ............. •:. . .. . ... ...,.. .... ....... . . . , . . , ...... . .....:r.:... ..•:'1-.·, .. .·....... ... ..• .• • • . .. . .,.•"'I.' .·- • ..... . .• ........:.. "-: .,..... .. .. ·.. . • ••• • ....• ••••• • • •• • • • •• • • ...·:.·. ...........·>. . •••• • • • • ••• . . .. ... • •• • • ........ : ..\ ·.•.. ' . •. • • • • • s • •• .... ... .. ..·-- ... ••• . • • .... • • .. • • • • • • •• . 1ltl .,~ .....-.. . ,-..,. ~ \--.-.::w.. ~ ~ ~-. .,,~:. i ~~ ~ 0 • • ~ t i • • .. ~ I ~ 0.6 • .•• ,/ • ••• , • ~ , •• I • ~ ••• ~ ·I".: ••• "If~~ ' .'l>·~ &j .. : ., • o ~ 'l>:t rr'l&.~t:f~"" <# ; . . .~· •t • •. I'\ •• •• •• • • • •• • • )•• + •i ~ ~ \ ~· • • • • • • - • • • • • • • • 0.4 1.4 2.6 2.2 mass (GeV) Figure VI.Sb Seat te rp lot showing the correlations between the and the IT + IT 0 rr p invariant mass for the rr - + - p~rrfrr if +IT - :i 0 0 invariant mass rr rr p channel. -2510 n p mass distribution of the data. TI This difference can be under- stood by a simple Regge exchange model where a vacuum-like trajectory interferes wi th a negative signature trajectory . The sign of the interference term is dependent upon the charge of the pions at the beam and fast pion vertex, enhancing one cross section and reducing the other. By looking at the TI + TI rr 0 0 0 decay of the w as we did for the n , we observe copious production of reactions (lb). The scatterplots in 0 Figs. VI.5 show densely pop ul a t ed bands a t the w 0 clu stering of events near the w p threshold. mass with a dense We find that there is a relatively narrow (compa r ed to man y other baryon resonances) enhance0 ment just above the w p threshold. Previous results on this enhance- me nt by thi s and other experiments were surruna ri zed in Table I. 7. Fig. VI.6 shows t he rr+ rr - rr 0 The prominent w 0 0 mass spect ra in t he region of the w . peak has bee n fitted by a Breit-Wigner shape with a quadratic background (see discussion of t hen 0 these fits are summarized in Table VI . 2 below. peak). The wid ths of the + - 0 pe aks are due to the finite resol ution in the rr rr rr 0 MeV in the region of th e w (FWHH) . The results of mass of about 28 The erro r s on the cross sections in Table VI.2 include the contri bu tions from t he normalization errors. No tice that unlike the n° case, the rr+ and rr 0 tions for the w errors). p ro duc tion cross sec- are nearly equal ( in fact t hey agree within their The approximately equal cross sections would indicate t ha t -252...+- n ..... p ~7Tf..I- p7r +rr - rr 0 Fits to a. . . . . . -. . . . . . . CJO peak ...-.--~-.-,.....,....,._,_..,_,.....,_,_,....,...,...._.....-.-...,..........,._,..-.-..-.-.~,_.,_,,.....,.-,..__., (a) n;pw 0 cr'-'=38.9±2.5 µb 6 4 (b) 7r£pw 0 erc.>=36.5±2.8 µb 4 2 o~ · ~ - __._._..._.._. . . . . . . . . . . . _._.. . . . . . . . . . . . . . . ._._. . . . . _._.__._. . . . . . _._._.____. . . . . . . . . . ~ 600 700 800 rr+,rr-1T 0 mass 900 (lvie\') 1000 Figure VI. 6 Plots of da/dm for TI + - n " 0 0 masses in the region of the w . are the results of the fits discussed in the text. The curves -2530 only one trajectory was dominately responsible for the w (see the discussion of the production n° production). Table VI.2 + - 0 Fitted parameters for w +'lT rr rr 0 peak + 784.19±0.76 788.45±0.95 Width (FWHM, :teV) 26. 7±2.3 31.8±3.1 Events in peak 3086±197 2518±191 Observed cross section (wb) 38.9±3.1 36. 7±3.4 losses 39. 7::::3.2 38.2±3.6 losses and unseen decays 44.3±3.6 42.6±4.0 48±8 % 68±13 % Mass (MeV) Corrected cross sections (µb): for low t t 1T1T 1T 7T Fraction ob estimated total a( rrp+iTw p) (Table I.6) 0 events were selected for further study by cuts on the The w 1T +1T - 1T 0 mass at the w0 peak: 740 to 820 C-IeV for the 1T + data and 745 to 8?- :J :!eV for the 1T r data. The ratio of the full w 0 Breit-1.Jigner to the portion within these cuts is used to correct cross sections (such as 0 0 that of the w p resonance) for those w This ratio is 1.261±0.097 f or the n events on eit.h er si'd e or t.h e wQ 0 r ( eve nts lost by this mass cut. + and 1.319±0.090 for the rr . ' tne wQ wings 0 0 effect of the background events under the w ) The were use d to stu d y t h e peak. The wings were defined by cuts of 600 to 960 MeV excluding the region selected by the 0 w peak cuts. -254- Figures VI. 7a-b 0 Plots of the weighted A distributions for events in the w 0 solid histogram) and in the w peak (the wings (the dotted histogram). The dotted line is a constant fitted to the wings data and t he solid line 0 is a fit of (a+bA) to the w peak data. 200 in WO cut wings cut (outside . I 100 I I I I I I • T • I I I I 1,.J,.. I I I •r• I I 1 I I I I I I I ... ' I I I I JI , t I I I 1 1 It It 1 I I 1 I 11 I 1 t ., I I I 11...a.. : : : : : : : : : : : : I I 11 1 1 1 : : ::+: : ::: : :: :::: : : t t I I I 4 .. : : : , .....• t I 1, I I I : : : : : :: 1 I t •r• I I I I I I I J : I t I I I JI I 11 a ti I I I I I .. • • I t I t I t I' 1 1 I I I I I I I 1 1 t 1 11 '' • .... : ! :: : : : : : 1 1 I I I I 1 I I : I I:: : : : : 1 I :: .. ,., r ·T~~T•·----· "\-r-1-:- .. ·:-•,,.,...- • .. I ....'• I I : I"'\ : I , I: I : t It ·t·•11·~~~, ~---:--;-~r ::··~.! : : : : : : : : : : : : I : I I t 1I1 I I .,I I : : t.-f .! I: : : :• I I t I I 111 !.~! I I I I I I I 1-6..11 I I I I I I I I I ~~ . I 1 I: I 1 I 1 11 I I 1 ·•r··t•• I I I T• I I t It I I •-:-1 I : I I t I I I I I I t •y I I I 0 0.0 0.5 A 4lp+xf5_1 2 /3(~f~/9-m~) 2 Figure VI.la 1.0 -256- p47Tf 1r+ 1T-1Top 1T 200 in WO cut wings cut (outside 100 ...... ........ I I f • I t t t : ,,. t 1 1 : 1 1 I .:: : I : ,;-. I l.t"'\ ; ...._1 I I ,1 I 11 It I I: I : : • I I: : I I I I ·~-. t 111 I I I I : : : I t I I I . !I:! I •1 It I I: .! :J .. ::: 11 I I I -~: :!!: :: :::: : f t I I I I I I ! .~.! : : : ; t I I I I I I I 1•1• I I : : : :: : :: :~ ! : •..... I t I I ..• I I : I ! : : : 11 I , .. I t ,~~~--4~~·-··-··r-~--I I I I I I I l.J-1 I I I .. •' • ~J ~ I 0 0.5 0.0 A 4!p+xp_l 2 /3(tvf~ 119-rn~) 2 Figure VI.?b 1.0 -2570 We determined the number of background events in the w peak cut from the integral of the background distribution gotten from the fit to the rr+TI-TI 0 mass distribution. This result was checked by studying the distributions of the radial Dalitz variable, A, for events in the 0 w A runs from l a t the center of peak and wings (see Figs. VI.7). 0 t he w Dalitz plot to 0 at the edges and is g i ven by: 4 1-P+ x :P_ 12 (5) 3 (M2/9 - m~)2 w -+ -+ where P+ and p + - ,, are the 3-vector mom e nta of the TI 0 (or rr TI TI ) r es t frame, X w mass of a pion. 0 t he n o n- w 19 75) . 0 For w is the ii + TI TI 0 + and TI 0 in the w invariant mass, and m is the TI decays t he A distribution is propo rtional to A; events show up as a dis tri b ution uniform in ,\ [Atherton Thus in Figs. VI .7 the A distributions for win gs events ar e 0 flat while those for w peak events are linear in A on top of a con0 stant piece f rom the background under th e w peak. 0 The w peak data was f i t by a+b 1\ so that t he value of a correspond s to the number o f 0 bac kground eve nts under t he w peak . The results of t hese fits agreed + - with t he background inte gr als fr om the n TI TI 0 mass fits. A we i g hted + - 0 av e r age of t he results for the w background from fits to t he TI rr TI 0 mass dis tri bu tions and the A distributions (Figs . VI. 7) gave 23.7±2.0% for the TI + and 21.1±2.4 % for the TI Fi g . VI.8 shows the da/d t 0 in t he w peak. IT ii - 0 w backg round. distributions for t he ii + and TI events These distributions were fitted by an exponential and + -? gave slopes of 4.68±0.24 (GeV/c) - for the ii data and 4.99±0.27 -258- Figure VI.8 Plots of do/dt 0 IT if (beam to fast rr ) for events in the w curves are the results of fitting Ae bt to the dat a. peak . The -259- rr±p 41Tf Wop 103 ..--.------..--.---------------------- 10° 0.0 0.1 0.2 0.3 0.4 -tmr (GeV 2/c 2 ) Figure VI.8 0.5 0.6 -260(GeV/c) -2 for the rr 0 to correct the w data. production cross sections (Table VI.2) for the loss of events at low I t I. ' rrrr the rr The results of these fits were then used These corrections amounted to 2.2±1.8% for + cross section and 4.1±1.3% for the rr 0 tion, Table VI.2 gives the w 0 the unseen w 0 + - w ~TI TI 0 TI cross section. In addi- production cross section corrected for decays by using a branching ratio of 89.6±0.6% for the mode [Particle Data Group 1978]. 0 Fig. VI.9 shows the w p mass distributions for TI+ and rr 0 in the w + - peak. events 0 The histograms show t he TT rr TT p mass distributions 0 for events in the w 0 wi ngs rescaled to the w so as to represent the non-w 0 peak background integrals 0 background signal beneath t he w peak. 0 The scatterplots in Fig. VI.10 show that the w p peak is not a reflection of a ± 0 rr~w r resonanc e . In addition, Fi g . VI.lla indicat es that the peak is not associated with the 6++ resonance as the n +p mass distribution has its maximum at about 1150 MeV (well below the 6 rnass) in the 0 region of the w p peak. tion with the 6 ++ 0 The events in the w wings show some associa- as can be seen from the band of events just above a + rr p mass of 1200 MeV in Fig. VI.llb. 0 The curves in Fi g . VI.9 are the result of fittin g the w p mass distribution with a Breit-Wigner shape (f(m)=rR) and a po l ynomial background giving the parameters in Table VI.3. The cross section errors in the table include the contributions from the normalization errors. 0 Table VI.3 also lists the peak cross section corrected for w 0 events in the Breit-Wigner tails outside the w from the mass distribution. The lo w I t rrTT peak cut and so lost I loss corrections of 3.9±5.3% -261- + n;ci'p x ,,.;-wop {JJO CiJ 3 0 bkg bkg •• • t • i• '• t 1 2.0 2.4 w p mass 0 2.8 3.2 (GeV) Figure VI.9 0 w p mass distributions for the " + and rr data. results of the fits described in the text. The curves are the 0 The histograms are the w p mass distributions from the backgrounds under the ~o peaks (see text). -262- 4 •• •••• ••• • •• . .. . .,,.. "'i:...• •..• •• •'!-•• • •••••• • •••• • •• • ..... .. ··: • • • • ::.. .... ; . .. . : :. • ·'f1'..,.. •.. • • • • ..,, •• ' •• • •• • , ..... ... ...-.'.·:.. .. . • • • • • • > •: •• •I• • • .• • • • • .s··,.":...... .-..:......\ ...·.s.·... . • • • • • • • ......... .. , • ••• . ·......: ,,,,...,....,.,.... ..... · .. • ... • . .. ~ .. • ..• ,,,,......."...,..,.,'\__ ;.•s.......• ,·.... • • • •• • .. .. . .i'. •..•.... • ,~·: I • ~ • ~: • i6' I ~ ~·. \ -~ .·~ • 'f' ,. ... ': . . '!'J.. •• ..,. ~ " • " •iV• • • ~· . . . . . , ·: • ......s. •• • .~ - ~ • I ~ t. ~ • ·- • •.:;,•( '• • o• • • • ---~.~ • _. 1"• • ~, .... ...... •• • • • • • ••• • '"'· •• ..."'(1: • ~· • " #- ·- • • • • • • ~~ ·v('"; ~· .. •• .•• • • • • ••••• • • ..... " ... .....,. .. . . • •."" .· :-.i • •• •• ••• .. .. •• •• ... .•.:-." ·. . ... • • • .,, ...... . ,\..... :•... .. ..... . •!• •• •.. ,,.. • • • ': i. ( ....~ :·.. : • • .. : : : , ,..~ =,~ - 0 3 +'M ._ 2 :·.~ :..~, \ . •."'( ¥1 ·- • ,•. t::: • ~ • • I • • • • ..,~~ • !\ \ .. 1"". • • •• • • •• • • ••• •• • 1 1.6 2.4 2.8 3.2 mass (GeV) Figure VI.10 Scatterplot of the " + 0 invariant mass versus the w0 p invariant mass _ l;J r 0 for events within the w peak. The rr plot is similar to this one. -263- n+p-+rrt cu 0 p cuo~n+rr-.,,.o 2.0 • , •• • • • •• • • • • • •• •• • • • • • • •• • , , •• • • . • • • •• • • • ••• •• • .. • • . • , • . . • • •• • • • •• • • • ... • • •. • • .. • .. • • ... .. • • • • .• • ... • ... - .. ..•,,... .. • •..... • • • • • •. • . .... .·.:.. ...... ' .: .. .. .:..: ..........: . .. .• • • • : • • • • • • ... ,... . . • . . ··;,..,. ... •• • • •• •• • •• •• • •. • • , • ·.,·.. .. . . • • • . . . . . . -: • • • • • • : . :.·,:::-.·. ....· . . \: • .. ., ...1.. . ........·- . . • •• • • • •• • • ...• . .,.,,.... ,.,............... ·. . . :... • •• 'Pt,,..•#: ••• • :: • ........ \.••• •..s ... .... ,,., .......... .,. ... . • .•• • ••••• .... • • • . • • • • • • ... ;;.. . ... . .,,,,. ....:. .:. .._......· :. . • • • • • ~ # ,...._. :>Cl) i· ) t!J .........,. ~ • rn • ·~ #. • • • • •t • : ~ 1.5 ~ 00 ~· s I # • • • • .,. • ~: ,~ '\. ·~: I. •• + ~ '• .._, ;;,r_ • :._• .. .,. "\ ./ + •. ~1...1-i : ~· .. s ;1ifil,,q.~. • ... ~ • •• ••• , • • •• ~.... I : • • ~ ·, •• 1:-. -..-..; • • #. • .ttf: ..~·· ...,.., • • ~• • , • ~ • .... , • •!" '· :"'-i. t" •• • • •• ... ~·. ••• ...• •r. •t•.a. • • • • • • ••• • • 1. ' ....-. ..... \ • .~. ~· A • ~· ~·. ~· ~ ·~""'., ··.~ 1.0 1.5 ~ ~. 2.5 2.0 w0 p mass {GeV) 3.0 Figure VI.lla + 0 Scatterplot of the rr p invariant mass versus the w p invariant mass 0 for events within the w to this one. peak. The plot for the n data is sir.J.lar -264- . 2.0 . .' ' • . • > '-" •• .. ... .. . ... ...... ·-·......... ·'·, .. • 8 • •• • • ~·· • ,_ + • t.: ... • • .t • • • :. ·~ • tt ,.. • . . . !.!#.... . .... ..... ... ' +•t...,.-,.,1• #...• ·i~·· ·~~·'.!l •• #. ~~,· ~ .... . :1.x.d.. ...,..: ;~: d • IC• - ' • • '• . .........; ~• ::.1...!•./.,_ ·~ '·: ~· • .. •• ... ~~= ··~~ ~ •• • •• #t- • • • ... ~ • •• • ••• • • t..• • ~~··:. ....... ."1!,; • • ,,. • .....,.......... ·.,._ .... ....•: . .... :· ..... . • • • :.,t ~11~ • • '·. ... • • ~ • ·-i p • •• • 1.0 . 1.5 , ,. • • • • : • - • I • •• • • • . • • •• • • • •• • • • • • • • • • • • ... • \ • • • • • • • ... • •• • • • • • • . I 2.5 3.0 Figure VI. llb 1T +p similar to this one. + - 0 invariant mass versus the :rn-rrp invaria nt mass for events within the 0 (;.) wings. The n l • mass {GeV) Scatterplot of the . • • •• • •• • •• • . ......... ,·~r..i:..~~Y4'!"~··:~·~.·:?.l.,..::.1:: ... \'. sti"·~11..~... • ~. • •• ' • • ' • -·· • •• • • • • . • • •• • .. .. • • •\ • ••I :... • • • ~· •• . • • . . • ... ,,. .. ...... ...... ,.·......,,.• ' . • , • • :·•• · : · . A .. • • • ..... . ~. cd 1.5 - • • • • •• •• • • • • • • •• • • • ~· •• • •• • • • • • • • • • • •·~ •• • • • •••• • 4 • • • • • • •• • • • • • • •• : • • • •• • • •• •• • ,. ( •• . 00 fJl • • • •• . • • •• • • • •• • # • CJ.) ~ • • • • • • • • • •• • ~·• •• • • ... • •• • • • • ,--.. •• . .. • • • • •• • plot is once again -265for the rr + cross section and 7.6±3.5% for the rr also included in Table VI.3. the dcr/dt cross section are These correction values were gotten from 0 Tf Tf distributions for w p masses below 1.9 GeV (see below) and 0 so are different from those quoted earlier for the total w production. 0 Finally, the cross sections corrected for the unseen decays of the w are listed in the table. Table VI.3 0 Fitted parameters for the w p peak Tf + 1T Mass (NeV) 1787. 8±6 .4 1786.3±5.5 Width (FVJ:fM, MeV) 86.3±12 . 8 67.7±10.4 Fitted cross section (wb) 7.16±0.89 5.13±0.63 9.4±1.5 7.3±1.1 10.5±1.6 8 .1±1.2 Corrected cross sections (µb) : 0 For w peak cut and t 0 And for unseen w By summin g the Tr rr rr de cays + and rr loss data and fitting as before, we find a mass of 1788.7±4.5 MeV and a width of 80.7 ±8 .6 MeV for the resonance. Refitting the rr + and rr data separately with the mass and width fixed at these values gave cross sections in excellent agreement with those g iven in Table VI.3. Fitting with a mass - dependent width ( see Chapter V, Z=O) changed the cross section values by only a few percent. wise, using the low t rr rr correction figures for the overall w0 produc - tion gave a change of only a few percent, well within the quoted errors. Like - -266- Figures VI .12 a - b Plots of do/dt regions. 0 rrrr for events in the w 0 peak for differen t w p mass The curves are from fits of Aeb t to t he distribu t ions . -267- 103 I , ' ' ..., , ' ' , n+p4rrtw0p f 1•1••1••••1••1•1·1 102 ~ 103 ~ M<l.9 1.9~M<2.1 Figu re VI . 12a J. -26 8- 1T-p 41Tf~op 103 -------------,--1_f_l_i_j-·-1-1-1r~1-1-1-1-1-1~~1-1! 10 2 rm 10 ~ 3 M<l.9 ! ro 102 ~ 1 0 3 ~..._..,,,_ . ~ .p-i--...t.N ~ I ~ I .I-;- . i 1.9,;;;M<2.1 1--:0-"'=- l »-1 ~ 10 2 ~ 3. ..-> 103 : ~~ t i t t J., rptft~ :+--+- 101 f 100 a ~0.0 I I M~2.3 : ] 1 ~i ! 10-1. j~ T~ 102 z 2.1:S:.M<2.3 ' -~+ I 1 j 1 , , I , 0.1 , , , I , , • 1 I , , 1 , I • 0.2 0.3 -tmr (GeV2 ,lc 2 ) Figure VI.12b 0.4 , .. , I La~ 0.5 0.6 -2690 0 To continue our s tudy of the w production , we divided the w p mass distribution into four regions: below 1.9 GeV, 1.9 to 2.1 GeV, 2.1 to 2.3 GeV, and above 2.3 GeV. 0 w p resonance. The first region thus contains the However, a large fraction of the events in this region 0 are non-resonant background under thew p peak: 42.1±4.2% in the if and 45. 7±3.9 % in the if data. Table VI.4 gives the slopes resulting from fits of exponentials to the do/dt 0 + if if distributions for the four w p mass bands. Figs. VI.12 give these do/dt fitted curves. The results are in fair agreement with those of 'IT if distributions and the Milgram et al. [1974], though t heir results have a slightly larger slope (~6 (GeV/c) -2 ) the difference between t he t wo experiments is not statistically significant. Note t ha t our results indicate that t here 0 is no change in t he t-dependence with increasing w p mass . In partic - ular, there is no change in the t-depe ndenc e of events on-resonance and off-resonance. Table VI .4 do /dt 0 I if slopes for w p mass bands -? slone ((GeV/c) -) 0 w p mass region (GeV) if + if <1. 9 4 . 62 ±0.44 5.82± 0 . 48 1. 9- 2.1 5.27±0.55 4 . 90±0.62 2.1 2.3 5.08±0.66 6.00±0.61 ;;::2. 3 4.86±0.4 1 4.05±0.50 -270- 100 .., ;... ! __...... ,..a :j__ -...- 1 ~ I: :' -r··I$" f 10 f- t ~--<>- r- I b I - -- - - - · - : ·. i I 0 I .,.t _____ b. 0 ,---I -j : I : 100 10 1 s (Ge\' 2 ) Figure VI.13 Plot of the s dependence of the production cr oss section fo r The data is from several experiments including this one. is a fit to as -n giving n=0.09±0.13. 0 + - 0 w ~rr rr rr decay mode only. The curve The cro ss sect ion s a re for the --2710 Fig. VI.13 shows the s dependence of the w p resonance production cross section. In addition to the data presented here, lower energy points from our previous papers [Davidson 1974 and Linglin 1974) and the results from other experiments [Milgram 1970 and Sisterson 1970) have been included. The cross section shows little s dependence, and a fit of asn yields -0.09±0.13 for n. This supersedes our previ- ous result of -0.66±0.06 which was based on only 3 data points [Davidson 1974) and a slightly lower value for the production TI 0 cross section of the w p cross section from our experiment (the earlier paper did not include all the corrections). This rather flats depen0 dence fits very well with a diffractive excitation picture for the w p resonance [Lednicky 1975]. 0 This w p threshold enhancement has been seen in several other experiments at various energies and with K and proton beams in add- ition to pion beams (see Table I.7). The small width of this peak has ~lilgram lead us and several other aut hors [Atherton 1975 and 1970 for example] to interpret it as a previously unknown N* or a new decay mode of a known resonance. There are two known N* resonances of good 0 standing which have masses near that found for the w p resonance: N(1780) and N(l810) (about 160 and 200 0 the w p resonance. [Particle Data Group 1978]. ~!eV Both have widths respectively) far larger than that observed for 0 Since the w p peak is very near threshold, other authors have investigated other models in search of a non-resonant explanation for the peak. Milgram [1970] investigated diffraction models and a Double Regge Pole exchange model and we also tried a -272Regge model as reported in our earlier paper (Davidson 1974]. Simple models of this kind fail to reproduce the narrow peak; they produce a broad enhancement usually 200 XeV or more in width much like the A 1 enhancement in TI diffraction. Some analyses (~ilgram 1970 and Theocharopoulos 1974 for example] obtained better matches to their data with more complex models at the expense of introducing many parameters into the model. However, these experiments had lower stat- istics than this one and observed a slightly broader peak which made it easier to match a model to the data. In conclusion, we find a relatively narrow threshold enhancement 0 in the w p mass . 0 Both the total w production cross sections and the N* ~w 0 p cross sections are independent of the charge of the beam to a good approximation. * cross section is also independent of the The N beam energy; indicating that it is a diffractively produced state. At * or a new decay mode this point it is unclear whether this is a new N of a previousl y observed state. Determination of the spin-parity of this state can shed light on this question. -2730 4. Angular Distributions of the w p System 4a) Phenomenology of Angular Distributions We will now turn to studies of the an gu lar distributions of the w0 p system in an effort to determine the spin-parity of the N* . 0 we will present results for the two lowest w p mass bins. Mostly Events in the 1.9 to 2.1 GeV mass band are ta ke n to illustrate the angular dis,, J. tributions of the background events under the N 0 mass band (w p masses below 1.9 Ge V) . 0 for events in the w peak in the lowest Likewise, angular distributions wings serve to illustrate the effects of the back0 ground events under the w ~o te peak. that two separate background 0 sources are involved; one is for all the events in the w cut and the 0 other for events in the w p resonance region. 0 The decay of the w p system itself was studied using the angles 8 PP and ¢ PP described in Fig. VI.14. The coordinate system described by the figure is the standard Gottfried - Jackson [Gottfried 1 964 ] system 0 in the w p rest frame. The angles, 8 pp and ¢ pp are of the outgoing -+ proton (p) relative to the z -axis defined by the direction of the tar-+ 0 get proton ( p . ) in the w p rest frame. The y -axis is given by the l normal to the production plane (;bf). 0 We expect that t he w p resonance will h ave a small spin va lue. 0 The w p p + (J =1-) and the proton (J =1/2 ) spins can combine to give a total spin of 1/2 or 3/2. 0 Since the w p resonance is very near thres- hold, the decay is probably via an S-wave or P-wave (orbital angular momentum, L=O or L=l). Coupling the total spin (S) and orbital angular -274momentum can give total angular momentum states with Jp's of 1/2±, p + The decay of a J =1/2- state has an isotropic angular distribution. The decay angular distribution of the Jp=3/2± state is given by: W(8,¢) 3 4ri(l+a.) ( p p a-1 Rep 13 312 312 112 112 312 112 {sin 2 8 + a(cos 2 8 + 1/3) } + {cos 2 8 + 1/3 + asin 2 8} + sin28cos ¢ + Rep where the angles (8, ¢ ) are the same as (8 p pp ,~ 312 pp _ 112 , is the dens it y matrix for t he w p r esonan ce. depends on the s and t of the resonanc e production. is at a fixed s and p matrix. = P_ 112 mm sin 2 8cos2 ¢}) ) defined above and 0 mm (6) In general o mm This expe riment , is inte grated over t to yield a constant For example, Dickey [1978] assumed pmm '=O except for P _ 112 = 1/2. , 112 112 The parameter a is the ratio: (7) where M is th e helicity ±3/2 amplitude and M and M are helicity 1 2 3 ±1/2 amplitudes (M 0 1 0 is for an w helicity of ±1 and M is for an w 2 helicity of 0) . We can relate t he helicity amplitudes to the amplitudes (M S) 1 for states of defini te orbital angular momentum L and total spin (S) [Chung 1971): 2 ?L+l ) l/ 1 MC\ ' A ) = l _-<LSO ;\ I J>-><1-.\. ( - A ) I SA> i'L ( w p LS 2J+ 1 2 'J.J p LS ( 8) -2750 and A are the w w p where J is the total angular momentum and A proton helicities (A=A - /. ) . w and The N(A ,A ) helicity amplitudes are w p p equal to the M , M , and M amplitudes discussed above [Dickey 1978] 1 2 3 and are reduced from 6 amplitudes to 3 by parity conservation. The 0 w p system can have S=l /2 or 3/2 and have L's up to 3 for Jp=3/2± (2 for Jp=l/2±). By setting all the p for S-wave decay (J =1/2 - ~S amplitudes equal to 0 except M05 - p or 3/2 ) or M for P-wave decay (J =1/2 15 + 3/2 ), we can rewrite equation (7). + or For the S-wave case, it is found that a=l which results in an isotropic decay for a Jp=3/2- object [Dickey 1978]. For Jp=3/2+ via a P- wave, a can be written as: 9 a= - - lOy+l where y is the ratio (9) IM1 112 2 / IM1 312 2 . 1 1 Thus y is the ratio of the probability of the P-wave decay occurring in a total spin 1/2 state to the probability of total spin 3/2 and is a parameter to be determined from the data or a more fundamental model of the dynamics of this s:::rong decay. 0 The deca y of the w The first set, 9 angles. A plane (nw) 0 to the w 0 in the w was studied by using two different sets of pn and rest frame. 0 ~ ·pn , are of the normal to the w decay These angles are measured relative Gottfried - Jackson system which is the same system described 0 above but now transformed to the w rest frame (see Fig. VI.15a) . These distributions can be compared to previousl y published results [Atherton 1975 and Davis 1972] and as will be seen, show a strong -276cos 8 pn dependence. 0 of the w The other set of angles, 6 ¢ and nw nw , are again 0 decay plane normal but now are defined relative to the w 0 In the w helicity s ys tem (see Fig. VI .15b ). 0 coordinate system z-axis is given by the w rest frame, the he licity direction which is oppo~o ~ site to the outgoing proton direction in this frame (w =-p). The xz- plane is given by the z-axis and the target pro ton direction [see 0 The w Jackson 1965]. helicity angles were studied since predictions 0 of their distributions and of t he w density matrix in this frame were made by assuming spin-parities of 1/2 0 for the w p resonance and 3/2 [Dickey 1978 ] . 0 The w is a well k nown particl e with a spin - pa rit y of 1 . The angular distribution of the no rmal to its decay plane can be calculated given its density matrix el e ments, p W(8,:p) 3 n 4 rl P00 co s 2 e + P 11 sin. 2 s - p mm , . ') e [Jackson 1965]: ? (10) 1 _ 1 sin~ cos-¢ - ./2 Rep 10 s in2 8 cos 6 ) 0 where 8 and ¢ are either se t of angles defined above for the w . t hat in genera l 0 the w Note densi t y matrix is a func tion of the decay angles 0 of the w p resonance, 8 pp and n' pp The density matrix elements deter - mined later are constants, having been int eg rated over t hese angles. The one-dimensional distributions (in t egrated over the other angle) are: W( ¢) 1 2 n (1 - 2p _ cos2¢) 1 1 ( 11) -2 77 - ]_ ( p w(9) cos 2 8 + p ll si n 2 8 ) 2 00 3( 1 - Poo) 4 ( 1 + [ ( 1 2a ) 3 Poo- 1 1 - Pao ( 1 2b) ) c o s28 ) Fr om equations (12), we see that by fitting the cos8 dist r ibutions of 0 the w with the form a ( l +a cos 2 9) we can calculate the 0 density 2 0 00 0 matrix elemen t of the w : ( 13) Similarly, by fitting the ¢ distribution with c (l+c cos2 ¢ ) 0 2 calculate the we can o _ 1 density matrix element: 1 (14) - 20 1-1 The real part of the 0 10 densi t y matrix element can be determined by fitting the bivariate distribution (in both 8 and ¢ ) which we have no t done. 0 The density mat r ix elements of the w's from the decay of thew p res onance are depende n t on the decay angles of the resonance [Jackson 1965]: w p ",(8 1\1\ ' pp , qi pp N ) w wp r mm' 0 where the w 0 (8 J* D (¢ m,\ pp pp ,¢ ,9 pp pp (15) ) WP J ,O) p · , D , , , ( ¢ mm m I\ pp ,8 pp ,0) and w p resonance density matrices are l abeled as such. -278- w N is a normalization factor determined from Tr p =l and W (e wp 0 the decay angular distribution of the w p s ys tem. The PP ,¢ pp ) is D~A. (¢,8,0) are the rotation matrices for spin J and M(A. , A. ) is the amplitude for the w p 0 decay into a state with w Dickey's A. 1 and A. 2 helicity A. w [1978]); also A. =A. - A. W 0 from equation (15) in the w and proton helicity A. P and A. '= A'- A. '. W p integrating over the¢ angles, W(e nw ,8 pp this chapter. (see w Using P,, 1 AA decay angular distribution (equation (10)) results in the joint angular distribution wee the W(9 p nw ,9 pp ). nw ,¢ nw ;e pp ,6 pp ) or, by Dickey 's predictions for ) distributions are discussed in the final section of -279- 7r±p~Tif wop w0 p rest x=yxz z ..... ~p • y x • . I Figure VI.14 0 Definition of the w p Gottfried-Jackson frame angles e pp and ~ pp used 0 to study the w p system decay angular distributions. -280- TI±p ~n·f W Op w0 rest x=( ftbxftf)xz y=zxx z x Figure Vl.15a 0 Definition of the w 0 to study che w Gottfried-Jackson frame angles 8 decay angular distributions. pn and 6 used · pn -281- 7f±D~rr±w ~ f 0p w0 rest .... ..... "" x=yxz y=pixCJO z=~o=-p _ rr :fiCtJ =ff+ ..,. x rr- .-.+ -- • , If/ z "IT ~ -o 1T ..' x Figu re VI.15b Definition of the w Q helicity f rame angles 8 the ~ 0 decay angular distributions. nw and ~ used t o study · nw -2824b) Observed Ang ular Distributions Fig. VI.16a shows the normalized Y~ moments for the data as a 0 function of the w p mass. These moments are defined b y : I w.Y~(B . , ¢ .)/I w. l . l l ~ l l . (16) l where the sums (ove r i) are over the indi vidua l events and w . is the l ith event's weight. The angles 8 . and¢. are the values of the 8 l and ¢ pp angles (Fig . VI .1 4) l for t he ith event . pp The differential cross section in terms of <Ym> is just: Q, dJ (17) d:ll where cr rr is t he cross sect ion int egra ted over the solid angle: 4 da f dQ ( 1 8) d ~1 As can be seen from the p lots, the mome nts are very small and consis- 0 tent with zero up to an w p mass of about 2.1 GeV . Although only the m=O moments are sh own, the real and imaginary pa rt s of the m~O moments are also zero below 2.1 CeV. 0 The momen ts for events in the w 0 are essentially the same as those for event s in the w wings peak (see Fig. VI.1 6b) . The moments distributions serve to direc tl y illustrate the change 0 in the angular distributions with the w p mass. They can also be com- pared to such distributions presented by other authors [Atherton 1975] and to our earlier preliminary results [Davidson 1974 and Linglin 1974). -283However, the moments obscure some of the details of the angular distributions due to their normalizations. For an angular distributions given by a (l+a cos 8+a cos2 e) , the first t wo moments are related to the 2 1 0 a. coefficients by: J 0 <Y > 1 0.163 a al /i2rr (1 + a/3) 2a 0 <Y 2> 1 + a 1 ( 19a) /3 2 0.084 a 2 3/zo:r (1 + a/3) 2 1 + a /3 2 ( 19b) The small normalization constants thus lead to smal l moments for sub stantially non - uniform angular d istributions. - 0 .5 and a~=l.2, For instance, for a = 1 va l ues near t hose observed (see below), t he mome nts 0 0 have the values of - 0.058 for <Y > and 0.072 for <Y >. 1 2 Above about 2.5 GeV, all the moments (up to £=4) take on large values indicating the the angular distributions are very sharply peaked in this regi o n. Thus we now turn to the cos 6 informat ion. pp and ~ ' pp distributions for more detailed -284- 1 . I ~-L-r A -,t #-F _+ - - ~o ~-+-..,+ +-+-+.: v -1 /\. ONO ~ \ I ./ -1 I ' ' I -1 • -1 . ' 1.6 2.0 2.4 2.8 1.6 cJ 0 p mass I 2.0 2.4 (G ev'7') , 2.8 3.2 Figur e VI.16a Distributions of the normalized 0 in the w 0 Yi ~oments for t h e peak v ersus the w p mass. TI+ and TI - e ven ts -285- -1 /\ ,,, 0 " CX\2 L.~ \ .1 -1 . 1+ + I l\ + ++-r-r- \ ~l1-:+++-;..t +-+-_ - - - t t• ~o \ ·I rt ' -1 , , I I , I , , I , , - --1 1.6 2.0 2.4 2.8 1r"t-rr-rr 0 p 1.6 2.0 mass 2 . ~1 2.8 3.2 (GeV) Figure VI.1 6b Distributions o f the normalized Y ~ moments for the " + and 0 the w wings versus t he TI + TI 0 rr p mass. TI events in ------. -286Figs. VI.17 and VI.18 show the cos 9 tions for w0 p masses below 2.1 GeV. PP and~ . PP a ngular distribu- These distributions are of the same angles used to calculate the moments displayed in Figs. VI.16. The cosS distributions for h i gh er masses are g iven in Figs. VI.19; PP the corresponding ¢ in ¢ PP pp distributions are not shown as they are uniform (much li ke tho se in Figs. VI.18). The curves with the case PP distributions are from fits to ao(l+alcos8 +a2cos 2 e ) and those with pp pp These func- the ¢pp d istributions are f rom fits to co(l+clcos ¢ pp). tional forms were chosen from examination of t he distribu tion s and the 0 expectation that the w p resonance would have an S-wave (L=O) or P-wave (L=l) dec a y (equation (6) The cos 8 fo r examp l e). distributions for masse s above 2.1 GeV (Figs. VI.19) pp show a forward peak at cos8 0 pp =+l which becomes stronger as t he w p The higher masses also show lar ge values of t he Y~ mass increases. moments due to these forward peaks (see Fi g s. VI.16). above 2.1 GeV, th e functional form wi th wh ich the cos 8 For masses pp distributions wer e fit does not reproduc e the n arrow forward peaks but gives good fits to the case 0 the w pp <0.8 data. This forward peak is more pronounced for 0 wings events as compared to t he w VI.19b and VI.19a). peak events (comp are Fi gs. Th is forN ard peak corresponds to forward going protons with a low momentum tran sfe r from t he target to t he autoing proton (low J t pp J ). Since the events have a fairly low I t Figs. VI .8 a nd VI .12 ) fo r the most pa rt, the forNard case Tr'!T pp J (see peak is due to contributions from events of the form illustrated in Fig. VI.4a 0 with the G 0 replaced by an w or a rr + Tr rr 0 system. - 287- n+p4rrt~ 0 p TI-p4rrrw 0 p 15 ~.--.~--.--..--.--.--....--T---..--r--.--.------------~~ ~ 10 rl v .....-.. 0-i 3 ._,, 0 s5 . '\-I N v 10 ....--... 0... 3 ...._.. c s5 \Iii 0) M -1 0 0 1 cosePP (p z==:Pi) [w 0 p rest frame] Figure VI .17a Distributions of cos8 0 0 pp of the outgoing proton for events in t he w peak with low w p masses . The 8 pp angle is defin ed in Fig. VI.14. -288- n+p4ntn+n-rr0 p n-p4n!TI+n-n°p 15 r--1~~--r-r-r--.--.---r-.....--.-.....-or-..--r-"1.--.---,.-.---. . C\J v P:10 0 I~ +'f:. t.: ...._,, s5 \/11 . O:J 0 -1 0 1 cosePP (p z=p 1) [ -rr+iT-1T 0 p rest frame] Figure VI. l 7b Distributions of cos e wings with low TI 0 pp of the outgoing proton for events in the w +TI - rr 0 p masses. -289- . ,.-...! ~ -- l , _ : j - j - ;- ! - '- '-'.- :' ; . I i i : ' ,J .~ -; ' ;~~1 J l i i : i J 4 t· 0 ._'~_..__..__....___,__j___._~__.___._~~ ...___....__...___,__~ 0 90 180 270 0 90 I .....___._~_.__] ...__. 180 270 360 Figure VI.18a Distributions of the 0 the w VI.14 . ~ · pp 0 angle of the outgoing proton for events in peak with low w p masses. The ~ pp angle is defined in Fig. - 290- r N \. ' r r t=: f _...... r Pi 0 ik ' I +I~ ....1 i-r! ~ ..._ _ ~ ~ .-l d ,, i I ~ ....-i ~ , _ ·_ ! .; • l• ~-·- i .---.-~-.. --~--' -..:::=--~ --- - ~ : rl l,· - ; _ 1 ~ t ___.__, -- ·- ' ' - : l , . ' - ·- ,_·_ : ·, _ • , ' I ' -+- -- · l ' } I r ~ . ' · • _.,- ' I : j ' 4 ~ ~ ~ i 0. t 0 ~ j - - ...~ I I ~ ~ I I ~ , : l ~--' _j l ' ..__...__...._....___,_~ 90 . ~ _L._.__.__._l_..___.__..__....._~·-,..L_.__..__.__~.~.L._._-~ 180 270 ¢pp 0 90 180 270 360 yccitb>~ftf) rest frame] (p z==pi [ rr+1r-1T 0 p Figure VI . 18b Distributions of the 0 w wings wit h l ow TI ~ pp angle of the outgoing proton for events in the +TI - TI 0 p masses. --.... - 291- 0 0 n+p4rrt~ p n-p4rr1~ p 2Qr___._,____,_,_-.--__._____,._,..-.--.---.____,____.__, . v ........... C1'J C'J 0 ~ 310 "--" s ~ ,a 3, VII M . C\J 0.. Clot 0 CJ:') Ul 0 C) "d " b "C ,-.. 0 ~ 3 ..._.,, 940 "11 . Ct:! C'J 0 c:7:~~~~~,,__.._L~~~~~:....:_.__._J -1 0 -1 0 1 cosePP (:P z=pi) [w 0p rest frame] Figure Vl.19a Distributions of cos 8 0 0 PP of the outgoing proton for events in the w peak with high w p masses. -292- ~+p~ntn+n-n°p n-p~n1n+n-n°p 20...------__...__.___.,_v.._..___ ~_ ___.._______ _ . . _ , 0----------------------------- 0 _..... -1 0 cosecfP -1 0 1 (p z=pi) [n+n-1T p rest frame] Figure VI. l 9b Distributions of cos8 0 PP of the o utgo ing proton for events in the w . . , , . h + - 0 wings witn nig rr n rr p masses. -293The case PP distributions for the lowest mass band (<1.9 GeV), 0 which includes the w p resonance, show a backwards peak at case (Fig. VI.17a). 0 wi thin the w + - PP =-1 This backward peak is only evident for the events peak . The cos8 0 distributions for the w wings events pp 0 with a rr rr rr p mass below 1.9 GeV are essentia ll y flat with a small forward peak and possibly a small cos 2 9 pp component (Fig. VI.17b). The next higher mass band (1.9 to 2.1 GeV) cose 0 forward peaks for both the w 0 peak events and the w wings events; thou gh once again t he forward cas e 0 stronge r than t ha t of t he w The ¢ pp distributions show pp 0 pp peak of the w wings events is peak even ts (Figs . VI .1 7b and VI.17a). distributions are uniform in some of them exhibit a sligh t cos ¢ pp ~ pp for the mos t part though dependence. The ~ pp distributions were fit by c (l+c cos ¢PP) ; the results are given in Table VI.5. 0 1 values found for c The are sma ll with nearly half of them being consistent 1 with ze ro. Table VI.5 ~l valu e s from dcr/d¢ 0 w 0 w p mass band(GeV) Tf p l+c ~p 1 fits to the distributions 0 peak events w Tf Tf + wi nos events + <1. 9 0 .15 8±0 . 083 0.203±0.084 0.190±0.092 -0.073±0.104 1. 9-2.1 0.016±0.094 -0.11 0±0 .1 00 0.012±0 . 082 0.140±0 . 092 -294Table VI.6 2 Results of l+a ~~ cos 2 8 1 da/dcos8 1T 0 w p mass band (GeV ) fi ts to t he distributions + 1T _ _a_l-- _ _a_2-0 w peak events <l. 9 -0.55±0.1 6 1. 14±0. 38 - 0.48±0.12 0.23±0 .23 1.9-2.1 0.60±0.20 1. 03±0. 43 0.33±0.19 1.19±0.49 0 w wings events <l. 9 0.22±0.17 0.70±0.37 0.13±0.16 0 . 68±0.36 1. 9- 2. 1 1.1 4±0 .21 1.44:'::0.44 1.01:'::0.23 1.66±0.53 Table VI.6 g ive s the results (for masses be low 2.1 GeV) of fitting a (l+a cos 9 +a ?cos 2 6 ) to t he cos 8 distributions in Fi gs. VI.17. 1 0 pp pp pp The backwa r d cos8 0 pp peak in t he lowest mass band for t he w is evide nt as a negative value for t he a tri but ions. 1 coefficient for these dis - This backward peak in t he cos8 0 pp dis tri bution in the w p resonance r egion has been seen in pr ev iou s experiments Davis 1972, Chie n 1976, and Wohl 1978) . ison between th e cos8 peak data [~lilgram 1970, To provide a better compar0 pp distributions for various mass bands and w event se lectio ns, we have calculated the as ymme tr y paramete r for the cos8 pp d istributions : w- w A + (15) -295where W+ is the sum of weights for events with cos 8 sum of weights for events with cos 6 Table VI. 7 and in Fig. VI.20. pp <O. pp ~ and W is the The results are given in In this way the relative differences between the mass bands are more obvious. As is seen in Fig. VI . 20, masses above 1.9 GeV have greater positive asymmetries (or forward cos 8 0 pp . 0 pea-s k ) as t,h e w p mass increases. Only for w 1. 9 GeV is there any appreciable negative asymmetry. peak events below \.Je will discuss this asymmetry further when we investigate the spin - parity of the 0 w p resonance later in t h is chapter. Table VI. 7 Asymmetry of the da/dcos8 0 distributions 0 w peak events w 0 P. win7s e ve nts w p mass band(GeV) 'lT <1. 9 - 0.151±0.059 - 0.188±0.058 0.023±0.070 - 0 . 060±0.069 1.9-2.1 0.194±0.067 0 . 0 54± 0 . 073 0.385±0.056 0.271±0.063 2 . 1-2.3 0.575±0.068 0.381±0.068 0.519±0 . 068 0.394±0.073 :::::2 • 3 0.750±0.056 0.689±0.070 0.837±0.058 0.669±0 . 064 The cos8 pn and ¢ decay plane (~ =~ x ~ that of the TI VI.24. w + + - 'lT 0 pn angular distributions of the normal to the w where 0 The 8 in the w pn and¢ 0 tributions for the w + pn b ·+ is the direction of t he TI+ and p is rest frame are given in Figs. VI.21 thru anales are defined in Fig. VI.15a. "" 0 The dis - peak events with w p masses below 1.9 GeV show -296- ' -r ~ '-r-r-~ i ... -------... ----...... -. --.:..-. -... -. -. ---.. -.. -1 ~ ·t -t ~ ,...,____,~~~~~--- r.:-:. -................. ---· ~b . I ... ;__.t-_ _. ' 'I . .... --... -.....i -I ~ ...j ! I r .. ·+· .. ~' ' -j ' ~ I JI -~ •:) .::: .-..1 ·~ ' - ~ ....... ! ... . ~ ..,.. r ' r' l ' 'I ! r-l---; ! ·- 0~ r ~ ~ L ' .,.. r "" '' .4. ~·· ----i ...'' i ·- ,,- .., ---: ~~r ~, .·---' . . . - -. l. ~.-:; . .') ~ .j ~ ... .:!'"...... ~ .,... .. ··n · ;•""· i j ' ~ '~ 1" ' - f---""? +--~!:-~ ,. ..J ... f -- ,::: w L_:.__..l--1,.~_..__· _.____; ."'1 ~ ;:) l •') c -~· Figure VI.20 Plot of the asynmetry of the cos e tion from isotropy ) versus t h e . in t h e w0 wings. ~ 0 PP distributions (as a percent devia- . 0 p mass tor events in the w peak and - 297 - n-p~rr1w 0 p n+p4rrt~ 0 p 10r----T--r-r--r-~~~-r-~--T"-------------------- ~. ,.... v ......._. ,,,._._ ..c Jl1 5 3 ....._, a :t .._.., + Q tlt 0 ~ 00 0 0 "O . ,-! '-..... N v b ,-.,.. "d P-t C> a 5 '-"' e Y11 . ~ ~ 0 -1 -1 0 -- 0 1 cosBpn (ii"' z=pi ) [w 0 rest frame] Figure VI.2la Distributions of cos S 0 in the w VI.lSa. 0 pn of the normal to the w 0 peak with low w p masses. The decay plane for events apn angle is defined in Fig. -298- n+p~ntn+n-n°p n-p~n!n+n-n°p 10.----.--.-.--.--.-.-..--.---.---.-,,,_....-..--..--..,.-----. 0) _.• v .......... t:l.. ,,_.... ..c ::t ............ t: 5 't: +i== ........., a ~ ~ 0 ~ t/J 0 0 "O . ..-I N v ,-... '-.... b ~ 'd If: ...t: 5 t;: '-" a Vll ...... Ct> 0 ,__,__~ _____.....__.__.__.__.______._______,_____...______ -1 0 -1 cosBpn (fi+- z=pi) rest frame] [7r+n-rr 0 0 Figure VI. 2lb Distributions of cas e pn of the normal to the TI +rr - plane (n+_ ) for 0 · · ' h l ow TI +TI -TIo p masses. events in t h e w wings wit. 1 -299- CJ) :j 0 a..1 3 I 1 ,- ... ti l j l -+I 1-L l -+I I I I l l 1 s~ t I : : I I ! I t QI Figure VI. 22a Distributions of the 0 events in the w in Fig. VI.15a. ~ 0 pn angle of the normal to the w 0 peak with low w p masses. The¢ pn decay plane for angle is defined -300 - 1T-p~1Tf"1fi-1T- nop ~- -4 lj t ; I - +- T! ~ j ~ j l 1 1 \ •• 90 ! 0 180 270 ¢pn . __.___.__. . . . . .~_.___.___....__,1 90 180 270 360 '---'--·~~----.l-...L-.....-· z==pi (fl+- [ n+ 7T - 1TO ..... .... .... ) )iOC1TbX7T f rest frame] Figure VI.22b Distributions of the ~ e vents in thew 0 pn + - plane for angle of t he normal to t he rr rr wings wi th lo w rr + - 0 ;r rr p ma sses. -301- n-p4rrrw 0 p ~+p~rrtw 0 p 10..---------~-.--....-.----------------.----- 0 ..._.__....._.....____._-'-"~~-----~-'--'---4--'--'--'-__.~_,.j -1 0 -1 0 1 cosepn [Gt.> 0 (fiCJ z=p1) rest frame] Figure VI.23a Distributions of cos8 ·' in tne w 0 0 pn of the normal to the w 0 ' h ' nig " h w p masses. pea·k wit decay plane for events -302 - t 0 -1 0 -1 0 1 cosBpn (fi+- z=pi) [rr+n-rr 0 rest frame] Figure VI.23b Distributions of cos9 0 t he w pn of the normal to the TI ' rr +rr - rr 0 p masses. wings wit h h'ign . . +TI - plane for events in -303- Figure VI.24a Distributions of the 9 0 for events in the w 0 pn angle of the normal to the w 0 peak with high w p masses. decay plane -304- n+p~ntrr+n-n°p rr-p~n~rr+rr-rr 0 p 2 .......,-_,-- r- ·1 . Cf) l ro ~· ;!__ fr I:; i +t:. 1 r t::: r ! 1 , j l I ! . l -t- I -1.. l f · I _J_ 1 ~ I j -+- I T ;fl;,· 'f.:-~+ l t. C\2 1 1 . 1 1il i ' ~ 1 !=1 ir _,__ \;TI n~ ~ ~r-- r--r . .j i j o~'-+--;-+--+-+-'1'-'~~_..,..-+--+--+--1--+--+-+-..__,,__.,,_.;,•--'l--\-~ ~ l ~ J ~~3r i' r t" ~ f !~ + t= ........... J I ~ 2I i~' ~ : d \Yi~.••l ~ _L l j -i 1 : l-l-1 j' 1. -i-i '¥1\' 2 F\ l ' \cj) '-t1 ! --r 1--~ ~ l ' r , : _.......-=-· ~ . . ____-.::· 'J , ' ~ : ' j 1 1:-f" li-+-! '--~-...r--T- j j i '~ • ~1j - ·i ..-I I I I 1 ro-r i · ~. (' .- ~ : l ! ;· i t ~ I • 0 ~ .j .j I ' 0 _J • 90 ! I L ' l _...., . ...;.. _J.. 180 270 0 ..... ! 90 .!.. I I ........ 180 270 360 .... z==pi yccfrbxftf) Pe-.::t .a. ......... frani.e] Figure VI.24b Distributions of the ¢ 0 events in the w pn angle of the normal to the wings with high IT + - 0 TI TI p masses. _j IT + rr plane for -305a large cos 2 8 pn anisotropy (Fig. VI.2la). The curves in Figs. VI.21 and VI.23 are the result of fitting a (l+a cos 2 epn) to the data. 2 0 with a cos8 pn term gave small values to this term's coefficient as 0 expected from the w values for a 2 Fits decay distribution (equation (12a)). 0 Note that only the w are listed in Table VI.8. 0 events have large a 2 values while the w nearly isotropic and have small a 2 The fitted peak wings distributions are coefficients (see Figs. VI.2lb and VI.23b). Table VI. 8 ~ 2 2 values from fits of l+a 2 cos 8 n to the do/dcos8 0 w 0 w p mass band(GeV) TI pn distributions peak events + TI w TI 0 winos events + TI <l. 9 1. 12±0. 39 1.85±0.54 0.30±0.27 0.01±0.23 1.9-2.1 0.83±0.42 0.69±0.39 0.01±0.20 -0.32±0.17 2.1-2.3 0.11±0.27 0.96±0.42 -0.43±0.16 0.12±0.30 ;:;:2 • 3 0.10±0.22 0.14±0.25 -0.33±0.16 -0.50±0.14 The ¢ pn distributions in Figs. VI.22 and VI.24 were fit by the form c (l+c cos ¢ +c cos2 ¢ ); pn 2 pn 0 1 for the low masses. thew 0 the results are listed in Table VI.9 The choice of this functional form was based on decay distribution (equation (11)) and the lack of any strong non-isotropy in the ¢ pn distributions. -306Table VI. 9 Results of l+c cos$ +c cos2¢ fits to the n 1------pn-2 do/d ¢ TI 0 n distributions + TI w p mass band(GeV) ___ c l -- 0 w peak events <l. 9 - 0.095±0.085 0.143±0 . 085 - 0.135±0.084 - 0.013±0.086 1.9 - 2.1 - 0.094±0.098 0 .110±0. 089 -0.285±0.100 - 0 . 044±0.113 0 w wings events <l. 9 -0. 012±0. 092 -0.082±0.093 0.002±0.102 0.086±0.101 1.9-2.1 - 0.219±0 . 078 -0.101±0.080 0.092±0.094 -0.014±0.100 Using the fitted values for a 0 the w Gottfried - Jackson frame 0 by use of equation ( 13). from Ta b le VI.8, we have calculated 2 0 00 density matrix element for the w The values for 0 0 00 are given in Table VI.10 and plotted versus the w p mass in Fig. VI. 2 5. 0 data and the w wings data have 0 0 value for non - aligned w 00 0 The high mass w peak values near 0.33, the expected production. 0 For the lowest mass band (w p masses below 1.9 GeV), we find that thew's are produced with their spins aligned along the ta r get proton. Atherton et al. reported a similar alignment of the w's produced in ppw find 0 00 0 where t hey has a value of 0.57±0.03. Simi l arly, the c given a value for the (14). [ 1 975) have The c 2 2 coefficient of cos2 ¢p n (from Table VI.9) will o1 _ 1 densit y matrix element by using equation coefficients in Table VI.9 are essentially zero. From -307- Table VI.10 0 w Gottfried-Jackson frame p 0 0 w w p mass band(GeV) TT 00 density matrix element 0 peak events + w TT 1T wings events + TT <l. 9 0.515±0.046 0.588±0.046 0.394±0.050 0.336±0.051 1.9-2.1 0.478±0.057 0.458±0.057 0.336±0.044 0.254±0.047 2.1-2.3 0.356±0.056 0.494±0.054 0.223±0.048 0.359±0.061 ;:::2.3 0.354±0.045 0.363±0.050 0.250±0.046 0.202±0.045 -308- 0.?5 o.5o -. "T T 1" j r 7Tt v 0.0 0 ~. . .J---..t. . ____.L_.......t..-. _..._........_--! -1-........1. Li l 1.5 Figure VI.25 0 Plot of the w 0 the w wings. Gottfried-Jackson frame 0 0 00 density matrix element of 0 versus the w p mass for events in the w 0 peak and in the w -309- looking at Figs. VI.22 it appears that even for those data sets with a non-zero value of c 2 (not within a standard deviation of 0), the distributions have no obvious cos2 ¢ 0 that p _ in the w 1 1 pn dependence. Gottfried - Jackson frame is zero. Figs. VI.26 and VI.28 show the cose 0 to the w 0 cos8 pn and ¢ nw from Figs. VI.21, nw distributions for the normal 0 helicity frame are def i ned in Fig. VI .1 5b. In contrast to helicity frame. the helicity angle distributions are flat, 0 showing no alignment of the w VI.11 gives the a nw The w deca y plane in the w and t he angles 8 Thus we conclude along its direction of motion. valu e s from fitting a (l+a cos 2 8n w) to these dis 2 0 2 tributions ( se e also the curves in F igs. VI.26 and VI.28). helicity frame p Table values derived from the fitted a 00 2 0 The w values are given i n Table VI.12 and are in g ood agr e emen t with the v alue of 0.33 for an unaligned state. Table VI .11 ~ 2 2 values from l+a 2 cos 8 w fits t o the dcr/dcos 8 0 w 0 w p mass w distribut i ons peak events 0 w wings events + + band(GeV) iT <l. 9 - 0.11±0.20 -0 . 00±0.20 0 . 21±0.26 0.38±0.29 1.9-2.1 0.06±0.22 - 0.40±0.17 - 0 . 02±0.19 0.23±0.25 2. 1- 2.3 - 0.07±0.23 - 0.32±0.19 -0.04:±:0.22 -0.11:±:0.24 ;;::2 • 3 - 0.37±0.14 -0 . 17±0.22 -0.61±0.12 - 0.70±0.11 7i TI iT -310 - 0 0 n+p~rrt~ p n-p4rr1~ p __ ________________________,___ 10~~~..__..,.-r- . <» ~ a Cl) 0 tll • I ~ \ l 0 0 ,..... " ro v ,,,....... "d b '"O . 0 ~ 3 "'--" s ¥11 . C) 5 t tt+ t + ....... -1 0 1 cos6 r.>n (ft~ 2=CJ) [w 0 rest frame] Figure VI.26a Distributions of cos6 0 in the w VI. lSb. 0 nw of the normal to the w 0 peak with low w p masses. The 6 nw decay plane for events angle is defined i n Fig. - 311- n+p~ntTI+n-n°p n-p~nrn+n-n°p 10-----~---~~------------------Ol • -' v ........... ~ t: 5 't.: ~ ,D. +t; ......... 3 s d 3 0 <:1:) 00 0 ....... 'd C\l . 0 " v ,.,...... b ~ "C ,'f:. +t: 5 ~ '-""' a Vll C'J ...... 0 '--"--"'--..__.....__,__,____,__,______._--4.-_.__..~~__.--A.--l -1 -1 0 0 1 cosBwn (fi+- z=v3 1l') [7r+rr-,,.o rest frame] Figu r e VI. 26b Distributions of cos8 thew 0 nw + - plane for events in of the normal to the rr rr + - 0 wings with low TI rr rr p masses. -312- n-p4rr!~ 0 p 2 ,.._..,,___ _..,._..,...,-.--r-.-.........-----..-....--...-·--,-.--..-,--i--i--,.--r""-,.-] TI+p4rrtw 0 p j ! l J_ . I ! -l- ! . -v \j_ I t l I I I I l l j \ -V j \i \ti j I ' I ~ ~\\11 j \ r l f M S(f 1 .. 1 t ! ~ r· ~y:J fr_, ~ I 1· ...-! t. I ' T ~ / .1, --r+ J i l ~... l _._:-,l I -- ~l + 1 7-+- I LJ ; ; 0 90 180 270 0 l • ...... ! j I I I ·~ · I· • I I ! i I ' ! j i ~~ - 1 ' ' -· -1- 0 90 ' _._J 180 270 360 z=w yocwxpi) rest frarne] Figure VI.27a Distributions of the ¢ 0 events in the w Fig. VI.15b. 0 nw angle of the normal to the w 0 peak with low w p masses. The ¢ nw decay plane for angle is defined in -313- ¢G;n (fi+- z=v3 1T [7r+1T- 1r0 rest Figure Vl.27b Distributions of the 0 events in the w ~ nw angle of the normal to the rr + - 0 wings with low TI rr rr p masses . + TI plane for -314- n+p4rrt~ 0 p n-p~rrf ~ 0 p 10------------~--------------------- . C') N v ......... C4. Cll 3 .......... ~ ,a ~ 5 8 Vil . "l"-4 N ~ 3 0 Q!\ en 0 C,) 'd ' """' b "tj t op.. 3 S10 vu ~ C\1 0-------------------------------0 -1 0 1 -1 cose<.>n (fi~ 2=w) [w 0 rest fram.e] Figure VI.28a Distributions of cos8 0 . ' in tne w 0 nw of the normal to the w 0 . h h'ig.h w p masses. pea.k wit decay plane for events -315- 10 1T+p~ntn+ rr-1Top rr-p-?1rfn+ n- rrop f t i--,_......- ++ t t 0 -1 -1 0 0 cos8wn {ii+- z=v3rr) [7r+n--1TO rest frame] Figure VI.28b Distributions of cos8 thew 0 nw wings with high TI of the normal to the rr+TI- plane for events in + - 0 TI TI p masses. 1 -316- rn w 1T +p~~.f+,~,Op 2 ~-p-~rr-~'OP ll - , f W ·1-t--i--,---r__,.....--.... , --i---j"""T--r---r-t • •l l+ Tl I 1 J_\j/ . N r l T l o~f-1---~...-1i--1---1---i---1---1-'~,---..----------------..,._--.,.._,...._____ ~ ~ t l _.__ l i -!- I . .I ! i ~ I ! ~.-;- l -L l 1 I' ...__.,__,__._.,__....,__.._,_1......_..,___,,_...1_...+__..~_..____.__....__._.........._......_.1...-...-_ • 90 180 270 0 90 ! j _j_J I- I ~ I 180 270 360 ¢wn (fi~ z=w ycxwxpi) [~)o rest frame] Figure VI.2 9a Distributions of the ¢ 0 events in the w 0 nw angle of the normal to the w 0 peak with high w p masses. decay plane for -317- n+p~ntrr+n-n°p n-p~Tirn+n-rr 0 p 2 0 ~-r --v- r I 1 7 1 . t 1 .. 1 · '0:3 ~ ~ I,_ ~ t' 1 1 1 • ' - I _,... r ; ~-+-l- I '· ! d ti _L_ l _Ll 1-1·-t~ I ! ;-1 If ..._i..____ ~ +t.: 2 r~ 1 1 ,i \! Yii J rtI.. ~ ~1 ff + l ! -T-- I ' · - I'· ~) l I _._ j I' -l- , !, ';, '1 ' I I c-'"":'--1·j...,;~;-+~ J r 0t 0 I a 90 ' I I 180 270 ¢VJn (ft+- 0 90 I > z=V-311' yocv37rxpi) [n+n-rr 0 rest frame] Figure VI .29b Distributions of the ~ nw + - plane for angle of the normal t o the TI TI 0 . . . h h'ig,h n +TI - TI 0 p masses. events in t h e w wings wit ' 1 180 270 360 -318Table VI.12 0 w helicity frame 0 0 w 0 w p mass band(GeV) 1T 00 density matrix element 0 peak events + w winos events 1T 1T + 1T <l. 9 0.309±0.047 0.333±0.045 0. 377±0. 050 0.407±0.050 1.9-2.1 0.345±0.047 0.230±0.051 0.328±0.042 0.380±0.049 2.1-2.3 0.317±0.054 0.254±0.053 0.324±0.050 0.308±0.057 :;::2 • 3 0.240±0.040 0.293±0.055 0.163±0.042 0.130±0.042 The distributions of the ~ VI.29. nw angle are given in Figs. Vl.27 and As is evident from the plots, these distributions (especially 0 for low w p masses) show a marked cos20 dependence. · nw have been fit by c 0 (l+c 2 cos2~nw) (see equation (11)) with the results being given in Table VI.13. from the c 2 The distributions The o _ density matrix elements derived 1 1 coefficients are given in Table VI.14. 0 from these results, the w As can be seen 0 density matrix defined in the w helicity frame has equal diagonal elements (values consistent with 1/3) and a significantly non-zero non-diagonal element (9 _ ). 1 1 -319Table VI.13 fits to the cos2© -c 2 values from l+c 2~nw dcr/d ¢ 0 w 0 w p mass band(GeV) TI w distributions 0 peak events + TI w TI win·gs events + TI <l. 9 0.267±0.080 0 .492±0 .078 0.209±0.092 0. 200±0. 096 1.9-2.1 0.268±0.101 0.442±0.093 -0. 154±0.082 -0.089±0.096 2.1-2.3 0.208±0.104 0.339±0.100 -0.102±0.101 -0.120±0.115 .:?:2 • 3 0.116±0.081 0.312±0.103 0.021±0.087 0.040±0.100 Table VI.14 0 w helicity frame P _ density matrix element 1 1 0 0 w winos events w peak events 0 w p mass band(GeV) 1T <l. 9 + + -;r TI -0 .134±0. 040 -0.246±0.039 -0.105±0.046 -0.100±0.048 1.9-2.1 -0.134±0.051 -0.221±0.047 0 .077±0 .041 0.045±0.048 2.1-2.3 -0.104±0 .052 -0 .170±0.050 0.051±0.051 0.060±0.058 .::::2 • 3 -0.058±0.041 -0.156±0 .052 -0.011±0.044 -0.020±0.050 1T -320As discussed earlier, the w0 and N* decay angular distributions 0 are correlated though the dependence of the w 8 PP and~ angles (see equation (15)). PP density matrix on the We present these correlations as fractions of events in each of 9 regions of a cos8 versus cos8 PP plot. The correlations between the 8 pp nw (or cos8 and 8 nw pn ) angles are given in Tables VI.15 and VI.16 as the region fractions from the (case pp ,cos8 nw ) plots. The region fractions from the (cos8 plot are given in Table VI.17. pp ,cos8 pn ) Note that an uncorrela t ed distribution would have 1/9 (or 0.111) of its events in each region of the plot if the individual cos8 distributions are fairl y uniform. -321- Table VI.15 cos8 ---pp versus cos8 correlation 0 results for w peak events cos8 ~~~~~~~~'--pp cos8 - - nw range - -1/3 to +1/3 -1 to -1/3 iT ran -ge +1/3 to +l + ( w0 p mas s < 1 • 9 Ge V ) +1/3 to +l 0.150±0.022 0.119±0.018 0.094±0.020 -1/3 to +1/3 0.199±0.028 0. 066±0. 013 0.104±0.021 -1 to -1/3 0.097±0.015 0.103±0.024 0.067±0.013 iT + (w0 p mass: 1.9-2.1 GeV) +1/3 to +l 0.089±0.020 0.064±0.015 0.154±0.023 -1/3 to +1/3 0.109±0.031 0.109±0.020 0.149±0.027 -1 to -1/3 0.089±0.021 0. 072±0. 017 0.165±0.023 iT - (w0 p mass <l. 9 GeV) +1/3 to +l 0 . 132±0. 021 0.092±0.017 0.074±0.017 -1/3 to +1/3 0.152±0.023 0.087±0.017 0.078±0.015 -1 to -1/3 0.161±0.023 0.107±0.019 O.ll7±0.020 rr - (w 0 p mass: 1.9-2.1 GeV) +1 / 3 to +l 0.109±0.022 0.054±0.014 0.1 46±0.02 4 -1/3 to +1/3 0.106±0.021 0.165±0.044 0 . 135±0.023 -1 to -1/3 0.087±0.019 0.086±0.018 0. ll2±0. 022 -322Table VI.16 cos8 -p versus cos8 correlation 0 results for w wings events cose range ---nw -1/3 to +1/3 -1 to -1/3 n + (w 0 +1/3 to +l p mass <1.9 GeV) +1/3 to +l 0.130±0.032 0.089±0.018 0.136±0.032 -1/3 to +1/3 0.082±0.018 0.085±0.018 0.114±0.024 -1 to -1/3 0 . 097±0.019 0.115±0.020 0 .151±0. 023 1T + 0 (w p mass: 1.9-2.1 GeV) +1/3 to +l 0.049±0.014 0.106±0.018 0. 213±0. 027 -1/3 to +1/3 0.094±0.017 0. 061±0. 014 0.149±0.021 -1 to -1/3 0 . 072±0.014 0 . 072±0.015 0.184±0.024 TI - ( w0 p mass <l. 9 GeV) +1/3 to +l 0.120±0.022 0.120±0.023 0.125±0.022 -1/3 to +1/3 0.129±0.022 0.047±0.013 0.106±0.022 -1 to -1/3 0.144±0.035 0.087±0.019 0.122±0.023 TI - ( w0 p mass: 1.9-2.1 GeV) +1/3 to +l 0. 081±0. 017 0.092±0.019 0.171±0.027 -1/3 to +1/3 0. 071±0. 016 0.071±0.015 0.140±0.023 -1 to -1/3 0.087±0.017 0.106:!::0.026 0 .182±0. 027 -323Table VI.17 case ---p versus case correlation 0 results for w peak events cos8 ~~~~~~~~~~p case ranP"e ---pn-=-=- -1 to -1/3 rr range - -1/3 to +1/3 + +1/3 to +l 0 (w p mass <1.9 GeV) +1/3 to +l 0.213±0.028 0. 096±0. 023 0.063±0.013 -1/3 to +1/3 0.067±0.014 0. 077±0. 014 0 .107±0. 017 -1 to -1/3 0 .166±0. 021 O.ll6±0.017 0.094±0.024 iT + 0 (w p mass: 1.9-2.1 GeV) +1/3 to +l 0.122±0.031 0.070±0.015 0.160±0.023 -1/3 to +l/3 0.078±0.022 0. 094±0. 021 0.142::0.026 -1 to -1/3 0.086±0.020 0.082±0.016 0.166±0.024 iT - (w 0 p mass <l. 9 GeV) +1/3 to +l 0.214±0.028 0 .10 2±0 . 018 0.102±0.018 -1/3 to +1/3 0.041±0.012 0.086±0.016 0.085±0.016 -1 to -1/3 0.189±0.025 0.098±0.018 0.083±0.018 iT - (w 0 p mass: 1.9-2.1 GeV) +1/3 to +l 0.132±0.023 0.120±0.038 0 .131±0. 023 -1/3 to +1/3 0.037±0.012 0.102±0.025 O.ll9±0.022 -1 to -1/3 0.134±0.024 0.083±0.019 0.142±0.024 -3240 5. Discussion of the w p Resonance Spin-parity Analyses 0 The information contained in the angular distributions of the w p 0 and w decays has been used in an effort to determine the spin-parity 0 of the w p resonance [Lednicky 1975). m The lack of any significantly o non-zero Yi moments below an w p mass of 2.1 GeV has been taken to 0 indicate that the w p system is in an S-wave state. This then estab- lished the possible spin-parities of the N* as 1/2 or 3/2 - . Lednicky used the results of several experiments wi th results similar to those 0 reported in the previous section to conclude that the w p resonance had a JP of 3/2-. The observations that bear directly on this conclu"'), sion are a "nearly" isotropic N N region and the large p decay with moments nearly zero in the 0 00 value for the w 0 [1974) in the w Gottfried-Jackson frame. found by Atherton et al. However, as we pointed out ·;{ earlier, the N decay distribution contains a significant non-isotropic piece which is not apparent in the moments due to their normalization. Dickey [1978) has further shown that either the 1/2 or 3/2 * spin-parity choice results in an isotropic distribution for the N decay. 0 Dickey has also calculated the w 0 density matrix (in the w * decay and has found that either spin-parity helicity frame) from the N 0 choice results in a diagonal matrix for the w . If the spin-parity is 0 1/2-, then one obtains equal elements (all 1/3) in the w matrix while those from the 3/2 density matrix for the 3/2 choice contain cos 8 choice is: PP density terms. The w 0 -325- (5-3cos 2 e PP p w nun (1+3cos 2 8 0 I 0 )/6 pp 0 pp , the w flat (20) pp )/12 density matrix for either JP predicts the flat distribution in cos8 The prediction of a 0 (5-3cos 2 8 0 When integrated over cos8 VI.2Sa). 0 0 )/12 ~ nw nw which we observe (Fig. distribution is obviously wrong (Fig. VI.26a), but the reason for this failure is currently unclear. 0 With the w decay angular distribution from equation (lla), we get the following joint distribution in the angles W(8 pp ,6 nw ) 3 2 (1+3cos 2 e pp + (5-3cos 2 8 epp and enw by )cos 2 e nw pp (21) )(l-cos 2 e )/2 nw This distribution gives the pattern shown in Table IV.18 (as a fraction of events in each region) and can be compared to the results of this experiment shown in Tables VI.15 and VI.16. As can be seen, the pre- dieted pattern is not evident in any of the distributions. However, the data distributions suffer from low statistics and have errors larger than the deviation of the 3/2 distribution (the 1/2 prediction). prediction from an uncorrelated -326Table VI .18 Predicted cos8 p p versus cos8 correlation pattern for J =3/2 cos e cos8 range p range -1 to -1/3 -1/3 to +1/3 +1/3 to +l +1/3 to +l 0.117 0.100 0.117 -1/3 to +1/3 0.100 0.133 0.100 -1 to -1/ 3 0.117 0.100 0.117 ---nw - We can partially overcome th e limited statistics by combining the 9 numbers into just 2. These two numbers are t h e fractions of events in the regions of the plot that are enhanced or reduced relative to the uncorrelated distribution (0.111 per region). The enhanced regions are the center (0.133) and the four corners (0 .11 7) in Table VI .18. The reduced regions are the remaining four with values of 0.100 each. p The predicted enhanced values are 0.556 for J =1/2 - and 0.600 for J p = p p 3/2-; the r edu ced values are 0.444 for J =1/2 and 0.400 for J =3/2 . Table VI.19 summarizes the data r esu lt s. are inconclusive. As can be seen, the results The N* region data does not match either prediction. 0 The off-resonance and the w win gs data match the Jp=3/2- prediction very well for an unknown reason. -327Table VI.19 Combined cos8 0 versus cos 8 Tf 0 correlation fractions + Tf w data w p mass Enhanced Reduced Enhanced Reduced peak <1. 9 0.474±0.038 0.525±0.046 0.571±0.044 0.429±0.037 peak 1.9-2.1 0.606±0.048 0.394±0 .047 0.619±0.062 0.381±0.039 wings <1. 9 0.599±0.057 0.400±0.040 0.528±0.054 0.442±0.043 wings 1.9-2.1 0.579±0 . 044 0.421±0.036 0. 592±0. 048 0.409±0.043 Both the Lednicky and Dickey analyses and our earlier paper 0 [Davison 1974] argue that the w p s ys tem is in an S-wave state due to the lack o f any significantly non-zero moments in the region of the 1, N . However, as we pointed out earlier ( eq uations (19)), the normal- izations of the moments can result in small values even if the angular distributions are significantly non-isotropic. In fact the cos8 pp distribution in the N* region (Fig. VI.17a) was found to have a significant backwa rd peak even thou gh the moments h ave ve r y small va lues. The hi gh er masses have cos8 pp distributions with very strong forward peaks and do show large non-zero momen ts. The backward pea k in the N* cos8 pp of ,non-zero off-diagonal terms in t he N ence with the background amplitude. distribution may be the result density matrix or of interfer- The lack of any si gnificant ¢ pp dependence seems to rule out the existence of any non-zero off-diagonal -328density matrix elements. 0 On the other hand, the fits to the w p mass * distribution showed that nearly 50% of the cross section in the N region is due to background. If the resonance had a P-wave decay (L=l) and the background was an S-wave state, then interference between their amplitudes could generate a cos8 distribution. pp term in the angular Since there are approximately equal amounts of the 0 resonance and background cross sections for w p masses below 1.9 GeV, it is likel y that the resonance and background amp lit udes are of comparable strength. the cos 2 e PP Thus the cos8 pp interference term could hide dependence from the resonance's P-wave decay. The choice of a P-wave resonance in the above example was made since the S-wave assumption seems to be invalid. Dickey's predictions based on this assumption are also not completely supported by our data. 0 The lack of the predicted isotropy in the w p decay has been discussed; 0 the prediction of an isotropic decay distribution for the w in its 0 helicity frame comes from Dickey's calculation of a diagonal w den - sity matrix whose terms are all 1/3 after int egrating over the N* decay angles. Our results support the values of 1/3 for the diagonal 0 elements of the w density matrix but we find a significantly non-zero value for p _ based on the observed strong cos2~nw dependence (Fig. 1 1 VI.27a). However, the observation of a cos2 ~ nw dependence of similar strength in the mass band above the N * (Fig. VI.27a) indicates that the background may be the source for the non-zero p _ e l ement. 1 1 the pattern predicted by Dickey for the (cose pp VI.18 is not seen in our results (Table VI.15). ,cos9 nw Finally, ) plot in Table However, there is -329- * is in an some evidence (Table VI.19) that the background under the N S-wave state with Jp=3/2-. We thus find that it is quite likely that Lednicky's result of 3/2 0 for the spin-parity of the w p resonance is in error. The basic assumption of an S-wave decay seems to be unsupported in light of our In fact, as discussed above, a P-wave decay for the N* with an data. 0 S-wave background may be needed to explain the w p angular distribution and in particular the peak at cos8 PP =-1. If the resonance is in fact a P-wave state, then there are two knmvn resonances whose masses 0 are good matches to that found for the w p resonance. These are the N(l780) with a JP of 1/2+ and the N(l810) with a JP of 3/2+ [Particle Data Group 1978]. 0 This match is due to the P-wave w p state having possible J p I s of 1 /2+ , 3/2+ , and )~ /2+. An S-wave wQ p state can only p have a J" of 1/2 ances. or 3/2 and will not match any of the known reson- At this time we can make no definite conclusion except that further work is needed to resolve the question of the spin-parity of 0 the w p resonance. -330Appendix A FAST Algorithm The software trigger algorithm was designed to calculate approxiwately the mass (m ) of the products in the bubble chamber recoil- x ing against the fast forward pion. This recoil mass is then compared against preset limits (i.e., m0 <m <m ) to suppress the taking of x ~ u pictures of elastic scatter and pion diffraction events. To reduce the time needed for this calculation, only the horizontal (spectrometer magnet bend plane) projection of the fast track was used. We begin the analysis of the trigger algorithm with m x in terms of the four vectors of the beam, target and fast forward particles: 2 x (1) m or, in the laboratory frame with t being the invariant momentum trans fer from the beam to the fast pion: 2 x (2) m The laboratory energies of the beam (Eb) and fast pions (Ef) are very large compared to the pion mass, thus by using the approximation E ~ p (where p 2 = E 2 + m2 is the magnitude of the 3-vector momentum) and rewriting eq. (2), we have: 2 m 2 - m ~x~~~P + 2m p t 2m · p (3) -331- Using eq . (3) and the limits to be imposed on rnx, we can set coarse limits on the fast track momen t um: pf pf ~ ~ pmin pmax 2 2 m - m u p Pb 2m p Pb - (4a) 2 2 mi - m 2m e (4b) p Note tha t the term with t is left out of both limits because it is a l ways less than zero (thus p max is at t = 0) or i t is neg l igible compared to the energy difference (Eb - Ef) term (which dominates at low momen t a). Before continuing wi th the derivation of a better test for the low mass cut (mx ~m i) , let us study the momentum tests (eqs. (4b)) using the measured quantities. (4a) and Basica ll y, the tr i gger program uses the spark positions x , x , x and x measured in the stations at 4 1 2 3 z , z , z and z , respectively (see Table A.l). 1 2 4 3 As can be seen from Fig. A.l, the scattering angle (8) is simply gotten by: (5) where the small angle app r oximation (sin6 ~ tan8 ~ 8) has been used. A particle of momentum p is bent through an angle S+S 0 in the magnet, but since stations 3 and 4 are positioned such that a particle of momentum p 0 appears to have zero bend angle, only the differential bend S i s measured directly. Thus we have: -332- e f Bd2 (6a) or, r ewriting as: s (6b) Thus we have the maximum and minimum bend angles given from the minimum and maximum momenta: smax 1 s0 p 0 (- - L) p . smin 6oPoC-P- mi n Po 1 L). max Po The trigger uses the quantity d 3 (?a) (7b) (the sagitta at station 3) defined as: x4 - xl ( z4 - zl ) (z3 - zl) + xl - x3 to perform the tests required by the cuts. relate d 3 (8) Using Fig. A.l, we can to S by observing that for a particle with scattering angle e and differential bend s we have: (9a) -333- (9b) Using eqs. (9a) and (9b) with the definition of d , we find: 3 (10) The test then made on this quantity is: d 3min < d 3 < d 3max (lla) which corresponds to the requirement: (llb) since d . and d are gotten from B . and 6 by using the min max 3min 3 max constant given in eq. (10). This test is used to place some limits on the fast track momentum: (llc) However, near p max (or equivalently, near mx ~ m0 ) a better test is ,,, needed which takes into account the scattering angle (i.e., non-zero t) . -334- To produce a better approximation for high momentum, non-zero t events, we return to eq. E ~ p (2) and now use the approximation: 2 +~ (12) 2p which yields: m 2 + _ rr _ cL 2 Pb (13) Now we can write t in terms of laboratory quantities: (14a) and t h en using the above approximati o n for Eb and Ef and the small angle approximation, we have: (14b) We now introd u ce the notation: (15) so that (14b) becomes: t ~ (16) -335- since the approximation will be used for large momenta, pf ~ pb' so o << 1, we can simplify (16) by neglecting terms in o2 to get: (17) Combining with eq. (13b) and using (15) , we have: 2 2 2 m - m Pb p x e 2 c1-o) + pbo ~ 2m 2m p p m 2 TI 0 - -- 2pb (18) or, by neglecting the third term (pb is large compared to mrr), we have: 2 2 m x - mp 2m (19) p Now we return to eq. (6a) and include the sextupole correction to the magnetic field (about a 3% effect) so we have: p s (l+bx 2 ) 0 0 (60+6f) (20a) and: (20b) where x is the horizontal displacement of the particle from the magnet's center: -336- (21) Thus we have: 1 - cS (2 2) Now, using eq. (19), we can write, by neglecting terms in e 4 and 2 2 m - m x p Pb - 2m (23) p Now, we can use pb ~Po and (since Sf << S ): 0 (24) 2 in the right-hand side of eq. (23) to get (neglecting terms in 8 Bf): 2 2 m -m B (1 - .!__ (o - x p)) 2m 0 Po . b p ~ s ·f - 2 e2 s0 c~ 2m + b 2 3 ) · (25) p This equation can then be translated into a test to require m x > m 9., as: 2 2 9., p m -m 2m p )) (26) -337- Note that the left size is (from eq. (4b)): 2 2 9, p)) m -m 2m -s min .. p Finally, in terms of the measured quantities d 3 and x 2 - x 1 (2 7) , we have the test made in FAST to eliminate triggers on elastics events: d I• min (28) where the constants are given by: d'. min ct (29a) (24-23) (zm-zl) (z4 -zl) (z2-zl) Before the above tests (eq. 2 (29b) (lla) and (28)) can be made, the raw spark chamber spark data as read into the computer memory must be processed. This processing converts from time to position units, giving the spark positions in the overall spectrometer coordinate system. In addition, the two sets of sparks from each of the two X wands in each station are merged to yield a single set of sparks for each station (treating station 4 as two substations 4R and 41 then concatenating their spark sets into a single list). This spark setup process is described in more detail with the description of the spark chamber analysis program TORTIS in Chapters II and III and in Appendix -338- B. FAST begins searching for tracks by trying sparks from stations 1, 3 and 4 until a set (x , x , x ) is found such that the value of d 3 1 4 3 calculated from the set satisfies the conditions given in eq. (lla). To locate a spark in station 2 to complete the track, the sagitta at station 3 (d ) is geometrically projected to station 2: 3 z -z ( 2 l)d z -z m m (30) 1 Using this and the line connecting x 1 and x 4 (also used to calculate d ), a predicted position for the x spark is calculated. 2 3 ference between the actual and predicted x 2 The dif- spark positions is: (31) FAST required r to be within a preset limit for the track (~ow with four spark coordinates) to be a trigger candidate: Ir ! < wr . (32) This candidate track was checked for an interaction vertex outside the bubble chamber by calculating the X positions of the track at the front and rear bubble chamber windows: (33a) -339- (33b) and requiring these to be within a preset range of the beam centroid: (34) where the constants x ( r 0 (beam center position), wb (beam width) and wr window) were determined empirical l y . If the track satisfied all these conditions, the quantity MMF (the right side of eq. was calculated and the final trigger test (eq. (28)) was made. (28)) If the trigger condition was satisfied, a bubble chamber picture was taken for the event. -340- Table A.l Definition of quantities in Appendix A Positions along Z-axis of: z. 1. spark chamber station i (i runs from 1 to 4) front of bubble chamber z r rear of bubble chamber interaction vertex z m spectrometer magnet center x. measured spark positions in each station e scattering angle s differential bend angle in spectrometer magnet of particle with momentum p 1. design momentum of the spectrometer (14 GeV/c) bend angle of particle with momentum p 0 (61.2 mrad) zf I 0 Zr Lz zl Figure A.l z2 zm xm See Table A.l for definitions Z3 X3 Schematic illustrating FAST track analysis algorithm (not to scale). The spectrometer design angle has been suppressed by having the Z-axis lie along the beam. zo y x Spectrometer Coordinate System Z4 X4 I I f-' ~ w / -342Appendix B TORTIS Track Finding and Spark Chamber Calibration 1. Track Finding The raw spark chamber data consisted of the separations between the first fiducial pulse and any sparks (and the second fiducial pulse) in time as counts of a 20 MHz crystal-controlled clock. TORTIS first recognized and removed from the spark lists the second fiducial pulses. A running average was kept for each wand of the time (in clock counts ) between the two fiducial pulses. From the known sepa- ration between the fiducial wires, the current speed of sound (6xfid/6tfid) was calculated for each wand and used by TORTIS to convert the spark positions from time to a space position: (1) where the x 0 constants (one per wand) gave the location of the first fiducial wires in the spectrometer coordinate system. These constants also included a correction for the width of the first fiducial pulse since all the sparks and the second fiducial had their pulse center position recorded by the center-finding circuitry. The x 0 constants were subject to change from electronic drifts and physical movement of the spark chambers. Thus they were initially set by survey measure- ments and then fine-tuned and tracked by our calibration procedures (see sections 2 through 4 of this Appendix). Each measuring station of the spectrometer consisted of two pairs of similar spark chambers (for instance, station 1 had 2 XY and 2 UV chambers). Since each chamber had better than a 90% probability of -343making a spark for a track, the probability of each station having at least one spark for a track was better than 99%. After the spark mea- surements were converted to positions, the spark sets from these two chambers were merged into a single set (OR'ed). Thus each station had only one set of X and one set of Y (also a U set and V set if station 1 or 3) measurements of the sparks in that station. done separately in X and Y (or U and V). The merging was As the lists of sparks were merged, a check was made for sparks from the same track which occurred in both chambers of a pair by looking for spark pairs whose difference was less than a prechosen window (±0.l inches). These two sparks were then replaced by their average to give a single spark at the station instead of two sparks from the same track. The distributions of the differences between the positions of sparks in the chamber pairs were used to adjust the relative alignment (of the x 0 constants) of these chambers and to determine the spark chamber setting errors. Once TORTIS had a list of sparks at each station, track finding was done independently in the X and Y-views with the resulting X and Y-tracks then being matched together by use of the sparks in the UV chambers. The X-view track finding algorithm used by TORTIS was simi- lar in some ways to that used by FAST and described in Appendix A. pair of sparks in stations 3 and 4 (after the magnet) were used to calculate the track position (in X) at the center of the magnet as shown (xi is the spark position and zi is the longitudinal position along the beam of station i, with the subscript m representing the magnet center): A -344- x m x 3 - (2 -2 ) [ 3 m x4 -x3] 2 4 -2 (2) 3 By assuming the event's vertex was in the center of the bubble chamber (the origin of the spectrometer coordinate system), an approximate spark position in station 1 was calculated using the calculated magnet center intercept (xm) for the track candidate (xBCO is the transverse location of the beam center at the origin) : (3) TORTIS then searched the station 1 spark list for a spark near x T 1 using a very wide window which was twice the full width of the beam (in X) at the bubble chamber (about 1.5 inches). If no such spark was found, TORTIS selected a new pair of stations 3 and 4 sparks and began the process again, continuing until all the stations 3 and 4 spark pairs (all combinations of sparks from the stations 3 and 4 spark lists) were tried. If a statiori 1 spark was found within the search window about xlT' it was used along with xm to calculate a predicted spark position at station 2: lr x m-x 1 ] (2 m-22) z -z m 1 (4) The station 2 spark list was then searched for a spark near the x T 2 position using a window of about 0.4 inches full width. If such a spark was found, the candidate X-track then had a spark a each of the four spark chamber stations. The X-track was accepted and added to the X-track list if the intercepts of the extrapolated track with the front and read bubble chamber positions (at zBCF and 2BCR): -345- (Sa) x1 - (Sb) (Sc) were within a window about the beam center (a similar cut was used in FAST, see Appendix A). The search for Y-tracks was simpler then that used for X since the spectrometer magnet bent the particles in the X-plane. TORTIS began by using sparks from stations 1 and 4 to calculate a predicted position at station 3: = y4 - ( z -z ) 4 ry 4-y l] 3 l z -z l 4 (6) 1 Then the station 3 spark list was searched for a spark near y T. 3 The search window (±0.25 inches) was large to allow for a small bend in Y due to finge field focusing in the magnet. If a spark was found in station 3, it was used to calculate the intercept of the track with the magnet center: (7) which was then used with the station 1 spark to calculate a predicted spark position at station 2: (8) The window used in searching the station 2 spark list was smaller (±0.15 inche~ than that used in the station 1 search since the Y-bend -346was explicitly taken into account by calculating y . m A good Y-track was then one which had sparks at all four stations after the above procedure. As with X, TORTIS tried all pairs of stations 1 and 4 sparks to find all the possible Y-tracks. After finding X and Y-tracks independently, TORTIS then matched the two track projections to yield the final track representing the trajectory of the fast particle. tested as matched tracks. All pairs of X and Y-tracks were Since station 4 consisted of two sets of XY chambers (each set being two separate spark chambers) mounted side-byside with the beam passing between them, the first requirement for a matched track was thus that both the X and Y-track have their sparks in the same module (or half) of station 4. The spark positions at sta- tions 1 and 3 of the matched track were then used to calculate predic~ ted spark positions in the UV chambers: where i is 1 or 3. Cx.)._ +y.) I 12 )._ (9a) Cy.)._ -x.) I .fi )._ (9b) The UV spark lists at the two stations were then searched for sparks within a window (±0. 2 inches) Of these predicted values. The track was accepted as a go od matched track i f a good UV spark was found at either station 1 or station 3 or at both stations (for the spark to be good, both u. and v. must have been within the )._ window around uiT and viT). )._ Some extra tracks were picked up by allowing a matched track to be made up o f the single X and Y-tracks (if only 1 of each was found) provided they came from the same station 4 module. Ambiguous and wrongly matched tracks were resolved or -347removed outside of TORTIS (for instance, HYBRID used the track match x2 and the SC-BC match x2 to select the best track). 2. Calibration Test Quantities Although the spark chamber positions were initially set by the survey, an internal calibration was made using tracks found by TORTIS to fine tune the constants and correct for any run-to-run electronic or mechanical drifts. We did this by using the constraints that tracks were continuous so the magnet center intercepts as extrapolated from the front and back halves of the spectrometer (i.e., using stations 1 and 2 or 3 and 4 sparks to give two separate extrapolations to the magnet center) were the same. Similarly we had the weaker con- straints that the average bend angle in the Y-projection was zero and that the elastic peak (in the missing mass) had to fall at the proton mass. Thus we defined a series of test quantities calculated by TORTIS for each track whose average values were used to correct the spark chamber alignment constants for each data run. Before calculat- ing these quantities, TORTIS corrected the stations 3 and 4 spark coordinates by a small amount to remove a small effect introduced by the geometry of the spectrometer. The effect was due to the z-axis being defined as the beam center which was bent at the magnet (through the survey angle, e0 , or 61.2 milliradians). This meant that the magnet center intercept extrapolations from the front and rear halves of the spectrometer were not being calculated for the same plane (perpendic~ ular to the z-axis) in space. dent on xm 12 These corrections were small and depen- , the magnet intercept in X as extrapolated from stations -3481 and 2: (10) The correction terms added to the X and Y spark coordinates were then: x (lla) co or (llb) The constraint that the two magnet center intercepts extrapolated from both sides of the spectrometer agree (on the average) leads to the first test quantities: y 3 (12a) - - y These quantities were the same as those used and similarly for xTsT to search for station 2 sparks when track finding. Y-track as a (12b) 2 straight line with position y 0 If we consider the at the origin and slope a so that the spark position at station i is given by: Yo + azi + i=::i where i=::.]_ (i>l) is the amount station i is misaligned. (13) From this form, yTST can be found to be: '2 - D23'3 + D23[:~=::]'4 (14a) -349(z4-zm) (z2-zl) (14b) (z4-z3)(zm-zl) which just depends on the misalignment factors. It can also be shown that yTST and xTST are directly proportional to the difference between the magnet center intercepts extrapolated from the two halves of the spectrometer. The other Y-projection test quantity was the the bend angle of the track's Y-projection which was calculated as the difference of the track's slope before and after the magnet: - [y 2-y l] (15) z2-zl Here again we can express S in terms of the explicit misalignments y only: (16a) (16b) (16c) For the X-projection, the final test quantity was ~ST which related the missing mass (m) to the proton mass: x (17) where m was calculated using the measured track parameters which gave x the momentum (pf) and the scattering angle ( 8 m2 x SC ) : (18) -350where pb is the beam momentum and Eb and Ef are the beam and fast energies. This can be related to an angular test quantity much like 8 : y (19) where p meter. and 0 e0 are the design momentum and bend angle of the spectra- This quantity differs from S in that it does not measure a y deviation from zero, but from the bend angle associated with an elas~_ tic event with m =m . x p 3. Initial Calibration Using t he survey val ues as a starting point, a series of three special runs were made to calibrate the spectrometer. In these runs, a low intensity be a m was steered to the right or left of its normal center by using the 03.1 steering magnet (see Chapter II) so the beam would miss the dead spots in the spark chambers. In addition, the first run type (with beam steered right) had the spectrometer magnet turned off so the beam was undeflected. By measuring the apparent bend angle in X, the misalignments in X of station 2 and 3 were rected ( rel ative to stations 1 and 4). The corrections were given by: C <S > 3 cor~ x (20a) (20b) where <8 > was the observed average X- bend angle. x After correcting the appropriate constants and with the beam still steered right, the -351spectrometer magnet was once again turned on. The measurement of then yielded the beam momentum: (21) <S >+e x 0 Finally, by steering the beam to the left and measuring yet again, x the correction to the alignment constants of the left half of station 4 (relative to the right half) was gotten from comparison with <S > x measured for the beam steered right (with the magnet on): C ( <S > 4 x L - <S > ) (22) x R In addition, these runs yielded the beam center position at the origin (xBCO) and the measurement of the width of the beam in X. The Y-con- stants were handled in the normal manner as discussed below. 4. Tracking the Calibration with Data Runs Since all the beam pulses for which the spark chambers were fired were recorded on magnetic tape, the data runs were used to track the shifts in the spark chamber constants. This resulted in a set of spark chamber location constants for each run. These constants then effectively welded the entire spectrometer into a single rigid unit which other constants (used in HYBRID) connected as a whole to the bubble chamber. The test quantities discussed in section 2 of this Appendix were used to calculate the corrections to the constants. Some of these quantities were averaged separately for tracks in the two modules of station 4, thus treating station 4 as two separate stations in a sense. Before being added to the sums used to calculate · the averages, the test quantities were required to be within a window -352about zero that served to make the average more sensitive to the position of the centroid of the distribution. The yTST and xTST quantities were averaged over all the tracks (in both station 4 modules) and the misalignments of the station 4 modules were taken to be relative to one another, absorbing any overall misalignment of station 4 into those of stations 2 and 3. For instance, in terms of the explicit misalignment formalism used earlier, we have (under the assumption s 41 +s R=O): 4 (23) Similarly, Sy and ~ST were averaged over all the tracks to eliminate the station 4 misalignments. In addition, both of these were also separately averaged over tracks in the left and right station 4 modules. Once again, using the explicit misalignment formalism and tak - (24a) lc<s > - <s > ) = s ;c 2 y L y R 4 4 (24b) where the L and R subscripts indicate quantities qveraged over the left or right station 4 ~odules. Similar formulae apply for X but in that case, By is replaced by Cm~ST' where: cm Poeo (25) 2m p 2 p b Given these averages, the spark chamber alignment constants were corrected according to the formulae in Table B.l. In the table, those -353averaged quantities with the L or R subscripts were averaged over tracks in only one half .(left or right) of station 4 while all other averages were over all tracks. Also, the station 3 UV constants were adjusted along with the XY constants: (26a) (26b) Finally, in addition to these corrections to all the chambers at a station, the constants of the individual spark chambers in a pair were adjusted relative to one another so the residuals from the OR'ing (of the redundant chamber pairs) were centered on zero. Table B.l Constants correction formulae x y > + C3D2f m<mTST> -<yTST> + C3D23<Sy> station 2 -<x 3 C3Cm<mTST> c 3 <S y > 4 right O.SC4Cm(<mTST>R - <mTST>L) O.Sc (<Sy>R - <Sy>L) 4 4 left O.SC4Cm(<~ST>L TST ... <mTST>R) O~Sc 4 (<Sy>L <Sy>R) These corrections had only small effects on the constants, particu~ larly when compared to the setting (measurement) error of a single spark chamber (which was about 0.018 inches). The numbers given in Table B.2 were gotten by histograrnming the differences between the constants used in adjacent runs. Table B.2 lists the sigmas of the resulting distributions as all the average values were considerably - 35 4less than 0 . 001 inches. Table B.2 R.M.S. r u n - to~run change s in the s par k chamber constants (in inches) station x y 1 0 .003 0.002 2 O.Oll 0.007 3 0.007 0.008 4 right 0 .Oll O.Oll 4 l eft 0.012 0.013 -355Appendix C Computer Trigger Efficiency Determination The calculation of the computer trigger efficiency wa s discussed in Section 5 of Chapter IV. This e f ficiency is the product of the RESID, DEL3, and HMF cut efficiencies wh ich were calculated b y the use of equations (IV.13a-c). This procedure required that we have the means and v a riances for RESID (~ and oR) , DEL3 (d and oD) , and XMF (~ and oM) parameterized as functions of the fast particle's momentum ~ vector (p). These functions were determined from Monte Carlo studies using the ray tracing program developed for the geometrical acceptance calculations (see Section 4 of Chapter I V). The test quantities were calculated from the generated spark positions using the same formulas and parameters used in the computer trigger program. For these ~onte Carlo studies, the effects of the spark chamber resolutions and multiple scattering of the fast particle were included in t h e model of t h e apparatus. The Mo nte Carlo studie s also s how ed that the online c orn- puter program's b ubble chamber fiducial volume tests (see Appendix A) were so conservative that no correction was needed for the very few events lost due to th es e cuts. The Monte Carlo studies allowed us to construct a table of the means and v ariances of RES ID and DEL3 for selected values of the fast momentum (p) and the scattering angle (6). We then fit these value s to the empirical formula: q(p,e) (1) -356where q stands for a mean (r or d) or variance (o~ or 06). These fits gave acceptable results in describing the variations of the means and variances as functions of p and 8. Though this formula gave the mean of RESID (r) as a function of p and 8 , the actual value of r (p,8) was dependent on the spark chamber location parameters. We examined the model for RESID gotten from the Monte Carlo studies by using the actual online computer trigger RESID's from samples of the data. We compared the actual RESID distributions to those gotten from the integral: g(r) = f f(p, ) p, 8 1 ~ oR(p,8) exp{-(r-r(p, 8 )) 2 /20~(p, 8)) dpd6 where g(r) is now the calculated distribution of RESID from the Monte Carlo r(p,6) and 0R(p,8) functions. (~r) (2) as gotten The integral is over the (p,8) region occupied by the data with f(p, 8 ) being the experimentally observed distribution of e v ents in p and 8 . The integral was numerically evaluated by generating ideograms based on r(p,8) and 0R(p,8). The resulting means and variances of these ideograms were then compared t o the means and variances of histograms of the actual RESID values. The comparison showed that r(p,8) and oR(p,8) were ade- quate for modeling the data except for an empirical additive correc tion to r(p, 8 ) by a constant value ( -1.6 units for the IT+ experiment and -2.3 for the rr experiement) so that the model ~ESID's were dis- tributed about a centroid near zero. The MMF test quantity was evaluate d using the formula: ~(p) = A + Bp + Cd2 + Dp2 (3) -357where p and d were gotten from t by: 1 p (4a) /p2+ p2 z x d = pz (4b) PX -+ where px is the component of p along the beam direction and p 2 is the -+ horizontal component of p transverse to the beam (i.e., the x and z -+ components of p in the general coordinate system). The values of the coefficients A, B, C, and D were gotten by doing a least squares fi t - -+ of rn(p) to the values of MMF from the data. Table C.l show s an exam- ple of the results of the fit as compared to the a priori values cal culated from the experimenta l geometry parameters and the computer trigger program algorit h ms. Table C.l - ->- m(p) coefficients fit t ed a priori A - 533.5±1.5 -537.3 B 7555±29 7521. 7 c - 3737±40 (not evaluated) D - 100±140 0 The A te r m is very dependent on the precise va l ue s of the spark chamber location parameters which are subject to slight drifts with time. In particular, by stud y ing the v ariati o n in the average of: DM = MMF - (A + Bp) (5) -358(using the a priori values for A and B) with roll number, we were able - + to define groups of rolls in which we then did the fits to m(p) to obtain values of the coefficients for each group of rolls. - The result- + ing sets of coefficients were used to calculate m(p) in finding the average of: - DM' + MMF - m(p) (6) which showed no dependence on roll number, recoil mass, or fast momentum. - + Thus we found that m(p) with a roll-group dependent parameteriz- ation was a good model for the average value of MMF. The dispersion of MMF about its mean was gotten from the dispersion of DM' from equation (6) for each roll group. This observed DM' dispersion was found to be larger than the value obtained from the Monte Carlo studies. The Monte Carlo value, however, did not take into account the residual fluctations due to secular drifts of the apparatus. An additional check that was made was to calculate the fraction of elastic roll elastic events which would have been accepted as inelastic events by the trigger program. The results of these cal- culations and the fraction actually observed (calculated from the MMF's actually used by the trigger program) are given in Table C.2. The fraction calculated from the observed events is overestimated because about 5-10% of all the events are events that occur while the spark chambers are still live after being fired by an earlier event (in the same beam pulse). The bottom line of Table C.2 gives the observed fraction corrected for these extra events. 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