P̅P Backward Elastic Scattering Between 0.70 and 2.37 Gev/c Citation Yoh, John Kzun-Ke (1970) P̅P Backward Elastic Scattering Between 0.70 and 2.37 Gev/c. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/TA1E-VN55. https://resolver.caltech.edu/CaltechTHESIS:09012015-105054487 Abstract ̄pp backward elastic scattering has been measured for the cos θ cm region between – 1.00 and – 0.88 and for the incident ̄p laboratory momentum region between 0.70 and 2.37 GeV/c. These measurements, done in intervals of approximately 0.1 GeV/c, have been performed at the Alternating Gradient Synchrotron at Brookhaven National Laboratory during the winter of 1968. The measured differential cross sections, binned in cos θ cm intervals of 0.02, have statistical errors of about 10%. Backward dipping exists below 0.95 GeV/c and backward peaking above 0.95 GeV/c. The 180˚ differential cross section extrapolated from our data shows a sharp dip centered at 0.95 GeV/c and a broad hump centered near 1.4 GeV/c. Our data have been interpreted in terms of resonance effects and in terms of diffraction dominance effects. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Barish, Barry C. Thesis Committee: Unknown, Unknown Defense Date: 19 May 1970 Additional Information: Title varies in the 1970 Caltech commencement program: Anti-Proton-Proton Backward Elastic Scattering from 0.70 to 2.37 Gev/c Funders: Funding Agency Grant Number Atomic Energy Commission UNSPECIFIED Record Number: CaltechTHESIS:09012015-105054487 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:09012015-105054487 DOI: 10.7907/TA1E-VN55 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 9129 Collection: CaltechTHESIS Deposited By: INVALID USER Deposited On: 01 Sep 2015 20:33 Last Modified: 23 May 2024 23:38 Thesis Files Preview PDF - Final Version See Usage Policy. 45MB Repository Staff Only: item control page

PP BACKWARD ELASTIC SCA'l'TERING BE'J'WEJ..;N 0. 70 J\ND 2. 3~( GEV/C 'l 'hesis by ,John K. Yoh In Partial F'ulfilllnent of the Requirements For the Degree of Doctor of Philosophy Ca.l.i..1."ornia Institute of 'l'echnology Pasadena, California 1970 (Submitted May 19, 1970) ii ACKNOWLEDGMENTS The author wishes to thank his advisor, Professor Barry Barish, for adv i ce and encouragement. The author also wishes to extend his gratitude to Professors Jerome Pine and Alvin V. Tollestrup for help and advice during and after the experiment . The author is also in- debted to the other members of the collaboration who are involved with the e x periment. These include Mr. Howard Nicholson of Caltech, Drs. Alan S. Carroll and Robert H. Phillips of Brookhaven National Laboratory, and Claude Delorme, Fred Lobkowicz, Adrian C. Melissinos and Yori Nagashima of the University of Rochester. The author is also indebted to the support personne l of the three institutions, in particular to Messrs William Friedler, Hans Grau and Jack Sanders. The aid and support from the BNL computer ce nter staff and the AGS EAO group are also gratefully acknowledged. This research was supported by the U.S. Atomic Energy Commission. iii A BS'f RAC'!' pp backward elastic scattering has be en me asured for the cos 0 - cm reg ion be twee n - 1.00 and - 0.88 and for the incide nt p l a bora tory momentum r eg ion between 0. 70 and 2.37 GeV/c . These meas ur emen ts, done in intervals of approximately 0.1 GeV/c, have bee n performed at the Alternating Gradient Synchrotron at Brookhaven National Laboratory during the winter of 1968. The measured dif- ferential cross sections, binned in cos e intervals of 0.02, have cm statistical errors of about 10%. Backward dipping e x ists below 0.95 GeV/c and backward peaking above 0.95 GeV/c. tial The 180° differen- cross section extrapolated from our data shows a sharp dip centered a t 0.9.5 GeV/c and a broad hump centered near 1.4 GeV/c. Ou1· dat.:i have been int0rpretl>. <l in t e rms of resonance effects and in turms of diffraction dominance effects. iv TABLE OF CONTENTS CHAPTER I: INTRODUCTION CHAPTER II: EXPERIMENTAL APPARATUS AND METHODS (a) Introduction and experimental layout 8 (b) Beam target and magnet 14 (b-i) Beam and p identification and counting 14 (b-ii) Target 24 (b-iii) Magnet and momentum measurement (c) Fast counters and logic Introduction 28 (c-ii) Trigger counters, logic and rates 30 The gas threshold Cherenkov counter 37 (c-v) The forward outgoing particle time-offlight system 42 Recording and monitoring of data 44 (d-i) Introduction 44 (d-ii) Wire spark chambers and the recording of digitized spark positions 44 . (d-iii) PDP-8 computer and int erface system of recording the data 50 Data recording -- summary of data taking procedure 51 (d-v) The contents of the data recorded 58 (d-vi) Monitoring of the data taking 59 Evaluation of the apparatus and data taking system CHAPTER III: 36 (c-iv) (d-iv) (e) 28 (c-i) (c-iii) Counter bits -- scintillation counter information for analysis (d) 24 60 ANALYSIS OF THE DATA (a) Introduction 65 (b) Reconstruction of e vents 66 (b-i) Introduction 66 (b-ii) The finding of event tracks from the digitized spark posit i ons 67 (b-iii) Procedure for removing spurious tracks 69 v (c) (b-iv) Reconstruction inefficiency 72 (b-v) Analysis of triggere d events which fai l the reconstruction proc ess 74 SP.l.ec t:ion or backward c•hrnt:ic pp ('Vf'nts 75 (c-1) Introduction 7 ') (c-ii) Topology selec tion criterion 77 (c-iii) Reconstructed vertex criterion 80 (c-iv) Velocity criterion 82 (c-v) Momentum criterion 84 (d) Corrections to the normalization 85 ( e) Monte Carlo of the apparatus acceptance 90 (f) Calculation of the differential cross sections and errors 94 Summary and assessment of the analysis procedure 96 (g) CHAPTER IV: RESULTS-- PP BACKWARD ELASTIC DIFFERENTIAL CROSS SECTIONS (a) Differential cross section for each angular bin 103 (b) The 180° des and slope extrapolated from our data 103 (c) Comparison of our data with other existing data 116 (d) Features of our data 117 CHAPTER V: (a) (b) RESONANCES: AN INTERPRETATION OF THE DATA Introduction and the probable absenc e of strong Regge u channel effects 119 Resonances and the pp system: theoretical considerations 121 (b-i) (b-ii) (c) (d) !he coupling of resonances to the pp system 121 Features_of resonance contribution to elastic pp sc attering 123 Other expe rimental and theoretical evidence for boson r es onances 130 (c-i) Other experimental evidence 130 (c-ii) Theoretical models predicting boson resonances 134 What our data say channel about resonances in the direct 140 vi (e) (d-i) Narrow resonances 140 (d-ii) Broad resonances 142 Conclusion CHAPTER VI: 147 DIFFRACTION, AN ALTERNATE INTERPRETATION OF THE DATA (a) Introduction and motivation for this interpretation 149 (b) Spin-orbit optical model 155 (b-i) Formulation of the model 155 (b-ii) Spin-orbit optical model and our data 158 (b-iii) Assessment of the spin-orbit optical model -- does it reproduce other elastic and polarization data ? 162 Diffraction dominance and pp elastic scattering 167 pp (c) (c-i) (c-ii) Brief survey of other diffraction type models 167 Features of diffraction dominance in pp elastic scattering 168 (c-iii) Assessment of diffraction dominance and suggestion for further e xper ime ntation CHAPTER VII: 169 SUMMARY AND CONCLUSION (a) Summary 171 (b) Conclusion 173 Appendix A : Beam transport system 174 Appendix B: Wire spark chambers 178 Appendix C: Inef~iciencies events References in reconstruction o f triggered 189 198 vii Index of Figures Figure Number Contents Page Feynman diagrams for the s and u channel contributions to backward elastic scattering of pp, rc_p , and K+p. 2 1. 2 re p elastic scattering at 180° 4 1.3 K+p backward elastic scattering data 5 2.1 Layout of the separated beam transport system 10 2.2 Layout of our apparatus 12 2.3 Beam liquid differential Cherenkov counter 17 2.4 Beam Cherenkov and 2.5 Distribution of beam momentum, positions and slopes 22 2.6 Rectangular field. model for a dipole magnet 27 2.7 Improving momentum determination using mass slit counters 29 2.8 Triggering area in P-R space 33 2.9 The trigger logic flow chart 35 2.10 Gas threshold Cherenkov counter 39 2 .11 Cherenkov pulse-height channel distributions 40 2.12 Time-of-flight channel distributions 43 2 .13 Wire spark chamber signals and digitizer operation 47 2.14 Trigger and event recording timing diagram 53 3.1 Topology of a desired backward elastic event 68 3.2 Distribution of VD and MTD for backward elastic events 79 1.1 3.3 3 .4 2 curves 18 2 distributions for events passing and failing velocity criterion (MM) - . (Mp) time-of~f light %acceptance curve as a function o f cos Bcm 83 93 viii 3.5 Flow chart of the ana l ysis procedure 97 4.1 Our data in µb/sr 106 4.2 Our data in µb/GeV 4.3 Linearly extrapolated 180 µb/sr 4.4 4.5 2 Linearly extrapolated 180 µb/Gev2. 107 0 des and slope in 113 0 des and slope in Exponential extrapolated 180 in µb/Gev2. 114 0 des and slope 115 5.1 Angular momentum barrier for pp and nN systems. 124 5.2 Shape of the resonance contribution to the des 127 5.3 qq model predicted meson states 137 5.4 Meson states predicted by the daughter trajectory model 139 Resonance prediction for 180° des using total cross section resonance candidates 145 Forward elastic pp des and diffraction model curves 150 6.2 Diffraction nature of l arge angle pp elastic des 153 6.3 3-dimensional compilation of pp elastic des be low 2 GeV /c 154 5.5 6.1 6.4 6.5 Spin-orbit optical model curves of the 180 and slope 0 des 159 Spin-orbit optical model curves in the region of our data 160 Spin-orbit optical model curves for elastic · scattering below 1.5 GeV/c· and for polarization measurements 164 A. l Beam ray trace 176 B. l Wire spark chamber construction and operation 179 C.1 Calcomp plotter pictures of several triggered evt~nt s I l) J 6.6 ix Index of tables Table Number Contents Page 2.1 Beam counter sizes and positions 15 2.2 Beam fluxes and rates 21 2.3 Non-beam scintillation counter sizes and positions 31 2.4 ·. Positions and sizes of the sensitive areas of the wsc 46 3.1 Sizes of all corrections to the normalization 87 3.2 Properties of the analysis and data at each momentum 99 pp backward elastic des obtained in our experiment (µb/sr) 104 4 .1 2 4.2 pp backward elastic des in µb/Gev 4.3 pp 180° elastic des and slope using linear extrapolation 4.4 5.1 - 105 109 0 pp 180 elastic des and slope (exponential extrapolation) 111 Boson resonance candidates above twice the proton mass 131 - 1 - CHAPTER I: INTRODUCTION In the study of high energy interactions, the des (differential cross section) at extreme angles has been very useful in revealing the important mechanisms responsible for the interaction. Strong contributions from s (except s-wave), t or u channels usually lead to d cs with characteristic peak ings or dipping at extreme angles with characteristic dependence on energy. (1 . 1) or In the case of elastic scattering, the forward des is not very useful in revealing any mechanism aside from the diffraction which dominates forward scattering. Thus, the des for elastic backward scattering is crucial to the exploration of any important u channel and s channel mechanisms contributing to the elastic scattering. Figure 1.1 shows the Feynman diagrams corresponding to the s and u channel contributions to the backward elastic scattering of (a) pp; (b) n - p; and (c) K+p. Away from the low energy region, s channel contribution to elastic scattering is no longer dominated by s wave. Thus, the indi- vidual partial wave amplitudes of the important terms contribute larger values to the extreme angles (1.2) • In the event that s channel is dominated by a particular resonance near a certain energy region, the s channel contribution to the e x treme backward elastic des is characteristic. The size of the contribution peaks at the position of the resonance while at the same time there is backward peaking at the position o f the resonance ( 1.3) • However, interferenc e fr om other contributions s uch as u channel effec ts or background may obscure this behavior. - 2 Figure 1.1: Feynman diagrams for the s and u channel c ontributions to the backward elastic scattering of (a) pp, (b) n -p . and ( c ) K+p. Quantum numbers of the s and u channels are given. Possible candidates for the contributions are given in parenthesis. p B 0 Q (S,T,U ??) 0 p p B = 2 u~ Q = 2 ( ?? ) p p T p p p n (a) s / / ./ n- p B Q =1 0 / (e.g. , N*O) B = 1 u ----7 Q = 2 I I (e. g. , N*++) / r 1(- / / s / p / K+ K+ p / B I n (b) / p I p =1 u~ Q =;. 2 (z*++??) B 1 Q 0 - 1 s s =1 K+ / / / / +I ( e .g.' /\ 0 , L..o) K p 1 (c) I I p - 3 In 1( p backward elastic scattering in the region 1.65 ·- 5.3 4 GeV/c(l. ), the des at 180°, shown in Figure 1.2, revealed many sharp structures. For example, there are sharp bumps at 1688 and 1924 and a sharp dip at 2190, all of these can be attributed to resonance effects in the direct s channel. Indeed, this set of data was useful in indicating the properties of the resonances as well as suggesting possible existence of a new resonance at 3245 MeV. In the backward elastic differential cross section of other processes, it is possible to see similar structures in the event of strong resonance contribution from the s channel. u channel effects· may also be important in the backward elastic region. In the event that strong s channel and background contribu- tions are absent, the u channel contribution, if it is dominated by a single (or an exchange degenerate set of) Regge trajectorie s, produces a backward elastic des (do/du, in this case) which has energy and angle 2 2 dependence of s a (u) (l.S) where a(u) is the function corresponding to the dominant trajectory. Thus, the do/du at u = 0 would have as-a dependence where a= 2 - 2a(O). of u shows an e ba(u) . At a particular s, do/du as a function d~pendence where b is 2 in(s). These behaviors are shown by K+p backward scattering; we have plotted the do/du near 180 ° of K+p scattering . . . F igure . l • 3 a and th e s l ope as a f unction o f s in 6 of d o /du in Figure l.3b(l. ). The data indicate that the des is consistent with the hypothesis that i t is . dominated by the A y the A , a in cas e of exchanging degeneracy) trajectories. (and/or In this particular case, there are good reasons to suspect that u channel effects may dominate since the s channel is an exotic channel (1. l) Plot of do/dn against incident Figure 1.2: f or ~ p e lastic scattering at 180°. the N* resonances are shown. the data. momentum (laboratory) The positions and properties of The line drawn is a free hand curve of The error bars are statistical. Phys. Rev. 164, 1661 (1967). Jr From Korrnanyos ct al . , See thi s article for the source of other data points. TT -p ELASTIC SCATTERING ~ t llERKELEY Holland 1\ ol.(160") 200 f NIMROD Dukt o\ al. (IG5•) + TlllS EXPEfllMENT ~;~,~00 (Kormanyos et.al.) :t , w t . ~· ··· ·' . ... fl •IO • .. ,., v .. ,,,w••, ::o ·- 4- 2190 213 l•tz,?.-1 P.<z,7.+I z 2'4~ I 1'12_?·-I 3 P0 IGoV/c) I 3245 2~50 ''·'z.?:i!_____ _ ~r_.i_._.,__~ 4 5 ~Carroll T et al. I I • GOLDHABER et ol. • BARRELET et ol. • HIRSCH et ol. • BLAND et ol. •COOK et al. • BETTINI et al. o BANAIGS et al. . (a) 1000; I I 10 IT I I 1T 1 I I ~ ::l.. I 0 J Pi ~ .,,,le:, "'......u ..... 1 ~H? 100;__ ? ~ m 0 I I I I x I ~ :J I I IJ.. j I I I I 0 I - I I -10 0.4 ! 0.8 1.2 1.6 2.0 2.4 2.B 3.2 T ·11 I I 50- iC; i x I I I I I I I (b) T I xI T T : I I t : I x I J.. T Tl* I 11£ I 1 I .L I I I I ...L J.. .l T I x' J- T x' _f-I I ...L ,--+---x~ I .i I \J1 ...L .~. - I s cos 8* < - O. 94 } - Is cos 8* < - 0. 80 Data of Carroll et al. I 3.6 .L Li_ PLAB(K+) GeV/c I 1.0 2.0 1.5 P. (BeV/c) me Figure 1.3: K+p backward elastic scattering (a) des and (b) slope near 180°. of the data, see Ref. 1.6. u :~/.lf f I_[ I -f1-0-~ 1f I I I >Cl.I ' E bi v du I I x I jlTI : I ! r ~ 0 du -o U lI TI I 500'- dcr T I :; dCT -(u)=-(o)e For the sources 2.5 - 6 and thus its contribution to the scattering i s not expected to be dominant. pp backward scattering exhibits many features which do not occur + + for eithe r rt-p or K- p backward scattering since (1) B 0 instead of B = 1, and (2) B = 2 and Q = 2. B the s channel has the u channel requires an e x change of Many massive (with mass greater than 2 proton mass) 0 non-strange mesons have been indicated by previous experiments(l.S~ In addition, there e x ist theories which require the existence of such ( 9 mesons 1. ) • It is expecte d that pp may coup 1e to some or a 11 o f t h ese resonances in the s channel if the y exist. Thus, pp backward elastic scattering is a sensitive probe of such resonances. It is hoped that the coupling may be strong enough so that features similar to those s e en in rt-p backward scattering may also be observed in pp backward scattering. As far as the u channel effects are concerned, no B = 2 and Q = 2 resonance has been observed or indicate d in experimental data . Therefore, it is likely that no distinct cha r acteristics indicative of u channel dominance would be observed. It is therefore likely that the s channel effects, if any, are easie r to observe. On the other hand, if there are significant contributions from the u channel, pp backward elastic measurements are sensitive to it. It is thus interesting to obtain pp backward elastic scattering data over a fairly wide range of energies as we ll as a wide enough range of angles in order to extract the backward slope. We have measured the pp elastic scattering dif f erential cross section with 10- 20 % statist i cal accuracy in the ~omenttun range 0 . 7 to 2.37 GeV/c - 7 - incident p momenttun (corresponding to the center-of-mass energy in the range 1.99 to 2.56 GeV). At each momentum, we obtain 5 to 7 angular data points with cos ecm between - 1.0 to about - 0.88. Preliminary results have been published(l.lO). This experiment, performed at the AGS partially separated beam 5 in Brookhaven National Laboratory during the fall of 1968, is a missing mass spectrometer experiment using a 37.5 cm long liquid hydrogen target, several counters and twelve wire spark chambers with digitized magnetostrictive readouts. We were able to measure the differential cross sections of pp annihilation into two charged mesons at extreme angles the same apparatus. (1.11) . simultaneously using essentially Part of our apparatus was used previously for b ac kw ar d pi and K scattering on protons (1.12) • This experiment was performed by a collaboration of members from three institutions: California Institute of Technology Barry C. Barish, Howard Nicholson, Jerome Pine, Alvin V. Tollestrup and John K. Yoh (the author) Brookhaven National Laboratory Alan s. Carroll and Robert H. Phillips (now at SLAC). and University of Rochester Claude Delorme (now at the Universit.y of Madagascar). Fred Lobkowicz, Adrian Melissinos, and Yori Nagashima (now at Caltech). - 8 - CHAPTER II: a. EXPERIMENTAL APPARATUS AND METHODS Introduction and Experimental Layout We wish to measure the des (differential cross section) of pp backward elastic scattering. Therefore, we need to have a beam of p's incident on some hydrogen and to count all the pp backward elastic scattering events inside a well determined angular region. Many accelerators have beams of partially separated negative charged particles with sufficient momentum range which we wish to cover (about 1 - 2 GeV/c)(Z.l). We thus need a system to identify the p's in the beam as well as to determine the momentum, position and direction distributions of such incoming p's. The p's are in- cident on a liquid hydrogen target. To identify the pp backward elastic scattering events, we have to look at the final state particles of such reactions. The recoil proton from a backward elastic event (we only consider the region of cos ecm less than - 0.90 or so) carries away essentially all the momentum of the system. The final state antiproton is left with a momentum of the order of 100 MeV/c or less. Such an antiproton has a range in hydrogen of the order of 0.3 cm and thus is not able to get out of the target. The final state antiproton will very likely be stopped and annihilated in the target. The likely annihilation of the stopped p is not easily distinguishable from an annihilation of p in flight. Thus, the p from a backward elastic event will not be useful in identifying the event. recoil proton. All our information must come from the - 9 We can (and will) use four criteria to determine whether a forward outgoing particle is a recoil proton from a backward elastic event -- (a) pology. charge, (b) momentum, (c) velocity, and (d) to- The charge and the momentum, along with the scattering angle which we obtain from topology of the event, allow us to select only 2 2 those forward particles which satisfy backward elastic kine matics< • ). The velocity, in conjunction with the momentum, allow us to remove all 2 3 forward pions and kaons< • ). The topology criterion allows us to remove all events with scattering not inside the target and all events 2 4 with more than one large angle scattering< • ). We describe briefly our apparatus and their layout in the following paragraphs. We indicate inside parenthesis the relevant sections of this chapter where further detailed information is g iven. Beam: Beam Transport We use the short branch of the partially separated b e am 5 at 2 the AGS in Brookhaven National Laboratory( .S). Figure 2.1 contains a layout drawing of the beam transport system, which contains 7 quadrupoles, 3 dipoles, 2 electrostatic beam s eparators, 2 beam stops and a mass slit. A detailed description of this system is given in Appendix A. Beam: p Ide ntification and Counting We us e a system of aperture · scintillation counters and (s 1 , s 2 s 3 ), one d i fferential Cherenkov counter< 2 • 6 ) and ( for low in- c ident' mome ntum only) a scintillation count e r time -of - f li gh t system to de t e rmine whe ther an incident particle i s a ~ and also whethe r will p ass thr oug h the tar.ge t. it Th es e c ounter s , mos t of which a re s hown -B G-IO G-11 . G-12 G-1 3 Q~c-Ji. }~~ ~ G-14 J--AGS PROTON BEAM H-MOMENTUM SLIT ,(HORIZONTAL FOCUS) I . V-FOCAL POINT V- MASS SLIT (VERTICAL FOCUS) MA~S SI.II COUNTERS M1-M,--1>, BEAM COUNTERS 03 -s, S2, S3 I 06 BGAM C HERE-N KO I/ COUNTER - ~ 07 SEPARATED BEAM Fl~U~E 2. f Layout of the separated beam transport system. Q1 -Q are quadrupole 7 magnets, o -D are dipole magnets, S is a sextupole magnet (not 1 3 .sext used), and BSI and BS2 are electrostacic separators. Also shown is the experimental area with the beam telescope, the Cerenkov counter (C), the liquid H target, and the large aperture, momentum 2 analyzing magnet (D ). 4 "'0"' - 11 in Figure 2.2 (a figure of our entire apparatus), are discussed in detail in Section (b-i). A scaler system using the signals from p passing these counters allows us to determine the number of useful through our system. Target As shown in Figure 2.2, a 37.5 cm long liquid hydrogen target is situated just downstream of the s 3 counter (2.7) • The target, placed inside a vacuum box, is described in Section (b-ii). Recoil Proton: Charge and Momentum Determination In order to determine the charge and momentum of the forward particles, a large dipole bending magnet with gap 48" wide by 18" high is placed downstream of the target. To either side of the magnet (upstream and downstream) there are sets of 4 wire spark chambers with digitized magnetostrictive readouts (2.8) • These wsc (wire spark chambers) record the trajectories of passing charged particles. Thus, knowing the trajectories allows us to determine the charge and momen tum of the forwa.r d par tic le. described in Section (b-iii). The details of this procedure are The characteristics of the wsc are described in Appendix B and the procedure for recording the part ic le trajectories is described in Section (d). Recoil Proton: Velocity Determination We ~se both a scintillation counter time-of-fli g ht system and a 2 9 threshold gas Cherenkov counter< • ) to help us determine the velocity and henc e (i f we know the momentum) the type of part icle going f orwar d (2.3) . The time-of-flight system, described in Sect ion ( c -v) .• compares the time of arrival of the signals from the count er s 3 and - 12 - Trajectory of beam particles during data taking Trajectory of beam particles during momentwn calibration Gas Cherenkov Counter T counter ~r----\---:==l====="f==i q 1 ,Q 3 and~ RO - R4 Wsc /f9 -12 <.1-4 0 Magnet Magnet shielding coun ers ~~--------If-----.., Wsc #5-8 --~ Liquid H2 ~ target 0 I.I"\ Hx&Hy -~ s2 0 A u -4 - 13 from the set of counters T 1 - T 10 • The Cherenkov counter, discussed in Section (c-iv), is placed downstream of all our other apparatus and has a threshold of 1.1 GeV/c for pions. Recoil Proton: Topology of Event In order to separate real events from background, we need to know that only one scattering has taken place. set of four wsc upstream of the target. the incident trajectory. Hence, we need another This allows us to determine This is also necessary so that we can obtain the scattering angle for the backward scattering and also obtain the distributions of position and direction for all incident p's to be used for the Monte Carlo of the acceptance of our apparatus. Need for a Triggering System The characteristics of the wsc (wire spark chambers) are that it can only be triggered a small number of occasions every beam pu 1 se (2.10) • Since each beam pulse gives us of the order of 10 4 p's, we must use a triggering system to decide when we should trigger our wsc. Our triggering system contains three sets of counters P, R, and T (see Figure 2.2) and uses the coincident requirement. p identification system as a Only certain combinat i ons of P and R counters which satisfy a loose momentum criteria will satisfy our 2 . . requirement . < • 11) • triggering " proSection ( c-ii ) d e s c ri"b es t h is cedure in greater detail. Event Recording System Our analysis is not done on line. information on each event. Thus, we must record the We record wsc information and some counter information (along with the information on the velocity of the forward - 14 particle from the time-of-flight system and Cherenkov counter) on magnetic tapes to be processed off line. This procedure is given in detail in Section (d). We conclude this chapter with a brief assessment of our experimental apparatus and methods (Section (e)). b. Beam, Target and Magnet (b-i) Beam and p Identification and Counting Beam 5 at the AGS in Brookhaven National Laboratory, which is described in Appendix A, supplies us with a collimated charged particle beam with a certain definite momentum acceptanc e and pion background. This beam is focused near the target. We must accept and count only p's which, if not scattered, will pass through the entire target. In addition, since the wsc (wire spark chambers) have memory time of the order of 1000 nsec, we would like to not count and use any p's which come within some specified period of time (500 nsec) of a previous particle. This enables us to reduce the amount of tri gge re d events with spurious trac k s (2.12) • We discuss each of these problems -- aperturing, p determination and spurious track reducing -- separately. All the position and sizes of the counters used for the beam system are given in Table 2 .1. Aperturing We r ej ect from consideration all particles which do not satisfy a three-fold coincidence s , 1 s 2 and s 3 (defined as S = S 1*S 2 *S 3 ). These circular scintillation counters are placed so that a straight line through all three counters automatically intersects all o f the - 15 Table 2.1: A. Beam Counters, Si zes, and Positions Beam time-of-flight counters (M counters . 1 - M ). 7 Also ca l l e d the ma ss s lit 7 ide ntical counters (scintillation). size: 1-1/2 11 wide by 1/8 11 thick (height irrelevant) pos : placed nex t to DJ and behind the mass slit in the beam transport system (see Figure 2.1). They are in a vertical row with no overlap. B. Beam ape rture counters (S - SJ) 1 size: sl J" round by 1/4" thick pos : ( z ) ** at z = J scintillation c ounters. s2 2" round by 1/4" thick at z = - 39" - 75" SJ J - 1/8" by 2-1/4 11 ;*1/8" t at z = - 11-7 /8" ( x ,y)centered on beam line. C. Beam liquid differential Cherenkov counter . size o f the radiator cell is 6 11 in diame ter and 1 / 2 to l" thick. position of radiator is centered on beam line and at a Z o f about - 50". D. E. Beam halo counter Au. size: 12" by 22" (high) by 1/4" thick with a 2" r ound hole . pos : the 2" round hol.e is centered on beam line at z = - 39-7 /8". Beam hodoscopes Hx 1 to Hx 4 and Hy size: 1/2" by 2" by 1/4" thick. pas : at z = - 35-J/4". 1 to Hy . 4 8 scintillation count er s. Rx an'd Hy are a rr anged in vertical an d horizontal non-overlapping rows centered on the beam line. * s ** z 3 i s s e t at 45° to the beam line so as to pres ent a circular aperture o f 2-1/4" diame ter to the beam. = 0 at the center of the target. sid e . z is negative for up s tream - 16 lar gc t:. (s b e am line. 3 is actually oval dul' 0 to the fact lltat .1.t h : ft.'.·> w.r.t This was ne cessary in order to place target as possible. s 3 as close to the Nevertheless, it presents a circular aperture normal to the beam line.) We will now equate a beam particle with a count in S. p Identification Two systems are used in identifying the p's in the beam. 1. 2 6 Liquid Differential Cherenkov Counter< • ) A ~.:chematic Cl1vn~nkov cross-sectional drawing of the liquid differential counter Js shown ln Fi.gure 2.3. Tlw two 1 l.nc~s -- the dash line and the dot-dash line, illustrate the operation of this counter. The movable diaphragm mirror is adjusted so that Cherenkov radiation from a p would strike the C bank of photomultiplier tubes while radiation from a pion would strike the C bank. The difference i n radiation angle is due to the fact that pions of the same momentum are much faster than p's and thus have a larger Cherenkov angle. Figure 2.4a contains a plot of the proportion of coincidences from the Cherenkov count e r for each S as a function of diaphragm mi1...-01: pusU:iou ~:etting \vard s tlw left, the pion ra diation strikes C's; at a typical momentum. counter is sensitive only to p. At th f.~ sc~tting to- at the right, the The p peak is at least a factor of 20 higher than the dip between the p peak and the pion peak giving e vidence that much less than 5% contamination of pions underneath the p peak is expected. is in the 0.5% level. 2.0 GeV/c. Checks show that typical pion contamination Efficiency for p's is better than 90% near - 17 Figure 2.3: Schematic drawing of the beam liquid differential Cherenkov counter. The C's are the coincidence signal and the C's are the veto signal. All scales are approx imate. movable radiator cell < • beam particle trajectory ............. '~ ""- movable diaphragm mirror *"<"---""" ' .......... ............. ""' ""-~ ' - ' ............. ............. ............. R._!adiation_ _ _ -~ _ _ -.......... . ""' l_ -pion radiation ""'---------------- ' I \1 }, curved mirror I\. I \ I I n C's \ approximately 5" e's photomultiplier tubes SCALE II 100% lOOi (a) r ~ 50% ~ 50i Ill 6b co c:Of.) ·rl t/l ·rl QJ t/l u c:QJ QJ u c:QJ 10% "O •rl u c: •rl pions 0 u ~ l i p's "O •rl u c: \ - 1 ns clip on s 3 and Cherenkov vetoing pions I : I 'I I 0 .IJ 'I H 0 ' •I u c:QJ 5% ' . I I I .' ..... ./II ' I ' I QJ u c: I 2nsec .IJ ·rl ~ ·rl I Of.) c: ·rl ~ •rl 1% I 1% -- Of.) Beam Cherenkov counter diaphragm mirror position setting * I' -1 I I I .. I I I J p's I I 'I . ' ' Beam time-of-flight delay between s3 and the M to M counters 1 7 Figure 2.4: (a) %of Cherenkov coincidence vs. diaphragm mirror pos i tion . If , in the Figure 2.3, the diaphragm mirror moves to the left, the C's would then receive the pion radiation. of-flight coincidence vs. time-of-f light delay. ' I s •rl Of.) I ' ! . :I 1.14 ..c: .. -- .. : I QJ "-.../ I pions ' '' 1.14 <::'<- \ •rl ,_, 0 ~ Of.) 10% •rl ..c:Of.) 5% . \ ------- O ns clip on s 3 ; I I ,_, ,_, / \ \ _ _ 1 ns clip on s3 (b) (b) %of beam t ime- to"" 00 - 19 The liquid differential Cherenkov counter is adequate in identifying p's and rejecting pions above 1.0 GeV/c. However, below 1.0 GeV/c, the efficiency in counting p's deteriorates . Thus, we use the Cherenkov counter to count (and reject) pions along with using a time-of-flight system described below. 2. Beam Time-of-Flight System 2 13 A set of 7 counters( • )(called the mass slit counters since they are placed next to the mass slit in the beam transport system -see Figure 2.1) about 14' upstream of the target is used in conjunction with the s 3 counter to give us a time-of-flight measurement of the velocity of the beam particles. ~ of about 0.7 while the pion has a ~ Below 1.0 GeV/c, the p has a of about 1.0. difference in time-of-flight is about 4 nsec. response as a function of time delay. Thus, the Figure 2.4b shows the The solid and dotted lines are the response for the time-of-flight system alone while the dashed line is the combined response of the time-of-flight with the Cherenkov counter set to reject pions. Again, we see that the pion background undeineath the ~ peak is reduced to the 1 % level. clip the Notice that we s 3 signal with a 1 nsec cable to give us a broader peak. Reduction of Spurious Tracks in the wsc We use a pile-up system to reduce spurious tracks in those events which we record. is situated nex t to the beam. The beam halo counter A (see Figure 2.2) u s 2 and the two counters count all the particles in When either of these counters register a count, a pile-up ga te is triggered which prevents any following particles to be counted within 500 nsec. This gate, which typically reduces . the - 20 amount of usable beam by 10-20%, cannot however, entirely cure the multiple track problem since the trigger system takes about 300 nsec to fire the wsc. Any particle which arrives between the . backward elastic event and the firing of the chamber will be recorded along with the backward elastic event. To help us decide which track belongs with the backward elastic event, two arrays of 4 2 11 by 2" wide and 1/4" thick scintillation counters called the beam hodoscopes are arranged in horizontal and vertical rows. analysis. The signals from these counters are used in the Any track which extrapolates into a counter which did not fire is removed in case of multiple tracks. This procedure is necessary only for a small percentage (of order of 1%) of all events. Scaler Counting System Our wsc impose a dead time of 20 msec each time. they are . d(2.14) triggere • All p's satisfying our aperture and pile-up criteria which arrive during the time in which we are sensitive to backward ela s tic events must be counted. We use a series of logic modules (Chronetics 100 series -- 100 megacycl~s( p's. 2 .lS)) and scalers to count In addition, several other beam quantities such as S (the beam · particles, not necessarily p's, satisfying aperture and pile-up criteria) are also counted in order to monitor beam quality. Table 2.2 lists the momenta where data were taken, the total p flux at each momentum, typical S and p per pulse, pi/p ratio and trigger rate. Figure 2.5 shows the distribution of momentum, positions and directions of the incident p's at three typical momentum (2.16) . . d h Note that the spread in the distribution is ue to t e - 21 Table 2.2: Beam fluxes and rates for each momentum •. The "Real" momentum is the actual average momentum at the center of the target. The • 1 pu 1 se correspond s t o a b out 1 • 5 x 10 12 c1rcu • 1 at1ng • rates per typ1ca pIs in the AGS. setting. Runs labeled L are special runs with low bending magnet Trigger rates are usually higher for these runs. In our final results, the data at 1.585 and 2.125 which has been marked with an *were combined to form the 1.59 and 2.155 data. Momentum Nominal Real (GeV /c) (GeV /c) p Total flux (empty) full in millions s p pi/p per typical pulse Trigger rate per 1000 p's 0.68 o. 703 7.0 8K 0.5K 15 .0 1.10 o. 77 0.812 9.1 20K 0.9K 21.0 1.05 0.89 0.873 20.0 13K LOK 12.0 1.00 0.92 0.935 9.5 33K 2.5K 12.0 1.05 0.97 0.987 ( 6. 2) 54.2 46K 3.5K 12.0 1.00 1.09 1.115 ( 4.2) 29.8 26K 4.0K 5.5 1.00 1.34 1.338 (11.0) 38.8 24K 8.0K 1.9 1.05 1.45 1.447 43.0 24K 8.5K 1.8 1.15 l.585AH* 1.580 ( 7.5) 24.5 32K 11.0K 1.8 1.10 l .585AL* 1.580 ( 3.0) 15 .8 32K 11.0K 1.8 1. 30 1. 585BH* 1. 589 10.8 40K 16.0K 1.5 1.05 l.585BL* 1.589 4.4 40K 16.0K 1.5 1.30 l.585C* 1.596 7.9 26K 12.0K 1.1 1.15 1. 585D 1. 610 63.3 30K 11.0K 1.8 1.15 1. 70 1. 716 78.2 35K 13.0K 1.8 1.10 1.815 1. 797 60.3 55K 22.0K 1.5 1.05 1.8 1.844 73. 7 40K 15 .OK 1.6 1.10 2.0 2.032 73,5 55K 22.0K 1.5 1.10 2. 125H* 2.155 59.8 55K 28.0K 1.0 1.10 2 .125L* 2.155 21. 7 55K 28.0K 1.0 1.40 2.365 2.370 48.4 75K 45.0K 0.6 1.05 ( 3.0) ( 7. O) (10.0) (10.5) Momentum distribution (in units of 1%) 2.00 GeV/c 1.45 GeV /c Nominal momentum : 0.77 GeV/c 20% 40% Horizontal position distribution (in 30% units of 1 cm) 20% 1::1 J I Vertical position distribution (in units of 1 cm) N N s =1=1 '.:J J I 30% 20% 10%. I Figure 2.5: Distribution of momentum, positions and slopes of the incident p beam L I II 1 I Figure 2.5: (continuation) Orfo 30% Horizontal Slope Distribution (in units of 10 mr) 20% 10% 0%1 c=' I e=1 '=, I I d k I N _ I.A) 40'f, Vertical Slope i Distribution 30% ' (in units of 10 mr) 20% 10% 0%1 I I ~ 1 - 24 wsc resolution and multiple scattering in addition to the intrinsic 2 17 properties of the beam< • ). Typically, we accept a momentum bite of ± 3'fo and keep the mass slit spacing narrow (about 1/8"). as measured by Au and The total number of beam particles s 2 per pulse is about 150 K. Since the beam pulse period is about 400 msec, this corresponds to a 0.3 megacycle rate. We have checked that this rate is tolerable since several data runs at a lower rate give answers which agree with the answer at the typical rate. Target (b-ii) ( 2.18) We use a cylindrical liquid hydrogen target 14-5/8 11 (37 .2 cm) long and 3" (7.6 cm) in diameter. The target envelope is a single jacket of 14 mil mylar surrounded by 40 layers of 0.3 mil aluminized mylar acting as superinsulation. The target, shown in Figure 2.2, is housed in a vacuum box 15-3/4" wide set at 45° to the beam line. The liquid hydrogen in the target is maintained at atmospheric pressure near the boiling point and has a density of 0.0708 gm/cm (b-iii) 3 2 19 < • ). Magnet and Momentum Measurement The magnet n4 we use for momentum analysis is a 48D48 dipole magnet with an aperture 18" high by 48" wide. The useful aperture, however, is restricted by the hole in the magnet shielding which is 14" x 28" upstream and 16-1/4" x 46-1/4 11 downstream of the magnet. The size of these apertures is chosen such that any particle from the target which will go through all the wire spark chambers will not strike the shielding wall. - 25 . (2.20) The shielding, an iron-wood sandwich which contains iron layers of thickness 3/4", l", and 6" is attached to either side of the magnet by long bolts and brackets. Its purpos e is to min imize the stray field outside the gap of the magnet. High stray fields would incapacitate both the magnetostrictive readouts of the wire spark chambers and the photomultiplier tube (even with shielding around it). Studies have shown that the magneto- strictive wire will not function with high transverse f ields (of the order of 50 gauss) although longitudinal fields of up to several hundred gauss can be tolerated. Since the field inside the gap goes as high as 15 Kgauss, stray fields of 1% of the central field cannot be tolerated. In addition, the photomultiplier tubes, even with shielding, cannot withstand hundreds of gauss. Without any magnet shielding, the field at the beam line 50" from the side of the magnet is still about 1% of the field at the center of the magnet (i.e., about 100 gauss); the shielding reduces the field so that at the beam line 25" from the side of the magnet (just outside the shielding), the field is reduced to about 0.1% of the field at the center of magne t gap. Even then, the wire chamber readout wires of chambers 9-12 (downstream of the magnet) must undergo special treatment whenever we switch the polarity of the magnet (the wire must be remagnetized and the pick-up amplifier must have its polarity switched also) • The momentum of the particle which goes through the magnet is obtained from the amount of bending obtained while traversing the magnet. The field at the inter ior of the ma g net gap has been - 26 - 2 21 obtaine d through the use of a nucle ar magnetic resonanc e prohe < · ). We then use th e rectangle field approximation to calculat e the mome ntum. For a particular fi e ld B at the center of the ma g net, we n ppro::d.matc the field by .:i vertical field B over a length T., the (' rrec Livl~ 2 22 l.eng tli wbicli ha s beeu c mpiri.ca .1 ly delenn.i.ned to b e ( • L ) 0 99991 155.60 cm/(l + (B/255.51 Kg) • ). The mome ntum of the particle traversing the magnet is then p 12 2.9978 B L(l + x + y 12 ) 1 / 2 . . 2 1/2 lOO(sin a+ sin ~)(l + x' ) wher e x ' and y' are the incident horizontal and vertical slope, is the i ncident horizontal angle and angle ( see Figur e 2 . 6a). a c c urnl: f'. to <.:!try Pl Llie is the outgoing horizontal Studies have shown that this formula is . . , /2.22) w ithin O. J 11, • r«• (· t a ngl!~ ~ a Fi gure 2. 6 s hows some of th e geom- l'i.e l.d a pprox imation. We c an thu s obtain the mome ntum of a particle at the magnet. To obtain the momentum at the interaction vertex, we simply correct f or ioni z ation losses. In order to select backward elastic events using kinematics, we must have a good idea of the momentum of the incident p. We calibrate the incident momentum by triggering on every p and changing the polarity of the magnet to bend negative instead of pos i tive p:-irt i cl.es into t h e ws c downstream of the magnet. 1111 ' 11111111 c ;rl i.b1-;11 ion ror t•a c li o f Olff mome nt :a . We do thi s mo- The res ultant c.li s tr .i - bution in momi ·. ntum i. s t y pically tha t of F i gure 2 .7b. Real Vertical Component of The Magneti c Field CD JBy dz= 8 L IL L 0 8 -CD z .s;; along magnets center llne ...B = By only ,... m 'I-L I I I 2 \ \ P\ I I I 0 L z- 2 N . \ I ;-N~ / / -...J :' / / /p Rectangular Field A ppraximation ---Le--~ \a I I I ,..-.e, \! y I / >,v_ 22 - ,... m !•=sin (a) p ~2 =sin (,8) e, + 22 L -p- = -p =sin (a)+ sin (p) 8x P =cos (a) - cos (/J'J where p = I L 2.9978 p 2 I I 0 80 Relation Between The Horizontal Deflect ion of o Track And Its Momentum ( b) (a) Figu r e 2 .4) Rectangula r fie ld model for a dipole magne t. L 2 z- - 28 It i s possible to obtain a better estimate of the incident momentum by using the property of the beam transport syst e m. Appendix A, which handles the beam transport system, indicate s that at the mass slit, the horizontal (x) position of the beam is strong ly correlated with the momentum -- particles with momentum higher than mean momentum tend to have positive x at the mass slit (s e e Figure A.l of the Appendix A). A set of 7-1/2" wide scintillation counters is placed vertically . (2. 13) next to t h e mass s 1 it • The momentum distribution o f p's hitting each mass slit counter is shown in Figure 2.7a. By com- bining the 7 distributions correcting for the shift in central momentum, we obtain a total distr i bution of Figure 2.7c instead of 2.7b for the same p's. Since the momentum spread in the distribution is also due to multiple scattering and the wire spark chamber reso. (2. 23) , t h e improvement . . momentum d etermination . . . actua 11y 1 ution in is better than indicated. In any case, the FWHM i s reduced from about 1. 7% to about 1.0%. c. Fast Counters and Logic (c-i) Introduction During each beam pulse, thousands of p's are incident on the target. We can record a maximum of 15 trigger e d events (2.24) • Also I each time We trigger, the WSC (wire Spark chambers) require ·a 20 msec dead time to allow us to record the event and to allow the wsc to recover. Thus, without losing any acceptable backward elastic events, we would like to trigger on as few events as poss i ble. We use a trigger system of fast scintil l ation counters and fast log ic (a) (b) M3 N '° (c) -1% oc;i +1% +2% +3% -1% O<fo +1% +2% +3% Figure 2.7: Momentum distributions of in~ident p's at ~.O GeV/c nominal momentum for: (a) p's hitting a particular mass slit counter. (b) all p's. (c) all p's corrected according to which mass slit counter it hits. - 30 modules (2.25) to test for the trigger condition. We are able to reduce the tri ggering to about 1 per 1000 incide nt p's. war d elasti.c e v e nts ar e Jost except for dead time . No back- We will cJjscus s th e tri gge r condition, logic and rates in Section (c-ii). Counter :information i. s useful for analy sis . kiHl\vlcd ~~< ' of whi c h counter r e gisters a count (or a may be h e lpful in r e moving a spurious track. bits for each triggered event. For exampl e , p artic ul ~ir lhc e V<'.nl: We record 48 binary 35 of these bits which contain the counter and various 'coincidence information are discussed in S e ct ion (c-iii). The other 13 bits contain in format ion on the velocity of the forward p ar ticle essential to remove pion background underneath our rec oil protons. Thi s includes the information from the gas thresh- Clwn' nkov counter (Section c-iv)) and a forward outgoing old p ;11"t. ic I ,, (c-ii) L inw-of-f: l i.ght syst t.!m (S ec tion ( c -v)). Trigger Counters, Logic and Rates Logic We test for the trigger condition using a system of scintillation counters (listed under "non-beam counters" i n Table 2.3 with 2 25 thei r si zes and positions) and logic modules < • ). To sa t isfy our trigger condition, we require a coincidence o f: 1. An i ncident p. This is determined by the p identification system d e scribed in S ec tion (b-i). 2. A forward outgoing positive particle with momentum close to that of the incident p and whose trajectory passes through the wsc (wire s park chambers). This condition is tested by the combination of three Table 2.3: Non-Beam Scintillation Counter Sizes and Positions Position Size Counter Name x pl 3" z (thickness) 7" 1/8" - x :l - 4" z Y.. to - l" - 3-1/2" to 3-1/2" 38-1/4" 1-1/2'' to 1-1/2" same same same l" 4" same same p4 same 3-1/2" to \ 6-1/2" same same PS p6 same 6" to 9" same same same 8-1/2" to 11-1/2" same same - 12-1/4" to 11-3/4" 175-3/8" same same p2 same p3 RO 14" 24" 1/2" - 30" to to -16" Rl same - 24-1/2" to -10-1/2" R2 same - 14" to O" same same R3 same - 4" to 10" same same Ql same 7" to 21" same same Q2 same 16-1/2" to 30-1/2" same same Q3 same 26-1/2" to 40-1/4" same Q4 12" 22" 1/4" 9" to 21 " same 19-1/2" to Qs T.(i = 1,3,5,7,9; non-overlapping) 31-1/2" - 28-1/4" to 8-3/8" - 11" same to 11 11 same 139-1/4" same 1 5 (7-3/8") 13-1/2" 1/4" - 10" to 3-1/2" 182-5/ 8" T . (j = 2,4,6,8, 10; non-overlapping) J ·. same same - 3-1/2" to 10" same w I-' - 32 counter hodoscopes P, R and T (see Figure 2. 2, page 1.2). The P R combination is used to restrict the momentum acceptan c e of the forward particle . Figure 2.8 gives a plot of the hori z ontal pos i tion at the P counter plane ( x p) vs. the horizontal position at the R count e r plane ( x R) for all particle trajectories. The area inside the solid line satisfies the triggering criterion in P and R. Da s hed lines drawn in Figure 2.8 show the locus of points with the same momentum p corning from the center of the target. T counters are required for triggering. This is used to reduce the aperture for triggering as well as to provide an additional coincidence requirement to reduce accidentals. Note that the T counters are also used for forward outgoing particle time-offlight system. 3. An absence of a nega·t ive charged forward pa r ticle w ith ess e n- tially the incident beam momenttnn and slope. This i s tested b y a combination of P Q counters. This beam veto reduc e s the trigge r rate by a substantial amount. Many mechanisms can be responsible for the large amount of incident p which satisfy cond ition 2 and yet have a forward negative charged particle with fairl y high momentum. Two such mechanisms are a) pp annihilation i nto ~ulti-pions in which one (or mo r e) positive and one negative pion goe s fo r wa r d, and b) pp into pn n+ in which the momentum transfer to the p is small. We have studied the possibility that a real backward e lastic event is v e toed by this condition. Since the final stat e p will probably annihilate in the target, a forward pi minus giving a beam vet o i s possible . The conclusion is that th e re is a n eg lig ibl e l oss - 33 Figure 2.8: Triggering "area" in P-R space. x p is the horizontal po- s i tion of the trajectory in the plane of the P counters. corresponding position in the plane of the R counters. xR is the Va l ues of x p and xR inside this "area" impli e s that the event satisfies the P-R counter criterion for triggering. Lines show the loci of events from the center of the target with specified momentum. xR in inches x p in inches 2 10 // .Q,. -10 // .Q,. Triggering area of P-R criterion -20 "---- --+'--- - - - - - -L-- - - -- - ---- - -- - - -- --- ----- ----- --- - 34 (see Section (d) in Chapter III). Electronics The trigger electronic logic system consists of a numb l•r of 2 25 fast (100 megacycles) logic modules< · ) used to identify, with a resolving time of about 10 nsec, the trigger condition. It also sends the trigger signal to the wsc pulsing system, the computer int erface, and the master gate to generate a dead time during which the p counting system and trigger logic modules are inactivated. See section (d-iv) for f urther details on the operation of our recording system after the arrival of a trigger logic signal. The logic of the tri gger system is shown in Figure 2.9. Counter signals from the photomultipliers are shaped into standard 2 25 pulses by discriminators (Chronetics 104( • )). These pul ses are cor related to see if the trigger condition is satisfied. The modules with an x in the upper ri ght-hand corner are those modules which are gated off b y the master gate during the dead time. that without these particular modules, no It is easy to see p can be counted and thus no further trigger can b e accepted. Rates The rates for trigge ring at each momentum is shown in Tab le 2.2. It is about one trigger per thousand incident p. Even though the trigger rate is only about 0.1 ~, the number of events which satisfy the trigger condition is still rather large since the average flux of p per pulse is as high as 45K. At incident mo- me ntum of 1. 5 GeV/c or higher, this rate is intolerable. I f w~ acce pt an average of 14 trigger per pulse, we hav e 280 msec of dead - 35 Figure 2.9: The trigger logic flow chart (modules which are gated off by the master gate are shown with an x in the upper right-hand corner; veto enters through the Side). low momentum high momenttnn ]t---<1~-!--t----' <11 ffi-1 i : I 1----'.1---t ~ f -- - - - - ' . l - - - - - - - ' - 36 - time. Since each beam pulse lasts only about 400 msec, we are only able to use 1/3 of the beam! It would be useful to reduce the trigger rate further since the actual number of backward elastic events is only about 1%of all the triggered events. Several possibilities can be considered: 1. The (PR) triggering area (see Figure 2.8) can be reduced. use fewer combinations of P and R counters in our trigger. would narrow our momenttnn acceptance. We can This Due to the finite size of the target and counters, the maximum reduction possible without losing any backward elastic events is less than 1/3. 2. We could use the gas Cherenkov counter (see Section (c-iv)) to veto all events which give a pulse since recoil protons are below threshold f6r this counter. However, the reduction is only 15%. Most of the triggers are apparently due to low momentum protons or pions below the threshold for the Cherenkov counter . Thus, it is possible to reduce the trigger rat e by about 40 %. the gain . . not too s1gni . . f icant . <2 • 26 ) an d a 1 so . since . We d i. d no t d o it is since we are interested in measuring pp going into pi + missing mass, . . . . . .K + missing mass or p + missing mass (2.27) • Another possible way to reduce trigger rate is to us e the timeof-flight system. However, at high momentum, our s ystem is not good enough to separate forward pious from forward protons. (c-iii) "Counter Bits"(Z.ZS) __ Scintillation Counter Information for Analysis Digital c ounter information for each ev ent is us ef ul both in - 37 analysis and in the efficiency calculation of the counters. We cover these uses in the appropriate section in the analysis chapter. 35 of the 48 available bits record the informat i on of whether one or a combination of counters fired. The remaining 13 bits record the i nformation from the gas Che renkov counter and the forward outgoing particle time-of-flight system (see the next two sections). Briefly, the co.u nter bits work as follows. Counter signals are delayed and timed to arrive at the counter bit modules just after they receive the interface signal after each trigger (seed-iv). The counter bit modules remain receptive for a duration of 50 nsec . The arrival of a counter signal during this period will flip the module. The modules are then read by the interface and the informa- tion is written onto magnetic tape. The modules are then reset to await the arrival of the next triggered event. (c-iv) The Gas Threshold Cherenkov Counter One of the two systems we used to measure the v e locity of the forward particle is the Gas Threshold Cherenkov counter (2. 9) • This counter is a large 4' diameter aluminum cylinder 8' wide (see Figure 2 . 2 for the position of this counter) containing Freon-12 gas under about 8 atmospheres (about 120 psi) pressure as a Cherenkov radiator. The refractive index of this gas under this pressure is about 1 . 009. Pions with momentum above 1.1 GeV/c will Cherenkov radiate in this medium. The corresponding threshold for K's and p's are 3.5 and 6.5 GeV/c, respectively. Since such high momentum particles are kinematically impossible to produce for our incid e nt momentum, we - 38 assume that any time we receive a coincidence from this counter, a pion has passed. Although a high energy proton or kaon could in principle produce a pion with sufficient momentum to trigger this count e r, this is expected to b e rare ( 2.29) • Figure 2.10 shows a cross-sectional view of this counter and also demonstrates how this counter works . Note that the photomulti- plier tubes sit at the top of the c ounter and thus they are not in the particle's path. Hence, we do not need to worry about Cherenkov radiation in the quartz window of the counter or the glass windows of the photomultipliers. Not shown in the figure are the heating coils necessary to keep the whole counter above 40°c. This is . (2.30) necessary in order to prevent the Freon-12 from condensing • Although the counter is a cylinder 4' in diameter, the useful radiation distance, due to the placement of mirrors, is typically about 25i•. A total of about 50 photons are produced. (The Cherenkov radiation is focused by the curve-mirror and flat-mirror system into an area covered by light pipes.) have about 10% quantum efficiency. electrons are produced. Our phototubes (2.31) Thus, an average of 5 photo- The resultant signal from the photomulti- pliers are mixed and fed into a 64-channel pulse height analyzer. The output is recorded in 6 binary bits of the count er bits. Figure 2.lla shows a typical pulse h~ight distribution for forward particles near the incident momentum. Figure 2.llb shows the portion of the events in 2.lla which are tag ged as pi's by the time -of-flight system discussed in the next section. shown as an arrow. The cut we usually use is All ev e nts above this arrow are usually discarded. - 39 Figure 2.10: Schematic drawing of the gas threshold Cherenkov counter. The dashed lines are rays of Cherenkov radiation from a particle with velocity above threshold (about 1 . 1 GeV/c for pions). tubes approx. scale o" s'" 10" Light pipes Cherenkov radiation ____ f- _ _ __ /~ --- .---- Cherenkov r~ation_ -- -- -e - ~-- the Cherenkov an le -----~-.. -- --- -- - - -- -- ----+- -- ===mirror Particle trajectory Curved mirror - 40 Figure 2.11: Cherenkov pulse height channel distributions for: (a) Particles with momentum about 1.61 GeV/c (b) Particles in distribution (a) which are tagged as pions by the time-of-flight system. (c) Particles with momentum about 0.92 GeV/c (below threshold for Cherenkov radiation even for pions). 400 overflow Number (a) 300 200 100 40 20 60 Cherenkov pulse height channel number (b) so 20 pedestal 100 so I 40 60 0 oO pedestal cut l (c) - 41 From 2.llb we see that we usually remove 75-85 •/, of all the pi's by throwing away all events with Cherenkov puls e height channel above the arrow. Figure 2.llc shows a distribution of particles with mo- mentum below threshold. We see that less than 2 % of such particles have a Cherenkov pulse height above the arrow. Thus, we expect to lose less than 2% of protons by making this cut. As mentioned above, the counter cannot separate about 20% of the pions from the protons. counter. experiment This is not due to the design of the Although the counter was not built expressly for the (2. 9) and the geometry is not ideal, the mirrors are adjus- table and we can still focus the light without significant loss in our geometry. We could have better performance by using photo- . l"ier tu b es w i t h h.igh er quantum e ff.iciency . <2 • 32 ) . mu 1 tip jected due to cost. This was re- We used some available photomultiplier tubes which gave adequate performance (2.31) • Actually, the major source of inefficiency for pion counting comes from the possible scattering of pion with the front wall of the counter. Any scattering with large transverse momentum transfer would result in final state particles with bad geometry. Even if the particles Cherenkov radiate, the light may not be focused onto the photomultipliers. We found this by looking at the pulse height of those pions which pass through the counter unscattered (we put a scintillation counter behind the counter in coincidence while using a collimated beam of pions). better than 95%. The efficiency for those particles is The thick walls of the counter cannot be reduced since we require 120 psi inside the counter. - 42 For low momenta, we could have used a liquid Cherenkov 2 33 · counter < • ) which cou 1 d count pions down to 0. 3 GeV I c or 0. 4 GeV I c and still have proton threshold above 1.0 GeV/c. However, for these particles, the time-of-flight system discussed in the next section does a g ood enough (c-v) job. The Forward Outgoing Particle Time-of-Flight System (TOF) We shall abbreviate the system by TOF in the following section. The time delay between the arrival of the signal from the T counters and the signal from s 3 counter (for the relative positions, see Figure 2.2, page 12) provides us with a way to measure the velocity of the forward outgoing particle. For particles o f the same mo- mentum, the pions will have a shorter delay time than protons. The TOF system works as follows. The signal from s , shaped 3 by a discriminator, arrives at the pulse height analyz er and starts a 2.5 gigacycle clock scaler. The signal from the T counters stops the scaler and the elapsed time for the clock scaler is read and recorded using 6 binary bits. There are 64 channels and each succes sive channel is separated by about 0.4 nsec. The FWHM of the system is about 2 nsec. We show in Figure 2.12a a typical TOF channel distribution for part i cles close to a particular momentum. resolved pion and proton peaks. We see clearly Thus, the TOF system can be us e d to remov e the pion background at low momentum whe re the gas Cherenkov counter cannot count pions. Above 1.2 GeV/c, the pion and proton peaks are not well - 43 Figure 2.12: Time-of-flight channel distribution for low (0.99 GeV/c) and high (1.61 GeV/c) momentum particles. 0 2 nsec 4 nsec 0.99 GeV/c 200 pions pions 1 f protons 1.61 GeV/c Events with Cherenkov pulse height greater than 22 (all pions) Events with Cherenkov pulse height less than 22 (protons and some pions and kaons). 200 TOF channel No. 27. - 44 separated. bution. Figure 2.12b shows a typical higher momentum TOF distri- We also show in different shadings the event distribution for those events with gas Cherenkov pulse height above 24 (almost definitely pions) and below 24 (contains both pions and protons). We can reject all events with TOF channels less than 27 without losing many protons. d. Recording and Monitoring of Data (d-i) Introduction The an~lysis of our data is done off-line< 2 • 34 ). For each event satisfying our triggering criteria, the various information about the event is recorded on magnetic tape by a system consisting . . (2.35) o f a PDP- 8 computer with tape drive and interfacing . The information from the wire spark chambers (described in detail in Appendix B) specifying the spark positions are digitized by a system of clock scalers. (d-ii). This procedure is discussed in Section In Section (d-iii) we describe the PDP-8 and the interface system of recording the data. Section (d-iv) contains a surrnnary of the data recording procedure includ{ng triggering, wire spark chamber pulsing and counter bits. Section (d-v) contains a list of the information recorded for each event. We describe in Section (d-vi) the procedures we used to monitor the data takin g . (d-ii) Wire Spark Chambers and the Recording of Digitiz ed Spark Pos it ions To r e cord the positions of the particle trajec tori e s f or each - 45 triggered event, we use 12 wsc (wire spark chambers). The se wsc are divided into three sets of four wsc and measure the incident p, the recoil proton, and the momentum analyzed recoil proton · trajectories. The positions and sensitive area sizes of the 12 wsc are given in Table 2.4. We describe the construction, operation and characteristi c s of the wsc in Appendix B. We shall briefly describe the operation in the following paragraph. A trigger logic signal (specifying that the trigger condition has been met) is sent to the wsc pulsing system. The pulsing system then applies the charge from a storage capacitor across the wire chamber planes through a thyratron circuit. Spark avalanches occur at the points where ionization from passing charged particles exists. Fiducial lines which are placed at both sides of the sensitive area are simultaneously pulsed. The magnetostrictive readout wire then transmits the magnetostrictive wave pulses into readout amplifiers. The resultant signal is transmitted into a digiti z er. The signal from the readout system of the wsc is a string of pulses specifying the spark positions for each coordinate in series. The pulse signal from each coordinate in a wsc is transmitted back into magnetostrictive pulses of successive coordinate so that the final signal of the 24 coordinates of the 12 wsc are in s e ries. Part of a typical signal train containing two coordinates is shown as "input" in Figure 2.13. We digitize the signal in order to store the information in magnetic data tapes. The fiducial line at the edge of the sensitive ar e a is pulsed at the same time as the sparking of the wsc. The position of the - 46 - Table 2.4: wsc Sizes and Positions of the Sensitive Areas of the wsc Sensitive area z position x position y posit ion I {regions 1 and 2) 1 36" (x) by 18" (y) 2 same' 3 same 4 same - 18-3/4"* -33" to 3"* - 15-3/4"* - 12"* 9-1/4"* -9" to 9" same same same same same same {regions 3 and 42 5 18" (x) by 9" (y) 12-3/4" - 2" to 16" - 4-l/2"to 4-1/ 2 " 6 same 19-1/4" same same 7 same 25-1/2" same same 8 same 31-3/4" same same ~regions 9 5 and 62 36" (x) by 18" (y) 144-1/2" -19-1/4" to 16-3/4" -9" to 9" 10 same 153-1/2" -21-3/4" to 14-1/4" same 11 same 162-1/2" -23-3/4 11 to 12-1/4" same 12 same 171-1/4" -26-1/4" to same * 9-3/4" For the fiist four wsc, the z distance is the distance normal to the chamber from the center of the target. Since the wsc is set at 45° to the beam line, the distance from the target center to the beam · line intersect of each wsc is thus a factor of (2) 1/2 larger. The x position is measured with respect to a coordinate system set at 45° to the beam line. x = 0 is the beam line. - 47 Fig~re 2.13: The wire spark chamber signals and the digitizer operation. TRANSMITTER RECEIVER T R T .R SERIAL CONNECTION OF MAGNETOSTRICTIVE PICKUP LINES z Q <I) I- 0 0.. ~ x "'x 0 ...e zx ... a: g ct 0:: .... Ii: I<I) "" "" ::I I- <I) Tlf-. PULSE RESET LOGIC STOP SCALERS DISCRIMINATOR I DISCRIMINATOR 2 OISCRIM IN ATOR 3 DISCRIMINATOR 4 DISCRIMINATOR 5 0 j:: <I) <I) MASK z t: ~ "" e ... INPUT ~ I:: 0:: ~ <I) r <I) 0:: <I) 0.. 0:: I0:: <I) <I) <I) iii 0 ~ x 0 N N c:i x 0:: a: <I) ~ 0.. 0:: g <I) Ul ct n ~ SPARKING INTERVAL STOP ALL SCALERS nSTARTALL SCALERS f f STOP SCALER I n E RESET SCALERS START ALL SCALERS _ _ _ _ _ ___, i5 <I) 0.. 0.. ~ rn ·--..i STOP ALL SCALERS RESET SCALERS "'9 ' n SPARKING INTERVAL _Il _Jl .... STOP SCALER I STOP SCALER 2 nSTOP SCALER 2 f STOP SCALER 3 tSTOP SCAL ER 3 fl nSTOP SCALER 4 -------------- STOP SCALER 4 SCALER SWITCHING LOGIC - 48 2 36 fiducial was surveyed and measured to a great accuracy< • ). we can use the fiducial pulse as a reference. Thus, The time delay between the spark pulse and the fiducial pulse thus represents the distance between the position of the fiducial line and the spark position. I Figure 2 .13 shows ·a schematic drawing of the operation of the . . . <2 • 37 ) • d igitizer ' . 1 near t h e receiver . . Th e f"d i ucia gives a pu 1 se wh ic h arrives first -- called the first fiducial or starting fiducial. This signal starts four 10 megacycles clock scalers. pulse received then stops one successive scaler. Each subsequent At the end of each coordinate segment, all scalers still running are stopped by the interface. The scaler readings are then transferred into the buffer and eventually written onto magnetic data tapes (seed-iv). The interface issues a mask pulse prior to each coordinate designed to screen out the noise due to chamber sparking. This mask pulse, adjustable in timing, is issued about 5 microseconds after the second or stopping fiducial of the previous coordinate and is terminated about 3 microseconds prior to the first fiducial. Note that the noise pulses are the transmitted pulses which were picked up by the amplifiers of each coordinate and thus arrive before the first fiducial of each coordinate. The leading edge of the mask pulse stops all the scalers. The four scalers are read and reset during the existence of the mask pulse. The first pulse after the mask pulse is terminated is assumed by the interface to be the first fiducial of the next coordinate and any subsequent pulses are assumed to be spark pulses or the second fiducial. If any noise pulses arrive before the first fiducial and - 49 after the mask pulse is terminated, difficulties occur. Such occur- rences were kept at a tolerable level (less than l/2<fo) by continuously monitoring the output of the digitizer and the timing of the mask pulse. For each coordinate, since only four scalers are used, a maximum of 4 spark positions can be recorded. beyond the fourth one is lost. Any spark position Since the scalers are 10 megacycle scalers, the time delay between the first fiducial and the spark signal is digitized in 100 nsec steps. magnetostrictive wave is 5.2 x 10 5 Since the velocity of the cm/sec, this corresponds to steps of 0.52 mm. We will make a few comments on the serial readout system . Compared with the parallel readout system where each coordinate has its own digitizing system, the .serial readout system requires fewe r scalers and electronics. It is also simpler to operate and monitor. Since our dead time of 20 msec is imposed by the recovery time of the wsc, the additional time required to serially digitiz e the 24 coordinates ( about 3 msec) does not make us lose any beam . two disadvanta ges in the serial readout system. There are Since all 24 co- I ordinates are interconnected, trouble shooting is more difficult. In many instances, the trouble spot cannot be local ized irnmed iate.ly . In addition, any reduction in resolution due to the readout s y stem, such as one particular pick-up coil being too wide, could cause similar resolution loss in all subsequent coordinates whose signals, because o f the serial readout configuration, have to pass through the amplifier of this coordinate. - 50 (d-iii) PDP-8 Computer and Interface System of Recording the Data The interface system allows the PDP-8 to communicate with the various electronic systems such as the digitizer, counter bits, scalers, trigger electronics, etc. It coordinates the reception of the data. The procedure which the interface system is involved in is as follows (we will summarize all the data taking procedure in the next section). 1. The interface receives the trigger logic signal specifying that the trigger condition has been satisfied. It is understood that another signal has been sent to pulse the wsc. 2. The interface than sends a signal (called the "BUSY") to the master gate for a duration of 20 msec. During this period, the trigger logic modules are gated off (see Figure 2.9). 3. The interface handles the counter bit information as described in Section (c-iii). The information is stored in the buffer and even- tually written onto magnetic tape. 4. The interface a ct ivates the digiti zer s y s t em to ha n dle the arriving spark signals. For e ac h coord i nate, a ma sk pulse i s i ssued at the appropriate time and the scalers a re read. The f our scaler reading s ar e comb i ned into one 60-bit word (12 bits are s ufficient for e a ch number since the scaler count never exceeds 1900. r emaining 12 bits a re blank . ) The All the spark information, which is stor ed i n the buffe r , take s 24 wor ds f or each ev e n t . Dur ing ea ch b e am pulse, the interface can put a max imum o f 15 2 38 eve nt r ec o rds c o ntaining 30 60-bit words e ach( • )( 24 s park in for- - 51 - mation words, counter bit information word and 5 blank words) in the buffer. The size of the buffer imposes this limit. If 15 events were' accepted, any additional events (and p) for that beam pulse are rejected. At the end of each beam pulse, the information in the buffer is transferred into the magnetic data tapes. In addition, the PDP-8 also make special calculations on items which we wish to monitor (see Section d~vi). The user is allowed to interrupt data taking to print out the information stored in the buffer. This allows us to check the format and contents of the event records and aids us in trouble-shooting and monitoring. (d-iv) Data Recording - Summary of Data Taking Procedure We are now prepared to describe the over-all data taking procedure. Data are separated into data files called "runs" which usually last 1-2 hours. These runs are separately identified. Thus, runs with significant inefficiencies can be discarded without affecting the rest of the data. For each run, the PDP-8 writes run records (whose contents is described in the next section) before and after all the event records. During a data run and before the beam pulse arrives, the entire data system is dormant -- the trigger logic is gated off. The gate is removed upon the reception of a signal from the AGS signifying the beginning of the beam of p's. The trigger logic then tests each incoming p to see if the trigger condition is satisfied (see c-ii). We will now describe what occurs when an event satisfying t .h e trigger - 52 condition is det e cted (Fi g ure 2.14 is a timing diagram of what occurs all timings ar e approximat e ). 1. At T = 0 to 20 nsec , the event occurred. throug h the apparatus. It takes 20 nsec to go The scintillation material in the count e rs receives li ght. 2. It take s of the order of 50 nsec to get through the photomultiplier and an additional 20 nsec cable delay before the trigger logic receives the various counter signals. 3. The trigger logic, after about 50 nsec electronics delay, decides that the event satisfies the trigger condition. It s e nds four signals: A) One to pulse the wsc; B) to the interfac e; C) to the delay module which eventually turns off the interface again after 20 msec, and D) to the prompt event gate to turn the master ga t e on before the interface sends the BUSY signal. Note that the trigge r lo- gic is now incapacitated by the master gate. We s hall now follow each of the signals. Al) The pulse driver (Appendix B) receives the trigger log ic signal after about 10 nsec cable delay. A2) T is now about 170 nsec. After a delay of 20 nsec, the pulse driver sends an 800 volts, 80 nsec-wide pulsing signa l to all the 1 2 pul se r s . A3) After a delay of approximately 20 ns ec ( f or transit time in the cables), the pulsers receive the pulse driver signal. A4) The pulser fires t h e thyratron about 60 nsec after it rec e ives the pul se driver signal. AS) The thyratron is turne d of f b y the inductive kickbac k produced I 0 nsec .... ::r (1) __ _ _ _ 100 nsec c 160 nsec Trigger logic . receives counter signals Event Occurs rt >rj T - - - - - - -______t I ~ ~ ::l '1 (1) (1) rt . x N Trigger logic decides event satisfies trigger condition. Signals sent to A, B, C and D. "O ...... Ill .p. OQ •• (1) . .... ...... '1 ~ >gg ...... (1) I 180 nsec ...... '1 T I I 200 nsec 220 nsec I 240 nsec I_ 260 nsec 280 nsec 300 nsec rt Ill ..... ::l !3 ..... (b0... ::l A : WSC system Pulse driver receives signal Interface receives B: computer . interface Pulse driver H sends signal I Pulser r Pulser Pulser thyratron thyratron 1-'l recei- f-------': activated de-activaves signal ted Coincidence gate for the counter bits .on (for 50 ~ nsec); delayed counter signals arrive at bits Discharge occurs Counter bits and sensitive modules clamped to prevent - damage from wsc discharge noises OQ <! Ill rt en '1 (1) (b ::l '1 (1) Ill rr "O 0 "O '1 '1 0.. 0 ..... x ::l a· ()Q rt rt ..... lb . 8..... (1) :I ()Q a. ..... C: delay module r-~e la~ ~~du le --4 receives ~al lb OQ 11 Ill 9 ,.... (') 0 :I rt D: master gate ______, Master gate receives signal. Several trigger and beam modules gated off. ..... c :I !b 0 ::l V1 w T-----+ l_ about 400 nsec 2 µsec 8 µsec _ ______ _____!__________ _ _ _~ 3 msec 15 msec 20 msec ~ t-'• )Q c: l'i Cl) Wsc readout system starts ~~~~~~~~~~~~~~~to send signals A: wsc to interface system . HAll N t-' ...i:- wsc signals sent to interface. Ready for next event """ (l g rt t-'• ::l c:Cl) --::n:; B" computer--~ interface Counter W"BUSY" bits are signal read and sent to ~ reset .master · gate Digitizer handles wsc spark signals until all wsc signals are received (about 3 msec) 0.. '-' Interface turned off ......i by de lay module signal t-3 11 '"'" OQ OQ Cl) l'i Ill ::l 0.. Cl) =n Delay C: delay module D: master gate ,... module sends 1 signal to interface .ii.. Receive additional "BUSY" s igna 1 from computer interface. ~ Master gate is kept on for 20 more msec <! Cl) ::l rt Ii ro (l 0 Ii c.. !-'• ::l OQ rt t-'• a !-'• ::l OQ .. "BUSY" off. Master gate is off and trigge r and beam modules are on. c. !-'· Ill OQ Ii :I> .a V1 .i:- - 55 by l ll l ' u ·n.i. I i.ll l'. <'d).'.< ' of" Lile pu] ~;e d1·ivv1 · :dr,nal , which a1- 1 I v!•:; about 20 11sec aft e r tlte thyratron AG ) i:~ fired. Tllt.' spark clischargt' take s about JO ns t•c to form; abm1t: thus , .i t occurs 30 nsec after the thyr atron j s fired; T i s now about 300 ns e c. A7) After a delay of about 8 nsec due to transit d el ay in the ma gn e tostrictive readout wire and in the readout amplifiers, the s i g nal train o f the spark information begins to arrive at the digili. 7. l ' ,- , which ha s b een anticipatin g the signal Lit t> si g nals keep arriving and a bout 3 msec. ( see B-5 be low); is proc esse d for a duration or All the spark informat i on has be e n sent and the readout system is ready for the next event (note, the readout amplifier system is not turned off). However, as mentioned in (d-vii), the wsc requires recovery time of the order of 20 msec. B) Th e iriterfac e syste m; Bl) Th~. interface r ec eives the trigger log ic signal after a cable delay o f about 20 n sec. H2) Coinc id e n c e gate f or the counter bits ( for a duration of 50 n scc ) .i. s sent; tl1 e appropriate counter si gnal s, delaye d for an a pp r opriat e t ime (typically 100 nsec), a rrive during the p e riod of the ga te and thus are allowed to set the bits . l\:l) A f t •.· r tltc previous st:e p, at T [lpprox i inately 250 n sec , l" •HllllPT hit s module s ;,i~; wl' ll as other sensitive the modu"IC '. S ar e c]am ped t o prevent the wsc spa rking nois e f rom creating disturbances . The clamping lasts until aft er the wsc spark discharges - 5G - (at T approximately 300 nsec). B4) Afterwards, the counter bits are read into the memory buffer and reset. BS) At T about 2 µs e c, the BUSY is issued (this signal lasts for a du1~ation of 20 msec) to the master gate. For the duration or this signal, the master gate gates the trigger logic off (see D2 below). BG) In the meantime, th e interface prepared the digiti7-er to receive Llie wsc spark ::;i.gnals. These signals, in the f orm of a train of pulses, arrive for a duration of 3 msec starting at T about 8 usec. The interf~ce transfers the scaler readings of each coordinate to the buffer after the digitizer treated that coordinate (see d-ii). 137) The interface received the delayed signal C (see C2) which turns tile inter.face off except for the BUSY; the interface now awaits tile next trigger logic signal. BS) i\t t = 20 msec, the BUSY is stopped. The master gate is now off · and tlw trigger logic is reactivated. New events can now be accepted and we go back to step 1. C) Delay module Cl) At T about 180 nsec, the delay module receives the trigger logic signal. C2) After a delay of 15 msec, it sends a signal to the interface to turn the interface off except for the "BUSY" signal, which remains on for an additional 5 msec. - 57 - D) Master gate (when this gate is on, the trigger logic is turned off; (see Figure 2.9). Dl) The master gate receives the fourth signal from the trigger logic -- the "prompt event gate"; this turns the master gate on for 30 µsec; however, prior to the end of this period of time, the master gate receives D2) The "BUSY" signal from the interface; the BUSY is continuously sent for 20 msec during which the master gate is kept on and the trigger logic kept off. Thus, at the end of 20 msec, we are ready to start again at step 1. This process continues until either 15 events are accepted or the signal from the AGS specifying the end of the beam pulse is received. The data taking system except for the PDP-8 is now dormant. During the 2 seconds between each successive beam pulse, the PDP-8 writes the event record information onto magnetic tapes and does calculations for monitoring the data taking. taking is described in Section (d-vi). The monitoring of data The data taking system now awaits the next signal from the AGS indicating the next beam pulse. Our buffer is only large enough for 15 event records. It is possible to increase the buffer size so that more event records can be accepted per pulse. However, since the beam duration per pulse is only 400 msec while the dead time per event is 20 msec, accepting 15 events per pulse already implies that we are only using 1/4 of the beam. Thus, accepting more events per beam pulse would only be im- portant if our trigger rate or beam intensity is high. This is true - 58 only for the highest momenta. Thus, any gain we make would not be significant over-all. (d-v) The Contents of the Data Recorded Data recorded on the magnetic tapes For each triggered event, we record on data tapes: 1) . d (2.38) . 24 60-bit wor s (each word stored as 10 6-bit characters on tape) each consisting of 5 12-bit numbers. The first four are the scaler readings of the digitizer for the signals from a coordinate representing spark positions. The last number is blank to provide a check on the format of the record. If the last number is not blank, then we know something is wrong. 2) A 60-bit word containing 48 bits of counter information (see c-iii). 3) 5 blank 60-bit words. This also allows us to check the format of the record. For each run we record at the beginning and at the e nd a record of 30 60-bit words containing the information of the condition under which the data is taken, some identif ic ation numbers and the scaler readings specifying fluxes and number of triggered events. The run condition information which we record includes nominal momentum, NMR frequency of the bending magnet, beam charge and type, and magnet polarity. Each run is identified by an individual run number. The scalers which we read include those which scale p flux, number of triggers and number of beam pulses. Data recorded manually Important normalization numbers such as p flux are also recorded manually to double check. In addition, the condit i on o f the - 59 apparatus such as the counter voltages, spark chamber conditions, etc., are also recorded in case of any question on the data. (d-vi) Monitoring of the Data Taking During the data taking, we must make sure that the apparatus is functioning . properly and that the various important ratios such as trigger per p are constant. We use the PDP-8 as well as several manual· monitoring procedures to do this. PDP-8 monitoring of data taking The PDP-8 prints out at the end of each data run several items which it calculates or increments based on the events recorded. Among the items which it calculates is a number reflecting the wsc efficiency for each coordinate. This number is calculated by com- paring the number of sparks in each coordinate with the number of sparks of the other coordinates in the same set of 4 wsc. Any ab- normal drop in any of the 24 efficiency numbers indicates inunediately that the wsc system is not functioning properly. The total number of events with each binary bit is also printed out. Thus, any fluctuation in the percentage of any of the numbers also indicates a possible inefficiency. The PDP-8 also keeps track of the format of the event records; the number of events with format errors is printed out f or each run. Manual monitoring of the data taking We calculate the beam and trigger ratios for each run and make sure they do not fluctuate wildly. Condition of the apparatus, such a s the voltages, are recorded continuously and checked. Efficiency checks are also performed on the R counters using sandwich counters - 60 for coincidence. Any data runs which contain data taken while the apparatus was not functioning properly are discarded. e. Evaluation of the Apparatus and Data Taking System We will evaluate our experimental system through three criteria: A) Rate of backward elastic events. B) Appropriateness and efficiency of our equipment, and finally C) Data systems. A) Rate of Backward Elastic Events We will first discuss the beam. Appendix A and in Section (b-i). Table 2.2. The beam is described in The beam rates are summarized in The number of p's is sufficient (for our experimental system) at high incident momentum. becomes much smaller. At the lower momenta, the number At high momenta, the pi/p ratio is quite acceptable (about 1) but deteriorates at lower momenta. Since the beam was designed to be used above 1.0 GeV/c, the fact that we have appreciable numbers of p below 1.0 GeV/c is already quite satisfying:·. Our geometry has a laboratory acceptance of about 22 msr. The smallest aperture is the sensitive area of the 12th wsc, which is 3' by 1-1/2' and is about 14' from the target. Since we require a mo- mentum spectrometer and therefore a magnet, it is difficult to shorten the distance to the target. takes up 8 1 • In our case, the magnet and its shielding Therefore, unless we are willing and can afford to use larger track recording devices, the geometry cannot be improved. Another major factor is the dead time. 50% of the be am due to dead time. Typically, we lost about One way to reduce the loss is to - 61 tighten the trigger. We have discussed this in the section on triggering (c-ii) and concluded that only slight improveme nt can be made. Dead time can be shortened. For example, if we use proportional . (2.39) wire chambers , most of the dead time can be eliminated. ever, there are problems such as cost. How- Also the development of these chambers has only occurred since we took our data. B) Appropriateness and Efficiency of o.ur Equipment As we have mentioned before, we need to identify the incident p, identify the forward outgoing recoil proton by its velocity and to recognize the backward elastic event by its kinematics and topology. We must also have a trigger system to selectively trigger our wsc. Bl) Incident p identification. Our p identification system is very efficient in rejecting pions and counting p's (see b-i). contamination of pions is about 0.5 % and about 90% at high momenta. B2) Typical p counting efficiency is Thus, improvements are not necessary. Recoil proton identification by velocity. This identification is not absolutely necessary. We can do a background subtraction if there are large numbers of pions in the signal since no process will give an enhancement of pions with momentum close to the incident momentum (2.40) . However, we need to remove the pions if we were to get a good idea of the angular dependence of the des (differential cross section). Background subtraction for each angular bin would give reduced accuracy. We use two methods to obtain the velocity of any forward outgoing particle -- Cherenkov radiation and time-of-flight. The gas Cherenkov - 62 counter has a threshold of 1.1 GeV/c for pions. This is constrained by the fact that the index of refraction of the radiator is only 1.009, we can get more Cherenkov radiation and lower pion threshold if the index of refraction is higher. However, this is difficult to obtain, since under atmospheric pressures, no gas has refractive index above 1.002 while no liquid or solid has refractive index b e low 1.20. We have decided not to use higher pressures since doubling the pressure only lowers the threshold by 30%. The time-of-flight system we used has a resolution of 2 nsec FWHM. It is difficult to obtain better resolution since the counters themselves are l ' long. Although we have used the position of the particle trajectory as it passes through the counter to correct for this, the improvement in resolution is not significant. Other methods for determining the velocity of a particle in- . (2 .41) eludes measuring the energy of the particle . However, this cannot be easily done to an accuracy useful for us. B3) Kinematics -- momentum spectrometer. To determine the kinematics of the event, we use a momentum spectrometer consisting of a bending magnet with two sets of wsc to measure the deflected and undeflected trajectories. We need a good momentum measurement to discriminate against the inelastic background. Using a magnet system rather than other systems (such as range counters to measure energy) is a . d . (2.41) . reasona bl e c h oice ue to the superior resolution We have chosen wire spark chambers (wsc) to measure the position of trajectories becaus e of the large area possible, low cost, high rates, simplicity in operation and the ability to obtain digitized results. - 63 T li t · 111<.1jlff di s;.1dv a nla g l' mag1wt. is tli ,• i nahi]iLy o l pl a cii1 g Ll1t• w:H' i11:dd 1· ll1< • Thi s r e su] t s in a g real reduction of .solid angl e s s ince tl w f art hest wsc must be placed about 14' awa y. However, i f we wish t o u s e track recording devices which can be placed insid e the magne t, we wi ll probabl y r un into the problem of add e d cos t and c omplication s in l og i s ti c s (the s pact.~ inside the magnet would b e cramp e d and troubl e - s hootin g would be di f ficult). Bl+) :f.:.:iggL~ r • 1u a 1~· .t y s ys t e m. The tr i g ge r r e quir e me nts are d e alt with ad e - b y tlw p countin g sys tem and the va r ious tri gge r counter s . Wr. have d is cu s s e d (in c-i.i) ways to ti g ht e n the trigge r and c o nclud ed that the system we used is quite adequate. BS) Eouipment operation. · The various counters and ws c we used are quite eff icient. 99.5 %. Typical scintillation counter efficiency is about Typical wsc efficiency is about 99%. Equipme nt breakdown occurs occasionally and the amount of beam t i me lost due to this factor is about 10%. C) }_)a~ .1 Sys Ll'lll Ou1· da t a ;1re nol anal y;-:cd on-li.n e . The on-] i.n(• comput e r s ys t e m o nly 1·c c ords Lil e dat a and monitors the data taking. o f our The c a pabilitie s on-l i ne system is limited by the memory size (4K 12-bit locations) and the fact that we may have up to 15 events per 2.4 seconds. The computer is only free during the beam off time (about 1.8 s e c.). Even if memory is no problem, the PDP-8 will only be f ast enoug h to analyz e on the order of 5 events per pulse. Thus , i f we wish to have an on-line analysis system , we n ee d a mu ch ·iarger computer (memory size at l e a s t 20K). At R NL, i t is possible to tie our experiment on··line with the PDP-6 computer which exists at the AGS . Since we would not be the only user, prob l ems due to multiple usage may occur. The phys ic a l loc a tion of the PDP-6, which is not very close to our equipme nt, could also cause some problems. Actually, the preliminary ana lysis for our experiment is done within a very short ti.me from the data taking time (usually 5 to 10 hours) by using the CDC-6600 computer next to the AGS . Therefore, we do have almost instant feedb ack, which i s the major advantage of the on-line analysis system . - 65 CHAPTER III: a. ANALYSIS OF THE DATA Introduction The magnetic 1 data tapes contain records of the spark positions and counter bit information for each triggered event. We must use this information to determine how many backward elastic events are among them. The analysis of the magnetic data tape information is done off- 3 line at the Brookhaven CDC-6600 computer center in two stages( .l). In the first stage, as described in Section (b), we reconstruct the event trajectories from the digitized spark position information. Given the event trajectories, we can calculate various quantities such as momentum of the recoil proton, angle of scattering, position of interaction vertex and the topological 1uantities which measure the 3 2 amount of additional scattering(s)< · >. These quantities, along with the forward par,t icle velocity information from the gas Cherenkov counter and the forward particle time-of-flight system, are used in the second stage of the analysis, which is described in Section(c). This stage consists of making various selective cuts which remove background. In the case of momentum background (i.e., events satisfying all other cuts but have slightly wrong momentum), we make a background subtraction. elastic pp events. We thus arrive at the number of backward These events are separated into several angular bins. To obtain the correct normalization, we study all sources of normalization errors in Section (d). The normali z ation corrections due to reconstruction inefficiency and s e l e ctiye cut losse s are - 66 handled by Sections (b) and (c), respectively. We use a Monte Carlo 3 3 program( . ) to calculate the angular acceptance of our apparatus. This is described in Section (e). Having obtained a corrected number of backward elastic events and the angular acceptance of our apparatus for a particular angular bin, we can calculate the _differential cross section (des) for this angular bin. This is covered in Section (f). We obtain the error of the des by combining the statistical error, Monte Carlo error and other errors associated with corrections, uncertainty, etc., in Section (f). A summary and assessment of the analysis procedure is presented in Se ction (g). b. Reconstruction of Events (b-i) Introduction In the first stage of the analysis, we reconstruct the event trajectories from the magnetic data tape information. The track- finding , which is detailed in Section (b-ii), involves finding at least three sparks whose position lies on or near a straight line. The horizontal and vertical coordinates of each set of wsc are treated separately. The trackfinding is two dimensional. The desired topology of a background elastic event, as shown in Figure 3.la, requires the existence of (1) an incident p beam track, (2) a recoil proton track in the second set of wsc (downstream of the target), and (3) a recoil proton track in the third set of wsc downstream of the magnet (the track would have been horizontally deflected by the magnet). 35% of the reconstructed events fail to have a - 67 track in some region (either the horizontal or vertical view of any of the 3 sets of wsc). They must be discarded since the topology, momentum or scattering angle would be unspecified without a track in each region. We study such events in Section (b-iv) and Section (b-v) and show that aside from an insignificant number, no backward elastic events are lost by rejecting such events. 30% of all event.s have more than 1 track in some region. We must throw away all but one of the tracks since the desired topology allows only one track per region (see Figure 3.la). We throw away any spurious track by using var i ous topolog ical properties of a backward elastic event and also some counter information. This pro- cess is described in Section (b-iii). The reconstruction process is e x pected to be inefficient for some number of events. We study the inefficiency in Section (b-iv) and conclude that about 5 % of the backward elastic events fail to be reconstructed correctly and are lost. As mentioned above, we discard all reconstructe d events which iack a track in any region. We account for these events by studying any possible sources which may give rise to these e vents. The conclusion of this study, which is described in Section (b-v) is that the nt.nnber of reconstruction events discarded is close to e x pectation. (b-ii) The Finding of Event Tracks from the Digit iz ed Spark Positions For each region consisting of four horizontal or vertical coordinates, we have the numb e rs spe cifying the spark positions (a ma x imum of four spark positions are accepted by the readout system of each coor dinate). Through the knowledge of the spatial pos i tion o f - 68 Figure 3.1: (a) Horizontal and vertical views of the topology of a desired backward elastic event showing particle traj ec tory (dot-dash line), wsc planes (solid lines), bending magnet. x's are the expected sparks for this event. (b) Extrapolated x and y positions of tracks at planes z VD i s minimized) and z =magnet center. = z v (where (x,y)AB is defined as the ex- trapolated ( x ,y) using tracks from regions A and B. Reconstructed vertex is defined as Zv· -, - - -------:-i : mag nr0t CCll t 7 r Z=Z VJ U~t I .-·---_ . ~~~' . . ~ · ~t region J !I ----· L ____J I - . - · .+-- : -...i._ :. region 1 (a) . Z=r :f ~!-~-H-H-· 1 11 I magnet center t ---·--·--· region 4 region 2 - - -- - -- - -· Ly VD (x,yl 3 , 4. (x,y) .... 6 ::> t -¥ (x, Y )1, 2 . --------·- The plane z z v where VD is minimized .-· - . Magnet center plane - 69 3 4 the wsc fiducials( • ), we can derive the two-dimensional position of each spark from the digitized spark number. Since no track can 4 . . . any one coor d.inate, th" i s gives a maximum o-f 4 k in 1 eave two spars combinations of possible tracks. We accept only tracks which satisfy the following: 1. A loose criterion for straightness. The reconstructed track is obtained by a least-square fit. 2. We allow at most one missing spark. 3. The track must have a slope which is topologically acceptable. These conditions are implemented by using a procedure developed . d(3.5) b y M • Hin • (b-iii) Procedure for Removing Spurious Tracks The topology of a backward elastic event precludes the existence of more than one event-associated track in any region. For regions having more than one track, the spurious track is removed using topological and counter information. This applies to about 25% of the events. Before we describe the procedure, we must say a few words about backward elastic event topology. The tracks from regions 3 and 5 (see Figure 3.la) ' should meet at the center of the magnet since they . belong to the same particle. allowed. No scattering between region 3 and 5 is The same is true for the tracks from regions 4 and 6. This condition should be satisfied by good events except for multiple· scattering, chamber resolution, etc .. We can define a quantity to measure the degree of agreement with this condition. This quantity, - 70 which we call Magnet Track Deviation (MTD) is d e fin e d a s the deviat ion between ( x ,y) . and ( x,y) . wher e ( x ,y) is the trac k 3:4 5, 6 A,R pos it ion at the plane of the magn e t c e nt er for the tracks from /I. <t nd IL n~g ·ion s We ckmonstrate thi.s quanti ty in F .i g u re J. Jb. '1.' IH·r e inu s t h P one a nd only one scattering between regions I, 2 ;rncl L·e g ions 1111..~e t ~~, Lf. This impl ies that the trcicks fr om re g ion s 1,2 mus t those from regions 3 7 4 at a c ommon point except for multiple s catt ~· ring, etc . Aga in, we c an define a quant i ty to measure this -- Vert ex Deviat i on (VD), which i s define d as the minimum v alue of 3 4 1 2 the three-dimensional deviations between ( x,y,z ) ' and ( x ,y,z) ' (whe r e x and y a re the horiz ontal and v e rtical position for the tracks fr om reg ions 3 and 4 at z = z ). The d efinition of VD i s also s hown i n Figure 3.lc. ThL~Se topolog ic a l quan t itie s will be studied in detail in Sec ti on ( c -ii) where we us e these quantities to c ut out the backµ round. It i s sufficient to s ay now th a t the t ypica l size of MTD and VD for go od eve nts are 0.5 and 0.1 cm, respec tive l y. The proc ed u re for removing spurious tracks is: 1. I f there is more than one track in r egion · 1 or 2, we reject any tr ack with lar ge angle (more than 70 mr) w.r.t the beam line or far away from the b eam line (mor e than 5 cm away). This ensures that we are only d e al i n g with the beam track which passes through th e ape rture counters. 2. In ~eg ion s 1, 2 , and 5, we can use the counter info rmation. The count er hodoscopes Hx a nd Hy a re situated right nex t to the first se t o f ws c (r egion 1 and 2) while the vertical counte r s R 0 - 71 to R 3 are situated next to the third set of wsc and thus ca n help us remove spurious tracks in regions 1, 2, and 5 (R counters cannot give any information of the vertical position of the trajectory). We extrapolate the tracks to the plan e of the counters and require the appropriate counter to be hit. Extra tracks arriving outside the 50 nsec coincid e nce gate of the counters can thus be removed since they are not associated with the trigg ered event . 3. Now we use the quant ity MTD (magnet track deviation) defined in the last pa ge. Since the correct combination of tracks from regions 3,4,5, and 6 should have a small value of MTD (o f order 0 . 5 cm), we pick the combination with the smallest MTD a s the correct tra cks. 4. Finally, there remains a b out 1% of the r econstructed evertts which still have spurious tracks in regions 1 and 2. The spurious tracks are rejected by accepting the two tracks in regions 1 and 2 which, whe n combined with the tracks in regions 3 and 4, give the vertex of int e raction (the position whe re VD i s minimiz ed ) -- see F i gure 3.1) which is closest to the center of the tar get. This process is re l a tively unimportant since only 1% o f the rec onstructed events i s affected. This procedure enables us to obtain a u nique se t o f tracks for each event except those dis c arded due to mi s sing tra c ks in some regions, . We can now derive the topolog ical and kinematical properties o f e ach event s u c h as t h e momentum and ang le of scatt er ing and us e the m to separate backward elas tic e v e nts f rom ba ckground. - 72 (b-iv) Reconstruction Inefficiency The trackfinding and spurious track removal procedures may be inefficient. We must find out about the size of this inefficiency and und e rstand how it will affect our normal ization. A detailed analysis of the i n efficienc ies was undertake n. The details of this analysis and its results is fully described in Appendix c. We will, in the following few paragraphs, describe briefly the methods we used and the answer we obtained. First, we convinced ourselves that our criteria for straightness, slope, and position of acceptable tracks are reasonable. A study of the slopes and positions of good backward elastic events indicates that our criteria are loose enough. Our criterion for straightness invalves calculation of a chi-square for each combination of track sparks. Distributions o f chi-square for tracks also indicate that our cut is loose enough. Any i nefficiency in trackfinding must therefore be due to missing sparks. Wsc inefficiency can be calculated based on the relative number of tracks with one spark missing and the number of tracks wh ich have all four sparks. We must assume that the inefficiency of each wsc is not correlated with that of any other wsc. i~efficiency This type of is basically an eq~ipment inefficiency and will be handled later i n the section on apparatus inefficiency. However, it is known that efficiency for two sparks in one wsc is . (3.6) lower than efficiency for one spark in the same wsc • Also, since our wsc can only accept up to 4 sparks, the efficiency for more than ~· tracks must be drastically lower than that for one track. - 73 This correlated inefficiency is important if there are many tracks or extra sparks. Regions 3-6 have few extra sparks or tracks (typically about 10% of the events have more sparks than can be accounted for by one track). Correlated inefficiency is thus ex- pected to be small (less than 1%)• This is verified by finding very few events which have only two sparks in a region 3,4,5 or 6 indicative of a track with two missing sparks. In regions 1 and 2, more than 1/2 of the events have extra sparks. Detailed study of this region (described in Appendix C) involving scanning computer plotted pic3 7 tures of spark positions< · ) and artificially inserting a beam track when no beam track is found gives us the result that there is an inefficiency of 3 % in addition to the wsc uncorrelated inefficiency. Thus, the trackfinding inefficiency is 3% in addition to the wsc uncorrelated inefficiency. We study the spurious track removal inefficiency by 1) using an alternate method of spurious track removal, and 2) looking at the second best combination of tracks in case we use topology to decide on the besttracks. We find a 2% inefficiency in the spurious track removal procedure we used. These effiGiency studies are done for different incident momentum, different wsc efficiencies, and different beam halo rates. No strong correlation of the inefficiency with momentum wsc uncorrected inefficiency or rate has been detected. Thus, for our entire data, there is an over-all inefficiency in reconstruction of 5~. - 74 (b-v) Analysis of the Triggered Events which Fail the Reconstruction Process We claimed that the trackfinding inefficiency is the sum of th e un c o rre lated ws c inefficiency (which is between 1-5 %) plus an Hdd i.t.ionnl cornd.:Jted ineffi.cl.ency in re gions '1,2 of about 3 1/ • • t hi. s ~; o, is If we must be ahl c to account for the 'l arge number of tri g - gere d events (about 35%) which fail the reconstruction process (i.e., missing a track in some region). Region 1 and 2 (at the first set of wsc) The trigger condition requires a count in both 8 2 and 8 . As 3 seen in Figure 2.2, this necessarily implies that a particle passes through the first set of wsc. Yet, 5 % of the triggered events miss a t rack in e ither region 1 o r 2. This is reasonable since uncorrelated wsc inefficiency is typically 1% while there is an additional corre1atc>cl wsc .i.ncl'fic :i c n cy of R<.~gions 31, i n regions l and 2. J and 4 (the second set o f wsc) About 5 1/ , of triggered events miss tracks in regions 3 or 4. s 3 a nd the P counters are re quired in the trigger condition. Now Since P counters cover an area smalle r than the sensitive ar e a of the second set of wsc, one also expects that a particle should have gone through regions 3 and 4. Typical uncorrelated wsc inefficiency for the second se t of wsc is about l~. t il e fact that The remaining 4 % mi ght be accounted for by scattering or s 3 is actually quite far from the second set of wsc. Sca ttering mi g ht g ive a track which is not straight enou gh to be acceptable. In ad dition, p g oing into n forward which annihilates in - 75 the P counter would also fail to have a track in the second set of · ( 3 .s) - going into nn is typica 11y lOoc? o f t h e tota 1 cross section wsc ( pp and about 5% of the n's, if it strikes the p counters, will interact to give a final-state charged particle). Thus, we conclude that the 5% missing track events in the second set of wsc is reasonable. Regions 5 and 6 (the third set of wsc) Approximately 30% of the triggered events have no track in regions 5 or 6. However, the wsc does not cover 15% of the counter area. The remaining 15% of missing track events may be accounted for by 1) events where particles strike the pole face of the magnet giving tracks in regions 5 and 6 unacceptable by our slope criterion for trackfinding (observed to be about 2%)· 2) pp into nn at the p counters or the pole face of the magnet whe re the n interacts at the R counters to give a count there (this could account for about 5% to 10% of all triggered events). 3) Events indicating beam interacting with the aluminum frame of the wsc so that the T-R counter is triggered by one of the resultant products (about 5%)· Although the reasons given are not entirely satisfactory, it would appear that most c. of~ missing track events can be accounted for. Selection of Backward Elastic pp Events (c-i) Introduction Having reconstructed the event trajectories, we can proceed to select the backward elastic events. To do this, we use several quantities derived from the event trajectories as well as the velocity information from the Cherenkov counter and the time-of-flight system. The first criterion we use is the topology of the event. As - 76 - mentioned in pages 68 (Figure 3.1) and 69, the re 1uir e me nt that there is no additional scattering other than the backward elastic scattering forces any good backward elastic event to have small values of MTD (magnet track deviation measuring the deviation between the tracks from regions 3 and 4 and the tracks from regions 5 and 6 at the magnet cente r plane) and VD (vertex deviation measuring the closest approach betwe en the incoming p track and the recoil proton track). reject any event with large values of MTD or VD. We thus The procedur e for the rejection is described in (c-ii). The second criterton used to reject background is the reconstructed vertex (which is the point of closest approach between the reconstructed p beam t r ack and the reconstructed recoil proton track) . We require this reconst r ucted vertex to be inside the hydrogen target . We handle this cut in Section (c-iii). We use the velocity and momentum information as our thi rd and f ourth criterion. Knowing the momentum of the forwa rd outgoing particle allows us to decide whe ther the event f its t he e lastic kinemat i c s . Knowing the velocity in addition to the momentum o f the f orwa rd particle enables us to decide the valid i t y o f our a s sumption that the f orward partic l e is a r e coil proton. We are able to r e ject all background b y u s in g these c riteria. We sha l l list briefly a summary of our reconstruc tion and s e lec tion proc edures in terms of the amount of triggered e vents whi c h pass e ach s t age . 1. About 65% of all t r i g ger e d e v e nts can be rec onstr uc t e d su c c e ssfully . - 77 2. Abou t 40•,t, of all triggered ev e nts have. MT]) and VD which arc acceptabl e. 3. About 25 % of all triggered events have, in addition, a rcconstructed vertex which is acceptable. 4. Finally, the number of backward elast i c events (i.e., those in addition to the above, pass our velocity and momentum criterion) is about 0.5-1.5% of all triggered events. The inefficiency in reconstruction is is 0 %, in vertex cuts is is less than -0. 99. 5'fo, in MTD and VD cut s 0%(except for those events where cos Bcm The typical inefficiency for the cos B bin cm between -0.98 and -1.00 is 7%) and in velocity cuts is 2% and in momentum cuts is about 3<'fo . Thus, the cumulative inefficiency in r ec onstruction and selection is slightly more than 10%. (c-ii) Topology Selection Criterion (Cutting on MTD and VD) As mentioned on pages 68 (Figure 3.1) and 69, we expect the values of MTD and VD to be small for backward elastic events we \vish to acc e pt. This is <lue to the requir e me nt that we acct~ pt those events with one single backward elastic scattering. only The HTD and VD should be 0 except for the deviation of the reconstructed tracks from the actual event tracks due to multiple scattering and wsc reso lut ion. In addition, the MTD is a small non-zero numb e r even for the actual track if the entrance and exit angles -0f the recoil proton trajectory w.r.t to the magnet are not the sa.me. The distribution of these quantities for good elastic events is expected to peak near 0 and drop off rapidly away from 0. Therefore, to find out where we - 78 should make a cut, we must look at the actual distribution of MTD and VD for good backward elastic events. Figure 3.2 shows the distribution of VD and MTD for some typical backward elastic events. We see that the standard deviations of VD and MTD are about 0.1 and 0.5 cm, respectively. be similar to a Poisson distribution. The shape appears to We have chosen 1 and 5 cm as the limits for VD and MTD, respectively and essent i ally no elastic eventswith good topology are lost by these cuts. The background level is very low and we estimate that less than 1% of the events within our cuts are events with either additional large angle scattering or events where the track in some region does not belong with the rest of the event. About 5 % of all reconstructed events fail the VD criterion. 3 9 Looking at computer drawn pictures< · ) of these events shows that these events probably have more than 1 scattering between the first and second set of wsc. MTD cut. About 30% of the reconstructed events fail the Half of these events have tracks in the regions 3,4,5 and 6 sugges t ing that there is an additional scattering between regions 3 and 4 and regions 5 and 6. The scattering cent e r often appears to be the pole face of the magnet or some counter. The remaining half appears to be events which scatter in air or have more than one scattering center. This may be due to the forward particle being a low momentum particle which may be bent quite drastically by the magnetic field so as to hit the side of the ma gnet. In any case , very few of these events have vertical tracks in region 4 and 6 whic h a r e parallel, which is necessary for acceptable backward elastic event 1000 800 800 Number of events ambiguity limit (see Appendix C) l 600 400 I Number of events 500 I I I r1 II 400 I ambiguity limit (see Appendix C) I I I 200 200 0.50 0.25 1 1.0 VD in cm Figure 3.2: l I I I Distribution of VD and MTD for backward elastic events . 2.0 MTD in cm 3.0 Note that the MTD peaks away from o· due to the difference in horizontal entrance and exit angles into the magnet making MTD I O. -...J l.O - 80 topology. The topology criterion thus removes about 35 •~ of all recon- structed events (or 25% of all triggered events) with no signif icant loss (less than (c-iii) 1%) of backward elastic events. Reconstructed Vertex Criterion We are only interested in the backward elastic events asso- ciated with the hydrogen in the target. Thus, we must find a way of : removing all other backward elastic events from our signal. The position of the interaction vertex can be reconstructed using the tracks from regions 1-4. The z position of the reconstructed vertex is the plane of z where the tracks from regions 1 and 2 deviate the least from the tracks from regions 3 and 4. in Figure 3.lb. We show this We use thi s information to help us remove any back- ward elastic events not associated with the target. We make a vertex cut at ± 16 cm, rejecting all events outside this cut. We can lose events if the reconstructed vertex is outside this cut while the actual v er tex is inside this cut. e vents if i t is the other way around. We can gain Since there is still a sizable amount (3.2 cm) of hydrogen target outside this cut, we e x pect the losses and gains to balance out. is large. ecm less than -0.998,. a small c hange in However, for cos This is true if the scattering angle slope or intersect due to multipl e scatter ing or chamber resolution causes a large change i n the reconstructed z position of the vertex . Thus, a lar ge number of backward elastic events a r e Jost which a r e not' balanced b y the number ga ined . In gen e ral, this cau ses a typic a l loss - 81 in the angular bin between -0.98 and -1.0 of about 7%. This result has been obtained by comparing our usual vertex procedure with seve ral alternative procedures detailed below. 1. We obtain the number of events inside a ± 8 cm cut and compare it with the number of events inside the± 16 cm cut. except for the first bin (where -1.0 = cos Typically, ecm = - 0.98), the two numbers are in a ratio of 1/2 to within statistics (which is typically 2. Since about 18% of the target hydrogen remains outside the ± 16 cm cut, we expect and find about 18% more backward elastic events outside our cut (except in the first bin). 3. For several momenta, we took data with targe t empty of hydrogen. The actual hydrogen associated events number will be the target full number minus the target empty number. It turns out that the rate of backward elas tic events for an empty target is typically less than 5 % of the full target rate and the statistical error is very poor (usually we have 0 or one empty target event per angular bin). Nevertheless, the results obtained with this proc ed ure agrees with our usual procedure except in the first bin. At each momentum, we calculate the correction in our first bin b y u sing number 1, 2 and (if we took empty tar get data at that momentum) 3 proc e dures me ntioned above. The correction is typically 7%. About 15% of all triggered events are rejected due to a vertex outside the ± 16 c m cut. 25% of all triggered e v e nts still remain. The inefficie ncy of this cut is l ess than 1% except at the first bin. Not e that we us e only 32 cm o f hydro gen target i n ou r f inal c alcu- - 82 lation of des (differential cross section). (c-iv) Velocity Criterion The next criterion we use to select backward elas tic events is the velocity criterion. We can remove most of the pion background from the recoil protons by consider~ng the gas Cherenkov and time-ofAs mentioned in Chapter II, Sections (c-iv) and flight information. (c-v), the gas Cherenkov pulse-height channel exceeds channel 24 for about 80% of the pions above 1.2 GeV/c and less than 2% of the protons while the time-of-flight system can separate protons from pions below 1.2 GeV/c. For each momentum, we select the limits of our cut in the time-of-flight system delay channel such that combined with a gas Cherenkov pulse-height channel cut at channel of 2% of protons. (M ) p 2 (where (MM) 24, we lost of the order For example, Figure 3.3 shows a plot of 2 (MM) 2 - is the missing mass squared assuming the pp going into a proton plus the missing mass), for events inside (3.3a) and outside (3.3b) our velocity cuts. For the backward elastic events, the missing mass is a proton so that we expect the events to peak near (MM) 2 - (M ) 2 • p peak near (MM) If the forward particle is a pion, we should get no 2 _ (M )2.(3.10) p In d ee d , in Figure 3.3b, except for a small peak which is due to proton leakage, no peaking is observed. The leakage is about 2% of the peak in Figure 3.3a. this velocity cut is about 2%. studied for each momentum. Thus the loss for Loss due to the velocity cut is The losses are about 2% to wit h in sta t istics. a/_ • Hence, we app 1 y a 2 p correction to all momenta for this loss (3 .11) • The numb e r of remaining triggered events cut by the velocity criteria varies considerably with the momentum. At low momentum, - 83 2 2 Figure 3.3: (MM) - M distributions for events (a) passing and (b) p failin our velocit ' criterion for rotons. (a) 300 1.61 GeV /c 200 100 --- 100 0 -0 . 3 -0. 2 -0 .1 0.0 (MM) 2 - M p 0. 1 2 i n (Ge V) 0. 2 2 (b) 0.3 - 84 the cuts remove all but approximately 2% of the triggered events while at the higher ,momentum, the number of events surviving this cut 1 could be up to 20% of all triggered events. (c-v) Momentum Cr it erion The final criterion used to select backward events utilizes the momentum of the forward particle. However, since not all the pion background is remove d, we cannot use a simple cut procedure to obtain the backward elastic events. We use a background subtraction procedure. In Chapter II, Section (b-iii), we described the way we measure the forward particle momentum. incident p momentum. We also mentioned how we calibrate the Assuming that the target particle as well as the forward particle are protons, the four - vector of the missing particle is completely determined. If the missing particle has mass nea r the proton mass, then the interaction must b e elastic. Any inelastic strong interaction of pp producing a proton going forward must produce at le a st one nucleon and one pion in addition. The missing mass would then be very much larger than the proton mass. Studies show that our experimental resolution is such that we will not confuse an elastic event with an inelastic event. For future reference, we should note that the studies also indica t e that inelastic missing masses would have (MM) 2 - (M ) p 2 (missing mass squared minus proton mass squared) larger than 0.2 GeV/c. Figure 3 . 3 shows a distribution of (MM) passing all other criteria . 2 - (M ) p 2 f or events We note that the background l ev e l is - 85 much lowe r than the signal level. ' ground by a linear function of (MM) Figure 3.3a). Thus, we c an approx imat e the back- 2 (shown as t he dashe d l i ne in The linear function is obtained by fitting the d a ta in the bin s adjacent to our signal bins. In the ca s e of Figure 3.3a, t he signal bins contain those events with (MM) and 0.1 GeV 2 2 - (M) p 2 betwe en -0 . 1 • and t h e background bins we use to obta i n the linear function c ontain those events with (MM) 2 -0.1 and betwe en 0.1 and 0.2 GeV • 2 - (M ) 2 p between -0.2 and The limits of our signal bins are chosen to be at least 3 standard deviations awa y from the elastic peak. Thus, we e x pect the amount of real background elastic events mistakenly in the background bins to be very small. loss of e lastic events is evaluate d at each momentum. The amount of Thes e evalu- ations are based on studies with narrow velocity cuts which remove as much pion backg round as possible. The average loss is a bout 1-1/2% which produc e s a normali z ation error of 3% since events in the background bin s r e sult in double subtraction. with (MM) 2 - (M ) p 2 larger than 0. 2 GeV 2 We nev e r h ave to use events as background so that inelastic proton contamination does not cause any problem. correction f or this loss at all momenta (3.12) We apply a 3% • The resultant numbers of backward elastic e vents are obtained for each ang ular bin in cos e cm of 0.02. The diff e rential c ross section can thus b e obtained if we know the normalization c orrections and angu l ar acc e ptances of our apparatus for each angula r bin. d. Correc tions to the Normalization In or d er t o obta i n the cor r e ct normali za t i on , we mus t find out - 86 the necessary corrections. In Table 3.1, we list the sizes of all n o n- ze ro corrections at ecich momentum. o l' Je ss than We liave lumped a]l corrections 11· :i.nt:o a combined column labeled "Misc e llaneous Correc- tions'' which is estimated to be Jojo at all momenta. In the following pAra g r a ph s, we will discuss all the correc tion s . Rl•c 011 s t nlc t ion i.n e f f:i.c i.enc i ei; As mentioned in Section (b-iv) and in Appendix C, the reconstruction inefficiency is ficiency and 5%consisting o f 3%correlated wsc inef- 2%spurious track removal inefficiency. Selection criteria losses The selection cut losses are discussed in Sections (c-i) to (c-v) and we concluded that the loss due to: 1. Topological cut (cuts in MTD and VD) is less than 2. Reconstructed vertex cut is less than less l han -0.98, the f irst bin, when~ 1%. 1% (except for cos Gcm the loss is typi c;illy 7 'j.). 3. Veloc ity cut is 2%, and 4. Mome11tum subtraction procedure is 3<fo . Ap paratus inefficiencies Apparatus ine ff iciencies could arise from inefficiencies in b e am counter, trigger counter, trigger elect ronics, wsc system, r e adout-computer i nterface system and in tape system. Inefficiencies in beam counter do sin ce the same counters count p f lux. not affect our normalization Inefficiencies in trigger count et·s have b een studied using the overlap regions between two adjacent counters and the extrapolated positions of the particle Table 3.1: Sizes of all corrections at each incident momentum in % · Only those corrections which are larger than 1% are listed separately. All corrections less than 1% are lumped into the miscellaneous correction of 3% . Actual correction applied at each momentum is larger than the sum of all corrections since (1) corrections should be applied by multiply ing by (l/(l-% correction) rather than (1+% correction) since these corrections are for losses and inefficiences and (2) corrections should be applied one after the other . Incident Momentum · (GeV/c) Recon. Ineff. Vel. cut loss Mom. loss Wsc Ineff. Counter Ineff. Beam abs. Misc. Corr. Sum of all corr. Actual corr. Applied 0.703 0.812 0.873 0.935 0.987 1.115 1.338 1.447 1.590 1.610 1. 716 1.797 1.844 2.032 2 .155 2.370 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 0.1 0.1 0.5 0.2 0.8 0.6 2.6 2.8 4.0 2.6 4.1 1.8 4.3 5 .6 3.2 6.0 1.3 1.3 1.3 1.3 1.3 1. 3 1.3 1.3 1. 3 1.3 1.3 1.3 13.2 11.8 10.9 10.0 9.6 9.2 8.8 8.5 8.1 8.1 7.9 7.7 7.7 7. 3 7.0 6.6 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 27.6 26.2 25.7 24.5 24.7 24.1 25.7 25.6 26.4 25.0 26.3 23.8 26.3 27.2 24.5 26.9 31.0 29.4 28.8 27.4 27.7 27.0 28.6 28.5 29.6 27.9 29.5 26.7 29 . 5 30.3 27.5 30.0 J..3 1.3 1.3 1.3 CX> -...J - 88 trajectories. The number of coincidences is compared with the number of singles and an inefficiency can be derived for each counter. Based on a study involving 30,000 triggered events, we found that the inefficiencies in P, R and T counters ranges between 0 0.4% and 0.5 to 4.0%, respectively. 0.4'fu, 0.0 to The over-all P, R, and R counter hodoscope inefficiencies are 0.1%, 0.1% and 1.1%, respectively. Thus, the trigger counter inefficiency is a total of 1.3%. The inefficiencies in trigger electronics, readoutcomputer interface and tape system are found to be less than 1% each. The inefficiencies are continuously monitored and any data with inefficiencies in these systems in excess of 1% are discarded. The inefficiencies of the wsc (wire spark chambers) can be obtained if we assumed that the inefficiencies are uncorrelated. Then the inefficiency of each chamber in a set of four wsc can be derived from the relative number of four spark tracks and three spark tracks in which a spark is missing in that particular chamber. We found that the combined inefficiency of the three sets of wsc lies in the range between 0.0% and 6 .0%. They are listed in Table 3.1 for each momentum. In section (b-iv), we mentioned that there is an additional correlated wsc inefficiency in the first set of wsc. However, thi s is considered a reconstruction inefficiency. also studied the pos~ibility We have of dead spots in the ws c by looking at the number of tracks and the number of missing sparks inside 2.5 by 2.5 c m bins for each wsc. We d id not fi nd any clust er of bins (4 to 10 bins) with abnormally low numbe r of counts or high numbe r of miss ing Hparks. Thus, we did not detect any dead spots. - 89 Beam and Flux Corrections These corrections include beam absorption corrections , wrong momentum and wrong particle (i.e., non-p) contamination corrections and corrections due to some beam particles not going through all of the target. A certain amount of beam particles are absorbed (i.e., suffer interactions) in going through the target. Thus, the effective beam going through the entire target is less than the beam counted by the beam counter system. The amount of beam absorption can be calculated from well-known total cross section and elastic cross . d (3.13) section ata • Typically, inelastic interactions absorb the beam while only large angle elastic scattering absorbs the beam 1. (3 .14) . ef f ective y • The correction necessary d ue to b b earn a sorption is given for each momentum in Table 3.1 and is typically 8%. Beam contamination by non-p's is discussed in Section (b) of Chapter II where we discussed the beam counting system. tamination level is less than 1%. The con- Beam contamination by wrong mo- mentum p has been studied and found to be of the 1% level. However, this contamination is the major cause of our momentum selection cut inefficiency since if we misjudge the incident momentum by a sufficient amount, any backward elastic event would not have good enough kinematics to be accepted as a backward elastic event. Thus, this contamination has already been corrected for by the correction for the momentum selection procedure. Less than 1 1j 1 o f the beam would mi.ss any part of the target if the b e am particle does not interact. This i s ensured by the - 90 placement of the three aperturing counters. Trigger condition inefficiency The trigger condition has a veto requirement (see Chapter II Section (c)) which may veto some of the real backward elastic events. The veto is triggered when there is a forward negative particle with momentt.un close to the incident momentum. This is possible since the final state p will annihilate and thus may release some high momentum pi minuses. However, since the annihilation is essentially at rest, any pions emitted will probably be released isotropically. Then, the veto would be satisfied only if the pion goes forward inside a solid angle of 1/30 sr or 1/360 of the entire solid angle. Since the average ntnnber of pi minus released by pp at rest is about 1 or 2, the probability of the veto condition being satisfied for a backward elastic event is less than li· Miscellaneous Corrections Several of the corrections mentioned above are less than 1%. They are not listed separately in Table 3.1 tion The combined correc- due to all these small corrections is estimated to be 3% and is not a function of incident momentum. e. Monte Carlo of the Apparatus Acceptance In order to calculate the differential cross section, we need to know how much solid angle for each angular bin is accepted by our apparatus. We only accept backward elastic events which have appro- priate particles passing through the various trigger counters and the sensitive areas of the wsc. We use a Monte Carlo program to - 91 generate events and follow the trajectories to see if they go through the necessary apparatus (3. 3) . • Interactions are generated inside the hydrogen target with the interaction vertex distributed according to beam characteristics. The z vertex (along the beam line) is distributed randomly inside the target except for a bias to simulate absorption of beam. The x and y distributions are gaussian with the parameters obtained from calibrating the b earn (3.15) . We follow the path of each recoil proton from the generated event, correcting for multiple scattering and nuclear interaction. Any event having recoil proton trajectory failing to pass through a required area is rejected. Other events which will have unacceptable reconstructed kinematic or topological quantities due to large angle nuclear scattering are also discarded. For cos cos ecm bin of 0.02, we generate M events with random ecm inside that bin. some limit cp 0 The cp is also generated randomly inside chosen such that any event with abs(cp) greater than cp 0 cannot possibly be accepted by our apertures. cos This is true for Bcm away from -1.0 since our apparatus acceptance is skewed it covers large positive x regions but does not cover large negative x regions . If N events succeeded, the proportion of the solid angle of the angular bin which we accept is then (N/M time cp 0 (in radians)/ 3.1416. Two separate programs (3.16) have been written to c h ec k f or consistency and the results are in agreement. program (3.17) Similarly, a ray trace also gives results agreeing with the Monte Carlo - 92 program results. In Figure 3.4 we show a typical acceptanc e percentage curve at one incident mome ntum. first bin (cos The acceptance is typically 40 ·~ for the ecm between -1.0 and -0.98) and drops off to a 10% shoulder at the fourth or fifth bin. Then, the percentages drop rapidly to zero in two or three bins. We have decided to discard all bins which have an acceptance p e rcentage of less than 5%since the percentages for such bins are unreliable due to the reasons discussed be low. Errors and uncertainties may be introduced into this procedure. Angular biases are easily introduced if our inputs (beam characteristics, position of apparatus, etc.) are wrong. This bias is especially critical for the first and the last few bins we accept. We have determined that the error needed to shift the percentages for the first and the last few bins by about 5 % can be any one o f the following; 1. Beam momentum 1% 2. Be am position 1/4" 3. Beam slope 2 mr 4. Ma gnet field strength 1% 5. Horizontal position of the apparatus 1/2 ". For example, the dashed line in Figure 3.4 is the percentage acceptance curve with the momentum of the beam shifted by 1%• The percentages of the intermediate bins (2nd to 4th u s ually) are not strongly affected by these errors. The positions of the apparatus were measur e d accurate l y and the beam characteristic s and the magnet field stre ngth were continuously monitored. Thus, we believe that the values quot e d above are upper - 93 Figure 3.4: Typical %acceptance curve as a function of cos ecm at one incident momentum based on results of the Monte Carlo prog ram. Dashed curve is the result of a one percent shift in mome ntum or magnet field streng th Normal Monte Carlo results 50 % Monte Carlo results for 1% shift in incident momentum or magnet field strength 10% ,... / / I I I I I I I I / /I about 0.3% I I - 0 . 90 -0. 95 cos ecm . -1. 0 0 - 94 limits to the variation or inaccuracy of these quantities. We con- elude that the uncertainties or error introduced into the solid angle acceptance is 5 % for the first bin and for the bins with percentage acceptance less than 10%. It should be noted that the sta- tistics of the Monte Carlo events for each angular bin is about 2% and we have smoothed the percentages acceptance at each momentum by making adjustments of f. 1-2%. Calculation of the des (Differential Cross Sections) and Errors We now proceed to calculate the final des (differential cross sections) S( x ) and error E(x) for the angular bin centered at cos ecm = x for each momentum. des For this bin, we have the number of backward elastic events N(x), the combined correction factor COR(x) which is in general near 30% (see Section (d)), and ACC(x), the percentage of solid angle accepted by our apparatus. Let D be the density of hydrogen in the target (which is 0.0708 gm/cm 3 in our case (3.18) ), F be the net flux of p's from which we obtained the backward elastic events, A 0 be the Avogardro's number, and L be the length of target which we used (32 cm), then the des is S(x) = lOO*N(x)* (1 + COR(x))/(ACC( x)~~D*F*Ao"'L) The factor of 100 comes from the fact that we have angular bin size of cos ecm of 0.02 which is 1/100 of the entire soli4 angle. 2 . 27 The result is in cm /sr (or mb/sr within a factor of 10 ) and - 95 can be converted into mb/GeV 2 by multiplying it with an incident momentum dependent factor of 3.1416/k 2 where k is the cente r-of-mass momentum. Errors In the final des, we quote with it an error which is a combination of statistical and systematic errors . The statistical errors vary between 7 and 20%. They are based 3 9 on the number of backward elastic e vents in each bin( .l ). All of our normali z ation corrections with the exceptions o f beam absorption and the uncorrelated wsc inefficiency carry with them uncertainties and errors which are of the same size as the corrections themselves. For most of the corrections, the size s are 1% or less . Thus, the errors associated with them can be ignored since the stati stical error is at least 7%. 1% The corrections which are larger than include the momentum cut loss (3%), velocity cut loss (2%), re- construction inefficiencies (3% and 2%), and , f or the first bin only, the vertex cut loss (7 %). The combined error is 5.1% and 8.7 % (for the first bin). The Monte Carlo of apparatus acceptance carries with it possible errors which are 5% for the first bin and bins with acceptance percentages less than 10%. Thus, the combined non-statistical errors are: 1. For the first bin, 10.0%. 2. For bins with acceptance percentages less than 10%, 7. 2%. 3. For the remaining bins, 5.1%. When this is combined with the statisti c al errors, the final - 96 - errors are between 10 to 20%. g. Summary and Assessment of the Analysis Procedure Summary We present in the following a brief summary of the analysis procedure. 1. Figure 3.5 shows a flow diagram of this procedure. For each triggere9 event, information recorded includes the digi~ tized wsc spark positions and the counter bits (containing the signals from the gas Cherenkov counter and the time-of-flight system). 2. The event trajectories are reconstructed from the digitized wsc spark positions. We demand that there is an incident p beam track, a forward recoil proton track and a deflected (by the magnet) recoil proton track. In case of spurious tracks, counter information and topological considerations are used to remove the spurious tracks. 3. Reconstructed events having sufficient tracks are tested for the topological criteria. Events indicating additional scattering are rejected. 4. Events with reconstruction vertex outside a certain limit ( ± 16 cm) are discarded. 5. Events with forward particles failing our velocity criterion are cut. 6. Remaining events are used in a background subtraction procedure (as a function of missing mass squared) to obtain the net number of backward elastic events. 7. Corrections to the normalization are calculated and applied. 8. Percentage of solid angle accepted by our apparatus is calculated - 97 Figure 3.5: Flow chart of the analysis procedure. approximate. All percentages are The percentages of corrections are obtained by studies on inefficiencies and losses. 100% All triggered events I ' 65% 35% fails reconstruction process due to insufficient tracks. Reconstruction inefficiency is 5%. Reconstructed events I 25% fails topological cuts in VD and MTD. Loss of backward elastic events is less than 1%. It 40% Events with good topology I 15% fails vertex cut. Loss of backward elastic events in acceptable target region is less than l°f, except for the first bin, where the loss is 7oj, . 25% Events with good vertex About 24% fails velocity cut or is removed by momentum subtraction procedure. Loss of backward elastic events is 2% for the velocity cut and for the subtraction procedure. I 3% 0.5-2% Good backward elastic events Solid angle aoceptance calculated by the Monte Carlo program Corrections to the normalization I I ._____ _ _----..1 1 1 Final differential cross sections Recorded incident p flux I - 98 by a Monte Carlo program. 9. Differential cross section and errors are then obtained using the number of backward elastic events, percentage acceptance and normalization corrections. Finally, Table 3.2 contains a list of quantities describing the nature and size of our data at each momentum. We give, for each momentum, the total p flux used, the number of backward elastic events, and the total solid angle accepted. Assessment 1. Is our analysis procedure necessary and sufficient ? Are there alternate methods which are more efficient in obtaining the desired results? To answer these questions, we should first define what we want to obtain . We are interested in obtaining the differentia l cross section for pp backward elastic scattering on hydrogen. Thus, it is necessary that we determine the scattering angle, whether a triggered event is a backward elastic event and whether the interaction is associated with the hydrogen in the target. In order to determine the scattering angle, we need to determine the incident p beam track and the r ecoil proton track . Thus, we need to record the positions of these tracks and to reconstruct these tracks . This we have done. Now, we must find a procedure to separate backward elastic events from the background events which trigger our apparatus. As mentioned in Chapter II, the likely annihilation of the final state Table 3.2: Properties of the analysis and data at each momentum. Momentum background is the level found by the background subtraction procedure. - 6 (in 10 ) Total cm Solid ang. (in msr.) Number of Elastic ev. Momentum. Background (in °/o) Total Correc. (in °/o) Corrected No. Elas. 6 ~v. per 10 p-msr 0.703 7.05 90.0 180 17.8 31.0 0.371 0.812 9.12 93.7 120 17.5 29.4 0.182 0.873 20.0 96 .8 194 20.6 28.8 0.129 0.935 9.51 98.7 56 32.2 27 . 4 0.076 0.987 26 .7 100.5 199 32.7 27.7 0.095 1. ll5 29.8 105.6 302 6.0 27.0 0.122 1.338 38.8 ll3.8 517 33.8 28.6 0 .151 1.447 41.8 117 .o 664 15.5 28.5 0.174 1.590 63.2 122.5 839 23.5 29.6 0.140 1.610 63.3 123.7 956 10.9 27.9 0.156 1. 716 78.2 126.3 1082 11.8 29.5 0.142 1. 797 60.3 130.0 636 20.3 26.7 0 .103 1.844 73. 7 131.2 809 12.0 29 .5 0.1 08 2.032 73.5 137.0 426 17.6 30.3 0.055 2 .155 81.5 145. 1 367 29.7 27.5 0.040 2.370 48.4 151.7 129 37.2 30.0 0.023 Incident Momentum (GeV/c) p flux l.O l.O - 100 antiproton is not useful since it cannot be easily distinguished from a pp annihilation in flight event. we have on the recoil proton. Thus, we must use the information We have used kinematics and the velo- city of the recoil proton to help us remove inelastic interaction events. It is necessary to use the velocity criterion to remove as many forward pions as possible since it is possible for the pion background to show an enhancement (or suppression) at momentum close to t h e recoil proton momentum (3.20) • When we determine that the for- ward particle is indeed a proton, it is still necessary to reject all inelastically produced forward protons. the kinematics of the event. This is done by considering The kinematics for inelastic events with a proton in the forward direction is sufficiently different from elastic kinematics that all such background can be cleanly removed. Thus, we can use a background subtraction method to remove the small amount (about velocity criterion. 15%) of pions which was not removed by the Thus, we have identified a backward elastic event. It should be mentioned that we reject all events which, according to the reconstructed tracks, show more than one scattering. Such events will disable our scattering angle or momentum . . (3.21) d eterm1nat1on • Finally, we should reject all backward elastic events not associated with the hydrogen in the target. We found that our re- constructed vertex is a good indication of the actual vertex. Thus we make a vertex cut wel.l inside the target and reject all events outside this cut. This procedure has beE:'n studied nnd i s found to bt:' - 101 efficient except for a slight inefficiency in the straight forward direction which we correct for. Thus, we have handled all the necessary methods in obtaining our results. Our procedure is suffi- cient in determining the nwnber of backward eJastic events since there is no way for a significant number of non-elastic events to simulate both the recoil proton momentum and velocity. Alternate procedures include those which involve different equipment (which we investigated in the last section of Chapter II). / However, any method to obtain the differential cross section of pp backward scattering must do the things mentioned above. main ideas of the analysis cannot be changed. Thus, the We have made all possible corrections such as correcting for the ionization loss of the momentum in order to improve the quality of our analysis. One major area in which the efficiency of our procedure can be improved is in the computing. Our two analysis programs, the recon- struction and the selection programs, each take up about 30K memory storage and requires 50 msec approximately to process each event. Since the CDC-6600 charges according to program size and the total amount of time the program is using the computer, the peripheral processing time used to read the computer tape or write the library tape turns out to be quite expensive. The additional cost is com- parable to the central processing of the events. We should have used . (3.22) a more efficient tape handling procedure, such as double buffer i ng . Another way to reduce cost is to use a smaller computer to do . . t h e pre 1 iminary ana 1 ysis ( reconstruction )(3 .23) . tightened the trigger. We could also have This would reduce the number of trigge red - 102 events to be processed. However, as we mentioned in the section on the triggering system, significant reduction in trigger rate is impossible. - 103 - - trnSULTS- - PP 11/\Cl<WJ\H.1) 1n,/\S'J.' I c IH .l''FI•: 1rnNT I /\I, C: IWSS s l•:CT IONS CllJ\l'Tlm IV: a. Differential Cross Sections for Each Angular Bin We now give the des (differential cross section ) for backward elastic pp scattering which was obtained in our experiment. We pr e sent in this s e ction the des for each angular bin at each incident The angular bin size we used is 0.02 in cos B which cm 2 corresponds to 0.004 to 0.03 GeV in du. In the next section (b), momentum. 0 we extrapolate the 180 des & slope at each momentum. In Section (c), we compare our data with other existing data in or near the regions \vliit'li W\' cover . SPction (d) contains a discussion of the major features observed in our data and the extrapolated data at 180°. In this Chapter, we use "µb" for microbarns, "p" for incident p beam momentum and "E" for center-of-mass energy which is equaled to (s) 1/2. 2 Table 4.1 and Table 4.2 give the des in µb/sr and µb/GeV , respectively . We have listed the central values of cos -t for each bin. B , -u and cm These values are close to, but not e x actly the · median o r we ighted average of cos B , -u and -t f or the bins. cm dit:fl' l"Pttce iA sm:Jll. (typi.c.ally less than 0 . 0005 Figure /~.I in cos (-) c n1 ). plots the data in µb/sr. at t:ach mome ntum vs . cos () Figure 4. 2 plots the data in µb/GeV 2 at each momentum vs. u. are both log vs. linear plots. b. The The 180° des and Slope Extrapolated from our Data The behavior of the des and its slope at 180° is of great They cm - 104 Table 4.1: Des obtained from our experiment in µb/sr. P is incident momentum, E is sqrt(s), TO is T at 180° and uo is T0/200. given underneath the des. -T is Errors are ? P i n (GeV/c), E in GeV and TO, UO in (GeV)-. TO-UO T0-3UO T0-5UO T0-7UO T0-9UO T0-11UO'ID-13UO uo 3UO 5UO 7UO 9UO Cos cm is -0.99 -0. 97 -0.95 -0.93 -0 .9 1 -0.89 -0. 87 p = 0.703 uo = 0.00220 E = 1.990 TO = 0.43938 225.3 43.1 329.3 57.9 361.1 68.4 279.3 70.8 284.5 89.3 o.o o.o p = 0.812 uo = 0.00284 E = 2.022 TO = 0.56778 87.1 25.4 112.8 31.4 149.1 39.0 179.l 46 .1 211.8 52.7 182.4 52.1 p = 0.873 uo = 0.00322 E = 2.041 TO = 0.64424 73.3 16.4 89.2 17.5 86 .o 22.3 145.8 30 .1 123.0 29.8 85.4 26 . 8 p = 0.935 uo = 0 .00362 E = 2 . 061 TO = 0.72495 44.8 16. 9 49.3 19.9 78.2 24.7 86.4 31.1 40.7 32.3 o.o o.o p = 0.987 uo = 0.00397 E = 2.077 TO= 0.79476 83.9 14.7 68.1 14.7 55.5 16.3 55.4 16 .4 105.3 25.0 47.2 21.4 p = 1.115 uo = 0.00487 E = 2.120 TO = 0.97386 102.9 15.5 101. 9 14.2 90.7 14.6 101.6 16. 9 46.1 12.3 74.0 17.8 p = 1.338 uo = 0.00653 E = 2.197 TO= 1.30589 p = 1.447 uo = 0.00738 E = 2.235 TO = 1.47548 146.6 19.9 137 .o 17.4 97.3 16.4 109.1 18.5 10L7 19 . 9 73 .8 23.3 179.2 21.1 134.8 15.4 113 . 1 15.2 97.5 15 .1 73.2 15.1 68.4 19.9 p = 1.590 uo = 0.00852 E = 2.286 TO = 1. 70370 136 .9 16 .o 140.9 13. 7 93.4 13.1 80.1 14.7 76.1 16.4 o.o o.o p = 1.610 uo = 0.00868 E = 2.293 TO= 1.73607 153.5 17.2 113 .5 11.3 108 .3 12 . 2 81.2 11. 3 86.7 13 .2 84.6 14.6 p = 1.716 uo = 0.00955 E = 2.330 TO = 1.90929 137 .0 15. 5 112.4 10.5 106.5 10.5 79.0 10.2 75.9 11.3 90.7 12.5 o.o p = 1.797 uo = 0.01022 E = 2.359 TO = 2.04335 p = 1.844 uo = 0.01061 E = 2.375 TO= 2.12174 p = 2.032 uo = 0.01220 E = 2.441 YO = 2.43919 p = 2.155 uo = 0.01325 E = 2.484 TO = 2 . 64980 p = 2.370 uo = 0 .01511 E = 2.558 TO = 3.02240 91.4 11.4 90.8 10 .1 101.1 11.9 92.1 9.4 67.5 10.1 63.2 8.5 80.6 12.0 92.3 10 .4 58.8 11.4 67.6 10.4 70.0 12.5 48.6 9.7 33.8 14.7 47.3 11. 2 58.4 7.6 38.0 6.0 34 .1 5.9 41.0 6.8 31.6 7.6 28.3 6.8 19.7 6.7 . 49,3 6.4 28.8 5.4 26.4 5.2 12.6 5.2 22 .5 6.1 16 . 2 6.6 13.4 7.5 30 .3 5.7 17.4 5.5 14.4 4.9 7.9 9.2 4.6 6.5 12.2 7.3 18:2 7.4 -u is llUO 13UO 0.0 o.o o.o o.o 0.0 o.o o.o o.o o.o o.o o.o 0.0 o.o o.o o.o 0.0 0.0 o.o o.o 0.0 0,0 - 105 Table 4.2: Des obtained from our experiment in µb/GeVsq. P is incident momentum, E is sqrt (s), TO is T at 180° and UO is T0/200. Errors are . 2 given underneath the des. P in (GeV/c), E in GeV, and TO,UO in (GeV) . -T is -U is cos cm is p = 0.703 TO-UO T0-3UO T0-5UO T0-7UO T0-9UO T0-11UO'JD-i3UO uo 3UO 5UO 7UO 9UO llUO 13UO -0.99 -0.97 -0.95 -o.93 -0.91 ~o.89 -0.87 uo = 0.00220 6443.5 9417.7 10326.7 7987.0 8317.8 E = 1.990 TO= 0.43938 1233.2 1657.0 1955 . 1 2023.9 2555.5 o.o 0.0 o.o 0.0 p = 0.812 uo = 0.00284 1928.8 2496.2 E = 2 . 022 TO= 0.56778 561.8 694.6 3299.9 3962.8 4688.0 4037.0 862.8 1021.2 1166.1 1154.0 o.o p = 0.873 uo 0.00322 1429.9 1739.2 E = 2.041 TO= 0.64424 319.7 340.8 1677.8 2843.6 2399.7 1665.9 434.5 586.8 581.3 533.9 o.o p = 0.935 uo = 0.00362 E = 2.061 TO= 0.72495 p = 0.987 777.2 293.7 854.3 344.5 uo = 0.00397 1327.0 1077.0 E = 2.077 TO= 0.79476 233.0 232.6 0.0 705.7 560.2 o.o 0.0 o.o 875.9 1665.2 259.2 394.7 746.2 338.0 0.0 0.0 o.o o.o o.o 1355.3 1498.2 428.2 538.4 877.2 257.2 0.0 0.0 = 1.115 uo = 0.00487 1328.4 1314.6 E = 2.120 TO= 0.97386 200.2 182.7 1169.9 1310.4 188.0 217.5 594.3 159.0 954.7 229.3 p = 1.338 uo = 0.00653 1411.1 1318.1 E = 2.197 TO= 1.30589 191.6 167.2 935.8 1049.7 157.9 177.9 978.8 191.5 710.5 224.5 p = 1.447 uo = 0.00738 1526.6 1148.0 E = 2.235 TO = 1.47548 179.5 130.9 963.1 129.5 830.2 129.0 623.8 128.5 582.6 169.4 o.o o.o = 1.590 uo = 0.00852 1010.0 1039.5 E = 2.286 TO= 1.70370 117.8 101.1 689.2 96.6 591.2 108.4 561.0 120.6 o.o o.o o.o o.o uo = 0.00868 1110.8 E = 2.293 TO= 1.73607 124.5 821.8 82.0 784.0 88 . 4 587.7 81.6 627.8 95.3 612.3 106.0 o.o p p p = 1.610 p = 1.716 uo = 0.00955 0.0 0.0 E = 2.330 TO= 1.90929 901.8 101.7 740.0 69.0 701.1 69.3 519.8 66.9 499.5 74.3 596.7 82.4 p = 1.797 uo = 0.01022 E = 2.359 TO= 2.04334 562.3 70.1 558.2 62.2 415.0 62.0 496.0 73.6 361.9 69.9 430.2 208.1 76.8 90.4 p = 1.844 uo = 0.01061 E 2.375 TO= 2.12174 599.0 70.5 545.2 55.7 374.2 50.2 546.7 61.8 400.5 61.9 287.9 280.1 57.6 66.4 2.032 uo = 0.01220 2.441 TO= 2.43919 300.9 39.2 196.0 31.0 175.8 30.6 211.1 35.0 163.0 39.2 145.7 101.7 34.9 34.7 p 2.155 uo = 0.01325 E = 2.484 TO= 2.64980 234.0 30.2 136.8 25.5 125.1 24.7 60.0 24 . 5 106.6 29.1 76.7 31.5 63.3 35.7 p = 2.370 uo = 0.01511 E = 2.558 TO = 3.02240 126.0 23.6 72.2 22.8 59.7 20.2 32.9 19.0 28.2 27.1 50.9 30.2 75.6 30.8 p E 0.0 o.o - 106 Figure 4.1 : Our e x perimental data in µb/sr . (Solid line in the linear fit). £ our data 500 . 200 H 100 100 Cooper (Ref. 4.3) ! Lys (Ref. 4.4) 1.590 0.987 f _! 100 50 0.812 200 ~ ~ ..a 100 ::l. 50 *~ "'O ............ 100 b "'O 50 100 50 I 1 -1.0-0.95-0.90 -1.0 -0.95-0.90 -1.0-0.95-0.90 -1.0 -0.95-0.90 Cos Bc.m. - 107 Figure 4.2 Our experime ntal data i.n µb/sr 0.703 1.844 ~2 10,000 2 ~ 0.987 5000 f 1000 500 Hf 200 1000 22 1.590 ~~f 500 2.032 ~ 2000 N > Q) 1.115 1000 ~ .0 ::i.. 200 2 1.610 IOOO 1000 500 500 ~ b 1000 -0 ~2 £ 200 ~~~I 1000 2 500 500 H 2~££~ 1.338 IOOO ~~~ 100 · C ::s 2000 ~H 1.716 22 2.155 ~ y 100 £ ~ ~50 I II q 0 .987 1.447 1000 rtt 1000 500 0 .0 -0.05 -0.1 2 ~~ . tI r 100 1000 2 .370 . Ii 1.797 500 0.0 -0.05 - 0.1 22 ~ ~ ~ ~ 0 .0 -0.05 -0.1 2 u in Gev I 0 .0 -0.1 -0.2 - 108 interest. At each momentum, we extrapolate these quantities from our data. At each momentum, we have 5 to 7 angular data points. decide to fit using only two parameters. Thus, we We fit our data to both a linear function (a + bx where x is 1 + cos ecm) and an exponential f unction (a e bx) using stan d ar d 1east-square f itting procedure (4.1) . Usually, all our data points at a momentum are used. However, in the case that the fit is poor (confidence level less than 50%), we investigate the fit neglecting one or two largest angle bins. If the fit is improved significantly, we use the results of the better fit. The results of the linear and exponential fits are qualitatively similar. Compared with the linear fit, the exponential fit gives larger (smaller) slopes when there is backward peaking (dipping) which is expected due to the nature of the exponential function. polated des at 180° is about the same for both fits. The extra- We have inves- tigated the results of fitting with fewer data po!.nts and also with a qua d ratic f unction f it. Te h extrapo 1 ate d 180 ° d cs an d s 1 ope d o not vary very much, especially where the fit is good. Table 4.3 and 4.4 give the fitted values of the 180° des and slope for the linear and exponential fit, respectively. and 4.4 plot the 180 0 Figures 4.3 slope and des of the linear fit as well as their 2 ratio as a function of momentum in µb/sr and µb/GeV , respectively. Figure 4.5 plots the 180 2 µb/GeV. 0 slope and des for the exponential fit in The linear fit has been drawn as solid lines in Figure 4.1. Table 4.3 : Extrapolated 180° des and Slope for Linear Fit (A + B(l + cos Bcm )) B/A Chi sq. A B 2 (µb/GeV ) 4 (µb/Ge V ) (GeV -2 ) Chi per. 18.66 10 . 01 5592 .3 1600 . 1 475026. 6 254929.8 84 . 94 45.59 0.26 0 . 26 1242 . 2 462.4 15 .88 5.91 1731.3 541.5 96845.5 36050.8 55 . 94 20 . 82 0.73 0.18 65.0 16 . 4 738.8 363.2 11.36 5.58 1268.7 319.7 44734.2 21993.8 35 .26 17 .34 1.54 0.51 o.o 2.061 0.7250 o.o 0.0 45.5 17.3 282 . 1 384.8 6.21 8 . 47 787.9 300.3 13488.3 18400.0 17.12 23.35 2 .00 0 .67 0.987 2.077 0.7948 0.0 0.0 85 . 7 15 . 3 -499.8 348.0 -5.83 4.06 1355.5 241.8 -19885.4 13845.1 -14.67 10.21 0 .26 0.13 1.115 2.120 0.9739 o.o 0.0 102.8 15.8 -96.6 356.9 -0.94 3.47 1326 . 1 203.5 -2560.5 9457.3 -1.93 7.13 0 .38 0. 19 Pinc B E -T A (GeV/c) (GeV) (GeVsq) (µb/sr) 0 . 703 0.0 1.990 0.4394 0.0 o.o 195 . 5 55.9 3648.8 1958.2 0.812 o.o 2.022 0.5678 o.o 78.2 24 . 5 0.873 0.0 2.041 0.6442 0.0 0.0 0.935 o.o o.o o.o B/A o.o o.o 2.197 1. 3059 0.0 148.7 15.8 -642 .o 245.7 - 4.32 1.65 1430.4 152 . 0 -9461. 2 3621. 7 -6 .61 2.53 2 .04 0 .5 1 1.447 0.0 2.235 o.o 1.4755 0.0 172 . 0 15.0 -1054.4 220 . 5 -6 .13 1.28 1465 . 2 127 . 8 -12173.0 2545.7 -8.31 1. 74 1.47 0. 37 1.590 2 . 286 1.7037 -952 . 0 248.3 -6 .23 1.6 2 1127 .4 102.0 -8243.2 2150.1 -7.31 1. 91 2.91 0.97 1.338 o.o o.o o.o 152.8 13.8 1.610 2.293 o.o 1. 7361 o.o 153.6 14 . 9 -1028.1 301.9 -6 .69 1. 97 1111.8 107.8 -8573 . 2 2517. 6 -7 . 71 2 .26 1.26 0 .63 2 . 330 1. 9093 0.0 139 . 3 11. 7 -75 9. 1 195.7 - 5 .45 1.40 916 . 9 76 . 9 - 5233. 6 1348.9 -.5 . 71 1.47 1.20 0.40 o.o 1. 716 o.o o.o I-' 0 '° 1.797 2.359 2.0433 0.0 0.0 96 .9 8.5 -376.7 115.6 -3.89 1.19 595.9 52.3 -2267.6 696 .0 - 3.81 1.17 4.50 0.90 1.844 2.375 2.1217 0.0 0.0 101.3 7.9 -421. 7 100 .9 -4.16 1.00 599.8 47.0 -2354.6 563.3 -3 .93 0.94 8.75 1. 75 2.032 2.441 2.4392 0.0 0.0 51.0 5.1 -227.6 64.7 -4.46 1.27 262. 9 26.4 961.5 273.3 -3.66 1.04 4.47 0.89 2.484 2.6498 40.1 4.6 -246.5 61.6 - 6 .14 1.53 190.3 21.6 -882.2 220.5 -4.64 1.16 9 .16 1.83 3.0224 29.0 5.1 -274.1 91.3 -9.46 3 .15 120.5 21.4 -754 .1 251.2 -6. 26 2.09 1.66 0.55 o.o o.o o.o 2.155 o.o 2.370 o.o o.o 2.558 o.o o.o o.o I ,.... ,.... 0 Extrapolated 180° des and Slope for Exponential Fit -- A*exp(B(l + cos ecm )) or Tabl e 4.4: A*exp( BU); B* is t he Slope using only 3 Point s B E -T A (GeV/c ) (GeV) (Gevsq) (µb/sr) 0. 703 0.0 1.990 0.4394 0.0 0.0 211.3 48.4 11.8 6.7 0 .812 2. 022 0 . 5678 0.0 0.0 90.2 21. 1 8.4 3.4 2 . 041 Pinc o.o 0.0 Chi sq. GeV- 2 B* -2 GeV 6044.0 1385 . 7 - 53.5 30 . 6 - 53 . 5 30.6 0 .4 1 0 .4 1 1996 . 2 466.3 -29. 5 11 . 8 -47 .4 34 . 4 1. 29 0.32 1339.3 266 .2 -24.7 11. l - 13.5 26 . 4 1.64 0.55 A B 2 ( µb/GeV ) Chi per . o.o o.o 0 . 6442 68. 7 13 .6 8.0 3.6 o.o o.o o.o o.o 0 . 935 2 . 061 0 .7250 o.o o.o 44. 1 16 . 4 8 .0 7.4 0.0 0.0 765 .1 284.6 - 22.2 20.4 -39.6 33.8 2.90 0 . 97 1401. 5 276. 7 19.5 13.3 26.1 20.6 0 . 18 0 . 09 1326.6 204.0 1. 8 . 7. 2 6.4 11. 3 0 . 38 0 . 19 1490.1 181.2 8.8 3.4 14 . 8 8 .2 1.93 0 .48 1623.6 175.0 13.7 2.8 15 . 8 6.0 0.47 0.12 o.o 0. 873 o.o o.o o.o o.o o.o 1.4755 190 . 6 20.6 - 10 . 1 2.1 o.o o.o o.o o.o o.o o.o o.o o.o 1 .590 2.286 1.7037 o.o 163 . 8 18.1 -9.1 2.5 0.0 0.0 1208.5 133.4 10.7 2.9 10 . 1 5.3 2 . 92 0. 97 1. 736 1 162 .6 18.8 -9.6 2.7 0.0 1177 . 1 135.9 11.0 3.2 10.0 4.6 1. 09 0. 54 146 .3 14. 7 -7.6 2.0 962.6 . 96 .8 8.0 2. 1 6.4 3.9 1.03 0 . 34 o. o o.o 2 . 077 0 : 7948 0.0 88.6 17. 5 - 7.8 5.3 1. ll5 o.o 2. 120 0.0 o.o 0.9739 102 . 8 15.8 -0.9 3.5 1 . 338 2 . 197 1. 3059 o.o 154.9 18. 8 -5. 7 2.2 0.987 o.o 1.447 o.o 2.235 o.o o.o 1.610 2.293 o.o o.o o.o . 1. 716 2.3 30 1. 9093 o.o o.o o.o o.o o.o 0.0 t--' t--' t--' Tabl e 4.4 (continued) 1.797 0.0 1.844 2.359 o.o 2.375 2.0433 97.7 10.1 -4.3 1. 7 o.o 0.0 o.o o.o o.o 600.7 62.3 4.2 1. 7 6.9 4.7 5.18 1.04 636 .5 60.1 5.2 1.4 10 . 7 4.2 9.40 1.88 289.7 34.2 5.6 1.6 11.6 4.4 4.39 0.88 o.o o.o 2.1217 107.5 10.2 -5.5 1.5 2.032 2.441 2.4392 0.0 0.0 56.2 6.6 -6.8 1.9 o.o 2 .155 2.484 2.6498 0.0 o.o 49.6 6 .4 -11.4 2.6 0.0 235.3 30.2 8.6 1.9 12.8 4. 3 6 .48 1.30 2.3 70 0.0 2.558 0.0 35.1 7.6 -18.5 6.2 o.o o.o 145.9 31.5 12.3 4.1 13.2 6.2 0.59 0.20 o.o o.o 3.0224 0.0 0.0 o.o o.o ..... ..... N Mass in GeV 2.0 i ll 2.1 2.2 2.3 2.4 2.5 2. 0 - 1~l -10 f .from 180_ des extrapolated our data 0 r tl ro ....... .0 '-' . I loo II [ Ir f- ro Ul ~ •.-l *~ i:r:i Cl.. "Cl ....... .b "Cl Figure_J±_._ 3: "T" 6 ? :1 11 ! .J.. i .J.. I If I I I ~·~ 0 I i Ill •.-l i:r:i '"C ...' +10 I 1.5 Plab in GeV/c li '""' ro bO ~ .co ..... i,.. I' 1.0 ,, 0 '"C 0 1 0.5 I I I~ I 1-1 w 2.5 I I ......... .0 ::i 2. 4 Cl.. fT ~ ~ u ro co Q) 2.0 I i I I I r l f ~ ~ fn bO ]j I SO I 2.3 Q) I I ~ 1-1 ,...., I I iy 2.2 (b) cm - I 200 2.1 ! Data of Cline (Ref. 4.2) for -0.95> cos e > -1. (a) I to-' to-' Mass in GeV I I I' I ' '.I' 20 I l ' I1 I I ' l I I 1.0 1.5 2. 0 Plab in GeV/c Extrapolated 180° des and sfope (b/a) using linear fit (d~s =a+ bx where xis 1 +cos 9 ) . cm - 114 Figure 4.4: Linearly extrapolated 180° des (in µb/GeV 2 ) and slope -2 (in GeV ) (where des= A+ Bu). ·- -- -- I -----,-- T I I l-0-I II) N ... t-<H H>-1 -. 0 N H>-1 H>l . H).-.l ~ -. - ~ .0 .._, N l--0--j N N . . - ~ ....,- . I I - 0 N • i- 8up1ead p.:i:el'\)pea 8u1dd1p 0 -- '<: "' p.:i:e~oea I I r-1 I N I 0 0 ...... + 1 -. - . I I 0 0 I C""l I ~ I 0 u-i: (V/H) ado1s 0 081 I I I I .0 t'O ...... p.., .... II) N 0 ~ N N,_ ·- C""l - ... N co .._, ~ N .... ...... N 0 N .... - ......0 . ~ 0 0 0 II) I 0 0 0 N I 0 0 0 .-I I 0 0 II) I 0 0 N I - 115 Figure 4.5: Exponential extrapolated 180° des (in µb/GeV 2 ) and slope -2 Bu) -9 (in GeV ) (where des =A e • In (a), the line is a s dependence line. In b the dashed line is a ln ~ I N 1-jo--l J( I x l--0-I . 0 I x \ ~ N . ......, . ~~ ('t') N ,-... ,.0 line. I N N ~~3.5 . I.I") l----0-y-l \ .-I N 0 N 0 '""------.Li . ----------{>---~ J--------------'M :> Q) c.!> 0 0,...., .-I i::: 0 - 0 () ...::t N I :Q) > •.-1 (/} (/} ra ;:.:: c.!> l I I I I I ,.0 Cl! . .-I I.I") N i::: •.-1 ll< -~ ...::t N • >-- N CV) N "'.._, "ra"" ·- N N,_ .-I N~ -0. .-I 0 ·0 0 0 I.I") I I 0 0 0 0 0 0,...., N ZAaQ/qrt U"J np/.Op I I 0 0 I.I") 0 0 N I - 116 c. Comparison of our Data with Other Existing Data To check the reliability of our data, we compare our data with other existing data of pp elastic backward scattering. have been plotted along with our data in Figure Cline et al. (4. 2) These data 4.1 and 4.3. studied the elastic cross sections in the back- ward hemisphere from 0.3 to 0.7 GeV/c incident p momentum. poi.nts i.n th<:~ angular bin closest to 180° (cos () --LOO) liave been included in Figure consistent with ours. 4.3. Their data between -0.95 and cm Their data appear to be The sharp drop of the 180° des as momentum increases appears evident in both sets of data. 4 3 Cooper et al. < · ) measured the backward hemisphere pp elastic scattering near 1.3 GeV/c. cos B cm Their data point nearest 180° (covering between -.90 and -1.00 has been included in Figure 4.1. The normalization is in agreement. Lys et al. uear 1.8 GeV/c. (4.4) measured the bac kw ard elastic pp scattering Their data, included in Figure 4.1 along with our 1.797 GeV/c data, are in agreement with our data. Additional bubble chamber data on pp backward elastic : . (4.5) , scattering is expected to be forthcoming soon. It should be noted that all of the results mentioned above are bubble chamb e r results and thus lack statistics. slope of the des near 180 0 Also, the angular cannot be determined with any confidence from these data to check the slope we obtained. Purely on the basis of these comparisons, it would appear that the reliability of our data is of the order of 10%, whi~h is the approx imate si z e of the errors we quote. - 117 d. Features of our Data As a function of momentum, we see several structures in the extrapolated 180 1. 0 des. A dip centered near 0.95 GeV/c (2.07 GeV in E) which is about 300 MeV/c (or 100 MeV) wide. The 180° des drops sharply from about 4 2 300 µb/sr near 0.6 GeV/c (based on the data of Cline( • )) to about 50 µb/sr near 0.95 GeV/c. It rises slowly to about 200 µb/sr near 1.45 GeV/c. 2. A broad hump centered at 1.45 GeV/c (2.24 GeV in E). is about 800 MeV/c (or 250 MeV). This hump These two structures could be manifestations of the same mechanism aince they are close to each other. The slope of the des at 180° is correlated with the ~bove structures. At momentum below the position of the dip, there are evidences of backward dipping. At momentum above the position of the dip, there are backward peakings up till our highest momentum. The backward peaking above 0.95 GeV/c is confirmed by the data of Cooper (4.3) and Lys (4 . 4) • There does not appear to be any significant smal l er structures in either the 180° des or its slope. At each incident momentum, we also look for correlation between the number of backward elastic events and the momentum by finding the number of events whose incident p passes through particular mass slit counters ( 4. 6) • No significant dependence is observed. Our des in the angular range cos ecm between -0.88 and -1.0 do not reveal any strong structures aside from backward peaking or dipping. - 118 There are indications at several low momentum points of the backward dipping turning over at larger angles (see Figure 4.1). evidenc.e is, however, not conclusive. This We have also looked for any dips or btttnps in our angular des which are statistically significant or which occur at particular cos 8 more than one mome ntum. cm or at particular values of u for To do this, we investigate our data with smaller angular binning (cos ecm bins of 0.01). No such structures aside from backward peaking or dipping are observed. - 119 - CHAPTER V: a. RESONANCES: AN INTERPRETATION OF THE DATA Introduction and the Probable Absence of Strong Regge u Channel Effects Chapter I has mentioned the possibility of resonance contri- bution s i.n the direct 1:1 channel t:o backwar:d elastic scattering of pp. In th is chapter, we attempt to study whether the behavior of our data is understandable as being the result of resonance which couples to PP· In Section (b-i) we discuss the possible coupling of pp to any boson resonances. Section (b-ii) describes the characteristics of elastic scattering of pp in the presence of a resonance in the direct s channel. We list in Section (c-i) the resonance candidates which have been sugge sted by other data. In Section (c-ii), we describe several theoretical models which predict the number and position of various resonances which couple to pp. We attempt to correlate our data to the resonance situation in Sections (d-i) (covering narrow -- less than 50 MeV-- resonances) and (d-ii) (covering broad .r esonances). We conclude this chapter with Section (e), which summarizes the resonance situation. Before we proceed in a resonance interpretation of our data, we would like to make a few comments on the possibility of our data being dominated by a single Regge trajectory {n the exchange u channel. In that case, d cr/du, as mentioned in Chapter I, should (a) have a exp(2*ln(s)*b*u) dependence at each momentum, and (b) have 180 2 be s a(0)- 2 as a function of momentum. 0 Figure 4.5 shows the ex- d cr/du - 120 . ponentially extrapolated 180 0 do/du and slope. evidence for Regge dominance is seen. appears to follow s -9 fairly closely. Below 1.4 GeV/c, no Above 1.4 GeV/c, the 180 0 do/du This could indicate that the backward scattering is dominated by a trajectory with o:p) approximately -3.5 (S.l). However, the slope of the fit, shown in Figure 4.5, does not seem to follow the ln(s) dependence which is indicative of single Re gge u channel dominance. The normal exponential fit us es almost all our angular data 2 covering a u region of up to 0.2 GeV • It is possible that u channel 2 effects are dominant only for u less than 0.2 GeV • Thus,we investi- g ate an alternative exponential fit using only 3 smallest angle data points at each momentum. 2 Gev . This covers a region of u less than 0.07 The extrapolated 180° do/du is within the error bars of the extr apolated values for the normal exponential fit. However, the ext rapolated slopes above 1.7 GeV/c become much larger. alt.1~ r natlv e ; ll ' t) uow sl.oiws a s x'i:; in Figure 4.5. 1 · onfoll. ~1 l 1.ml. We show the The slopes above l.4 GeV/c with on J.n(1-1) monu..•ntum d~pendcnc e (~1how11 in Fi g uru l~. S ). ' The slopes are typically 10 (GeV) -2 :ll:I Une {l poss ibly in- .<licating that the b of the dominating trajectory is about 3 (GeV)-Z(S.l) (the trajectory is o:(O) +bu). Thus, we c onclude that our data a.re consistent with a strong u channel contribution from a single Regge trajectory only in the region of u less than 0.07 Gev 2 above incident momentum of 1.4 GeV/ c. Even in that region, our data are inconclusive. Other interpretations , s uch as those discussed in this chapter, can explain the features in - 121 our data suggesting Regge behavior. Since there are good theoretical reasons to believe Regge behavior to be weak (B =Q = 2 particles are not expected), we can probably ascribe all the features observed in our data to resonance effects. b. Resonances and the pp System: (b-i) Theoretical Considerations The Coupling of Resonances to the Pp System Giyen the existence of a boson resonance X with definite quantum numbers (mass M, spin J, parity P, charge conjugation c, isospin I, etc.), several statements can be made about its coupling to the pp system. In particular, the coupling is constrained by 1) threshold constraints, 2) isospin constraints, 3) spin-parity-charge conjugation constraints, and possible 4) angular momentum barrier constraints: 1) Threshold constraints. X can couple to the pp physical system only if its mass is greater than 2 M • p However, if the mass is slightly below threshold, the tail of the resonance could influence the pp behavior above threshold. 2) Isospin constraints. Since both p and p have isospin 1/2, the pp system can couple to X only if X has isospin 0 or 1. 3) Spin-Parity-Charge conjugation constraints. For a boson resonance X with spin J, the par i ty and charge conjugation of X is restricted if X is to couple to pp . Following the usual convention , we shall define the parity P (or charge conjugation C) to be normal if P(C) is (-l)J and abnormal if P(C) is (-l)J+l. Both p and p are spin 1/2 fermions. For a f ermion-antif e rmion - 122 system, P = ( - l .)L+l and C = (-l)L+S where L is the relative angular .' 2 momentum and S is the total spin(S. ). Thus, the pp system can only couple to the following three of the four possible combinations of P and C: 1. Singlet-(S)- S = 0 implying J = L, P abnormal and C normal. 2. Normal Triplet -(NT)- S = 1 and J = L ± 1 implying both P and C are normal. 3. Abnormal Triplet -(AT)- S = 1 and J = L implying both P and C are abnormal. Thus, if X has normal P and abnormal c, i t cannot couple to pp~ It should be noted that the simple quark model (which we will cover in Section (c-ii)) prohibits the existence of bosons with such a combination of P and C assuming all bosons to be made out of quark- . antiquark pairs. 4) This is true since quarks are fermions • Angular momentum barrier constraints. The coupling of X to the pp . system may be suppressed totally or strongly by the angular momen~ (5. 3) . tum b arrier • One would expect that the pp interaction would be characterized ! by a distance corresportding to the proton. radius. This is what one expects if optical type interaction is dominant. The inter- action distance for pp can be obtained by considering the forward diffraction peak. Fermi. One finds an interaction distance of about 1.0 Then, the max imum angular momentum state that the pp sys tem could couple to strongly would be kr + 1 (k is the cm momentum, r is the interaction distance). However, at all momenta this number is below the J of the leading trajectory (see - 123 Figure 5.la, a plot of the leading boson trajectory and the curve kr + 1 against s). Thus, if the recurre~ces on the leading trajectories do exist, their coupling to pp could be reduced by the angular momentum barrier. This possibility is not in con- flict with the observed strong coupling of pi-N system with the nucleon resonances (see Figure 5.lb). As far as the strength of the coupling of boson resonances to pp is concerned, we would expect Ke (elasticity) to be of the order of 1 0.1 or less. A massive boson resonance can decay into many channels and thus is not expected to couple to pp very strongly. Another item which affects the search of boson resonances in the pp system is the possibility that there are many resonances at nearly the same energy. thus be obscured. The effects of any single resonance may For e xample, in the theory of the daughter tra- jectories, the number of resonances at the same region of energy would be of the order of 10 (see Section (c-ii)). (b-ii) Features of Resonance Contribution to Elastic pp Scattering We now investigate the behavior of the elastic amplitude, elastic total cross section and the total cross section caused by the presence in the direct s channel of a resonance with spin J, parity P, charge conjugation c, elasticity Kel and mass M (corresponding to cm momentum k for the pp system)( 5 • 4 ). Except for the last few para- graphs of this section, we shall only concern ourselves with the pure resonance contribution and ignore any interference effects. Recall that the pp system, for a particular J, occurs in three p lab in GeV/c Plab in GeV/c 0 1 2 3 2 1 0 4 3 (b) (a) * PP~ B nP ~ N 2 J = M + 1/2 J ~ = M2 ...... 6 "' .p. I / / i+ ...., I - ---- = / · 2 t- J ;cfo D l 2 r -lOfermi - • 4 Figure 5. f : r = 1.0 fermi 6 8 2 2 s or M2 in GeV Angular momentum barrier for the (a) 4 6 pp and (b) 1tN systems 8 - 125 combinations of P and C -- the Singlet, Normal Triplet and Abnormal Triplet (see the previous section). Since elastic scattering of pp is a strong interaction, P and C are conserved and no transition between these states is possible. Thus, each state must be treated . separately. We shall first obtain the values of the total elastic cross section Sel and the total cross section Stot for a definite isospinparity-charge conjugation state. In this case, we obtain, at in- cident momentum corresponding to the peak of the resonance, 2 SI,s (411/k ) l (J +l ) (K )2 2 2 el = e. l (5. la) SI,s = (41T./k2) l (J + .!. ) tot 2 2 (5. lb) The pp state is equally in I Kel = 0 and I = 1 states. Hence, iso- spin gives an additional factor of 1/2 in stot and 1/4 in s from each vertex). el rfli2 Also, the pp initial state is 1/4 Singlet, 1/4 AT (abnormal triplet) and 1/2 NT (normal tripler)(S.S) for unpolarized incident beam and target. Thus, Sel(pp; S--singlet) = se 1 (pp;AT) el I,s (S.2a) = (l/8)Sell,s (5.2b) (- S) = S (Pp;AT) = 1/2 S (pp;NT) = (l/8)S I,s tot pp; tot i tot tot (S.2c) Sel(pp;NT) S (1/16)8 where Stot(pp;S) is the Stot for a singlet resonance. Having determined the size of the total elastic cross section , due to pure resonance contribution, we now study the angular shape of the des or the elastic amplitude. The normalization of the des can - 126 be obtained by integrating the des and comparing it to the total elastic cross section. For each spin state s, m , and m ' s s (s is the combined spin, m s the initial z component and m ' the final z component of the spin), i s 5 6 there is an elasti~ amplitude< • ) I iL-L' nl/2(2L + l) 1/2 1 I=O 2< (dfi - 8 fi ) L,I.' (dfi" - + (5. 3) sf~=l))(LsOrn ILsJm )(L'sm'rn' IL'sJm) YL,m' ( 8 , cp) l. s s s s where dfi is a delta function of the final and initial states, Sfi I is the S matrix of the final and initial state for isospin I. For each of the three permissible spin-parity-charge conjuga- tion states, the shape of the des is proportional to the sum of the spin amplitudes absolute squared. It is different for each of the three cases. Case (1) - Singlet -- s = o, L = L' = J and therefore ms = ms I = 0. In this case, there is only one spin amplitude s = m s -- the one with = m I = 0 and it has only one non-zero term with L = L' = J. s The amplitude is proportional to Y O only. J and is equivalent to the spinless case. The shape of the des is We show this shape for several J's in Figure 5.2. Case (2) - AT (Abnormal Triplet) -- s = 1, L = L' = J. In this case, there are 9 spin amplitud e s -- m and m ' can s s be either -1, O or 1. Each spin amplitude has only one term where - 127 Figure 5.2: Shape of the des for pure J-P-C states. For the normal triplet states, there is a free parameter G = GL=J+l/GL=J-l: Normal triplet G Singlet -·-·· G Abnormal triplet · 0 2/3 1 _ - - - G = - 2/3 J ,, ,, / ~·· ·-·- _ · -:... .. ,,,. ~-·-· -- l J =2 J =3 J 4 J 5 .. • I '1· .r ..' o.o 0.2 0.4 0.6 0.8 l.olcos 8 10 .0 0. 2 o.4 0.6 0.8 o.o - 128 L = L' = J. Actually, (JlOO!JlJO) is zero. tudes with m s zero. Therefore, the ampli- = 0 do not contribute and only 6 amplitudes are non- The shape of the des is I (JlOm s !JlJms )(Jlm'ms '!JlJm) s YJ m m' ( 9,cp) I 2 (5.5) m ' s' s which simplifies to a sum proportional to FAT(e) = 2(J + l)JIYJol2 + 4IYJ1l2 + 2(J - l)(J + 2)IYJ2l2 (5.6) Of course, this is valid only for J larger than 1. In these cases, · 0 2 for the same value of J and Kel' the coefficient of thejYJ I t erm is exactly 1/2 of the corresponding term for the singlet case. The shape of this function, shown in Figure 5.2 for several values of J, is similar to a pure YJ 012 shape (at 0 0 or 180 0 , the AT is 1/2 of the I S). Case (3) - NT (Normal Triplet) -- s = 1, L = J ± 1, L' = J ± 1. In this case, each spin amplitude has 4 terms for the 4 combinations of L and L' and there are 9 spin amplitudes. The des is proportional to (LlOm ILlJm )(L'lm'm 'IL'lJm ) YL' . s s s s m' ( 8,cp)i L-L' (5.7) where GL and GL' are the relative coupling of the r esonance to the Land L' states. They are not necessar ily the same for L = J + 1 and J - 1 due to, for example, angular mome ntum barrier which may - 129 favor the L = J - 1 state. m' Thus, we get 9 terms containing YJ±l form' = O, ± 1 or ± 2. The shape of the des is dependent on the free parameter G G L=J-1 . = GL=J+l/ We show FNT( B) for several values of J and G in Figure 5.2. For values of G near ±1, the For G near O, the YL significiantly from F • 8 shape of FNT approximates the shape 1 and YL 2 The des at 0 terms dominate and FNT deviates 0 0 and 180 , for the same normalization of Sel' ranges between 1/4 and 1 of the F - 8 value. Since the pp system has twice as much probability of being in the NT state, the des at 0° or 180° for the NT case, for the same value of J and Kel of the resonance, would be between 1/2 to twic e the corresponding value for the S case. In the presence of background or other resonances, there may be interference terms as well as pure resonance and background terms. The behavior would then be more difficult to decipher. However, if there is a particular resonance which couples strongly to pp and which has a high J, the des should show peaki ng at e x treme angles. The peaking at backward angles should disappear as we move away from the resonance mass. We can search for this type of behavior. The spin of the possible resonance can be suggested by the slope of the backward elastic cross section near 180°. there are several difficulties. However, For a definite assumption of J , the slope will depend on the spin-parity-charge c onjugation of the resonance. Interference and background terms may also obscure the spin determination . Nevertheless , if we asswne any backward peaking to be caused by dominance of a single resonance, we can establish a - 130 minimum value of its spin. by a pure YJ 0 The sharpest possible peaking is produced amplitude. For any suggested resonances whose spin and elasticity (or the product Kel (J + 1/2)) are known, we can see if our · 180° data are consistent with their existence. To do this, we use the analogue of the optical theorem to relate the 180° resonance amplitude with Ke (J + 1/2) (which is proportional to the total cross section). 1 There are, however, may degrees of freedom in this calculation since the result depends on whether the resonances are in singlet, abnormal triplet or normal triplet states. c. Other Experimental and Theoretical Evidences for Boson Resonances (c-i) Other Experimental Evidence We shall now discuss the experimental status (excluding our data) of the resonances which have quantum numbers capable of being coupled to pp. Table 5 lists the boson resonances candidates found in three expe1:iments. These experiments found statistically significant bumps which can be interpreted as resonances and they are also capable of giving the width of each bump. experiments by A, B, and C. We shall label these Other experiments with poorer statistics also see structures interpretable as res.onance effects. A) ' (5. 7) CERN missing mass spectrometer experiments . This is the first series of experiments which covered the boson mass region 0.5 to 2.5 GeV for I larger than O. recoil proton at fairly small t and momentum analyzed. For incident n beam, the 2 (-0.l to -0.4 GeV ) is detected They discovered 4 statistically signi- - 131 Table 5.1: Boson resonance candidates above twice the proton mass. A similar table appears in the wallet sheets and data booklet by the "Particle Data Group" including all boson resonance candidates above 1.7 GeV. Those candidates marked with an* could be kinematic en- hancements (5.10) • Mass (MeV) Width (MeV) I Experiment 1929 ± 14 35 1 A 2086 ± 38* 150 1 B 2190 ± 10 85 1 c Comments The "S" meson I=l Enhancement in crT is 6 mb. possibly due to N* threshold (one pion production rises in this region from 0 to about 5 mb - see 4 Cooper( 5 .l ). pp to nn data of . (5.18) sees weak er strucBricman ture. 2195 ± 15 13 1 A 2260 ± 18* 25 1 B 2345 ± 10 140 0 c 2370 ± 17* 57 1 B 2382 ± 24 30 1 A The "U" meson. Possibly seen by . h.igan an d Mic . h.igan s t. <5 • 16 ) • Mic 2380 ± 10 140 1 c Enhancement in crT The "T" meson. Possibly seen by Kalbfleisch( 5 . l 5 ). I=O Enhancement in crT is 3 mb. I=l . is 2 mb. Evi- dence for this is also seen in pp to nn(S.lS). Could be caused by N*(l400) threshold. 2500 ± 32* 87 1 B 2620 ± 20 85 1 A 2800 ± 20 46 1 A 2880 ± 20 15 1 A - 132 - ficant bumps with mass above the split A B) 2 which they labeled R (a triplet), s, T, and U. than 2 M • p GeV( 5 · 7 ). In a continuation, they covered the region above 2.5 The last three have masses greater . d p d tota 1 cross-section . BNL pp an measurements (5. 8) . They covered the mass region 2.05 to 2.7 GeV and found bumps which can be resolved into 2 I = 1 and 1 I = 0 bumps. They were able to give the enhancements to the total cross section for these bumps as well as the mass and widths. However, the positionsof these bumps occur near N* thresholds (see 3) in the next page). They cannot resolve any narrow resonance with widths of the order of 5 MeV. C) BNL-Carnegie-Mellon missing mass spectrometer (5. 9) . They measured the same process as the CERN experiment except that they detect the recoil proton at small u. They found four statis- tically significant bumps above twice the proton mass. However, there is a strong possibility that these bumps ar e caused by . . h (5 .10) k inematic en ancements • d If these bumps are in eed caused by r e sonances, then the two spectrometers disagr ee 1uite significantly (see Table 5.1). Other experiments measuring the pp system include: 1. Two sets of data studying processes with pp i n the f inal state in . "1 (5.11,5.12) addition to other final state partic es • These bubble chamber data suffer from poor statistics and definite conc lusions cannot be drawn. . (5.12) However, the data of Diamond does suggest a possible enhancement in the combined mass of pp n e ar the T me son - 133 r eg i on (2190 MeV). 2. 5 In the S meson region (1924 MeV), Cline < • l3), in a bubble chamber experiment, studied the pp backward s cattering and cla~ued hemisph(~ re to see two structures. elastic The statistics a re poor. 3. 5 4 In the T meson region (2190 MeV), Cooper( .l ) found that a s izable portion of the bump in the total cross section can be a c counted f or by the one pion inelastic channel (indicative of N pr oduction). * thre shold The y failed to see any sharp structures in the topo- log l cal cross sections. However, the possibility o f a broad r esonance . in the T meson region is not ruled out. 5 Kalbfleisch (S. l ) reported a narrow enhancement in the ppn channel near the T meson supporting the possibility of a narrow resonance there. 4. 5 6 Michigan and Michigan St. ( .l ) both studied the U meson region in bubble chamber exposures and reported enhancements in the KK3n c hannel there (narrow and supposedly highly inelastic). In addition, 5 7 Lys in Michi g an( .l ) claimed to see an onset of backward peaking in pp e lastic scatt e ring near 1.8 GeV/c (2380 MeV). howev e r, weaken 5. Poor statistics, their claim. A g roup at CERN measured the process pp 4nn covering 2.05 to 2.7 (5 .18) . GeV, inc 1uding the T an d U regions . in both T and U regions. They again see structures The structure in the T meson region appears to disa g ree with the total cross-section enhancement if both are assumed to come from the same resonance with a reasonable assumption o f J. The structure in the U region is consistent with a resonance producing the enhancement observed in the total cross section. Th i s - 134 provides additional evidence that the bump in the total cross section in the T region is probably due mostly to N* threshold. 6. Folded angular cross sections of pp into charged pi or charged (5 . 19,5.20) . . k aon pairs h ave b een o b taine d b y comb ining two experiments which covered the region 2.0 to 2 . 55 GeV. charged p i on data of strong J There is evidence in the = 3 and J = 5 partial waves suggesting possible resonances in these spin waves. The behavior of these cross sections near the U meson region (2380 MeV) is verified by the Michigan bubble chamber exposure (5.21) . It is interesting to 5 22 ) using a quark-antiquark model (discussed note that Goldhaber< · in the next section) predicted the existence of a J = 3 and a J = 5 resonance near 2.2 GeV which should couple to both pp and charged pion pairs. The two poss i ble resonances suggested by the charged pion data occur near the T meson region ( for the J region (for the J = 3) and the U meson = 5) and their widths a r e quite broad( 5 • 20). How- ever, these values are obtained from a fittin g program and the solution may not be unique. In conclusion, although there is some e vidence for resonances in the pp system, none have been well established. (c-ii) The oretical Models Predicting Boson Resona nc es The CERN missing mass data showing the possible e x istenc e of heavy me s ons has l ea d to a numbe r o f theoretical mod e ls att e mpting to predict the e x act number, position (in the mass charact e r i stics o f h e avy boson r esonan c es. . . two such mod e ls, the qua r k-ant1quar k model 2 vs. J plot) and We shall briefly d e scribe ( 5 . 22 ) a nd the d a u g h te r - 135 trajectory model. (5.23) 91 (guark-antiguark) model ! . (5. 24) . According to the quark model of Gell-Mann and Zweig , some of the bosons established experimentally can be classified into being members of octets and singlets with the same J, P, and C. three octets and singlets with J . d (5. 25) esta b lishe • Thus, PC = 0 -+, 1 -- and 2++ have been wel l In this model, the 0 -+ and 1 -- mesons are assumed to be the two S wave combinations of qq (each having spin 1/2). Further combinations can be made if we accept the formation of qq~q, if we allow higher L states, or if we accept radial excitations. example, the 2++ can be viewed as the P wave triplet J combination of qq. For =L + 1 We have chosen to discuss the simple quark 5 22 mo d e 1 < • ) wh ere mesons are f orme d b y qq on 1 y and on 1 y spin excitations are allowed (i.e., no radial excitation is allowed). In this model, mesons must occur only in octets and singlets with strangeness and I both less than or equal to 1. In addition, just like the pp system, states with normal P and abnormal C are not allowed (see page 121 ). Thus, for each L larger than O, there should be 4 multiplets (3 triplet and 1 singlet). states with L = 1 are 0 +I- , +I- 1 For example, the +- and 2++ • , 1 2 States with different L are expected to have different mass 's. In addition, the four multiplets for each L are expected to be further split by either spin-orbit terms or tensor terms. However, if we assume that the rotational excitation splitting is more than the spin-orbit or tensor splitting, then we expect the multiplets for . 2 each L will cluster around certain mass values. In practice, this - 136 - assumption appears to be correct. A comparison of the mass 2 of several mesons tentatively classified as L = 1 states suggests that they cluster around mass 2 2 of about 1 GeV . Also, spin-orbit . l ' . (5.26) . sp 1 itting appears to d ominate over tensor sp itting expect to see clusters of resonances. Thus, we If spin-orbit splitting does . dominate over tensor splitting, the mass 2 splitting due to the spin- orbit interaction is definite -- ( -2L-2), -2, 2L and 0 for the triplet J = L - 1, J = L, J = L + 1 and singlet states, respectively. Experimentally, no "exotic" mesons (i.e., mesons which cannot be made out of qq) have been confirmed. In addition, all predicted mesons for L = 0 and many predicted mesons for L = 1 have been found. The high mass boson candidates found in the CERN missing mass 5 7 experiment( . ) fall on the p,A 2 trajectory and thus may be identified as higher J states associated with the qq model. 5 states found in pp 4 occur Also, the 3 and + - (5.20) are predicted by this model and n n at approximately correct values of mass 2 <5 • 27 ). In Figure 5.3 we present a graph of all the predicted qq states with mass 2 vs. J and mass states are put where the mass 2 2 vs. L. The position of the known actually e x ists. In conclusion, we should mention that there mi ght be radial excitations which may create high mass states with low spins. the existence of such states will not force model. Thus, us to abandon the qq The prediction of the absence of "exotic" mesons is an integra l part of th.e qq model and there are many recent attempts to · f ind such mes ons. - 137 6 J 5 Figure 5 . 3 : Ex pected mass states of the model plotted against (a) J , and (b) L, and (c) allowed decay modes . All masses are approximate. These figures were taken from an article by G. & S. Goldhaber (Ref. 5.22). qq 4 3 2 - -, - - - ... 4 5 6 ( 8eV) I- ~~t----t-~-~~-~t----+--~---1 "A p pro • •m!1• 3 2 0 L•O;S L• I ; P OD rrrn L • 2;0 L • 3;F L • 4;G L•S;H [[Il] ITIJJ DID UIIJ ' 0 11 011 021 0 1 s~ 'f, 'F1 1f4 'G,'G,'G,'G, 1H ,H 1 H 5H 4 5 ' • ("2··2·•3·· 2"3.. 3•q .. 3· ·4· ·4 -'!;"" 4 .. 5.. 5•·5 .. g or R m mi ~ 2 ·1T, l • I 2 7T , ! .. 0 .-. 311, I • I 3 IT, 1• 0 TT l • l TTW l• I M 4 lT 4 7T, I • 0 r -1 ... ' ' kK orK1K 1 I> I, 0 or K 1 K 2 l • l 0 K 7'7T'? l 2 J 7T7T7J l "O .... 0 ~- _ ~~-~~ _0<_0 _,._~.;i_.&_~ - - -- ~~ - - ~ K_rr_l •_!~f--1\L.....m__El_ ; ,,. ,, l • ~ or Kw 01 •0, lmt • I, __ JL_raii ~1 "1 • mi a _m___J\l_~ ~l • O or l , f:JBe low l hrtshol d 2 \C01t (M~ s s) 1 - 138 Daughter trajectory model In many models of high energy physics, the ex istence of a single trajectory is unacceptable terms with J t = 0. (5.23) • At t = O, there must be compensating = J 0 - 1, J = J 0 - 2, etc., where J 0 is the trajectory at These terms could arise from "daughter trajectories" which sit below the established leading trajectories and are usually expected to be parallel to the leading trajectories. . If this picture 2 is correct, at the position of mass of a member of the leading trajectory with spin J, are are J daughters with spin J - 1, J - 2, . .. 0. Thus, we may expect the existence of at least the mesons states depicted in Figure 5.4. Established non - strange mesons have been placed on the appropriate spots in Figure 5.4. As can be ob- served, the number of different states is at least 10 above the pp threshold at each "cluster". The masses of the states at each cluster are expected to be the same if the assumption of daughters being parallel to the leading trajectory is correct. Hence, our hope of deciphering the individual resonance appears to be rather difficult if this is indeed the case. The qq model could also allow "daughter"-like trajectories if radial excitations are allowed(S. 28 ). Thus, both models predict many resonances which cluster together. The qq model predicts 12 states at each L (1 I = 0 and 1 I = 1 state for each octet plus 1 singlet state) while the daughter trajectory model predicts 10 or more states at each cluster above the pp threshold. Hence, if either one of these models is correct, we can see the individual resonances only if there is a dominant resonance or if a particular resonance is very narrow. Phase shift analysis can - 139 Figure 5.4: States expected in the daughter trajectory model where circles are states possibly seen and x's are expected states. each x or circle, there is a I 0 and f ) • = 0 and a I = 1 state (e.g., the A2 Thus, in the region of s, 10 states are expected. u 6 5 For PP threshold 4 3 2 1 t in GeV 2 - 140 eventually be done to decipher the individual states. Polarization measurements are needed to do this, however. d. What our Data Say about Resonances in the Direct Channel (d-i) Narrow Resonances In the direct channel, we cover the mass range 1.99-2.48 GeV. Thus, we are sensitive to bosons in this range of energy. see resonances? How can we If the 180° des as a function of momentum shows a structure of Breit-Wigner shape accompanying backward peaking, this would be a clear indication of the existence resonance. of a direct channel Otherwise, any sharp structure in either the 180° des or slope may indicate resonances. The possible absence of the characteristic Breit-Wigner shape in the des and the backward peaking may be attributed to interferences. In a reg ion where no sharp structure is observed, we may set an approximate upper limit on the value of l/2(J + l/2)Kel of any possible resonance in that region. We shall first study the possible existence of narrow (widths less than about 50 MeV) resonances. Many resonance candidates listed in Table 5.1 have such narrow widths. Our 180° des and slope (see Figure 4.3) show structures. no narrow Our po i nts at 2.197 GeV (near the T meson) and at 2 .375 GeV (near the U me son) do not show significantly larger 180° des or sharper backward peaking compared to adjacent points. The only sharp structur e in the 180° des is a 100 MeV wide dip n e ar 2 .06 GeV. All our 180° des can be fitted on a smooth curve to within one standard deviation. Although our 180° slope shows backward peaking above - 141 2 .07 GeV , the slope does not appear to be much sharper at any particular ene rgy. Thus, no evidence for narrow resonances which couple strongly to pp is seen. Furthermore, at each momentum we can divide our data into bins 5 29 in which the incident momentum differs by 3-4%( · ). We are sensi- tive to a 20% variation in des between different momentum bins at e ach o f o ur incident momenta. No such variation is observed. 11 s now :·11'1: npp1·ox :lmn t:<.:~ up1.w r 11.mHtJ for l/2 (.J + l /2)K . for any (' 1111r1 · o w r• · HO'Clil \Wt!B Le t 1 C<>mpatih]e wl.th our datll. lt is possible to have a resonance strongly coupled to pp not s howing up in the e lastic des. with the backg round. This may occur due to interference However, any interference which cancels the e ffect of such a resonance requires a special phase relationship b e tween the resonance and background amplitudes. This is not e x - pe cted to hold for more than a small fraction of resonances, Thus we sha 11 assume that this is not the case in the following discussion where we d e t ermine an uppe r limit for 1/2(J + 1/2)Kel. Th e e nhancement of dip in the des caused by the resonance amplitude at 180° is proportional to the square of 1/2(J + l/2)Kel ( 5 .JO). Our data are taken at approximately 40 MeV intervals. We do not see any narroW bumps or dips in excess of 10% of our 180° des. none of the data points show effects larger than 15 µb/sr. Thus, For resonances with widths between 20 MeV and 50 MeV, we can set an upper limit of 0.2 for l/2(J + l/2)Kel" This is so since at l e ast on e of our data points must be within one half-width away from the resonance and t hus ou r data a re compatible with a maximum resonance des of 40 µb/ s r. - 142 For resonances with widths about 10 MeV, our data are compatible with an upper limit of 0.3 for l/2(J + l/2)Kel for these resonances. This is so since the resonance may be 2 or more half-widths away from one of our data points and thus resonance des of 100 µb/sr is allowed. 5 7 The T and U mesons< · ) and several mesons suggested by pp Jata(S.IS,S.lG) are believed to have widths of the order of 10 MeV nnd thus, if they really couple to pp, probnbly havt: 1/2(J + l/2)Kel l e ss than 0.3. One additional comment needs to be made. If there are many narrow resonances which are clustered close to each other, we would not be able to see the individual resonance effects. However, since 0 each resonance amplitude (for J larger than 0) peaks sharply at 180 , one expects to see backward peaking caused by a combination of these resonances. Interference should not destroy the backward peaking :; ilK(' rni"ly i:es01H1nc (•s i n t:h C;\ Hume J-P-C state interfe re with each Indt.HHI, abovi:: 2. 1 CeV, there is backward peaking which app e ars nlher. Lo hold up to our highest momentl.Ull point. Thus, this may indicate possible existence of nlDllerous resonances above 2.1 GeV. .both the Note that qq and the daughter trajectories models described in Section (c-ii) predict the existence of about 20 resonances between 2.1 and 2.5 GeV capable of coupling to pp (see Figures 5.3 and 5.4). (d-ii) Broad Resonances Our data revealed two broad structures (by broad, we mean resonances or s tructures with widths larger than about 50 MeV). is a 100 MeV wide dip near 2.05 GeV. The slope near 180 0 There turns over f rom bac kward dipping into backward peaking as the energy passes - 143 2.05 GeV. The second structure is a 250 MeV wide bump in the 180° des centered near 2.25 GeV. Backward peaking exists ova:- the entin\ range of the bump but it does not appear to go away at energy above the bump. If e ach structure comes from one resonance, the n the dip being about 100 µb/sr deep, implies that the resonance associated with it has a l/2(J + l/2)Kel of about 0.3. The resonance as.sociated wi th the bump is also expected to have similar value since the bump is about 100 µb/sr. These structures are not identifiable with either the total cross section bumps( 5 .B) at 2190 MeV, or the pp into charged pion pair structu res 2345 MeV and 2380 MeV (5.20) . which occur at 2.12 GeV (250 MeV wide) and 2.29 GeV (165 MeV wide). It is possible that the dip is actually caused by an absence of i:t~sonance · ( C· 1. ine near 2 . 05 GeV. 5 . 13 ) Indeed, our data combined with the data of ( s I·1own in . F igure . 5 • 3) indicate a bump in the S region (1924 MeV) below the dip in our data. Our bump at 2.25 GeV is consistent with a comb ination of the three suggested resonances in the total pp cross section measuremenets. · rn the following paragraphs and in Figure 5.5, we show an attempt to fi t our 180 0 des in the region of our bump with only the three resonances and their values of l/2(J + l/2)Ke . 1 Fi tt ing of our bump structure us ing the total cross section "resonances" As suming that the 180° des is entirely due to the effects of t he . d (5.8) thr ee resonances suggeste db y t h e tota 1 cross section ata , we can calculate the 180° des with the only following freedom: l. We have to assume the P-C state of each resonance (i.e., singlet, - 144 AT or NT. See pages 121 and 125-129 ). If two or more resonances are in the same P-C state, interference between the two resonance amplitudes occurs. Also, the size of the 180 0 amplitude is dependent on the choice of the P-C state . 2. For any resonance in the P-C state of NT (normal triplet), the 180° amplitude has an additional free parameter which varies between 1 and 2. For the othe r P-C state, the 180 0 . amplitude is completely determined by l/2(J + l/2)Kel' except for the sign, which depends on whether J is even or odd. 3. In the case of two resonances interfering, the relative J is important since YJO(l80°) is proportional to (-l)J. Each resonance amplitude at 180° is C times (l/4k) l/2(J + l/2)Kel 5 3 times the Breit-W i gner momentum dependent function< • ), where k is the cm momentum, C is a factor dependent of the choice of P-C state . -1/2 C is 1 for the singlet state, (2) state) and between (2) -1/2 and (2) 1/2 for the AT (abnormal triplet for NT (normal triplet) state. Figure 5.5 shows the predicted des at 180 combinations of assumptions. 0 for particular We see that the fit to our data in the region of the broad bump is quite adequate. Note that it i s crucial to have the low mass resonance and one (and only one) of the high mass resonances in the same P-C state so that the cons tructive interference will prevent a dip between 2.19 GeV and 2.34 GeV. Other wise, the combination is not unique. There i s e videnc e that part of the 2 .19 GeV bump is due to N* . (5 14) thre s hold · • Th us, the l/2(J + l/2)K for the possible r e sonance . el at 2.19 GeV may be reduc ed from the value of 0 .4. Howe ve r , we c an - 145 Figure 5.5: Resonance prediction in the 180° des using the total cross section resonance candidates and their values of X = l/2(J + l/2)Ke . 1 The open circles are our data extrapolated to 180°. The solid line is the prediction for either one of the following combinations I, II, or III. Mass(GeV) Width(MeV) x 2.19 85 0.4 2.34 140 2.38 140 II NT,C = 1 Singlet NT,C 1.33 0.3 NT,C Singlet NT,C 1 0.2 Singlet * 1 III * I NT,C = 1 Singlet For the three combinations, (-l)J is assumed to be opposite for the * 2.19 and 2.34. For combination III, X of 2.19 is assumed to be 0.3 instead. Mass in CeV 2 .0 2 .• 1 2.2 2.3 2.4 2.5 f 200 do/dn in µb/sr * t 100 t II l 50 I 0.5 1.0 2.0 1.5 Incident momentum in Ge V/c - 146 still obtain the fitted curve in Figure 5.5 i f l/2(J + J/2)Kel is 0.3 ( see combination III). If we were to add some background amplitudes as well as possible amplitudes for resonances below our mass range, we see that we may be able to ap proximate our 180° des fairly well. The resonance inter- pretat .ion of the broad bump is also supported by the persis t e nt backward rw~'l k ing . The slope n e a r 180° suggests that some o f the reso- nances .• Jf th ey exist, have J's larger than l. Although the existence of the three total cross section resonanc es is c onsisten t with our data, the amount of f reedom i n our fit is suff icient to make any definite statement difficult. We stnnmarize our findings about broad resonances as follows: 1. Our data suggest weakly two possible resonance structures -- a 100 MeV wide "resonance" at 2.05 GeV and a 250 MeV wide "resonance" at 2.25 GeV. Both resonance structures suggest a value of 0.3 f or 1 /2(J + l/2)Kel ' However, the e~idence is weak since the first resonance candidat e is suggested by a dip wh ile the sec ond is suggested b y a ln unp wli.l c li doc:> nol look Ukc a Bre.lt:-W:lgner hump. Al s o, thoug h bac kw ar d peaking accompanies the bump, the peaking d oes not g o awa y at e n e rg ies above the bump. 2. . (5.20) . The struc t ures in pp into pion pairs , if they e x ist as resonances, c ould not couple v ery strongly to pp . 3. Our d ata in the region of the broad bump can be fi tted by the c ombination of the t hr ee total cross section res onance c andidat e s. The number of assumption s for this fit is suf ficie n t to make it difficult f or us to s ay tha t our data s upport the existen ce of t h ese - 147 three resonances. e. Conclusion on Resonances We do not provide any strong support for the existence of any single resonance previously suggested. The only resonance candidates whose coupling to pp was at all determined were the total cross-section b umps (5.8) • We cannot rule out the existence of these resonances and the strength of the suggested couplings are not incQmpatible with our data. We believe that the coupling of any other resonance to pp is limited to l/2(J + l/2)Kel of below 0.3 although this may not be true if still other r .esonances lie close to that resonance. If we assume that J is of the order of 5, the elasticity Kel is thus limited to below 10%. This small elasticity is not unexpected since any massive boson would have numerous other decay channels. In particular, the multipion and multi-K-pion channels would be expected to dominate (from phase space factors if not from other factors). Under the qq and daughter trajectories models, bosons are expected to exist in clusters. This would be compatible with the dip at 2.05 GeV in the 180° des found in our data since it lies between the S and T clusters. However, one would then expect a similar dip between the T and U clusters near 2.26 GeV. This is not observed. Thus, these models do not appear to be as fruitful as one might expect. Our experimental data thus revealed that it is hopeless to try to see definite resonance behavior of individual resonance states in backward elastic scattering. Either there are too many resonances close together or the resonance couplings are too weak fo1· unmistakable - 148 resonance behavior to be seen. Thus, to understand the resonance situation, it would appear that we must study the individual inelastic channels of pp, do a phase shift analysis using polarization as well as elastic data, or - - do combined pp mass plots of reactions with p and p in final state. - 149 - CHAPTER VI: a. DIFFRACTION, AN ALTERNATIVE INTERPRETATION OF THE DATA Introduction and Motivation for this Interpretation It may be possible to ascribe the dominant b e havior of the pp elastic cross section to diffraction. Since diffraction is basically quite different from resonance effects (duality connects resonance effects with exchange process but not diffraction although it is considered Pomeran exchange< 6 • 1 ~. It is interesting to see if the ma- jor features of pp elastic scattering can be e x plained by diffraction alone. In this section, we shall give a brief history and motivation for diffraction dominance in pp e l astic scattering. Sections (b - i) to (b-iii) will describe a particular optical model a nd its prediction for the elastic cross section, expecially in the r egion of our data. Section (c-i) covers a brief survey of other diffraction-type models and section (c-ii) contains a discussion of the general f eatures expected from diffraction d ominance . Section (c-iii) contains an assessment of the diffraction dominance inte r pretation of the pp elastic scattering with suggestions for future e xperimentation to test this interpretation. Forward elastic differential cross section measureme nts e x ist in abundance . (6 .2) t y pe models and they have been successfully fitted with d i ffraction- ( 6 3) • • Figure 6.1 contains some pp forward elastic data showing the strong diffraction peak. 6 3 phenomenologists used< · ) cons i st In general, the mod e ls which many o f sunnning partial waves up to L approx imately equal to kR (k is cm momentum and R i s the radius o f the diffraction sphere). A gradual cutoff utilizing an additional para- - 150 Figure 6.1: pp elastic des in the forward diffraction region. The open circles and triangles are data of Coombes et al., Phys. Rev. 112, 1303 (1958) while the x's are data of Berryhill and Cline (page 335, Proceedings of the 14th International Conf. on High Energy Physics, Vienna, 1968 (CERN)). The lines are the spin-orbit optical model curves, which are described in Section (b). 0.1 500 200 I[ "' "' "'l I"' 100 do/du in 2 mb/GeV 0.2 " t in GeV 0.3 t t 0 . 75 GeV/c I 1.4 GeV /c 0.86 GeV/c Model curve for 1.4 GeV/c Model curve for 0 . 8 GeV/c 50 20 10 5 \ \ \ \ \ 2 \ 2 - 151 mete r called "skin depth" is sometimes used. Many models also have opac ity f actors whi c h allow some of the lower partial waves to be t ransmitt e d through the sphere. to an in teg ral over J 2 des o f R 0 The sum over PL(cos e) i s convert e d ((2L + 1) sin 1/2 0 ) fr om wh i ch one obtains a (J (kR sin U)/ s in 0) 1 2 It should be stre ~ sed that the • c onvers ion o f the sum in t o an int e gral involves McDonal d 's expansion o f Legen d r e Poly nomial PL(cos G) xJ 2 ( x )J3( x )/6) 4 + sin 112 e ( ) = J 0 (x) + 2 sin 1/2 0 (J ( x )/2x 1 + .... (where xis (21 + 1) s i n 1/2 e) whe r e only the first term is kept. Thus, the approximation is only valid for small angles. Fig ure 6.1 shows the forward pp elastic data fitted with a t y pe of diffraction model (see Section (b)). Anti.shrinking (i.e., decr e ase in the slope of the peak as momentum increases) of the d i ffr a c t i on e x ists. The current d a ta suggest that the radius in the d iff r ac t i on model d r ops from about 1.6 F e. rmi at low momentum to about 6 4 1. 2 Fc nni a t: i. nc id e nt momentum much h i gh er than l.O Ge V/c< · ). So i.t i s we ll establishe d that diffraction dominates the behavior in small _angle pp elastic scattering. Data at -t = 0.5 GeV 2 region indicate that there is d i p in the des which appears to be at approximately the same t position independent of incident momentum (although at lowe r momentum, the dip 6 a ppear s at slig htly smaller t value)( .S). . . . . <6 • 6 ) . is t h e f. . irst d i. ff raction minimum It is believed that this Hence, diffraction s c attering could still dominate in this region of not-so-small ang le scattering . One might therefore ask whether diffraction dominates the entire - angular range in pp elastic scattering. - 152 Other supporting evidence for diffraction dominance in large angle pp elastic consists of: l. The sharp dip in 180° des which we observed near P incident (p) - 0.95 GeV/c might well be the second diffraction minimum coming into 0 the physical region. The slope of the des near 180 in this momentum region is consistent with the incidence of a diffraction minimum since there is backward dipping before the minimum appears and backward peaking at incident momentum above the occurence of the minimmn. This concept is schematically illustrated in Figure 6.2a 2. Preliminary unnormalized data of pp elastic scattering in the backward hemisphere in the incident p momentum region between 0.3 and 6 7 0.75 GeV/c by Cline( · ) appears to be consistent with diffraction dominance. The shape of the des, plotted in Figure 6.2b, indicates the possible incidence of the second diffraction maximum into the physical region. The maximum does not remain in constant t. This is consistent with diffraction models since the t values of maxima and minima shou ld· increase wit l.1 momentum (6.6) when they occur at low 1110111cntum. 3. 8how Elastic scattering data of pp at wide angles by Daum et bmnps and dips at each momentmn. a1~ 6 · 8 ) These structures appeared to remain at approximately the same values of t and can be interpreted as diffraction structures. Some of these data, combined with some other pp elastic 6 9 scattering data < · ) , are s h own in Figure 6 . 3 , a 3 -dimensiona 1 compilation. Observe the bumps and dips which appear to dominate the entire angular range . - 153 Figure 6.2: (a) Schematic drawing of elastic des as a function of -t for diffraction model. (al) momentum below incidence of diffraction dip, (a2) at incidence, (a3) above incidence of diffraction dip showing backward peaking. 6 7 (b) Schematic curve of data of Cline< • ) ~s a function of t showing the first diffraction dip. physical region unphysical region (b) 300-400 MeV/c \ \ 500-600 MeV/c (\ 90 180° -t---- 600-700 MeV/c 0.2 0.3 0.4 -t in Gev 2 0.5 0.6 - 154 - Figure 6.3: A three-dimens..ional compilation of pp elastic data. No. 1 6 6 is Cline's data< • 7 ), 2 is the data of Barish( · 9 ), 3 is the data of 6 9 Berryhill( • ), and 4 is a combination of Daum's and our data. 1.73 1.0 I do-/d.0.* 0.1 (mb/sr) PLAB in . Gev/c 1.0 0.0 COS BcM -1.0 - 155 Diffraction dominance could also be motivated from the theoretical standpoint. The existence of strong annihilation channels . (6.10) . . . f or ta k.ing t h is view even at t h res h o ld wou ld b e a strong incentive The probable absence of u channel exchange effects also enhances the possibility of diffraction dominance. h. §pin-Orbit Optical Model (b-.i) Fonnulalion of th e Model The spin-orbit optical model which we will discuss in this section is a diffused black sphere optical model with spin orbit terms. In deciding on this model, we are motivated by the following considerations: 1. The model should be as simple as is compatible with the data. have thus used only diffraction terms. We No background terms possibly indica ting resonance or exchange effects are included. The number of free parameters are kept at a minimum. 2. Sinc e we are dealing with large angle scattering, the small angle a pp roximation used in diffraction fit to the forward peak (see pages 149-151 ) can no longer be used here. Thus, we should use a model which involves partial wave sums. 3. Sinc e both incident and target particles have spin, we must consider the possibility of spin-orbit and spin-spin contributions. . . scattering . (G.S) revea 1 tion measurements o f pp e 1 astic Polariza- appreciable polarization indicative of significant spin dependent contributions. In addition, sp i nless diffraction models have zeros in the predicted cross section which are not observed in pp elastic scattering (s ee - 156 - Figure 6.3). Spin dependent terms would enable these zeros to become minima instead although non-diffractive background could also do this . We have decided to neglect the spin-spin terms and only consider spinless and spin-orbit terms . It may be argued that spin-spin terms , involving the spins of both particles, would not contribute as much to the des as the spin-orbit terms. It remains for us to par ameteri ze the spinless and spin-orbit partial waves. We have decided to use a model similar to the one use d 6 8 by Daum et a1.< • ), which in turn is a mod i ficat i on of an idea by Frahn and Venter( 6 .lO) . The Daum model f i tted their pp elastic des between 1 . 73 and 2. 97 GeV/c fairly well although their polariz ation measurements at the backward hemisphereappe ars to be in slight dis6 8 agreement with the prediction of the mode1< • ). We now formulate the spin-orbit optical model , which is a black (i.e., complete absorption of lower partial waves) dif f used (i.e., gradual cutoff of higher partial waves) sphere mode l. In the absenc e of spin-spin contributions, the scattering mat rix can be expre sse d . (6 . 12) in the form (6-1) wher e f and g are the usual non-flip and spin-flip amplitudes , s+1 and 2 are the spin vectors and ~ is a unit v ec tor pe rpendicular to both ~ initial and fi nal ~p mome nta. The des can then be ex pre ssed as des= !fl 2 + 2lgl 2 (6. 2) The t wo amplitudes can be e xpande d in terms o f the f our partial wave amplitudes (3 triplet and one sing let) for each L o f which on ly I - 157 -· two are independent 00 f(e) ( k)- L ((L+l)~++L~_)PL(cos e) 1 (6-3) L=O 00 g( e) I (i/2k) <£\+ - £\) PL 1 (cos e) (6-4) L=l where ~± are the triplet amplitudes for angular momentum L and spin = L ± 1. J We have parameterized the values of ~± as 1 (6-5a) Re (RL±) - 2 h(L) 1 + Im (1\±) = 2 u-d(h(L))/dL (6-5b) where -1 h(L) = (1 + exp ((L - kR)/kD)) (6-5c) + k is the center-of-mass momentum, u- are the spin parameters characterizing the J = 1 ± 1 spin terms, R is the rad i us and D is the skin depth (which is about the size of the region whe re h(L) falls from 1 to 0). Combining (6-5) with (6-3) and (6-4), we obtain 00 1 ~ . fi _ Im (f) = (i/k) L'__i (L + 2) P (cos 9)/(1 +A) 1 (6-6a) L=O 00 f r _ Re(f) (l/k) L ((L + ~)u + u' /2) PL(cos 9)A/(kD(l + A) ) L=O 2 (6-6b) 00 gi _ Im(g) 2 1 - (l/k) I<u'/2) PL (cos e) A/(kD(l +A) ) (6-6c) L=l gr _ Re(g) = 0 (606d) - 158 where u =(u+ + u ) /2, u' = (u+ - u - )/2 artd A 3 exp((L = kR)/kD). The fi term involves a sununation of PL's with coefficient (L + 1/2) times h(L) ; (1 + A) -l. h(L) is a function which is 1 for L less than k(R - D), practically 0 for L greater than k(R + D) and falls rapidly from 1 to 0 between the two limits. The f. term is 1 essentially identical with the spinless amplitude of a radius R and skin depth D. Both f r and g. involve sums where the coefficient includes the term d(h(L))/dL 1 =A/(kD(l + A) 2). This term is practically 0 for L outside the region between k(R - D) and k(R + D) and peaks at L = kR. We have parameterized in this fashion since it is believed generally that the spin effects are important only at the "skin" of the sphere (6 .13) . Since both f and g. are dependent on u and u' r 1 ' these terms represent the spin-orbit contributions. At small angles, the f. term dominates and the result of this 1 model agrees quite well with the usual diffraction model. the forward region, the f r Away from and g. terms become comparable in size to 1 f. for u or u' of the order of 0. 2. 1 We sha 11 see i .n the next two sections how this model agrees with our data and other existing data . (b-ii) Spin-Orbit Optical Model and our Data We have attempted to find out what results this model gives in the region of our data. R, We allow 5 free parameters: o0 and Dk where D = D0 + Dk/k, u and u'. Figure 6.4a shows our extrapolated (linear) 180° des as a function of incident momentwn. Figure 6.4b shows our extrapolated I Mass in GeV 2.0 II- 2.1 ~ 2.2 ...... Mass in GeV 2.3 2.4 2.5 2.0 2.1 2.2 lJ1 I.Cl 2.3 2.4 (b) (a) -10 ll I ,. I' ~ f n f f II ,....... 2oor ....... I I 0.. 0 Ill ,.0 '-" J Cll I .-I ti) lodr 0 r r r 0 00 ...-l 10 1 j I 1- 50 L (/) Ir I H ......_ ,.o ;i s:: I I i... •.-l •G "O ....... b "O I 2.5 1. 1. .o 20 I I I I I 1.0 P b in GeV/c 1.5 2.0 la 0 Figure 6 .4: Spin-orbit optical model curve for (a) 180 des and (b) slope (b/a) (des = a + b(l + cos e )) between -0.95 and -1 . 0 cm compared with our extrapolated data (open circles) and Cline's data at cos e cm (close d circles, Ref. 6.7). - 160 Figure 6.5: Our experimental data in µb/sr with optical model curves. 1.590 0.987 100 f100 1.844 200 \,... 100 ~ ..0 ::i.. 50 c *q 'U "'-.. 100 .b 'U 50 0.935 100 50 -1.0-0.95-0.90-1.0 -0.95-0.90 -1.0-0.95 -0 .<)0-l.O -0.95-0.90 . Cos Bc.m. - 161 slope at 180°. tum. Figure 6. 5 shows our data at seve r a l incident momen ~ The solid lines in these figures are the spin-orbit optical model c urves for the following values of the parame ters : 1. R = 0.88 Fermi. This is constrained by the asswnption that the dip at 0.95 GeV/c ;i s the second diffraction dip in the f. term l. (i.e., the spinless term). 2. n 0 0.03 Fermi and Dk= 0 . 065 Fermi-GeV/c. Th i s is necessary to 6 7 give the peak at 0.5 GeV/c (Cline's data)( • ) and 180° the correct normalization and to give the correct normali z ation in the 180° de s in the T and U region (1 . 4 and 1.8 GeV/c, respe ctively). 3. u = 0.09 for P inc (p) less than 1.25 GeV/c = 0.40 otherwise. The spin dependent terms have dips whe re the spinless term ( f .) has l. bumps and vice versa. Thus, the value of u b e low 1 . 25 GeV/c is determined by the deviation of the dip at 0.95 GeV/c f rom O. has a dip at 1.5 GeV/c which is not observe d in our data. must be much higher at 1.5 GeV/c to fill in the dip. f . also l. Thus , u In p r actice, u must be about 0.4 at 1.5 GeV/c to give the cor rec t normal ization. Between 1.0 and 1.4 GeV/c, the s iz e of u is unimportant. We have used a s tep function although a gradual increase is also acc e ptable. Above 2.0 GeV/c, if u is decreas e d, the 180° des would b e somewhat smaller and a g r ee b e tter with our data. 4. u' = 0. 5 . The size o f this parameter is unimportant. If t his value is reduc e d by a factor of 2, u c an be change d sl ight l y to c omp e nsat e and the res ult wi ll b e essential l y the s ame . F r om t h e f i g u re s , we see t ha t the op tical mode l curv es fit t h e - 162 - data quite well. In particular, the bump at 0.5 Ge V/c and the dip at 0.95 GeV/c in the 180° des are reproduced ac c urat e ly . Howe v e r, the r e is a slight dip at 1.3 GeV/c which may be i nconsistent with our data (the dip in the model curve is about 20%). to b e the same for f., f 1 r I f we restrict the radius and g. and allow only spin - orbit terms of 1 the form we used, this slight dip cannot be removed. This is due to the fact that it is in between the bump in f. and bump in f . 1 r • This dip can be removed if we allow spin-spin terms or if we allow different radius for the spinless and spin-orbit terms. However, this would impiy the addition of several free parameters and complicate the mod e l, which we prefer not to do. The angular shape of the data (see Figure 6.4b and 6.5) is also reproduced fairly well. The model curves give backward dipping below and backward peaking above 0.95 GeV/c. Thus, this simple model with 4 energy-independent parameters .. and one variable parameter (which takes on only two values) r eproduces the results of our experiment to a good degree. In the n e xt section , we shall compare the prediction of this model with other pp elastic data and see how it fares. (b-iii) Assessment of the Spin-Orbit Optical Model - Does it Re- - produce Other PP Elastic and Polarization Data? For the same values of the parameters we use to reproduce our data , we try to see how closely the model prediction matches other data. We consider three pp elastic regions: 1) forward di f fraction r e g ion, 2) low energy elastic data region, and 3) other . elastic data - 163 regiomand also polarization data of pp elastic scattering. Forward diffraction peak region As we mentioned in Section (a), the optical model, with just a spinless term, fits the forward diffraction peak very well with the assumption of a radius of about 1.2 Fermi. In our model, the spin- orbit contribution enhances the forward diffraction slightly. How- ever, the radius of 0.88 Fermi which is necessary to match the 180° des is incompatible with the data on forward diffraction peaks (the spin-orbit optical model curve for 0.88 Fermi is drawn as a dashed line in Figure 6.1, which contains the forward diffraction peak data). The spin-orbit optical model curves are too gentle and the too low. o0 des is Thus, it would appear that if our model is to reproduce the behavior at both o 0 function of angles. and 180°, we may have to vary the radius as a Nevertheless, the qualitative features of the forward diffraction peak are reproduced by our model. Low energy elastic data region The existing pp elastic data in this region consist of some forward diffraction peak data discussed above and the backward 6 7 .hemisphere elastic measurements of Cline< • ) which cover 0.3 to 0.75 GeV/c (data at higher momentum is forthcoming). Cline's data are sketched in Figure 6.6a along with the result o f our spin-orbit optical model, which is drawn in dashed lines. fit is quite good. resu l t values. Qualitatively, the However, it would appear that a better fit would if the bump-dip structures are moved to slightly smaller t This is consistent with increasing the radius slightly to about 0. 95 or 1. 0 Fermi. Thus, the data i n th i. s r e gion al so sug gest - 164 Figure 6 .6: The spin-orbit mode 1 curve (solid lines) compared with - (a) Cline's low momentum pp elastic data (Ref . 6.7). (b) Berryhill's data at 1.4 GeV/c (Ref. 6.9 and page 335 of Proc. Int. Con£ . on HEP, Vienna, 1968 (CERN)). (c) pp polarization measurements at 1.73 GeV/c (Ref. 6 . 8). . 0 ...... I . l.f') 0 N :> Q) ,0 i:: ......... . Q) u ......... ·rl 0 13 - 0 I .µ 0 Cl) 0 u 0 . l.f') 0 0 V\ 0 ...... V\ ,....., ,...... V\ N :> 0 • 0 ol a ~ "O "O - ! 0 0 ...,; 3. ' 0 ~JS/q w ~ UPI.DP"i ~ ---". - ~ r E 0 JS /QW 0 . l.f') ,....., 0 p.. l~ ~ l.f') UP/.DP O>u . 0 I ...... u - 165 a slight variation of radius with angle. Other elastic data regions I We shall concern ourselves with only the intermediate momentum region (incident momentum less than 3 GeV/c) which includ es 5 9 6 9 6 8 data by Barish( • ), Berryhill( · ) and Daum( · ). Data at higher momentum exist, but are not useful beyond the first diffraction dip due to poor statistics . c luded in Figure 6. 3. The intermediate region data have been inIn Figure 6 •.6b, we show a plot of the data by Berryhill with the results of our spin-orbit optical mod e l. We see that the structures apparent in the data are reproduced quite well by the mode 1 curve. Again, a slightly better fit would result i f we increased the radius so that the dip and peak occur at smalle r t values. Polarization data Daum et al. ( 5 .B) also measured the polarization of pp elastic scattering using a polarized proton target. Thus, we can compare the results of our model with the polarized data since the polariza tion, in this case is Pol. 2 Re (fg*)/dcs. (6.7) We show the polarization data and our optical model results in Figure 6.6c. We see that the fit is qualitatively quite reasonable in the forward region but deteriorates towards the backward hemisphere . The size of the polarization is of the same magnitud e as the optical model results. Even if there is disagreement in the size , - 166 we can adjust the value of u' which affec~the polarization drastically but only affects the des slightly. The major prediction of the model as far as polarization is concerned is the prediction of zeroes at the position where the elastic des shows dips. since Re (fg*) These zeroes are caused by zeroes in f. 1 = f.g. + f r gr i i and g r is identically 0 in our model. The polarization data do suggest zeroes or minima at the appropriate places although the data are not sufficiently good to be decisive. If these dips are actually minima rather than zeroes, this would probably imply that spin-spin terms (which contributes to gr) are not negligible. The fact that the zeroes or minima appear as predicted by the spin-orbit optical model indicates, however, that spin-orbit terms do dominate over the spin-spin terms. Another result of our model is that the polarization should be positive only (slight negative polarization is allowed only near 180°). This is verified reasonably in the forward hemisphere. Daum et al. fitted their data with a similar model but allowed the parameters to vary at each momentum without energy dependent constraints. However, their model results are similar to ours. In conclusion, the spin-orbit optical model fits the data qualitatively quite well. The shapes of the structures in the elastic scattering and polarization data of pp are reproduced by the model. However, quantitative fit would require varying some of the parameters which we have kep~ fixed. For example, the forward diffraction data requires a larger radius than was used by us to fit the 180° des. Also, data near 90° suggest that the radius may have to be in- - 167 creased in that angular region to shift the dips to the observed values. Polarization data may also be better fitted if spin-spin terms are introduced. However, any attempt to make a more sophisticated model would destroy the simplicity and beauty of this model. In addition, the current state of the data -- especially the polarization data -- is such that a detail fitting with a complicated model with many additional free parameters is unwarranted. Considering that over the entire range of momentum below 3.0 GeV/c we used only 4 energy-independent and 1 energy-dependent parameters, the fact that the spin-orbit optical model qualitatively fits the data is quite impressive. Thus, diffraction dominance of the pp elastic scattering appears to be justifiable. c. Diffraction Dominance and pp Elastic Scattering (c-i) Brief Survey of Other Diffraction Type Models Other parameterizations of partial wave amplitudes have been . d ata o f many reactions . <6 • 14 ) • use d to fi• t e 1 astic Usually, these involve either introduction of opacity factors reducing absorption of lower partial waves (grey sphere models) or different parameterization of the ~± amplitudes in page 157. However, these changes are un- important qualitatively in that the positions of the structures are not shifted by significant amounts. Another alternative is to use the complete pp amplitudes . inc 1u d ing al 1 spin terms (6.12) • This will give a total of 5 scattering amplitudes for each L instead of 2 (3 additional amplitudes representing - 168 spin-spin contributions and containing PL added). o, s, PL1, s and PL2, s are The detail fitting to the data would therefore be more versatile at the expense of more parameters. In any case, it is ex- pected that spinless terms like (2L + l)PL would still dominate the des. Thus, the result of this kind of model would still be quali- tatively the same as our spin-orbit optical model. It is also possible to use a multiple scattering model to try to fit data with bump-dip structures (6.15) • In brief, d oubl e scattering would give a flatter decrease as a function of angle than single scattering. Destructive interference between the various scattering amplitudes would lead to bump-dip structures whose position depends on the relative strengths of the scattering amplitudes. One can also go further by assuming the quark or parton structure of p 6 16 and p< • ). However, the result of this type of model would be similar to that of our diffraction model. Thus, other models give results qualitatively similar to that of our simple spin-orbit optical model. (c-ii) Features of Diffraction Dominance in pp Elastic Scattering Now we discuss the general features which are expected in any type of diffraction dominance model. The essential nature o f a diffraction model is the interference of yarious L waves which causes the interference pattern. The position of the bumps and dips should be dependent on the radius which one assumes. The bumps and dips should occur in a regular pattern and, as a function of energy, should stay at fairly constant t values (at large angle regions, the t values of thes e structures - 169 - . (G.5) ). should increase slightly as energy increases Spin-dependent terms are not expected to be important in th e f orward diffraction peak region. However, the spinless contribution decreases quite rapidly as angles increase. Thus, spin dependent t erms will contribute significantly and fill in some of the inte r ference dips in the spinless contribution. If diffraction structures still dominate at backward angles, then we expect that the shape of the des will be as drawn in Figure 6.2a. However, spin dependent terms may modify this kind of structure. (c-iii) Assessment of Diffraction Dominance and Suggestion for Further Experimentation Diffraction dominance in the forward elastic pp scattering is we ll es tablished. The existence of the first diffraction dip and a second maximum can also be viewed as evidence of diffraction dominance. Thus, diffraction dominance in the forward hemisphere is fai r ly .iustiCjable. f\s .for the backward hemisphere, the data of Cl i ne( 6 .7) at low momentum appear to be consistent with diffraction dominance al- t hough finer structures (with poor statistics) suggesting possible resonances were claimed. of Berryhill near 180 0 (6.9) , Cooper Otherwise, the intermediate momentum data (5.14) and Lys (5.17) as well as our data (see Figure 6.4 and 6.5) are consistent with diffraction dominance. We conclude that, although direct channel resonance effects may be. present, diffraction dominance of pp elastic scattering is - 170 consistent with existing data. Indeed, there is no major structure in the pp elastic scattering which contradicts diffraction dominance. In order to test this concept, it is essential to 1) get better measurements (with statistical errors of the order of our experiment) of pp wide angle elastic scattering at intermediate or high momentum to try to see diffraction structures, and 2) get better measurements of polarization with polarized beams and target to look for diffraction structures. Eventually, a phase shift analysis, in addition to clearing up the resonance situation as describe d in the last chapter, may be able to force us to either discard or accept diffraction domi nance in pp elastic scattering. - 171 CllAP'J'lm V IJ: a. SUMMARY i\ND CON CT.US lON Summary We have presented data on pp backward elastic scattering in the intermediate energy region, the methods we used to acquire them, and two interpretations of the data. Our experimental apparatus is essentially a missing mass spectrometer using wire spark chambers with digitized magnetostrictive delay line readouts to records the events. li qu id hy droge n targe t. Antiprotons are incident on a The recoil proton fr om a backward elastic event is idcnt ·ified by a c ombination of time-of-flight me asurement s and gas threshold Cherenkov counter measurements. It is momentum analyzed by a magnet sandwiched between two sets of wire spark chambers which record the recoil proton trajectories. An off-line program reconstructs the event trajectories from the s park positions and another program makes the appropriate cuts to remove all background events. war d elast ic events. We thus obtain the net number of back- We calculate the angular acceptance of our apparatus usin g a Monte Carlo prog ram. We study all sources of in- e[ficiL'1Kies and losses and obtain the values of the various correct i ons necessary to obtain the proper nor mali z ation. to obtain the differential c r oss section for scattering for We are then able pp backward elastic 16 momenta between 0.7 and 2.37 GeV/c incident p momentum in several angular bins for cos eCtn between -1.00 and about -0.88. The Jat a which we obtained agr ee with three other sets of pp - 172 back\vard elastic measurements in the regions where there are overOur data show a sharp dip at 0.95 GeV/c and a broad hump near laps. 1.4 GeV/c when the 180 function of momentum. dicate 0 differential cross section is viewed as a As for the slope away from 180°, our data in- backward dipping below 0.95 GeV/c and backward peaking above 0.95 GeV/c. We do not see any strong evidence for a strong u channel cont r ibulion from a si.ngle Regge trajectory over the entire range of our data. T\1is is not unexpected since u channel exchange for pp elastic interaction would require the existence of particles with B and Q equal to 2. Our data show Such particles are not known to exist. no behavior which can be attributed to any single resonance suggested by previous experiments although the broad hump could be due to the combination of effects from the three possible resonances found in pp total cross section(S.B). Except for very narrow (widths less tha:i 10 MeV) resonances which we may have missed, we believe that our data indicate that the coupling of pp Lo auy r e sonance in our mass region is li.mited to l/2(J + l/2)K e.1 of less than about 0.3. Resonances in our mass range either couple too weakly t o pp or are too close together for any single resonance to reveal itself unmistakably in backward elastic pp scattering. Diffraction dominance appears attractive since diffraction is known to dominate the forward pp elastic scattering and no strong u channel effects are expected (as mentioned above). We have attempted to reproduce our data with a simple diffraction type model and found very good qualitative agreement. This model with the same - 173 va lues of the pn rameters is also qualitatively cons:Lstm1t with otlt1;•r elastic pp data. b. Conclusion Our data revealed that it would not be profitable to search f or unmistakable characteristics of resonances in backward elastic - pp scattering. The resonances are either too close together or couple to pp too weakly for the individual resonance characte ristic to show itself clearly. Thus, resonances in the direct pp channel must be reveale d by other means -- 1) searchin g the inelastic pp c hannels, 2) searc hing the combine d pp mass plot for reactions with p and p in the fin al states, and 3) using phase shift analysis o f pp using elastic as well as polarization data. Our data suggest that diffraction dominance may be approxi- mately true for the entire angular range in pp elastic scatte ring . All the qualitative features of our data as well as other elastic data can be ascribed to diffraction dominance. Although this does not rule out possible resonance effects, it does suggest that resonance contributions in the elastic differential cross sections e ven at extreme large angles, may be small. An accurate polari- ;.-, ation mea sur e ment would do a great deal to strengthen or weaken this possibility. Thus, our data, although it cannot add much to the resonance si tuation, do attractive. enable the diffraction dominance idea to appear more - 174 APPENDIX A: BEAM TRANSPORT SYSTEM The beam transport system we used is the short branch of the partially separated beam No. 5 at the AGS in Brookhaven National Laboratory (2.5) • ) It is shown in Figure 2.1 (page 10 • The system consists of 7 quadrupoles, 3 dipoles, 2 electrostatic beam separators, 2 beam stops, a mass slit and a vacuum system covering the first part of the beam transport. A sextupole exists to correct the chromatic aberration of the beam but was not utilized in our experiment. At the Alternating Gradient Synchrotron (AGS) of Brookhaven National Laboratory (BNL), every 2.4 seconds, an accelerated proton beam of proton intensity between 0.7 to 1.5 x 10 12 particles strikes an internal target (which is flipped into the beam) for a duration of app~oximately 400 msec. The beam transport system we utilized, the partially separate d beam No. 5 , focuses partic 1 es prod uce d at lo to a target at the 10th magnet of the G-superperiod. o The target, a Be wire 1 mm in diameter, is pointed at 10° so as to present the smallest possible source to the beam transport system. The momentum of the beam particle is selected by the first dipole bending magnet while the two electrostatic separators, coupled with the mass slit, reject the majority of particles with the wrong e/m ratio. The first three quadrupoles Q , Q and Q are special magnets 1 2 3 with most of their material above and below · the magnet. cari be placed very close to the AGS main ring. Thus, they Their purpose is to focus .a ll particles of the appropriate mome ntum within a J 14 mr - 175 horizontal and ± 9 mr vertical acceptance into a parallel beam. Such a beam is bent horizontally by the first dipole (the particles o f the desired momentum are bent 6°). Figure A . l shows a ray trace diagram for both horizontal and vertical deviations from the beam line of the extreme angle rays. Q and Q focus the particles of desired momentum p 0 hori5 4 zontally at HO and vertically at V. Particles of slightly different momentum will focus at places which are off to the side of the beam line. This allows us to place momentum slits at the appropriate place s which will cut off all particles with momentum more than a certain allowance from the desired momentum p • 0 slit at H+ 2 For example, the momentmn in Figure A.l is so placed that all particles with mo- mentum above 1.02 p 0 will be removed. During most of our experiment, we set the momentum slit at ± 3 %. All particles are focused vertically at v. This allows us to remove wrong velocity particles (i.e., pions and kaons) by using the two beam separators to deflect these wrong velocity particles ver~ically V. and by using a mass slit with a narrow vertical aperture at The pion background of the p beam is reduced by more than a factor of 50. o2 , which is situated right after q 5 , is used to b e nd the beam to our branch of the beam system. not used. The sex tuple , situated at H , 0 is n3 bends the beam further away from the other branch, sweeps away any low energy junk created at the mass slit and recombinesmomenta at the hydrogen target. Finally, Q and Q f ocus the r e main i n g beam at tl1e targe t a rea . 6 7 ----------------------------------------------------------------------4 ________ !:~~~~·-------\ ~ \ 2 -- v ~ .~ 0 . en .c. )( -2 ' ----------~--I . . Trajectories in Horizontal Projections (x) . -----._ '' -2 \k~ H+2 ~~·t . --- ______ .., . 1L' ', )J -; ·~..,,. I . --ic::::::::: ' , ·j' ' . '.'- ' ~ ' QJ ' ' 0 .c. 0 c: Trajectories In Vertical Projection (y) / P=P0 "" --- - ---p=l.02 ----p-- ------- +2 0 "4 Qc! 03 .1--tt---I ~ ....... Os 04 z (Inches) Figure A.1 Ray traces of the trajectories of particles passing through the beam transport system. . · ·· · · · · · · ·· · · · · ··· · · ·- I-' -..J °' - 177 The size of the beam at the target area, as can be seen in Figure A.l is less than 1-1/2 inches in diameter. - 178 - APPENDIX B: (B-i) WIRE SPARK CHAMBERS Introduction For each incident particle event meeting the trigger condition, we must record the positions of the trajectories of the 1) incident p, 2) the outgoing recoil proton before, and 3) after its trajectory is deflected by the magnet. This is necessary in order to reconstruct the event and determine whether the event is a backward elastic event. We use three sets of four wire spark chambers with magneto- strictive delay line readouts(B.l) to record the three trajectories. The physical construction of the wsc (wire spark c hambers) is described in Section (B-ii). discussed in (B-iii). The high voltag e pulsing system is Section (B- i v) contains a discussion o f the clearing field system which removes ionization products from earlier particle s and sparks. We describe in Section (B~v) the gas system used to maintain a mix ture of neon, helit.un and alcohol vapor needed for optimum sparking characteristics. The magnetostrictive delay line readout system is described in Section (B-vi). Sections (B-vii) contains a discussion of the characteristics and response o f the wire spark chambers, including the r esolution, memory time and recovery time. A brief assessment of the use of thes e wire spark chambers in our e x periment is contained in Section (B-viii). Figure B.l shows a schematic drawing of the components and operation of the wsc. - 179 - Pulsed High Voltoge T wire PLANE B \.--Poth of Ionizing Portico! \ Figure B. 1 Schematic of the operation and components of the wire spark chambers. A spark forms along the path of the ionizing particle. Current £1ows through the wires (denoted by arrows) coupled by the spark. Marker pulses are placed on the magnetostrictive lines by the fiducial wires. - 180 (B - ii) Physical Construction of the Wire Spark Chambers Figur e B-1 shows a schematic drawing of the wsc. The wi re planes each consist of parallel coplanar wires 25 mils thick and th e centers 50 mils apart etched onto fiberglass epoxy sheets 3/4 mil thick. Two wire planes are mounted on a 1/8" thick fiberglass frame so that they are 1/4" apart. The wires in one plane are set per- pendicular to the wires on the other plane. All the wires on each plane are connected to a bus bar (one for each plane). One of the bus bars is grounded while the other is connecte d to the output of the high voltage end of the pulsar system to be discussed in the next section. Magnetostrictive wires are placed between the sensitive areas of the wsc and the bus bar to detect the current of a spa r k. For support, the fiberglass frame is further mounted on a 1/2" thick altnninum jig plate. A mylar envelope is put on the outside of the wire planes to maintain the n e cessary gas mixture between the planes. (B-iii) The High Voltage Pulsing System When a logic signal f rom the trigger logic ar r ives, the wire spark chambers must be triggered. That is, high voltage must be applied between the planes of the wsc in a short time so that the i onization from passing charged particles can be accelerated and made to produce spark avalanches.. certain wi res. This will produce current flow along i The readout system records the information of which wires have current flow and thus allows the positions of the sparks to be determined. The process of pulsing the wsc planes is as follows: - 181 - 1. A pulse driver converts the trigger logic signal into an output of 800 volts with a width of 80 nsec. There is a delay of about 20 nsec between the input and the output. The timing of the pulsing system is included in Figure 2. 14, the timing diagram for our entire recording procedure (pages 53 and 54). 2. The pulse driver output is shared by twelve high voltage pulsers (one to each chamber). The principal elements of the pulser are a storage capacitor and a hydrogen thyratron (B. 2) h T e storage . capacitor, charged to a high voltage of between 4.8 to 5.6 kilovolts, shares its charge with the chamber capacitance through the thyratron, which is shorted about 60 nsec after the pulse driver signal is . received. Tlte thyratron is clamped off by the inductive kickback produced by the trailing edge of the pulse driver pulse. Thus, the chamber capacitance is charged only for a period of 20 nsec. The actual high voltage across the wire plane is about 60% of the original high voltage across the storage capacitor. Since the spark formation time is about 30 nsec, the thyratron is switched off before the dis charge. This limits the energy dissipated and prevents the spark from becoming self-sustaining and damaging the chamber. If the spark discharge does not occur, the chamber is discharged through a bleeder resistance R such that the time constant RC is about 200 nsec. 3. High voltage power supply exists for each pulser to charge the storage capacitor. The actual time of discharge (see Figure 2 .1.4, page 53 and 54) occurs approximately 300 nsec after the event . This delay is imposed - 182 by (a) the counter photomultiplier delay and cable delay prior to the trigger logic, which totals about 100 nsec. (b) the trigger lo- gic module delay of about 50 nsec and (c) the pulsing system delay of about 150 nsec (20 nsec pulse driver delay, 60 nsec thyratron delay and 30 nsec spark formation time plus more than 20 nsec of cable delay). (B-iv) The Clearing Field We apply a DC clearing field across the two planes of the wsc to sweep away ionization from old tracks. A DC clearing field of 17 volts is used which gives the wsc memory time of about 1000 nsec (B • J) • Large amounts o f resi d ua 1 ionization remain a f ter each spark avalanche. These are removed by a pulse clearing field of a few hundred volts which is applied after each pulsing of the wsc. (B-v) The Gas System Optimum response of the wsc is obtained by using a mixture of 4 90% He, 10% Neon and 1% Isopropanol(B. ) (we discuss the response under different circumstances in Section (B-vii)) . This mix ture of gases is maintained between the wire planes using one of the following systems 1. (B .5) : A feed-through system which forces the gases through the wsc mylar envelope using a slight overpressure to maintain flow. There are outlets for each chamber consisting of tubes whose openings are just below the surface of a liquid to allow gas to escape. 2. A r ecycling system which purifies the exhaust gases cycles the gases tj:lrough again. (B ;6) . and re- Small amounts of additional gas are add e d continuously to compensate f or loss throug h leakage. - 183 Both systems bubble the gases through Isopropanol at o0 c which gives the desired proportion of Isopropanol~ (B-vi) The Magnetostrictive Delay Line Readout System The information of which wire(s) carried the spark avalanche current must be obtained so that the spark position can be determined. This is handled by the magnetostrictive delay line readout system. Magnetostriction(B.])' a deformation induced by a change in magnetization, will propagate with the speed of sound. If the material is a wire, the transverse deformation waves can be suppressed. Thus, magnetostrictive waves can travel down a wire. 3 We use a wire made of iron-cobalt(B. ) which is placed next to the wires of each plane (see Figure B.l). The current going to or coming from the bus bar must pass over the readout wire. This in- duces a magnetostrictive deformation wave in the wire which is propagated to both ends of the wire . The wave is damped at one end . The wave is picked up at the other end by a coil of wire and amplified into a signal. Fiducial wires (see Figure B.l) marking the limits of the sensitive areas are placed over the readout wire and are pulsed every time the wsc is pulsed. This provides reference signals from which the spark signals can be calibrated. The de- formation wave in the wire we use has a velocity of 5.2 x 10 5 cm/sec. This allows the position of the spark current wire to be determined w.r.t the fiducial wires through the time delay between the arrival of the two pulse signals. The output of the readout amplifier for each coordinate is tt·ansmitted to the readout wire of the next coordinnte through a - 184 transmitter (see Figure 2.13, top half, page 47). So, the entire spark signals from all 12 wsc come in a single wave train. This serial readout signal train is handled by the digitizer, as described in Section (d-i) of Chapter II (page 44). That section also contains a brief discussion of the merits and faults of the serial readout system. (B-viii) Characteristics and Response of the Wire Spark Chamber System In this section, we discuss the various characteristics and responses of the wsc, including memory time, recovery time, and resolution. Memory time We have applied a DC clearing field of 17 volts across the wire 3 planes, restricting the memory time of the wsc to about 1000 nsec(B. ). The memory time has to be within certain limits. The actual spark chamber discharge occurs approximately 300 nsec after theeJent (mentioned in page 181). Thus, the memory time must be at least seve- ral factors larger than this number. In our case, we have verified that the memory time is at least 100 nsec more than the 300 nsec normal spark discharge delay. This is done by artificially delaying the wsc discharging by 100 nsec. No appreciable decrease in effici- ency is observed. On the other hand, we are limited by the rate of incident particles. Since the beam halo rate is as much as 1/2 megacycle, one particle arrives each 2000 to 4000 nsec . Thus, to prevent the recording of too many spurious tracks, we would like to have the - 185 memory time as short as possible. Since the memory time has to be at least of the order of 300 nsec, we have chosen 1000 nsec as a s•fe compromise. In order to decrease the number of extra tracks, we use a pile-up gate which prevents any p that comes within 500 nsec of any previous particle from initiating a trigger. reduced our useful p flux by 15 to 30 percent. This actually Most of our extra tracks come from passage of particles during the 300 nsec between the event and the spark discharge. Recovery time After each spark avalanche, there remain electrons, ionized ions and energy stored as met~stable atoms which could give delay ionization. If these are not removed prior to the next pulsing of the wsc, another spark avalanche will be initiated at the same spot. This is clearly undesirable. We want as few extra sparks as possible. Thus, these electrons, ions and metastable atoms must be removed. The mobility of the electrons in our gas mixture is of the order of 10 3 2 cm /sec-volt which gives a clearing time of about 10 microsec for 17 volts across 1/4". So the electrons cause no problem. 2 . The ion mobility is much slower -- about 2-5 cm /sec-volt which imply a clearing time of about 10 msec. We speed this up by applying the pulsed clearing field of several hundred volts so that the ions are removed in about 1/4 of that time. Residual energy from a discharge can be stored as metastable atoms which could produce delay ionization up to 100 msec. However, isopropanol vapor, having low l e vel ionization energies, tends to absorb the energy from metastable atoms and get ionized. This - 186 process, called "quenching", allows the stored energy to be dissi9 pated within about 10 msec(B. ). Hence, the recovery time for the wsc is approximately 10 msec. We impose a dead time of 20 msec between successive trigge r s to safely allow the wsc to recover. This is done by gating several critical beam counting modules and trigger logic modules off for 20 msec after each trigger. Spark position determination The measured spark positions may deviate from the actual spark positions for many reasons. The spark chamber inherently possesses several sources which contribute to this problem~ Spark jitters(B.lO), defined as displacement of the spark from the real path of the ionizing particle, are a function of the gas composition, the DC clearing field strength, the amount of delay prior to sparking and the angle of incidence o f the particle path. Quenching vapor (in our case, the isopropanol) restricts the avalanche to the region of the primary ionization electrons. Hence the size of the spark jitter would be inve rsely correlated with the number of primary ionization electrons. We used an optimized mi x ture of 90% He, and 10% Ne which has a primary ioni z ation density of 22 cm-l This·gives an average standard deviation of the spark position of ± 0. 4 nun (B • 1l) • Primary electrons may dri ft due to the DC clearing field. If the ionizing particle enters at an acute angle, this dri f t will affect the position resolut ion. The size of the de v iation would be depend- ent on the angle of incidence and d e lay in sparking. - 187 In addition to these inherent deviations, two other items affect the resolution: the wire spacing and the digitizing frequency. The wires are spaced 1.25 mm apart. The current flow in each wire is proportional to the strength of the coupling between the spark and the wire when more than 1 wire carries current from the same Thus, the spark determination could be better than ± (1.25 mm)/2. spark. We use 10 megacycle scalers to clock the signal in the digitizer. The position is thus quantized in steps of 0.52 mm (the velocity of . the magnetostrictive wave being 0.52 x 10 7 mm/sec). This limits the spark determination. All these factors suggest that the deviation in the determination of spark position should be of the order of 0.5 mm. A study of the distribution of sparks for straight tracks shows a standard deviation slightly less than 0.9 mm. Two-spark resolution The two-spark resolution is limited by the size of the pick-up coil and is about 3 mm. However, since we require only one track in each chamber, this fact is unimportant for this experiment. (B-viii) Assessment of the wsc System in Relation to our Experiment We assess our wsc system in terms of spark position determination, repetition rate and time lost due to wsc failure. Spark position determination Does the deviation in spark determination affect the momentum determination significantly? 250 mr . The typical bending by the magnet is The lever arms of the two sets of wsc to either side of the magnet are about 60 cm. A deviation of 1 mm would imply an error of - 188 1.7 mr in angle. Therefore, we expect a possible 3/4% error in mo- mentum determination from chamber position determination alone. This is not excessive since multiple scattering and beam spread cause similar deviations in momentum determination. The over-all result in momentum determination is shown in Figure 2.7c (pa ge 29). Considering the various inherent deviations whi c h cannot be removed, the position determination of our wsc is as well as can be expected. Repetition rate 20 msec dead time is a significant waste. If we have 15 triggers per pulse, at least 75 % of the beam is wasted. However, the recovery time of 10 msec cannot be reduced unless we do not spark our chambers (which could be achieved by using wire proportional chambers (2.39) ). Fortunately, this was not necessary since our trigger rate was not always so high. On the average, we used 60 % of the beam. Time lost due to wsc failure 10% of useful beam is lost due to failure of the wsc system. Some typical problems include gas system trouble, pulser failure, 2 etc.(B.l ) quate. The operation during the rest of the time is quite ade- - 189 APPENDIX C: (C-i) INEFFICIENCIES IN RECONSTRUCTION OF TRIGGERED EVENTS Introduction As we mentioned in Section (b) of Chapter III, there are in- efficiencies in reconstruction of events. We quoted a backward elastic events due to these inefficiencies. 5%loss of In this appendix, we elaborate on the methods we use to derive this number. In Section (C-ii), we describe two major tools we use to study the inefficiencies. Section (C-iii) contains a description of the sizes of the inefficiencies and the methods we use to obtain them. Reconstruction is inefficient only if: 1. Some of the tracks associated with the backward elastic event were not .found. 2. The event associated track was mistakenly discarded in the spuriou s track removal procedure. 3. Reconstructed tracks give kinernatical or topological reconstructed quantities which differ from the actual quantities by sufficient amounts to make us discard the event. We find that there is a 3% inefficiency in the trackfinding procedure in re g ions 1 and 2. There is also a 2% inefficiency in the extra track removal procedure. No loss due to item 3 above is found. (C-ii) Tools used to Study Reconstruction Inefficiency Two important tools are used to study the reconstruction inefficiency: 1. Scanning and detailed study of selected events. . (C.l) A spec i a 1 program h as b een written . When it is us e d with the reconstruction program, we obtain for each event (or selected - 190 2 . . h t h e positions . . even t s ) a Ca 1 comp p 1 otter (C • ) picture wit o f the sparks from the wsc plotted geometrically. pictures for several events. Figure C.l contains For each event, there are two views a horizontal view with the sparks from regions 1,3, and 5 and a vertical view with sparks from regions 2, 4, and 6. This allows us to treat the wsc data like optical spark chamber pictures. We per- form various optical scans to check the reconstruction procedure. The program also prints out the raw spark positions, the counter bit information, the track(s) found in each region and the tracks accepted by the spurious track removal procedure. For each track, we print out the positions of the sparks associated with the track, the extrapolated slope and intersect (at z chi-square of each fitted track. = 0 plane) and the This allows us to make a detailed study of pathological events. 2. Modifying the reconstruction procedure A mo d ified version of the reconstruction program written to check the reconstruction procedure. (C. 3) was We concentrate on checking the trackfinding efficiency in regions 1 and 2 where, as we will mention in the next section, sizable inefficiencies are suspected. We also check the spurious track removal procedure by using a different method in removing spurious tracks. To check the trackfinding inefficiencies in regions 1 and 2, the modified reconstruction program bypasses these regions. That is, it creates artificial tracks in regions 1 and 2 designed to give acceptable reconstructed vertex and VD (vertex deviation). Thus, any event with the appropriate tracks in regions 3, 4, 5 and 6 - 191 F i gure C.l : Calcomp plotted pictures of triggered events. (a) An e vent with the desired topology. Note that the tracks from regions 3 and 5 meet very closely at the center of the magnet . So do the tracks from regions 4 and 6. (b) An event with e x tra spurious tracks (dashed lines) in regions 1-4. Ex tra tracks in regions 1 and 2 removed since the extra tracks have wrong slope for beam particle. Ex tra tracks in regions 3 and 4 removed since they do not me e t the tracks fr om reg i ons 5 and 6 at the center of the magnet. Z:Z v-!-I . .i·b ! magnrt centrr I . .....-·- ·-- ·~ :_ . __:_=-~~~ - -target / (b ) region J . I' :· - -. 1 1 -. 1I x Lz I . t .- ~- ..:f:l::t-· - · - -- - - · -· t-tr regiot;l 5 .. ·- - ~ -m~Z=fv ;; region 2 magnet tenter region 4 -- - - - - - - - - 1 z region k ~ - 192 - satisfying the MTD (magnet track deviation), momentum and velocity criteria will be accepted as backward elastic events. Any events gained by this modified procedure could represent inefficiencies in trackfinding(C. 4 ). To check spurious track removal procedure, the modified reconstruction program uses a procedure based entirely on topological quantities VD and MTD. No counter information is used. The com- bination of tracks which give the smallest MTD and then VD are considered the event associated tracks. MTD a and VD a In addition, ambiguity limits are defined (see Figure 3.2, page 79) so that more than 95 % of backward elastic events would have MTD and VD less than these limits. The percentage of events which have more than one com- bination of tracks with MTD (VD) less than MTD (VD ) are obtained a and these events are selected for detailed study. a We can use topo- logical quantities such as MTD, VD and the information on whether 5 the tracks in regions 4 and 6 are parallel(C. ) to help us decide whether the combination of tracks with the minimum MTD and VD are indeed the best choice. (C-iii) A. The Sizes of the Reconstruction Inefficiences Inefficient Trackfinding (i) Given the existence of the sparks, the trackfinding inefficiency is less than 1%. Given the existence of the sparks from a track, trackfinding is inefficient only if there are program errors or misalignment of sparks. Program errors include the slope and straightness require- - 193 ments of the reconstructed tracks. Misalignment due to multiple scattering or chamber resolution may cause significant numbers of tracks to b e rejected by the slope and straightness criteria. For each tra<·.k .found, we calculate a chi-squarE' asHwnjng s tanda rd devlattonH of 0.5 cm. Al.J tracks with chi-,.;quare greater than 6.6 are rejected. A survey of several hundred tracks f or backward elastic events reveals that about 97 % of tracks have chisquare less than 0.5 and only 1/2% has chi-square exceeding 1.0. Since the chi-square distribution is expected to be a Poisson distribution, this implies that the cutoff at 6.6 is safe. l~ Much less than of true tracks should have chi-square exceeding that number. Thus the straightness criterion has inefficiency less than 1%. There is also a slope criterion on the tracks found. In regions I, 2, 3 , 4, and 6 only those tracks which extrapolate through the target is acc e ptable (no slope criterion for tracks in region 5 is possible due to the bending of trajectories through the magnet). A study of several hundred backward elastic events reveals that there a are no events with track slopes in those regions which are anywhere close to the limits set. This implies that any loss due to the s lope criterion is unlikely. Thus, the inefficiency in the slope criterion is again less than 1%. (ii) There is an apparatus inefficiency of between 0 to 5% causing missing sparks. This is discussed on page 88 and this inefficiency is not considered a reconstruction inefficiency. This inefficiency is obtained by assuming the wsc inefficiencies to be uncorrelated. - 194 (iii) In the absence of more than 1 track in each region, the apparatus inefficiency mentioned above does reflect the actual inefficiency. If there are no other spark(s) besides the 1, 2, 3 or 4 sparks of a single tracks, we can check for correlated inefficiency easily by scanning. Knowing the number of 4-spark and 3-spark tracks gives us some idea of the number of 2 spark tracks to expect assuming no correlated inefficiency. A scanning of about 500 pictures of events shows that the number of 2-spark tracks is as expected. Thus, in this case, the uncorrelated apparatus inefficiency does reflect the actual inefficiency. (iv) In the presence of more than one track or extra spark, the apparatus inefficiency still reflects the actual inefficiency in regions 3, 4, 5, and 6. Correlated inefficiency exists in cases where there are more than one track. Wsc sparking efficiency for two sparks is much less t h an t h e spar k ing e f ficiency for one spar k (C.6) • In our case, the fact that we accept a maximmn of 4 sparks per wsc may also contribute to correlated inefficiency. ficiency is expected. Therefore, additional correlated inef- We will consider this a reconstruction in- efficiency. The size of the inefficiency would be correlated with the percentage of time more than one track wsc. goes through a particular set of By scanning about 500 e vent pictures, we conclude that the additional correlated inefficiency in regions 3, 4, 5, and 6 is less than 1%. Multiple tracks exist for about 15 % (S j J for all trigg ered - 1 95 events in regions 3 and l; (.5 a nd 6). Sc ann ing s hows that th e amount of event s wh ere there is (in either regions 3, 4 , 5, or 6 ) one track with two other spar ks possibly from another t rack is as expected if t h e uncorr e lated a pparat us ine ffic iency re flects the ac tual ineffic iency. ( v.) In the presence of more than one the ~_e t r~c k or extra spark, is, in re gions l and 2 , an addit iona l correlated ineff icienc y o f 3%. About SO °fo of triggered events have multipl e tracks in reg ions l a nd 2 . Scanning i s not very us eful since there are many extra tra c ks or sparks i n the be am track region. Even though there are an average of 1.25 beam t racks p er event, the number of events whe r e no b e am tr acks are fou nd c a nnot be accounted for b y the un correlated wsc ineffic iency a l one. The trigger requireme nt i s such that a particle must h ave gone through regions 1 and 2 . Thus , ad ditional correlated ineff icie nc y is suspected. The modifi ed reconstr u c tion program giv es us the s i ze of th is cor r e l ate d ineff iciency. 1 and 2, we ge t By b y p assing the track find i n g i n reg i ons N b ac kwa rd elas tic even ts, where the n orma l p ro - cedure gives us M events . Note th at for the se studies, the ver t ex cut is not made since the v ertex informa tion is lost b y not finding the b eam t rack . thus X c The correlated i neff i c i ency in regions 1 and 2 is = (N - M)/N - Xunc where Xu nc i s the u ncor r elated wsc ineff iciency in region s 1 and 2 . We hav e applie d thi s p roce dure to 5 se t s o f data r un s and obtained th e following resu l ts : - 196 Date name and momentum M (N - M) (N - M)/N A(0.812) 108 3 2. 7 ~, 0.1 % 2 .6 <fr, B(l.590) 91 3 3.21, 0.8% 2 .41, C(l.844) 262 11 4.0<fo 1. 7% 2 . 3 ~, D(l.338) 227 23 9.2<fo 2.9<fo 6 .3<fo E(l.797) 460 16 3.4% 1.3% 2 .1 % Total-weighted average 1148 56 4.7 % 1. 7% 3.0<fo x x unc c We have .studied the possible correlat i on between X and such c factors as uncorrelated wsc inefficiency in regions 1 and 2, incident flux density and incident momentum. B. No str ong correlation was found. Inefficiency in Spurious Track Removal About 30% of the events with sufficient tracks to be tested for backward elastic events have multiple tracks in some region. We check the spurious track removal inefficiency by usin g the modified procedure mentioned in page 190. In the modified spurious track removal procedure, we pick the combination of tra cks with the smalles t MTD and VD. A study of several hundred events with e x tra tracks convince us that the amount of ambiguous events is less than 2<fo . The se ambiguous events are those which have two or more combinations of tracks with MTD or VD which are reasonable (i.e., within the ambi guity limits as defined in page 192). Thus, the ove r-all normalization correction needed for all the events is l e ss than 30<fo times 2% = 0 .6 °fo which we shall neglect. Thus, the modified spurious track removal procedure is less than l °/o ineffi cient. - 197 We obtain the spurious track removal inefficiency of our normal reconstruction procedure by finding the number of events gained by the modified procedure. Data name and momenttnn We find the inefficiency X Normal procedure Modified procedure xstr A(0.812) 108 110 1.8% B(l.590) 91 97 6.6°fa C(l.844) 262 267 1.8% D(l.338) 227 230 1.3% E(l. 797) 460 468 1. 7% Total 1148 1172 str is 2 .1% which we round off to 2.0'fo Note that this actually constitutes an inefficiency in the spurious track removal procedure of about 7% since only 30% of the reconstructed events have multiple tracks. C. Inefficiency due to Reconstructed Values Differing from Actual Values of the Kinematic or Topological Quantities This inefficiency arises from the various selection cuts we use in obtaining the backward elastic events. We consider this inefficiency to be selective cut inefficiency and study it in the the appropriate section (Section (c) of Chapter III). We sununarize the reconstruction ine fficienci e s her e. an additional correlated ineff i ciency in regions 1 a nd 2 of There is 31.. There is also inefficiency in the spurious track removal procedure of 2'fo. Thus, there is a total reconstruction inefficiency of 5 %. - 198 REFERENCES 1.1 For example, resonance contribution in the s channel gives a Breit-Wigner amplitude for a particular spin wave. ] •2 0 For L greater than O, the amplitudes, which are functions of PL , PL 1 - and (for pp) P 1 2 , tend to give stronger contributions near: the extreme angles. I. 3 Resonance amplitudes arc Breit-Wigner functions. at the position of the resonances. Thus they peak Backward peaking comes from the PLO term in the resonance amplitude. 1.4 Kormanyos et al., Phys. Rev. 164, 1661 (1967). 1.5 See, for example, Chapter 9 of "High Energy Collisions of Elementary Particles" by Eden, University Press, Cambridge, 1967. 1..6 A.S. Carroll et al., Phys. Rev. Letters l!, 1282 (1969; and S. Tewksbury, 1.7 thesis, University of Rochester (unpublished). 11 "Exotic r e sonances are those which cannot exist und e r the simple quark model (where all baryons are made up of three quarks and all mesons of quark-antiquark). For example, Z*(B = 1, S = 1) is exotic. 1.8 We discuss this in Chapter v, Section (c-i). The January 1970 data booklet by the Particle Data Group (LRL and CERN) con- tains a table of many heavy meson resonances (pp. 20 and 21). ' 1.9 We discuss this in Chapter V, Section (c-ii). 1.10 J.K. Yoh et al., Phys. Rev. Letters 11, 506 (1969). - 199 1.11 H. Nicholson et al., Phys. Rev. Letters 23, 603 (1969); and B.C. Barish et al., Phys. Rev. Letters 23, 607 ( 1969). 1.12 (K-p) A.S. Carroll et al.' Phys. Rev. Letters 23' 887 (1969). (K+p) A.S. Carroll et al.' Phys. Rev. Letters Q, 1282 (1969). + (rr- p) A.S. Carroll et al.' Phys. Rev. Letters 20, 607 (1968). 2.1 For example, both BNL and CERN have partially separated beams in this momentum range. 2.2 If the forward proton in a pp interaction is a result of elastic scattering, the momentum is significantly higher than if the scattering is inelastic. 2.3 Knowing the velocity and momentum of a particle allows us to ' determine the e/m ratio and thus the type of particle it is. 2.4 Multiple scattered events are difficult to handle and therefore they are discarded. We account for this in our Monte Carlo program when we calculate the solid angle acceptance. 2.5 Designed by B. Barish of Caltech and T. Kycia of BNL. This beam covers the momentum range of about 0.7 GeV/c to 2.4 GeV/c (up to 3 . 0 GeV/c for the other branch of the beam) and provides about a factor of 100 in reduction of pi's for a p beam. 2.6 Cherenkov radiation is emitted whenever a particle in a medium has velocity faster than the speed of light in that medium. The standard reference for Cherenkov radiation is Jelly's "Cherenkov Radiation and its Application", Pergamon Press, New York (1950). The liquid differential Cherenkov counter - 200 we use was constructed by B. Leonti.c and associates of BNL. We thank him for permission to us e this count er. 2.7 s 3 is placed as close to the target as possible since we are using it to aperture the beam, which we want to pass through the target . 2.8 We used wire spark chambers constructed by J. Fischer of the Instrumentation Division of BNL. See report No. 11031 (BNL) by J. Fischer titled "Digitized Spark Chambers in HighEnergy Physics". 2.9 The gas threshold Cherenkov counter was loaned from W.A. Wentzel of Berkeley for which we thank him. The optics of this counter are more suitable for a target situated closer to the counter. Fortunately, the mirrors are adjustable. Thus the performance of this counter is acceptable for the geomentry of our experiment. 2.10 See Appendix B, Section (B-vi) for a discussion of the recovery time needed for the ionization from previous sparks to dissipate. 2.11 See Figure 2.8 (page 33) for an idea of the loose momentum cr i terion imposed by the combination of P-R counters. 2.12 Most of the spurious tracks resulted from the delay between the event and the spark discharge. It takes approximately 300 nsec to apply high voltage to the wsc. 2.13 The sizes a~d positions of these counters are given in Table 2.1. These counters have 3' air light pipes. 2.14 See Figure 2.14. See Figure 2.14 for the timing diagram. - 201 2.15 Chronetic logic modules were on loan from BNL HEP . 2.16 These distributions were obtained from wsc reconstruction of beam tracks. 2 .1 7 Wsc resolution and multiple scattering accounts for a large portion of the spread in momentum and slopes but is not important for the spread in position of the beam. 2.18 The target was constructed and maintained by the BNL AGS target group. 2.19 The vent tube is directly connected to atmospheric pressure. We found that the boiling rate is such that the volume of bubbles inside the target is less than 1%. 2.20 The gap between successive plates of iron increases the magnetic impedance between the plate. The inner plates became' sa- turated before the nex t plate was coupled strongly into the magnetic circuit . 2.21 The nuclear magnetic resonance probe meter s we re manufactured by Varian Associates. We used H 0 and 2 n2 o as samples in the probe. 2.22 S. Tewksbury, thesis (University of Rochester) unpublished, 1969. He studied the magnet n of this e x periment in great detail 4 including doing a field map of B ( x,O ,z) along z f or several y x value s at many momenta to obtain parameters f or a particular parameterization by Danby et al. ("Thr ee -dimensional projection of magnetic beam transport elements" in Proc. of Particle Acc. Conf., Washington D. C., Mar ch 1-3, 1967). This paramet er i z at i on was verified at B = 11 Kgauss b y - 202 - measuring the values at y = + 8". The predict e d value s and measured values di f fer by less than 0.3%. 2.23 As we will mention in Se ction (B-viii) of Appe ndix B, wsc position determination would cause a momentum spread of about 3/4'fo. 2.24 This is limited by the size of the buffer in the PDP-8 since we write the events on tape only at the end of each pulse of the beam. During the first part of the e x perime nt, only 10 triggers per pulse are taken. 2.25 Logic modules used are Chronetic 100 megacycle logic modules borrowed from BNL HEP. 2.26 We are saturated only during the high mome ntum runs. For the remaining momenta, a 40'fo reduction in tri g ger rate is not very useful. For e x ample,if we have 5 trigge rs per pulse, reducing the trigger rate by 40 'fo would enable us to use 13% more beam. 2.27 . . Curren tl y, we are ana 1 yzing pp into pi.+ an d r h o and preliminary results are e x pected in a few months. 2.28 Half of the counter bits use EG & G electronics modules. The other half use electronics made at Caltech by A.V. Tollestrup. 2.29 - - + could result in the pion having mo- For example, K p into pi E mentum higher than the initial state kaon. 2.30 At the pressure we are using, the Freon-12 will condense if the temperature is below 25°c. 2.31 We used RCA-7046's borrowe d from T. Kycia of BNL. Although the i r - 203 quantum efficiency is low, they are quite fast (2 nsec rise time). · 2.32 Quantum efficiencies of 20% are possible. For example, RCA 4522's are S" tubes with fast rise times (2.5 nsec) and high quantum efficiencies (up to 29%)• 2.33 However, they cost $900 apiece. A liquid Cherenkov counter considered for another part of this experiment. We could have built a liquid Cherenkov counter with threshold of 1.0 GeV/c for protons had it been needed. 2.34 The preliminary analysis is done at the CDC-6600 computer usually within 5 hours of the data taking. 2.35 The interfacing uses modules manufactured by Computer Control Co. Inc., Framingham, Mass. The interfacing, digitizer, and PDP-8 programs were designed and written by H. Pate and modified by A. Entenberg (Rochester University), B.C. Barish and A.V. Tollestrup. 2.36 The positions of the wsc and fiducials were surveyed to 1/16" both when they were installed and when they were removed. 2.37 The digitizer is designed and constructed .by the instrumental division of BNL. It includes 4 scalers (Texas Instrument Co., modified to count in base of 8) and an oscillator (10 MHz Tektronix time mark generator) with several fast logic modules (developed at BNL; R. Sugarman, F. Merrit, W.A. Higginbotham, Nanocard Counter Circuit manual, BNL report 711 (T-248)). 2.38 The PDP-8 uses 12-bit words. Thus, 5 PDP-8 words are combined : to form a CDC-6600 60-bit word. - 204 2.39 G. Charpak et al., Nuclear Instr. & Methods 62, 262 (1968). 2.40 This is not absolutely true since for a particular incident momentum, some process like pp into pi and A could resuJt in 2 large numbers of forward pions with mome ntum close to incident momentum. However, the width of the A 2 and the fact that we are using wrong kinematics (i.e., assuming proton forward) will spread the enhancement out so that any en hancement would be very weak compared to the elastic peak. I 2 .4 1 Methods for determining energy of particles includes total absorption counters and range counter. Their resolution and efficiency are much worse than magnet-wsc spectrometers. 3.1 The first stage program is written by A.S. Carro l l and the second stage program by A.S. Carroll and the author. 3.2 These reconstructed quantities may be different from the actual quantities. This will be considered in later discussion. 3 .3 The Monte Carlo program is written by Y. Nagashima. 3.4 The positions of the fiducials are surveyed. 3.5 The trackfinding procedure is modified by M. Hind from a pro gram used in a CERN experiment. 3.6 This is true to robbing of energy between sparks. 3.7 See Section (C-ii) of Appendix C. 3.8 Bricman et al., Physics Letters 29B, 451 (1969). 3.9 See Section (C-ii) of Appendix c. 3 .10 See reference 2.40 above. 3.11 As mentioned in Ref. 2.40 above, pi 0 ns could have a weak en - - 205 hancement underneath the elastic peak. Thus, we do not correct for. the loss at each momentum separately since chance coincidence could put the pion enhancement either in our signal bins or background bins (see the next section (c-v)) at a particular momentum. 3.12 The studies indicate that the correction at each momentum ranges between +7% to -2%. However, the statistics are poor usually based on less than 10 events. 3.13 R.J. Abrams et al., Phys. Rev. Letters 18, 1209 (1967); C. Daum et al., Nuclear Phys. B6, 617 (1968). 3.14 Our criteria for backward elastic events will only reject about 35% of events with additional forward elastic scattering of incident p. 3.15 Although the actual distribution is not really a gaussian, the approximation is sufficiently adequate. 3.16 A simpler Monte Carlo program has been written by the author to check the program written by Y. Nagashima. 3.17 Written by the author. 3.18 At one atmosphere near boiling point. 3.19 Usually, we have between 25 to 200 events per bin. 3.20 See reference 2.40, 3.21 For example, additional scattering in the magnet region will not allow us to determine the momentum of the particle. 3.22 In our data tape, each event record is a separate block. had If we put several records in each block, the tape reading time would have been drastically decreased. - 206 3.23 As we mentioned in the previous chapter, the re is a PDP-6 at the AGS which we could have used. 4.1 The standard least-square fitting procedure involves minimizing the chi-square by flipping the error matrix. See page 365, Mathews and Walker, "Mathematical Methods of Physics", Benjamin, New York (1964). 4.2 D. Cline et al., Phys. Rev. Letters ±_l, 1268 (1968). 4.3 W.A. Cooper et al., Phys. Rev. Letters 20, 1059 (1968). 4.4 J. Lys et al., Phys. Rev. Letters ±_l, 1116 (1968). 4.5 D. Cline has informed us of pp bubble chamber film up to 0.85 GeV/c which is under analysis. Mendelkern of UC Irvine was reported to have pp bubble chamber film near 1.0 GeV/c under analysis. 4.6 See Figure 2.7 (page 29) for a distribution of incident momentum of p's hitting each mass slit counter. 5.1 If a(O) of a trajectory is -3.5, then the physical states lying on this trajectory would have mass higher than about 2 GeV if the slope is 1 GeV -2 This would be in agreement with the trajectory being a dibaryon trajectory (masse s would be expected to be heavier than two protons). However, note that the u dependence of our a(u) is about 3 GeV -2 . If this is true, then one might expect mass states of about 1 GeV. 5.2 See, for example, page 19 of "Meson and Baryon Spectrosco~ by D.B. Lichtenberg, Springer-Verlag, New York (1965). '· - 207 5.3 This idea was suggested both by Professor Frautschi of Caltech and Dr. A.S. Carroll of BNL. 5.4 For a general discussion of angular distribution of scattering cross sections, see Blatt and Biedenharn, Rev. Mod. Phys. 1 24, 258 (1952). A more detailed discussion of the pp elastic system is contained in Lys, Phys. Rev. 186, 1691 (1969). 5.5 It is easy to demonstrate that pp is 1/4 singlet and 3/4 triplet. pp is 1/4 abnormal triplet and 1/2 normal triplet since there is L L 3 1 = J abnormal triplet states and L 2 + = (J + 1) +(J - 1) = 2J normal triplet states. 5.6 r. Blatt and Biedenharn, Rev. Mod. Phys. 24, 258 (1952). 5.7 M.N. Focacci, et al., Phys. Rev. Letters 11.., 892 (1966); and R. Baud et al., Physics Letters 30B, 129 (1969). 5.8 R.J. Abrams et al., Phys. Rev. Letters 1.§., 1209 (1967). 5.9 E.W. Anderson et al., Phys. Rev. Letters 22, 1390 (1969). 5.10 Yen at Argonne has calculated the positions of the expected enhancements due to pi minus p going to (N or N*) and (pi or rho) for the particular geometry of the experiment of An.-Jerson (ref. 5.9) at the suggestion of C.N . Yang. The positions correspond to the positions of the btnnps found in the experiment. Thus, kinematic enhancement is likely. However, to have the size of the bumps as observed, the coupling would have to be very strong. 5.11 M. Ad e lholz et al., Nuclea r Phys. Bl4, 255 (1969). 5.12 Diamond (Wisconsin -W.D. Walke r group) privatE:~ commun :i.ca tion. - 208 5.13 D. Cline et al., Phys. Rev . Letters l.l, 1268 (1968). 5.14 W.A. Cooper et al., Phys. Rev. Letters 20, 1059 (1968). 5.15 Ka l bfleisch et al., Physics Letters 29B, 259 (1969). 5 . 16 G.A. Smi t h (Michigan State), private cormnunication . 5.17 J . Lys et al., P hys . Rev . Letters ll, 1116 (]968). 5.18 C. Bricman et a l . , Ph ysics Letters 29B, 451 (1969). 5.19 D. Fong, thesis (Caltech, 1 968) a n d ri . Fong et al., to be published . 5 . fO H . Nicholson et al., Phys . Rev. Letters 23, 603 (1969) and Caltech report CALT-68 - 197. 5 . 21 J.W. Chapman et al., Phys . Rev. Letters ll, 1718 (1968) . 5.22 G. and S . Gold h aber, i n "Advan ces in Particle Physics" edi t ed by Cool and Marshak, Interscience, New York (1968). 5.23 D.Z. Freedman and J.M . Wan g, Phys. Rev. 153, 1596 (1967). 5.24 M. Gel l -Mann, Physics Letters ~' 214 (1964); and G. Zweig, CERN preprint 8419/Th. 412. 5. 25 The 0 -+ includes :n:, ·k K (890), 5 . 26 K, r1 and probably xo. m, and cp . The 1 includes (.) , The 2++ includes A , K* (1420), f 0 and f'. 2 See Ref. 5.22 and Da l itz's article in "Proc. of 12th Intern ational Conf. on High - Energy Physics" UC Press, Berkeley (1967). 5.27 The positions and widths of the 3 and 5 are 2.12 GeV (less than 250 MeV wide) and 2290 MeV (less than 165 MeV wide). These can be identified with the L = 4, I = 1 states in Figure 5.3c. 5.28 Radial e x citation in the qq model would allow low-ly ing trajectorie s in addition to those in Figur e 5 .3. - 209 5.29 We use the mass slit counter information for this study. See Figure 2.7 (page 29) for the distribution of incident momentum for particles hitting each mass slit counter. 5.30 See Section (b-ii) of this chapter. 6.1 Usually, the diffractive background is treated apart from exchange and direct channel resonance effect and one writes A= Ad.ff+ Ad ua 1 where Ad ua 1 is either Ares or Aexc 1 6.2 See, for example, Coombes et al., Phys. Rev. 112, 1303 (1958); and Armenteros et al., Phys. Rev. 119, 2068 (1960). 6.3 See Ref. 6.2 and, for example, Greider and Glassgold, Annals of Physics ..!Q, 100 (1960). 6.4 It is possible that antishrinking continues at higher momentum so that the radius of pp elastic diffractive peak approaches that of the pp elastic diffractive peak, which is about 0.7 Fermi. 6.5 See Figure 6.2 6.6 Diffractive minimum arises due to interference of the partial waves. Diffractive minimwn should be at constant t at small angles but should be at lower t at large angles . Letters~' 6.7 D. Cline et al., Phys. Rev. 1268 (1968). 6.8 C. Daum et al., Nuclear Phys. B6, 617 (1968). 6 ,.9 J. Berryhill and D. Cline (private connnunication-Wisconsin), and B.C. Barish e t al., Phys. Rev. Letters .lZ., 720 (1966). 6.10 The diffraction scattering can be viewed as shadow scattering of the absorption of the wave by inelastic processes. - 210 6.11 Frahn and Venter, Annals of Physics]]_, 135 (1964). 6 .12 Goldberger and Watson, ' "Collision Theory" (New York, Wiley, 1964) contains a rigorous derivation of the scattering matrix of two fermion systems (Section 7.3). 6.13 See. Ref. 6.11 and also E. Fermi, Nuovo Cimento II, Supp. 1, 84 (1955). 614. For example, the model of Ref. 6.11 allows the radius of the + 1 term to be different from the radius of the J L J L - 1 term. 6.15 T.T. Chou and C.N. Yang, Phys.Rev. 170, 1591 (1968). 6.16 For references on quark model, see references 5.22, 5.24 and 5.26. The parton model might be considered a generalization of the quark model and is developed by Feynman. that the proton contains point-like constituents. It assumes See S.D. Drell et al., Phys. Rev. Letters 22, 744 (1969). B.l Constructed by J. Fischer of BNL. B.2 The pulsers were manufactured by Instrumental Division of BNL. B.3 Ref. 2.8, Figure 5 is a plot of sparking efficiency vs. delay for different values of the DC clearing field. B.4 Isopropanol, spectral grade, obtained .from Kodak Co. Roc hester, N.Y. B.5 The feed-through system was used during the early part of this experiment. The recycling system was constructed by R.H. Phillips. B.6 The major contamination is water vapor. This is removed by - 211 running the exhaust gas through a liquid nitrogen cooler to condense the water vapor and also through some activated charcoal to absorb other impurities in the gas. B.7 See R.M. Bozarth, "Ferroril.agnetism" D • .Van Nostrand, New Jersey, (1951), pages 595-712. B.8 The iron-cobalt wire supplied by W.B. Driver Co., Newark, New Jersey, under thetrade name Remendur. B.9 This is achieved with about 1% isopropanol vapor. B.10 Similar to the spark jitte~ observed in optical spark chambers (see O.R. Frisch (editor), "Progress in Nuclear Physics", Vol. 9, McMillan, New York (1964) pages 3-26 ). B.11 100% He, 75 % He/25% Ar and 90'fJie/ 10% Ne gives primary ioni zation densities of 5, 14, and 22 cm -1 , respectively, which imply average standard deviations of ± 0.8, ± 0.5 and ± 0.4 mm, respectively. B.12 Among the major sources of wsc failure are gas flow stoppage, impurities in the gas, too much or too little alcohol in the gas, etc. C.l Written by A.S. Carrol l . C.2 Manufactured by California Computer Products, Inc. C.3 Modified program called ROCHEK developed b y the author. C.4 As mentioned in Chapter III, only backward elastic s c attering would r e sult in a forward proton with momentum close to the incident momentum. C.5 Since the b e nding magnet should not alter the vertical trajec- - 212 0 tory, the track in regions 4 and 6 should be close to parallel. C.6 Multi-spark efficiency is reduced due to robbing of energy. In our case, the two-spark efficiency is still of . the order of 90% and is usually acceptable.