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Measurement of the total cross section for the π - 2π reaction p(π⁺, π⁺ π⁰)p near threshold Suen, Nelson 1993

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MEASUREMENT OF THE TOTAL CROSS SECTION FOR THE it-27rREACTION p(Π+,Π+Π0)p NEAR THRESHOLDNelson SuenB.A.Sc. University of British ColumbiaA THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF PHYSICSWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAAugust 1993© Nelson SuenIn presenting this thesis in partial fulfilment of the requirements for an advanced degree atthe University of British Columbia, I agree that the Library shall make it freely availablefor reference and study. I further agree that permission for extensive copying of this thesisfor scholarly purposes may be granted by the head of my department or by his or herrepresentatives. It is understood that copying or publication of this thesis for financial gainshall not be allowed without my written permission.Department of PhysicsThe University of British Columbia6224 Agriculture RoadVancouver, CanadaV6T 1W5Date:o Avr.44 ici13AbstractA feasibility study for measuring the total cross section of the 71--27 reaction, 71- +p --> 7r ± 7r°p,was performed at incident pion kinetic energies of 195 and 201 MeV. It was not possibleto measure the total cross section with the present apparatus. Modifications andimprovements to the present apparatus are presented.iiTable of ContentsAbstractList of Tables^ viList of Figures viiAcknowledgement^ xiDedication xii1. Introduction^ 11.1 Motivation for the Experiment^ 11.2 World Data on Reaction 21.3 ...Survey of Chiral Symmetry^ 41.3.1 Weinberg and Schwinger 41.3.2 Olsson and Turner^ 51.3.3 Oset and Vicente-Vacas 51.3.4 Current Theory^ 51.4 Predictions of the Olsson-Turner Model^ 61.5 Chiral Perturbation Theory^ 81.5.1 Feynman Diagrams 101.5.2 Sensitivity of the 7-7r (Pole) Contribution^ 152. Description of experiment^ 232.1 Introduction2.2 General Approach^ 232.3 Details of Set-up 24iii2.4 A Brief Tour of a Reaction Event^ 312.5 Strategy for Eliminating Background Reaction Events^322.6 Conclusion^ 363. Modelling of experiment 363.1 Introduction^ 373.2 Phase Space 373.3 Simulation^ 423.4 Conclusion 484. The Experiment^ 494.1 Introduction 494.2 Initial Set-up^ 494.3 Running of the Experiment^ 514.4 Conclusion^ 525. Experimental Results 535.1 Introduction^ 535.2 Analysis of Data 535.2.1 Time-of-Flight Cut^ 545.2.2 Events in the AE vs E Plane^ 555.2.3 Normalization of Spectra 585.3 Cross section^ 605.4 The CH2-C Spectra 615.5 The Subtraction Problem^ 63iv5.6 Conclusion^ 676. Redesign of experiment 686.1 Introduction^ 686.2 Hole in the S1-S2 Telescope^ 686.3 Increasing Time-of-Flight Separation^ 706.4 Triplet Lens^ 716.4.1 The Triplet Arrangement^ 726.4.2 The Triplet Simulation 726.4.3 Results from the Simulation^ 736.5 Conclusion^ 787. Final Conclusions 79Bibliography^ 80Appendix A Electronics^ 82Appendix B Listing of Routines for Driving MOLLI^ 86Appendix C Detectors^ 92vList of Tables1.1^World data on the 7r ±p —> Ir + 71-°p channel1.2^Scattering lengths predictions from different theoretical models^81.3^Proportion of contributions to the total cross section for different diagrams for their+ 7rO channel^ 121.4^Proportion of contributions to the total cross section for different diagrams for the71- +7r± channel 122.1 Maximum angles and n^35C.1^Detector sizes^ 92viList of Figures1.1^World data on the li- ±p —> ir + ir°p channel^ 31.2^Feynman diagrams showing 11--ir scattering imbedded in 7-27 scattering^31.3^Tree level diagram^ 91.4^Loop level diagrams which contribute to scattering amplitudes^91.5^Total cross section (ir+ r°) based on the Donoghue (ChPt) scattering amplitudes 101.6^Total cross section (7rtr+ )^ 111.7^Feynman diagrams for the Ir+iis ) channel^ 111.8^Feynman diagrams for the 7± /r± channel 131.9^Different contributions to the total cross section^ 141.10 Different contributions to the total cross section 141.11 71- ± ir° channel, total cross section divided by phase space^161.12 7r + ir+ channel, total cross section divided by phase space 171.13 Fractional change in the total cross section^ 181.14 Fractional change in the total cross section (7+ 7°) compared against existingexperimental error levels^ 191.15 Fractional change in the total cross section (r+7+) compared against existingexperimental error levels 191.16 The ratio of E's for the two channels: E(ir + 7-+ )/E(7 + 71-O), with same variation in thealpha parameters as previous defined (see Fig. 1.11)^ 211.17 Changes in the E ratio due to the variation in the alpha parameters as well as a±20% change in the A coupling constant^ 222.1^Confinement of protons to small cone angles 242.2^Experimental Set-up^ 25vii2.3 A 'uniform' distribution of pions 292.4 A 'uniform' distribution of protons 292.5 The 'band' structure for different masses in the AE vs E plane 302.6 Typical 'pile-up' event 312.7 Typical event vetoed by the 'C' detector 332.8 Pile-up events are those that appear in the left window 343.1 (phase space of w +p --> w + w°p channel) 383.2 (phase space of ir+p -› ir+ 15)p channel) 383.3 (phase space of w+p --> w -l- w'p channel) 383.4 (phase space of w +p --> ir + w°p channel) 383.5 (phase space of w +p -› w +p channel) 393.6 (phase space of w +p -> w+p channel) 393.7 (phase space of w +p -> ir+p channel) 393.8 (phase space of w +p -> w+-yp) 403.9 (phase space of w+p -› w+-yp) 403.10 (phase space of ir +p -› w+ -yp) 413.11 (phase space of ir +p -> w+-yp) 413.12 (phase space of w+p -> w+-yp) 413.13 Reaction events as seen in the AE vs E plane 433.14 Surface plot of reaction events 433.15 Reaction events as seen in the .6,E vs E plane with C veto enabled 433.16 Surface plot of reaction events with C veto enabled 43viii3.17 Elastic scattering background 433.18 (A-±p —> 71- +Tp events as seen in the AE vs E plane) 453.19 Or -Fp —> ir +-yp events as seen in the AE vs E plane) 453.20 (71- ±p —> 7- + T±p events as seen in the 1E vs E plane) 463.21 (7r+p —> ir+,ep events as seen in the AE vs E plane) 463.22 (en —> irtip events as seen in the AE vs E plane) 473.23 (en ---> 7i- + ep events as seen in the AE vs E plane) 473.24 (ir'n —> ir ÷ irp events as seen in the AE vs E plane) C veto enabled 483.25 (en ---> 7r ± ir-p events as seen in the AE vs E plane) C veto enabled 485.1 Typical spectra from a CH2 target run 535.2 Detail of Time-of-Flight spectrum from a CH 2 target run 555.3 Typical Si vs S2 spectra 565.4 S1 vs S2 detail, raw spectrum. 575.5 Surface plot of Si vs S2, raw spectrum 575.6 Si vs S2 plot, with time-of-flight cut 575.7 Surface plot of S1 vs S2 spectrum with time-of-flight cut 575.8 H2 spectrum in the S1 vs S2 plane, with no time-of-flight cut 615.9 H2 spectrum in the S1 vs S2 plane, with optimal time-of-flight cut 625.10 Negative contours in the Si vs S2 plane 645.11 Si Signal Instability 655.12 Subtraction of two S1 spectra, Run 34 minus Run 29 655.13 Instability in S2 signal. 66ix5.14 Subtraction of two S2 spectra, Run 34 minus Run 29^ 666.1^Angle correlation between outgoing pion and proton 696.2^The triplet set-up^ 716.3 Raytrace of monoenergetic protons with Tp =36 MeV^ 746.4^Field gradient of Q1 as a function of axial distance z 756.5^Field gradient of Q2, as a function of z^ 756.6^Raytrace of outgoing protons from the reaction w+p —> 7r + ir°p, with divergence in thex,y directions < 5°, y direction (dcd plane) 766.7^Raytrace of outgoing protons from the reaction w+p —> 7r + ir°p, with divergence in thex,y directions < 5 °, x direction (cdc plane)^ 77A.1 Block diagram of 'beam' logic.^ 82A.2 Block diagram of 'detector' logic. 83A.3 Block diagram of 'event' logic.^ 84A.4 Various modules.^ 85C.1 Target geometry 93C.2 Detector geometry^ 94xAcknowledgementsFirst and foremost, I would like to thank Dr. Richard Johnson for supervising andsupporting this work. His insights, experience and humour have been invaluable in thecompletion of this work. I would also like to thank Dr. Ami Altman for his assistance inso many areas and his excellent explanations for so many of my questions. Special thanksmust be given to Dr. Eli Friedman for his PH3J5 program for performing the Monte Carlosimulation and his readiness in sharing his knowledge; and also to Dr. David Axen forreading this thesis. Finally, I would like to thank my old friend Patrick for his good adviceand encouragement.xiDedicationTo the Rose of Sharonxi iChapter 1Introduction1.1 Motivation for the ExperimentThe motivation for performing this experiment has its roots in the study of the stronginteraction, in the low energy regime. Early theoretical work in the field have been basedon the idea of chiral symmetry' breaking. Contemporary treatment of the subject in termsof quantum chromodynamics (QCD) still relies on the idea of chiral symmetry which is theonly rigorous formalism of QCD at low energies.Traditionally, the test of the validity of various theories that make use of chiral symmetrybreaking takes place in trying to measure physical quantities associated with the reactionira + 7re3 --> 71-7 + 7r° (7-7r scattering), perhaps the most fundamental of all hadronicprocesses'. Because of the short lifetimes of the pions, 7r-ir scattering cannot be observeddirectly. Instead, one resorts to indirect means: one such method involves themeasurement of cross sections for the w-27 reactions. Cross sections for these reactions' Chiral symmetry in this case refers to the symmetry that exists if quarks were massless. In terms of quarktheory, the QCD Lagrangian in the chiral limit would consist of two separate parts: one for right-handedparticles another for left-handed particle with no coupling between the two. Hence, in the massless quark limit,the left-handed states do not mix with the right-handed states. In the real world, chiral symmetry is notpreserved since quarks are not massless.2 'most fundamental of all hadronic process' because a-ir reactions involve the self-interaction of the lightestparticle in the hadron spectrum of particles.1Chapter 1. Introductionnear threshold can be used to calculate w-w scattering quantities (Fig. 1.2). Early work[15,16] in the field suggested the behaviour of it-'r interactions is embodied in a singletheoretical parameter' other physical quantities such as scattering lengths are given interms of Contemporary theory based on QCD such as chiral perturbation theory makessomewhat different predictions from those of earlier theory. It is the intent of the currentexperiment to test the predictions of existing theory by measuring the cross section of a ir-2irreaction. For a survey of measurements of different ir-2ir channels and the theoreticaldescription of chiral symmetry breaking refer to [3,23].1.2 World Data on ReactionFor the it-2w reaction, w + p —> w+ w°p, very few measurements have been performed to date:indeed no measurements exists near the threshold energy (T,r+ = 164.75 MeV).T,r÷ (MeV) Ottb) Reference230+13 18+1 [10] (1975)275+15 48+1'5' [10] (1975)294+4 120+50 [11] (1972)300+? _ 110±40 [30] (1963)Table 1.1 World data on the 7r +p ir+ 7CO p channel(reproduced from [2]).3 Known as the 'chiral symmetry breaking' parameter.2Chapter 1. Introduction10 3 ^iiiiii^llllll^ lllll10 -2 .1^1111^ll 1 lll 111111^1111111^11111111^1111111^11111111^11160^200 240 280 320T Tr+ (MeV)Figure 1.1 World data for the 7r + p —> ir+ ir° p channel (reproduced from [2]). The Oset and Vicente-Vacas model was used to generate the curve for the total cross section.p^/pole diagram7r-27^p^(rv+^o ■N^ /,o AxN^ x,„..„......„.„...„......:7TN+ ,'NN,,,,,N.z oAL,z^-.^0,7 + 21^ N..., Nx^ N.,z 7T-7TFigure 1.2 Feynman diagrams showing 7r-7r scatteringimbedded in 7-27r scattering.equivalent3Chapter 1. IntroductionIt is not at all surprising the data is sparse since, as we shall see, the measurement of thecross section for this reaction is a challenging undertaking, due to the host of backgroundreactions.1.3 A Semi-Historical Survey of Chiral Symmetry1.3.1 Weinberg and SchwingerThe first work on chiral symmetry was performed by Steven Weinberg during the early1960's. Weinberg introduced chiral symmetry breaking to current algebra and the partialconserved axial current (PCAC) hypothesis', in order to calculate the ir-ir scatteringlengths'. Based on this approach, Weinberg also developed a Lagrangian for the 7-7interaction [13]. At about the same time, Schwinger, using a different approach arrived ata different ir-ir Lagrangian [14].4 the notion of a partially conserved axial current originates from the idea allowing the quarks to have a smallmass (a few MeV's) and therefore breaking the chiral symmetry. It can be shown that the preservation of chiralsymmetry implies the conservation of the axial current. To slightly break the symmetry with small quark massesimplies that the axial current is partially preserved.5 the scattering is defined as1 bin a =a 24n 1- e°where a is the scattering length and X is the wavelength associated with the incident particle.4Chapter 1. Introduction1.3.2 Olsson and Turner: generalization of the 7-7 Lagrangian derived by Weinberg andSchwinger.During the late 1960's Olsson and Turner [15] constructed the most general form of the 7r- irLagrangian, which can be considered as a family of Lagrangians because it contains a singlefree parameter E. According to this model, at low energies, E the chiral symmetry breakingparameter alone determines the strength of the 7r-ir interaction at low energies.Furthermore, the Weinberg and Schwinger Lagrangians are two specific cases of the Olsson-Turner family of Lagrangians corresponding to the E values of 0 and 1, respectively.13.3 Oset and Vicente -VacasThe model constructed by Oset and Vicente-Vacas for 7-27r reactions, adds to the Olssonand Turner model the effects of the intermediate isobar states of the N* and A [22].1.3.4 Current TheoryOne obvious short coming of the Olsson-Turner model is that it does not include 71--7-rescattering effects. Modern theories that include rescattering effects make significantlydifferent predictions on the scattering lengths. One such approach based on QCD is chiralperturbation theory (ChPT) [17,23,27]. Predictions made by ChPT for the 7r+p ---> ir + ir°preaction will be discussed below.5Chapter 1. Introduction1.4 Predictions of the Olsson -Turner ModelIn the framework of chiral symmetry, the Olsson-Turner Model makes specific predictionsthat can be experimentally verified. Specifically, we wish to investigate the nature of chiralsymmetry breaking by studying 7r-ir scattering amplitudes at zero relative momentum.Because of the short lifetimes of the 7r, measurement of the amplitudes must be doneindirectly. One such method is to measure the cross sections of the 7rN .- 7r7rN (ir-2ir)reactions, near threshold [15].According to Olsson and Turner's model, the total cross section at threshold for the 7r-27rreactions is given by [10,16,20]a OW — Tr icIV)=a(iTnN)2Q2S x(phasespace)For the reaction w+p --> 71-+ 7r° p, the total cross section becomesa =a(TE +Tr °p)2 Q 2 X (phasespace)^ (1.2)where^Q = momentum of incident ir + in the center of mass systema(7°71- ±p) = the reaction amplitude at threshold, dimensionless in this notation6Chapter 1. IntroductionS = statistical factor accounting for pions in the final state; S = 1/2 if finalpions are identical; S = 1 otherwise.The threshold amplitude is related to the chiral symmetry breaking parameter in thefollowing way [15,19]24a(Tc+TE°p)= 1.51 +0.6^ (1.3)Furthermore, the s-wave^scattering lengths ° for isospin I =0 and I =2 are given bya2 _ +2a 5 _7o2and3m7,2a0 -5a2 -where fr = the pion decay constantm,,. = pion mass6 Because the spin (intrinsic angular momentum) of the pion is zero and at threshold the angular momentum1= 0, only s-waves are present.Symmetric wave function (boson symmetry) under the interchange of pions of a 7r-ir system further dictates thatthe isospin be even. Therefore for the ir-7r system at threshold, I =1 isospin components vanish leaving only1=0,2 components [3]. In terms of the scattering lengths a, only ao and a2 remains.(1.4)(1.5)7Chapter 1. IntroductionCombining (1.4) and (1.5) yields and using fir = 93.3 MeVao = (0.156 -0.0560 Om -7:-1-a2 = -(0.045 +0.0224 Om TcIn summary, according to the Olsson-Turner model, by measuring the total cross section a,the threshold amplitude a(7 ± 7- °p) can be determined using (1.2). It follows that by (1.3)allows is determined and by (1.6),(1.7) the scattering lengths are found. Table 1.2 givesthe values for the scattering lengths for E = 0.ao a2Weinberg [18] (Olsson-Turner^=0) 0.16 0.045Gasser & Leutwyler [17] (Chiral Perturbation Theory) 0.20 -0.042Table 1.2 Scattering lengths predictions from different theoretical models. a, are in units of (m„) -1 , where Iis Isospin.1.5 Chiral Perturbation TheoryGasser and Leutwyler [24] have made predictions on the 7r-ir scattering lengths using ChPt(see Tab. 1.2). Based on Gasser and Leutwyler's work, Donoghue [28] has calculated the7r-2- chiral scattering amplitudes. ChPt makes use of chiral effective Lagrangians [27], whichare classified according to expansion in terms of energy. The lowest order Lagrangian is ofthe order E2 (energy squared). At this order, the 7--7r Feynman diagrams are at 'tree-level'(1.6)(1.7)8n7,Figure 13 Tree level diagram. (1)^(2)Chapter 1. IntroductionFigure 1.4 Loop level diagrams which contribute toscattering amplitudes.(Fig. 1.3); that is, no rescattering effects are considered.The predictions made at this order reproduces the scattering lengths proposed by Weinberg[1] (which corresponds to the Olsson-Turner model with E =0). The Lagrangian at order E4has been calculated by Gasser and Leutwyler [27]. At this order, calculations involve one-loop diagrams (Fig. 1.4). Imbedded in the Lagrangian to order E 4 are two 'free parameters'« i and ii2 which are to determined by experiment.In what follows, the 7-7 scattering amplitudes (see [28]) derived by Donoghue will be usedin conjunction with the intermediate isobars A and N* portion of the Oset and Vacas-Vicente model to generated cross sections for the different 7-27 channels. The followingcalculations will follow the approach by V. Sossi [29]. Figures 1.3 and 1.4 show the crosssection generated by this approach. The solid curves for the total cross section aredetermined by setting the parameters of the Lagrangian to values derived in ref. [28]« i = -0.007 and a2 = + 0.0139Tr +p^71. -1-71. Opit^ ili1,1111.11/^111.11pole term + leading terms +pole term + leading termspole term10 ° -10 -1150^200^250^300^350TTr+( MeV )4001 o 2Chapter 1. IntroductionFigure 1.5 Total cross section based on the Donoghue (ChPt) scattering amplitudes along with isobars describedby the Oset and Vacas-Vicente model. The solid curve is determined by setting = -0.007 and « 2 = + 0.013. Andthe vertical dash marks represent points calculated by varying ± 100% and « 2 +50%.To determine the sensitivity of the cross section to the parameters a l and &2, calculationswere performed by varying the parameters by 100% and 50% respectively (these points areshown as vertical dash marks in Fig. 1.3 and 1.4). The 7 + 7+ channel is included here forcomparison as will be discussed.1.5.1 Feynman DiagramsFigure 1.7 depicts the Feynman diagrams for the 7r +p ---> -71- + -7r °p reaction. The diagram ofprimary interest is the pole (1), for studying 7-7 scattering (see Fig. 1.2). The set of 3-point1010 -2150^200^250^300^350T ,(MeV)400Chapter 1. IntroductionTr+p^-rr+Tr+nFigure 1.6 Total cross section (see caption on Fig. 1.2).^+1 ^/rr+7T 14.n + — ■ — 4 — .- — ir°^IT \\  / , itI^ -N^IT I 0.'\ ins1 J.- P^ P^P^ p(3)^(4)^ (5)\^o / \ + / +^+Tr11^\, Tr + // Ito^+ \ IT +/^0 //1' / it IT \^/^TT /Tr  /^\1 /1^4^\ f^I\ 1^11 I/ \ II \V I^\^I^/ P P^^p^p^n^p^p^P^P(7) (8)0 1^(61^I I^n I^I^+Tr+ 1 t +Il ^rro ;Tr I n+ I n + 1 rt.+ 1 it " I^I 71"10 ^ Ii^I^IAI^I.^0I^0 ^f I^I^I I^I^I^ I^1^II^I^I^I^I^I I I^I P^p^n^p p^n^n^p^P^n^p pFigure 1.7 Feynman diagrams for the 7r + ir° reaction channel. Note:3-point diagrams involving isobars are not depicted. Diagrams (2)-(8)are called in this paper the 'leading diagrams' for this channel.11Chapter 1. Introductiondiagrams (6)-(8) in Fig. 1.7 are incomplete, as only nucleon states have been shown. Thereare 22 other 3-point diagrams containing a mix of (nucleon-0), (nucleon-0-0) and (nucleon-0-N*) states (see ref. [3] for more diagrams). All diagrams contribute to the total crosssection and are used to determine the total cross section. For this channel, the pole termaccounts for 30% of the total cross section at T„ =180 MeV and less at higher energies(Table 1.3). Even at modest energies, isobar states begins to dominate causing the poleterm contribution to diminish to 10% at 240 MeV (Fig. 1.9).T,+ (MeV) 180 240% of total cross section^apole diagram 30 10leading diagrams(see Fig. 1.7)48 44isobars and nucleons diagrams 22 46Table 13 Proportion of contributions to the total cross section for different diagrams for the eirO channel.T„,(MeV) 180 240% of total cross section^apole diagram 88 45leading diagrams(see Fig. 1.8)1 37isobars and nucleons diagrams 11 18Table 1.4 Proportion of contributions to the total cross section for different diagrams for the el' channel.Figure 1.8 depicts the Feynman diagrams for the ir +p 7+ 7+n reaction. Again, the set of3-point diagrams are incomplete, as only nucleon states have been included. But overallthere are far less number of diagrams for this channel especially those that involve the1271n^pp(2)Chapter 1. Introduction^(0)^ (4)+ / \71IT //IT +^+ \^+ /^+ /TV \ 7 / 7 // \ 1 1 l^A\/^//^V^ \/ / n^n^P^p^n(5)+/^I ^I p^n^p^nFigure 1.8 Feynman diagrams for the 7r + 7r+ channel. Note: 3-pointdiagrams involving isobars are not depicted. Diagrams (2)-(5) arecalled in this paper the 'leading diagrams' for this channel.isobar states. There are only 11 other 3-point diagrams containing a mix of (nucleon-0),(nucleon-0-0) and (nucleon-A-N`) states (see ref. [3] for more diagrams), in contrast to the22 for the ir + ir° channel. Further, in sharp contrast, for this channel, the pole term accountsfor 88% of the total cross section at T, r+ =180 MeV (Table 1.4). Isobar states play muchless of a role for this channel whose contribution to the total cross section increases from11% to 18% between 180 MeV and 240 MeV (Fig. 1.10).13Chapter 1. Introduction+p^ir+7rop40 1111111iIII^i11.1!■ 1[11.1111130 pole term + leading terms + other terms_ob10pole term + leading termspole term _______i0170^190^210^230^250T 7T+(MeV)Figure 1.9 Different contributions to the total cross section.Tr +p^Tr+Tr+n11111111 111 111111111 111 11111^11140pole term + leading term10pole term180^200^220^240T, (MeV)Figure 1.10 Different contributions to the total cross section.1430 - pole term + leading term +Chapter 1. Introduction1.5.2 Sensitivity of the 7-7 (Pole) ContributionAs mentioned above, the pole diagram accounts for only a fraction of the total cross section;since the physics of 7-7 scattering is imbedded in the pole term the magnitude of itscontribution to the total cross section is determined by the parameters « 1 and &2. As shownin Figs. 1.5 and 1.6, by varying the these parameters and looking at the changes in total crosssection one can determine the sensitivity of the pole term.It will be shown below that the 7+ ir° channel is 'insensitive' to changes in « 1 and '&2 in theregion near threshold (say, from threshold up to 320 MeV). By 'insensitive', two things areimplied: first, the variation in cross section is small relative to other channels such as the7r± 7+ and second, perhaps the most important reason, the variation is small relative toexisting experimental error levels'.For Figures 1.11 and 1.12, the phase space dependence of the total cross section a has beendivided out. It is evident that for the 7r+ 7r° channel that the variation in cross section is farsmaller than errors on existing data points. For this reason, it is not possible to extractuseful information about the « 1 and a2 parameters, without improving on the previousexperimental error levels which are typically ±50% of a. To pin down the alpha parameterserrors should be reduced to — ± 10% of a. In contrast, the variation for the ir + 7r + channelis larger or comparable to errors on existing data points.' i.e., the size of the experimental errors on existing experimental data.15Chapter 1. Introduction+ 07T +p --> 7T 7T pFigure 1.11 7r+ ir° channel, total cross section divided by phase space (dimensionless). The vertical dash marksrepresent points calculated by varying -«, +100% and «2 +50% (from the base values of « 1 =-0.007 and«2 = +0.013), while the broken line outlines the region mapped out by this variation.16-rr +p -4 Tr +7-r +n1^1^1^1^11^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^16150^200^250^300^350T Tr+ (MeV)4005-Sevior et al. [2]Kravtsov et al. [26]1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1 1^1^1^1^1^1^1^1^1^1^l^ll0Chapter 1. IntroductionFigure 1.12 ir+7r+ channel, total cross section divided by phase space (dimensionless). The vertical dash marksrepresent points calculated by varying ii i +100% and '&2 +50% (from the base values of Ei,= -0.007 andEi2 = + 0 .013), while the broken line outlines the region mapped out by this variation.17Chapter 1. IntroductionRecent measurements by Sevior et al. [2] near threshold contain errors which are smallenough to constrain the alpha parameters. The errors for the Sevior experiment aretypically — 20% of the total cross section, which are less stringent than the 10% requirementfor the 71-± 7r° channel. Figure 1.13 show the fractional change in the total cross section asa result of varying the alpha parameters: it is immediately evident that the 7r± ir° channelcross section is far less sensitive to such variation. Figures. 1.14 and 1.15 show theexperimental error levels for existing data.150^200^250^300^350^400T ,T+ (MeV)Figure 1.13 Fractional change in the total cross section as a result ofvariation in the alpha parameters, for the irtir ° and 7rir+ channels.18experimental error level on existing dataChapter 1. IntroductionTr +p^7T+Trop1.0 =0.80.6-b0.4 =0.2 —0.0experimental error level on existing data150^200^250^300^350^400T n+(MeV)Figure 1.14 Fractional change in the total cross section comparedagainst existing experimental error levels.rr+p —> Tr +Tr +n1111^11111^1.111111111^11111^11111.00.8 —0.60.4 —0.20.0150^200^250^300^350^400T n+(MeV)Figure 1.15 Fractional change in the total cross section comparedagainst existing experimental error levels.19Chapter 1. IntroductionIf one defines the quantity E = (rips, where a is the total cross section and ps is the phasespace, then another approach is to consider the ratio of E's for the two channels:E(71-+7+)/E(irtir°). Figure 1.16 shows the plot of this ratio, again with same variation in thealpha parameters as previous defined (see Fig. 1.11). In contrast to Figures 1.11 and 1.12,which shows a small cross sectional variations at energies near threshold and thenprogressively larger variations at higher energies, the ratio displays a large changes nearthreshold with progressively small changes at higher energies. While constraining the alphaparameters still require the experimental errors to be smaller than 20% and 10% for the7+7+ and 7r + ir° repectively, this approach offers a different perspective in analyzing the crosssection data. Figure 1.17 shows changes in the E ratio due to the variation in the alphaparameters as well as a ±20% change in the A coupling constant. It is clear that for theratio, changes due to the alpha parameters dominates when compared to those arising fromthe A coupling constant.203.5 _ 1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^13.0 =„,variation in a, and a 20.5 -....- ......1i1^i^i^: N, Ni^Ni . \I^i ,•I:^N___I _ — .:„.,...^I^i^\s..„...... : 1; 1••-...„..,^I■,. ..----....,^: -.....■:.. ....„^i : "....---. L''. ■.,.. I1•,.,......I .......■.... ---, ---1 ---- --- •- _J1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1200^250^300T rr+ (MeV)0.0 ^150 350 400Chapter 1. IntroductionFigure 1.16 The ratio of E's for the two channels: E(ir + 7r± )/E(ir+ 7r°), with same variation in the alphaparameters as previous defined (see Fig. 1.11)211^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^I^1^1^1^1^1^1^1^1^1^I^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1_— — variation in a 1 and a 20 0 0 0 0 ±20% in A couplingboundary defining variation in a, and 02boundary defining variation in A coupling=,^1^1^1^1^1^1^1^1^,150^2001^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^I^1^1250^300T 7T+ (MeV)1^1^1^1^1^1^1^1^1^1^1^1^1350 400Chapter 1. Introduction-----.3.02.5Q4_w2.01.54-+kw1.00.50.0Figure 1.17 Changes in the E ratio due to the variation in the alpha parameters as well as a ±20%change in the A coupling constant.22Chapter 2Description of Experiment2.1 IntroductionThis chapter will address how one measures the cross section of reaction (2.1). Theexperimental apparatus and the technique for eliminating the background events will beintroduced.2.2 General ApproachThe purpose of the present experiment is to measure the total cross section for thereactionsnip -.7c++7r°-Fp^ (2.1)near threshold energy of 7r° production (164.75 MeV). At a first glance, this measurementappears relatively simple. However upon closer inspection one finds that there are anumber of other reactions occurring at the same time. Therefore, the difficulty in themeasurement is to separate the events arising the principal reaction from those of thebackground reactions. The first category of background reactions arises from other 7r+pchannels (reactions (2.2)-(2.4)).I Henceforth in this paper, reaction (2.1) will also be referred to as the 'principal' reaction. Of course, thisconvention is only a necessary prejudice of this paper.23Chapter 2. Description of ExperimentThe second category (reaction (2.5)) arises from 71-+ collisions with neutrons which arepresent together with the protons in the solid the C and CH2 targets.Ignoring the background reactions for a moment, the technique that can be used to measurethe total cross section is to take advantage of the small angles 2 (Fig. 2.1) of the outgoingprotons near threshold. For example, for beam pions with kinetic energy of T„ =220 MeV,the reaction protons are confined within a cone of (0p)Mi, =36° [3]. The angles are smallerfor lower T„, with (Op)max — 7° at threshold. Hence, if there were no competing reactions,one can account for all events by simply detecting the outgoing protons within the cone.Before going on to discuss how to distinguish background events from those of the principalreaction, it is necessary to introduce theexperimental set-up.2.3 Details of Set-upTargetsThe targets used in the experiment are solidcarbon (C) and polyethylene (CH 2). Due tothe low energy of the reaction protons and+T=220 MeVoutgoing protons confined within coneFigure 2.1 Confinement of protons to small coneangles.2 i.e., angle of the proton with the beam axis24Chapter 2. Description of ExperimentFigure 2.2 Experimental Set-upep -Tc+ +p^ (2.2)Tc +P ' 1E + + Y ÷P^ (2.3)ep - e+ic++n (2.4)en - TE++e -f-p^ (2.5)pions, it is necessary to use very thin targets' (- 0.2 g/cm2). The reason that 2 different3 A CH, target with thickness of 0.5 g/cm2, will stop protons with kinetic energy up to 22 MeV and pionsup to 9 MeV.25Chapter 2. Description of Experimenttargets are used are as follows. Since we are only interested in the events arising from 7+14 2(i.e. w+p) collisions with the CH 2 target, some method must be introduced to remove theunwanted events from w+C collisions. The way to achieve this is to make 2 separatemeasurements: one with a CH 2 target and an other with a C target. The results from the2 measurements are then subtracted (CH 2 events - C events). Subtracting the C events fromthe CH2 events effectively removes the events from scattering off carbon leaving only theevents from scattering off the 2 protons. This method has already been successfullyimplemented in measurement of the total cross section of the single charge exchange (SCX)reaction /IT —> w'n [7,8]. A more detail treatment of this subtraction method is discussedin [5,6].The Proton AbsorberAn aborber made of polyethylene (CH 2) with thickness 1.9 g/cm2 is placed in front of thebeam window to remove protons that have 'leaked' through with the beam pions.Beam Defining CountersFour scintillator counters (NE102) V, Bi, B2 and B3 are used for beam definition. Anincident beam pion accepted is defined' as the coincidence of B's anticoincidence with V.The purpose of the V or 'halo' counter is to eliminate any stray (outside the main beam)4 i.e., in boolean algebra B1 AND B2 AND B3 AND (NOT V).26Chapter 2. Description of Experimentparticles that causes a coincidence in the B counters (see Appendix A and C).The Event DetectorsEvents are defined by a group of 4 detectors, also NE102 scintillators: C, S1, S2 and S3.The S1 and S2 detectors make up the 'telescope' array which is the heart of the experimentfor looking at reaction events. The principle of how this telescope works will be discussedin detail below. The rest of the detectors C and S3 are used to reject unwanted backgroundevents. The C or 'cylindrical' detector is used to reject events from background reaction(2.5). The S3 veto detector is used to eliminate events from background reactions with highenergy particles that manage to traverse the entire array of detectors and target, 'coming outthe other side'. These particles mainly arise from elastic scattering and beam particles thatdid not interact' with the target. An 'event' is defined' as the coincidence of Si and S2,anticoincidence with C and anticoincidence with S3 (see Appendix A and C).The S1 -S2 Telescope ArrayA single scintillator detector by itself cannot identify what type of particle has traversed it.To see why this is the case, we first investigate what happens to a charged particle travellingthrough a medium. For a charged particle whose mass is much greater than the mass of the5 i.e., the strong interaction.6 In boolean form, an 'event' is (Si AND S2) AND (NOT C) AND (NOT S3).27Chapter 2. Description of Experimentelectron, energy loss in traversing a medium is due primarily to the interaction of theparticle with the atomic electrons in the medium. The mean rate of energy loss due to theionization of electrons is given by the Bethe-Bloch formula' is given bydE 47ENz 2e 4Z{ (2me 13 2c 2 )In ^ _02dx mep2c2^A1-02)(2.6)where^me = electron massz = charge (in units of e) of traversing particle/3 = v/cv = velocity of traversing particleZ = atomic number of atoms in mediumN = number density of atoms in mediumx = path length in mediumI = an effective ionization potential, averaged over all electrons — 10Z eVSuppose that we have a very thin' medium (Si) with width dx, then knowing all the mediumparameters, one can extract the velocity of the traversing particle by measuring dE. Thereis no way to identify the mass of particle since (2.6) is independent of this mass. The wayto identify the particle is to determine its total energy by adding a second thicker mediumA semi-classical derivation of this formula is given in [8]. This equation is the 'basic' Bethe-Bloch formulawithout any terms for shell corrections or density corrections at higher energies.8 The 'thin' assumption is to simplify the argument making the velocity approximately constant through themedium. For a finite ox medium the velocity is through the medium is not constant but one can easily devisean algorithm to extract the velocity upon exit of the medium by dividing the entire medium into smaller piecesand accounting for the velocity difference upon entrance and exit of each little piece of material and proceedthen through the entire medium.28Chapter 2. Description of Experiment(S2) which stops the particle completely. The second medium records an energy depositionE. Hence, the total energy of the traversing particle is E+ dE. The mass M of the particleis given by13 in (2.7) given by (2.6).In practice, one does not calculate the mass explicitely to identify the particle. By plottingTr" kinetic energy distribution^ Proton kinetic energy distribution20^2015 -z'10 -15 -z°10 -10 20^30K (MeV)r40^50^ 0^10^20^30^40^50^60^70K (MeV)Figure 23 A 'uniform' distribution of pions. Figure 2.4 A 'uniform' distribution of protons.the S1 signal versus the S2 signal (i.e., AE vs E) one can readily identify a particle. Sendinga host of particles with the same mass but different energies through the S1-S2 telescopewill trace out a unique 'band' in the AE vs E plane. To show this effect, imagine sendinga uniform distribution of 7+ with kinetic energy between 0 and 50 MeV (Fig. 2.3) and also29Chapter 2. Description of Experimenta uniform distribution of protons between 0 and 70 MeV (Fig. 2.4). Figure 2.5 shows theband structure corresponding to each type of particle.Simulated 31 vs S2 Data50(It, 4030o 20z10UJf)-0I0^10^20^.30^40^50S2 CHANNEL NO. (2 MeV PER CHANNEL)Figure 2.5 The 'band' structure for different masses in the .6,E vs Eplane. The top group is the proton band while the bottom is the pionband. Progressively larger massess would trace out bands higher upin the plane.30Chapter 2. Description of ExperimentCS1^S2 S3Figure 2.6 Typical 'pile-up' event. The two gammarays come from the decay of the 7e.2.4 A Brief Tour of a Reaction EventWith the telescope, we are now ready to look at reaction events. As shown above, one cannot only identify whether a pion or proton has struck the S1-S2 array but also the energyof the particle. A beam pion begins upstream and then through the aborber, through theV halo veto, gets accepted by B1 B2 B3 and then reacts with the target. Let us suppose thatthe principal reaction takes place then what is emitted from the target is a proton, a Irk, anda 7-°. The ir° will escape without being detected'. The proton is restricted by phase spaceto be within a certain angle: all that is needed is to make S 1-S2 large enough to cover thecone angle, catching all protons and some of the ir + with the detector. In this way, with the9 In principle, one can detected the ir° via its decay to 2 gamma rays. In reality due to the high energy ofthe gamma's (interaction cross section falls off with increasing energy) from the 7r° of this reaction, a very largeand expensive detector is needed.31Chapter 2. Description of Experimentabsence of background reactions, the total cross section of the principal reaction isdetermined.2.5 Strategy for Eliminating Background EventsTo eliminate the background reactions, we need to determine which background events willfall in the acceptance angle of the S1-S2 telescope. Since we can achieve mass and energyresolution with the telescope, if the background events have energies which are radicallydifferent than (2.1), then they will appear in a different region of the AE vs E plane. So,the general strategy in modelling the background is to send a distribution of particles thatbelong to the phase space of a particular background reaction and determine theirsignatures in the AE vs E plane.The result of this analysis (see Chap. 3) is clear, to distinguish events from the reaction ofinterest and background reactions, one should consider a smaller group of outgoing protonsthat fall in the kinematical cone: those that strike the S1-S2 detector accompanied by a ir+,(Fig. 2.6) Thus we ignore those protons that hit the telescope without an accompanyingpion. The reason for rejecting these protons is that they fall in a region AE vs E riddled withbackground events. However, the signatures of the smaller group of (proton & irk) or 'pile-up' events are uniquely determined in the AE vs E plane, with the only exception of reaction(2.5). This reaction also possesses simultaneous events of the form of either 71-+p or 7r -p,32Chapter 2. Description of ExperimentTVtC//^(< ^............B3Target /S1^S2 S3Figure 2.7 Typical event vetoed by the 'C' detector.which appear in the same region of the AE vs E plane However, this competing reactionis accompanied by an additional charged pion. This difference is used to eliminate theoverlap in events: a cylindrical veto counter (C) is introduced to reject simultaneous irpevents coincident with another charged ir (Fig. 2.7).As it will be discussed later (see Chapter 5), the use of time-of-flight will be very importantin separating another type of background events from those of the principal reaction. Thesebackground events are different from those' above. In this case the background comes'° i.e., reactions (2.2)-(2.5).33Chapter 2. Description of Experimentfrom the beam interacting with the 'B' and 'S' detectors. In a very real sense, thesedetectors are themselves targets, producing a host of events. The trick here is to isolate onlythose events that are coming from the target: this is where time-of-flight separation iscrucial.To summarize, the elimination of the background events is a 2 stage process: first oneAngle Correlation Between 7-1 + and p1^1^1^1^1^1^1^1^1^1^11^1 ----:^":98°, °,:vif°'"°:" : ,,,.cr-_)^° Pe :7, ,?,g ,t, 01, % Pbrgb° ° ,0 -;°*0 *^°,,,^,,-0 15 00 t 4141( SS0t,0° °,40;`01:4„0° ° 0^ °.., .0, „40tv'' oc, 0%0 :„ 00., At,0,% *0 0 020 - .25 -^ *g, ®°5 7.° 0 f 4.0 :',"°% 0 * 0^" 000 .° 01 0  it °°-°.%°°000 '013: 4°0,3010;0 00:^*0:0 ito *0 % 0 : °° 01 0 * 00°^0%0^ ,t,sto:ref,„ s00°, 0 o ,2.0 0° ^0.o0„. o %^,,,,,v 00,„ 4 0 - 00^. 0.le t^,, - i^,fgAsto°1 ° : . i° 7*, °,, ° °°.,$>: °^° ;^0° 'f°:. 0 8ego 0:8 g,.! : 0 °^00* g,,, 8 0:0 °*.: 0 0 0go. (0080,00 824:0020,,s0.060 0^o^04, 00o 0 „„ At oy 0,.. ..,9,,,,,,,4. o°.^,00 k o 000 0o .°; *0^0^ 0o 0g° .opile—up region.^,,^o^,,^. 0 0^o^o^ °'0 : ^o,, $^977 p -> 7i IT p*+ 0 0050^100^150^2000, (deg.)Figure 2.8 Pile-up events are those that appear in the left window.eliminates the 'detector' background using time-of-flight; second having separated out thetarget events during the first stage, then one uses the 'pile-up' events to separate 'target'background events from those of the principal reaction.301034Chapter 2. Description of ExperimentBy restricting the accepted events to pile-up events, one can only measure a fraction of thetotal cross section of (2.1). This fraction is sometimes referred to as the 'efficiency' n . Fromphase space considerations alone, the proportion of pile-up events to total events yieldsn = 0.22, at an incident pion kinetic energy of 200 MeV. Table 2.1 shows different values ofn at different pion kinetic energies, with an acceptance angle corresponding to (0p)., forthe first 3 energies and 30 ° for 200.0 MeV.T,,, (MeV) (01). (0.,+). 71167.0 7.19° 40.96° 0.120180.0 18.40° 175.61° 0.159190.0 23.28° 176.55° 0.184200.0 26.99° 176.86° 0.221Table 2.1 Maximum angles and n (percent of total cross section measured) from phase space calculations atdifferent energies.Figure 2.8 shows the correlation between angles of the outgoing 71- ± 's and protons: the pile-up events appear in the window on the left. Monte carlo simulations that account for non-linearity of light output in the scintillor detectors and a 10% FWHM il photoelectronstatistics give 71— 15%.11 'Full Width at Half Maximum'. For an explanation of photoelectron statistics as it relatives to energyresolution of scintillator detectors see 'Glenn F. Knoll, Radiation Detection and Measurement, John Wiley & Sons(1979), Chapter 10.35Chapter 2. Description of Experiment2.6 ConclusionIn this chapter, we have described the expermental apparatus; also, the 2 different typesof background events were introduced: the first comes from the beam interacting with thedetectors while the second comes from background reactions. Different methods foreliminating these background events were introduced. In the next chapter, we will look indetail the technique for eliminating events from background reactions developed fromMonte Carlo simulation.36Chapter 3Modelling of Experiment3.1 IntroductionIn the previous chapter, we discussed the use of 'pile-up' events for measuring the crosssection of reaction (2.1). Much of this analysis is based on the Monte Carlo simulation ofthe experimental set-up. A 'standalone' routine 'PH3J5' was written by Eli Friedman of theHebrew University Jerusalem to perform this analysis. We will demonstrate how eventsfrom reaction (2.1) can be isolated from those of reactions (2.2)-(2.5).3.2 Phase SpaceTo gain a better understanding of the difficulty in separating the reaction events frombackground reaction events, let us consider the phase space of all the reactions.All the calucations below are performed at a kinetic energy of T ir, =200.0 MeV, for theincident 7r + .For reaction (2.1) ir±p —> W + 7r°p, Figures 3.1-3.3 show the number distributions in the kineticenergy space for each of the particles on the right-hand side of the reaction. An importantphase space feature of the reaction is shown in Fig. 3.4, where we see that the outgoingprotons are confined to a relatively small angle, (0p).= 270 .37250Tr+ Kinetic Energy Distribution^ Proton Kinetic Energy DistributionI^I^1^I^I^ i^i250 1+^+ 0IT p -, IT IT p+ ^07T p -, 7T 7T p200H 200H150 -z100 -I150 -z100 -50H 50H10 20^30^40T (MeV)50^60 10^20 30^40^5T (MeV)11? i^60^70Figure 3.1^ Figure 3.2Chapter 3. Modelling of ExperimentFigure 33^ Figure 3.4For elastic scattering (2.2) w+p —> ir+p, Figure 3.5 shows that the kinetic energy range of theoutgoing w's do not overlap the range of outgoing r's of (2.1). However, Figure 3.6 shows38Angle Correlation Between Tr* and p10080 -• 60 -(D- i,Scz° 40-20 -100^15019„, (deg.)00 200Chapter 3. Modelling of Experimentthe kinetic energy range of the outgoing protons contains the range of the protons from theprincipal reaction (2.1). It is already evident by including the elasic channel in our analysisthat some way must be used to separate the reaction events from background events.Tr* Kinetic Energy Distribution^ Proton Kinetic Energy Distribution60rt+p50 -40 -z 30 -20 -60 ^50 -40 -230-20  --rrTp^rr*p10 -100^150^200T (MeV)10 -50^100^150^200T (MeV)50Figure 33^ Figure 3.6Figure 3.739200Thrl 100^1 5 0T (MeV)Chapter 3. Modelling of ExperimentFor reaction (2.3) 7r±p --› 7±-yp, Figures 3.8-3.9 show a substantial overlap in the energyranges of the outgoing 71-+ 'S and protons with those of the principal reaction.For reactions (2.4) 7r+p .--> 7r+,-+n and (2.5) w+n --> w+71--p, the phase space distributions arealmost identical to that of principal reaction, because the particle masses associated withthese reactions are virtually identical to those of (2.1).Tr* Kinetic Energy Distribution^ Proton Kinetic Energy Distribution8040 -60 -5030 -z20 --1--,-t 200z 40 -20 -105050^100^150T (MeV)Figure 3.8 Figure 3.9The conclusion that one comes to by considering the phase space distributions is thedifficulty in measuring the reaction cross section of (2.1) since the energies of the outgoingparticles are very simular. In the next section, a technique is proposed to measure the crosssection of the principal reaction based on Monte Carlo simulation.40Angle Correlation Between p and -y80:52,40 —mn20 —60 —o^o^o•^o..°°4•„•.e:°> %.• ° toe °^°°°• ••^ ••••,„• ° • • .1." •°"„,98°.^'•90°,19.^°8;e: tier 444°-141/tize° :* °.$ °..9•0•*8 •••• •* °^•°:91°° • * 7;18'14 ;;999:;:•••^••• .4°^.•••^°"8 ° 8*^:s is%%,!° .*°^oirr+p^/1. +7P00^50^100^150^200By (deg.)60 —20 —Chapter 3. Modelling of Experimentm8-50 —a) 100 —2000150 —0Angle Correlation Between rr+ and 7+p^Tr 7p„40 .9t,^°%:„:^• „ s °° °.°,.9.^.°°„!•*4::et: As..i°!°°°°. •°°.°%°°....° °^•^ . 9 °;te...t^° 99.11^.%to°.• • ,1t°20050^100^150en, (deg.)Figure 3.10^ Figure 3.11800Angle Correlation Between rr + and p0^100^150^200(deg.)Figure 3.1241Chapter 3. Modelling of Experiment3.3 SimulationMonte Carlo simulation of reactions (2.1)-(2.5) yield the following results in the AE vs Eplane. For the analysis below, the acceptance angle for the S1-S2 array has been set to 30 °(see sections 2.3, 2.4) and the incident pion kinetic energy, to 200.0 MeV. The total numberevents in the AE vs E plane are typically — 5000, based on 20 000 events 'Monte Carloed'.It will be shown below that the pile-up events can be used to measure the total cross sectionof reaction (2.1).For reaction (2.1) w±p ---> wrfw °p, Figure 3.13 shows three distinct groups are present in theAE vs E plane. The lower band is created by 7.+ particles while the higher band protons.The events outlined by the polygon window are the 'pile-up' events created by simultaneous7r+ and p hits of the S1-S2 detector (see section 2.4). The C veto (see section 2.2) has beendisabled, for this figure. For Figure 3.15, the C veto has been activated; one can see thatthe middle proton band on Fig. 3.13 has disappeared in this plot as a result of a scatteredIr+ triggering the C veto.The question arises: where do the w's in the lower pion band come from? The only w+that one should see are those that fall with the acceptance angle, and hence counted as a'pile-up' event. The other w+'s that fall outside the acceptance angle should simply not becounted. The w's in the lower band are from 'pile-up' events. There are many pile-upevents where the protons are of very low energies and gets stopped in Si and hence one42.. •Chapter 3. Modelling of Experimentrr+p ->^+rr'p86w 4207r+p^•r+•°p0^20^40^60^80^100E (MeV)Figure 3.13 Reaction events in the AE vs E plane. Figure 3.14 Surface plot of reaction events shownin Fig. 3.13.•1. +p ^1 +7 0 pTr'p -> -R+71- Op.6.??E81500..0^20^40^60^80^100E (MeV)Figure 3.15 Reaction events in the AE vs E plane,with C veto enabled.Figure 3.16 Surface plot of events shown in Fig.3.15. (note: this Figure and Fig. 3.14 do not havecommon scales 'out of the AE vs E plane').86w 42043Chapter 3. Modelling of Experimentonly sees the 71-± coming through both detectors. Such an event looks like a 'lone pionevent'. There is no ambiguity associated with 'lone proton events' appearing in the protonband, since the phase space of the l.'s is not restricted to the acceptance angle (see Fig.3.4).7cl-fp —> -rr'p86a)w 420I^I20 40^60^80^100E (MeV)Figure 3.17 Elastic scattering background.For the elastic channel (2.2) ir±p ir+p, Figure 3.17 shows that outgoing particles fallingwell away from, the 'pile-up window'. Hence, this background reaction is removed.0044Chapter 3. Modelling of ExperimentFor (2.3) 7r+p —> ir+-yp, Figures 3.18-3.19 show that events fall outside of the pile-up window.ir+P - 7 +7P8 7T +p . 7'-rpFigure 3.18 Figure 3.19021^1^10^20 40 60E (MeV)80 1004586>a)w 4a20Chapter 3. Modelling of ExperimentFor the reaction (2.4) Ir+p —> -irtir+n, there is a pion band as well as a group of simultaneousi+71-+; both features lie outside the pile-up window: (there is a single count in the pile-upwindow, which is considered negligible).Tr+p -> rr+Tr+nFigure 3.20 Figure 3.21The background reaction (2.5) T±n —> rte p, appears to cause the most difficulties. Thephase space of this reaction is virtually identical to (2.1); as well, the reaction products onthe right-hand side are almost the same. It is not suprising then that the signature of thisreaction in the AE vs E plane (Fig. 3.22) looks very similar to that of the main reaction (Fig.3.13). In particular, one sees that there is a significant number of events in the pile-upwindow, representing — 27% of the total cross section for this reaction. There is oneimportant difference between this reaction and (2.1): both pions on the right-hand side areTr +p , Tr -Err +n0^20^40^60^80^100E (MeV)4686>a)._.w 4a20Chapter 3. Modelling of Experimentcharged. We will take advantage of this fact to eliminate this background. By using thecylindrical veto C most of the events from this reaction can be eliminated (Fig. 2.7). Theno. of events now appearing in the pile-up window is approximately 0.7% of the total crosssection. In principle, this method of removing the events from reaction (2.5) is redundantsince the subtraction of CH2 and C spectra (see sec. 2.3) should eliminate this backgroundaltogether. Nonetheless, we have chosen a more conservative route by eliminating eventsfrom this reaction before the subtraction. It is evident that the '0.7% of the total crosssection' background mentioned above should be eliminated in the CH2-C subtraction.Tr +n --> Tr +Tr pFigure 3.22 Figure 3.23Tr +n -> Tr*Tr -pI^f^I0^20^40 60E (MeV)80 10047Chapter 3. Modelling of ExperimentTr +n —> 7r +7TFigure 3.24 Figure 3.253.4 ConclusionIt is evident from the phase space of the different ir+p channels that it is very difficult toisolate the events from the principal reaction (2.1). We conclude that to measure the totalcross section, one possible strategy is to consider the 'pile-up events' in the AE vs E plane.This strategy successfully isolates a fraction of the events from the principal reaction.86w 420rr +n^rr 4-71- 0^20^40^60^80^100E (MeV)48Chapter 4The Experiment4.1 IntroductionA feasibility study of the apparatus based on chapter 2 was performed at TRIUMF, on theM11 beam line during July and August of 1992. This chapter is devoted to highlighting whatoccurred during the experiment.4.2 Initial Set -up: Additions and Modifications to Original Set -upEven during the intial set-up, it was apparent that a large background signal was present dueto the beam interaction with the S detectors. Therefore, several steps were taken to try andreduce this background and isolate the events coming from the target.Absorber IntroducedIt was discovered early on during set-up that protons that have leaked through along withthe beam pions appeared in the S1 vs S2 plane. In order to eliminate this background, a6 mm CH 2 absorber was introduced placed in front of the beam window (see Fig. 2.2).The S2 ProblemAttached to the S2 detector, are 2 photomultiplier: S2-Left and S2-Right. During a trialrun, it became apparent the signals from the S2-Left and S2-Right photomultipliers did not49Chapter 4. The Experimentmatch up: when the signal (No. of counts versus channel number) from one side wassuperimposed on the other, one signal was skewed relative to the other. This problem, asit was discovered, was a result of a rate dependance of the photomultipliers caused by a highvoltage setting ( —1800 V). The voltage was lowered and to compensate for this, anamplifier was used to boost the S2 signals.Upon inspection of the S2-Left and S2-Right signals matching was achieved. However,while the matching problem was solved another problem with the S2 photomultipliers wastransparent to the experimenters was discovered only during analysis of the data (discussedin Chapter 5).S1 ThresholdAnother technique was used to further lower the background events. The threshold ofacceptance (discrimination level) was raised electronically on the S1 detector, to rejectunwanted high energy events appearing away from the events in the 'pile-up' window.S2 Detector Moved DownstreamTo achieve better time-of-flight, the S2 and S3 detectors were moved 11 cm downstream'.It was not possible to further increase the time-of-flight because of the S2 detector size.' The convention is that the beam starts 'upstream' from the beam pipe and proceeds 'downstream' throughthe target and detectors.50Chapter 4. The Experiment4.3 Running of the ExperimentCalibrationIt is necessary to calibrate the S1-S2 array detectors: that is, to assign actually energies tothe channels2 corresponding S1 and S2 signals. The calibration was performed by sendingpions and protons known energies through the S1-S2 array. Beam pions of 196.4 MeV and'leaked-through' beam protons of 29.3 MeV were used. Both energies are the kineticenergies just before the target.Main RunsAfter the initial set-up, the main runs for attempting to measure the cross section took placeat 2 different energies' 195.2 MeV and 201.2 MeV. Each run is about 10 hours long, witha total number of beam events of 10 10. A rough estimate of the cross section ( — 10 gb)suggests that the number of events from the principal reaction — 150 events at 195.2 MeV.The number of events at the higher energy is expected to be higher (perhaps a factor oftwo) since the cross section increases with energy (see Fig. 1.1).2 Channels here refer to the channels of the analogue to digital converters (ADC) used to record the signals.3 i.e., the kinetic energy of the incident 7,-+ at the center of the target.51Chapter 4. The Experiment4.4 ConclusionIn spite of the difficulties encountered during the intial set-up of the experiment is waspossible to collect data at 2 different energies. In the next chapter, we will describe theanalysis of the data and also the results extracted from the data.52600200 1000/PLOT 8114400^600S2ADC200 1000600 800200 400 1000TOTAL COUNTS = 10507731./PLOT XH340000 ^30000 -20000 -/0000 -0120000100000 -80000 -60000 -40000 -20000 7S2RAOCTOTAL COUNTS - 10903096.TOTAL COUNTS = 10986264.50000 ^4000030000 -20000 -10000 -TOTAL COUNTS - 10946222.25000 "20000 -15000 -10000 -5000 -1500^200000 500Chapter 5Experimental Results5.1 IntroductionIn this chapter, the method for analyzing data will be outlined; as well, the results from theexperiment will be presented.== EXPERIMENT 655 RUN 28 18:15:50 1-SEP-92 14-11.47-1993 14:45/PLOT XHI^ S [AOC^/PLOT 892^ 521.ADCFigure 5.1 Typical spectra from a CH, target run. Vertical scales represent the number events; Horizontalscales represent energy in 'channel no.'.5.2 Analysis of DataThe analysis of the results was performed using the TRIUMF software packages MOLL',NOVA, FIOWA and REPLAY (see Appendix B).53Chapter 5. Analysis of ResultsThe procedure is relatively simple: for a particular run, play back the data event by eventand histogram the signals for the various detectors. Figure 5.1 shows the spectra from theSi and S2 detectors for a typical run.5.2.1 Time-of-Flight CutFigure 5.2 shows a detail of the time-of-flight spectrum between the B3 and S2. Thespectrum identifies where events originate from along flight path across the experimentalapparatus. The first two peaks describe events taking place in S2 and S1. The small bumpof the right-hand side represents events coming from the target. However, it is clear thatthe 'tail' of the S1 and S2 peaks are superimposed on the target peak. The time-of-flightstrategy is to introduced a limit of acceptance in time: e.g., only those events appearing witht > channel 350 are accepted. Such a 'cut' should eliminate most of the background eventsfrom 51 and S2. However, because the tails of S1 and S2 overlaps the target peak, thereis no way, with the existing set-up to eliminate all the S1 and S2 events. In principal onecan 'stretch' out the time-of-flight spectrum by increasing the distance between the targetand each element (B3, Si, S2). But realistically one cannot get an arbitrarily largeseparation because of detector size limits and loss of event particles through the air. Thelimiting factor in the present feasibility study are the sizes of Si and S2: to preserve thecone angle (see Fig. 2.1) for capturing all the protons from the principal reaction. The time-of-flight problem will be discussed in more detail in Chapter 6.54Chapter 5. Analysis of Results== EXPERIMENT 655 RUN 28 18:15:50 1—SEP-92STIME/PLOT %H5(X=100,499)700000TOTAL COUNTS = 11936656.I^I S215—MAY-1993 13:47600000 —500000 —400000 —300000 —200000 —100000 — 51TargetB.30 '^I100^200 300 400 500Figure 5.2 Detail of Time-of-Flight spectrum from a CH, target run. The vertical scale represents theno. of events while the horizontal represents time in 'channel no.' with each channel denoting 50 ps(picoseconds).5.2.2 Events in the AE vs E PlaneFigure 5.3 shows the 2-diminensional spectra in the Si vs S2 plane (AE vs E). Startingfrom the top left plot and progressing clockwise, the first plot is the 'raw' spectrum withouta software time-of-flight cut. There is however, a hardware cut for all spectra introducedin S1 (see sec. 4.2) and hence no events appear below channel 120 of S1. The second andthird plots are the spectrum with a time-of-flight cuts at channel 350 (see Fig. 5.2) and withthe same cut but the S2-left signal only, respectively. For comparison the last plot shows551000800 -600 -V1400 -200 -01000S20^500 1500^2000S IVSZ_CN2/DENSITY 7.5310000 800 -(71...600400200 -0 500 1000S21500 2000/000 ^800 -600 -400 -200 -S IVS2L_CN I/DENSITY 854200 800 1000^1000 ^800600400 -.200 -^0 ^0 400^600S2(qv)747oiO.a(.77OJLi)0)IIC0000(,)00) (7)(00C0(00Chapter 5. Analysis of Results-- EXPERIMENT 655 RUN 28 18:15:50 1-SEP -92 15-MAY-1993 14:23S 1VS2/DENSITY 7: SI^ ^/DENSTY 852^ S1VS2_CNI0^500^1000^1500^2000S2Figure 53 Typical Si vs S2 spectra.a spectrum with the time-of-flight cut at channel 375.Figures 5.4-5.6 show first and second spectrum in more detail. Figure 5.4 (time-of-flight cutat channel 350) will be the one used in the attempt in extracting events from the principalreaction. This time-of-flight cut represents the maximum possible channel for rejecting S1and S2 events but without undesirably rejecting target events. B3 events cannot beeliminated since its signature in the time-of-flight spectrum is much too weak.56== EXPERIMENT 655 RUN 28 18:15:50 1-SEP-92S1VS2_CN117-M4Y-1993 15:51/DENSITY ZS20 _500 1000S22000Chapter 5. Analysis of Results== EXPERIMENT 655 RUN 28 18:15:50 1-SEP-92^ == EXPERIMENT 655 RUN 28 16:15:50 1-SEP-92/DENSITY 1S1^ S1VS2^15-MAT-1993 14:11^/SURFACE %S1^ S1VS2^15-MAY-1993 14:13 1000800 -600 -Li)400 -200 -Figure 5.4 Si vs S2 detail, raw spectrum.^Figure 5.5 Surface plot of Si vs S2, raw spectrum.== EXPERIMENT 655 RUN 28 18:15:50 1-SEP-92S1VS2_CN1/SURFACE %S2^15-MAY-1993 15:13Figure 5.6 Si vs S2 plot, with time-of-flight cut.^Figure 5.7 Surface plot of Si vs S2 spectrum withtime-of-flight cut.57Chapter 5. Analysis of Results5.2.3 Normalization of SpectraIn order to subtract C target spectra from those of the CH 2 target. One must account forthe number of beam events' arising from 2 separate runs for the 2 different targets as wellas the different number density of each target (i.e., the different number of scatterers).Let^I = no. of beam events 2N^= number density of target particles in cm -3Az^= thickness of target in cmn^= Nix , area density of target particles cm -2AI^= no. of reaction events (or no. of particles scattered out of beam)And, let the subscripts C, CH2, H2 denote the corresponding particles.Then, the normalized spectra (per unit beam per unit scatterer) for H2 isAl ^AICH2 _^2In nu Irvir n „,„''2 '`2^`-'''2 ''-'''21 A beam event is defined as B1 AND B2 AND B3 AND (NOT V).2 There is an implicit time interval associated with I in the 'event by event' scenario.58A/cIcnc(5.1)Chapter 5. Analysis of ResultsBut,1H2 =ICH2^and^nH2 =nCH2Because the H2 molecules are bound to the C atom for the CH 2 molecule.For data analysis, we rewrite (5.1) in the following formICH nCHAl II =AICH2^2^/cnc2 2 mc (5.2)Equation (5.2) gives the no. of H2 events normalize with respect to a CH 2 run.n can be calculated fromn=(N Ax)= co NA 8^ (5.3)where^O^= pAx , the thickness of the target in g/cm 2NA = Avagadro's numberco^= molecular weight in gP^= the density of the target in g/cm3For CH2 :^with ScH2 = 0.1480 g/cm2^ncH2 = 6.352 x 1021 cm2For C:^with Sc = 0.1824 g/cm2^nc = 9.166 x 10 21cm259Chapter 5. Analysis of Results5.3 Cross sectionThe total cross section a (in cm2) is given by the well known equation(5.4)Where^I^= is the beam intensity in particles per unit timeA/^= change in intensityA..1C^= thickness of target in cmN^= number density target particles in cm -3n^= area density of target particles in cm 2Hence, the total cross section for H2 is essentially (5.1). The parameter n is introduced toaccount for the fact that only a fraction of the total cross section in measured because weare only considering events in the pile-up window.AIH 2 n a H2- n IH2 H2For a single proton, the cross section is0 = a uH -22(5.5)(5.6)600 o •00..o DO.,C7 L9E8 0000" 2APAA000 0000• • •^o 00000000000 ^CODMOOChapter 5. Analysis of Results5.4 The CH2-C Subtraction SpectraThe C target produces a simular set of spectra. As discussed in section 2.2, to obtain theH2 cross section one must subtract the CH 2 spectra from C spectra. Figures 5.8 and 5.9show the result of such a subtraction, with spectra normalized with respect to the CH 2 targetrun, eqn. (5.2). Figure 5.8 is a 'raw' subtraction without any time-of-flight cut introducedExperiment 655 — 201 MeV — Tcut=0^— Run 28/2930Q(I)c 40020501 00 ^0.........................10^20^30^40^50S2 (2 MeV per channel)Figure 5.8 H2 spectrum in the S1 vs S2 plane, with no time-of-flight cut. The total no. of events inthe plane is 2 879 241, while in the pile-up window the no. of events is 364 556.61Chapter 5. Analysis of ResultsExperiment 655 — 201 MeV — Tcut=350 — Run 28/2950a)E 40(1)- 30Q20co10U)0 ^0 10^20^30^40^50S2 (2 MeV per channel)Figure 5.9 H2 spectrum in the S1 vs S2 plane, with optimal time-of-flight cut. The total no. of eventsin the plane is 241 790 while in the pile-up window it is 32 019.while Figure 5.9 represents the maximum possible cut. The time-of-flight cut has decreasethe total number of counts in the entire plane by a factor of 12. While in the pile-upwindow, the events have decreased by a factor of 11. Nevertheless, the number of countsin the pile-up window is 32 019, which remains much higher than the expected number ofevents from the principal reaction.62Chapter 5. Analysis of ResultsBased on the number of beam events IcTh = 8.082673 x 109 for the CH2 run, a total crosssection of ow= 100 and n = 0.15, a rough calculation using eqn. (5.5) shows that the numberof events expected in the pile-up window is --150  events. Hence, the present backgroundis some — 200 times larger than the signal.The large background is the result of events originating from the different detectors,especially S2 detector which is very thick (11cm). The strategy for removing the 'detector'events had only limited success since there was a lack of time-of-flight resolution forseparating out the target events, due to the limitations of the present apparatus.5.5 The Subtraction ProblemA serious problem was discovered during the analysis of the data. Subtraction of the CH 2and C spectra yielded negative numbers in the Si vs S2 plane. Figure 5.10 shows thenegative contours in the 51 vs S2 plane for Fig. 5.9. The negative peak is at --100  counts.This peak does not appear to originate merely from random statistical fluctuations (i.e.noise) but rather from variation in the structure of the S signals. That is, the source of thisproblem originates from an instability of the Si and S2 signals during successive runs Toillustrate this instability, let us consider the Si and S2 signals from 4 different runs of thesame Carbon target at the same energy (201 MeV). If the S signals are stable, thensubtraction of the normalized spectra with respect to the number of beam events should63Chapter 5. Analysis of ResultsExperiment 655 — 201 MeV — Time Cut=350 — Run 28/2935E  300C.)25eL20(015(r)100^2^4^6^8^10^12^14S2 (2 MeV per channel)Figure 5.10 Negative contours in the Si vs S2 plane.yield a 'zero' result with some accompanying noise. Figures 5.11-5.14 show that no suchmatching exists. Two reasons have been proposed to account for the 'drift' in the S signals.First, the problem may orignate from instability in the photomultipliers. Second, the energyof the beam is drifting; it is known that the uncertainty in kinetic energy of the beam pionsis ±0.2 MeV, on the M11 beam line at TRIUMF. This subtraction problem remainsunsolved and if the existing apparatus is used should be the subject of further study.64120000 ^100000 -80000 -0000 -0040000 -20000 -0Chapter 5. Analysis of ResultsS1 ADC from 4 Carbon Target Runs0^100^150^200S1 (Channel)Figure 5.11 Si Signal Instability.S1 Subtraction Run 34 minus Run 290X(I)'E —2000—3 -200^400^600I I 1^800S1 (Channel)Figure 5.12 Subtraction of two S1 spectra, Run 34 minus Run 29.50 250 300100065200^400^600^8000 1000Chapter 5. Analysis of ResultsS2 ADC from 4 Carbon Target RunsS2 (Channel)Figure 5.13 Instability in S2 signal.S2 Subtraction Run 34 minus Run 2940003000 -2000 -V)1000 -0C)—1000 -—2000^0 200^400^600S2 (Channel)800^1000Figure 5.14 Subtraction of two S2 spectra, Run 34 minus Run 29.66Chapter 5. Analysis of Results5.6 ConclusionFrom the present feasibility study, it is apparent that several problems need to be overcome:first the background will have to be decreased by 2-3 orders of magnitude and second, thestability of the S1-S2 detectors will have to addressed, before meaningful cross sectionmeasurements can be obtained. In the next chapter, different methods will be explored toimprove on the present apparatus.67Chapter 6Redesign of Experiment6.1 IntroductionIn this chapter, alternative ways of measuring the cross section of the principal reaction willbe considered. Modifications to the original apparatus will be introduced.6.2 Hole in the S1 -S2 TelescopeAs seen in the previous chapter the large number of reactions taking place in the S1-S2detector has introduced a large background. One way to deal with this problem is tointroduce a 'hole' in the center of both Si and S2 and hence allow the beam to pass throughthe array without the possibility of interaction. There is however, a disadvantage to thistechnique: some of the legitimate 'pile-up' events will be lost. From phase spacecalculations, at an incident pion kinetic energy of 200 MeV, about 6.5% of pile-up eventswill be lost as a result of a hole equivalent to a 5° cone angle. Therefore, the parameter n(representing the percentage of total cross section measured) will be further reduced by 1percent to 14%. Figure 6.1 shows the events lost for a 5 ° hole. The total number of eventsin the entire plane is 5000. The total number of pile-up events is 1106 and the total numberof events lost as a result of the hole is 72.Using Monte Carlo transport simulation, assuming the distance between the target and 'S'detectors is — lm, and a hole size of 5 °, about 2% of the beam interact with the 'S'detectors. Hence, we can estimate that the number of events in the pile-up window willdecrease from 32 000 to 700 (using the sample run in sec. 5.1.5).68Chapter 6. Redesign of ExperimentAngle Correlation Between Tr+ and p30^ pile—up region^25 -^°,17 69 iiia; oiii te>p,, 0 08°.° 7 2., orix,.cin 2 0 - '4 '1'00; s/41,8%lbo ir;;;;..40.' c:;::411%,": 00^.0 .00.1,, vs..—^0.;:0t?, ,,}41-, (0 0,. 0,^..io —^.°808..8.47,2.tifityg.zire.0rop:..,:,,,,,i; ,,, ..^7  7 8 a.p. 0°801/4. o ° ° 8 ° b .*: ^0 00,0^o8 t.99,!. 00 , 0,!,, $0: 0, :%04.; ok. ,,, 8 ,°,0, , 0 0 * 0: 0 00-O.0 .5 0 e 4.1 t., .^ .0Oee .. 0 O .^00 ^°o i: 00 ,,,t,0 0 o^0^0 '''^so  0^.0 00t^...^0. 0^0^000^ 50^100 150 200%^. rejection region for 5 ° hole^0 ,1_ (deg.)Figure 6.1 Angle correlation between outgoing pion and proton. The 'L' window in the lower leftregion represents events lost for a 5° hole.There are two ways to introduce a 'hole' in the S detectors. One is to physically cut a hole.The difficulty in this technique is to assure that there will be proper light collection in theS detectors. The other is to introduce beam veto detectors much like B1, B2 and B3downstream of the target and before the S1-S2 array. While the advantage to this techniqueis that one does not need to modify the S detectors, the disadvantage is that the vetodetectors introduced will themselves have a background signature.+ 07V p -> 7 lT p-8 15 -00o69Chapter 6. Redesign of Experiment6.3 Increasing Time-of-Flight SeparationIt is obvious that the larger the time-of-flight separation, the better events coming from thetarget will isolated from those of the detectors, particularly S1 and S2. However, thedistance between the target and the S detectors cannot be arbitrarily large, since a'dimininshing returns' phenomenon starts to take effect because the outgoing protons fromthe principal reaction get absorbed by air. For instance, at an incident pion kinetic energyof T„ = 200 MeV, the mean kinetic energy of the protons is — 30 MeV. At a distance of0.775 m, half the protons will be lost. A way to reduce the effect of this problem may beto use a 'bag' of helium to fill the distance between the target and S1-S2. To get an ideahow much the distance between the target and the S detectors needs to be increased, let ussuppose that the incident w+ kinetic energy is T„ =201 MeV. To separate the 'peak' arisingthe target events (see Fig. 5.2), we need to shift the peak to the right by about 100 channels(5 ns). For complete isolation of the target 'peak', we use the fastest possible particlecoming from the target which is a 2-+ with kinetic energy of 201 MeV (elastic scattering) todetermine the increase in distance needed to achieve this time-of-flight separation. Theincrease in distance needed is 1.37 m. Repeating the calculation with it's with a kineticenergy of 60 MeV (these are the maximum kinetic energy it's from the principal reaction),the increase in distance needed is 1.07 m. Clearly, it is not possible to let the outgoingparticles from the reaction to travel through air since as shown above over half the pile-upevents would be lost.70Chapter 6. Redesign of ExperimentL.^d^L.^d^L.7*, p^D^g1^g2^gl01^Q2^Q3Figure 6.2 The triplet set-up.6.4 Triplet LensWith increased time-of-flight separation, not only does one runs into the problem of particleloss through air but also the requirement of large S1-S2 detectors. At a distance of 2 m, tocover a 30° cone angle the S detectors would have to be 1.07 m in diameter. Oneinteresting method has been suggested to overcome both of these problems. Essentially, themethod proposes to use a magnetic quadrapole triplet as a lense to focus outgoing eventparticles, keeping them within a reasonable size envelope downstream from the target. Andby housing the triplet with a vacuum pipe, one can achieve a huge time-of-flight separation(a distance of — 3 m between the target and S detectors can easily be achieved).71Chapter 6. Redesign of Experiment6.4.1 The Triplet ArrangementFigure 6.2 shows the triplet set-up used for the simulation below. Each quadrapole (Q1, Q2,Q3) has a bore diameter of D = 20.3 cm (8"), with a typical field gradient of g — 0.6 KG/cmand effective length of Le = 0.49 m. The parameters that one adjusts are 'd' , the distancebetween the quadrapoles and 'g' the field gradient. For simplicity, a symmetric triplet willbe used, i.e., the distance between Q1 and Q2 equals that between Q2 and Q3; and the fieldgradient in Q1 equals Q3.6.4.2 The Triplet SimulationTo model the effect of the triplet on outgoing particles from the principal reaction, twosoftware routines from TRIUMF was used: RAY 1 RACE' and REVMOC. The firstroutine makes use of a field map of the quadrapole triplet and raytraces particles throughthe system; the optics (focii, focal length, etc) of a particular triplet arrangement can bedetermined. Unfortunately, one needs to use a second routine to raytrace particles from theprincipal reaction because RAY'11(ACE can only handle very small particle divergences.REVMOC is a monte carlo beam transport program that performs the final raytrace withevents from the principal reaction.Raytrace by Arthur Hayes, April 1980.72Chapter 6. Redesign of ExperimentTo summarize and elaborate on the method used:1. Use RAYTRACE to find an optical set-up for a parallel stream of particles(e.g. protons) of fixed momentum. The optics of the system is then 'tuned' sothat there is focusing in both transverse directions x and y. The focii for bothtransverse directions are made to coincide.2. Duplicating the set-up from RAYTRACE, use REVMOC to raytrace eventsfrom the principal reaction.Note: All analysis will performed in vacuum, at an incident pion kinetic energy of 200 MeV.6.4.3 Results from the SimulationProtons from the principal reaction are used to see the effect of the triplet. It is evidentthat the range of the momentum (10-340 MeV) and the range of the divergence ( — 0-30 °)are too large for a realistic size triplet lense to handle. For example, for quadrapoles withbore diameter D = 20.3 cm, 94% of protons gets rejected':for bore diameter of D =30.5 cm, 88% gets rejected.To see the effect of a smaller range of divergence, we limit the x and y divergences to beless than 5°. For quadrapoles withbore diameter D =20.3 cm, 63% of protons gets rejected;for bore diameter of D = 30.5 cm, 41% gets rejected.2 'rejected' implies that a particle has drifted outside a cylinder defined by the quadrapole bore diameter.73Chapter 6. Redesign of ExperimentRay Envelope for Triplet1 1 1 1 11 1 11 11 1 1 1 11111111111111111.11111111111111111 ,,,,, 1111111 1 1 1 11 1 I I 1111 II I I 1111 1111 1 11111111111111 8 ^lllllll 11111/1/111111111111111 lllllll 11111111 l^llll 11111111 lllllll 1111111111110 1^2^3^4^5z (m)Figure 63 Raytrace of monoenergetic protons with Tp = 36 MeV, zero divergence in the transverse (x,y)directions.Plots from analysis with constraint of < 5 ° divergenceTriplet TuningFigure 6.3 shows the result of tuning the triplet set-up for a beam of monoenergetic protonswith Tp = 36 MeV. This energy was chosen because it is the mean energy of outgoingprotons at an incident 7 + energy of Tir , =200 MeV. For convenience and without loss ofgenerality, the proton beam is chosen to have zero divergence in the transverse (x,y)directions.Note: 1.^The triplet occupies the space z= (0.00, 2.92)m for this part of the analysis.Subsequent analysis will shift the triplet to another location in z.74Chapter 6. Redesign of Experiment.302. The beam envelope with the single focus (divergent-convergent-divergentplane) is chosen to be the y direction.3. The beam envelope with the double focus (convergent-divergent-convergentplane) is chosen to be the x direction.4.^Rays from both envelope converge at a focus at z— 4.43 m.Field Gradient of 01 and Q3^Field Gradient of Q2Lt„..1111, .150.10cn. .0020^40^60z (cm)0 80 0 20^40^60^80z (cm)Figure 6.4 Field gradient of 01 as a function of^Figure 6.5 Field gradient of 02, as a function of z.axial distance z. 03 has an identical field gradient.The settings for focusing as shown in Figure 6.3 ared = 60.0 cm g1= 0.258 kG/cm g2 = 0.248 kG/cm.Figures 6.4 and 6.5 show the field gradient of each quadrapole with these settings.755040302010E0---10—20—30—40—501111111111^11^1111 1 1111111^)111111m^)111 )11111^uuuuuuduul1 1 mil li^1u 11111^n 1111^nuuu10^1^2^3^4z (m)Chapter 6. Redesign of ExperimentRaytrace with protons from the principal reactionFigures 6.6 and 6.7 show the result of the monte carlo simulation for a triplet with the abovesettings. The two vertical lines define the location of the triplet, z = (1.53,4.45) m, which isdifferent from the previous location along z axis. It is apparent that even restricting theparticles to divergences of less 5°, the beam envelopes are still unrealistically large.Raytrace of TripletFigure 6.6 Raytrace of outgoing protons from the reaction ir+ p^ir+ ir°p, withdivergence in the x,y directions <^(dcd plane).7611111111111111111111111111111111111111 1111111111111111111 ^11111111,111111111111111111 1111111111111111t11111 15 -10 -5-E(-)^0—5 -- 10 -—15 -—200^1^2^3^420Chapter 6. Redesign of ExperimentRaytrace of TripletFigure 6.7 Raytrace of protons from the reaction 7r + p —> ir + 7r°p, with divergence in thetransverse directions < 5° . This figure shows the x direction (cdc plane).77Chapter 6. Redesign of Experiment6.5 ConclusionIn this chapter, several methods have been proposed to improve on the current set-up.Introducing a hole in the S detectors and increasing the time-of-flight separation remain twofeasible methods in dealing with the background. Preliminary calculations show veryimpressive reductions in the background by implementing these methods. Nonetheless,these calculations only suggest that the background appears to be within the same order asthe events of interest. It is difficult, if not impossible to test out these methods withoutfurther experimentation. It was also shown in this chapter that the triplet lens will not beuseful in helping the gain more time-of-flight separation since the outgoing particle enveloperemain unrealistically large.78Chapter 7Final ConclusionsA feasibility study for measuring the total cross section for the 7r-27r reaction, 7 +p --> 7+ 7°pwas performed. The data collected was not useful in extracting the total cross section.However, the data was useful in accessing the background events for the existing apparatus.The background signal is 2-3 orders of magnitude larger than the 'reaction' signal. Severalways were introduced to help reduce the background: however, it was not possible to stateconclusively that these methods will reduce the background sufficiently to extract a crosssection measurement without further experimentation. In chapter one, we also showed themotivation for performing this experiment in the context of chiral perturbation theory whichsuggests that in order for this reaction to be useful in extracting information about r- irscattering, the experimental error for the total cross section must be less than — +10%.This constraint poses another challenge for measuring the total cross section for thisreaction.79Bibliography[1] Steven Weinberg, Phys. Rev. Lett. 17 (1966) 616.[2] Martin Sevior et al., Phys. Rev Lett. 66 (1991) 2569.[3] Neil Fazel, M.Sc. Thesis (1992) University of British Columbia, unpublished.[4] Eli Friedman, Triumf Research Proposal, Experiment 655 (1991), unpublished.[5] Eli Friedman et al., Phys. Lett. 231B (1988) 39.[6] Eli Friedman et al., Nucl. Phys. A in press.[7] Eli Friedman, Triumf Research Proposal, Experiment 598 (1990), unpublished.[8] Eli Friedman et al Phys. Lett. 302B (1993) 18.[9] J.D. Jackson, Classical Electrodynamics, 2nd ed., John Wiley, Chapter 13 (1975)[10] Yu. A. Batusov et al., Sov. J. Nucl. Phys. 21 (1975) 162;Sov. J. Nucl. Phys. 1, (1965) 374.[11] M. Arman et al., Phys. Rev. Lett. 29 (1972) 962.[12] B.R. Martin, D. Morgan and G. Shaw, Pion-Pion Interactions in Particle Physics,Academic (1975).[13] Steven Weinberg, Phys. Rev. Lett. 18 (1967) 188.[14] J. Schwinger, Phys. Lett. 24B, (1967) 473.[15] M.G. Olsson and L. Turner, Phys. Rev. Lett. 20 (1968) 1127.[16] M.G. Olsson and L. Turner, Phys. Rev. 181 (1969) 2141.[17] J. Gasser and H. Leutwyler, Phys. Letters 125B (1982) 312.[18] A.N. Ivanov and N.I. Troitskaya, Soy. J. Nucl. Phys. 43 (1986) 260.[19] J. Lowe et al., Phys. Rev. C 44 (1991) 956.[20] M.G. Olsen et al., Phys. Rev. Lett. 38 (1977) 296.80[21] D. Mark Manley, Phys. Rev. D 30 (1984) 536.[22] E. Oset and M. Vicente-Vacas, Nucl. Phys. A 446 (1985) 584.[23] J. Gasser and H. Leutwyler, Phys. Rep. 87 (1982) 77.[24] J. Gasser and H. Leutwyler, Phys. Lett. 125B (1983) 325.[25] J. Gasser and H. Leutwyler, Phys. Lett. 125B (1983) 321.[26] A.V. Kravtsov et al., Nucl. Phys. B 134 (1978) 2622.[27] J. Gasser and H. Leutwyler, Ann. Phys. (N.Y.), 158 (1984) 142.[28] J.F. Donoghue et al., Phys. Rev. D 38 (1988) 2195.[29] V. Sossi, Phys. Lett. B 298 (1993) 287.[30] V. Barnes et al., CERN Report 63-27 (1963).Appendix AElectronicsFigure A.1 Block diagram of 'beam' logic.82Appendix A. ElectronicsFigure A.2 Block diagram of 'detector' logic.83^ 'INHIBIT SCALERS'CBSC212 BIT 0OR LAM^TDC START^ GATE ADCTRIGGER CAMAC(C212 STROBE)B SAMPLE'BLOCK EVENT HARDWARE'B•S•COR VETOSTOP'COMPUTER'END BUSY PULSEMASTER'COMPUTER BUSY' (OUT. REGISTER BIT 0)START222GATE NIMt(OUT. REGISTER BIT 1)Appendix A. ElectronicsFigure A.3 Block diagram of 'event' logic.84BIT0BITBITTDCB SAMPLE ^B•S•CC -0ND021OUTPUTREGISTER0 e__,.... MASTER1 •--.— END BUSY2.^SCALER CLEARJ11STARBURSTSTOPS---•RF--•CAP. PROBEwipSTOPSTOPC212COINCIDENCEBUFFER...____OR LAMSTARTOR LAM STROBEoilXTERMINATEAppendix A. ElectronicsFigure A.4 Various modules.85Appendix BAnalysis SoftwareListing of Routines for Driving MOLLIE'There are 3 routines (define, dplot and scalers) in 3 source files (definel.for, dp2.for, andsca.for).definel.forC this version is for multiple time cuts analysisCSUBROUTINE DEFINECCCALL PTITLE1('EXPERIMENT 655')CALL PTITLE2('RUN NO. ')CC DETECTOR HISTOGRAMSCCALL TH1ST(1,'S1ADC$')CALL PHIST(1, 0.0, 2.0, 500, 0)CALL THIST(2,'S2LADC$')CALL PHIST(2, 0.0, 2.0, 500, 0)CALL THIST(3,'S2RADC$')CALL PHIST(3, 0.0, 2.0, 500, 0)CALL THIST(4,'S2ADC$')CALL PHIST(4, 0.0, 2.0, 1000, 0)c***********************************************************************C S1 VERSUS S2 HISTOGRAMSCCALL TSCAT(1,'S1VS2 @S2gS1@$')CALL PSCAT(1, 0.0, 40.0, 50 , 0.0, 20.0, 50)CMOLLI stands for 'Multi Offline Interactive Analysis' and is a software package for offline analysis of data.for more information see the documentation titled 'MOLLY by Anne W. Bennett (1983) and Corrie Kost (1985).CCCC86Appendix B. Listing of Routines for Driving MOLLICCALL TSCAT(3,'S1VS2_CN2 @S2@S1@$')CALL PSCAT(3, 0.0, 40.0, 50 , 0.0, 20.0, 50)CALL TSCAT(4,'S1VS2L_CN1 @S2@S1@$')CALL PSCAT(4, 0.0, 20.0, 50 , 0.0, 20.0, 50)CALL TSCAT(5,'S1VS2R_CN1 @S2@S1@$')CALL PSCAT(5, 0.0, 20.0, 50 , 0.0, 20.0, 50)CALL TSCAT(6,'S1VS2L_CN2 @S2@S1 @$')CALL PSCAT(6, 0.0, 20.0, 50 , 0.0, 20.0, 50)CALL TSCAT(7,'S1VS2R_CN2 @S2@S1@$')CALL PSCAT(7, 0.0, 20.0, 50 , 0.0, 20.0, 50)C***********************************************************************C TIME OF FLIGHT HISTOGRAMSCCALL THIST(5,'STIME$')CALL PHIST(5, 0.0, 2.0, 1000, 0)CALL THIST(6,'TCAP$')CALL PHIST(6, 0.0, 2.0, 1000, 0)CALL THIST(7,'TRF$')CALL PHIST(7, 0.0, 2.0, 1000, 0)CRETURNENDCCCCAppendix B. Listing of Routines for Driving MOLLIdp2. forC this version is for multiple time cuts analysisC SUBROUTINE DPLOTCC CSUBROUTINE DPLOTCCCOMMON /EVENT/ RAW(50)C COMMON /IREC/ IRAW(50)CREAL*4 TCUT1 /350.0/REAL*4 TCUT2 /360.0/C^REAL*4 TCUT3 /375.0/INTEGER*4 EMASK /1/INTEGER*4 BMASK /2/CREAL*4 S1ADC, S2LADC, S2RADC, S2ADCREAL*4 STIME, CAP PRB, RFINTEGER*4 BITS —INTEGER*4 EVENT, BSAMPLES1 ADC = RAW(2)S2LADC=RAW(5)S2RADC=RAW(4)S2ADC=S2LADC + S2RADCSTIME = RAW(7)CAP_PRB=RAW(8)RF=RAW(9)CBITS=RAW(11)EVENT= (EMASK .AND. BITS)BSAMPLE= (BMASK .AND. BITS)C^WRITE(6,*) BITS,EVENT,BSAMPLECIF (EVENT .EQ. EMASK) THENCALL HIST(S1ADC, 1., 1)CALL HIST(S2LADC, 1., 2)CALL HIST(S2RADC, 1., 3)CALL HIST(S2ADC, 1., 4)CALL HIST(STIME, 1., 5)CALL SCAT(S2ADC, S1ADC, 1. , 1)CALL SCAT(S2LADC, S1 ADC, 1. ,4)CC88Appendix B. Listing of Routines for Driving MOLLICALL SCAT(S2RADC, S1ADC, 1. ,5)IF (STIME .GT. TCUT1) THENCALL SCAT(S2ADC, S1ADC, 1. , 2)END IFCCIF (STIME .GT. TCUT2) THENCALL SCAT(S2ADC, S1ADC, 1. , 3)CALL SCAT(S2LADC, S1ADC, 1. ,6)CALL SCAT(S2RADC, S1ADC, 1. ,7)END IFEND IFIF (BSAMPLE .EQ. BMASK) THENCCCALL HIST(CAP_PRB, 1., 6)CALL HIST(RF, 1. , 7)END IFRETURNEND89Appendix B. Listing of Routines for Driving MOLLIsca.forSUBROUTINE SCALERS (*,*,*)CC= = Suen versionC= = To fill the scaler valuesCIMPLICIT NONEinclude 'molli$DIR:scalers.inc'include 'molli$D1R:molli_units.inc'include 'molli$D1R:mflags1.inc'include 'molli$DIR:pointer.inc'include 'molli$DIR:irec.inc'INTEGER*2 INT2(2)INTEGER*2 MASK(6)/1,2,4,8,16,32/INTEGER*4 KOVER/16777216/CC default integer declaration in INTEGER*4CINTEGER INT4, NWORD, IPOINT, IVAL, K, I, J, NVALUEEQUIVALENCE (INT2(1),INT4)C^C= = Each scaler uses 2 INTEGER*2 words in IREC.C= = These are combined to a single INTEGER*4 word in SCALERC= = Ignore this Type SCALER event if it is the first event of a runCINT2(1)=IREC(KOUNT+4)INT2(2) =IREC(KOUNT+5)IF(INT4.EQ.1)RETURNNWORD=IREC(KOUNT+1)/2NBLOCK= (NWORD-5)/14IF(NBLOCK.LT.1)RETURN1F(NBLOCK.GT.n_scal_m)THENWRITE(prunits(1),50)NBLOCK,n_scal_mIf(log)WRITE(prunits(2),50)NBLOCK,nscalm50^FORMAT('OType "SCALER" Event with ',I4,' block;',/,*^' Array sizes in ANALYZE can handle only',i3,' blocks')RETURN1END IFDO J =1,NBLOCK90Appendix B. Listing of Routines for Driving MOLLIIPOINT=KOUNT+8+14*(J-1)C nscale is 6DO I =1,NSCALEINT2(1)=IREC(IPOINT)INT2(2)= IREC(IPOINT+ 1)SCBUF(I,J) = INT4SCALER(I,J) =SCALER(1,J)+INT4IVAL = I+ (J-1)*NSCALE!POINT = [POINT + 2ENDDOENDDORETURNEND91Appendix CDetectors are made of NE102 plastic scintillator.B1 0 32 x 3.2 mm (0 1.3" x 1/8")B2 0 32 x 3 2 mm (0 1.3" x 1/8")B3 0 27 x 3.2 mm (0 1.1" x 1/8")S1 0 2032 x 16 mm (0 8" x 1/16")S2 0 355.6 x 101 6 mm (0 14" x 4")S3 0 365.8 x 12.7 mm (0 14.4" x 1/2")C (outside dia.) 0 203.2 x 340 x 3 2 mm(0 8" x 13.4"^x 1/8")Table C.1 Detector sizes.92Appendix C. DetectorsTarget Locations: T1 for 220 MeVT2 for 195 MeVFigure C.1 Target geometry.c'393Appendix C. DetectorsNot to scale; all dimensions in mm.Figure C.2 Detector geometry.94


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