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V“? 74 .. : f . _ 3a.. itiéx's’nxév \ . .ma‘llflh‘d‘! “1350“" eM‘O-I a x -( m . u s v I 2 F IHIWWMl”WNW"!”WW”IIIHIHIHI 913 009085 This is to certify that the dissertation entitled BOYCE MILTON HUMPHRIES presented by A STUDY OF MASSIVE ELECTRON PAIRS AND ASSOCIATED PARTICLES PRODUCED AT THE CERN ISR has been accepted towards fulfillment of the requirements fop Z 2 VL - D degree in W f 3%»:(6 fl; Major professor Date /3 M49 [‘77, J MSU-is an Afflrmatiw Action/Equal Opportunity Institution 0-12771 p K i Michigan State \ LIBRARY University ‘J PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. D r—————,_______—=———_______——— ATE DUE DATE DUE DATE DUE fit MSU Is An Affirmative Action/Equal Opportunity Institution emulator-omit} III In,“ I!‘ , I A STUDY OF MASSIVE ELECTRON PAIRS AND ASSOCIATED PARTICLES PRODUCED AT THE CERN ISR By Boyce Milton Humphries A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics and Astrononnr 1991 11( obs Th: ing rap 0111; in t trai met 01" incr Wits rises \9 ‘3 éj’é— /7 ABSTRACT A STUDY OF MASSIVE ELECTRON PAIRS AND ASSOCIATED PARTICLES PRODUCED AT THE CERN ISR By Boyce Milton Humphries A total of 105e+e‘ events, 9e+c+ and le'e‘ with an invariant mass greater than llGeV/c2 produced in pp collisions at a center-of-mass energy of 62.3GeV have been observed. Lead-scintillator shower counters measured the energy of the electrons. Their momenta were measured by a drift chamber array inside a 1.4 T superconduct- ing solenoid. Cross sections are presented as a function of mass, transverse momentum and rapidity. The quantity sd'a/dfidylFo is expected to be a function of 1' = (mz/s) only rather than a function of both m and s for the Drell-Yan model. Comparison in this quantity with data at a lower energy (J?) confirms this prediction. A mean transverse momentum of 2.20 :i: 0.20 GeV/c was found. The average transverse mo- mentum, taken from several experiments, was shown to increase linearly as a function of J3. The tranverse component of the vector sum of associated particles is seen to increase with rising transverse momentum. The multiplicity of associated particles was found to be constant as a function of mass. As a function of pr, the multiplicity rises from 5 at 0.5 GeV/c to 8 above 3.0 GeV/c . ACKNOWLEDGEMENTS I would like to thank the many people who provided the help and support that made this thesis possible. I would like to thank my advisor Bernard Pope for many years of support and guidance. I would also like to thank Jim Linnemann, Stuart Stampke, Bernard Pope and Carlos Salgado for the many weekly meetings that were so important to this research. To the members of the CMOR collaboration, I am very grateful for their advice and ideas. Special thanks to Leslie Camilleri, Christoph Von Gagern, Timothy Cox, Hans-Jurgen Besh, David Hanna, Mike Tannenbaum and Giuseppe Basini. I would also like to thank Marie Anne Huber, our group secretary, who made our stay in Geneva so pleasant. iii Contents List of Tables List of Figures 1 Introduction 1.1 The Quark Model ............................. 1.2 The DrelloYan Model ........................... 1.3 Quantum Chromodynamics ....................... 2 The ISR and the R110 Detector 2.1 The Intersecting Storage Rings ..................... 2.1.1 Beam Energies and Currents ................... 2.2 The Coordinate System ......................... 2.3 The Detector ............................... 2.3.1 Solenoid .............................. 2.3.2 Drift Chambers .......................... 2.3.3 A Counters ............................ 2.3.4 B Counters ............................ 2.3.5 Luminosity and the MM Counters ................ 2.3.6 L Counters ............................ ‘ 2.3.7 Y Counters ............................ 2.3.8 ST Counters ............................ iv vi vii 12 12 13 13 16 22 27 2.3.9 Shower Counters ......................... 27 2.3.10 Lead Glass ............................. 40 2.3.11 Strip Chambers .......................... 41 3 Event Selection 44 3.1 The Trigger ................................ 44 3.1.1 Hardware Thresholds ....................... 44 3.1.2 Software Filter .......................... 45 3.2 Cuts on the Data ............................. 45 3.2.1 RAW to DST ........................... 46 3.2.2 DST to CON ........................... 46 3.2.3 Good Electron Pair Candidates ................. 46 3.2.4 Good Track Requirements .................... 46 3.2.5 Good Cluster Requirements ................... 48 3.2.6 Two Good Matching Clusters & Tracks ............. 49 3.2.7 The Background Estimate .................... 49 3.2.8 Final Event Selection ....................... 51 4 Cross Section Extraction 64 4.1 The Monte Carlo Simulation ....................... 64 4.1.1 Distribution Thrown ....................... 65 4.1.2 Geometric Cuts .......................... 68 4.1.3 Leakage, Smearing and Energy Cuts .............. 69 4.1.4 Cluster Formation ........................ 72 4.2 Acceptance Correction to the Data ................... 75 4.3 Cross Sections ............................... 76 4.3.1 Single Electron Distributions ................... 87 4.4 Systematic Errors ............................. 87 V 4.4.1 Summary of Systematic Errors .................. 5 Associated Particles 5.1 Associated Particle Acceptance 5.2 Associated Particle Distributions 5.3 Charge Ratio ............................... 6 Conclusion A Changes Bibliography vi 99 101 101 101 118 121 122 126 List of Tables 2.1 2.2 2.3 2.4 3.1 3.2 3.3 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Description of drift chamber modules .................. 17 Characteristics of drift chamber signals ................. 19 Characteristics of lead glass SF-5. .................... 40 SF-5 lead glass composition by weight. ................. 40 List of cuts ................................ 47 The final cuts ............................... 50 Efficiency of cuts ............................. 61 Composition of shower counters ..................... 70 Efl‘iciencies for 2 track to cluster matching cuts ............ 75 a and p1 efficiencies ........................... 76 Cross section d’a/dmdyI,=o ....................... 77 The scaling-invariant mass cross section ................. 78 The transverse momentum distribution ................. 82 Radiation lengths of material ...................... 98 Energy balancing in the C and D counters ............... 99 Systematic Errors ............................. 100 vii List of Figures 1.1 Comparison of Feynman diagrams for different processes ........ 6 1.2 Feynman diagrams for electron pair production. ............ 7 1.3 Feynman diagrams for deep inelastic scattering. ............ 8 2.1 The ISR and PS. ........................... ‘. . 13 2.2 The plan view of the R110 detector ................... 14 2.3 The end view of the R110 detector ................... 15 2.4 Electric field in drift chambers ...................... 17 2.5 The beam curve .............................. 21 2.6 Shower counter modules ......................... 25 2.7 A shower counter segment ........................ 26 2.8 Attenuation curve for scintillator light ................. 28 2.9 Energy sharing in shower counters .................... 29 2.10 Cluster frequency for let calibration ................... 31 2.11 Cluster frequency for 2nd calibration .................. 32 2.12 C/(C+D) for electrons .......................... 33 2.13 C/(C+D) for muons ........................... 34 2.14 Percent change of observed energy in angle scan for 3 GeV electrons. 36 2.15 Percent change of observed energy in angle scan for 4 GeV electrons. 37 2.16 Front glass arrays ............................. 39 2.17 Back glass arrays ............................. 42 viii 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 The a distribution ............................ 53 The C/(C+D) distribution ........................ 54 The R.: distribution ............................ 56 The ma distribution ........................... 57 The p; distribution ............................ 58 The depth distribution .......................... 60 Error in efficiency of cuts ......................... 62 Efficiency error .............................. 63 Likelihood curve for (pr) ........................ 67 The longitudinal shower distribution .................. 71 Triggering efficiency of TOF in D counters ............... 73 Multiplicity distribution in D counters ................. 74 Invariant mass dependence of cross section (comparison with experi- ments) ...... - ............................. 78 Invariant mass dependence of cross section (comparison with theory) 79 The K factor plotted as a function of mass ................ 80 The scaling-invariant cross section .................... 81 The rapidity distribution ......................... 83 The Feynman a: Distribution ....................... 84 The transverse momentum distribution ................. 85 (pr) as a function of J3 ......................... 86 H (cr,y,r) ................................ 88 The energy distribution of the electrons ................ 89 The transverse momentum distribution of the electrons ........ 90 The rapidity distribution of the electrons ............... 91 Azimuthal angle distributions (before correction) ........... 95 Azimuthal angle distributions (after correction) ............ 96 ix 5.1 The mean multiplicity as a function of the transverse momentum . . 103 5.2 The mean multiplicity as a function of the invariant mass ....... 104 5.3 dn/dit ................................... 105 5.4 dE/do ................................... 106 5.5 «(ET/do .................................. 107 5.6 1111/de ................................... 109 5.7 dEj/do, .................................. 110 5.8 dErj/do, ................................. 111 5.9 pr,- versus p1- ............................... 112 5.10 (mi) as a function of pr ......................... 113 5.11 (pr) as a function of prj ......................... 114 5.12 —p1-,- cos ..................... 117 5.15 Charge Ratio ............................... 119 A.1 Efficiency Changes ............................ 125 Chapter 1 Introduction 1.1 The Quark Model Today there are several hundred known “elementary” particles, so it is helpful to begin with some classification of them. There are three major groups; hadrons, leptons, and gauge bosons. The leptons and gauge bosons are at present considered to be elementary: at energies available at today’s accelerators, no evidence for structure has been detected in leptons or gauge bosons. Hadrons, on the contrary are composite particles. Several hundred hadrons are known to exist as compared with three lepton families. In 1964 Gell-Mann[1] and Zweig proposed that hadrons were composed of quarks. These quarks would be spin 1/2 fermions, carry charge +2/ 3 and -l / 3, and have a baryon number of l/ 3. Baryons such as the proton and neutron are composed of three quarks. Mesons such as the 1r+ and 1r‘ are composed of a quark and an antiquark. In 1964, only three flavors of quarks were needed to account for all the observed hadrons. Today there is evidence for five quarks and a sixth is expected. Since quarks are fermions they must obey the Pauli exclusion principle. Yet there are certain baryons such as the A‘H' and 0‘ that have three quarks with the same charge, baryon number and flavor. It is therefore necessary to add another quantum number to quarks called color. Quarks come in three colors (red, green, and blue). But when quarks combine to make hadrons they do so in a way such that their net 1 2 color is zero. That is, hadrons are colorless. In the 1960’s high energy electron beams were used in deep inelastic lepton-nucleon scattering. It was found that the electrons were scattered with large transfer of momentum more frequently than had previously been expected. This suggested that the nucleon has internal structure, in analogy to Rutherford scattering. Consider an incident electron with energy E being scattered by an angle 0 with a final energy E". These inelastic collisions are generally described in terms of the energy transfer V and momentum transfer q where qu—E' and qupu—pL. The general form of the cross section is do _E' 4mm2 2 0 3 d—-—q’du= E q” —{2W1(u,q )sin 2 + W3(V,q )cos2 —} where a = 1/ 137 is the fine structure constant. It was discovered that at large values of u and q', 11W; depended only on the ratio qz/u. This phenomenon, predicted by Bjorken[2], is known as Bjorken scaling and suggest that the structure observed in the nucleons is “pointlike”. 1.2 The Drell-Yan Model In 1970 Drell and Yan[3] proposed that lepton pairs seen in hadron-hadron collisions [4] were produced by quark-antiquark annihilation to a virtual photon and its decay. ha+hs-+1+l-+X The Drell-Yan model was important in that it made precise predictions. The total cross-section could be predicted with the knowledge of the colliding hadrons’ parton distributions f:'(:c) and ff(:c) where x is the quark’s fraction of total momentum of the hadron. d’a' 81m 2 I'm d—_Msz =9}Ms(‘,,1 + z ) Z e?{f9(21)f:(22) + f$(zl)fb(a:3)} 3 The Drell-Yan model also makes a prediction for the angular distribution of the dileptons do (1 cos 0 o<1+c0320 where 0 is the angle between the quarks and leptons in the center of mass of the virtual photon. The “naive” Drell-Yan model also makes predictions about the distribution for transverse momentum of the electron pair, pr. The W of lepton pairs should be zero. However this assumes that the quarks have no initial transverse momentum. From the Heisenberg uncertainty principle the quarks are expected to have an average 111» z 0.3. It turns out that the data have a higher average p1 that increases with beam energy, which is not predicted by the model. Another problem with the Drell-Yan model is that it predicts a cross-section that is lower than that observed. This discrepancy is usually expressed as the ratio of the measured cross-section to the predicted cross- section and is known as the K factor. These two failures of the Drell-Yan model are generally attributed to the absence of strong interactions in the model. 1.3 Quantum Chromodynamics Today QCD is regarded as the most likely candidate for a theory of strong interactions. The partons in QCD are quarks and gluons. The quarks come in 3 colors and have some non-zero mass. The gluons, which are massless, mediate the strong force. The gluons have a total of 9 color and anti-color combinations, but one is colorless, so there are 8 gluons that interact with a coupling constant a,. Since gluons have color charge, they interact with each other. This interaction makes QCD a non-Abelian gauge theory which differs greatly from QED. In QED an electric charge, because of the virtual electron-positron pairs, polarizcs the vacuum. The charge density is higher near the charge and gives an effective coupling constant as. This is given by a ___ a(#) E 1-9i51109(3i) where Q is related to the energy of the probe and u is the lower cutoff energy. In QCD a quark would be surrounded not only by virtual quark-antiquark pairs but also virtual gluon pairs as well. If there were only quark—antiquark pairs, QCD would behave in much the same way as QED. But the quark can surround itself with gluon-pairs which tend to decrease a. closer to the quark. The virtual gluons have the greater effect and a. decreases nearer the quark. More quantitatively 121r “‘(Q) = (33 — 25,)1n(§;) where n, is the number of quark flavors and A is the QCD scaling parameter. Note that as Q becomes large a, approaches zero. This is known as asymptotic freedom. For this reason, perturbative methods can be used in QCD for predictions in high momentum transfer interactions. At lower Q2 values a. becomes large which helps explain why no isolated quarks have been observed. In fact, partons which interact through the color force are expected to be confined in such a way that they form color neutral hadrons. Because predictions from QCD based on perturbative theory rely on a. being small, little is known about the low energy limit of QCD. Unfortunately, the scattering of hadrons inevitably involves these “soft” interactions, as well as any “hard” collision that might occur. Since no one has been able to calculate the soft collisions, we must rely on measured and parameterized quark and gluon densities that describe the distribution of partons in initial state hadrons and fragmentation functions that describe how the final state partons evolve into hadron jets. It is not immediately obvious that this approach is valid. However Collins, Soper and Sterman [5] have proved the validity of factorization to all orders in perturbation theory for leading twist. 5 Factorization being valid, the Drell-Yan cross-section can be calculated as a per- turbative theory series in a.(Q3), 0 = Z GHQ'MI: Is=0 where Q2 plays the role of the momentum scale in the Drell-Yan process. At each order of perturbation the A,- coefficient can be expanded in a series of logarithms of Q3/19- An = BMln"(Q’/A') + B -1 ln"’1(Q’/A’) + These logarithms arise from multiple hard collinear gluon radiation. Since ln(Q3/A’) is proportional to 1/a(Q’), summing over all the terms in the perturbation series is required if all terms proportional to some given power of a,(Q’) are to be taken into account. The leading log approximation (LLA) retains only the largest power of ln(Q’/A’) at each order of perturbation. The advantage of the leading log approxi- mation is that it leaves the Drell-Yan cross section unchanged except that the quark densities acquire a Q2 dependence, the same dependence as that of quark densities in deep inelastic scattering. Figure 1.1 shows the Feynman diagrams contributing to four different cross section. The diagrams for deep inelastic scattering, neutral currents and charged currents differ only by the initial boson (top left of each Feyn- man diagram), a photon for deep inelastic scattering, Z0 for neutral currents and Wi for charged currents. Otherwise the diagrams are the identical. While lowest or- der predictions agree well between deep inelastic scattering, and charged and neutral currents, predictions of the Drell-Yan cross section are about a factor of 2 below the measured values. In a paper by Altarelli, Ellis and Martinelli [6] the cross section do/dQ’dzp is calculated in QCD retaining all terms up to order a,(Q’). Expressed in terms of the bare quark and gluon distributions the cross section is given by do”? , 41m;2 3 111231 1dr; (1Q: (AB-+1IA)——9SQ2;C, 0 :1— 0 ‘z—z- DEEP INELASTIC NEUTRAL CHARGED DRELL YAN SCATTERING CURRENTS CURRENTS PRODUCTION >~ a /— .5 /— as >.. I §< ' ' N —— Quark NW Photon mm Gluon ------- 2° Boson ---------- Wt Boson asst? Figure 1.1: Comparison of Feynman diagrams for different processes. {[9i1](31)§i2](32) + (1 H 2)] [5(1 - Z) + 9(1 ‘- 3) (a'(t)2qu(z)t + ao(t)fq.DY(z))] l } where z = T/(zltz) = Qf/s and t = ln Qz/p'. P,,(z) and P"(z) are respectively +[(q[;](21,t)+[11(3nt))9m(32)+(1 H2)]0(1— z)[a'() P,,(z )t+a.(t)f,,Dy(z ) the quark-quark and quark-gluon splitting functions. The terms a.f¢.py(2) and a,f,,py(z) are associated with the diagrams of figure 1.2b) and 1.2c), respectively. Because of infrared and collinear singularities in the terms meY and fmpy it is more convenient to express the cross section in terms of Qf-dependent quark distribution functions which gives dam, 41m:2 d__zl 111—z, T—Q,(AB (IX): 9562—72.: glj-jo 31032 {[q inanimate + (1 H 2)] [6(1 — z) + a.(t)o(1 - 2) (sum) - 255(2)» ' DRELL YAN PRODUCTION » >- / b) Figure 1.2: Feynman diagrams for electron pair production. + [(q[,1](zi,t) + 175:1](31atl) 9m(32) + (1 H 2)] a.(t)0(1 — z)(f..ov(z) - fa.2(z))} The terms a.f,,g(z) and a,f,,3(z) are associated with the diagrams of figure 1.3b) and 1.3c), respectively. Therefore the contributions of order a, in deep inelastic scattering have been subtracted out and replaced by contributions of order a, from Drell-Yan. The two terms (fq,DY - 2f“) and (fmpy — f“) are free of singularities since the singularities in Drell-Yan cancel those in deep inelastic scattering. a,(t) (fs.DY(z) - 2f9.3(z)) = “$593533: —6-—4z +2(1 +2”) [1%1—__-_-z—L)'l]+ + (1+ 4—31) 6(1 - 2)} DEEP INELASTIC SCATTERING ~ at? °> L2<§< Figure 1.3: Feynman diagrams for deep inelastic scattering. sensors) — 1.12)) = 335?; {12' + (1 - 2r] In (.1_-_>: + g - 52 + g}. (1.1) At sub-asymptotic energies, the (fq,Dy(Z) — 2 f,,3(z)) correction is large and positive. This is true for pp scattering (where the leading term is proportional to small sea densities) as well as for the (not so obvious case) of 1rp and pi) scattering (valence- valence processes). In contrast, the correction due to the (f,,py(z) — f,,3(z)) term is small and negative even for pp scattering. One test of the QCD theory is the prediction of the qr distribution. Initially only certain regions of the qr were predicted, making comparison to data of limited use. But an expression for the distribution of qT has been found [7]. This expression for 9 the qr distribution satisfies the following requirements: 1. The 0(a,) perturbative distribution coming from one-gluon emission is recov- ered at large qr. 2. Soft gluon resummation is performed at leading double logarithmic accuracy in the qT «i Q region. 3. Only terms corresponding to the emission of soft gluons are resummed. 4. The integral of the qr distribution reproduces the known results for the 0(a.) total cross sections. 5. The average value of q} is also identical with the perturbative result at 0(a.). 6. All quantities are expressed in terms of precisely defined quark distribution functions at a specified scale. To perform the calculations the cross section is split into two pieces. do dQ’dquy = X(9i'a Q’w) + Y(q§~, Qzay) (1.2) The X term is an integrable distribution but is singular at qT = 0. The Y term is finite as qr —+ 0. By performing a Fourier transform of X into impact parameter space the collinear singularities can be factored into the parton distribution functions of deep inelastic scattering. After a resummation is performed in impact space, a second Fourier transform returns X back to qr space. As a result the equation for the Drell-Yan cross section is . do dab . ___ = — "qT‘b 3 3 5(5'.Q'.u) 2 a . dQ’dqtdy N (f 4w ‘ R“ 1Q .308 + Y(qT.Q .10) (13) where N = 41ra3/9Q35, sweaty) = ff 314,342?” MW) — 11 {[1 + Da.(k’)] meme”) — 3} (1.4) 10 and R(b’,Q',y)= 1103113211”) [1+a'(t)4( 31“ 242—: 11.2%] +35%): [/ _fq(z)H(zg/z,zg,P2)+/;d—fq(z)H(zo32/211924 +a__.(t)1 211' 2 [1.313(2) We" /z 23,105+ /;d —f.(z)K1(z‘1’,23/z, 103)]. (15) Other expressions needed for the calculation are AT/fg = [(1 + r)’/4ch'(y) — 711/3 (1.6) and 21rD = (961 -%1r3 — 311,). (1.7) The 1’ term can be split into the qq' annihilation term and the Compton scattering term. },(qTrQ2 y=) a.(t)4 9(QT1 0213/) + (125:); 9(QT1Q21y)1 (1'8) The annihilation term is given by dz H(:c an") 1 (131 HO”. 1’3) Y 2: 2’ = -_ 1 1, 2 1, C(qT Q y) S {/fi.' (31 —- 3;.) $13; 74.." (22 — z2) 3132 +‘qla"{/‘:fia (__zldjlfz +) [H(zl,z;) (I + (“i—i) ) - 2H(z?,3 3)] + /; (21—13:) [Hanan (1 + (2:) ) — 2H(z,,eg)] 1 + fi-e' (132‘:th H(Z;,$3) (1+ (3;) ) — 2H(zl,zg)] + a: (“4:20 33) [H(z,,zz) (1+ (3) ) — 2H(z‘,’,zg ] +H(z;',zg)1n ((11::;]8 _:3} (1.9) 11 while Compton scattering) gives “(#1532130 = {Lg/l ‘1‘“ (31’3” [=5__::23 — r _21'(z;z'1" — T)2] qT fin (21 — :31) (212;)3 _1_ 1 JETKAsza) [2:321 - 1' _ 21133:)? 21):] 913' we" (32 - $2) 3132 (3132) __ ;d_:_'K,(z2,zz) [1—2:( _ 2)] 91' $2 +§[/‘:TT':dz (31 — cf 1+)K1(31,z;)3____(1:2z;-): 1 (1323132 - r + M»... _TKM )T—T] +(1H 2)}. (1.10) The product of the quark-quark distribution functions is defined as Honcho )= 5: ., {q“'(z..Q')«1‘,'(z..Q’) + (1 H 2)} (1.11) and the products of the quark-gluon distribution functions are given by K1(3113zaQ )- - 2 e, [991(311Q2) + Q51](311Q2)] 9m(321Q2) (1°12) and K200112321 Q2) = 2!: 9} [9531032, 03) + 6?](32, (23)] 9l1](311Q2)~ (1°13) The expression in equation 1.3 for the qr distribution was initially derived for the production of the W and Z bosons. Only the definitions for H, K1 and K3 differ for Drell-Yan. The numerical result for the qr distribution for p-p scattering as well as data can be found in reference [8]. Comparison between these predictions and the final data of this experiment are found in figure 4.11 of this thesis. The qr distribution of the prediction are determined using the parton densities given by Duke and Owens with acceptable values of the QCD scale A. No other free parameters were used, nor any intrinsic transverse momentum. Chapter 2 The ISR and the R110 Detector 2.1 The Intersecting Storage Rings The ISR, the first large proton-proton storage ring accelerator, consisted of two con- centric rounded squares with one rotated by 45° with respect to the other (see figure 2.1). There were 8 intersection regions with the beams making a crossing angle of l4.7°. The rings were usually filled with protons which circulated in opposite direc- tions. The ISR was filled by two lines, one for each ring, connected to the CERN Proton Synchrotron. Usually the PS accelerates protons to 26 GeV. The protons were then extracted from the PS through a transfer line and injected into a ring of the ISR where they were accumulated by stacking. This continued until the ring was filled. Then the second ring would be filled. 2.1.1 Beam Energies and Currents Although the ISR usually ran with beam energies of 31 GeV it also ran with beam energies of 15, 22, and 26 GeV. Typical beam currents during the later years of the ISR were 32 Amps in each ring. The ISR was also capable of running with particles other than protons. Data from protons on antiprotons, proton on deuteron, deuteron on deuteron, proton on alpha and alpha on alpha were all collected from runs at the ISR. 12 13 EENLARGEMENT E O Inside Outside X The y-direction is vertically upwards Figure 2.1: The ISR and PS. 2.2 The Coordinate System The system of coordinates used in this experiment (see figures 2.1, 2.2 and 2.3.) are a right handed Cartesian set (my, 2) with the origin at the center of the solenoid, a pointing towards the center of the ISR rings, y vertically up and 2 along the solenoid axis in the direction of ISR intersection region 8. When spherical coordinates (r, d), 0) are used, at = 0 is in the 2-2 plane and 0 = 0 is along the +2 axis. 2.3 The Detector 2.3.1 Solenoid A uniform 1.4T magnetic field was produced by the superconducting solenoid. The 2000 amps of current needed to generate this field were conducted through niobium- titanium wires embedded in a copper matrix. This matrix was then wrapped around 14 Back Lead Glass / Strip Chamber —7 Front Load Glass / 8 Counters \ arm Chambers \:::;::: : :11: . . . 7/ \\\s : J/ A Counter! §\\\\F"f:: / . \- / manna . \\\\ rim-g..;sss::susz.;z~;az=fins: !!!§i!§§m§l\ Superconducting / I: IILII I Lr 1 X Coll [ l L J z 0 1m Figure 2.2: The plan view of the R110 detector 15 Cryostat and Cell Magnet Yoke ‘ A Counters \ \ : ::: . : \ ./ .55; a... \ ‘II . leer ----- ~...::-. ‘I-.: ........ ---------- ‘II-g. 555 Ummmflé Strip chamber chambers (MWPC) B Counters m. L, Figure 2.3: The end view of the R110 detector 16 a stainless steel core to provided the needed strength. Strips of pure aluminum surrounded this matrix and provided a current path and thermal sink in the event of the magnet going normal. This was one of the first large superconducting solenoids built for a high energy physics experiment. The coil had an inner radius of 70 cm, an outer radius of 89 cm and was 170 cm in length. Soft iron pole pieces capping the ends of the solenoid and a yoke, also of soft iron, provided the magnetic flux return. The magnetic field had a uniformity to within 1.5%, with the greatest distortion near the hole in the iron end pieces provided for the beam pipe. 2.3.2 Drift Chambers The drift chambers were designed to measure the momentum ofcharged particle tracks over the full azimuth in the solenoidal field of the magnet. This was done by measuring the radius of curvature of the track, from which the momentum can be found if the magnetic field is known. It was necessary that the chambers be rigid and yet be low in mass for minimum energy loss and photon conversion and that they be able to resolve tracks nearby in a space in the face of high track multiplicity. The chambers were constructed in self contained sectors. These sectors combined to form cylindrical layers. Three layers were complete cylinders (DCMl, DCM2, & DCM3), and two others (DCM4, & DCM5) were inserted between DCM2 and DCM3 or placed within the acceptance of the lead glass. Each sector consisted of two 6 mm thick gaps, inner and outer. Sense wires and field wires were mounted axially and the position of these two were exchanged between the two gaps. The sense wires were 20pm gold plated tungsten wires strung at a tension of 40g. Field wires were 100nm of copper beryllium, with 100g of tension. The sense wires were held 3 mm from the cathode planes by 3 mm x 3 mm x 6 mm glass beads every 50 cm. The time recorded from the sense wires and the wire’s position provided the azimuthal 17 Table 2.1: Description of drift chamber modules Module D01 D02 D03 D04 D05 Mean Radius ( cm ) 20.0 34.0 49.2 63.8 49.0 Length ( cm ) 80.0 103.0 127.0 150.0 150.0 Sense-Field wire pitch( cm ) 1.28 1.49 1.91 2.20 2.20 Sense-Field dist. 13 15 19 22 22 Number of Sense Wires 96 144 160 64 96 Number of Sectors 4 6 8 4 6 Cathode Lines per Cell 16 20 24 28 28 E eEd x . 6mm e c 0 "' I eEc , x eEd 'l‘ 'l 7’5 '1‘ x. . x 0 Sector Boundary ——v 0 Sense Wire 22! Delay Line x Field Wire .- Cathode Circuit Figure 2.4: Electric field in drift chambers and radial coordinate of a particle hit. To measure the z coordinate, delay lines were glued to the cathode running parallel to the sense wires. These delay lines were read out on both ends and the time of the arrival of the pulse recorded. The difference between the two times gives the z coordinate. The average spatial resolution was measured to be 0,: 0.8 cm. Because of the high impedance (see table 2.2) the noise was kept low while low R/ Z kept resistance losses down. 18 To compensate for the Lorentz force of the magnetic field, two components for the E field were needed, E. and E4 (see figure 2.4). This was done by adjusting the individual cathode strips to give the resulting field pattern in both angular Ed and radial E.2 components. The resulting field values were E4 = 1.0 1% and E, = 1.2 13. Unfortunately, it was impossible to maintain a uniform drift field near the field wires. For this reason a polyatomic gas was used to reduce the dependence in the time-distance relation on the field. This is possible because there is a velocity plateau above some critical E field. Argon was added then to prevent the polymerization that occurs in a high radiation environment. The result was 50-50% mixture of argon- ethane with a typical drift velocity of 50 % . The sense wires were held nominally at a voltage of +1.7kV. The delay lines were at ground. Tests at the CERN Proton Synchrotron (PS) test showed the linear time-distance relationship to be constant to 1% and gave a position resolution as good as 170nm. A survey of the drift chambers were made each time the solenoid was opened. Cosmic ray data were taken with the magnet on but the beams off using the Y e A e A 0 Y trigger (see section 2.3.3 and 2.3.7 for a discussion on the A and Y counters) and used for positional information of the drift chambers. The cosmic ray tracks had the advantage of having twice the number of points and three times the lever arm of normal beam data. To determine the track, a fit was made to minimize the residuals using the position of the drift chambers and the simple time-distance relation. This was an iterative process with the the survey value being the initial values. Thereafter the center of curvature of the chambers was constrained and parameters being fit for were left out of the corresponding fit. The distance from a sense wire was given by a quadratic in time multiplied by a small angle dependent factor to allow different drift properties of the electron when the track was not normally incident. Different constants for each side of each gap were required. The best position resolution with beam on was found to be 400nm rms, with uncertainties being in the time-distance 19 relationship and the exact shape of the chambers. In order to find the momentum resolution, a Monte Carlo program was used that generated tracks with known mo- mentum and points with the measured resolution. These points were then supplied to the usual track fitting routine. The momentum was found to be Apr/p1- = 3% pr( GeV ) for tracks with all 8 points Apr/p1- = 15% p1( GeV ) for tracks with only 5 points Apr/p1- = 7% pr( GeV ) for overall average These numbers agree fairly well with those obtained from tracks fitted from the two halves of cosmic ray tracks. Table 2.2: Characteristics of drift chamber signals Delay 2.3 £- Impedance, Z 550 (1 DC Winding Resistance, R 110 Q/ m Attenuation of Chamber 2.5 db/m Line-to-Line Variations in Delay and Impedance 3% rms Internal Reflections (Typical) <1% Length (Depending on Module) 80 — 150 cm Drift Chamber Read Out The electronic readout for the drift chambers handled 580 sense wires and 1160 delay lines. The delay lines were amplified by a factor of 10 by a hybridized emitter follower circuit. Signals from 580 sense wires and 1160 delay lines were led out of the solenoid by 3m of R0174 cable, amplified by a factor of 160 and clipped to a 60 ns pulse length. The signals were then connected to the counting room by 35m of RG58 cable. They were discriminated and then fed into the time-digitizing system. The same system digitized times for the scintillation counters and back lead glass signals (see section 2.3.10 for a discussion of the lead glass). The dead time of the discriminators was ~60ns. 20 2.3.3 A Counters The “A” counters consisted of 32 scintillators forming a barrel hodoscope. Located between the D01 and DC2 drift chambers at a radius of 26.5 cm each counter was 87.5 cm long, 4.8 cm wide and 0.6 cm thick. The counters were read out at both ends, giving a total of 64 A counter signals. Light guides were used at both ends of the counters to direct the signal outside the solenoid. A second set of light guides, connected to the first through the air gap in the magnetic endcaps, channeled the light to Mullard XP2230 phototubes. These phototubes were chosen because of their short rise time of 1.6 ns and their high gain. The short rise time was necessary because they are used as the reference time zero of the event. The high gain is needed to boost the weak signal from the thin A counters, made weaker by the long light path. These phototubes were mounted on the return yoke of the magnet and encased in p metal shields to minimize the magnetic field. 2.3.4 B Counters The “B” counters were positioned just outside the solenoid at a radius of 87.5 cm and covered the area between the iron yokes on both sides of the magnet. They formed two hodoscopes of 12 scintillator counters each. Each counter was 184 cm long, 11.2 cm wide, 1 cm thick and was read out on both ends. Short light guides directed light from the B counter to 56AVP phototubes. The signal from the phototubes was then split, with one part going to discriminators and timers and the other part going to LeCroy 2249 ADC’s for digitization. The B counters were used to detect electromagnetic showering in the coil by electrons and photons. 21 Beam Curve for Measuring heff a) 70 _H'rl'fl'r'T'TrWHrr'"Fr"'i""Ivrr'_ 4.1 _ a C _ 0 Old MM Counters 4 :3 - . O 50 : C1 New MM Countersx0.005 — 0 _ /[3\ j 2 I I 2 50 _— 550; j E p’ at 3 4O :- ,' \ -+ 30 ; 3 in i t .' O\ * 20 —- / ( - _ ' ‘ 1 1o _— é -_ O r-l 1 l l l ill—16711 1 I [1 L1 1 Li Ll l 14 >®H ll 1 l 11‘ -4 -:5 -2 -1 o 1 2 3 4 vertical beam separation in mm Figure 2.5: The beam curve The beam curve was used to obtain the effective height of the intersection of the two beams. The two beam curves above come from the two sets of counters used to measure the luminosity, the “old” and “new" MM counters. 2.3 MI In lon lur b0 C81 “'1' 0116 To th' 22 2.3.5 Luminosity and the MM Counters Luminosity is defined as the counting rate per unit cross section or 1 dN L — ;_dt_o (2.1) In order to detect rare events it is necessary to have either a high luminosity or a long running time. In order to measure the luminosity at the ISR another equation is needed for the luminosity. Consider the case of two crossing rectangular beams in the lab frame, both with width 10, and height h. Furthermore the density in particles per cubic centimeters for each beam is n; for beam one, and n3 for beam two. The crossing angle is a and the particle’s velocity is v for both beams. The luminosity can be written as 1 (interactions E = — traversal ) - (lab traversal rate). (23) 0’ The number of interactions per traversal is Lorentz invariant and is easier to consider in the rest frame of beam two. The relative velocity of the two frames is given by H as a fraction of the speed of light. The variable 7 is the usual 7 = (1 — s')-1/ 3. Variables in this frame will be primed. Consider the traversal of one particle in beam one. Then interactions . == rate - traversal time (2.3) traversal wl I I = on v —. 2.4 2 11:; sin a' ( ) t 3 l t 9’- sin a' = an 3 a a z an 3 (2.5) 7 \/1 + 9%; 7 “i = 712/7 (2-6) thus interactions __ 071311) traversal - tan a/2 (2'7) 23 The lab traversal rate is simply lab traversal rate = nlwhvl. (2.8) Combining equations 2.2, 2.7 and 2.8 gives 2 anlngw hc L = ——— 2.9 tan(a/2) ( ) The currents in beam one and beam two are I; = enlwhv (2.10) I; = engwhv (2.11) respectively. A substitution to replace the width and density dependence with a current dependence gives 1 1113 c = Emma/2) (2.12) Since the beams were not rectangular h is replaced by heg- for the more general equation _ 1 I113 _ ce2 heg- tan(a/2) (2.13) where ha: = ”1(2)” ' I ”’(‘W (2.14) fp1(z)p3(z)dz and where p;(z) are the beam vertical densities. Since the currents are usually well known, only heg- is yet to be found. This is accomplished by measuring the beam curve [9] (see figure 2.5). The rate of interactions measured by the set of “MM” counters (see section 2.3.5) is related to the beam densities by the equation A A R(Az) = I: / p1(t + {Wt — 75w. (2.15) where A2 is the beam separation distance and R(Az) is known as the beam curve. This equation shows that the denominator of equation 2.14 is proportional to 24 R(Az)m if he“ is chosen to be minimum. Integrating equation 2.15 over the beam separation distance and rearranging gives / magnum) = [cf/p1“ + 325),)“: — 9;)dtdmz) (2.16) = k f / p1(t + 925),)“: - —A2—z)d(t + 925W — 92—”) (2.17) = k/p1(zl)dzl / p,(z,)dz, (2.18) which is proportional to the numerator in equation 2.14. So, h.“- can be rewritten as _ (Area Under Curve) ha: - (dN/dt)... (2.19) If the beam curve is Gaussian then heg = Zfia’bem = V21ra’b..mm,,. x 1.062 x FWHMmmcm. (2.20) Since the luminosity can be calculated the constant, s, that converts the rates in the luminosity counters to the luminosity can be found by the equation n = («IN/cit)“. L (2.21) Old MM Counters The “MM” counters were used to measure the luminosity. They consisted of eight scintillator sheets measuring 43 cm by 20.5 cm mounted in pairs on the four corners of the magnet not shielded by the return yoke. From the interaction region and looking inwards they appeared top right and bottom left. Looking outwards they were top left and bottom right. Therefore an interaction producing back to back particles would have to hit two sets of “MM” counters, a top set and a bottom set. A coincidence of four scintillators in this combination was used to define one real event. New MM counters The interaction rates of the old MM counters were too low to measure the luminosity of p~p stacks. So the new MM counters were designed to be high rate counters. This 25 Internal Guides 200M" Side Plates Mylar O O O = O o 0 External Guide Holes Iran Front Plate SCH EMATIC Figure 2.6: Shower counter modules A Sh lator piece 2.3.6 In on used. at C E 26 Flasher Systems Fibers D Counters ( Pole Piece External Guides (C'Counters Light Phototubes Guides g Figure 2.7: A shower counter segment A Shower Counter Segment. Each segment was comprised of 16 layers of lead and scintil- lator. Internal light guides directed light through the shower counter box and the iron end piece to external light guides connected to phototubes. was done by placing them close to the beam. These scintillation counters formed four telescopes pointing to the interaction diamond, where the beams cross, and start at 35mrad from the beam. Rates for the new counters were 200 times higher than the old MM counters. Measurements of hen- by the old and new MM’s usually differed by less than 2%. The beam curve as measured by the old and new MM counters is shown in figure 2.5. 2.8.6 L Counters In order to monitor the beam condition a set of counters called the “L” counters were used. These scintillation counters were maintained and operated by the ISR division at CERN but a copy of the signal was supplied to the R110 counting room. The L counters were located in pairs about 10m upstream of the detector and were separated 2.3 The of t 1 cr LeC. A cc these very 2.3.8 There sectio: 7.5 cu they c deposi muons Cerenk Check. 27 by approximately 3m. Each counter was 25.5 cm long, 21 cm wide and 1 cm thick. A coincidence in a pair of the counters would generate one background count. 2.3.7 Y Counters The “Y” scintillation counters covered the return yokes of the magnet with two groups of three counters on each yoke. Each counter was 120 cm long, 15 cm wide and 1 cm thick. The counters were connected to 56AVP phototubes and digitized by LeCroy 2249ADC’s. The trigger of diagonally opposite Y counters with at least two A counters selected cosmic rays passing through the center of the detector. Since these cosmic rays have a track length twice a long as those in regular events, they are very useful in alignment of the drift chambers. 2.3.8 ST Counters There was one “ST” scintillation counter located behind each back glass array (See section 2.3.10 for a discussion of the lead glass). These counters were 190 cm long, 7.5 cm wide and 1 cm thick, and were hung vertically. Provided with remote control they could be moved behind any column of the back glass array. A trigger on energy deposited in the ST counters gave a data sample with an enhanced proportion of muons and noninteracting pions. Since muons deposit a characteristic amount of Cerenkov light in the blocks of lead glass their signals could be used as a calibration check. 2.3.9 Shower Counters The shower counters consisted of four modules each with eight segments 150 cm long (see figure 2.2). Each module covered 0.88 radians and was referred to as a sextant. These sextants were enclosed in a steel box (see figure 2.6). Segments making up the modules were comprised of a wedge-shaped sandwich of 16 layers of lead and T (Lab C+ Q>_+C_¢L *LCfiazl. 0230 The a form, 28 Attenuation Curve for Shower Counters 0 2 FI I I I I I I I l I I I I I I I rfl I FI I I I I I I I I I I I I I I I Id b " -1 a 3 '3 0 right phototube O 3 1.75 - j 0 I . 4" L & Cl left phototube {’3 -i Q) L L .2 1.5 _ QC] d i H r o . U I o I 31.25 7 \ch o, 1 L- . \Q 0 9' . +4 : ’ ’ 1 gr 1 ' o ’0 4 r . 1 .6 : O 0' 0.0 Exam j £0 75 ’- OQO QUE] _. o : 0 2 .‘2 . . 3 L L Q o 5 : i 0.25 :- { I.1 1 1L1 1 11_l l 1 1 1 1 l L 1 1 1 l 1 1 1 1 l 111 11 1 l l l l l 1 lL-l -100 -75 -50 -25 O 25 50 75 100 displacement in cm Figure 2.8: Attenuation curve for scintillator light The attenuation curves for scintillator light in the shower counters have an exponential form. F an O COWHUO oeocw a LQ+CZCU Cm > Fractim a functi 29 Transverse Energy Sharing I I I r l I r I I I I I I I f I I I I T I I I I d Counter Struck .0 an I I I W I I I l I I I I I I I I 1 l 1 1 1 1 i L 1 1 1 l 1 1 Fraction of Energy in Counter 0 0.4 P: ._ 0.2 — . ; : - i -. Next Nearest Counter H.’ 3 0 in . . . i . Lil . l . . . 1+ 0 0.2 0.4 0.6 0.8 1 Fraction of Counter Width Figure 2.9: Energy sharing in shower counters Fraction of energy a particle deposits in the counter struck and the next nearest counter as a function of its position in the counter. scin‘ lay: and plat pror guid into the [nag teas Ofit of31 THIe A.“i of h Spec tract anot to ti Spec in tl the, Conv only the 1 30 scintillator (see figure 2.7). The lead layers were 0.5 cm thick and the scintillator layers were 0.43 cm thick. Each segment was individually wrapped in aluminum foil and separated from other segments by two layers of 100nm thick mylar. A 0.6 cm iron plate for the two upper modules and a 0.3 cm iron plate for the two lower modules provided support. Both ends of the scintillator layers were attached to internal light guides which grouped the first 4 layers into a “C counter” and the remaining 12 layers into a “D counter”. Light guides 85 cm long protruded through the steel box and the iron end piece to the C and D phototubes outside the solenoid and its strong magnetic field. The connection of the internal light guides and the external guides was made through a dry joint maintained by mechanical pressure. Since both ends of a segment were read out, and there were two compartments per segment, a total of 32 phototubes was used per sextant. The Flasher System A “flasher system” was used in the calibration of the shower counters. The source of light for the flasher system came from EG&G KN22 krytron tubes. Since the spectrum was too low in blue light, a filter was used to shift the spectrum. A fixed fraction of this light was channeled into the C and D counters via optical fibers while another fraction was went to the “reference counter” phototube. Light that went to the shower counter was fed in independently at each end through light guides specifically shaped to mimic the light distribution expected for real particles. Electrons and photons that struck the shower counters lost most of their energy in the counters. Typically the light generated in the scintillators is proportional to the energy of the incident particles. A consistency problem occurs when this light is converted to an electrical pulse by the phototubes. The pulse height is determined not only by the light reaching the phototube but also by the voltage supplied to the tube, the temperature of tube and the surrounding magnetic field as well as effects from ULQ+U. __L wC +CQLLQC The of i, the Sine moc' 31 Frequency of clusters for first calibration 50 I l I I ' I T I ' I ‘ I (0 L. " .. Q) - . 4.1 m - .. 3 " .. 7', 40~ — “- - . o ‘ ___ [__4_; +5 : f " _________ : 030_ I |————i ‘ 8 : L__2_i Q) Q- : _______ Z 20? t—_—T---l_-j . L """"""""""" 3 . i- _. 10»- a 0.1 l l 1 1 l 1 1 1 l 4 l 14 16 18 20 22 24 invariant mass (GeV) Figure 2.10: Cluster frequency for lst calibration The frequency of clusters in the shower counters for the four sextants is shown as a function of invariant mass using the original calibration constants. Both modules 3 and 4 are in the direction of the Lorentz boost and are expected to have the same frequency of clusters. Since modules 1 and 2 are away from the boost their frequency should be lower than both modules 3 and 4. This is clearly not true. Berra-mi AF hi. mi- __ The f] 0f iny;4 im’ari.‘ modu] 32 Frequency of clusters for second calibration 8350 l ' I ' r ' I ' I ' r .9 ;_ * s _—-. * 34°:_"L _ so— ' ___-i q 3 _ l . c ' _____ ___3__‘ G) 30‘ :_—_: ‘ 8 : ————I .__£€ Q) 0- : _ZJ m~ %;;——D1: --- --- . ___- I r i------‘ - 10- i — L____1 ‘ o-J l 1 l 1 1 l 1 l 1 l ‘ l 14 16 18 20 22 24 invariant mass (GeV) Figure 2.11: Cluster frequency for 2nd calibration The frequency of clusters in the shower counters for the four sextants is shown as a function of invariant mass using the second calibration constants. At values significantly above the invariant mass threshold, modules 3 and 4 agree with a higher frequency of clusters than modules 1 and 2. The a iron pl thickei than e 33 for Electrons in each Shower Counter -T...,....,.--.www.me. 5:“ r — sf- é -f g .3 1? 11‘; ‘ 03.111... 1 02 0.22 0.28 03 C/(C+D) Figure 2.12: C/(C+D) for electrons The average value of C / (C + D) for the 16 lower shower counters (counters with a 3mm iron plate at the front) is shown plotted as the solid line. The upper counters which had a thicker 6mm iron plate is shown as a dashed line. The spread for sets of counter is larger than expected. The d; sbower ”Blue 1 34 for Muons In each Shower Counter 1 ' ' ' I ' 'v ' 1 ' ' ' ' . r . 8 — _ 6 — H _ 4 e f — 2 — _ o 1 1 1 1 l 1 1 1 l_l1l—l 1 1 l 1 1 1 1 l 1Fl1 1 1 0.6 0.8 1 1.2 1.4 1. 6 4*C/(C+D) Figure 2.13: C/(C+D) for muons The distribution of 4.0 C/(C+D) was found for muons. Since the total thickness of the shower counters is 4 times as thick as the C compartment the mean should be at 1.0. This figure shows the C counters were initially underweighted. 35 ageing. The method used to overcome this problem was to supply a known amount of light to the phototube through the flasher system. Since a fixed fraction of light went to the phototubes and the reference counter phototube the amount of light reaching the phototubes could be determined by measuring the pulse height at the reference counter phototube. The problem of consistency was thus shifted to reference counters. Again this problem was overcome by supplying a known amount of light. This time a sodium iodide crystal with an americium source provided a constant distribution of light to the reference counter phototube. The shower counters were calibrated in an electron beam at the PS. The N al to flasher ratio in the reference counters and the flasher to 4 GeV electron ratio in each counter was found. The ratio of energy deposited in the C and D counters fluctuates from shower to shower. Advantage of this fluctuation was taken in order to find the correct balance of C and D counters, by minimizing the resolution of the total energy over a large number of showers subject to the constraint that the mean equal the energy of the incident particle. A detailed position scan was made along one of the counters (see figure 2.8). The result was an exponential form for the attenuation curve for each end. For each of the other counters five positions were measured and its attenuation curve determined. The energy sharing between counters was determined by a scan across the width of a counter. Figure 2.9 shows the fraction of energy deposited in the counter struck by the particle and the next nearest counter. This information was used in both the analysis program and the Monte Carlo program. Light leakage from the D to the C counters were also investigated by pulsing a light diode into the D counter light guides. Light that leaked into the C counters was measured to be less than 1 part in 1500. 36 Change in observed energy at 3 GeV >‘6_1...,.r..,r...Ir...,....r..fl 9 C A Second Calibration : g 5 :- D Rescaled Calibration : Q) : 1 'D ” s 4 - :1 — “a, I a '3 j _ Cl . Q) ~ . (I) 3 T :1 j .0 : A _ O 2 L A A ‘ C _ - .- _ 1:1 A I Q) I D A j C ’ j C I A A . .C ‘ . 0 EB— : c 1 : C : A j 0 -1 — — O I I L- 1. - 8- _2 h 1 1 1 1 l 1 1 1 1 l J 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 Ld O 10 20 3O 4O 50 angle in degrees Figure 2.14: Percent change of observed energy in angle scan for 3 GeV electrons. A small amount of the shower leaks out the back of the shower counters for a normally incident particle. As one increases the angle of incidence the leakage is expected to decrease until the shower is completely contained. If the C and D counters are weighted correctly, the observed energy should rise until a plateau is reached. This is observed for the rescaled calibration, but not the second calibration. The drop in the second calibration would be explained if C counters were under- weighted. 37 Change In observed energy at 4 GeV x 6 '- T 1 I I I I I I l I I I l f! r I I I y I , r r, 7“ 8" I A Second Calibration 3 g 5 _- Cl Rescoled Calibration : a) : C! [3 Cl : '8 4 :~ a _- g)’ 3 _- A ‘3 L .0 - A j 0 I j c 2 E‘ D A .1 '5; F E] A A A j 0') 1 L A _« c : . 0 2L A 1 .- A .1 5 0 . +J : A I C - I a: -1 — _ 0 : ‘ L l. :1 8- _2 L 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 11 0 10 20 30 40 50 angle in degrees Figure 2.15: Percent change of observed energy in angle scan for 4 GeV electrons. The observed energy is expected to rise until reaching a plateau as the angle increases if C and D counters are weighted correctly. 38 Complications in the Calibration The original calibration was performed in Sept 1979 at the PS in a 4 GeV beam of electrons. Data were then taken from Nov 1979 to Oct 1980. A second calibration was then performed from Oct to Nov 1980 which gave significantly different calibration constants. Some of the data taken between the calibrations required two clusters (see section 3.2.5) in the apparatus. The frequency of clusters in each sextant is shown in figures 2.10 and 2.11 as a function of the invariant mass. The inside sextants 1 and 2 (away from the Lorentz boost) were expected to be the same as were the outside sextants 3 and 4. The original calibration clearly disagreed with this reasoning while the second calibration was in agreement at the higher masses. Since the threshold for collecting the data was set using the original calibration the disagreement at the lower masses could be expected. The inaccuracy of the original calibration might have been due to the glue drying or the shower counters settling. It was known that external pressure on the counters could alter the observed pulse heights. After the calibration had been performed using the method of resolution minimization, the measured ratio of energy deposition in C counter to the total deposition (usually referred to as C/(C + D)) was found to disagree with the EGS Monte-Carlo predictions. It was also observed that the spread in (C/(C + D)) was large. Some of the counters differed from the mean by as much as 10%. The (C/(C + 0)) ratio for the 4 GeV electrons is shown in figure 2.12 after calibration. The counters are split into two categories according to the thickness of the iron plate at the front of the counters. A third indication that the C counters were under-weighted came from the (C/(C' + D)) ratio for muons (see figure 2.13). Since the amount of energy deposited by a muon is expected to be proportional to its track length 4(0/(0 + D)) should be equal to 1. Further evidence for under- weighting can be seen in figures 2.14 and 2.15 where the observed energy is shown as a function of the angle of incidence. One would expect the observed energy to increase with the angle until reaching a plateau (corresponding to maximum containment 39 H ER UUUU UUUUUUU 140 cm Figure 2.16: Front glass arrays 100 cm 40 of the shower). Instead the energy is observed to increase and then decrease (the triangular points). By applying a renormalization equivalent to an 8% increase in the weighting of the C counter weight the data (now given by the square points) become consistent with the expected behavior. For more information see reference [10]. Table 2.3: Characteristics of lead glass SF-5. Radiation Length 2.36 cm Density 4.08 g/cm3 Critical Energy 15.80 MeV Threshold Momentum 0.38 MeV/c Index of Refraction 1.67(at 5890 A) Angle of Total Internal Reflection 36.8° 2.3.10 Lead Glass There were a total of four lead glass arrays used in this experiment, a front and back array for each side of the detector. Because excessive radiation could cause yellowing in the lead glass, these arrays were mounted on a train and withdrawn from the interaction while the ISR rings were being filled. The arrays were made of blocks of Table 2.4: SF-5 lead glass composition by weight. $103 39.2% N030 1.8% K 30 3.9% PbO 55.1% SF-5 glass manufactured by Schott Glaswerk. The characteristics of this glass are given in table 2.3 and its composition is given in table 2.4. For a discussion on the calibration of the lead glass the reader is directed to reference [11] 41 Front Glass The front glass arrays consisted of 34 lead glass blocks which covered an area of 100 cm vertically by 140 cm horizontally (see figure 2.16). Each block had a width and thickness of 10 cm (4.2 radiation lengths). The length of the horizontal blocks was 35 cm, while those which extended vertically were 50 cm long. Back Glass The back glass consisted of a 12 x 14 array of 15 cm x 15 cm lead glass blocks (the 15 cm includes wrapping with aluminized mylar, soft iron foil and an outer mylar layer for electrical isolation) with a total height of 180 cm and a width of 210 cm (see figure 2.17). The length of each block was 40 cm except for the outermost blocks which were only 35 cm long. Each block had a five inch RCA 8055 photomultiplier tube glued to it using Kodak HE-lO. The tube was surrounded by a 1.1-metal shield. Further protection from the fringe field of the solenoid was provided by an iron box with a front face 3 mm thick and sides 6 mm thick that enclosed the lead glass array. 2.3.11 Strip Chambers The strip chambers were multi-wire proportional chambers (MWPC) which were sandwiched in between the front and back glass arrays. Each had an active area of 180 cm vertically by 210 cm horizontally. The two cathode planes, which were read out, enveloped the anode plane which was powered to 4.5 kV . There was a 1 cm separation between the anode and cathode planes. The anode plane was composed of 1000 gold-plated 20pm tungsten wires. Each wire was strung vertically with a 2 mm pitch and held at 3 places along its length by insulated support wire strung horizontally. The cathode plane nearest the intersection region contained 160 cathode strips flflflflflflfl 42 i1 10 cm 4 flflflflflfl Figure 2.17: Back glass arrays 43 which ran horizontally, while the second cathode plane had 192 strips that ran ver- tically. This provided projections in y and z of the shower. The cathode strips were 0.8 cm wide, 35 pm thick copper etched on a 75 pm thick Kapton board with a regular spacing of one strip per centimeter (This included the 0.2 cm etched gap). The strip chambers were constructed of 0.9 cm thick styrofoam to which the cathode boards were glued. The gas used in the chambers was 70-30% mixture of argon and ethane with an additional 0.1% of freon [11]. Chapter 3 Event Selection In this chapter the selection of events is described, starting with the trigger require- ments and ending with final cuts of the analysis program. 3.1 The Trigger The data were collected at the ISR starting from the beginning of 1980 and finally ending with the closing of the ISR in December 1983. In that time an integrated 1 were collected while an electron pair trigger was in op- luminosity of 249 pbarns- eration. The data were collected on over 3000 raw tapes. Each raw tape held an average of about 7000 events. There were several triggers used during data taking, concentrating on different physics analyses. Triggers included the pairs trigger, the singles trigger, the glass pairs, double sextant, total energy, gamma inside and gamma outside. 3.1.1 Hardware Thresholds The pairs trigger was used to collect the data of this thesis. Shower counter roads were defined as the sum of all eight phototubes of the C and D counters for two adjacent counters. Roads were not formed across sextants since there is a gap between the sextants. The formation of roads in the back glass was more complex, but was designed to select on energy concentrated in 3 x 3 block arrays. Up to six roads per 44 45 glass sextant could be formed. The requirement for the pairs trigger was two roads with more energy than a given threshold in two nonadjacent sextants. Furthermore, the total energy of these two roads was greater than a second threshold. 3.1.2 Software Filter In addition to the trigger cuts, events were subject to filter requirements as well. For the shower counters, each sextant’s road energy was calculated as the maximum two-counter combination, with the energies corrected for the 2 position. In the glass sextants, the software road energy was the maximum of the six hardware roads. At least two roads were needed to pass the pairs filter. If four or more roads passed the roads filter the event was accepted. Otherwise the event must have some combination of non-adjacent sextants with roads passing the roads filter cut and the mass calculated from the two energies and the opening angle must be above the mass cut. 3.2 Cuts on the Data There were three types of tapes which were handled by SOX, the R108-R110 analysis program. The first was the RAW tapes written by the on-line HP computer during runs at the ISR. The second was the DST (Data Summary Tape) which was a result of processing the RAW tapes using SOX. The format of the DST was such that when parameters were changed, e.g. calibration constants, it was sufficient to have a DST type tape as input to SOX to produce a new DST type output tape. The third type was the CON tape, which uses a condensed format. On CON tapes many of the direct measurements of the detector were replaced by higher level values. For example, the readout from the wires in the drift chambers was replaced by a list of track vectors and vertices. 46 3.2.1 RAW to DST One of the advantages of converting RAW tapes to DST was the reduction in the number of tapes for a given analysis. This was because, when making a DST, usually events passing only a single trigger were considered whereas a RAW tape usually contained events from several triggers. Since calibration constants were known better at the DST level, some cuts could also be tightened. 3.2.2 DST to CON Further reductions were made in the number of tapes when converting to CON tapes. Since the analysis program that used the CON tapes ran many times on the same data it was useful to have a large number of events on a single tape. 3.2.3 Good Electron Pair Candidates The analysis program began each event by looping over the tracks. If the track was found to be good then an attempt was made to build a cluster where the track struck the shower counters. If there were two good tracks with good clusters then the event was considered an electron pair candidate. Table 3.1 lists the requirements for a good cluster and track and the number of events passing. The data were broken into four sets and were taken at different times. 3.2.4 Good Track Requirements A track must have passed six requirements in order to have been considered a good track. First, in order that the measurement of the momentum from the track be reasonable, six points in the drift chambers were required. The track must have come within 5 cm of the z axis and its point of closest approach must have had an absolute value in z of less than 50 cm. This insured the track had passed through the interaction region. Tracks with momentum less than 1.5 GeV/c were discarded. A TahlelJLListstntL Old Cut Old New New Description 80 81 Half Normal Data and 82 Back Geo. Data Data Data Events passing 6841 5822 6886 4596 preliminary filter Tracks passing 83475 68910 82704 55667 preliminary filter Good Track Cuts number of tracks with 66114 52352 63000 43412 more than 6 hits tracks that come within 55844 44242 52718 36886 5 cm of z axis track’s closest approach 55797 44216 52674 36886 to origin has a z < 50 cm much > 1.5 GeV 18618 14548 16999 11744 xi/dof of track fit< 5.0 16617 12139 14237 10003 Web 16615 12136 14236 10002 Good Cluster Cuts track strikes shower counters 15591 11316 13283 9248 BMW..." > 1.0 GeV 14520 10504 12362 8671 mm. - and < 20 cm 13559 9608 11310 7917 cluster < 3 counters wide 11763 7551 9203 6368 Ed...“ > 4 GeV 9801 6066 7624 5247 Mung - ¢¢lug¢gl < 0.06 rad 7320 4075 5196 3533 __leu.“ — zdum-I < 15 cm 6952; 3724 4742 3255 _number of events with at 1965 r 650 857 631 least 2 good tracks number of events with two 715 263 442 301 good tracks pointing at nonadjacent sextants and M“ > llGeV XE number of events 615 229 369 259 with Edam,“ > 4.5 GeV Luminosity (pico barns) 102 40 66 41 X / Luminosity (events/pb) 6.0 :l: 0.2 5.7 :l: 0.4 6.0 :l: 0.3 6.3 :i: 0.4 48 further track quality cut was placed on the confidence level of the least-squares fit to the track (x2 per degree of freedom required to be less than 5). Finally tracks that struck the supports for the chamber were also removed. 3.2.5 Good Cluster Requirements If an event had a good track and struck the shower counters, an attempt was made to construct a cluster around the position of the struck counters (see Table 3.1). Before a cluster was built a seed counter was found: the counter hit by the track if the counter had at least lGeV or this failing, the next nearest counter to the track if it had at least 1 GeV. The cluster was then expanded outward until a counter was found to have had less than 50 MeV, a 2 position more 20 cm from the track’s 2 position or more energy than the previous adjacent counter added to the cluster. If the cluster expanded in this manner was more than 3 counters wide it was discarded as an electron candidate along with the corresponding track. Thus a cluster consisted of from 1 to 3 counters, each with a 2 position that matched the z of the track to within 20 cm, and at least 50 MeV of energy. This cluster was also required to have had an energy weighted (3 within 0.06 radians from the track’s d). An energy weighted 2 was calculated for the cluster. Unlike the energy weighted 41, only counters with at least 1 GeV were used. The 2 for the track was always calculated at a radius of 60 cm from the z axis, which corresponded to the average position for showers with normal incidence. At normal incidence, the average depth at which energy was deposited in the shower counters is 5.8 cm. Since this depth would decrease as sin 0, where 0 was the angle between the z axis and the particle track, 2 was extended by 5.8 . 62 — mu — 81110) (3.1) for a better comparison with the track. The corrected 2 of the cluster and the track were required to have agreed to within 15 cm. One further requirement for a good 49 cluster was that the cluster energy be greater than 4 GeV. 3.2.6 Two Good Matching Clusters & Tracks When a good track and matching cluster was found, a four momentum was formed for the electron candidate, assuming the candidate was massless and had an energy equal to the cluster energy. The direction of momentum was taken to be along the vector from the event vertex to the center of gravity of the cluster. Since the tracks of particles greater than 4 GeV were nearly straight this was reasonable even considering the solenoidal magnetic field. The four momenta for the candidates were then translated from the lab frame to the center-of-mass of the colliding protons. Events were rejected if they did not have a least two electron candidates with energy greater than 4.5 GeV, with showers in nonadjacent sextants. The mass found from the vector sum of the two candidates was required to be greater than 11 GeV, to reject T decays. 3.2.7 The Background Estimate Events that had good tracks and matching clusters were classified as n++, n..- or N+_ where the sign is given by the charge measured from the track. Drell-Yan events were of opposite sign while background events could have been either same sign or opposite sign. By making the assumption that the charge of a track for background events did not depend on the charge of the other member of the pair the expected background in the opposite sign events was found. First we make the following defi- nitions. 50 T ' t Cut Old Old New New Description 1980 1981 Half Normal Data 8: 1982 Back Geo. Data Data Data Events with two good all 615 229 369 259 tracks pointing to non- N1... 331 117 186 136 adjacent sextants with 71+... 218 80 124 90 with Ema,” > 4.5 GeV n-- 66 32 59 33 and M“ > 11 GeV Signal 91 :h 43 15 :i: 27 15 i 34 27 :l: 28 Vertex Cut all 518 180 272 198 A,:sy < 1.3 cm 17+- 289 92 139 107 11..., 181 62 88 84 n-- 48 26 45 27 Signal 102 :l: 39 12 :l: 24 13 :t 29 24 :l: 24 Vertex Cut all 514 180 270 197 A.1 < 2.5 cm N+_ 285 92 137 107 73...... 181 62 88 63 n-- 48 26 45 27 Signal 102 :l: 39 12 :l: 24 11 :h 29 25 :l: 24 Momentum Energy all 381 115 178 123 Equality Cut N+- 219 63 94 68 -0.10< a (0.38 714.4. 136 34 52 43 n-_ 26 18 32 12 Signal 100 :l: 32 14 :t 18 12 :l: 23 23 :l: 19 Longitudinal Energy . all 215 70 92 71 Deposition Cut N.... 134 43 54 45 0.1o< 5% <0.42 n++ 67 20 26 18 n_- 14 7 12 8 Signal 73 :l: 23 19 :l: 14 19 :l: 16 21 :l: 14 Transverse Energy all 157 53 63 48 Deposition Cut N+- 110 34 40 34 R. > 0.93 n++ 4o 14 15 8 n-- 7 5 8 6 Signal 77 :l: 19 17 :l: 12 18 :l: 13 20 :t 10 Invariant Mass Cut all 134 46 56 39 mm > 0.145GeV N+_ 98 30 36 30 73+... 31 12 15 7 n-_ 5 4 5 2 Signal 73 d: 17 16 :l: 11 19 i 12 23 :l: 9 Isolation Cut all 59 19 26 16 p: < 1.3GeV N+- 54 16 22 16 with half angle n++ 5 2 3 0 cone sise of n_- 0 l 1 0 25" Signal 54 i 7 13 :l: 6 19 :l:. 7 16 i 4 Minimum Depth all 57 16 26 16 Cut N.... 53 14 22 16 714.4. 4 2 3 0 n-_ 0 0 1 0 Signal 53:1:7 1414 19:l:7 16:1:4 11-- 51 number of events with two positive tracks number of events with two negative tracks number of events with a negative and a positive track N4... + 114.4. + n__ probability that a track will be positive Drell-Yan signal total number of background events number of background events with opposite sign It can be seen that n++ 71+- and thus the Drell-Yan signal was .5: 3.2.8 Final Event Selection = sz = 3(1-9)’ = 23110-9) =2W N4... — n+- N+- — 2‘/n++n__. (3.2) (3.3) (3.4) (35) (3.6) (3.7) After the cluster requirements were made, the remaining events were mostly a com- bination of true electron pairs, 1r°s with overlapping charged tracks, and a few Dalitz decay events. The final cuts were used to select electron pairs with as few 1r laps, etc. as possible. Table 3.2 list these cuts in the order they were applied, along with the number of N...., 11+... and n-- events that passed the cut. Also given are the total number of events that passed and the signal as defined in the previous section. Vertex Cuts To insure that the tracks had a common vertex, the distance of closest approach of the two candidate electron tracks was required to be within 2.5 cm in the z direction. 52 The higher resolution in the xy plane allowed the tighter cut value of 1.3 cm for Azy. This cut did little to enhance the signal over the background but was nevertheless expected of the true electron pairs. Momentum-Energy Equality The variable a _ (Eclnster a _ ptrack — 1) 1 (3.8) ETeluster' was used to match the energy of a cluster with the momentum of the track pointing to it. For a perfectly measured electron a would have been zero. Because of resolution a had some distribution about zero. The resolution is dominated by the measurement of the momentum which is inversely proportional to the transverse momentum, hence the 1 /E1~,,1,,,,.m factor. A major source of background came from a track produced by a charged hadron pointing to a cluster produced by a 1 from a 1r0 decay. Because the energy threshold was high, these events usually had an a greater than zero. Single charged hadrons rarely deposit all their energy in the shower counter, so their a’s would usually be less than zero. Figure 3.1 shows the distribution of a for electron candidates without any of the final cuts. The a cut was effective at removing background, but also removed some of the signal. Longitudinal Energy Deposition The C / (C+D) was found by dividing the energy deposited in the front C counters by the total energy of the cluster. A cut on this quantity was useful because the mechanism for energy deposition of electromagnetic showers from electrons and pho- tons is very different from that of hadrons. Electromagnetic showers proceeded as a cascade with electrons that produced photons through bremsstrahlung radiation, and photons that created electrons through pair production. These showers usually 53 g) 1 T ' T ' ' r r ' ' I l ' 1 ' I ' 1 q; . - +1 _ . C E i ‘ .g _ - 0 300 : ‘ O . c i “ O b- -r 1... -H ” s U _ _ 2 200 p 11.1 . n— F i 0 ~ . L L . g 100 — — E 1. .4 3 r - Z - . O L l 1 1 1 1 l 4 1 1 1 I 1 1 1 r r -O.4 O 0.4 0.8 -1 01 (GeV) Figure 3.1: The a distribution The distribution was from events with two good clusters and matching tracks. The arrows show where the low and high cuts were made. 54 400 200 Number of Electron Candidates [_l l O'(735/(C+D)1 Figure 3.2: The C/(C+D) distribution The distribution was from events with two good clusters and matching tracks. The arrows show where the low and high cuts were made. 55 started early in the shower counters, consisted of many particles and had a uniform shape. Hadronic showers were usually initiated from an interaction with a nucleus. These showers usually started later and were not contained in the shower counters. Therefore a cut on low C / (C+D) removed some of the-charged hadronic background (see figure 3.2). Overlaps of charged tracks with neutral particles, typically 1r°s, can produce clus- ters with large values of C/(C' + D). These clusters were removed with a cut on high C/(C + D). Transverse Energy Deposition EGS3 Monte Carlo studies of the transverse spread of the electron showers in the shower counters showed that on average over 96% of the energy was deposited in only two counters in the cluster. The quantity R, was defined as the ratio of energy in the two counters nearest the track over the energy of the cluster. Clusters in background events tended to be spread over several counters and therefore had lower R. values. The distribution of Rc is shown in figure 3.3 before any of the final cuts were made. The R, cut significantly enhanced the signal with high cut efficiency. Invariant Mass Cut One source of background was from Dalitz decays of 11'“ which gave real electron- positron pairs. These events were removed by cutting on the invariant mass found by combining the four momentum from the candidate track with the four momentum of any other track in the event. The quantity mg- for the candidate track was the smallest mass that could be formed from any of the tracks. Dalitz decays were removed by requiring that 111.:- be greater the the 1r” mass (see figure 3.4). 56 m . . , , . B 1500 _ — O 1 T :9 ‘0 1 1 C _ . o O L j C 81000 r- J +1 F 'l 0 _ . 2 11.1 - . w— _ e O . L. 500 r- - a: _Q “ ‘1 g _ 3 1— 2 00.7 T Figure 3.3: The R,: distribution The distribution was from events with two good clusters and matching tracks. Only events with both Re values above the arrow passed this cut. 57 (O . ,rr.r,. .Ir. 0 - . 5120 :9 - “C . C F - U _ 2 O c - -1 230”/\ H l- U 2 . LU . q... 0 "- L 0401- _o . E _ 3 Z r- t . ‘ Orrrmlrrrrlrrrrlrrrr O 0.5 1 1.5 2 2 msT (GeV/C) Figure 3.4: The ma distribution The distribution was from events with two good clusters and matching tracks. Events to the left of the arrow were rejected. 58 m .- I' I I I I r I I I I I I r fir I I c: 0) , _ ”’6 r :9 750 m '- ‘o 9 * C . . C 0 . - C ‘ - 52 500 e - 4.: 0 ‘ 1 2 ~ . L1J . - to. O _ . L. a: 250 .. LE) . 3 . Z .1 -‘ -‘ _l__l _LA1_ l ‘l#_-l O 5 1O 15 20 P4 (GeV/<32) Figure 3.5: The p; distribution The distribution was from events with two good clusters and matching tracks. Events with entries to the right of the arrow failed were rejected. 59 Isolation Cut A source of further background came from jet-like events composed of collimated charged and neutral particles. To determine if the candidate track was a member of a jet, the momentum from all particles within a 25° cone were projected onto the candidate track and summed. This quantity called p; would been large for a track within a jet and nearly zero for isolated electron tracks. Since electron tracks were not always isolated and may have been overlapped by a jet, this cut had only a 77% efficiency when p; out was greater than 1.3 GeV. The distribution of p; is shown in figure 3.5 before any of the final cuts were made. Depth Cut In order to know the energy of a particle it was required to pass through at least 13 radiation lengths of the shower counter. This was only relevant to particles hitting near the edge of the detector. Cut Efficiencies An estimate of the efficiency of a cut is found using the equation £5 = L}; = N31 — 2‘/nfi+nf_ #5 NE_ — 2\/nf+n§_ where the superscripts ‘ determine whether values were to be taken before or after the cut (See figure 3.7a) ). Since six values must be measured to obtain 65, determining the error in 65 was not a completely trivial task. A Monte Carlo was used to model the fluctuations that could occur in determining 85. Each pass of the Monte Carlo simulates performing the experiment under the same conditions of the real experiment (see figure 3.7c) ). In each pass the number lSuperscripts are either A for after the cut or B for before the cut. Subscripts are either 8 for the true electron pair signal or B for background events. Little n’s are used only for background events. 60 750 *- - 500 +- - 250 h Number of Electron Candidates Depth cm Figure 3.6: The depth distribution The distribution was from events with two good clusters and matching tracks. Events with tracks passing through less than 13 cm of shower counters were rejected. 61 of true electron pairs, 53, and background events, 8”, are generated from Poisson distributions P(SBlfis) and P(BBIfiB). The means of the two distributions [is and [23 were determined from the data (see figure 3.7b) ). Background events were then split up according to charge by the multinomial distribution M(nf_2nf+anf- lBBrfll ‘- fi)afizv (1 '— 13):) in agreement with section 3.2.7. The selected number of events passing was chosen from binomial distributions with efficiencies £5 for the Drell-Yan signal and GB for the background determined from the data. The same formula used to estimate the Drell- Yan signal in the data was applied in our simulation to estimate the signal before and after the cut. An estimate of the efficiency, 65 was found using these values and stored in a histogram. A distribution for 65 was then built up after many iterations. This distribution for the cuts can be seen in figure 3.8. Most of the cuts given in table Table 3.3: Efficiency of cuts Cut Cut Efficiency Azy and A: > 0.90 with 90% confidence level ma > 0.91 with 90% confidence level He > 0.87 with 90% confidence level C/(C + D) > 0.78 with 90% confidence level Depth > 0.96 with 90% confidence level a 0.87 :l: 0.06 p, 0.78 d: 0.08 3.3 are assumed to have perfect efficiency since estimates of their efficiency are equal to 1 within errors. The combined efficiency of the a and the 1); cut is found to be 0.68 :l: 0.10. When all cuts are considered one single cut the estimate of the efficiency is 0.67 :l: 0.14. 62 a) Number of Number of Number of Opposite sign p us-p us mmus-mmus events events events Before the Cut N f_ 123+ n§_ After the Cut N 1L 121+ af- b) Input parameters to Monte Carlo B 3 [1% = 125+ + n§_ + 2‘/nf+n§_ A A A A 68 = n+++n__+2‘/n n__ n?_ +n£_+2‘/n§+ns__ c) Monte Carlo Scheme P(53|fis) P(BB|fis) g? = 58 + nfL - 2 nf+n§_ M(n§_,n£+,n§_|BB,fig) \ \ \\ ”(SAIFF, £5) b(nfi_|nf_, é3)b(n§+|nf+, €3)b(n§_ In?_,ég)| /—\\ es = #‘é/fl‘s’ #3 = 5“ + "‘1- - Zvn‘im‘f- _/ Figure 3.7: Error in efficiency of cuts a)An estimate of error in the efficiency of a cut was made based on the number of opposite sign, N+-, plus-plus, N++, and minus-minus, N--, events before and after the cut. b)From these numbers an estimate of the true electron pairs, [13, the total background, [13, the fraction of positive charged tracks in the background, p33, and the efficiency of the cut for both the signal, 6'5, and background, 83, were made. A Monte Carlo then modeled fluctuation as if the experiment had been performed repeatedly. In c) the scheme for a single pass is shown. The signal, 53, and the background, BB, before the cut were generated from Poisson distributions. The background was then split according to a multinomial distribution for the differing charged track combinations. Binomial distributions in the dashed box generated the number of events passing the cut. Finally an estimate of the true electron pair before, 11?, and after, pg, the cut was used to estimate the efficiency of the cut 65. The estimated error in the efficiency of the cut was base the distribution of £5. 63 r I r r I r r I 1 I r r r l r 3 - — i- J b /% ‘1 2 r — 1 .— 0 1 1 L A J 1 1 L l 1 1 1 1 l 1 J 1 1 0 0.25 0.5 0.75 1 efficiency Figure 3.8: Efficiency error All the final cuts are combined and considered as a single cut. The probability density distribution for efficiency of the signal is found using the Monte Carlo described in this section. The mean is given by the arrow with the two vertical lines one sigma away. Chapter 4 Cross Section Extraction 4.1 The Monte Carlo Simulation A Monte Carlo simulation was written to evaluate the efficiencies and acceptance of the R110 detector for measuring electron pairs. This Monte Carlo modeled the geometry and energy resolution of the detector. In it two types of events, Drell-Yan and Upsilon, were generated. The Drell-Yan type event was picked and weighted according to an appropriate distribution. If the virtual photon of an event had a mass above 11 GeV and a rapidity (rapidity is defined as y = tank-1(E/ 11)) between -l.2 and +1.2, the “Monte Carlo In” histogram were filled with the event’s weight. The 4-momenta of the pair of electrons were then found, and the part of the detector struck, if any, determined. If the shower counters were struck by both electrons, their observed energy was selected using the known resolution of the counters, and their observed momentum rescaled to match this energy. The positions of an electron’s track and its cluster were also required to match. Differences between the two resulted when an associated particle overlapped the electron cluster, causing it to have a bad position in 2. If the electrons passed the geometric requirements and had good track to cluster matching, cuts were made on their observed energy and the mass of the reconstructed virtual photon. Events passing all these cuts were used to fill the “Monte Carlo Out” histograms. 64 65 An Upsilon event went through the same set of steps as the Drell-Yan event, but was considered to be background and thus excluded from the “Monte Carlo In” his- tograms. It was generated by an experimentally determined distribution [12][13][14] appropriate to the upsilon family of resonances. 4.1.1 Distribution Thrown Generating either a Drell-Yan or Upsilon event requires choosing 5 independent vari- ables, the 4~momentum of the virtual particle plus the decay angle. Drell-Yen Distribution In generating the Drell-Yan event, 3 different reference frames were used. The first was the center-of-mass frame of the two initial protons. This will sometimes be referred to as the ISR reference frame. The second frame was the center of mass frame of the virtual photon. The third frame was the lab frame of the detector. The first step in generating the Drell-Yan event was choosing the 4-momentum of the virtual photon. This was done by writing the general expression as a product of 2 simpler factors. (1‘0 1 «Pa = -—F(PT) dzldzgdprdcp 21rdz1dzg Since there was no dependence in 05, only the 2:1, 2:3 and p1 dependence remains. (4.1) The cross-section in 2:1, 23 can be written as d'a 41m2 " Z 8,?{fq,(Q2, zl)fd’é(Q21 33) + fsa(Q21 32)f¢1(Q21 31)} (4'2) i=1 dzldzg = 9131228 where f“ and fa are the parton distributions for the initial hadrons, Q was the momentum transfer and the summation is over the quark flavors. The structure functions used here were Duke and Owens [15] set 1. For the p:- distribution use was made of the empirical form [16] 10% (1 + PEP)" F(Pr) = (4-3) 66 From (PT) = [0” dWPTFU’T) (4.4) it can be shown that P0 = $208. (4.5) The value of po was obtained after an iterative procedure comparing M 0...; with the data. The values for (pr) have been found many times in this experiment in its various incarnations. In earlier data sets, values for (pr) ranged from a fit value to acceptance corrected data of 1.9 GeV/c to an average value of the raw data of 2.7 GeV/ c. Since then the size of the data set has increased, the Monte Carlo has been improved and the method of fitting has improved. Currently the value for the raw data is 2.0 GeV/c while the average of the acceptance corrected value is 2.2 GeV/ c. Values from maximum likelihood fits of the empirical form (4.3) to the current data set after acceptance correction were made have been within the range of 2.10 to 2.45 GeV/c. Fitting was done using the maximum likelihood method. The “standard” Monte Carlo for this experiment ran using (p1) = 2.3 GeV/c for the input 'distribution. From the final version of the Monte Carlo the likelihood curve in figure 4.1 was generated. The best fit occurs with a Monte Carlo value for (pr) 2 2.2 1'33“ GeV/ c . The next step was the decay of the virtual photon into the lepton pair. In the Drell-Yan model with quarks moving parallel to the incident hadrons the angular distribution of the lepton pair is 1 + cos2 0, where 0 is the angle between the lepton momentum and the beam axis in the dilepton’s center-of-mass frame. Because of large Q}, however, the incident hadrons are no longer collinear in the dilepton’s center-of- mass system. This forces one to define a new 7. axis for this system. The usual choice is the Collins-Soper frame [17] where the z axis is chosen halfway between the two incident hadrons. The azimuth is measured from the plane formed by the intersection of the two incident hadrons. In the Monte Carlo, the generated photon’s momentum 67 50 ,....,.... ....,....,-.-.,....,...., A __ : r< _ V ‘ C -s - — 4o -— — N " s '1 l - - 30 . - _ _ i A I 20 - % - + 10 — - 0 -J1 11111111 1 11L 1 1 1 1111 1l1 11 1l1 11 1ld 1.6 1.8 2 2.2 2.4 2.6 2.8 3 (GeV/c) Figure 4.1: Likelihood curve for (pr) The likelihood curve is found by running the Monte Carlo with different values of (pr) for the input distribution. Using the normalized distribution of pr out as the probability density function the likelihood, L. is found for each value of (pr) . wast distri T‘Di Thcq c050 T'afl 4.1.i The in tl tract 13.0 IDrM Beca the l COU1 that Plan 68 was transformed to the Collins-Soper frame, where the photon decayed. The angular distribution had the form 1 + (1 cos2 0 where a was normally set equal to 1. T Distribution The distributions of the upsilon resonances in mass [12], Feynman x [13], pg» [13], and c080 [14] were empirical forms taken from several experiments. The resonances T , T' and '1'" were included. or + or: + or» = 14.5pb (4.6) ‘3'; or (“EA-T?" + 0.3Oe-i(%)3 + 0.15e‘i(257-—7»u)' (4.7) 2‘2"; or (1.0 — [27])” (4-8) 2% 0‘ 84.12” (4.9) (1:10 or 1 + 0.31 cos” 0 (4.10) 4.1.2 Geometric Cuts The two electrons, now given in the center of mass of the initial protons were boosted in the -x direction into the lab frame. Knowing the lab momenta, the electrons’ tracks were projected through the magnetic field to see if they go through at least 13.0 radiation lengths of shower counter. Drift Chambers Because of the gaps at the top and bottom of the drift chambers (see figure 2.2), the 4: distribution measured by the detector was dependent not only on the shower counters’ positions but also the position of drift chambers. The Monte Carlo assumed that all planes in the drift chambers have an efficiency of 85% and required a least 6 planes to trigger per track. 69 The probability that a track striking n planes, with an efficiency of p per plane, would trigger 2' planes was given by the binomial distribution WWW) = (1:)?‘(1 — p)n-i The probability that at least m planes were triggered in such a case is B(;,=mnp) Zb(i;,np) The Monte Carlo simply found 11, the number of planes the track passed through, and assigned a weight of B(6;n,0.85) for that track. The weight of the event, if it was accepted, was then scaled by the product of the weights for the two electron tracks. 4.1.3 Leakage, Smearing and Energy Cuts Since the shower counters were not infinitely thick, some of the shower from the elec- trons would leak out the back of the counters. The energy contained in the counters was therefore less than the initial energy of the electron. The average longitudinal shape of electron and photon shower is [18] [19] given by (1E ba(E0)+1 ‘8? “ °I‘(a(Eo) + 1) t“(Eo)e"” (4.11) where t is the depth in the shower counter given radiation lengths, E0 is the initial energy of the electron, 1115‘ the energy deposited in the counters between the depth t and t+ dt and I‘ the usual gamma function. a is related to the position of the shower maximum and therefore is energy dependent: The dependence of a on the energy in GeV was given by a(E) = btmu 2 b(tmd — 1.5) = b[ln(E/e) + a — 1.5] (4.12) wh1 fro1 wht cha W85 Whe 70 where b 2 0.5, a 2 0.4 for electrons, e 2 “—52%?! and E is in GeV . 2., can be found from z., = Z fiz. (4.13) where f.- is the fraction of element i by weight and Z,- is its nuclear charge. The composition of the shower counters is given in table 4.1 with the density, charge of the nucleus and the fraction of the given element. From this table the Z" was calculated to be 76.8. The radiation length for a mixture of elements was approximated by 1 t‘ N _— Z;_,L§ where t’ is the relative thickness of the element 3'. Using table 4.1 again, the radiation length for the shower counters is 1.0 cm. To get the total energy deposited up to a Table 4.1: Composition of shower counters By knowing the thickness and density of the material, and the molecular weight of the elements, the fraction by weight of each element in the shower counters was found and used to calculate Z”. material thickness L,“ density element Molecular total Z fraction Weight mass by (cm) (an) (8/cm3) (ts/mole) (s/cm’) weisht olystyrene 0.4 42.4 1.03 H 1.01 0.032 1 0.005 ((1151)2 C 12.01 0.381 6 0.063 lead 0.5 0.561 11.35 Pb 238.03 5.675 82 0.932 depth t, the equation 4.11 is integrated from 0 to t giving 7(a(E0)i t) E = E" mama» mu) where 7 is the incomplete gamma function. Since the shower counters were calibrated to read 4 GeV for an electron with 4 GeV of energy and a normal angle of incidence, other energies will be read as 7(a(Eo),t) I‘(a(4 GeV)) 7(a(4 GeV),to) I‘(a(Eo)) E=& mm) Th. das an: at 4 71 c0016} WNW" I-i O . I . '43 I I I 'C I I ; 1730.012 [— I i '5 . I 1 _- I I 2 O 0.01 :- l j .E ; I 2 30.008 :- ' E :t'.’ - I - 0’ I I I c0008 . , 1 O E . _J _ I - 0.004 :— : { E I 3 0.002 f | j : I : 0 ' . . 1 - . e . ‘ O 12 16 20 24 t (radiation lengths) Figure 4.2: The longitudinal shower distribution The longitudinal energy deposition for a 4 GeV electron is shown as a solid curve. The dashed curve corresponds to a 10 GeV electron. The solid vertical lines mark the back of C and D counters for a normally incident electron, and dashed lines for an electron entering at 45°. Aft 5111‘ 4.1 The the in t oft 72 After the amount of energy deposited in the shower was determined, the energy was smeared according to a Gaussian distribution to reflect the shower counter resolution M = 0.004 + 041—5— (E in GeV) (4.16) 75— x/E Using the smeared energy, the momentum of the electron was rescaled and the 4- momentum of the photon reconstructed. Energy and mass cuts equivalent to those in the analysis, and a cut on the absolute value of rapidity less than 1.2, were applied. Drell-Yan events passing this cut were added to the “Monte Carlo Out” histograms. 4.1.4 Cluster Formation The Monte Carlo was used to check the track to cluster matching efficiencies from the data. In track to cluster matching, events were lost mostly due to bad 2 positions in the cluster. This usually resulted from an associated particle overlapping with one of the electrons, and therefore giving a bad time in the D counters. Clustering was done for each electron. The counter struck and the adjacent coun- ters were filled using an energy sharing curve that was measured for 4 GeV electrons in the shower counters at the PS (see figure 2.9). Each counter accumulated energy deposited in it and recorded a 2 position for each end. The 2 position was deter- mined by the earliest pulse detected at that end of the counter passing a threshold of approximately 0.6 GeV (see figure 4.3). It was possible for the recoil jet to overlap one of the electrons. A jet distribution with p7, = —pT., and flat in y in the region Iyl < 2.0 was used. Only the neutral particles in the jet deposited enough energy in the shower counters to have any effect. The measured multiplicity distribution of the neutrals with enough energy to affect the 2 position was used for the neutral multiplicity of the jet. To measure this distribution, the electron pair data set with all cuts but the 12,; cut was used. In each event, the energy a neutral would deposit in the D counters was found using the longitudinal shower distribution. Knowing the 73 Efficiency in Time of Flight in D Counters 0, _...-,.,,.,..,.,-...,..-. a“: 1 ‘ ‘ E : .00000“000”.. ..!. 8 _ 0.. ‘ o t g - O 0.8 : . 1 C r a . .; : . : U 0.6 '— . _.. C P .I .9.) P a : .2 i . 3: 0.4 +- ° — Q) - - . C . i o ‘ 0.2 - J .. O .. _ , 1 . -] .. I .. OW'IILIIIIL'ILLIIIJ 0 0.2 0.4 0.6 0.8 I energy of min I particle in GeV Figure 4.3: Triggering efficiency of TOF in D counters The probability of a particle triggering the TOF in the D counters as a function of energy[10]. 74 Multiplicity of Neutral Particles q) _' """ ‘I‘fl'lj "T""l I Mr" . g '6 Z I (I) E j Z‘ . 1 O 60 f 1 L. . . .4: - . ‘9 50 _— 1 O : j 40 :— 2: 30 :— 5 20 E -§ 10 :— '3 r l _ O ....1..141.ULI..|..1.#r—r-jn—1.EI.FI...I.._.E 0 1 2 3 4 5 6 7 8 9 1o multiplicity in D counters Figure 4.4: Multiplicity distribution in D counters Multiplicity distribution of neutrals with enough energy to trigger the D time of flight counters. Ac “811 D0 gr 75 energy deposited in the D counters, the probability that the particle triggered the time of flight was found from the DTOF efficiency curve (see figure 4.3). Summing the efficiencies for each neutral particle gave the expected number of neutral particles capable of triggering the time of flight in the event (see figure 4.4). The direction of the neutral particles was picked flat in 45,. about the jet axis. The variable 0“, the angle between the jet axis and the neutral particle, was selected from a distribution of 0,, based on a jet analysis [20] by this experiment. Two cuts made during the formation of the cluster were the d) and 2 matching of the cluster and track. The 03 of the cluster was calculated as the energy weighted average, as in the analysis program. The z of the cluster was the energy weighted average from counters with more than 1 GeV. The 05 and z for the track were taken at its intercept with a cylinder of radius 60 cm . While the estimated efficiency of the 4: cut from the Monte Carlo was over 99%, the z cut was significantly less. The 2 cut efficiencies are given in table 4.2. Table 4.2: Efficiencies for 2 track to cluster matching cuts Cuts Efficiency of electrons from Monte Carlo pm... - 2....“ < 20.0 cm 0.980 ]Z¢,.¢k - Zdnuu] < 15.0 cm 0.924 4.2 Acceptance Correction to the Data Acceptance corrected cross sections were found using the equation (fa—(2:) = Data(:c) — Back(z) dz: £6,115.42) where 3: might be the pr, m, p1,, etc. of the virtual photon or the electrons. The Data(:c) were the number of opposite sign events and Back(3:) the estimated back- ground in the opposite sign events. The distribution of the background because of 76 low statistics was taken from the same sign events with two good tracks and match- ing clusters. The normalization for the background was found from the number of positive same sign events, 131.4,, and negative same sign events, n_-, passing all cuts, and using equation 3.5. C was the luminosity as discussed in section 2.1.1. In the Monte Carlo, two sets of histograms M C;,,(z) and M Gouda!) were filled. M 05,,(23) accepted all of the generated Drell-Yan events with mass greater than llGeV and an absolute value of rapidity less than 1.2. The efficiency 6(2) was 6(3) — MCin(3) . ea and 6,, were the estimated efficiencies for the a and 12; cuts respectively (see section 3.2.8). These efficiencies were found from the ratio of the signal in the data with the cut applied divided by the signal without the cut (see table 4.3). All other cuts were left in. Table 4.3: a and p; efficiencies The efficiencies ea and em are found from the data by taking the ratio of the signal when the cut was applied to the signal without the cut. All other were applied for both cases. Cuts (+ -) (+ +) (- -) Signal Efficiency all cuts 105 9 1 99i13 no a cut 131 23 3 114:1:16 0.87:1:0.06 no p1 cut 189 63 15 127i24 0.78:1:0.08 4.3 Cross Sections The cross section d’a/dmdylFO for m > 11 GeV is shown in figure 4.5 and table 4.4. The data are in good agreement with other pp —v e+e‘ results [21] [22] obtained at the ISR. Results for the R209 experiment are based on their da/dm cross section [12] and converted by multiplying by the ratio .41: dmdy do y=0 dm 77 found from the Monte Carlo input distributions (see section 4.1.1). At Fermilab the CFS Collaboration [16] obtained the values of d’a/dmdyIFO for a J; = 27 GeV. The cross section of the Fermilab experiment at the lower J3 is lower than the data presented here by about a factor of 20 at m = 12 GeV/c and a factor of 1000 at m = 20 GeV/c. It is of interest to note that while the collider experiments at the ISR enjoy a higher cross section, the fixed target Fermilab experiment is compensated by higher interactions rates, so that both run out of events around 20 GeV. Table 4.4: Cross section d’a/dmdylyfl m in GeV/c2 Cross Section pb cz/GeV 11.5 1.82 :l: 0.28 13.0 0.56 :l: 0.11 15.0 0.33 :l: 0.08 17.0 0.13 :l: 0.05 19.5 0.13 :l: 0.05 Figure 4.6 compares the data of this experiment with the theoretical predictions of reference [8]. These predictions were obtained by calculating in QCD all terms up to and including order a,(Q’) that give rise to the so-called K factor. Comparing the total cross section above 11 GeV/c2 with the lowest order predictions, a K factor of 1.75 :l:0.60 is found. The K factor as a function of mass is shown in figure 4.7 together with a line representing the integral K factor. The quantity sd’a/dfidylwo in the simple Drell-Yan model is a function of 1' = (mz/s) only rather than a function of m and s separately. The validity of this scaling prediction is demonstrated in figure 4.8, where the scaled cross sections from this experiment and from CF S are seen to agree in spite of the large differences observed in dad/dmdylwo. The values for the points for this experiment are given in table 4.5. The quantities do/dy in figure 4.9 and der/dz;- (In center of mass frame 22p = 2p,/\/3) in figure 4.10 are shown with comparisons between the data and the Monte Carlo input, where the Monte Carlo 78 dzo/dm dy|,.o (pb cz/GeV) 10 E . I I I ' I . I ' I I I E O R110Currsnt f - CI R110 Previous - 10 _r A R108 1 E Js-GZJ 0 R806 g I <> 9 R209 3 1 1° It . * 5 fl) 1 s 5 f, f i _ 1O _— i 5 2., T i] 3 10-25— 6‘99, ‘2 E u, E -3: I‘llfil : _— A. __. 1O Ll Js-27.4 _4: ‘1 1' : 10 E- l J‘ E E 1 I E 10'” I I I . . I . L 1 L . L 10 12 14 16 18 20 22 24 m (GeV/02) Figure 4.5: Invariant mass dependence of cross section (comparison with experiments) The cross section d’a/dmdylFo in this experiment and others (R110 Previous [23], R108[22], R806[21], R209[12]) at ,/3 = 62.3 GeV and by CFS [16] at J; = 27.4 GeV. (The data of R209 have converted from their original form of dtr/dm.) Table 4.5: The scaling-invariant mass cross section m in GeV/c2 Cross Section pb GeV2 0.18 479977 :1: 67281 0.22 105505 i 19961 0.26 66581 :l: 15719 0.30 22449 :1: 9174 0.34 7995 :l: 5654 79 1 O _ v I . I . I I I I I ' I . I —. A : 2 Q) - O This Expenment . O - ‘ \ I- "‘ "o s I + Q . Theoretical prediction 2nd Order 0. 1 _ . _. V : . I O I I > “ ‘ ‘0 ~ ‘ '0 _1 \ 1 0 - _I b : i ‘0 ~ ‘ _ 1st Order K=1 > ~ ‘ -2 \ 1 O L l 4 l L l L l 1 l 4 l L l 10 12 14 16 18 20 22 24 m (GeV/(:2) Figure 4.6: Invariant mass dependence of cross section (comparison with theory) The cross section dad/dmdylwo is shown with the theoretical predictions[8]. 80 K FACTOR l l l llilllllLll lllllllll [Lilli IIIIIIIFTIIIIIIIIITIIIITIIITTIIIVII [Tl r O 12 14 1 16 I 18 20 22 I 24 m (GeV/<32) Figure 4.7: The K factor plotted as a function of mass. 81 7 1 0 Fr '— ' I [ ' ' I r I j 7 I I I I I I I r I I r I l I r r T I r I r I E 3 E O This Experiment Vs-62.36ev : 8 I- * CFS 49327.4GOV - 6 .0 10 :— —: Q. E 3 V I- . j o ” * ‘ J i i 5 >‘ 1 0 .- ‘ 1 'U E Q 5 t~ i t Z '0 4 + it \ 10 “:— —: b : 3 N L. . 'C L ‘ w .- c-I 3 . 1 0 E— Jlt j t. +. .. 1 O J l i l I l L l l l L J l l l l l l l L L l l l l l l l l l l J_L l 0.2 0.3 0.4 0.5 \/’r=m/\/s Figure 4.8: The scaling-invariant cross section The scaling quantity sd’a/dfidyly=o obtained in this experiment at J? = 62.3 GeV and at J; = 27.4 GeV by the CFS collaboration[l6]. 82 input is defined in section 4.1. The mean transverse momentum of the electron pair, (p1) , was found by varying the (pr) parameter in the Monte Carlo until the output distribution best represented the data. In this way (111) was found to be 2.2 :1: 0.2 GeV/c . The transverse momentum distribution, corrected for acceptance, is shown in figure 4.11 along the theoretical curve of reference [8]. The acceptance corrected data is also shown in table 4.6. Table 4.6: The transverse momentum distribution 1m- GeV/c Cross Section pb c/GeV 0.5 1.11 i 0.20 1.5 1.25 :l: 0.22 2.5 0.89 :l: 0.19 3.5 0.42 :l: 0.13 4.5 0.28 i 0.13 5.5 0.13 :l: 0.10 6.5 0.02 :l: 0.02 7.5 0.13 :l: 0.09 In contrast to the naive parton model, QCD predicts that the mean transverse momentum will increase as a function of J3 for fixed values of r. The value of (pr) obtained in this experiment compared with data obtained at lower J; [16] [12] [24] are shown in figure 4.12. A linear increase with J? is clearly seen. The form of the cross section in a region where second-order effect dominates is expected to be: dad/dp’rdydm’ = (l/a’P%)H(zr.y,T) where m, p7, and y are, respectively, the mass, transverse momentum, and rapidity of the electron pair, 1' = mz/s and 2:1» = 2pT/fi. At a given 1' and y the quantity s'pg-(daa/dpgdydm’) is then expected to be a function of 37 only, irrespective of fl. A plot of this quantity is shown in figure 4.13 for the events in the range 11 < m < 15 GeV/c2 (mean 1' of 0.19). The data of the CFS Collaboration [16] in the mass interval 5 to 6 GeV/c3 and at f = 27.4 GeV are shown in the figure. Note 83 A L- Y T T f r T j T Y I I—[ r T I I .0 _ 1 Q. - . v 6 __ _J >s C j ‘0 - - \ 5 +— —Y— _ b . 3 ‘U _ _ 4 — _ : + ., 3 — _ - I s . 2 ~— .. 7 -I . I " J 1 t- .1 p I b c! ’ 1 O *4 1 l 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 i 1 1 1 1 l 1 1 -2 -1. -1 -O.5 O 0.5 1 1.5 2 rapidity Figure 4.9: The rapidity distribution The quantity do/dy from the Monte Carlo is shown as a smooth curve. The data for this experiment is shown with error bars. 84 A ''IIII'IITII'II'III'II'I''I'I'I'III'Ir .0 Q. 12 - _ V In. '8 1° 7 m _._ ‘ \ _ . b ‘0 8 __ - 6 - _ b n .. 4,— .— 2 - _ I" - O 11 111111111l111111111l111 -1 -O. 5 -O.5 -O.25 O 0.25 0.5 1 Xr Figure 4.10: The Feynman a: Distribution The quantity da/dzp from the Monte Carlo is shown as a smooth curve. The data for this experiment is shown with error bars. 85 A 2 ll-TTT—IrITTTIUVII—[ITIF'TTTT'IITIrliTi‘rIUIIllIlTrTlIT4 5 Z O This Ex eriment Js-GZJGeV : Q) 1.75 r p _ O t R w 2 _ — e . 0 c - Q. : . V _ : - .1 s - I I 5. ‘ T I Q : 3 0.75 — l b ' . e1 ; . ‘O c I 0.5 _- - I 1 0.25 _ — 0 111111 1111111 lllllLLJ4l IILJIL llllJllllllll ll]u 0 1 2 3 4 5 6 7 8 9 10 pt (GeV/C) Figure 4.11: The transverse momentum distribution The cross section d’a/dmdy|,=o is shown with the theoretical predictions[8] 86 TT I I T I U I V I I l T I I I 1 I T I l U I I I T l I l l I l I I 2.8 _ m/Js-Jr-OJZ _ A - 0 R110 ~ %’ 2.4 — A R209 1 - 1 (D . * cps - A 2 - I Omega ; C: F -o.417 + 0.02734: I V 1.6 ~ - 1.2 _ — 0.8 - ~ 0.4 - — L - - -I O l l l l l l l 11L 1 1 L11 1 l l l l l I 111 L l l l l I l 1.1 0 1O 2O 30 4O 5O 60 7O s/S (GeV) Figure 4.12: (111) as a function of (5 The mean transverse momentum of lepton pairs produced in pp collisions plotted as a function of fl. results are shown from CFS[16], R209[l2] and the Omega collaboration[24] 87 that such a scaling form is incompatible with figure 4.12 having (pr) = a + flfi with a non-zero intercept. 4.3.1 Single Electron Distributions The energy, transverse momentum, (I), and rapidity distributions of single electrons as measured in the center of mass of the initial protons are shown for the data corrected for efficiencies and Monte Carlo In. The Monte Carlo In comes from events with virtual photons of mass greater than 11 GeV/c2 and rapidity between -1.2 and 1.2. Also shown are the distributions for the efficiency with arbitrary scale. The distribu- tion for efficiency corrected data and Monte Carlo agree reasonably well except where the efficiency drops off too low for observations to be made in the data. See figures 4.14-4.16. 4.4 Systematic Errors The Monte Carlo was written in such a way that a number of parameters and dis- tributions could be changed without recompiling and relinking. This helped insure that the correct version of the Monte Carlo was used. This was particularly useful for doing systematic error studies, where only a single parameter needed to be changed. K Factor The calculations of the cross section for Drell-Yan pairs from structure functions have always had a problem with normalization. This is due in large part to higher order diagrams involving strong interactions which are difficult to calculate. Our standard Monte Carlo uses a K factor of 1.70. Since only the lowest order diagram was used in the Monte Carlo, varying the K factor only changed the ratio of the Drell-Yan continuum to the T resonances. Using Monte Carlo efficiencies derived assuming K factors of 0.85 and 3.40 changed our measured cross section by only 6%. 88 s H(x7,y 7') 10 A +T T T I l I T I T _I—rt T T I TTTTTTTT I I U T T I I I I j T I I d % I O This Experiment Js-62.3Gev : r . O . * crs «Is-27.4Gev « s ‘- . t * * air It 1* A * °' I 5 IE) 10 t 1‘1 1 %‘ : + 1 : as _K . :5. I . Q \ _ - .3: 4 v 1 0 :— .. N .- : 2 No- b w 2* 1 l l l l I l l l 1 L1 L1 1 l L l l l I l l l 1 I l l l I 1 l l l 1 L1 1 l 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 XT=Zpr/‘/S Figure 4.13: H(21~,y,r) The quantity s’pa-(daa/dp’Tdydm’MFO as a function of zT(= 2111/ J?) 89 /‘>\ 2.8 .1— I l I I 1 1 l _: a) .. -I O . . \ 2.4 — 4 3 i + : V - .1 2 — _. . *- - LJ . - ‘o - . \ 1.6 — - b : q ‘o _ I 1.2 — _ - + 3 0.5 — .. : + + - 0.4 — + - l : \ 1 0 . 1 1 1 . 1 . 1 l . I . . o 7.5 10 125+ 15 17.5 20 Electron Energy (GeV) Figure 4.14: The energy distribution of the electrons The energy distribution for electrons shown for the data with error bars and Monte Carlo In as a curve. 90 lrfi' I F11r I I I T I T r r1 T I V’T 3.5 2.5 1.5 dG/de. (Pb c/GeV) IJJJLIIIllllllellllJLLLJ O IITIITTIIIIUTUTUIIIIIIIIIUIIIII 0.5 + L -0.5 L11-L11L11111L111111 .LL. r: 0 2.5 5 7.5 10 12.5 15 17.5 20 Transverse Momentum (GeV/c) Figure 4.15: The transverse momentum distribution of the electrons The n- distribution for electrons shown for the data with error bars and Monte Carlo In as a curve. 91 A TTITITTITTTIYTITTiTIIITIII—lTIIITIIllfilTI .0 ’- .1 D. V 10— 4 O > - . 3 8b _ b '0 6 - I — . ”$735K+ #17 . f \ 2_/++ \q 0 1111111111111111.111.1.l11.1‘.... -2 -1.5 -1 -O.5 O 0.5 1 1.5 2 Electron Rapidity Figure 4.16: The rapidity distribution of the electrons The rapidity distribution for electrons shown for the data with error bars and Monte Carlo In as a curve. 92 Parton Densities The parton distributions in the Monte Carlo were the Duke and Owens set 1 parton distributions. To test for sensitivity to this choice of parton distributions the Monte Carlo was run with Duke and Owens set 2 parton distributions. So that errors due to the K factor were not double counted here the K factor was adjusted so that M Cg" remains unchanged from the standard. The largest change to the measured cross section came from the Duke and Owens set 2 parton distributions with a difference of 2%. Energy Resolution Because the Drell-Yan cross section falls of rapidly as a function of mass, a detector with poor resolution would have observed more events by having allowed low mass events to pass the mass threshold. A change in the resolution in the Monte Carlo of 25% yielded only a 2% change in the measured cross section. Transverse Momentum Distribution The average transverse momentum for the electron pairs used in the Monte Carlo was 2.3 GeV/ c . When the Monte Carlo was run with an average transverse momentum of 2.0 GeV/c and 2.6 GeV / c, the change in the measured cross section was 3%. Decay Angle Distribution A distribution for the decay angle of the virtual photon is of the form 1 + (11 cos2 0 In the Drell-Yan model a = 1, and the decay angle is between the lepton and the beam axis. This view is somewhat complicated with the introduction of pr. Typically, in this case an axis is chosen half way between the beam and target axes [17]. The 93 Collins-Soper angle, 00-5 is the angle between this axis and the electron. With these QCD corrections a is no longer restricted to 1. Since our detector has no coverage at cos 0 near 1, we can expect acceptance to rise for small a and decrease for large a. Results from the Monte Carlo show a drop of 16% 1 of the cross section for a = 0. A rise in the cross section of 13% is seen for a = 2. Geometric Boundaries The shower counters consisted of 4 sextants with 8 counters in each sextant. Each sextant had edges at some (131 and (153, and at z=—75 cm and +75 cm. To confidently determine the acceptance of an event for an electron near the edge was difficult and would have required detailed simulation of the shower shape for a generated event. The Monte Carlo modeled only the average shower shape. As a check, cuts were made in both the data and Monte Carlo far enough away from the edges that the showers were well contained. For edges in z, electrons’ tracks projected to the back of the shower counters were required to have an absolute value in 2 less than 75 cm (The standard requirement . was that for a track to pass through at least 13 cm of the shower counters). This resulted in the signal from the data being reduced by 3%, the efficiency falling by 10% and the cross section rising by 8%. Edge effects in 4) were removed by accepting only electrons more than one counter from the edge. The signal from the data was reduced by 15%, the efficiency by 26% and the cross section rose 14%. Drift Chamber Efficiencies Earlier versions of the Monte Carlo did not model the drift chambers. Instead an overall track efficiency was used for acceptance correction. It was later discovered ‘If the acceptance increases, the acceptance corrected cross section from the data drops. 94 that the Data and M CM distributions in 45 did not match (see figure 4.17). This difference was most evident for the counters nearest the x=0 plane (at = :l:1r / 2). The reason for the lower acceptance of these counters was that particles may strike them without passing through all 8 planes of the drift chambers, (as can be seen from figure 2.3), and therefore have a low track efficiency. For this reason it was necessary to include the drift chambers in the Monte Carlo., The d) distribution of M C“. with drift chamber modeling along with Data are shown in figure 4.18 and show agreement within errors. 95 Without Drift Chamber Modeling I I l l ' m >- .. 44 - .. c " '1 ‘1; 20 — - q, - . . 4, 2 16 ~ — I. .. 2 I e 3 1 1 ~ a . . a . - 3 l» . . L L . 8 l- KX/H\/—Ml\ fi $ _ r m/Rtt ‘ :fi * 9 $ / j 4 + . j . +++ . o l l 1 I 1 I 1 l l 1 1 L l l 1 o 2 4 5 s 10 12 14 Te p-O’ V'90' p-iao' counters Figure 4.17: Azimuthal angle distributions (before correction) The distribution in 41 of the Data and M C“. without modeling of the drift chambers are shown above. The distribution was folded over at 41:0 and has bin size of half a counter. The difference between Data and M Cm was greatest near ¢=1r/ 2. 96 With Drift Chamber Modeling rva FfI T 20- - events + lilL oo 2 4 6 810121415 9-0' p-OO' p-1 80' counters Figure 4.18: Azimuthal angle distributions (after correction) The distribution in 41 of the Data and M Cm are shown above, this time with drift chamber modeling. The distribution was again folded over at 41:0 but now has a bin size of a drift chamber cell in the D01 module. The difference between Data and M Cm was greatly reduced. 97 In section 4.1.2 it was stated that the drift chambers were modeled assuming an efficiency of 85% per plane. The value of 85% comes from a study done on minimum ionizing (min-I) particles [10]. The energy in the C compartment, EC and D compartment, ED, of the trigger counter of these min-I events was constrained so that 36 MeV < Ec < 71 MeV and 120 MeV < ED < 200 MeV. Furthermore, the adjacent counters were required to have less than 5 MeV (therefore counters at the edge of a sextant were excluded and tracks passed through all 8 planes of the drift chambers). It was determined from these events that the efficiency per track of the drift chambers was 89%:l:7%. By using equations 4.1.2 and 4.1.2 it can be shown that tracks passing through 8 planes with an efficiency of 85%:l:4% per plane have an 89%:l:7% efficiency of activating 6 planes. The limits on the systematic errors from the uncertainty in the efficiency of the drift chambers was found by running the Monte Carlo with the drift chambers plane efficiencies of 90% and 81%. C and D Counter Balancing The calibration of the shower counters was done in a 4 GeV electron beam at normal incidence. The counters were scaled so that the total energy observed in the C and D counters equaled 4 GeV. But, since there were two compartments, calibration requires knowing the correct value for < C/(C + D) > as well as the total energy. Unfortunately the value of < C/(C' + D) > varied depending on how it was found. The < C/(C +D) > in the first line of table 4.8 were the values used in the calibration. Values from the second line of the table were found using the EGS Monte Carlo 3 [25], and gave the largest values of < C/(C + D) >. Data taken by Jakeway and Calder [26], and by Miiller [27] measured the shower shape in pure lead. Unlike the shower counter, there were no scintillator or air gaps between layers. Fits were made ’The EGS Monte Carlo is a computer program for modeling electromagnetic showers. 98 with equation 4.11 to their data with xa/do f = 1.5 for Jakeway and Calder data, and xz/dof = 1.8 for the Miiller data. Based on the composition of the shower counters, values for parameters b and Z were found. These values along with the corresponding < C/(C + D) > values are shown in the last line of table 4.8. The first Table 4.7: Radiation lengths of material A particle must pass through the beam pipe, the A counters and their support plus an the iron support for the C and D counters before striking the shower counters. Very little energy is deposited in this material because it is at the beginning of the shower, however it does tend to shift the shower so that more energy is deposited in the C counters. Therefore in the Monte Carlo the thickness of the C counters is taken to be 3.87 radiation lengths for the upper counters and 4.04 radiation lengths for the lower counters. Description Material Thickness cm Radiation Interaction Lengths Lengths A counters polystyrene 0.6 0.014 0.008 Support of A1 0.2 0.023 0.005 A counters Beam pipes Titanium 0.1 0.028 0.004 Lower support of Fe 0.3 0.170 0.018 shower counters Upper support of Fe 0.6 0.341 0.036 shower counters C counters 3.6 3.609 0.140 polystyrene 1.6 0.038 0.020 Pb 2.0 3.571 0.119 D counters 10.8 10.827 0.418 polystyrene 4.8 0.113 0.060 Pb 6.0 10.714 0.358 method used in this experiment for calibrating the shower counters took advantage of the fluctuations in the longitudinal shower shape and selected the (C/(C + D)) that minimized the energy resolution. The other values came from the EGS Monte Carlo and the parameterization of the longitudinal shower shape (see section 4.1.3). How an incorrect value of < C/(C + D) > would affect the cross section was explored with the Monte Carlo using the equation for the longitudinal shower distribution. The true energy deposited in shower counters was assumed to be that determined from 99 Table 4.8: Energy balancing in the C and D counters The upper shower counter were supported by an iron plate 6 mm thick. This plate was only 3 mm thick for the lower shower counter so that the lower shower counters had lower < C/(C + D) >. All values of < C/(C' + D) > are for normal incidence 4 GeV electrons. The values of b and Z were chosen so that < C /(C + D) > match calibration values in the first line and results of an EGS Monte Carlo in line two. For the next three lines the values for b and Z are the result of a fit to data by Jakeway and Calder [26], and Miiller [27]. In the final line b and Z are found based on the composition of the shower counters (see section 4.1.3). 3 mm Fe 6 mm Fe Description I) Z < C/(C + D) > < C/(C + D) > Calibration 0.4 30.5 0.275 0.295 Jakeway 0.426 52.6 0.230 0.248 Miiller 0.465 57.2 0.221 0.241 From Material 0.5 76.8 0.195 0.214 Composition equation 4.11. Coefficients for the C and D counters were chosen to match calibration requirements (C and D counters sum to 4 GeV, and < C/(C + D) > equal 0.295 for upper counters and 0.275 for lower counters for a 4 GeV beam at normal incidence). These constants were then used to find the energy observed in the detector. Using different sets of values for parameters b and Z, taken from table 4.8, different shower shapes were tested. (see Table 4.9). 4.4.1 Summary of Systematic Errors An estimate of the total systematic error is found from the sum of the squares of the percentage change for each parameter varied in table 4.9. Therefore A,’r=5’+2’+3’+8’+14’+16’+24"‘+9.52 01' A7 = 35%. Including statistical error the total cross section is therefore found to be 7.25 :l: 0.73 :l: 2.5 pb. 100 Table 4.9: Systematic Errors Systematic Monte Monte Signal Total % Change Errors Carlo Carlo Cross From In Out Number Section Standard pb pb of Events pb Standard 7.27 0.589 99 7.25 0 K factor = 1.50 in 6.41 0.523 99 7.21 -5 the Monte Carlo K factor = 1.90 in 8.12 0.657 99 7.28 3 the Monte Carlo Duke and Owens 7.27 0.594 99 7.41 2 parton distributions set 2 M). = 0.0.7137 7.26 0.569 99 7.51 3 A3. = 0.07571? 7.26 0.578 99 7.30 2 A3. = 020$]? 7.26 0.600 99 7.12 -2 1' Off 7.27 0.567 99 7.54 4 (p1 = 2.0) 7.26 0.609 99 7.01 3 (p7 =.- 3.0) 7.27 0.545 99 7.84 8 projection of electron 7.27 0.528 94 7.86 8 tracks must be within 75 cm at back of shower counters remove outer shower 7.27 0.437 82 8.26 14 counters in each sextant a: 0 in cos0 distribution 7.27 0.704 99 6.07 -16 a: 2 in cos 0 distribution 7.27 0.523 99 8.18 13 Drift Chamber 7.27 0.711 99 6.02 ~17 Efficiencies of 96% Drift Chamber 7.27 0.475 99 8.99 24 Efficiencies of 82% Shower Balancing 7.27 0.603 99 7.12 -2.1 J akeway and Calder Shower Balancing 7.27 0.607 99 7.11 -2.1 Miiller Shower Balancing 7.27 0.561 99 7.96 9.5 Calibration Chapter 5 Associated Particles 5.1 Associated Particle Acceptance A search was made for evidence of an associated jet by studying particles produced in the same event as the electron pair. Clusters of neutral energy observed in the lead glass and shower counters were assumed to be Iro’s, and charged particles in the drift chambers were assumed to be charged pions. Only particles with energy greater than 0.2 GeV were considered. Charged particles were required to project back to the electron-pair vertex. The. acceptance in rapidity, y, for charged particles was -l.2 < y < +1.2 over the full azimuth, 41. The acceptance for 1r°’s was —0.6 < y < +0.6 over the lead-glass acceptance (641 = 114°) and -1.1 < y < +1.1 over the shower counter acceptance (641 = 200°). The multiplicity of an event was defined as the number of charged and neutral particles satisfying the above requirements, excluding the two electrons. These multiplicities were not corrected for apparatus effects. 5.2 Associated Particle Distributions Over a third of the events in this sample are expected to arise from higher order diagrams (see figure1.2) and thus be accompanied by associated particles. The virtual gamma in these events should have higher transverse momentum since it will be recoiling of either the gluon or quark. Simple Drell-Yan is expected to contribute only at low transverse momentum. Therefore as m- of the virtual photon increases 101 102 one should see 1. an increase in the number of particles in the event 2. an increase in the number of particles in the opposite transverse direction of the gamma 3. an increase in the transverse momentum of the vector sum of the associated particle. These effects will be diluted due to the finite rapidity acceptance of the detector. In figure 5.1 indeed the multiplicity of the associated particles can be seen to rise with transverse momentum of the electron pair, in agreement with earlier observations at the ISR in conjunction with muon pairs [28]. This may be interpreted as evidence that low values of transverse momentum are less likely to be associated with a recoil jet. The mean multiplicity shows no strong dependence as a function of mass (see figure 5.2). The difference in azimuth, Q, between momenta of the associated particle and the electron pair was found. The distribution of Q is shown in figure 5.3 with the data split between electron pairs with transverse momentum less than 2 GeV/c and those with more. There is no strong variation in the Q distribution for pr < 2 GeV/ c, but for p1- > 2 GeV / c associated particles are produced predominantly at large Q, that is back-to-back with the electron pair. Events with electron pair transverse momentum less than 2 GeV/ c show little or no variation with Q, whereas for p1- > 2 GeV / c the distribution show a rise at large Q. The data presented in figures 5.1 and 5.3 imply that low transverse momentum electron pairs are produced by the basic Drell-Yan process with associated particles arising only from spectator jets. As the transverse momentum of the electron pairs increases, more associated particles are seen concen- trated in the central region and furthermore they tend to recoil against the electron pair. This is consistent with the increasing importance of second order diagrams involving a recoil jet in the production of lepton pairs of increasing transverse mo- mentum. 103 A 'TFTIHHIH"I'FFTIH'TT""1""1'"'1""I"' c 14 - A V . . >‘ 12 — ‘ .4: . .2 a 10 r - IE I. + . 3 2 8 - + _ Iv - + 1 + ‘ 8’ 6 — - a" - > t < 4 ~ — 2 - _. [- . o 111l1111l1111l111111111ln11111111111111111111111 O 1 2 3 4 5 6 7 8 9 10 Dr (GeV/C) Figure 5.1: The mean multiplicity as a function of the transverse momentum The mean multiplicity increases as a function of pr of the electrons pair. 104 A I I w I w I I I r 7 F c 14 — — V . x 12 I— .— 4H .6 l' E. 10 h" . -I E r 3 z 8 - _ Q, r + + .l 0" o 5 " 4 L- . ‘” ‘ l > < 4 r- _. 2 — _ o 1 l 1 J m l L l 1 J 1 l L l 10 12 14 16 18 20 22 24 m (GeV/CZ) Figure 5.2: The mean multiplicity as a function of the invariant mass No dependence of the multiplicity is seen as a function of mass. 105 _UII'IIIrIITIIllllirrlllillirlllllIIIITI [IITd 7 4.5 E- J 'o P : C - I L. 4 _— o p,>2.oo.v .1 v .. .1 3.5 E- o p,<2.ooov l 3 :- € 9 E 3 “O 2.5 r -3 \ I _+_ c: : 1 U 2 :+:'— j: i 1.5 E i) 9 1 T— 3 : 3 0.5 _- - O LllllllllLLLIILLJIIILLlLilkIIillLlllllllllll: 0 20 4O 6O 80 100 120 1 40 1 60 ¢ (degrees) Figure 5.3: dn/di’ The distribution for Q, the difference in azimuth between the transverse momentum of an associated particle, and the momentum of the electron pair, is shown above a) for electron pairs with pr < 2 GeV and b) for electron pairs with m- > 2 GeV. 106 A _HHVH,,nrrrmqrmi....,,rfll.,.rr..,,‘ to 3.2 :— —j E : o p,>2.oo.v : %, 2'8 E o p,<2.ocev :V 8 2.4 3 —3 i- «A ~ 1 2 — + .1 6- : i 3 1.6 I— —‘— a 14.1 E _+_; 0.8 }fi: | 5 0.4 E —: O :JlLllLllllLilelllJIlllllllllllLLlillLll11111 0 20 4O 60 80 100 120 140 160 Ch (degrees) Figure 5.4: dE/dQ The energy distribution of the associated particles as a function 9 is shown above a) for electron pairs with pr < 2 GeV and b) for electron pairs with p;- > 2 GeV. 107 p _IIIIIvfi'IT'HI'I'IIIFfiIfiII'I'I'II'I'IfHII. . C. L '0 2.8: q E L o p,>2.ocov ; > 2.4 ; +1 0 : O p7<2.OGOV : 0 : 1 e E i ‘D 1.6 L- 4 \P I 3 Lu I b i '0 1.2 :- "1 0.8 '— l + i J :i 1 0.4:»- Q r 1 r- 4 O 'erlll.ul.nulul.lnuLUHIHHI”11111211 O 20 4O 60 80 100 120 140 160 49 (degrees) Figure 5.5: dET/d‘I’ The transverse energy distribution of the associated particles as a function ‘5 is shown above a) for electron pairs with p:- < 2 GeV and b) for electron pairs with p:- > 2 GeV. 108 Energy (figure 5.4) and transverse momentum (figure 5.5) weighted (P distributions show similar results. The vector p'} of an event was formed by summing the momenta of the associated particles. The difference in azimuth, <15, between the transverse momentum of the electron pair and p; j was found. The distribution of (15°, again with data split between electron pairs with transverse momentum above and below 2 GeV / c. Since there only 105 opposite sign events the statistical error is fairly large. The distributions for m- < 2.0 GeV/c whether plotted with a weight of one, the energy sum or the transverse energy sum show no dependence in 4’,- (figure 5.6, 5.7 and 5.5). Distributions with p:- > 2 GeV/c show an increase at large 0,. The transverse momentum correlations between the electron pair and the asso- ciated particles were examined in the two-dimensional plot of prj, the transverse momentum of the vector sum of the associated particles, versus p1- of the electron pair(figure 5.9). The value for the sample correlation coefficient ‘ was found to be 0.38. The correlation observed between the two variables is what might be expected if a recoil jet were present. This correlation can be seen in figure 5.10, where the mean transverse momentum of the system of associated particles, (p1,) , is plotted as a function of p1- and again in figure 5.11 where the mean transverse momentum of the electron pair is plotted as a function of (p7,) . A completely contained jet with perfect resolution might be expected to have (p13) equal to pr, while imperfect jet containment would result in lower slope. Figure 5.10 clearly departs from the ideal- ized situation, especially at low p;- where the presence of spectator particles would dilute the effect of the jet. In an attempt to combine the azimuthal correlation and momentum balancing information, we constructed -p1-,. cos (15. The two-dimensional plot of this variable versus p1- of the electron pair is shown in figure 5.12. The value for the sample correlation coefficient for this plot was found to 0.46. For the vari- lAn anti-correlated sample would have a value of -1. An uncorrelated sample would have a value of 0. And a correlated sample would have a value of l. 109 A ' I I T I V F! r I r rT r I T T Fr] ' l T TT r r T I I I I' T T ‘ I l I T I l—I—r T 7 L I '0 1 — — C . . L- . 4 V F O p, > 2.0 GeV . 0.8 — o p, < 2.0 GeV __O—‘i '5 P - s : * \ O 6 l- j C _ D Z : 0.4 - ——<>— —< ‘4 _ . I t ' i 0.2 - d . 1 O L 14 LJ l L l l l LLL L 1 L1 l 14; l L l 1 l 1 L l l L l 1 Li L L L l l I l l l O 20 4O 50 80 100 120 140 150 ¢,(degrees) Figure 5.6: dn/de The distribution for Qj, the difference in azimuth between the vector sum of the momentum of an associated particle, and the momentum of the electron pair, is shown above a) for electron pairs with pp < 2 GeV and b) for electron pairs with pr > 2 GeV. 110 6 _frUT—[IfTTTfiIYrTTVUIUFTrI‘IVIUlYIIITT1T1III _{ T - d ‘0 - I c "' a *- 5 - o p,>2.ocov — s : , 1 _ O p,<2.0GeV O _ ‘ V 4 __ ‘ " - ': 9 . 4 Q t i “f 3 - _. .4 '0 E 1 2 - + _ l- .1 I. —4>—— . _ # .i 1 - j -1 L I O .LLllfllLllfILL]flJLllLllLLllJlllllllllLllllld o 20 40 so so 100 120 140 150 ¢,(degrees) Figure 5.7: dEj/dq’j The energy distribution of the associated particles as a function i,- is shown above a) for electron pairs with pr < 2 GeV and b) for electron pairs with pr > 2 GeV. 111 A y. ,fi ,.,.-,..,.,...fi,.,..,.r, W, 7 i 1 8 5 - s p,>2.ocev A L ' s g l o p.<2.ooev j —.._2. 8 41 ‘1 e i 3 'U . . \ 3 __ __j ._ . LIJ r + .0 . . Z —_<>—_ : 1- f + O _JljlllllfllLlllLLlLllllLllLlllfljllllllILJ11‘ O 20 40 60 80 100 1 20 1 40 1 60 ¢,(degrees) Figure 5.8: dETj/déj The transverse energy distribution of the associated particles as a function 9,- is shown above a) for electron pairs with pr < 2 GeV and b) for electron pairs with pr > 2 GeV. 112 10 IITI'ITVTFITIIrfillrfffrlT‘l'llrrl'lrrlrllrlrflT p..- (GeV/c) IIIITIIUIIlIIIIIIIITIUIIIIUT 5 ' - 4 _ - .. 3E- ' ° . 1 Edi . .° LlllfLLlllllllllfflLLJlllllllllllllLlllllLJllllL IIFT oh. llllll-llflllllLLllulllLfllllllllllLl 2:5 4 5 6 7 s 910 pT(GeV/C) O O!- _g— Figure 5.9: pr,- versus pp The net transverse momentum of the associated particles versus the the transverse momen- tum of the electron pair. 113 1o rrrr I'TllVYVYTTIIIIUUUIIYTTUIITIIIlllll'lrrr'fiff L < p,,> (GeV/c) U'I rIfiTrl—TllljlllrITllIIIUIIIjIUITfiWITITITFIII lllllllllllllllllilljlllllIllfllllllllllllJLLl 4 1" 3 2 , 1 ¢ ¢ ¢ 1 1- O :lllllfllllJllllllfllflllllljllL4LAlJJlelflllLL11 o 1 2 3 4 5 6 7 s 9 10 PI (GeV/C) Figure 5.10: (pm) as a function of p;- The mean transverse momentum of the associated particles as a function of the transverse momentum of the electron pair. 114 1O fTYrrTrrrrIFTrIVTrVrfTIYI'YYVY]VTTI'UTrYlVTII‘ITIIT I (GeV/c) O .- O) IIIFIIITIIIIIIIFYITTIlilllrI—TIrTT—FTIITYIITII d LllLJJlJlllfLlllllllllellllfllllllllllllLllJll LLllllLlLllJlllllLllLlLlllLllfllLfllJlllJ—lelflll 12 3 4 5 s 7 s 910 p,,(GeV/c) O orlli Figure 5.11: (p1) as a function of ij The mean transverse momentum of the electron pair as a function of the transverse mo- mentum of the associated particles. 115 5 Frrtl[rrfrrrtrrlrrfffiTIIIVVII[IttrlrrIrItlrTerVq Q - « " 4 i- d > 4 — . _ V I ' ‘ . I 3 _ . _ oq :— O 0 .1 a. - - .- « I- . d 2 i—. O . . . fl «a '9' ; . ° I o 1 m b . . . .‘ o 0 e ‘1 o - .. ~ 0 1 _... '. e -1 b i e 0 '1 I : ' ° 0 : ”."Q. ~.. I -1 o L— ; .0 '.e '. .‘°. . j g e i" N. ' : 1 1-0 ' 00.. 0 ° - _ r— .0 —4 1- . _4 C. , I I. . .. 1- L o 1 -3 hLLLIII‘LlllllljmllllllllllllllllllLllllllllllllllll O 1 2 3 4 5 6 7 8 9 10 PT (GeV/C) Figure 5.12: —p1~,- cos (1’ versus p1 The momentum of the associated particles projected onto the transverse momentum of the electron pair versus the the transverse momentum of the electron pair. 116 A 5 Pl[If]Ifl'l'lfrfrlfrt'Irlrflfifll'rflVIVIVIFTIIIIIFrY‘ U _ . \ F .. > 4 ”— j a) - . O . I 3 f + l sq 1- -1 .— _ o. 2 - T 1 .. : j ‘9' 4 4 (D 1 _— .4 O _ + j 0 - . I O P+ + -: -1 __ I. C I -2 :- -1 - I " -1 -3 plllllllllllllllllllllllllLlllllJmlllljlllmelmffllll-i O 1 2 3 4 5 6 7 8 9 10 D: (GeV/C) Figure 5.13: (—p1-,- cos 0) as a function of p:- The mean of the momentum of the associated particles projected onto the transverse mo- mentum of the electron pair as a function of the transverse momentum of the electron pair. 117 1O rITTIITrTlYrIIITTIfITUIIIrrIIIITIIIIIVT r l < p,> (GeV/c) + ‘ ’ O lllllllLLillll[lllLlLlflLlllllLlllllllf -3 -2 -1 o 1 2 3 4 -<:os,-. It can be seen that for values of —p1~’. cos <1",- below zero, little or no correlation exits. But above zero a strong correlation can be seen. 5.3 Charge Ratio There is some question as to which of the two higher order diagrams (figure 1.2) contribute most. An answer to this question could be provided with an accurate measurement of the charge ratio of particles in the away side jet. Events arising through figure 1.2)b would be initiated by a gluon. The charge ratio of particles from a gluon jet is expected to be one. For the figure 1.2)c the jet would be initiated by a quark. The rate at which this quark is a u. quark compared to a d quark, for proton-proton collisions, will be approximately M): = 2(2/3)’ = 8 Nahum): (1/3)2 For this quark jet one might naively expect this same ratio in the positive to negative hadrons on the away side. But since u quarks can give rise to negative hadrons and d quarks to positive hadrons the ratio can be much less. One could hope that the ratio of leading hadrons, which might remember the charge of the parent proton, would approach this ratio. Figure 5.15 shows the ratio of positive to negative hadrons as a function of z, where 119 = _ T r r r r T l I fil— fit ffI r t I—I l T r f 4 <5) 2.8 C- _. 1:: I e p,>2.ocev j C r 4 2.4 '_ — m ' '1 81 I o p,<2.ocov 3 L 2 — L 0 . 1.6 P 4} _ I a} 1 " .1 1.2 _ k ‘F s 0.8 _F <1; - i 1 r 4 0.4 f f — 1" .1 L -4 0 P 1 1 1 1 l 1 1 1 1 __l___L_L 1 1 i 1 1 1 4 L4,:l d O 0.2 04 0.6 0.8 1 Z Figure 5.15: Charge Ratio The charge ratio of the associated particles is shown as a function 2. 120 Another source of hadrons in an event were the beam jets. Since the charge ratio of these hadrons should be near one it is difficult to distinguish whether the charge ratio of one is due to the gluon initiated jet or merely the result of spectator particles. APPENDIX Appendix A Changes A number of changes have been made that affect the cross section in this analysis since this experiment’s last publications [23] [29] 1. concerning electron pairs. A list of these changes is given below. Since most of these changes occurred in the Monte Carlo, the estimate of the efficiency of the detector as a function of mass is shown for the earlier publication along with the current estimate of the efficiency. 0 Changes that affect the cross-section 1. The Monte Carlo now includes the resonances from the T which raise the efficiency of the lowest mass bin and thus lower the cross section. For details see sections 4.1 and 4.1.1. 2. The distribution thrown for the virtual photon in the Monte Carlo of the previous publication was flat in rapidity and had a mass distribution pro- portional to m“. The distribution is now thrown according to Duke and Owens structure functions as described in section 4.1.1. Because the struc- ture functions restrict the rapidity range of the photons as the mass in- creases, the efficiency of detection increases. 3. In both the previous and the current Monte Carlo the decay of the photon into the lepton pair was according to an angular distribution in 0 of 1 + 1These two papers were published based on the data included in the first two columns of tables 3.1 and 3.2 122 123 cos2 0. But the previous definition of 0 was the angle between the 7 and the electron in the beam-beam center-of-mass. The current (and conventional) definition of 0 or 005 is the angle between zcs axis and the electron in the rest frame of the 7 where 203 is half way between the two beam axes. See section 4.1.1 for more detail. 4. The previous Monte Carlo required the track of an electron to extend out the back of the shower counters and not out the sides. The current Monte Carlo requires only that the electron track pass through at least 13cm of the shower counter. This condition has been added to the data. The results in a cross section that is 8% lower. 5. No corrections were made for energy leakage from the shower counters in the previous Monte Carlo. The current Monte Carlo takes into this leak- age during calibration and running. Since there was overall more leakage during the calibration of the shower counters than when collecting data 3 the resulting cross section was lower. 6. Previously there was no modeling of the drift chambers in the Monte Carlo. Instead a correction was made based on the efficiency of two tracks pass? ing through 8 planes in the drift chambers. It was later discovered that tracks at the d: edge of sextants, particularly sextant edges at the top and bottom of the detector, had low efficiencies because they passed through less than 8 planes 3. The current Monte Carlo finds the probability of a track being accepted by determining how many planes of the chamber it passed through. For greater detail see section 4.1.2. 7. N 0 account was taken of the efficiency for matching the track to the cluster in 2 position. It was known that the efficiency of the signal plus background aCalibration was done in a beam at normal incidence, the shortest path through the counters. ’At least 6 hits were required per track. 124 in the data was r,» 70%. But it was not known what the efficiency of the signal alone was. Modeling of cluster formation in the Monte Carlo showed a similar efficiency of ~ 70%. See section 4.1.4 for details. . Previously the estimate of opposite sign background events was taken as the sum of plus-plus events, "++1 and minus-minus events, n--. But if the charge of a track in a background event did not depend on the charge of the other member in the pair the best estimate of the plus-minus background should have been 2m (see section 3.2.7). This change had little significance in estimating the background of the data set after all cuts were made since the background is small. But it did change the estimates of the efficiency of the a and the p; cut. A description of these cuts can be found in section 3.2.8 and section 3.2.8 with values of efficiencies found in table 3.3. . Since the cross section is no longer assumed to be flat in y, the cross section v=0 do dmdy Ay=2.4 has to be corrected by the Monte Carlo to give the value of v=0 dc dmdy Ay-OO 125 .0 N —T >‘ _ l ‘ fI ' ' r ' ' l ' ' I ' ' I I .. 0 I 1 $0175 :_ O R110Current ~ 12 E 0 R110 Previous : "LE1 0.15 _— 4: 0.125 L + i i E O o 0 0 8 (t i + 3 0.1 :— ° ° . . 0 ' ' ° 1 P o . I I ' . 0.075 _1_- a ' 4 0.05 E- d 0.025 :— «j 0 ' 1 . l . . 1 1 1 1 1 . 1 . . L 1 1 LL 1 1 . . 1 10 12.5 15 17.5 20 22.5 25 27.5 30 m (GeV/c) Figure A.1: Efficiency Changes The distribution of the efficiency as a function of mass is shown for the previous publication and the current. BIBLIOGRAPHY Bibliography [1] M. Cell-Mann. A Schematic Model of Baryons and Mesons . Physics Letters, 8:214, 1964. [2] J. D. Bjorken. Asymptotic Sum Rules At Infinite Momentum . Physical Review, 179:1547, 1969. [3] S. D. 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