sl \IIRIIIIIIII' ABSTRACT DEEP INELASTIC MUON SCATTERING AT 150 AND 56.3 GeV By Chuen Chang We have performed an experiment especially designed to test Bjorken scaling. Data of deep inelastic muon scat- tering were collected at the Fermi National Accelerator Laboratory with muons of l50 and 56.3 GeV. Heavy targets (mainly iron) were used in the expe- riment, so that events with q2 (four momentum transfer square) up to 80 (GeV/c)2 or w (scaling variable) up to 40 were possible. Up to five 3l" long iron core magnets were used as momentum analyzer. The detector consisted of plas- tic scintillation counters, proportional chambers, spark chambers, and an on-line computer. In the SLAC region, defined as q2(w + k) < 29.1, our data agree well with SLAC's, confirming p—e universa- lity. Outside of the SLAC region deviations from Bjorken scaling are observed. Possible explanations are examined. We estimate the two photon exchange contribution by comparing our u+ data to the p- data. DEEP INELASTIC MUON SCATTERING AT 150 AND 56.3 GeV By Chuen Chang A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics l975 ACKNOWLEDGMENTS The author wishes to express his gratitude to his thesis advisor, Professor K. W. Chen, for his encouragement and continued interest throughout this work. This experiment is a result of the cooperative effort of the following physicists: w. Vernon from the University of California, San Diego; S. C. Loken and M. Strovink from the University of California, Berkeley; L. N. Hand, 5. Herb, A. Russell and Y. Hatanabe from Cornell University; and K. H. Chen, D. J. Fox, A. Kotlewski and P. F. Kunz from Michigan State University. The assistance of R. Huson, P. Limon, R. Orr, T. Toohig, T. Yamanouchi, and other staff of the Fermi National Accelerator Laboratory is greatly appreciated. In particular, the author wishes to acknowledge the work of H. Vernon, D. J. Fox and P. F. Kunz on the spark chamber system, M. Strovink and Y. Hatanabe's work on the proportional chamber system, S. C. Loken and S. Herb's work on the toroidal magnets, A. Russell's work on the target counters, and S. C. Loken and P. F. Kunz's work on the PDPll software system. As for the MSU analysis, special thanks are due to P. F. Kunz for the development of the ii track hunting technique, to L. N. Hand for the development of the track fitting procedure, and to A. Kotlewski for the development of the Monte Carlo program. The author is very grateful to L. Litt for his contributions to the spectrometer calibrations. In the early construction stage, the great help of T. Reitz on setting up the apparatus, K. Rajendra's con- tributions to the supporting system for the magnets and the spark chambers, B. Meyer and D. Chapman's work on the PDPll online system, and B. Thelan's help on the spark chamber construction will never be forgotten. The author is very graterl to Professors J. Pumplin and H. Repko for many friendly and stimulating discussions. The author wishes to thank Mr. J. Hoekzema and Mr. F. Earley for their help in preparing some of the figures, Miss J. Marx and Mrs. T. Torres for their patience and excellent cooperation in the typing of this manuscript, and Mr. P. Schewe and Dr. M. Pratap for their help in correcting and smoothing up the English. TABLE OF CONTENTS ACKNOWLEDGMENTS LIST OF TABLES LIST OF FIGURES I. Introduction l.l Historical Background . l.2 Muon Electron Universality . . l.3 Lepton Nucleon Inelastic Scattering and Bjorken Scaling Hypothesis l.4 Two Photon Exchange Contribution to Lepton Nucleon Inelastic Scattering Cross Section . . . . . . . Experimental Setup NNNNNNN NN . O O O O O O O O \OGDNGU'I-hw N-J U D) ('1- 3’ cows» 0 O O (JON—l 3.4 Geometric Scaling of the Apparatus Acceptance and Resolution of the Apparatus The Muon Beamline The Targets . The Iron Core Magnets . . The Counters and Electronics . . The Proportional Chamber System The Spark Chamber System . . The Online Computer Analysis and Results The Reconstruction Program . The Monte Carlo Program . The Standard Cuts and the Inefficiency Cuts . The Results Summary and Conclusions iv Page ii vii 107 129 163 Page APPENDIX Some Theoretical Speculations About Scaling Breakdown . . . . . . . . . . . . . . l65 REFERENCES . . . . . . . . . . . . . . . . . . . l69 to N o o NNNN w (A) w 00 O O O O U"! h to N cowascn LIST OF TABLES The 150 GeV configuration The 56.3 GeV configuration The resolution of the appa atus at l50 GeV as a function of q and w . The resolution of the apparatus at 56.3 GeV as a function of q and w The muon beamline magnets The counters The scalers Some of the scaler ratios monitored online The primary tape format . The data samples and their Monte Carlo simulations . . The secondary tape format . The calibration runs The standard cuts The consistency checks + data The l50 GeV ratios fitted "Dc, - data 1‘ (M.C.) to a constant vi Page l4 l6 32 33 36 42 47 48 61 64 65 92 108 125 126 00000000 Page data carbon(M C ) .7 The l50 GeV ' .data (carbon+iron)(fi—E—) ratios fitted to a constant . . . . . . . 133 150 GeV(data) .8 The ”agia ratios fitted 56.3 GeV(M C ) to a constant . . . . . . . . . . . . . . l35 .9 The combined Saga ratios, w bins . . . . 140 .10 The combined 33:3 ratios, w2 bins . . . . 147 .11 Effects of the 1% E0 uncertainty . . . . l55 .12 Effects of changing the parameter R . . . 158 .l3 The BV counters . . . . . . . . . . . . . 160 .l4(a) The DCRl bits . . . . . . . . . . . . l6l .l4(b) The DCRZ bits . . . . . . . . . . . . l62 vii .10 .11 LIST OF FIGURES One photon exchange Feynman diagram for lepton nucleon inelastic scattering 2Mw1 and owe versus w for w > 2.6 GeV and q2 > l.0 (GeV/c)2 from the SLAC-MIT ep inelastic scattering experiment vw from the SLAC ep and ed inelastic gttering experiments . . . . . . Two photon exchange Feynman diagram for lepton nucleon inelastic scattering The two configurations of the apparatus The geometric scaling of the apparatus The acceptance of tEe apparatus as a function of B and q . . The acceptance of the apparatus as a function of E'. . . . . . . The acceptance of the apparatus as a function of w and w . . The FNAL muon beamline The radial dependence of the magnetic field . . . . . . . . . . . A typical counter bank The trigger logic . The cross sectional view of a proportional chamber module . . . . . . . . . The amplifier and discriminator circuit for the proportional chambers . . viii Page 11 13 20 22 24 28 35 4o 43 44 50 52 .12 .13 .14 .15 .16 .17 .18 .5 .6(a) .6(b) The latch and readout circuit for the proportional chambers The construction of a spark chamber module The details of a corner of a spark chamber . The spark gap circuit The amplifier circuit for the spark chambers The discriminator circuit for the spark chambers The time digitizer system . The kinematic region covered by the experiment . . The picture of a long target event The variables used in the reconstruction program The distributions (coordinate measured - coordinate expected) in cm The match distributions in cm The probability of finding N sparks out of the 6 hadron chambers as a funct1on of PBACK . The hadron chamber efficiency as a funct1on of PBACK The calibration runs Some systematic studies The target distributions ix Page 53 54 55 56 58 59 60 67 72 75 77 83 89 9O 93 100 110 .10 .11 .12 .13 .14 .15 .16 .17 .18 The binning system for the data stability checks . . . . The data stability checks The l50 GeV11 The measured and simulated E' and e distributions carbon (data) The 150 GeV data ratios (carbon+iron)(MC ) as a function of q2 carbon(aaéa) The 150 GeV ' data ratios (carbon+iron)(M .) as a function of w 150 Ge V(data) data) rat1os The 56. 3 Ge V ( The combined Saga ratios as a function of q2 and w The combined %3%3 ratios as a function of q2 and ”2 Page 113 114 127 130 132 134 136 144 151 1. INTRODUCTION We have performed an experiment at the Fermi Na- tional Accelerator Laboratory especially designed to test Bjorken scaling, which appeared to be confirmed by the deep inelastic electron scattering experiments done at the Stan- ford Linear Accelerator Center (l.l). Muons instead of electrons were used in our experiment. 1.1 Historical Background It was in 1937, by means of a counter controlled cloud chamber, that a penetrating component of particles was discovered in the cosmic rays, with mass intermediate between that of an electron and that of a proton (1.2). Later on, they were identified as muons, coming from the decay of pions, another kind of particles with mass inter- mediate between that of an electron and that of a proton (l.3-1.5). They turned out not to be the field quanta of the nuclear force postulated by Yukawa (1935) (1.6), for they did not interact appreciably with the nucleons as was shown by the experiments of Conversi, Pancini, and Piccioni (1947) (1.7). Since then muon scattering experiments have been performed on various targets, either using cosmic ray muons or muons produced artifically. 1.2 Muon Electron Universality Muons decay into electrons, and the lifetime is 2.20 x 10‘6 sec. The mass of a muon is 207 times the mass of an electron. They both are spin-g fermions, and behave according to the Dirac equa- tions. They both interact electromagnetically and weakly. So far the only differences we have observed between muons and electrons are their masses, and that they have their own associated neutrinos and anti-neutrinos. Somehow the neutrinos can tell the difference between muons and elec- trons. Say, neutrinos from pion decay, + n + p + up , do not produce electrons when they interact with materials. They produce only muons, through the following reactions (1.8): v+n+ +- u P u s — + vu+p+n+u Muons, electrons, and their associated neutrinos and anti- neutrinos are called leptons. We assign them either a muon lepton number or an electron lepton number. These two numbers are conserved separately in all interactions. The existence of heavier leptons cannot be excluded by theoretical consideration. l.3 Lepton Nucleon Inelastic Scattering and Bjorken Scaling Hypothesis Differences between muons and electrons have been searched for in many interactions, especially in elastic and inelastic scattering on the nucleons. Comparison of u-N and e-N scattering from similar targets can reveal differences between the way a muon and the way an electron are coupled to the electromagnetic field. So far no differences have been found between these couplings (1.9), and the way in which a lepton interact with another particle is well under- stood from quantum electrodynamics: it emits a virtual photon which is then absorbed by the other particle. This one photon exchange approximation for lepton nucleon inelas- tic scattering is shown in Figure 1.1, also shown are the kinematic variables one uses to describe the process. Because the emission of a virtual photon by a lep- ton is well understood, in a lepton nucleon scattering ex- periment one is really studying the absorption mechanism and probing the structure of the nucleon. If one measures mchmuumum uwpmmfimcw campus: covamF soy Emcmmwn cascxmm mmcmcuxm.couoca mco F._ weaned «conga “was mcwmmme Naipz~+wxu~3 menacm memcmgu Ezucmeoe Lao» omvmcFm .umeuma a_uca mcwgmuuaum couaop a mmop amuuco couam_ .momu> magnum couaop Fae.» .m xmcocm copay, _a_uwcw m FDO mzomoS... A 3.27m 2. 20582 $8.825 29.825 .50 203.2 only the energy of the lepton before and after scattering and the scattering angle (i.e., E, E' and O), and do not look at any of the final state hadrons, i.e., if one sums over all possible final states of hadrons and averages over the initial nucleon spin, the cross section should depend only on the two Lorentz invariant variables descri- bing the vertex, namely the four momentum transfer square (q2 = 4EE' sin2 6/2) and the energy loss (v = E-E'). The square of the invariant mass of the final state hadron sys- tem is given by the relation 2 2 w=M 2 + 2Mv - q , where M is the mass of the nucleon. The contribution of the nucleon part of the process can be expressed as 2n 39 W = f .i 4 ' 1 I pv Me 5( )(P "P'91

, E f where D is the normalization volume, [P > and IP' > are the Heisenberg state vectors of the initial and final nucleon states, and Ju(0) is the electromagnetic current operator of the nucleon at the space time point Xu = 0. NW must be a second rank tensor since the current operator is a four vector. One can construct the tensor wW out of the basic tensors. The most general form is wpv = Aduv + quqv + CPva + D(unV + quu) + E(unV-quu). wuv has pos1t1ve parity so no term in EpvaB Pan can appear. Since the electromagnetic current is conserved, 5%E-Ju(x) = 0, which implies that quwuv = 0 = wuqu. These relations eli- minate three of the five invariant functions, and wW is reduced to q q 2 1 P- P- 2 (am, - $1) mm W) + Emu - $34”on - a—zflsvwzm .v). Together with the contribution of the lepton part, which is given by l I l 2 = + .. wuv pup v pvp u ouv(pp +m ). where m is the mass of the lepton, and the factor (l/qz)2 coming from the photon propagator, the cross section can be written in the laboratory system as 2 —-2—— = 2—2%_ i—Z{Z[EE'(l-coso)-2m2]wl+[EE'(1+cose)+m2]wz}- One can neglect the lepton mass and obtain 2 2 1 d U ' 4"“ E— cos2 % [W2 + 2” tan2 g] (1.10). dq dv q E 1 In terms of OT and UL, the total absorption cross section for transverse and longitudinal photons, one has w = o , 1 ggz; T 2 - k q "2 ' 2 2 2 (01+Os) 4n a q +v where k = (Hz-M2)/2M = v - q2/2M (1.11). If we define R = oL/oT, then the differential cross section can be written as O 2 2 2 2 — d I 20 = [4“; E C052 %] (sz) [1+2(]+V2) tan 2] dq dv q E q l v 1+R On the basis of some formal field theoretical argu- 2 and ments, Bjorken in 1969 conjectured that in the limit q v + m, the two structure functions MN] and vwz become func- tions of the dimension1ess ratio w = 2Mv/q2 only, i.e., q + m V + m, Mw](q29V) + F](w)s vN2(q2,v) + F2(w) (1.12). Once the two functions F](w) and F2(w) are available from some low energy lepton nucleon deep inelastic scattering experiment, one can predict exactly what one is going to see at higher energy. Such a scaling law seemed to be con- firmed by the SLAC-MIT electron proton and electron deute- ron inelastic scattering experiments (l.l). The results are reproduced in Figures 1.2 and 1.3. This is quite puzzling because it was observed at values of q2 and v much lower than one expected, especially + when the simple 1 scaling low for o(e e' + hadrons) was 5 found to be badly violated (1.13-1.15). Actually there ampw| I/Wz 7,0 6.0 5.0 4.0 3.0 2£) C16 C15 C14 C13 ()2 OJ R=018 Figure 1.2 2Mw] and 0W2 versus w for w > 2.6 GeV and q2 > 1.0 (GeV/c)2 from the SLAC-MIT ep inelastic scattering experiment 0.70 0.60 0.50 0.40 0030 ‘ 0.20 0.10 0.00 0.35 0.30 0.25 0.20J 0.15) 0.10. 0.05. 0.00 Figure l.3(a) sz (deutron) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Figure l.3(b) sz (proton) 10 have been various theoretical speculations about the way Bjorken scaling might break down (1.16-1.19), especially since the discovery of the new particles (J/w; 0') (1.20- 1.21). A discussion of them could be found in the Appendix. 1.4 Two Photon Exchange Contribution to Lepton Nucleon Inelastic Scattering Cross Section Figure 1.4 shows the two photon exchange Feynman diagram for Lepton nucleon inelastic scattering, which is expected to contribute only a few percent, through inter- ference with the ordinary one photon exchange amplitude. This interference brings up a nonzero difference between p+N and u'N (or e+N and e'N) deep inelastic scattering, and was estimated by Fishbane and Kingsley to be of order aln2(q2/p2), where p is a scale mass, typically hadronic (~mp) (1.22). The existence of point-like constituents within the nucleons was assumed in their study. It is a fact that one cannot estimate the two photon contribution in a model-independent way. 11 mcwsmuumum uwymmchw comruzc c0pam_ Loe Emsmmwu cascxmu mmcmzuxm coaoga 03» q._ ms:m_u F30 wzomo<1 . a A.afll.\~vu.& @4’ 4/.N\ 7% / 2227.. 2.20.3032 NU - . :u €9,623 11 1 .11 T 2. 203.2 mfl , £93 22525 . 3.3.1 .50 2022 .. 1 _ 2. EXPERIMENTAL SETUP In this experiment muons from the decay of pions and kaons, were scattered from an iron target. A propor- tional chamber system was used to record the incoming muon track. A large aperture spectrometer, consisting of iron core magnets and wire spark chambers, was used to momentum analyze and record the scattered muon. The trigger re- quired a beam muon not accompanied by halo muons, and a scattered muon not vetoed by the downstream beam veto coun- ters. We also triggered on a random coincidence of a beam muon and a pulse generator to accumulate an unbiased beam sample for the Monte Carlo program. Data were taken at two incident muon energies, 150 and 56.3 GeV. The configuration of the apparatus was changed with energy to keep w acceptance and resolution constant, as shown in Figure 2.1. Tables 2.1 and 2.2 give the positions and alignment constants of the chambers, the positions of the trigger counter banks, and the positions and magnetic field parameters of the magnets for the two configurations. Two sets of data, called the large angle data (LA) and the small angle data (SA) were taken at each 12 mzumcmgam ms“ *0 mcowumczmmmcou oz» mcb 1 zofiuma 25m cezvonEoEueg E‘ EEIEE l E: nTflom 3 $8 on: 32 5 E mm “gum _.N mesmEE wqdum 130ng . AthOUtOI _aII|lEno.¢ . \\\\ H \..\x.. ,. ‘Nd... . . is/ .m SN E\ E E EE .me 9;? / Pm E mm .: E «m r1 1 e 09... 016.78 ~>EI om u... um 02.2.... mmupzaouo Bug :0” Lmacaou Emma m mo msmpczou oum> Emma msmpczou oum> ope; _>m .>m N): .E>: _. mxcmm cmpczou gmpmeocuumam um .mm .3. >mo mm.mm to >mo Om_ mzumgman< mzp mo mcwpmum uwgpmsoou mgh 390% .E. COL— . _ -—-4 ~.N mt=m_e 21 2.2 Acceptance and Reso1ution of the Apparatus To study the acceptance and reso1ution of our appa- ratus, Monte Car1o events were generated in the target and propagated through the apparatus. DetaiTs of the Monte Car10 program wi11 be given in the chapter on data ana1ysis. Rea1 beam trajectories co11ected at the same runs we took the data were used in the Monte Car1o simu1ations. The re- su1ts are given in Figures 2.3 - 2.5 and Tab1es 2.3, 2.4. A Monte Car1o event was considered accepted in Figures 2.3 - 2.5 if it passed the fo11owing cuts: |x| > 7%" or |y| > 7%" at SC11, SC12, SC13, /x2 + y2 > 6%" at SC14, SC15, and r = r < 33" at SC11, SC12, SC13, SC14, SC15. where SC stands for spark chamber. The first cut was neces- sary because the trigger banks had a 14" by 14" square ho1e in them. The second cut was to avoid the inactive regions in the midd1e of spark chambers. To make sure that the track was not outside of the magnets, which had an outer radius of 34", a 33" radius cut was app1ied. 2 Monte Car1o candidates were Many sma11 e or 10w q generated but not accepted, and one is not to take this area serious1y. For examp1e, the acceptance as a function of E' cou1d have been a 1itt1e bit different in shape and very different in abso1ute va1ue for the e bin: 10mr < e < 20mr ACCEPTANCE (°/o) 22 I 50 GeV IOO '- LT L1 1 O -i " IOO —1 4 SA sn J1 | O -* — ' 1 1 I l O 20 4O 0 20 4O 60 6 (mr) q2 (GeV/c)2 Figure 2.3(a) The Acceptance of the Ap as a function of o and q Baratus ACCEPTANCE (°/o) 23 56.3 GeV 100-- LA 10— IOO-i SA LA *7 SA 0 (mr) Figure 2.3(b) 1 1 I 1 0.0 32.7 65.3 0.0 7.5 15.0 22.5 q2 (GeV/c2)2 The Acceptance of the Ap as a function of 6 and q Baratus ACCEPTANCE (°/o) 24 I50 GeV LT Configuration Ioo— -_,——— 60mr<9<70mr 30mr<6<40mr IOO-J -i 20mr<9< 30mr 50mr <9 < 60mr 100‘“ _‘ F:— 40mr<9<50mr 1.1 l0mr<9<20mr IO" "" | n I I I I ’I I o 2/3 “/3 2 o 2x, 4/3 2 Figure 2.4(a) I E/E The Acceptance of the Apparatus as a function of E ACCEPTANCE (°/o) 25 I50 GeV SA Configuration ICXJ-i _. 30mr83 5:03.96 $0 a \ s 50.0.. .3530 :98: o u 1 W G / 10 . E 7: > 05350on E0 : 0v x 26 h\ E03 3.05 053.05 30308 332.3 0. Fwd... 053.05 83.205 vndNI . E 8. 95.283 233 cc». _ _ chEmmm cos: 22¢ 2: min. 9:5: no... cons. . Tab1e 2.5 The muon beam1ine magnets 36 Current (amp) Enc1osure Magnet 2 Y (ft) (in) 150 GeV 56.3 GeV E100 Iwo 4844.0 -O.62 3247 1254 4886.0 -O.26 4936.0 +0.70 1V0 17 - 100 830 325 E101 101 5336.5 12.14 2000 830 5345.5 12.40 1E1 5365.0 12.91 2070 795 5386.4 13.32 5407.8 13.52 1V1 5419.8 13.57 (OFF) (OFF) E102 1w2 5819.0 13.62 2082 775 5840.4 13.82 5861.8 14.23 1V2 5873.9 14.53 (OFF) (OFF) E103 1F3 6042.0 19.36 950 400 6048.0 '19.53 6054.0 19.70 103 6076.0 20.33 1000 360 6082.0 20.50 6088.0 20.67 E104 1E4 6333.9 27.68 1N28 1181 6355.3 28.09 6376.7 28.30 37 Typically, the beam yielded one muon per 107 to 108 protons. Halo to beam ratio was 40% to 100%. (It was 60% to 70% for the 150 GeV LA and SA data, 65% to 75% for the 56.3 GeV LA data and 95% to 105% for the 56.3 GeV SA data. It was 40% to 60% for the 150 GeV LT data.) Pion contamination in the beam was measured by varying the length of the absorber, and was found to be below 10'5 (2.1). Beam size at the target was typically 8" x 8". Most of our data were taken with positive muons. The beam1ine could be switched to deliver negative muons, with intensity about one third of that for positive muons due to the production mechanism. 2.4 The Targets As shown in Tables 2.1 and 2.2, the small angle data were taken with one carbon target (14" long at 150 GeV and 8.6" long at 56.3 GeV) and three iron targets (36" long at 150 GeV and 22" long at 56.3 GeV). The carbon target and one of the iron targets (the main target) were put on a target cart, as were the halo veto counter bank, HV] and HVZ’ one of the u lab counters, C3, one of the beam proportional chambers, PC4, and the two hadron proportional chambers, PCS and PC6. The target cart was moved downstream by 180" at 150 GeV and 110" at 56.3 GeV to collect the large angle data. 38 The main target consisted of 8 blocks of iron, 8“ x 8" in cross section, 3 7/8" thick for 150 GeV and 1 7/16" thick for 56.3 Gevsand 10 1/4" thick 8" x 8" plastic scintillation counters. These counters were pulse height analyzed. He are not going to discuss events coming from the two downstream iron targets, target II and target III. However, their effects on the main target events were in- cluded in the Monte Carlo simulations. We took also two sets of 150 GeV data with the 56.3 GeV configuration, one with positive muons and another with negative muons. Only one target was used, which was 77" long and consisted of 70" of iron, and 18 1/4" thick plastic scintillation counters. Heavy targets were used mainly because the beam in- tensity was low. The protons or neutrons in an iron or a carbon nucleus are not stationary, but the effects of their internal motion, usually called the fermi motion, scales. The uncertainty in v = -Efi9 due to this motion is about 14%. Another effect of using heavy targets is that of the wide angle bremsstrahlung, which is proportional to 22. In addi- tion, one has to worry about the energy loss and multiple scattering of the incoming and outgoing muons in the heavy targets. 39 2.5 The Iron Core Magnets Up to 8 toroidal iron core magnets, each 31" thick and 12" in ID and 68" in 00, were used in our experiment as the momentum analyzer and hadron filter. Their positions and field parameters were given in Tables 2.1 and 2.2. The reason that 3 out of the 8 magnets used for the 150 GeV running were not activated was given in Section 2.1. These magnets were well deguassed before the running. The momen- tum resolution of the apparatus, given in Tables 2.3 and 2.4, was dominated by multiple scattering in the magnets. As long as heavy targets were used in the experiment, "poor" momentum resolution was not a problem. Each magnet had 450 turns of conducting wire. The working current was 33 to 35 amperes. The radial dependence of the magnetic field is shown in Figure 2.7. Two methods of measuring the magnetic field were tried, and agreed to within 1%. ' The calibrations of the spectrometer were done by using a small but long toroidal iron core magnet (73" long, 2" in ID and 12" in 00) to deflect the muon beam into the spectrometer. The beam1ine settings and the position and current of the small magnet were changed systematically to cover a reasonable range of muon energy and illuminate different regions of the spectrometer. The results of the calibration runs will be given in the chapter on data analysis. 40 20 I I r I I I 0 Prediction from small toroid U Measured in magnet #7 19r- 18?- B(kG) 17- K5- |5 l l l l I l 0 5 l0 I5 20 25 30 35 r(inch) Figure 2.7 The Radial Dependence of the Magnetic Field 41 2.6 The Counters and Electronics In total we had 18 target counters, a11 pulse height analyzed. The other counters or counter banks are summarized in Table 2.6. The positions of the three trigger counter banks SA, SB, SC were given in Tables 2.1 and 2.2. Their active area is shown in Figure 2.8. Our trigger required a beam muon signal, 8, and a scattered muon signal, S-EV; i.e., T=B'S'8V. As shown in Figure 2.9, the beam muon signal was defined as 8 = 81'82'83‘C°HV, where C = C].CZ-C3 and HV = HV1+HV2. B], 82, 83 were three counters of 3%" diameter in Enclosure 104. 8104 = BI'BZ'B3 was the signal that a beam muon had come through the Enclosure 104 bending magnets. C1, C2, C3 were three counters 7%" in diameter used to define the active area of the three beam proportional chambers in the muon laboratory. Fast cables of velocity 0.97c were used to transmit the 8], 82, B3 and C1 signals to the discrimi- nators. The active area of HV1 (HV2 in Figure 2.1) was the same as SA, SB, and SC, and was shown in Figure 2.8. HV2 (HV.I in Figure 2.1) was a 15" by 15“ counter with a 7%" diameter hole. 8 counter signals and C counter signals were clipped to 3 nsec at the inputs to the discriminators. The scattered muon signal was S'EV, where S = 5A“ SB'SC and 8V = BVI'BVZ. The spectrometer counter banks SA, 58, SC were mounted behind the magnets to avoid being hit mmaampe Ex.ex.N eo.m me mm m: mmaoumomoa Emma m: op exewxem mopm yo me (I 82, Emma .... 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On tn E 0.. .58. in: uwmoa Emmmwgh mah m.N mgzmwm 45 by hadronic and electromagnetic showers coming from the targets. The scattered muon was required to go through all the magnets to give a trigger. The beam veto counters BV1 (BV' in Figure 2.1) and 8V2 (8V in Figure 2.1) were 12" in diameter. They were shielded from the targets by some high density concrete cylinders plugged in the magnets, as shown in Figures 2.1 and 2.2. The efficiency of S was moni- tored by a small counter telescope (ca11ed Stel) consisting of three 10" by 10" scintillation counters. The deadtime caused by having 8V in the trigger had to be corrected in order to get the correct (effective) muon flux for the data. The HV and 8V signals were discriminated in the DC pass mode to eliminate discriminator deadtime. Some of the 56.3 GeV small angle data was taken without HV in the trig- ger. The trigger rate went up by a factor of 2 to 3 when it was removed. Yet nothing abnormal was found in the data. The 8V counter signals were latched, and the probability of vetoing a trigger by the associated hadron shower could be studied. In addition to the event trigger discussed above, we also triggered an a random coincidence of the beam signal and a pulse generator (pulser). This pulser trigger, B-P, accumulated an unbiased beam sample which was essential to the Monte Carlo simulation of the data. 46 The two beam hodoscopes HA and H8 did not partici- pate in the trigger. Their signals were latched for later use in the off line analysis. HA was at the downstream end of Enclosure 103, while H8 was at the downstream end of Enclosure 104. The four 3" by 8" scintillation counters of HA overlapped each other to give better resolution. There were two DCR's (Discriminator-Coincidence- Register) used to latch the counters. Each of them could accept 16 inputs to form one 16 bit word. The first DCR H8 word contained HA]_4, three unused bits, S PCS, tel’ 1-4’ 8V], 8V2, B'P, and B'S‘EV; where PCS was the PC strobe (defined as C‘ (SA + P)); and B'P and B'S'8V were the pulser trigger and the event trigger respectively. The second OCR word contained SA]_5, SB]_5, SC]_5 and B'P + B'S‘EV. They were monitored on line to ensure that the counters were working properly. Sixteen 24 bit CAMAC scalers were included in the 'system as listed in Table 2.7. Some of the scaler ratios monitored on line are given in Table 2.8. 2.7 The Proportional Chamber System We put one proportional chamber, called PCl, up- stream of the Enclosure 104 bending magnets to record the y coordinate of the beam muon there (In our system y was positive on the east side and negative onthe west side, 47 Table 2.7 The Scalers Scaler Gate Meaning SPILL Spill no. of spills SEM event proton flux 8 spill muon flux (in the spill gate) 8 event muon flux (in the event gate) B-S EV spill no. of event triggers(spg) B-S-EV event no. of event triggers(evg) 8.P event no. of pulser triggers PCS event proportional chamber strobe B-8V event beam monitor B-EVéa)(b) event muon flux (8V dead time corrected) 3'5 eve"t 3232;! Séiigifltfi‘afifiigc‘" B 5 To”) 5“” 42:23.4 328332422346"- S event no. of halo muons going into the spectrometer 8104 spill muon flux in enclosure 104 3104-3104d(b) spill spill monitor (a)There were two independent B-8Vd signals and tWO B-B'Vd scalers. (b)"d" means"delayed by 60 ns (3 RF buckets)". 48 Empmzm mam mo mEEm mmmu mamm\m>mm EEEmE-mm <4 EEEom-oe EEEmoE-mm mo m.am man; >mu omp mcwcmmz ovumm mcEEEO mmeomwcoz mowmmm EmEmmm mam mo mEom m.m mpamh 49 while the z axis was along the beam direction). This chamber, if properly aligned with the three beam propor- tional chambers (PC2, PC3 and PC4) in the muon laboratory, would give us the energy of the beam muon. The most up- stream beam proportional chamber in the muon laboratory, PC2, consisted of two modules, measuring x and y respec- tively. The sensitive area was 7%" by 7%". The other two each consisted of three modules to remove ambiguities in reconstructing more than one beam track. The three modules of PC3 were oriented to give x, -bx + ay, -bx - ay, res- pectively, where a = /372, b = 1/2. In other words, they were making angles of 120 degrees with each other. The three modules of PC4 gave -y, by + ax, by - ax, respectively. A 12" by 12" uv proportional chamber and a 15" by 15" xy proportional chamber were used as hadron chambers just downstream of the main target (from the main target on, 1 1 u=5iy+X).v=/E(y-x)). Signals from each proportional chamber wire were amplified at the chamber and then transmitted to a latch system by ribbon cables. The proportional chamber strobe signal defined in Section 2.6 was required to latch all the proportional chamber signals. The proportional chamber system was gated off when the spark chambers were triggered. In Figure 2.10 we show the cross sectional view of a proportional chamber module. The two high voltage planes 50 6 mil Kapton film/ 1/32' thick polished copper strip tungsten wire (2 mm saci a) 3 mil Al foil HV plane L--‘—_.‘flb '97)" guard fi'hdfiEZEEZZEEZZfiEZZfi' \\\\\\\\\\\/\\\ 2““ S 0 ' d e r W” I 20,11 gold-plak 4... .. \\ \ // \\\\\\\\\\\\\\\\\\\\\\\\\\\ ///////////////////// \\\\\\\\\\\\\\\\\\\\\\\\\\\\\ :Sfifl“flflflfl“flfl“flflflfl“flflflh pr rinted \\\(\‘\’/\\\\\ \\\\\\\\ /'////’ ”)1” circuit L\\\\\\\\\\\\\\\\\\\\\\\ board Ill/ll,” I’Il’ w.\\\\\\\\\\\/\\\l\’\ll\\\\\/\\/\\\ ‘.l VII/ll A\\\\\\\\ \\\\\\ \\\\\\\\\\\\\\\\ ’///////////////l////\ \\\\\\\\\\\\ "' ”W \ \\ ‘\\\\\\\\\ l/l6u G-IO Figure 2.10 The Cross Sectional View of a Proportional Chamber Module 51 are separated from the signal plane by k". Approximately 50 gram weight of tension was applied to the wires. The so-called magic gas (66% argon, 34% isobuthane and 0.16% freon-Bl) was used. Typical working voltage was -5 KV. The amplifier and discriminator, and the latch and readout, are shown in Figure 2.11 and Figure 2.12 respectively. 2.8 The Spark Chamber System There were nine spark chambers in the system. Each one consisted of two planes, measuring x,y and u,v respec- tively, where u = —l (y+x) and v = —1 (y-x). The uv planes were necessary to :Emove ambiguities when two or more sparks were found in the xy planes. Also, chambers consis- ting of two planes are more efficient than chambers of only one plane. Figures 2.13 and 2.14 show how the spark chambers were made. The active region was 72" by 72". A dead region of 12" in diameter was created at the center of each of the spark chambers SC11-SC15 to get rid of beam tracks. The spark gap circuit used to fire the spark cham- bers is shown in Figure 2.15. A clearing field of +90 volts was constantly applied. The memory time was about 1 usec. The dead time of the system was found to be about 40 msec. 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For the spark chambers SC7, SC9, SCll, SCl3 and SClS sparks of x<0, y<0, u>0, v>0 were picked up and digitized first, while for the spark chambers 5C8, SClO, SC12 and SCl4 sparks of x>0, y>0, u<0, v<0 were picked up and digitized first. The spark chambers were filled with a gas mixture composed of 80% neon, 17% helium and 3% argon. Five percent of the gas mixture was flowed over some isopropyl alcohol maintained at 90°F before going to the chambers. The alco- hol was added to limit spark currents, thus improving the multiple track efficiency of the system. An LBL recircula- tor was used to purify and recirculate the gas mixture at a rate of about 2 cubic feet/hour/chamber. 2.9 The Online Computer All the information that we planned to use offline were digitized and registered in some CAMAC modules. The online computer, a PDP-ll/ZO, then read in this digitized information via a branch driver BDOll. It wrote the infor- mation out onto a magnetic tape after the spill gate went off. The tape written was called a primary tape. The tape format is presented in Table 2.9. 58 meansmgu scaam any to» “wauewu emwew_as< as» m_.m «gamed “2:6 sz. .oBEEtomB 055: o... 1N dm_ H" mm he mma «woes: : uztepe m a h m e. + >0mm1_ vaz_ m k mu Nmu N m It dam_;u .III+AIIIIz$III¢ .3mz. xmn _Ku mm xmh mm «:3 Oman. yo 9:2 OON 52630:. 59 mgmasmgu xcmam mg» com pwzogwu Lopmcvswgumwo one N_.N meamwa .m...1_0>m.m+ OF mixo 00“ IFS, HC. :34 m V) {H _.O .252. kLOodI X0040 mwmomhm Owkdzfikmwh mm< wsané emqu xoqu uu Tr. emu» I» «a» >m_+ 2. >600. mo... >50? .4. I/\/l .. m m... 0 .. O J n.o.lo ma a> Emacs mm. _.OH . .>E On I OJOImmmIkW . u. H ogmfiu|-uuun--unuiu-d oQQLd ._:»<1 l.4 _ TL .. . M _ 00. I O. 4% _ «v. 1. a an a _ . “v rill. 00 m. \f OOTH xw... .000 n. . u" _ \ H_.O r f imwvl xn r... 35-. ........ / $.26 in .W N H u H 35.... e w l- .3 ..... .3. mm m 0+ ulO mm‘ 1 f 0n w 60 empmam gmNPpwmwa me_H mch wF.N mgsmwm ~3ac_ .3 .203 .o .5 zoom .2 8% 5656:36 o o w...» 208 . Em nco; 60: .0505 m, L . . r um 2:88 0269: Son 0 .o v: _o:cou mmc: 2:3 3:: now. co:o~_co._cuc>m 3323 3328 uoEoo _ uoEwu mxuoB ~12 ON *_ v_uw~:u _ F 3% b L“ :5me 2 uco H :E: H m fl Emi :60m 5 _ _ _au :3 7% an 61 Tab1e 2.9 The Primary Tape Format Words Contents 1 - 15 ID words word #2 - run number word #3 — trigger number 16 - 47 16 24 bit sca1ers (2 words/sca1er) 48 - 49 2 DCR's (1atches of the counters) 50 - 53 4 TDC's (for SA, SB, SC) 54 - 55 not used 56 - 65 10 ADC's (pu1se heights of the main target counters) 66 - 39S spark chambers (8 sparks x 4 coordi- nates + 1 ID and overf1ow word) x 10 modu1es 396 - 643 proportiona1 chambers (16 wires/word) 644 - 661 8 ADC's (pu1se heights of the other target counters) 662 - 704 b1ank 16 bits/word, 704 words/trigger, 4 triggers/record 62 The computer had 16K 16 bit words of addressab1e memory space. A special disk operating system was devel- oped to maximize the use of this limited memory space. In addition to the tasks of data transfer, the com- puter also accumulated various histograms, plots and tables and calculated some ratios between the scalers, some of them were listed in Table 2.8. Another computer system, entirely developed and maintained by the Fermi National Accelerator Laboratory, was also important to the experiment. Through a terminal connected to this computer system one could read and change the beamline magnet settings easily. The TV cameras, beam- line flags and ionization chambers of this computer system helped one understand the beam1ine situations. 3. Data Analysis and Results Listed in Table 3.1 are the data samples that have been analyzed and the Monte Carlo simulations of these data samples generated on the CDC 6500 computer at M.S.U. Another two analyses exist, developed by the Cornell group and the Berkeley group (3.1-3.2). All three analyses used the same format for the secondary tape which we give in Table 3.2. Only integers were written on the tapes so that intercompari- sons between the analyses could be done without difficulty. even though they were developed and performed on different computer systems. Some of the 150 GeV small angle data were taken with the main target out of the beam and have been analyzed in exactly the same way as the normal 150 GeV small angle data. A comparison between these two data samples then gives the data data ratio carbon (fi—f—)/(iron+carbon)(M C ) as a function of q2 and m. In Figure 3.1 we show for each of the data samples the region where we have more than 10 events/AqZAw (after applying the cuts which will be described later), wiui qu = 4(GeV/c)2 and Am = 2. 63 64 .696 .ummgmu opus No man; mcwuapucpfimv .uao mm: Aug =va ummgmu :Nms mgufiuv vmuomggou aocmwoNNNNcw Noucaoo new consaso .mspu ummu >m .umpmgocmm mucm>m .u.z mg» vcm umepocm mumu on» Low mcose mo Longs: m>ppommwmfluv Numuzpocw No: mgmmmwsp compaav xpco mgmmmwgp ucm>wanv vmpomgsou New“ ummu NB?v m.m e.N Ne m.N N-:VNN o.m m._ Nm e.m N+1VN4 CNN 4N. ..ca< N N N _ mNN NNVN N awv moan cone LummNLN :oze . AGO—.v ADV .0..ka Anv 2 Amy z #:00 m mcopumpzswm opgou mucoz Nchu use mmpasmm moan mzh F.m,mpnmk 65 Table 3.2 The secondary tape format Words Contents 1 run no. x 105 + trigger no. 2 - 3 unused 4 ZMIN in 0.1 mm 5 unused 6 - 11 X measured at PC]_6 in 0.1 mm 12 - 20 X measured at SC7_15 in 0.1 mm 21 - 26 Y measured at PC]_6 in 0.1 mm 27 - 35 Y measured at SC7_15 in 0.1 mm 36 - 38 px, py and p2 in MeV 39 - 40 X and Y at Z=0 in 0.1 mm 41 - 43 p;, p; and p; in MeV 44 - 45 X' and Y' at Z=0 in 0.1 mm 45 x2 x 100 47 00F x 100 48 - 49 X fitted at PCS-6 in 0.1 mm 50 - 58 X fitted at SC7_15 in 0.1 mm 59 - 60 v fitted at PC5_6 in 0.1 mm 61 - 69 Y fitted at SC7_15 in 0.1 mm 60 bits/word 90 words/event 10 events/record 66 Table 3.2 (Cont'd.) Words Contents 70 full fit ZMIN in 0.1 mm 71 full fit XMIN in 0.1 mm 72 full fit YMIN in 0.1 mm 73 full fit E'in MeV 74 full fit 0 in 0.01 m 75 full fit x2 x 100 76 - 77 no. of fired wires found in PCS-6 and no. of sparks found in SC7_15 78 coordinates of PC2_6 and SC7_15 contri- buting to the beam track and the scattered muon track 79 no. of tracks found in the spectrometer 80 no. of beam tracks found 81 DCR] + DCR2 x 2‘6 82 - 83 ADC's 84 TDC's 85 B-EVd (event gated) 86 8 (event gated) 87 8104 (spill gated) 88 3‘04'B‘O4a (spill gated) 89 event trigger + pulser trigger x 220 + spill no. x 240 90 5 (event gated) 67 (A) é Nevent 4o-fl ‘ 2 >|O /) Aq Aoo ISO GeV doto 30‘ 8 OCT. LA Z OCT. SA 20— 2 Ag =4(GeV/c)2 Aw = 2 10- O— l l l o 20 4o 60 80 (12(GeV/c)2 Figure 3.1(a) The kinematic region covered by the experiment 68 (B) 40- A 90 of; A IO— '9 '02? V‘F‘N‘ 9910 .1920? 'I .6 Nevent quAoo >|O o o ‘Eh, 'II ‘2 ‘% VV (g; 9 Al V' o 99 db l V . A qu =4(GeV/c)2 Aw = 2 56.3 GeV data 8 APR, LA [Z] APR, SA C) Figure 3.1(b) T 20 ‘40 l l 6C) q2 (GeV/c)2 the experi The kinematic region covered by ment 80 4O 69 (C) Neven./Aq2Aa>>Io * 150 GeV LT doto E “4- 121 L17 qu = 4 (GeV/C)2 AQJ==2 p. 1 l J O 20 4O 60 q?‘ (GeV/C)2 Figure 3.1(c) The kinematic region covered by the experiment 80 5C) 255 70 _ W2=M2+q2(oo-l) KM: I40 (Gev)2 W2=AIOO (GeV)2 w2= so (GeV)2 W2= 20 (GeV)2 ‘ a ‘- l l l 20 40 so (1‘2 (GeV/c)2 Figure 3.1(d) 8C) 71 In addition to those listed in Table 3.1, auxiliary data were taken and have been analyzed to align the propor- tional chambers and the spark chambers, to calibrate the spectrometer and to measure the energy loss of muons in iron at several muon energies. 3.1 The Reconstruction Program Shown in Figure 3.2 is a picture of one long target event successfully reconstructed by the reconstruction pro- gram which consists of a track hunting part called VOREP and a track fitting part called FINAL. In front of the target are the two downstream beam proportional chambers. Another beam proportional chamber was too far upstream to be shown in the picture. On top of the target are the pulse heights of the target counters, properly normalized with respect to each other. The ADC's used to digitize the target counter outputs were 256 channel ACD's which overflowed when there were 4 to 6 particles or more. Downstream of the target are the nine spark chambers as well as the spark positions measured at each spark chamber in each view. One can easily identify, besides the scattered muon track coming out of the target, two halo tracks. Also shown in the picture is a table for the trigger counter banks SA, SB and SC, which, as mentioned before, consist of five parts numbered from top to bottom. SAl, pcm>m pmmgmu mcop a mo mgauowa och N.m mesmwu 5.3. 3:. 3... on... 3.». 8'1”. 324.73.“.“5 I-omruu I... In. 6.». ll. 8.... 62%. 32.. . at»: 5.}: . .4 a m I H .11: a . I). In! I... I... .1" II. I... (L 5.... I... I... 8.... 8.81. 88.. 8.0.. 3!... o o _ o a un n . .. q u a . .q u o o . c o—cn : o . o a on . __ . . _ . w _. o o _ o a an n .. . . _ _ . ._ w m u w m_um r q . n N a. . . \ «1. a N aj . ._ _ _ _ . _ ._ a . u N .r N r _ _ . _. a I an I u u. n N .. _ _ . _ _ _. a . . u u . . . . . N _ : u n . a I I . . . . _ ._. . Wm .. ... _ __._. u. _ ._ _ . _ _ J “N. u - .. III I I, I I I . . _ _ _ _ _ _ on. u _. k .u . _ . _ a . _ : m... I I I mm u m _ _ q . a .. .n... r . .m. . . u . n r a.» _ _ _ . _ _ _ __ a nu . ”u . . _ . _ _ . _ : n _ . . _ _ _ _ : a a m a. . r c a a; . . u . . . _ _ _ _ : . . A I. o I I I I . I . . _ _ _ _ _ __ r H H n a H _ _ __ F . m.xa-> toe. cuxu.> I ._ . wrung» zaum No «Nuts: m_u¢ N text cu:u_> a _ _ . . _ m... J: 3a .3632... WIN 313$ 43.3 a _ . _ . . . . : .szw.Avg—mmqumhmowwwcaflco _ 1 z _ zo_2am.c. z N ore or “a . a: a ohmifio I. mow H m r. I i“ we 23% . .35.: z. .33 5:28:28 52:: o. .3 if". .- . mom“ 1 ”moo—m: .. :m 23¢ . Incl. I 5’: . . r . . .V. .,' oodnnfiunnrofl- on no! w I r . _. _ . . . Z . I .2 _ p ._: m I. . . ._: . I I. _._ ..: 1.. I. ...H ._: In. I - .IIII I" III I I .II I f. _ . .F: Am I. _ _ .... u. - .u ..... .. .. F... . . . __ _ . _ . . ._ Mn _ .. _ . _ _ . .r I I I = H I I I M- ... _ . _.:. E an I. q . ._: an n . . a “I: p r r... .- _.. . . ...: a a o .I _ _ __: a I. _ _ ._: . a o .. s a o - o I. _ _ ._: a I. . . _.: a m~xa 3 :01. Ouxu_> I w.u¢ w tax. only—I I _ - wrua a» name to «No: a: . . . . mxuc :— ccuo no gonna: I. _ _ _ .: 43.8.2. E: 2.22: 3.3 a I. . . . _: .2492. on: 2.22: 28 a .mwzuz 2: 44¢ _ zo_»¢¢30_mz on ~uucC» 0204 4.:‘8 a ~muru2— l— 448. ¢o_»¢¢30~k IOU yucca» 0204 Aurtc & mom moo_mp.u fifim 23m wbm_ u m oo~mh n -m 23m 73 $81 and 501 are the ones on the top, whi1e 5A5, S85 and SC5 are the ones at the bottom. In the table, those parts which fired are assigned a "1", while those that were quiet, a "0". The reconstruction program first decoded the primary tape, then aligned the spark chambers and picked up the sparks forming a track view by view. Starting from the x view, the program picked up a spark, say XTS at SC15, and a spark X?4 at SC14, and calculated the slope defined as m m m9 .. 5.2113. 4X 215-214 e _ m the expected spark position at SC13 (213, 214 and Z15 were the chamber positions). Itane4x| was required to be less than 125 mrad for the 150 GeV data, and 204 mrad for the 56.3 GeV data. All the sparks found at 5013 were searched for that spark XT3 which minimized IAX13I = IXT3-X?3l. In cases that AX13 was inside a preset window, one had a three spark straight line downstream of the magnets. Otherwise one had only two sparks to define this straight line. What- ever the case, the program went ahead and picked up a spark, say XTZ, found at $612, and calculated the following: 74 = m .. _ x33 x14 ta"64x”14 233) , x -xm 83 12 tons = ——————— , 3x 283-212 Atane3x = tan63x-tan04X , _ m x32 ‘ X12 ‘ ta"93x(212'232) ’ tane = tane + Atane -:§g 2x 3x 3x ’ P33 xii x32 ' ta"92x(232'211) Figure 3.3 shows what these variables mean. P32 and PB3 were integers representing the bending power acting at the bending points 82 and 83 respectively. lAtan63x| was required to be less than 25 mrad/magnet for the 150 GeV data and 67 mrad/magnet for the 56.3 GeV data. Again, all the sparks found at 3011 were searched for that spark XT] which mini- mized IAxll' = IXTI-X?]l. A window cut was also applied. Whether or not this spark was included as a spark of the track, the program saved the sparks XTS, x?4, XT3 (if found within the window), xTz and x?] (if found within the window) as a candidate track. After trying all the sparks found at SC12, the pro- gram proceeded the other way around; it picked up a spark 75 EonoNq cowpozgpmcoumg on» :N com: mmpnm_gm> och m.m «Lamp; mm .Nu g 76 le found at sell and calculated the following: - (Z -Z )(l + Egg) + (Z -Z ) 82 11 P 83 82 ’ D— 83 tane = l [X -Xm + tane (Z -Z ) :82] 3x 0 33 11 4x 82 11 P33 ’ e .. x12 ' x33 ' ta"93x(233‘ziz)° After exhausting all the possibilities, first trying out all the XTZ'S and then all the XTl's for a fixed pair X?5 and XT4, the program repeated the whole procedure for the other possible pairs of X?5's and X?4's. Then the same procedure was followed starting with a spark found at SC14 and a spark found at SC13, and then, 5613 and 5015. Every new candidate track was compared to those already found. In cases where two candidate tracks were found to have more than one spark in common, the one con- sisting of fewer sparks was thrown away. After finishing up the x view, the search conti- nued on the y view, the u view and the v view in exactly the same way. In Figure 3.4 we mixed up the distributions x?-x§, YT-vfi, u?-u§ and v?-v$ into one distribution for the spark chambers SCi, i = 15, 14, 13, 12, 11 (in that order). Also shown in the figure are the distributions for spark chambers SCi, i = 10, 9, 8, 7 and proportional chambers P06 and PC5, which are shown together as one 77 "ml OISYIIIUIIIN 0‘ "I" Olin"?3 '00. l 338333:28%838838:2338;8888:88°° 00 )010' 1000. 0000‘000". OOCC‘OOG? O O ..... D 0 0 D 00. 0000’ 0000 o 3 900’ 0000. (WOO ' 00 n". 000 0 '000 O ooooooquM-mqmm cam-M00000 Nommmmovmummmmmg.NweNoNNNNNmNNNN ONNNNNNwmoNNoooOON .0IIIIUOIIOOII- .I ..... 00. ODNNOOOC- 1 n (4 O C C 7;); ICISO7JOUII 6.3%zill’!;7 3.626...“ 3. I‘ll}! 925.98%:63352531’ilfi {1"i‘il‘illz‘216‘il’666": 9. ill.- 3. .‘iiii:.“ 0i: giggiigfi o a o ..... o c c I o. o. o o oooooooooooooooooooooooooo iiflono-oocc-c Oils-Ii .qocuooooucoonn MO. I nuoo- olslfllwunw 05 «nu crux-.- 8888:888338888:8%88:3888:88883888o.ooo 8$ 318333:8828388331838833888:88 O 0 ............ 000" n n 0003 a 00800 08000800800000: wvvmmvmgmmmmmmommgmoowwwmmm n .. oodmmawmwwo in not-IO-nIo-o :0 cocoon-.0000. on... an or. 00‘ 0.0000. 1000‘ )00950000' 0001'. 0000‘!” §000. OOOO‘DOOO. m 10.0000. "'100‘000". m‘OC‘OOOd .‘I‘izc’. L:§I.;‘! a. ’fi’l;}§’ 36.65,!!! OO?¢I‘|- IIUQixi: ‘8'".l "litiigg‘ 5-}.0” ~I§ih 6.7! 'igaiiii :iiiziiiii 69;! figfigiisi it 0'. IIQOI 00.0.0.0... CDC... CI... :0'.. If IIIIIIIIIII O... i. con-oooouonacoo The distributions (coordinate measured - coordinate expected) in cm for SC15 and SC14 Figure 3.4(a) 78 HINDU! OISIIIIUIIOI 0' 8'60! Culliti MO. I 883838888:888338888:888818888:888818888z888838888:88° .. ”Mn 0 000 000 no. 000 0010 0000 0000 .56. no 0000 0000 0 0000 a... I M 0000 0 M 00mm m 0 00n0 n . .... . 0000 n comm m M WW)? 1 IMOI 0 v on M O 0010 0 0000 O o no,” 1: W 0000 n OOOOn b 0 000000 0 0 000000 n l 00.... O ODOMDO L 00c (tn 0 0 0000000 0 0 0000000 0 . nmmodmmmm . 0 N No NwNoomoqumon .. n. w 0 00 N n . . NOOMDMOOMOWOOMMMOC 000000000M00W0M002 0000000003000 .II..I.‘IODOOOII ICIIIOCIIOUIII a... I. IIIII 0.. I... IhltifYQA! 9621060P7t.l’ C’Iugg7150201.01*; “CI... lzsg§§glgigaSIia Ola-3009.677” I I III :- outings-(‘6’iltlflulli non-I ll .h 21.0,. 0.00.0!000l0000000800:...000000'0600500000000 3§§§000080:0§i::i!i iii Sl‘izig :ir‘,zlr§’ bi h5hll‘J1‘t on?! I‘.’.’°I"h oo-uooooo-o-o-oocouooo‘oooo out... uuuuuu o nnnnnnnn ¥1§1CC.0-.ooo LIIII‘IIII‘IIE ouncuuuuu-uuuu— "noon Mu’lrunw of 5'14 -:m-qua‘— uo. I. 883333883:388818888:888° m m :88883888 Jhmwmmfvo 0000000000 0003000000) ............................... ntOfflOOCOCOOOC NOMMWOOOOOMMWOOOO DC or SOMOO OOOOOWMOUOJ .. .0...‘l.l 0......ICOI ‘0000 ; n G 20mm 0 £030.10! In... I5 27.11.3532. gt'ilil I. 590’2,I’1L7;I¥: 9' 1.3 .003ng first“ 3...!- h‘. II. I I.” uh I I. .179113"! POI-EVA. ’01-‘61.- f‘fligod. '10:..- 5'; Illa-III!!! 9 37553;).‘66‘. onto-lune... ooooooo Q‘thiitu-uo- no once-Ononnnoo-ooo-o The distributions (coordinate measured - coordinate expected) in cm for SC13 Figure 3.4(b) and SC12 79 HINDI OISYIIBUTXOI 0' SPARK CHINKQ NO. 0 IINMNUUH?“ IIIOIOID-o 0’ 0008: 3&8. 300- 1000.0 00"? 30'3808: :200 so ;§:g )0 finch“ 8080 n:33§0:033 0. 070 0:2 3.3». 33:13! 3000 §§E°§§°f°§33z3333: 333933333 3 0 33:33.3? 333: 3333:?3333333333333- 3333' 333°: ° v-F‘V‘tv‘hfl'l—NF- NN'WNWUUUU r r-- --1-rD-*ul he: ruu-‘vfll‘flr I'l- CHHHWNNNM * luoafl—Ner‘uP—t'v can" u—uvnewvv'r \PNoN-ONO’VVhti-O'NO‘U", emu-e Dana-Iarfliaoaua IP-Omuwwwuwa’OrJOOI-OO .u— o.goons-tooO...Ito-0....IOQIOOIOOOIOIOIDOOOW I ' Dr I “HHMNWW ufmma 11'! ztuil't" -;r "91:! fr.- t‘:f no. .1 II P. on Gillan-Ow nun-aw...“ “My... VIPu—nufl vo— .0" ‘O—udl‘OO-I uai o— ‘\l «9 Nu. I 4 - .-. I u 0%00 )9) on J In. 300 )x, no o°€°5~1'33‘§-uba£. m nn-mnn. Moo-noon. no moc.1ou;grg. compooomomo 03:3 000 00-0 :M OO((" I" r‘. :0'”:%:';% MW 80 88.08 n.norn'1r~cr.:8- on; IIIIIUIIOOII OIIOO-II-O-o-NNMIN'4U oo.oo-no.n....-ou.ocunoo...ou..noon-coco.a. 0° - O 00 000 33.393083881331330 '0000.0000'0000. 0 van»- —~—-mu 9 w-aa I awn—n— 90 . 9 000 cog 7""! qwouo-lcooogfll» ’a-u'lo-‘u—Oc-‘e‘a-Ou‘.’ w-I-‘M- I ”Wu". ‘0000 000‘ 880 n..— a%,,or‘otfl.owmw var t knit-wt“ “huh-no.1 Duo-4'89 a ‘muono- r" g :3 C. O r- '.:L: 033‘) .a a n .J 'J 83 ooeeoaoaouaqaaaaaonooa saccoanaaooaaoaaonfi 169 30906 a a“ neon awaaoaouacoaooaaaao 6.: 30909999 .3.) .Iauea auauao a aecooemaaoaaooaoanaeoaooaao aaoeoaaun oaooacnoaac D. F ' IWU'J'MNNw-O—F Figure 3.4(c) The distributions (coordinate measured - coordinate expected) in cm for SCI] and SC10 80 IIUOI DISIEIMHIOI 0' I'll! cllfl‘!!! “O- ’ OH .0. I‘ll-I mu—nquV-n-v rum-mm "an. ‘ CPR-v- 3"”, Near a» {wuflouom-w” aru—o—uumam I"! II. “VI- “ ”CG-FII-‘b- l' “I“ r-uauwwu- M. m“*." k a O o O O C 1 a D F) 0 P J 3 § 0‘ 3838: 3333:3833: 8838:3830.oooo~oooc.ooou- once. 00 O ummumnommm ea-m. ”omens-eoaoooummmuumumm unoc- MH 2 ulna 'W sM-Ie (mu-=5: u). I '000 '0000 ‘0" loco-0.....ioi - ' . o 8%-. *WNfi—o uMWb-nw ~Wuwwuwuo—un‘o—uu ‘43 ‘0’70 . OOC'Ont '0’93.g00("0f(40. ‘0‘”) '0u}00.00f"\'00fl0.1nfi ‘0001.")n ‘ 000.3090'0’?’ f. ‘0’) 'JOOO. "00 f‘ 0.0000'0Im'..0000' )"00.(')(- “ 00. "on no nwl le‘l‘r mum: -- M "i.“‘fll‘a-Vk.‘ I' mun-W woo wnmuugowo ~03 .- n-Oflw-DNWNNP- Fra no “If”. 1 c 000 O O D o 3 a "'0010. 103 . §.§a§::ssagtszzz:szsg.s 33: 83828888:888838888z888828888:8°°°‘°°° ' 0.000POC00. HMO‘OO ‘ 0 " _ ' °'"°‘?¢828$: ”pug-pg..- 0 n o ooaooooo-o-oo-coa-o ”mmmwmouawouauuaamau Wmmonumao someone-O... mumomw‘xaauea ”can In-Jnaaeno" ’91-’.“°°1 Human-1" Durand-v.” Figure 3.4(d) The distributions (coordinate measured - coordinate expected) in cm for SC9 and 5C8 81 "'0' DISV'XWYIM 0' SDI" CM‘NI '00. I :8800.000°'0000 8888:3888 §5§88818888z888818888z88881 § ........ r 3100' ( 00000000 OOOOOOOOCO OHDOOOWOOQOC OCFCOOOO. OOCCOC PFCCFOO( OCCFOO gooooooooogooog 0000000000000000030 0 a u u ............................. 0§§60r000(0 09(06000 (a hull ran 0' o Roommoog CCWMHOAIVMM “wowgruroo n I I n.. gown 0°”va googoooowoooaogw room nan-nun nonouto- I qqqqqq 0.. I... ................ In i§tt02§ililr§hlzhisfllgl9t 95.!" i’izl'iso’Shlghsu‘iOIIOu‘G. uuuuu I II§I5!7.-;|Illtlifil l1 CIOIIIIIUOIIOOCOIOIQIJOOD. IIOIIIOIOIOI.O 00.5...I.III..O....I..OOIQI.1,501I 97’3IITI’IQIII 93$I"’QII979I‘§'OIII§’IIIT‘ .OIICOICOCIII00000 IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII ififitiii. . o o . ihbtb o...-....-.......c.o "If?" (.r '91:. .‘u. 0' "WW“ 3!?11 I '222338838:888818888:883838883:388838388:883818888:8888-oooo.oooo . find 00G «.101 08 ..a 0000 0.02 ))00 ”on: n... 0000 0000 h (lath 100) n -. 0?01 «10) nflflfi 1701 a... rrGflrn "ccso O f 00! 0 00.0030 .aI... .JP (OnLnC (0((OOOC OOOOODOHOO OCOOUOGHOGf uuuuuuuuuuuuuu a .000 00(0000 0080. 000000 00003000888 nflflnnr.0r~rniwa n “v“ “Jayson;anvIOlomgonOAIn.oaoO°0M a 51830 so ......................... u.u-.¢¢-a-..unouo a. lib«IIQ,.I’Q"t”l.‘ll.1l¢32"3‘9.‘LI‘!’I’§.‘II‘f.‘ ’I— I- I... nix-1.. 77'Qil”‘ ,1~,|x.l 0""...I". n... h’u‘ 0’ III-£5. i'fi DOI..9IUCC.I.°fl.I.0.IQDIIQUOOIQI.€I.........I..... O.‘CIIIIOB.I.....I.I.UIOC'.0...I........Il........ .,I°105I37.9099310.0.0110).9.l.fl.9.........§l’1.|. OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 00.0.0.0..0... :bhfigi‘i- .- o .0 i...‘ .ooo-ooo-u..-.ouoo.- The distributions (coordinate measured - coordinate expected) in cm for SC7 and PC6+PC5 Figure 3.4(a) 82 distribution (the last one). The window cuts for these ten distributions were 0.50, 0.25, 0.50, 1.25, 2.50, 1.75, 1.75, 1.25, 1.25 and 0.75 respective1y, a11 in cm. Every track found in one view was then coupled with a track found in another view and sparks were looked for in the other two views in the vicinity of the expected posi- tions. The resulting distributions, after applying the window cuts, are shown in Figure 3.5; again chamber no. 1 means SC15, whi1e view 1 means the x view here. If more than three sparks were found in the other two views, this pair of candidate tracks, together with the new1y found sparks was then saved as a matched track. For every matched track the program obtained R31: (XB1’YOBl’ZBl) and (tanelx, tanegy). By reconstructing the beam tracks and checking the target counter pulse heights the program also obtained Y severa1 possible interaction points R. = (X. int int’ int’ Zint)' The pair of beam track and matched track that gave the smal1est sin(Ae)/Atane? was then considered as the right pair, where . = - 2 . 7 $1n(Ae) /(tane]x-tane?x) + (taneIY-tane?y) , . ' = o "‘t" ta"91x (X31 Xint)/(ZBl Zint)’ I = O and tanelY (YBl Yint)/(zBl Zint)’ I‘- III'IIMIN 0' ’00! “In?! I "II I .‘I mum“ 9‘ ”I M. I "I I 83 QEQEWWWW Efi am a 0 gm ...... was ‘Mmmm wP‘;-‘ do. :lr-:. .— a. \..~::.. gfififlQuwnmmcmnm Egg. . o . ggg fi' ' .0100. a: 0.0 E85 pun 0 (.3 O I . “as . . on ‘83 . 1'10 :53 an; in” L1,. -4 ...- r 'e-v . rum - 'lI-t -.ul"" I I!" a IV:- 35'" u pro _«; 5 53‘. .3; a 2%: .. . s . «4:53 '«"..'..' J" .. . o...» s x ‘9 a, 5:58;?- W; - w c . .. “my .. sop-am-.. COM 4,.“ n~-~ n. .”2'.' u-s—w-c: -—~—-m.o:o~a «u».— § 5 § 2 g £3 33 518388 9% 233838 giggggggggg5gggggggggfgggggggggggigggggggggggggggg Hanan:nun-unna-'-"-"-"m-"m-"u- ..u';a-: ‘ unv- u! -. .mm- 11‘ stgv u. ‘“ Z rohn. v .-. rm.-uuon-nu—.~aa.wu woo-mom“ am QW" WM...1~-£:38 D -. on .. gag...".u-u....-.....u. on n. 'I The match distributions in cm for SC15 Figure 3.5(a) 84 .§§§§§§§%&Qw .3. 3333.333 mafia . o . efium too 50 c. meomp=n_eamwu goons use smumwavmwanmw WW: :3. z. 3% mm. . 1.. .. .L .1. ..-..v 3 7.7... . 3r. O O. . o n W“ . M. u on . r . _. a. . .. C X. a. an O ~00”.10II”W " M. a I. N. f n um 3.38 9.... on $3er E . mg. a m. . ecr ”Ur..ou.r .os.wwmem a... mam u u WW. 2...“ .30 n 5.8.33.“ .u. .3" m moon . u.@ u .wmrcu w.» 2.3... .wwuu flaw. wwo. .:. u . o. ”33 twin. .. :owk .12: .82.?2...? . man. as.“ C(PPLOC‘ .- "Mmawwufltfl onlcuwnn‘al In" w .u. .co umumWom.o «a . . n no. a” m a»... .. u 5.83. w" w W u....-....-.c....-.a.- gm... p Is: ~ 9:50!» '3‘ us tog—lam. II. 333333333wm :COSUQSM rgy Anvm.m 3333.; on urge-v9»: 7.4.: o . 15.1%.” 3i§§%§§%fiflwfi..w K'E'E’znw - a aw...“ “I go... a "a 1 3p, L-tmmh-iA-a. 3...... a un..................-- 3:32,»; 0 . a-.. .5 . - . ........-.- .- —-.¢§~c. .10-u-.. Aid u-u....u-.......o.-.--.u-.u....~.u..-...-....... ne:.- when a . 3"...- r f t 3;... a-.. myhm~ n- .n..-- -. In... :u-ul'oO-oc '0 *u...o..-. c IQIIII .0...DIQOOIo-IoouQuantum-Inluoulu - la: n I.".v 3‘ .- Dinni=tt=o l‘. m_um .03 so =3 3:033:3333333 33335 3:3 51”.»... 1 "35m. expo. . . 2?: W18. Efrunw .e .. 1....333333333333mmammemwmu £33m . Emmwimm .. 05.: )Iool. 2 3.2.x...“ .33. 3333....flammmmgmmflmm.. m4» 85 .3 3 . . 33.1.. .3. .3." 13333333333333$me3 ...1..3..§3..333§33.33333333.333 .133. M3 .3333 m “M 33m 3 15.0-10-nooulo-oooculoo-Iloco-llIn-oooloIOOIolO-uo r .5: - 5:33.30 3.; .c roupacunuu‘ l.l. Auvm.m mgzmwm 38.32.. or. _. x... «mm». .3 «oi... 2..me kr-nc am 1..- CW «mack n.. 91.3“. {km v 13¢~ - ul- livv n _ 3333 3...... .‘I Ox'V'JNI'II‘ 3' ’“ll CIIC‘" l III- I "'3' U'I'IIIUHII c! 5'!“ 8"“! I I!!! I mg“..- fifigéfigxmmmemwm 53;; ME 3 3383833” 0‘, .99 - in sg'éix‘iéin .11-o1.-o1....1o.1111....1 4 u-uzc. .m- o o o o o o o o o . o o o o n o o o o c o o o o o u 33% axmnm wukfiws “i“ 0 '0888100 2°°8 11°: .03 I . 0000- a . 000 :o 18138 . on :0 go 8- 1113 M.ao«o-oono.nm¢-a fl 3 ' 1 . 9’1 86 ma—uogotgm-auuoum- Mo smug-u 3-.~n—u.‘w~:.. 1 mum-wu-wovmu 1.- .- s .u.-~Jm o.- mu ‘m moans-Wm“ nan-o... 4 "an... no I 1. 3 1 n r 1 1. a r v n 1 4 r- momma-u $313311 90 L; .3 £3? .3 33.1 1(1' 3 4’33; . Ian "c “‘0" ”50.0300‘1 'fl:.. n-wrc‘ 8 n “an" . C 1'10111'4’ 1:0” ”E '3‘“ on ‘1 8" 1-o...-.........1-n..11no 3’4 .030 on; .11..” m—w to. mocca- . 41-11-19-113 ~—... 11:? . 1. nncu "1.1.3— .0 :onol: 1 :gwuo-a con—:m 8800.006 1 1 35.11188 fifi mmmuomu- nc¢u a- “an..-" on“ rum. “M19153: “3"“ s . '3‘ 1 1 . . 1. r . ’ — ..-..... .-.11..1!u...—3-I..1~ .....--..1....:,. . “-1.. _ . J "Macaro-o. cocoon-n- buntu-m-I-wmm $501-$343.” am” .1 “AR“ "“ . I u i The match distributions in cm for SC12 Figure 3.5(d) 87 iéfifiéfififiwfiwmhfim ..............§m§§ Wmm s m u . 9 "5mm” ppum sow Eu cw mcowuznwgumwv :uuaE ugh . . n n . ... :— ... A m . w c. 3 of. .3: u for}. :3. K. . IM‘ h u S. heocmunmumw w I f O . .L». 3.3.. . I, 7 1.... .n ”-3.0 0.1390 — 0.2; . Mun-Sto- u :6 u . .: 3W». . 0.. a 52.9.0. M («.800 r n-quo. §??~e..uncr.ao Mn.“ \o. a $2.922: 3.5.... .30 u. &. . r 5.2:}. 9.12.9 .nv. and y . . Luann Ohm-recrunrco . v 0.0 onuso§c .5} Two. ..Z..reur.dm n ¢. . n .‘ ' p . u .n ”m. a 253. m. . fl rwummw $10.11.? r. . n . . .o . . 2. f: 5%.? ”T. . . Sb :2 uni: 635....9... . I“... : .mcoo.3 n. . wane-o o. . 6'»; ..m ”kayo“ n _ .73.“;09 . a .55: e .o. _ ode-L a. To. _ 060°- . . - - l:- r org-In :5 un 5.551.: I»:- 8.33.3355m3meH .mgmmmcwmmvwm unmenm.‘ 3.33.33.39.23. mgmmgfifim m Amvm.m mssmwm 06 c .000 .tor on Coon {an n .5. New ar—.. .7.....‘ chn~r _ P: v 3.3.5 luau P. mu" m...- o. «a.- -—~ .0 .- *L.-~'h‘.hl .n..---.uu-.u-un- v. .v-Iuo-nuo 1" 88 i.e., it was a measure of how well the two tracks matched each other, while Atane? was an estimate of the error of (tane?x, tan6?Y), roughly o a l a o _ 2 o _ 2 Atane1 p /(tan61x tan64x) + (tane1v tan64Y) Now the program could easily search for sparks at propor- tional chambers PCS and PC6 and spark chambers SC7, 5C8, SC9 and SClO along the straight line defined by the two points Rint and RBl' The distributions resulting from these searches are shown in Figure 3.4. Unfortunately, as shown in Figure 3.6, the efficiencies of these chambers, un- shielded from the target, were found to be strongly v- dependent, as one would have expected. It was decided not to include them in the momentum fitting procedure. Without these chambers it was almost impossible to tell the right beam track from the wrong ones, so only events with one and only one beam track were considered in this analysis. Starting from (x31, Y8], 231(fixed)), (tan9?x, tane?y) and a roughly estimated (E')°, a nonlinear least- square fitting procedure was followed to improve the five unknown quantities to minimize 2 _ 2 Z -l x - i j (Y )ij(5x16xj + an 6Yj), °/o ICXD 5C) 2C) IC) 89 Figure 3.6(a) The probability of finding N sparks out of the 6 hadron chambers as a function of PBACK (150 GeV LA data) 50 IOO ‘fiBflK3K‘(Se\/) "/0 H30 5C) 2C) 90 Figure 3.6(b) The hadron chamber efficiency as a function of PBACK (150 GeV LA data) féiy O HPC (5+6) 0 HSC 7 A HSC 8 O HSC 9 A HSC 10* *one of the two modules didn't work. 50 IOO PBACK (GeV) 9] _ m e u where 6X1 — Xi - Xi(xBl’YBl’ tanng’ tanely, E ), 5vi ='Y? - v§(xB], YB], tanelx, tanBlY, E'), 2 2 and Yij = ans 3 (Zi'ZM)(Zj'ZM) + Gijom with 6M5 = 0.l/E', the rms multiple scattering angle per magnet, and cm = 0.l cm, the spark chamber measurement error, i,J summed over the chambers, while M summed over the mag- nets. Using the magnet field parameters given in Tables 2.1 and 2.2, the program traced down the scattered muon through the spectrometer, taking into account the muon energy loss in the magnets, obtained (X?,Y?), i = ll, l2, l3, T4, 15 for every new set of X3], YBl’ ta"61X’ taneIY and E'. The momentum fitting part of the reconstruction program was first calibrated with ideal events generated by the Monte Carlo program with no multiple scattering in the magnets. The results of fitting events of the April calibration runs are given in Table 3.3 and Figure 3.7. 3.2 The Monte Carlo Program A Monte Carlo program was essential to correct the nonscaling effects mentioned earlier. It was also useful in estimating the systematic errors. 92 .Aumcmms meEm mg» to Emmgumaav Emma coas as» =_ Han mm: mac. =mo swagomaa cog? c< Auv .AHmcmmE p—msm on“ mo Emmgpmaav Emma cons msp :P pan mm: mcop =xpm Lmagomam cog? =< Any .vmpm>wuum appa; we: was Hmcmme Fpasm as» “my Aginmumuv .Lmumsoguuaam m5 of; 3.25 3.3.3 cone 2: "mm .203: mNN-E. .22... $3 $232: :25. m5 5 :3 3.35 can... 23 "am .338 umoozbmcoufi 2: new .335 2:58“. 2: "a? m— «.0 H 0.5m F.nm n.m m.oo~ mum mp «.0 H m.mm m.mm m.m w.oo— “avenm m— m.o H P.¢m m.mm m.m w.oop Auvmnm mp F.o H p.mm m.m~ N.m m.¢m onmnm up P.o H ¢.om m.om N.m m.¢m AQVan NF F.o H N.Pm n.9m N.m m.¢m onm up _.o H «.m— ¢.m— P.m m.- Amvmmm up P.o H n._m n.—m N.m m.¢m onmmm mp —.o H m.m¢ a.~¢ m.m N.o¢ mom up F.o H ~.Nm m.~m ¢.m m.mm cwm ARV Agave «A>mwvsm afi>muvmu «A>muvam «A>mwvnm =3: mega cougaanwpau ace m.m mpnmh 93 was; cowpmgnw_mu mu“xm u \ .ouofl oo.m% OO.M~ oo.n~ oo.wm no.WWi. on W. 00 W" nu.ml ou._ru w HM {H 11 Hi. #1. 4. ,u P, h w in . 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S / t w , 4. :1 3.1 ,w ll . o . .Lahrr. m .u o w o v. xv m~ u «roam m hu.« wt."m u mnnym u M .hwhxnuu Bzmmm .HMZOQz 4 .w> wkzw>m onwqmqucu ugh Anvn.m mgzmwm unuxm m x .002“ oouun no.9“ nu..~ -rllu . r n u } (3‘ O 90. oqmn L '1 I ,'- v Ill I }.+,/’Fi' x m.n~ ou.«mu.nv quokm Uz_mu m 1H .»_uzuum ngmm m \ .OQQH .kmzwmz 44¢xm xpwz mum 22w 00.6— n?“— ‘H .m> wwzm>m onmemHqu ”if OO‘Gll OO'Ltl (".1 f.‘ .-....- o'“.-—-q' '—_.-._. .-.— LO'hLE JHJAJ J0 Uthnn CD' It]. I‘ U -‘r--'—-- ’“v -—- "TT_“" 7' (OWNS OO'OID 00'069 —_ 95 Nm.m~ mo.«mm.un n aco~m u mxmmg m .h~uxumm mszm .pmzou: m \ .000“ 44¢xw rpm: was; cowumcnmeo Ohm 02¢ mmw lllll f" U in f' v v, on 009 nu~ozc on-o§z OO‘OUI oo-o ' '-- OO'OVO. 00.055 00-056 00-021 SJNJA3 J0 MJUUHN Auvn.m «gamma u».mm u \ muon n- u. .. .q nu.u. n. m nn.un wn.mu no .~ nc nu nu.wru mu ”0 4 tr ? It i lb m ..r, in: T l H - Irl \ . . x .O 4. «a anfi - .w . nan»: l.l-v.1 'rw . H .. rbl IHJ .0 , a .1 f ( ,. ~ r . z“ «m N v.b~ mo.« Nu.nm w m nwmu mmu axuuw urnmm u .h—kYuam . L. . ‘1 L 1.51 .4( mm mt L1] [L1 .w> wpzw>w 3 zomkmmmu4¢u Zo—ao—O :3 O: "-.u03.:1‘ \‘ SJNJAJ 30 UJSHHN OO'OOZ 00'002 OD'C.Z ———'———-.._—'-.—- .——-..'.— _.-_ _. , 00'O£€ was; comumgnvpmu mg» Anvu.m mgzmwm 96 9] 343A) .10 MMJXIN ”swam m \ .oous mnnma m \ .onn~ nu.n. nu.un np.~rn 09b“ no...“ “6.010 00.0». ou.n»~ oo.~>— 23:) “aim” coma Down 00;. n'nWob 1.0 4 w 4} LF H. in i m .Iil/ nil. , M \.\ am m“ w I44 ”0 .. .o \ .Irs . id .H m" . x W . .r mm “HWH \ m r} \ m .. t m /H M Ma / “fl. m H A m. A: .L m... (1 TH Hm I? a a 4 __ m / _ m 1C!!- \P v). / t .l k W . M [—7 . 0 /|1| .\ 0 IN! ru /3_ l.l! 7“ 4H . m IV \ m u .ruuquw. .. z_ mummomma mam / x: .x\ c . .Hlfi .u xn.o~ u qua.” rm w "n.0n“..m " m:_ma u w .h_u:uam m m \ .ooo“ .w> mpzu>w wamm m \ .ooow .m> wpzm>m quxm rpm: onhcmmfiqcu .hmzocz 44¢:w rem: zomhmmeqmu me 23m mhw 23m mcag cowpmgnwpmu 05H Amvm.m mgamwu 97 “Luca m \ .ono_ muuxa u \ .ooo” nnwmw an ”n u.wfi Ln.m« nova no.0 amt». oo.». a..n, on.m. ow.w. nH.m cow. osua can. on.» me 0 Nu: m . . T; . . ~ w Tulip _ llx‘ M 'Hl . m . I: Ir .. . .. _. .., m '15.! h .,. 0 _ \ _ o, o / H \. - k v” \. T _ mm x . , _ cw t _ ozlld'l. .‘ a” — - 3hr.» a Li . w... * , u xgu \ mm 1%: r ”7’ ms / Ir'l — 44' . 1m /. .. .V I C \ m4 / l - w s. ml \ c T/. 4 / .11». .u I _ R ..u ” uflfinifi m _ mmnmma mum .Irl u mio~m _ .m Nm.o~ u auo_w u u mumma u .ntl w po.« .m.em u unfit; u m .hmaxnuo .hhuxuao mrumm m \ .000" .w> mhzm>u uzumm u \ .oood .w> wpzm>w .FMZOm: ngxw IF“: onpammRJGU .kmzocz 44¢:w Ipuz zoukcmmuqcu chm 23m wbm 23m 00%? 00‘0 00'0! {I ' “9 ‘bnl 00'05 SANJAJ JO "Juan” . a C OO'OJI oo-olt 06°09! 98 ' The program first read in a beam track from a beam tape generated by the reconstructibn program. Then several random numbers were generated to determine where the inter- action should take place, how much energy loss and multiple scattering should the incident muon suffer before it really interacted, which direction and what absolute value of the Fermi momentum the responsible nucleon shoud have. After transferring the incident muon into the rest system of the nucleon concerned, random numbers were generated to deter- mine the scattering angle and the muon energy loss. Trans- ferring the scattered muon back into the laboratory system, the program traced it down through the rest of the target and the toroidal magnets. We didn't include single scattering tail in the multiple scattering calculations, which was justified for thicknesses exceeding about l0 radiation lengths. Fermi momenta were generated according to a simple Fermi gas mo- del? The radiative corrections were taken into account by an effective radiator approximation. This method agreed with the exact formula given by L. N. Mo and Y. S. Tsai (3.3). Only when E' < %E did the two calculations dis- agree by more than 3%. The physical processes giving rise to muon energy loss in the apparatus are: u-e * 2 Pz-P2 f(P) = P /[l+exp(_éi_k__ri)], with P1. = 260 MeV and kT = 8 MeV. 99 scattering, u-N interactions, muon bremstrahlung and pair production. The effects of their straggling were taken into account in the Monte Carlo program, except for the pair production process, for which the expression for straggling is not well known. In the Monte Carlo program vwz was taken to be _ l p n vw - A(va2 + vaz), 2 p— I3 I l2 .3 where vwz - y (l.0621-2.2594y +l0.5400y -lS.8277y .4 +6.793ly ) and vwg = vwg(i.0172-1.2605x'+o.7372x'2-o.3404x'3), 1 M2 with x' = —., w‘ = w+ ——, and y' = l- x'(3.4). R was w qZ M2 taken as 0.52 —§ (3.5). q We also included the effect of the wide angle brems- strahlung, which was found to be important for events at low E' (3.6). In Figure 3.8 we show the results of some systema- tic studies, using the Monte Carlo program. Events generated by the Monte Carlo program were fitted and then treated in exactly the same way as real data events. The Monte Carlo tape format was quite similar to that in Table 3.2. The true E' and the true a values 50 42 34 26 18 10 100 1.05 1.04 2 M.C.(R=O.52 fl.) q2 1.03 M.C.(R=O.l8) 1.03 1.02 1.04 1.01 1.01 1.00 1.00 1.00 1.00 1.00 0 8 16 24 32 92(GeV/C)2 Figure 3.8(a) Some systematic studies (l50 GeV large angle configuration) 50 42 34 26 18 10 101 1.07 1.07 14.0. (R = 0.00) M.C. (R = 0.l8) 1.06 1.05 1.03 1.05 1.01 1.02 1.01 1.00 1.00 1.00 1.00 0 16 24 32' q2(GeV/C)2 Figure 3.8(b) Some systematic studies (150 GeV large angle configuration) 102 50 0.61 42 0'54 M.C. (R + m) 34 M.C. (R = 0.l8) 0.68 26 0.74 l8 0.82 0.71 10 0.95 0.91 0.97 2 0.99 0.99 0.99 1.00 -5 . l 7 0 8 16 24 32 92(Gev7c)2 Figure 3.8(c) Some systematic studies (l50 GeV large angle configuration) 103 504 .67 i .23 42 .88 i .12 M.c. (l48.0 GeV) 34 M.c. (149.5 GeV) .13 i .08 2 .01 i .04 1 .05 i .02 l.20 i 0.l4 1 .03 2 .02 1.02 i 0.02 0.95 i 0.06 2 .93 4 .05 1.04 4 0.04 0.92 4 0.08 0.86 i 0.22 -00 16 24 32' 42(GeV/C)2 Figure 3.8(d) Some systematic studies (150 GeV large angle configuration) 50 42 34 26 18 10 104 1.14 i .39 0.72 i .l9 M.C. (B(r) 1% lower) M.C. (normal) 1.09 i .08 0.95 i .04 0.98 i .02 1.00 i 0.13 1.01 i .02 1.02 i 0.02 0.93 i 0.06 1.02 i .06 1.15 i 0.05 0.99 i 0.08 1.27 i 0.29 0 16 24 32' q2(GeV/c)2 Figure 3.8(e) Some systematic studies (150 GeV large angle configuration) 50 42 34 26 18 10 105 1.54 i .41 1.02 i .13 dE M.C. (3; l0% lower) 1'19 i '08 M.C. (normal) 0.97 i .04 0.98 i .02 1.04 i 0.13 0.96 i .02 1.01 i 0.02 1.07 i 0.06 1.09 i .06 1.14 i 0.05 0.91 i 0.08 1.13 i 0.27 0 l6 24 32 q2(GeV/C)2 Figure 3.8(f) Some systematic studies (l50 GeV large angle configuration) 50 42 34 26 18 10 106 0.89 0'91 M.C. (with no radiative corrections) M.C. (with radiative corrections) 0.92 0.94 0.97 0.95 1.00 0.99 1.00 1.01 1.00 1.02 1.00 0 16 24 32' (12(GeV/c)2 Figure 3.8(g) Some systematic studies (150 GeV large angle configuration) 107 written on these tapes were used to obtain the resolution tables given in the previous chapter. They'll be used to 2 estimate the true w or true N one will be concerned with later on. 3.3 The Standard Cuts and the Inefficiency Cuts In Table 3.4 we list the cuts which the data events and the Monte Carlo events were required to pass. The geo- metry cuts were applied to the reconstructed coordinates. They insured that the scattered muon was well inside the apparatus. The E' > 3E0 cut was necessary because at lower energy the track hunting part of the reconstruction program was becoming inefficient while the momentum fitting proce— dure was becoming inaccurate. Also, at lower 5', the ef- fects of the radiative corrections and the wide angle brems- strahlung become too big to be correctly taken care of in the Monte Carlo program. In Figure 3.9 are shown the target distributions of all the data samples, before applying the target cut. The halo triggers, which underflow the distributions, were re- moved simply by applying the target cut. After applying all these cuts, the data of each run were binned according to Figure 3.10 and the yield of each bin, defined as the number of events in the bin per 108 Table 3.4 The Standard Cuts (a) Beam l. rE104 < 6 cm 2. one and only one beam track 3. rbeam < 9 cm and abeam < 2 mrad at Z = 2target (a) .. .. Geometry l. Ixfit' > 8 or lYfitl > 8 at SCll, SCl2 and SCl3 2. lRfitI > 6%" at SCl4 and SClS 3. lRfitl < 33" at SCll, SClZ, SCl3, SCl4 and $015 Quality(a) l. Dmin < l0 cm 2. x2/DOF < 5 5'”) E' 33-60 6(b) LA: 6 > l5 mrad, SA: 6 > l0 mrad, LT: e > 30 mrad (b) q2 q2 > 1 (GeV/c)2 (a).(b) . Target LA. -400 cm < Zmin'ztarget < + 200 cm SA: -500 cm < Zmin'ztarget < + 250 cm LT: -500 cm < zmin‘ztarget < + 500 cm 109 Table 3.4 (Cont'd.) (a) (b) ”£104: beam radius at the downstream end of the Enclosure l04 bending magnets, xfit and Yfit: reconstructed coordinates ~07 +1!2 Rfit' fit fit’ 0 . : minimum distance between the beam track and m1n the scattered muon track, 2min: 2 coordinate where D = Dmin , Ztarget: center of the ma1n target. Given here are the numbers for the l50 GeV data, scaled for the 56.3 GeV data. 110 mco_p=nwcumwu 688288 6:8 Amvm.m mg:m_m :o_uagamwmcou <4 >oo m.om Em.PP se sm.~_ L .1 _ t 1.. . J n_ " up now Q .// # “mm \ RNF cowuocamvmcou «m 1 comuocammucoo 88 n.8m . >88 om, . _ _ .1 n _ --e_1- - 1: .1 _ w, 41. up um_ I, I we. umo \\ “pm \1 um. nun cowuugaawmcou <4 >mu omp 111 Figure 3.9(b) I 1 APRIL LT(u+) DATA 35:. 2 z rat—1H _.,I____J—LJ F 1 l APRIL LT(u-) DATA 16% r 1" .49. ,_1,,__J;—r' ___F,,_J_11. 4m 11.5m The target distributions 112 CARBON TARGET DATA 150 GeV SA CONFIGURATION LEAD TARGET DATA 150 GeV SA CONFIGURATION .._.r"—1-l J . 1- H Om 12.5m Figure 3.9(c) The target distributions 100 50 6(mr) 25 113 40 20 10 0 50 100 150 250 E'(GeV) .Y (-.+) (+.+) (’9') (+9‘) Figure 3.10 The binning system for the data stability checks 10 20 92(GeV/C)2 x 40 114 150 GeV Data 0/2 ¥ 1 ‘3" ' 7):)“1ii111w11”1+‘+7 “+14% "‘ 0/2 4%144‘14’9iwwfi 4+7, ‘1 4114,41)“ ' d (2) 0/2 .F”‘ (1) 1 _¢+’é+”++‘+'+$1fii¢¢‘+ 1+4 __ __++_+H+++ Runs 399-419 Runs 458-465 SA configuration LA configuration Figure 3.11(a) The data stability checks (F) (E) (D) (C) (B) (A) 0/2 0/2 0/2 0/2 0/2 115 150 GeV Data 1+ 1 —¢+_§§¢+4¢$$¢9.-;+_¢_3. .——., -—— — .— - -— — —— -_ —— .1 JLLAIWWJH... 37,311., ._ ____________ “1415M“ .3 _l+_+_++4 44,312+;I+_1_ ”$4444 _. J}... i 4 WMRWMW“ 3644i” Runs 399-419 SA configuration Runs 458-465 LA configuration Figure 3.11(b) The data stability checks 0/2 0/2 0/2 03*) l 116 150 GeV Data _+_3+J 9 ¢¢¢¢3 —++§l—++4++ 1’ 97991114) iri“ 99'9“ “9 ‘9 I MH+“+¢1+§¢ 1 1 49144) 41— 484199 fl,- -—< 1 "‘1 ’“1LM1ITMRMI 12+? "7 9519”“ “‘ Runs 399-419 Runs 458-465 SA configuration LA configuration Figure 3.11(c) The data stability checks (5) (4) (3) (2) (l) 117 56.3 GeV Data 1 ‘~ 4% 944999949” .—. .— 0/2 1 W .¢9¢"._¢‘1¢¢¢¢¢¢4’¢¢ -¢¢¢¢+ . 1 W459!!! W‘I’b‘tfqmaU‘D‘D—é 0/2 -¢§,4m09-4MNV9995Mw0494’46¢¢£§p -— 0/2 I. "19% m+i“’%'9¢m9’+ 1') 1+ _ 1 4.300 °W¢§owow°mooo~¢ 0/2 ”+9494 3%99‘1’“ 99.19 _ 1 WGGE ¢fl§+c¢wo¢m¢@—4’ ‘14 4941.9 859111191 (1149 A "7 Runs 581-601 SA configuration Runs 539-563 LA configuration Figure 3.11(d) The data stability checks (F) (E) (0) (C) (8) (A) 0/2 0/2 0/2 0/2 0/2 118 56.3 GeV Data 409“ qmo¢+0¢¢ooon®0j 319 51494944411919911+ M119 ' “1’9 99344;“;9‘1154 999M “’099 chew—16949996964 41-9117Vfl54339¢£$1246¢$ —4 - 8+ 3897*,4’91‘18999 343931 - 1 4 . "9‘9-6 W949¢9m¢86883 i 'fib ¢¢¢—-¢¢$¢¢990é0¢'¢¢ov¢ ‘- ‘Oomm 90¢¢¢oowommj 9999 fit¢ AHI -$4’7¥¢ 4L- %;4>42¢¢4#P .2 9 Figure 3.11(e) Runs 581-601 SA configuration Runs $39-$63 LA configuration The data stability checks 119 56.3 GeV Data 2 I- _ ' - ¢ ‘ ’ ) 1 "-669" wo¢§¢¢ftm999004 :9 M¢“¢°3¢9—9¢“9¢ 75691 0/2 ”'4 ‘ ‘0‘”96 18091992909909“? 4’" 89¢4¢93¢¢9¢°196 999% 7 0/2' . 9 - 0/2 9 4. j - . (‘1'.‘1'1 1 m‘NDQ ‘01) .90 11100" i - . ~ ¢¢_.Q _§¢ .9. .— 0 Runs 581-601 Runs 539-563 SA configuration LA configuration Figure 3.11(f) The data stability checks (6) 1 0/2 (5) 1 0/2 (4) 1 120 150 GeV Data ._.._. .9.i4u__ 4 ”4&1 9’ (1.594”?- '— . i4)? %.¢¢.¢+_. _ _ ‘2— _§+_¢.¢¢¢ _ .— ._... ._§¢.&r.qofl.og__ _ Figure 3.11(g) Runs+611-620 Ll(u ) configuration Runs 622-631 LT(p') configuration The data stability checks (E) 1 0/2 (C) 1 0/2 (8) 1 121 150 GeV Data _.+ JVIL __ _. 411+, “SUM— -_ 9 —- 4— —.49w —- - ... J¢9_ pgfioL .— _. I" 4&9!» _. __ ._“ _1#41¢. ¢r$‘94L¢‘t_. __ Figure 3.ll(h) Runs 611-620 LT(u+) configuration Runs 622-631 LT(u') configuration The data stability checks 122 150 GeV Data 2 (-.*I l ._. .__ __. -¢wp‘L9 __. .2 __ _i 143—3???) fitted to a constant Table 3.6 The 150 GeV ratios 40(150 GeV LT(p+)/LT(0'))= const. Variable exp (const.) C.L.(%) E' 0.97 i 0.04 49 0 0.97 i 0.04 83 q2 0.97 i 0.04 77 m 0.97 t 0.04 33 (E', e) 0.97 t 0.04 74 (92. 0) 0.97 H- 0.04 42 +40% +20% ~20! ~40% +40% +20% -20% -40% '127 EIGeV) 100 150 200 ‘ _ I 1 F_—_ 1 l 1 I l l ‘9 F-_- .1; I.) ..... _. ... _ F——— l _ J 25 50 75 100 0(mr) 11+(daéa) Figure 3.12(a) 128 92(GeV/C12 0 25 50 75 +401 I I l l (9 +20: 0.. 4 _1_ +_ __ T + , -201 -40: 1 , l 1 ....___ t l l l 1 +20: 0 __ _ +_ __ __ ____ ____. -...___ i 9 -40 l l l - o 10 20 30 (A) + data) Figure 3.12(b) M C ratios 129 3.4 The Results The measured and simulated E' and e distributions of the 150 and 56.3 GeV small angle configurations are given by Figure 3.13. data The carbon(fi—f—)/(carbon+iron)(data ) ratios, as a function of q2 and w, are shown in Figure 3.14. For each of the w bins we fitted the ratios to a constant. The results are given in Table 3.7 and Figure 3.15. We con- clude that within errors the agreement is good. The errors are large because of the poor statistics of the carbon data. It should be noted that the normal 150 GeV small angle data consist of 10% carbon events and 90% iron events. After renormalizing the 150 GeV small angle data and the 56.3 GeV large angle and small angle data relative to the 150 GeV large angle data according to Table 3.5, we combined the 150 GeV large angle and small angle data and the 56.3 GeV large angle and small angle data, scaled up the 56.3 GeV data as explained in the previous chapter and data obtained the 150 GeV (data)/56. 3 GeV (M ) ratio as a function of q2 and w. The results are given in Table 3.8 and Figure 3.16. We conclude that the two sets of data scale with each other within errors, even though some sys- tematic effect can be seen. To reduce our statistical errors, we also tried combining the data samples together and compared the 130 I50 GeV SA configuration SCH) 6CX) COUNTS (EUYDA) l SCH) l |5CK) 1 l 1 1 -I)— IOCK) COUNTS (M.C.) 1 5CX) l J 1.2 RATIO M (CVVDA) |_o AACL CL9 3g. , 444,— l l p—. 4245821“; it 5C) Figure 3.13(a) IOC) H50 15' (GeV) C) 2C) 4K) 9(mr) The measured and simulated E' and 6 distributions 1 (I 'I‘ II. A It. I'll l' '9? Illllllli (l.l ll) 131 56.3 GeV SA configuration 6000 1 1 1 1 4000—- —- 4 COUNTS (DATA) 2000-— —— a 6000 l i l i 4000—- __ _ COUNTS (MID 2000-— 4_ s 1.2 1 4. i i 1 1— —_ s RATIO ' ¢ (,3 0 i ¢¢¢ é M.C. 0.9r- —- ._ 0.8 1 l L L 15 4O 65 (1 4O 80 5' (GeV) mm Figure 3.13(b) and 0 distributions The measured and simulated E' carbon/(carbon + iron) 0/2‘ 0/2 0/2 132 1 1 I 1 1 1 1 1 (”true>=10.2 -—”—_ (“true>=45'9 I + (mtrue>=6.9 . __. ._s__. =27.6 ___ (”true>=5'7 .____. =26.6 .__ (”true> 4'7 GD __"__ =15.6 1 1 I 1 1 1 1 l 1 2 5 10 2O 50 l 2 5 10 20 q2(GeV/C)2 carbon(aaga) Figure 3.14 The 150 GeV ' ' data (carbon + iron)(M C ratios as a function of q2 ) 133 carbon(aaga) Table 3.7 The 150 GeV data ratios (carbon + iron)(M C ) fitted to a constant'* carbon _ in( carbon + iron 1 ‘ C°"5t- true exp (const.) C.L. (%) 4.65 1.08 i 0.18 69 5.70 1.04 i 0.23 91 6.90 1.21 i 0.25 69 10.23 0.88 i 0.24 54 15.61 0.84 i 0.19 24 26.60 0.88 i 0.24 79 27.55 1.70 i 0.51 64 45.88 1.15 i 0.28 89 A11 1.02 i 0.08 74 *The data samples and their Monte Carlo simulations were b1nned according to wrec’ the reconstructed w, and the mean value of the true waa of a particular bin was obtained from the Monte Carlo events. carbon/(carbon + iron) 134 2.0 I 0' 1.5,..— 1 . o 6 0.5‘ . —-- constant f1t L021 008 XZ/DOF=4.3/7 0.0 i l 0 25 50 (”true> Figure 3.15 The 150 GeV carbon(gaga) . data (carbon + 1r0")(M.C.) ratios as a function of w 135 (data) 150 GeV M.C. data 56.3 GEV(W) Table 3.8 The ratios fitted to a constant 2n(150 GeV/56.3 GeV) = const. Variable LA configuration SA configuration exp (const.) C.L.(%) exp (const.)i C.L.(%) E' 0.97 i 0.03 35 0.99 t 0.02 94 e 0.97 i 0.03 96 0.99 i 0.02 35 92 0.97 i 0.03 78 0.99 i 0.02 7 m 0.97 1 0.03 19 0.99 i 0.02 31 (E',e) 0.98 i 0.03 43 1.00 i 0.02 77 (qz, m) 0.98 e 0.03 34 1.00 i 0.02 20 £n(150 GeV/56.3 GeV) = const. (LA & SA) 6. m cm mo.pee .u.z ac> Aa.o>.m et>>_. Aauee. >68 cm. 398. .a :6. 8 $8. .m 3.... 2.». 8... 3.2.. 2...... 8.9. 8.2.. 8.8. 3...». 3.8.... n m m on On on com 09 oo_ 09 um _ _ _ _ _ q A uoumnbuuoo VS + .. + 888$ 11 him)..- 8.898888% 3 1 1 in. $00. ”mm 1 l 1 3mm. 00. AV 1&0 O._ m 1 40:0— .13 ii. :35— *1: it 1“ rc> |-<>—- if -<1c> .1). uouombguoo V'l 137 Aawau. >66 6.66 66.662 .6.2 6;> .6.6..m 6666.. .6666. >66 66. ~A>68~>> 3 «Ao\>mw. «a 8.05 3K3 5.0. 3.00. 8.03 .06: 3.va 8.0: 3.5 360.6%. com 09 0 cm on o_ ow ov ON 09 um _ _ _ _ q 1 a a 1+ 1 MW 1 No m. ._. as .efiopebafiwfil . + + 61. + +6816 3 mv : 6 .. .. 1.m._ $8.06... m 1 1 1 96209 fiv+ 1 r +1 % O Jeo m .. . . JKVOWOLFTW _ _ 1441111111. 30%? WW 6 Z 6.. l l 1 m _ U _ _ _ _ r. 18 '4 1 1 1 1 1 1 1 1 2 ~ + = 40.0 m_____%_um___. A |.2 "' (w'rue)= 19.3 10 to' ID - a-..) 1..-..- q . 0 I“ U. 3:: > 1.2 ”- (w'fue)= 9.2 O In DATA 138 i l 1 a x '1 1 1 1 1 l 1 l 0.6 1 1 1 l E=I5O l 2 5 10 20 50 100 (6-563110381 (0.751 (1.88) (3.751 (7.501 (18.751 137.501 q2(GeV/c)2 150 GeV (data) ' M.C. . Figure 3.16(c) The data ratTOs C 56.3 GeV (M. .) 139 resulting distributions to the corresponding Monte Carlo expectations. Both (q2,w) plane and (q2,w2) plane were studied, and the results are given in Tables 3.9 and 3.10 and Figures 3.17 and 3.18. Two groups of curves are shown in Figure 3.18. The solid curves are the expected contributions due to the diffractive 0 production process. According to J. Pumplin and N. Repko, one expects (taking CC = 80w 2 1 mb) 2 2 1+ data _ 1 + v"? [1 + 2 . X (3 ta021311 M.C - 12 2 9 vngAC [1 + 2 11++Vqu tan2(%)] SLAC where 0w; 0.00024q2 exp(2.5 t ) min + 0.00095q2 exp (75 tmin). . _ 1 2 2 w1th tmin - zu§-{ (q +mw )2 - [/(w2+M2+q2)2.4M2wz — 2 /(w2+M2-mw2)2-4M2N2] }, 2 2 4m q and R9 = g (1.21). (mw-q ) We also tried fitting the data to the form 2 2 1+02 2 2 O = 1 + alq exp[(a2+a3w )tmin][]+2—T—TL%—tan (7)] S 2 2 vwz LAC[] + 2 l:!_Lfl_ tan2(g)] 1+RSLAC 2 140 Table 3.9 The combined data/M.C. ratios, w bins* (a) wrec<4’ = 4.1 (b) 4 = 5.5 £nq2(GeV/c)2 DATA/M.C. £nq2(GeV/c)2 DATA/M.C. 0.2 1.00:0.06 0.2 1.02:0.10 0.6 1.06:0.04 0.6 1.06:0.06 1.0 1.05:0.04 1.0 1.01:0.04 1.4 1.08:0.03 1.4 1.06:0.04 1.8 1.03:0.03 1.8 1.11:0.04 2.2 1.03:0.04 2.2 1.1110.04 2.6 0.99:0.05 2.6 1.08:0.05 3.0 0.94:0.05 3.1 0.96:0.03 3.5 0.97:0.04 3.7 0.87:0.06 4.2 0.92:0.05 (c) 8 = 8.0 (d) 12 = 11. £nq2(GeV/c)2 DATA/M.C. £nq2(GeV/c)2 DATA/M.C. 0.2 0.98:0.09 0.2 0.98:0.09 0.6 1.17:0.06 0.6 1.15:0.06 1.0 1.17:0.05 1.0 1.14:0.05 1.4 1.12:0.04 1.4 1.13:0.05 1.8 1.15:0.05 1.9 1.14:0.07 2.3 1.18:0.06 2.5 1.14:0.06 2.9 1.08:0.05 141 Table 3.9 (Cont'd.) (e) 16 = 16.3 (f) 24 = 24. £nq2(GeV/c)2 DATA/M.C. 0nq2(GeV/c)2 DATA/M.C. 0.1 0.88:0.09 0.2 1.07:0.07 0.4 1.12:0.05 0.6 1.04:0.05 0.8 1.17:0.04 1.0 1.13i0.07 1.2 1.10:0.04 1.4 1.24:0.11 1.6 1.0660.07 1.9 1.2160.09 2.0 1.13:0.07 2.4 1.07i0.10 (g) 32 = .8 (h) 40 = 46.1 9nq2(6eV/c)2 DATA/M.C. 9n02(6eV/c)2 DATA/M.C. 0.2 1.03:0.07 0.2 1.0610.06 0.6 1.06:0.07 0.6 1.12:0.14 1.0 1.17:0.17 1.0 1.00:0.10 1.5 1.21:0.10 1.4 1.09:0.13 *The data samples and their Monte Carlo simulations were b1nned according to wrec’ the reconstructed w, and the mean value of the true w, (wtrue>’ of a partTcular bin was obtained from the Monte Carlo events. 142 Table 3.9 (Cont'd.) (a) an = const. (b) tnR = c+b inqz (wtrue> const. TC.L. c b C.L. 1%) (%L 4.1 0.02:0.01 13 0.09i0.03 -0.036i0.012 76 5.5 0.04:0.01 1 0.11:0.04 -0.035i0.016 2 8.0 0.13:0.02 49 0.14i0.04 -0.007i0.023 38 11.0 0.12i0.02 76 0.10:0.05 +0.018i0.032 68 16.3 0.1110.02 22 0.11:0.04 -0.001i0.034 14 24.5 0.10i0.03 28 0.01:0.05 +0.102i0.052 73 33.8 0.0910.04 44 -0.01i0.07 +0.130:0.081 95 46.1 0.06:0.04 100 0.06:0.07 -0.007:0.096 74 A11 6 31 (c) lnR = c'+b'q2 (wtrue> c' b' C.L.(%) 4.1 0.05:0.02 -0.0024i0.0008 81 5.5 0.09:0.02 -0.0051i0.0015 21 8.0 0.14:0.03 -D.0024i0.0033 43 11.0 0.11i0.04 -0.0021i0.0060 65 16.3 0.12:0.03 ~0.0027i0.0082 15 24.5 0.02:0.05 :0.0303i0.0160 68 33.8 -0.03i0.08 +0.0506i0.0315 95 46.1 0.06:0.09 —0.0015i0.0431 74 A11 67 143 Table 3.9 (Cont'd.) RnR = const., q2 2 4(GeV/c)2 “rec <“true’ exp (const.) C.L.(%) < 4 4.1 1.01 1 0.02 5 4 - 8 5.5 1.04 i 0.02 O 8 - 12 8.0 1.13 i 0.02 59 12 - 16 11.0 1.14 i 0.03 91 16 - 24 16.3 1.09 t 0.04 74 24 - 32 24.5 1.22 t 0.07 88 32 - 40 33.8 1.21 i 0.10 -- > 40 46.1 1.09 i 0.13 -- A11 1 144 6 5 l 1 1 + L.— 1 + 1 1 A ' .6 1 S V I O U 1 U Q 1 1 (”two > - 245 § 1 —O— __.O_. —i (a) “1.15 #— O.89— + N (“True > -16 3 Data/Monte Carlo (based on scaling in 111’) 5 1 l —O— 10 1 l l 1 l 1 1 1 1 8 1 1 1 1 J l l l -1--- . 2 5 1o 20 so 1oo q' (GeV/c)l —h— _ Figure 3.l7(a)-(d) The combined Saga a function of q ratios as and u) 145 12> ¢¢¢ ¢ (P (w"u.>-||.O 1.0— — - -- --1 (f) .2- + + <60an -8.0 +_ .4 + Tom — -— — .— — _— —. — A m1 DATA/MONTE CARLO (based on scaling in w ) 6 1 1 LO— 0- 1‘0' 1 -O- o- l O l l l l l I 1 1 ‘ 1 1 1 1 1 l 2 5 IO 20 50 100 q'(GeV/c1' Figure 3.17(e)-(h) The combined %131 5 ratios as a function of q and w 146 1an(5 c‘+ b'qz 111 r I 1 +0.2'- +OJ- ¢¢+ 1 ¢ 6 6___--_--%--_- ~01— —0.2L 1 L I 1 I 1 +008— +004— é bI (lOO--—‘fl2fiV3—¢-—‘—"—‘—-‘FL'—"-‘ —OD4~ -ODBP 1 l 1 I 25 50 (wlrue > Figure 3.17(i) The combined Saga ratios as a function of q2 and w 147 .6.6666.6 6.66 6..6666.. 6..6 .6.6666.6 6..6666.6 6.66 ...6666.. 6.66 .6.6666.6 6.66 6..6666.6 6.66 6..6666.. 6.6. 6..6666.6 6.66 66.6666.6 6.66 66.6666.. 6.6. 6..6666.. 6.6. 66.6666.6 6.66 66.6666.. 6.. 66.6666 . 6.6 66.66.6.6 6.6. 66.666... 6.6 66.6666.. 6.6 66.66.6.. 6.6 66.666... 6.. 66.66.6.. 6.. 66.6666.. 6.6 .6.z\<.<6 6.6\>66.66 .6.z\<.<6 6.o\>66.66 .6.z\<.<6 6.o\>66.66 ..66..66666>V.6666666>V66 .6. 6.66..6666636.6666666>V6 .6. ..6..66666636.6vo666> .6. 66.6 6 . 63 .66.666 .6.z\6666 666.6666 66. 6..6 6.66. 148 .um. .66:m>m 6.660 66:62 6;. 566. 666.6660 663 :.6 66.66.6666 6 .o .Amagusv .3 was» as. .o m=.6> 6665 6;. 6:6 .3 umpuzgumcoumg 6:6 3 o. 6:.660666 6666.6 6.63 6:0.um.=s.m 6.660 66:02 6.6;. 6:6 66.6566 6.66 66.6 .6.6666.. 6.6. 6..6666.. 6.66 66.66.6.. 6.6. 66.66.6.. 6.66 6..6666.. 6.6. .6.6666.. 6.66 66.666... 6... 6..6666.. 6.66 66.66.... 6.6. 66.666... 6.6 66.6666.6 6.66 .6.666... 6.6. 66.6666.. 6.6 66.6666.. 6.66 66.66.6.. 6.. 66.666... 6.6 66.6666.. 6.6. 66.66.... 6.6 .6.666... 6.6 66.666... 6.. 66.666... 6.6 6..6666.6 6.6 66.66.6.. 6.6 66.6666.. 6.. .6.z\<.66 6.6\>66.66 .6.z\<.<6 6.6\>66.66 .6.>\<.66 6.6\>66.66 ..66..66666636.6666>v.6. .6. 6.66.66666636..6.vo66636.6 .6. 6.66.66666636..6666663666 .6. ..6.6666. 6..6 6.66. 149 Table 3.10 (Cont'd.) (a)£nR = const. (b) lnR = e + dnnq2 true const. C.L.(%) e d C.L.(%) 18.1 0.03:0.02 14 0.07i0.03 -0.032i0.018 25 20.2 0.06:0.01 73 0.08i0.02 -0.024i0.018 89 35.1 0.10i0.01 82 0.13i0.02 -0.02110.015 94 58.6 0.11i0.02 37 0.09i0.03 +0.014i0.017 34 93.4 0.06i0.02 8 0.21i0.08 —0.061i0.031 21 154.1 0.12:0.02 31 0.16i0.09 -0.022i0.043 24 A11 25 50 (wirue> (c) £nR = e' + d'q2 e' d' C.L.(%) 18.1 0.06:0.02 -0.0039i0.0018 40 20.2 0.0710.02 -0.0043i0.0029 96 35.1 0.12:0.02 -0.0030i0.0021 96 58.6 0.11:0.02 -0.0009i0.0021 29 93.4 0.14:0.05 -0.0055:0.0025 30 154.1 0.17:0.06 -0.005910.0051 32 A11 67 150 Tab1e 3.10 (Cont'd.) 2 an = const., q2 3 4(GeV/c)2 rec exp (const.) C.L.(%) < 9 18.1 1.02 i 0.02 7 9 - 25 20.2 1.04 i 0.02 72 25 - 49 35.1 1.10 i 0.02 78 49 - 81 58.6 1.12 i 0.03 54 81 -121 93.4 1.05 i 0.03 4 >121 154.1 1.12 i 0.03 28 A11 40 151 Data /Monte Carlo (based on scaling in w') 08- ! l l l 0 25 50 75 q' (GOV/C )' Figure 3.18(a)-(c) The combined Saga ratios as a function of q2 and W2 152 1.0 .. 1.0“— Doto/Mont'e Corlo (based on scolmg in w') o 25 so 75 o’ (GeV/c)‘ Figure 3.18(d)-(f) The combined gig—‘3‘- ratios as a function of q2 and NZ 153 lnR|w2= e' +d'q2 M +02. + <> 6 i +0.1r- -O.2- 1’ “F db +oolo~ +o.oos - d' oooo-————~————§————~—--—-——w———4—4 1H + -0.0IO— I ICC 200 (W2 ,>(GeV)2 iruc Figure 3.18(g) The combined %3%3 ratios as a function of q2 and w2 154 and found that we could get a good fit only when we exclu- 2 ded the two highest W bins. The fit gave a1 = 0.040 i 0.011 , a2 = -5.19 i 1.32 , and a3 = 0.396 i 0.080 with a X2 = 28.0 for 27 degrees of freedom. This fit is shown in Figure 3.18 as dashed curves. Our major source of systematic error was the 1% uncertainty in the incident muon energy E0. In Table 3.11 we show the results of comparing a data sample of incident energy 0.99EO or 1.01Eo to a Monte Carlo simulation of in- cident energy E0. It is apparent that the effect(s) we see in the larger N2 bins is (are) not affected by changing EO by i1%. We also studied the effects of changing the para- meter R we needed in the Monte Carlo program. The results are given in Table 3.12. In Table 3.13 the estimated inefficiencies due to shower partic1e penetrations are given. These inefficien- cies are hard to estimate because there is no good way to determine how often the BV counters were hit by delta rays. Since these inefficiencies were biased against high v events, removing them should raise the effects instead of suppressing them. In Table 3.14 the latch probabilities are given. 155 -- 6... -- .6.6 6.66 -- 6... -- 66.6 6.66 66.. 66.. 66.. 66.6 6.6. 66.6 66.6 66.. 66.. 6.6 66.6 66.6 66.. 6... 6.6 66.6 66.6 66.. 6... 6.. 6.66 -- 66.. -- 66.6 6.66 -- 6... -- 66.6 6.66 66.. 6... 66.6 66.6 6.66 66.6 66.. .6.. 66.6 6.6. 66.6 66.6 66.. 66.. 6.6 66.6 66.6 66.. 6... 6.6 ..6. >6.16.66 >66 66. >66 6.66 666 66. 6666 66666.66 .6....66 .66v6z\.66 66.6.66: 6.66.66666 6.>66v 63 6.6.6.66666 66 6. 666 66 6666666 ...6 6.666 156 -- 66.6 -- .6.. 6.66 -- 66.6 -- 66.. 6.66 -- 66.6 -- 66.. 6.66 -- 66.6 -- 66.. 6.6. 66.6 66.6 66. 66.. 6.6. 66.6 66.6 66.. 66.. 6.6 66.6 66.6 66.. 66.. 6.6 66.6 66.6 66.. 66.. 6.6 66.6 66.6 66.. 66.. 6.. 6.66 -- 66.. -- 66.6 6.66 -- .6.. -- 66.6 6.66 -- 66.6 -- .6.. 6.6. 66.6 66.6 66.. 66.. 6.6. 66.6 66.6 66.. 66.. 6.6 66.6 66.6 66.. 6... 6.6 66.6 .6.6 66.. .... 6.. ..66 >66 6.66 >66 66. >66 6.66 >66 66. 6666 6.66>66.66 6.>666 6: .666666666 .6....66 .666666.66 66.66666 ..6.666. ...m 6.66. 157 6 666 63 6666666666666 666 666.66.66 66 666: 663 .66 .6.. 66 66 66.6 666 666 .66 6:6 66 .6.. 66 66 66.6 66 666666666 6663 6666>6 6.666 66662 66.6 -- 66.6 -- 66.. 6.6. -- 66.6 -- 66.. 6.6. -- 66.6 -- 66.. 6.6. -- 66.6 -- 66.. 6... -- 66.6 -- 66.. 6.6 -- 66.6 -- 66.. 6.6 -- 66.6 -- 66.. 6.6 -- 66.6 -- 66.. 6.6 -- 66.6 -- 66.. 6.6 ..66. -- 66.6 -- 66.. 6.66 -- 66.6 -- 66.. 6.66 -- 66.6 -- 66.. 6.66 -- 66.6 -- 66.. 6.6. -- 66.6 -- 66.. 6.6 -- 66.6 -- 66.. 6.6 6.66 m . m w . m > w m mm C > G omP > w M mm C > U om? NAU\>U@vNU A>mwv0=LH3 . 66666. 6 .6....66 . 66626. 6 66.66.66 6 6 ..6.:666 ...6 6.66. 158 -- 66.6 -- 66.. 6.66 -- 66.6 -- 66.. 6.66 -- 66.6 -- 66.. 6.6. 66.6 66.6 .6.. 66.. 6.6. 66.6 66.6 .6.. 66.. 6.6 .6.6 66.6 .6.. 66.. 6.6 66.6 66.6 66.. 66.. 6.. ..66 -- 66.6 -- 66.. 6.66 -- 66.6 -- 66.. 6.66 66. 66.6 66.. 66.. 6.6. 66.6 66.6 66.. 66.. 6.6 66.6 66.. 66.. 66.. 6.6 66.6 66.. .6.. 66.. 6.. 6.66 -- 66.6 -- 66.. 6.66 -- 66.6 -- 66.. 6.66 .6.6 66.6 66.. 66.. 6.66 66.6 66.6 66.. 66.. 6.6. 66.6 66.. 66.. 66.. 6.6 66.6 66.. 66.. 66.. 6.6 ..6. >66 6.66 >66 66. >66 6.66 >66 66. 6666 .6666: 66.666.6z\.e+666z .6666: 66.666.666.666666 6.6\>66666 6.>66v 63 6 666656666 666 66.66666 66 6666.66 N..m 6.66. 159 nu 00.0 nn .0.. 0.0. nn 0..0 nn .0.. 0.0. nn .m.0 nu .0.. 0.0. nn N..0 nn .0.. 0... nn 06.0 nn .0.. 0.0 nn 05.0 nn 00.. 0.0 nn 06.0 nn 00.. 0.0 nn 06.0 nn 00.. 0.6 nn 0..0 nn 00.. 0.0 ..60. nn 60.0 nu 00.. 0.00 nu 00.0 nn 00.. 0.00 nn 00.0 nn 00.. 0.00 nn 00.0 nn 00.. 0.0. nn 00.0 nu .0.. 0.. nn 60.0 nn 00.. 0.0 6.00 nn 00.0 nn 00.. 0.00 nn 60.0 nn 00.. 0.00 nu 00.0 nn 00.. 0.00 nu 00.0 nn 00.. 0.6. 60.0 60.0 00.. 00.. 0.0. 00.0 .0.0 00.. 00.. 0.0 N..0 .0.0 00.. 00.. 0.0 m..0 00.0 60.. 00.. 0.0 .0.0 00.0 00.. .0.. 0.. 0.00 >60 0.00 >60 000, >60 0.00 >60 00. 6:66 6.66>66066 6.>660 .6666: 66.6660666~6+606z .6666: 66.666.666.666062 6 ..6.66666 6..6 6.666 160 Nmn0 600. 60n. xmnm 0.0 0.0. 0.6. .660 N0n. mco.uwgp6c6q 663006 op 6:6 muc6>6 0:.mo. .0 »p_..amnogq umumewpmm vagupm. N>m 56.: um50pm_ _>m ;p_3 6 :. mpc6>6 mcwu=.. .0 xpwpwnmnogm Cd.“ COP 0EU\00 c. 066:366 0>m 6:6 .6.6 :. 0Eo\00 :. L6pcaou .>0 6;» 0:286; 6.3660 6:56:66 op 66; m6.u.ugwa L63ocm 6;» m.o.;6»ms 6o pczoe< <0 <0 >60 0.00 <0 <0 >60 00. mg6uczo0 >0 6:. m..m 6.06. 161 6.0m 6.6m «.mm 6.6m N.wm 6.6m m: - o.o ..o 0.0 o.o P.o c.o m.a o_ o.~ m.N 6.N m.~ m.m o.~ ~>m mp 6.6 ~.m 6.m m.m m.o_ m.6 PZ .. m.mm o.mm _.mm 6.6m “.mm m.wm mom m. m.¢ F.F m.o ~.o o.6 m.~ 6m: N_ N.om ~.mm m.m~ 6.m~ 6._m c.6m mm: .. m.~m ..me m.F6 6.~6 m.6m m.mm mm: o. 6.6m F.FN P.6 ~.¢ o.6~ 6.o~ Pm: m m.m 0.. 6.. m.m_ - - .mpm m - - - - - - - N - - - - - - - 6 - - - --- - - - m N... m... 6.6 m.m m.~ 6.~ «<1 6 “.mo o.m¢ o.m¢ m.om m.m¢ ..6. m06 n.6m >06 om. .60Mpc6ug6a 0. >...._....06n.o._0 2666.0 mp.a .000 6:. Am06_.m m_am. The DCR2 bits (1atch probability in percentage) Tab1e 3.14(b) 56.3 GeV 150 GeV LA SA Meaning LA SA LT(+) LT(-) Bit 162 OI—mF-QDMOLOONwF-OMQ'OLOOQ mLOd'PQ'VQ'OO‘VNmeMOONkO Nd”? 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Rev. _1Q, 3697 (1974). J. C. Pati and A. Salam, Phys. Rev. Letters 31, 661 (1973). J. C. Pati and A. Salam, Phys. Rev. 010, 275 (1974). J. C. Pati and A. Salam, Phys. Rev. 11, 1137 (1975).