THESIS Date This is to certify that the thesis entitled LEPTONICALLY PRODUCED MULTIMUON FINAL STATES IN MUON SCATTERING AT 270 GEV presented by Daniel Adams Bauer has been accepted towards fulfillment of the requirements for Ph-D- degree in PhYSTCS Kh/K’fiw/i/ Major professor U»/3~79 0-7639 #__—.- LIBRARY Wu State University —-——' OVERDUE FINES: 25¢ per day per item RETURNING LIBRARY MATERIALS: Place in book return to remove charge from circulation records . ‘ 5" :' LEPTONICALLY PRODUCED MULTIMUON FINAL STATES IN MUON SCATTERING AT 270 GEV By Daniel Adams Bauer A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics l979 m pix ln\\muU i... .I Ll ABSTRACT LEPTONICALLY PRODUCED MULTIMUON FINAL STATES IN MUON SCATTERING AT 270 GEV By Daniel Adams Bauer This dissertation summarizes the multimuon data of Fermilab experiment E3l9. In particular, a search has been made for possible heavy lepton signals and for other non-hadronic sources of muon— induced multimuon events. Conventional explanations for such events are also discussed. The experiment employed 270 GeV tagged muons incident on a long iron—scintillator target/calorimeter which sampled the energy of the absorbed final-state hadrons. The scattered and produced muons propagated through a magnetic spectrometer made of toroidal iron magnets and wire spark chambers. Hodoscope counters and small-angle vetos formed the experimental triggers. A new analysis program MULTIMU was developed to reconstruct muon tracks. This was used to filter the 8.2 x l05 triggers down to about l.6 x l04 multimuon candidates. These events were visually scannedresulting in a true multimuon event sample of 449 dimuons and 64 trimuons. Detailed checks established finding efficiencies of (70 i 8) percent for dimuons and (89 i 8) percent for triumons giving Daniel Adams Bauer rates per deep-inelastic scatter of (6.3 i 0.6) x 10"4 dimuons and (4.l i 0.4) x lo"5 trimuons, uncorrected for produced muon acceptance. Monte Carlo methods were employed to model the most likely multimuon processes including associated charm production, w/k decay, hadronic final state interactions and QED tridents. Rate estimates from these calculations as well as general characteristics of the data implied that charmed meson production dominated the dimuon sample with small contributions from other hadronic sources. Histo- grams of produced muon kinematics for data and Monte Carlo were compared and hadronic model calculations subtracted. The resulting tiny signals appear in reasonable agreement with Monte Carlo calcu— lations of QED tridents. Using kinematic cuts to supress both hadronic and electromagnetic processes leaves no statistically sig- nificant signal attributable to the weak production of heavy leptons. Upper limits derived from this process were consistent with the best published numbers. The much smaller trimuon sample was adequately explained by a roughly equal mixture of hadronic sources and trident production. A few very high transverse momentum produced muons remain unexplained. ACKNOWLEDGMENTS It is a pleasure to acknowledge the many people who have con— tributed to this work. All modern high energy physics experiments require the cooperative efforts of many physicists. Members of our small, but dedicated, collaboration included: Bob Ball, C. Chang, K. N. Chen, Mehdi Ghods, Jim Kiley, Adam Kotlewski, Larry Litt, and Phil Schewe from Michigan State University and A. Van Ginneken from Fermilab. In addition to these physicists, the experiment relied on a whole host of additional people. During the design and construction phase of E3l9, the following people were essential: Dave Chapman, Frank Early, Mehdi Ghods, Sten Hansen, Ken Holtzmann, Bob Mills, and Ed Reyna. Furthermore, taking the data at Fermilab would have been much more difficult without the generous help of Sten Hansen and Kevin Beard. The assistance of the Fermilab staff, particularly from mem- bers of the Neutrino Department, was also vital. In the data analysis phase, Larry Litt provided encouragement and assistance in track reconstruction. The multimuon search relied on the graphics software developed by Paul Bander and John Hoeckzema. Special appreciation is due the many patient scanners who actually found the multimuon events. My principal aides in this effort were: Mary Brake, Mary Beth Kazanski, and Bill Spero. Two people provided much of the Monte Carlo code for E3l9. We used the basic methods and programs of Dr. A. Van Ginneken to calculate several processes in detail at M.S.U. Wai—Yee Keung from the University of Wisconsin checked many other multimuon processes with his own Monte Carlo. Both of them were very helpful in the interpretation of our data. I have certainly benefitted from physics discussions with Professors Wayne Repko and Bill Francis at M.S.U. Other people who have contributed to my training in high energy physics are K. W. Chen, Dick Hartung, and Larry Litt. I would also like to thank the members of my guidance committee, especially Professors M. Abolins and J. Kovacs for their aid in the absence of Dr. Chen. Finally, I must acknowledge the efforts and friendship of my fellow graduate students Bob Ball, Jim Kiley, and Phil Schewe. Dis— cussions among Bob, Jim, and me sustained all of us through the long analysis. I also want to thank Bob and Phil for the use of several figures and tables. Two special people played a prominent role in the prepara- tion of this thesis. Dr. Mehdi Ghods, the able administrator of our NSF grant, provided invaluable assistance with good humor throughout the experiment. Mrs. Nancy Heath combined great patience with friend- liness in the long struggle to type this thesis. While many friends at M.S U. contributed to my emotional well-being, two stand out as people to whom I will always be indebted. Jim Hylen, a fellow graduate student, was always willing to spend time para talking and to assist with anything. Karen Stricker was, and is, the person I could always count on to listen and to care. Finally, I want to thank my family and, in particular, my parents to whom I owe the determination needed to achieve this goal. LIST OF LIST OF Chapter I. TABLE OF CONTENTS TABLES . FIGURES . . THEORY AND EXPERIMENTAL BACKGROUND . l Introduction: Particles and Interactions . l. l. 2 Background . l. 3 Specific Multimuon Processes EXPERIMENTAL APPARATUS . 1 Overview of the Apparatus 2 The Calorimeter . 3 E3l9 Counters . 4 Proportional Chambers . 5 The Magnetic Spectrometer 6 Electronics 7 Fermilab and the Muon Beam Line 8 Riding the Muon Through the Apparatus NNNNNNNN . . . o . n e . U ]> -l > ANALYSIS . l Summary of Data Taken 2 Data Decoding and Initial Processing 3 Beam Track Reconstruction and Momentum . 4 Spectrometer Track Reconstruction 5 Spectrometer Track Momentum Fitting . 6 Multimuon Finding . . . . . wwwwww ....n. MONTE CARLO ANALYSIS AND MODEL CALCULATIONS . 4. l Philosophy of Monte Carlo Calculations . 4.2 Monte Carlo Methods . 4. 3 Simulation of QED Processes 4.4 Simulation of Hadronic Processes . 123 125 I33 I47 mnbr 5. MULTIMUON DATI SJ Status 0 5.2 Single M 5.3 Dimuon E 5.4 Trimuon 5.5 Exotic E m . CONCLUSIONS lntroduc Sumnary J 2 3 lnprover 4 6 6. 6 6 Third Ge APPBVDICES . A. The Hadron Ca B- Track Reconst C- Monte Carlo A REFERENCES . , Chapter‘ 5. MULTIMUON DATA AND INTERPRETATIONS . 5 1 Status of Data Analysis . 5.2 Single Muon Events 5.3 Dimuon Events 5.4 Trimuon Events . 5 5 Exotic Events 6. CONCLUSIONS ' . Introduction . . Summary of Multimuon Results Improvements in E3l9 . Third Generation Muon Experiments 0503030» #wN—a APPENDICES A. The Hadron Calorimeter . B. Track Reconstruction and Fitting Algorithms . C. Monte Carlo Algorithms . REFERENCES vi Page l52 l52 153 l59 l8l 195 T96 T96 l96 200 202 204 205 238 254 264 Table l.l Leptons . l.2 Quarks and Had: l 2...» Multimuon Def“ :c> Multimuon Rate N . E3l9 Counter 5.‘ N N Proportional U N w Tron Toroid Mal N 4) Spark Chamber l N (.11 Primary Data Ti N or. Typical NT Seal 0.- . E3l9 Data «9.) [\D E3l9 Scaler As Scaler Average 3.4 Fluxes for Data .5 BER Assignment Final E3l9 Ali .7 Beam Track Alg .8 Beam Statistic 3-9 PASSZ Cuts . 3T0 Secondary Tape 3.9 3.lO LIST OF TABLES Leptons Quarks and Hadrons Multimuon Definitions Multimuon Rate Estimates E3l9 Counter Systems . Proportional Chambers Iron Toroid Magnets Spark Chamber Properties Primary Data Tape Format Typical Nl Beam Line Tune for 270 GeV E3l9 Data E3l9 Scaler Assignments . Scaler Averages for a Single Run . Fluxes for Data Samples . DCR Assignments Final E3l9 Alignment Constants in cm Beam Track Algorithm . Beam Statistics PASSZ Cuts Secondary Tape Format vii lOO TO6 Table 3. m N_. p 1 .. . < -. w w . _. ___. ._4 _a __.- _n 4) 4:. 5‘) _ - 4: I) :a. _ - ' Zr. In C... N cr. ' . N (.71 N 5.10 Calibration 0‘ Calibration 0‘ Data . Positive Muon Negative Muon Scanning Critk Multimuon Cam Finding Effic' Beam Tape Fon E319 Monte Car Multimuon Accr Muon Trident ' Simple Cut Ate Simple Cut Tr' Calculatio” Hadronic Monti Single Muon c. Numbers and R1 Single Muon A, DImUOD Number: DTmuon Rates 1 Dimuon Kinema- He“)! LeptOn l Effects of Ki I DSP E vent dAIES .5 Pa Table 3.ll Calibration of the Spectrometer Using the CCM Calibration of the Spectrometer Using Monte Carlo Data . . . . . . . . . . . . . . Positive Muon Calibration . Negative Muon Calibration . Scanning Criteria Multimuon Candidate Types . Finding Efficiency Beam Tape Format . E3l9 Monte Carlo Results for Tridents . Multimuon Acceptance in pl for Tridents Muon Trident Total Cross Sections Simple Cut Acceptance for E3l9 Simple Cut Trident Results and Comparison to Full Calculation . . . . . . . . . . Hadronic Monte Carlo Results . Single Muon Cuts . Numbers and Ratios of Events . Single Muon Averages Dimuon Numbers (Sample A Only) Dimuon Rates and Sample Comparisons Dimuon Kinematic Averages Heavy Lepton Kinematic Cuts Effects of Kinematic Cuts . OSP Events Passing Cuts: Neutral Heavy Muon Candi— dates . . . . . . . . . . . . . . . 5.T0 SSP Events Passing Cuts--Hepton Candidates viii Page lll TTT TT2 TT3 TT6 TT6 T2T T27 T37 T39 T4T T43 T44 T5T T55 T56 T57 T60 T6T T62 T69 T7T T72 T73 Table 5. 5. 5. 5. 5. 5. ;\> 0'01th N Kinematics of Pion vs. Muon Trimuon Numbel Trimuon Kinema Trimuon Kinem‘ Trimuon Kinerna Summary of Har Comparisons v' Comparison of tions Contributions Loss Calculat Table Page 5.ll Kinematics of Dimuons with High Pi . . . . . . . T74 5.T2 Pion vs. Muon Induced Dimuons . . . . . . . . l80 5.l3 Trimuon Numbers and Rates . . . . . . . . . . l82 5.l4 Trimuon Kinematic Averages . . . . . . . . . l83 5.l5 Trimuon Kinematics for 6 Probable w Events . . . . T88 5.l6 Trimuon Kinematics for Trident Candidates . . . . l93 A.l Summary of Hadron Calibration Results for E3l9 . . . 22l A.2 Comparisons with Other Hadron Calorimeters . . . . 222 C.l Comparison of Muon Energy Loss Monte Carlo Calcula- tions . . . . . . . . . . . . 257 C.2 Contributions of Individual Processes to Moon Energy Loss Calculations . . . . . . . . 258 Figure l Deep Inelastic l ks Multimuon Ki nc w QED Multimuon 3> Contributing [ lations . (1;. Multimuon Diag Leptons or blea ‘as Multimuon Diag N N N Digger Hodosc N w Discriminator Chambers N .5) Latch and Reac Chambers . N 01 Mignetostrictj Spark Chambers .6 Zero-Cm ssing Chambers . 2.7 Spark Gap Firi 3~8 E3l 2. 9 Trigger L 9 E3l9 Hodoscope 2.l0 E3l9 Gate L091 2.ll Schematic of S 2.12 Layout of Fem Figure l.l l.2 l.3 l.4 T.5 l.6 2.T 2.2 2.5 2.6 2.7 2.8 2.9 LIST OF FIGURES Deep Inelastic Scattering Kinematics Multimuon Kinematics QED Multimuon Diagrams Contributing Diagrams to Bethe-Heitler Trident Calcu- lations . . . . . . . . . . . . . . Multimuon Diagrams Involving Production of Heavy Leptons or Weak Bosons . . . . . . Multimuon Diagrams for Hadronic Processes E3l9 Experimental Apparatus Trigger Hodoscope Counters Discriminator Electronics for E3l9 Proportional Chambers . . . . . . . . . Latch and Readout Electronics for E3l9 Proportional Chambers . . . . . . . . . . . Magnetostrictive Wand Amplifier Electronics for E3l9 Spark Chambers . . . . . . . . . . . Zero- -Crossing Discriminator Electronics for E3l9 Spark Chambers . . . . . . . . . . . . Spark Gap Firing Electronics for E3l9 Spark Chambers . E3l9 Trigger Logic Diagram E3l9 Hodoscope Logic Diagram . 2.T0 E3l9 Gate Logic Diagram 2.TT Schematic of Spark Chamber Time Digitizer System 2.T2 Layout of Fermilab and Detail of the Neutrino Area X Page 37 38 46 47 49 56 57 58 so 65 Figure 2. _. w 2. .5:— c...» m w c...) f...) _ . . . m .33. < A) N —- w o» w \1 4:.» ;\.>——' .5:- (,9 Moon Beam Tr Characterist E104 . . Aligning PCZ Conventions E3l9 Beam Pr Beam Momentu Layout of E3 meter Calibr MULTIMU (PAS Scattered Mu MULTIMU (PAS Scattered Mu Monte Carlo Coherent Tri duced Opposj Incoherent T Produced opp Unnormai i zed tributiOng Kinematic C0 Particles fr Backgrounds Further Dimu Hadronic Bac DTmuon Data caiculateu n "dent Mont Further Subt Figure 2.T3 Muon Beam Transport and Detectors . 2. T4 Characteristics of Dipole Magnets in Beam Enclosure E104 . . . . . . . . . . . . . . . Aligning PC2, PCT, and the Front Spark Chambers Conventions for Spark Chamber Coordinate Axes . E3l9 Beam Proportional Chamber Matching Conventions . Beam Momentum Determination . Layout of E398 and E3l9 Apparatus During. the Spectro— meter Calibration MULTIMU (PASSZ) Reconstruction Inefficiency vs. Scattered Muon Energy . . . . . . . MULTIMU (PASS2) Reconstruction Inefficiency vs. Scattered Muon Polar Angle . Monte Carlo Conventions Coherent Trident Monte Carlo Leading Muon and Pro- duced Opposite Charge Muon Energy Distributions Incoherent Trident Monte Carlo Leading Muon and Produced Opposite Charge Muon Energy Distribution Unnormalized Comparison of Transverse Momentum Dis- tributions . . . . . . . . . . . . Kinematic Comparisons of Single Muons and Leading Particles from Dimuon Events . Dimuon Data Characteristics with Calculated Hadronic Backgrounds . . . . . . . . . . Further Dimuon Data Characteristics with Calculated Hadronic Backgrounds . . . . . . . Dimuon Data Characteristics After Subtraction of Calculated Hadronic Processes Versus Results of QED Trident Monte Carlo . . . . . . . . Further Subtracted Dimuon Data Characteristics Com- pared to QED Trident Calculations . . . . xi Page 68 69 85 85 89 94 T09 TT9 T20 T28 T45 T46 T49 T58 T64 T65 T67 T68 Figure 5.6 Opwslte'Sig" 5,7 Same-519n Dim 5.8 High Pi. SSP . 5,9 Comparison Of GeV . - ' 5.l0 Trimuon DATA QED Trident R 5.ll More Trimuon Trident Resul 5.l2 Still Further Trident Calcu 5.l3 Trimuon Event 5.l4 Trimuon Data I Total Hadronii 5.l5 Trimuon Data . grounds versu 5.l6 Trimuon Event A.l Hadron Calorii A. N Hadron Calorii 2:- t...) . Dependence of Length of Had Single Muon E' meter . . . 5 Dimuon Event ' 6 Trimuon Event 7 Average Numbe or Single Mu. Avera e 1 for D9 Numbe imuon Ev. Figure 5.6 5.7 5.8 5.9 5.T O 5.T3 5.T4 5.T5 5.T O‘b A.l A.2 A.3 A.4 A.5 A.6 A.7 A.8 Opposite-Sign Dimuon Event . Same—Sign Dimuon Event High Pl SSP . Comparison of Hadron and Muon Induced Dimuons at l50 GeV . . . . . . . . . . . . . . . Trimuon Data Energy Distributions versus Calculated QED Trident Results . . . . . . . . . More Trimuon Data Kinematics versus Calculated QED Trident Results . . . . . . . . . Still Further Trimuon Data Comparisons with QED Trident Calculations . . . . . . . Trimuon Event Trimuon Data with w Contributions Subtracted versus Total Hadronic Background . . . . . . Trimuon Data After Subtraction of All Hadronic Back- grounds versus QED Trident Calculations . Trimuon Event Hadron Calorimeter Energy Calibration Hadron Calorimeter Energy Resolution Dependence of Calorimeter Response on Position and Length of Hadron Showers . . . . . . .. Single Muon Event Vertex Positions from the Calori- meter . . . . . . . . . . . . . Dimuon Event Vertex Positions from the Calorimeter . Trimuon Event Vertex Positions from the Calorimeter Average Number Particles Before and After the Vertex for Single Muon Events . . . . . . Average Number Particles Before and After the Vertex for Dimuon Events . . . . . . . . . . Page T75 T76 T78 T79 T84 T85 T86 T89 T94 T92 T94 2T9 223 225 226 227 228 229 Figure A9 Average Numbe for Trimuon l 1.10 Missing Energ All Average Missi Single Tluon E 1.12 Missing Energ A.l:l Average Nissr Dimuon Event All Missing Ener B.l Vertex Algori 8.2 Geometry for 8.3 Definition 0 Finding BA Geometry and Scattering Ef Figure A.9 A.lO A.lT A.T2 A.l3 A.T4 B.T 8.2 B.3 8.4 Average Number Particles Before and After the Vertex for Trimuon Events . . . . . . . . . Missing Energy for Single Muon Events Average Missing Energy versus Hadron Energy for Single Muon Events . . . Missing Energy for Dimuon Events Average Missing Energy versus Hadron Energy for Dimuon Events . Missing Energy for Trimuon Events . Vertex Algorithm Geometry and Conventions Geometry for Tracing Muons through Magnetized Iron Definition of the Hourglass Window for Track Finding . . . . . . . . . Geometry and Conventions for calculating Multiple Scattering Effects in Iron . . . . xiii Page 230 232 233 235 236 237 240 243 247 248 TH l.l Tntroducti on: and Interactions Physics can order and simplicity that all natural phe Frequently, though, and the limitations patterns. Careful e plify natural behavi then employed to gene The primary task (anc Properties in a large classification into a Mother data or to a Thus from the Particle physics, pat 0f particles and forc enduring, of such cla Particles into two gr lighter particles) am Imperties between tl CHAPTER I THEORY AND EXPERIMENTAL BACKGROUND l.l Introduction: Particles and Interactions Physics can be broadly defined as the search for underlying order and simplicity in nature. Physicists share a common belief that all natural phenomena can be explained by a few universal laws. Frequently, though, the sheer scale or complexity of such phenomena and the limitations of human senses combine to obscure underlying patterns. Careful experiments must be performed to isolate and sim- plify natural behavior, with insight, logic, and even speculation then employed to generalize the measured behavior to new regions. The primary task (and satisfaction) of a physicist is to recognize properties in a large and complex set of data that allow its classification into a few simple groups, which can be interrelated to other data or to already existing theories. Thus from the early days of what is now called elementary particle physics, patterns have been sought in the growing number of particles and forces discovered. One of the first, and most enduring, of such classifications was the division of all known particles into two groups: leptons (consisting initially of the lighter particles) and hadrons. While there are many distinguishing properties between these two classes (e.g., spin and internal structure), the I"05 feel the strong ("U ence regains even i particles. There h; universe, or over vv but no concrete CVTI any other symmetry of the particle fam useful in isolating A similar t rental forces gover forces were thought charges and nuclear among these phenomer fundamental interact real force (responsi (nuclear) force. In theories combining e clectroveak interact force and gravity ma The mathematical bea most compelling stin further effort. This disseri involved in the prot nucleon interactions structure), the most fundamental distinction is that leptons never feel the strong (nuclear) force and hadrons always do. This differ- ence remains even if it is postulated that hadrons are composite particles. There has been some recent speculation that in the early universe, or over very long time scales, some intermixing may occur, but no concrete evidence exists at present. Of course, there are many other symmetry properties which contribute to our understanding of the particle families, but the lepton/hadron split is particularly useful in isolating certain processes. A similar trend has been followed in the study of the funda- mental forces governing particle motion. Historically, many different forces were thought necessary to explain specific behaviors of masses, charges and nuclear dynamics. Recognition of the interrelationships among these phenomena has led to the current belief that only four fundamental interactions are needed: gravity, electromagnetism, the weak force (responsible for radioactive decays), and the strong (nuclear) force. In fact, the reduction continues still, with current theories combining electromagnetism and the weak force into a single electroweak interaction. It is even conceivable that the strong f0rce and gravity may be eventually included within one framework. The mathematical beauty of such a unified field theory is itself a most compelling stimulus to both theorists and experimentalists for further effort. This dissertation represents a study of the leptonic processes involved in the production of multimuon final states from muon- nucleon interactions. The data originated from a muon scattering experiment E3l9, co this work are (a) t my current gauge magnetic multimuon theoretical predict the advantages of u vatic determination easily recognizable acceptance and even E3l9 apparatus was retaining sections background for this descriptions of the rise to multimuons a relative rates to ju l.2 Background The first tn uade its debut just I electron was also thv subsequent discovery later.2 No other ch: lfnatter and almost the next lepton to b6 confusion at the time today. The muon bel experiment E319, conducted at Fermilab in l976. The primary goals of this work are (a) to search for possible heavy leptons predicted by many current gauge theories, and (b) to attempt to isolate electro- magnetic multimuon production processes allowing comparison with theoretical predictions at higher energies than previously studied. The advantages of using inclusive muon scattering include good kine- matic determination for all leptons, large incident energy, and an easily recognizable event signature. The disadvantages of low acceptance and event rates are due primarily to the fact that the E319 apparatus was not optimized for multimuon detection. In the remaining sections of this chapter, the theoretical and experimental background for this work will be discussed. I will present brief descriptions of the most likely specific processes which could give rise to multimuons and make order of magnitude estimates of their relative rates to justify the attempt to isolate leptonic processes. l.2 Background The first truly elementary particle discovered, the electron, made its debut just prior to the onset of the 20th century.1 The electron was also the first and only lepton until the prediction and subsequent discovery of its antiparticle, the positron, thirty years later.2 No other charged leptons are necessary to explain the nature of matter and almost all natural phenomena. Partly for that reason the next lepton to be discovered, now called the muon, caused great confusion at the timei3and indeed its raison d'etre is still a mystery today. The muon behaves exactly like a heavy electron, yet it cannot decay into a to an almost epheme neutral (and probabl to conserve moment they can interact wi experimentally disco realized that each c lhis sequential patt tothe lepton family l974.7 Since nobody ence of leptons, the Iassive additions to suggest that nonsequv readily visible as mv properties of the cup The first he: the electron and aga‘i venber, the neutron, the electron, are sui processes. However, veritable explosion c for ordinary matter. this assortment of Pa themselves were not e Stituents came to be cannot decay into an electron without transferring its "muonness" to an almost ephemeral particle, the neutrino. Neutrinos are neutral(and probably massless)leptons, originally invented by Pauli to conserve momentum in nuclear beta decay.4 Due to the fact that they can interact with matter only via the weak force, they were not experimentally discovered until the l9505.5 Soon after it was realized that each charged lepton had its own special neutrino.6 This sequential pattern appears to be preserved in the newest addition to the lepton family, the tau, which was discovered at SLAC in l974.7 Since nobody has yet uncovered the pattern behind the exist- ence of leptons, there is no reason not to expect further, more massive additions to the family. Some recent gauge theories even suggest that nonsequential heavy leptons may exist which might be readily visible as multimuon events.8 Table l.l summarizes the properties of the current lepton family. The first hadron, the proton, was discovered shortly after the electron and again several decades followed before the next member, the neutron, was added. These two hadrons, together with the electron, are sufficient to describe virtually all atomic processes. However, unlike leptons, the next few decades saw a veritable explosion of new hadrons, most of which seemed unnecessary for ordinary matter. Gradually, however, patterns were detected in this assortment of particles which led to the notion that hadrons themselves were not elementary but composite particles whose con- stituents came to be called quarks or partons.9 Although quarks MflEl.L--Leptons hnkle Mas (Antiparticle) (Me t 5g) 0(< f h*) 0.5 v“ (Tu) o ( u hfi 105 t (it) o ( 1- (1+) 1 TABLEl.2.~-Quarks 301 Lowe: ("k ________ hfiqmrk) JP = 0' (pseudo: lb?) .° 135 am M 5(3) ' n' (958) £03 nc (?) blbl a tit) Not Ye M” TABLE l.l.--Leptons Particle Mass 2 Decay width Predominant Decay Branching (Antiparticle) (Mev/c ) (MeV) Modes Ratios ve (Ce) 0(<6x10’5) Stable -- -- e' (e+) 0.511 Stable -— -- vu (5h) 0 (< .57) Stable -- -- u- (in) 105.659 3x10'16 (,3 e- 58v“ 98.6% vT (UT) 0 (<250) Not Yet Detected Experimentally T‘ (1*) 1782 >2.8x10'1O a‘ + 1‘v1 VT ~36% + h' neutrals ~33% + (23hi)neutrals ~32% l' = e' or p' h = hadrons TABLE l.2.--Quarks and Hadrons Q k Lowest Lying Meson Bound States Branching Ratios uar . - _ - f vector meson (Ant1quark) JP = 0 JP — l O . (pseudoscalar) (vector) to lepton pa1rs u (E) _ 1a°(135), n°(549) } 00(770), m0(783) 1 ~.01% d (d) s (E) n' (958) o (1020) ~ .05% I c (E) ”c (a) J/p (3100) - 14% ' b (B) :2 y (9460) ~ % t (E) Not Yet Detected Experimentally ‘ have never been see proper corrbinations quarks can account ' Since their concept‘ experiments has beer three quarks. Furtl experiments have dis ence of at least two carriers of the stro there is no convinci not be found and age signals. Table l.2 < family. Because of tl phenomena have been I vere usually treated seeped to have no co century were all of electromagneti sm.1 2 Preceding this uni fic actions have been des electromagnetism, one electromagnetic field distribution of the r theory, it became nec have never been seen directly (and some believe they cannot be), proper combinations of just three kinds of quarks and their anti- quarks can account for all naturally—occurring hadronic matter.10 Since their conception, much indirect evidence from scattering experiments has been found to support the existence of the original three quarks. Furthermore, recent electron—positron annihilation experiments have discovered new hadronsH which suggest the pres- ence of at least two more quarks and the appearance of the actual carriers of the strong force, called gluons. As with leptons, there is no convincing reason to believe that heavier quarks will not be found and again these may produce characteristic multimuon signals. Table l.2 describes the known constituents of the hadron family. Because of their ubiquity in nature, electric and magnetic phenomena have been known to humans for centuries. However, these were usually treated as isolated, albeit useful, curiosities which seemed to have no connection with each other. Not until the 19th century were all of these phenomena united into a single theory of 12 electromagnetism. The rapid development of mathematical techniques preceding this unification supplied the form in which all inter- actions have been described since, namely the field theory.13 For electromagnetism, one speaks of an interaction of a charge with the electromagnetic field, defined at all spacetime points by the charge distribution of the rest of the universe. With the advent of quantum theory, it became necessary to treat both forces and matter as “lumpy" — instead of continua interact via the ex force, the photon, r strength of the intv niques and the farm perturbative calculi pleted the transforn to quantum electrody all other field thec have confirmed its v 24 orders of magnitu In sharp con phenomena, the very discovery of nuclear lhe first theoreti ca by Fermi in the l930‘ description of the b magnetic leptonic in ling constant for su clear why this is ca tore potent electron vorked reasonably we failed badly for 0th lines, a much more p mthuoatical formali instead of continuous. As visualized by Dirac,14 discrete charges interact via the exchange of the carrier of the electromagnetic force, the photon, with coupling constant a = l/137 describing the strength of the interaction. The invention of calculational tech— niques and the famous Feynman diagrams, as well as proof that such perturbative calculations made sense for all orders essentially com- pleted the transformation from classical Maxwellian electromagnetism to quantum electrodynamics (QED).15 QED is still the prototype for all other field theories and by far the most successful. Experiments have confirmed its validity over spatial distances spanning at least 24 orders of magnitude.16 In sharp contrast to our familiarity with electromagnetic phenomena, the very existence of the weak force was unknown until the discovery of nuclear beta decay in the early part of this century.17 The first theoretical understanding of such radioactivity was supplied by Fermi in the l9305.18 His approach was a purely phenomenological description of the beta decay dynamics, generalized to all nonelectro- magnetic leptonic interactions (e.g., muon decay). Since the coup- ling constant for such processes was found to be about l0_5, it is clear why this is called the weak interaction in comparison with the more potent electromagnetic and strong forces. The Fermi theory worked reasonably well for some weak processes at low energy, but failed badly for others and diverged at high energies.19 In recent times, a much more promising approach has been found within the mathematical formalism of gauge theories,20 somewhat similar to QED ‘ in form, but with d gauge groups seem t forces into a singl possible at all ene have been built upov dard version is that group su(2) x um.‘ leptons to a left—he also having a right- boson which carries (lit and 20) act as t allows, in a natural The coupling constan experiment via the s simplest electroweak cated models exist wl leptons (i.e., massi Mmmmhfl n help reduce the num mnw,mn responsible for hold1 vas discovered early first performed.23 A lvenrhelms all others Strong interactions in form, but with different symmetries. The so—called non—Abelian gauge groups seem to be able to unite the weak and electromagnetic forces into a single electroweak interaction, with calculations possible at all energies for all processes. Although many models have been built upon these basic mathematical foundations, the stan- dard version is that of Glashow, Weinberg, and Salam based on the group SU(2) x U(l).2] This model assigns each sequential pair of leptons to a left-handed weak isospin doublet with the charged lepton also having a right-handed piece. Preserving the photon as the gauge boson which carries the electromagnetic force, three new bosons (w: and 20) act as the propagators of the weak interactions. This allows, in a natural way, both charged and neutral weak currents. The coupling constants and masses of this model can be related to experiment via the single parameter sinzew. Although this is the simplest electroweak theory consistent with experiment, more compli- cated models exist which require the existence of nonsequential heavy leptons (i.e., massive charged or neutral leptons with no correspond- ing neutrino).22 Thus an experimental search for such particles may help reduce the number of contending models. Finally, mention must be made of the strong force which is responsible for holding nuclei together. Like the weak force, it was discovered early in this century when nuclear experiments were first performed.23 Although it is very short range, the strong force overwhelms all others within nuclear distances. Until very recently, strong interactions were discussed mostly in phenomenological terms, — using such ideas as The explosion of ne of accelerators, uh stand strong i ntera terns which appeare try properties led I of quarks.25 Subsev conception of "color colored gluons. witl ability to be affect ture built on these Although QCD calcula have been made seem lepton scattering an culated in QCD is th gluonfusion.28 As' important hadronic 5 Before pursu cusses, it is useful of this work. Lepto tool in high energy details the kinemati nucleus simply to ab reactions are no ion is in higher energy interactions can be . . . . 24 using such 1deas as v1rtual p1on clouds or nuclear potentials. The explosion of newly—discovered hadrons accompanying the advent of accelerators, while threatening to overwhelm any attempts to under— stand strong interactions, also provided important clues. The pat- terns which appeared when hadrons were grouped using certain symme- try properties led Gell-Mann and others to postulate the existence of quarks.25 Subsequent theoretical work has led to our current conception of "colored" quarks bound together by the exchange of colored gluons, with color being the quantum number denoting the ability to be affected by the strong force. The gauge group struc— ture built on these ideas is called quantum chromodynamics (QCD).26 Although QCD calculations are quite complicated, the predictions which have been made seem to agree well with experimental results from lepton scattering and annihilation.27 One process that has been cal- culated in QCD is the interaction of photons and gluons called photon- gluon fusion.Z8 As we shall see later, this mechanism may be an important hadronic souce of multimuon events. Before pursuing the description of specific multimuon pro— cesses, it is useful to briefly review the experimental background of this work. Lepton-nucleus scattering has long been a favorite tool in high energy physics for two types of tests. (Figure l.l details the kinematics of this process.) Firstly, by using the nucleus simply to absorb momentum, several interesting QED and weak reactions are no longer forbidden and shed new light on these theor~ ies in higher energy regimes. Perhaps more importantly, the leptonic interactions can be assumed to be understood and the virtual photon 51 = .1 A o a . cos [(p0 p1 = polar angle of (=4EOE1 sin2(e/2) = 4-momentum tran: u : Eo ' E1 = energy transfer l”forgo = Bjorken scaling l = u/Eo =fractional ener i: + 2_ 2 [Zmpv M p q = center of momen Figure l.l .--Deep In .0 II II X ll 2 ll ‘ v/E cos'lrvao ammo) 1 a, u EH polar angle of scattered muon relative to incident muon - 2 4E0E1 Sln (8/2) 4-momentum transfer to nucleus squared - E — E o l energy transfer to nucleus squared q2/2mpv Bjorken scaling variable 0 fractional energy transfer 2 2 l 2m + w - 2 [pv Ipq] center of momentum frame energy Flgure l.l.--Deep Inelastic Scattering Kinematics produced can be tr of the nucleus, or 19505 an exhaustiv began to detail nu experiments now em into the nucleus. It was in Iultimuon events w diagram and releva various event type detectors were not number of such even clear that the ever pion decay. Specu' decay of either hea provided the major and analysis effort and neutrino scatte l.3 Secific Mult Before pro is necessary to ex in some detail. T mates and some ide which may allow le those of hadroni c ll produced can be treated as a probe of the electromagnetic structure of the nucleus, or even individual nucleons. Beginning in the late l950$ an exhaustive set of electron scattering experiments at SLAC began to detail nuclear structure.29 At higher energies, most such experiments now employ muons and heavy targets to probe more deeply into the nucleus. It was in such experiments at Fermilab that lepton-induced 30,3l (Figure l.2 shows the Feynman multimuon events were first detected. diagram and relevant kinematic variables while Table l.3 defines the various event types.) Unfortunately, the first generation detectors were not at all optimized to detect extra muons, and the number of such events was quite small. Even so, it quickly became clear that the events could not be from conventional sources such as pion decay. Speculation centered around the possible production and decay of either heavy quarks or heavy leptons. This uncertainty has provided the major impetus for increasing the detection efficiency and analysis effort for multimuons in the second generation of muon and neutrino scattering detectors,‘including those used for E3l9. l.3 Specific Multimuon Processes Before proceeding with a description of the experiment, it is necessary to examine the most likely sources of multimuon events in some detail. The aim is to obtain order of magnitude rate esti- mates and some idea of notable kinematic features, especially those which may allow leptonically produced events to be separated from those of hadronic origin. Detailed Monte Carlo calculations for 9] = cos'lfi - i5]. = polar angle simply e for p“- =E15‘ll’lei = transverse on (p1 for dimu . _ -1 A s ij ' COS [pl P = polar angle to“. = a]. - g. = azimuthal an) : ' 2 ll”- 4EiEj 51n (A = apparent mass ll: (E0 " ; Ei)/El = inelasticity Ell = nEo ‘ EH = missing ener = asymmetry of Figure l.2.--Multi 61 II II II II cos'lca - amount-r] polar angle between virtual photon and ith muon (written as simply e for dimuons where it refers to the produced muon) E.sine- t;ansverse momentum of ith muon relative to virtual photon (pi for dimuons where it refers to the produced muon) COS-1[61 ' Uj)/l61[lfij)] polar angle between ith and jth muons (A8 for dimuon events). ¢1 - ¢j azimuthal angle between ith and jth muons (Ad for dimuon events) 2 (neij/z) apparent mass of the (i, j)th muon pair (MW for dimuon events) 4E1Ej s1n (E0 - t E1)/EO, i means final state muons inelasticity of the event nEo - EH missing energy of the event (Ei ~ E.)/(Ei + E.) asymmetry of (i,j)th muon pair (a for dimuons) Figure l.2.--Multimuon Kinematics. TABLE l.3.--l’ultim Type of lhltiauon l. Dimuon a. Leading Particle b. OSP c. SSP 2. Trimuon 3. Exotic l. Vertex a. Hadronic b. Leptonic TABLE l.3.--Multimuon Definitions Type of . . . Multimuon E 3T9 Def1n1t10n l. Dimuon Two muons detected downstream of the target a. Leading For electromagnetic and hadronic processes, Particle one of the muons must be the scattered muon. We define this as the one with highest energy and call it the leading particle b. OSP Opposite sign (charge) muon pair c. SSP Same Sign (charge) muon pair 2. Trimuon Three muons detected downstream of the target 3. Exotic Events with more than three muons detected 4. Vertex The 2 (beam) position of the lst calorimeter a. Hadronic b. Leptonic counter of a hadron shower 9: the 2 position where the muon tracks come closest to each other if no shower exists. The calorimeter shower has at least 5 GeV Less then 5 GeV deposited in the calorimeter many of these pl‘OCi for the event rate: to be 50 l/Pb per ' The electrc muons, as shown in (Bethe-Heitler tric tridents), and char These fourth-order diagrams without tt servation. Sincec we immediately expe to be reduced from The process more explicitly, le coulomb field has b However, the triple Cllt to evaluate fo Sharply 0n kinemati meaningress. llithi eXltrimental intere 9%)”)th the i nvo it have utilized thl this Process as wil lqualitative under referring to Figure )"V‘llle prepagators many of these processes are presented in Chapter 4. As a rough guide for the event rates that follow, we take the proposed E3l9 luminosity to be 50 l/pb per nucleon. The electromagnetic processes which can give rise to multi- muons, as shown in Figure l.3, are muo-production of a muon pair (Bethe-Heitler tridents), photo-production of a muon pair (pseudo- tridents), and charged heavy lepton pair production and decay. These fourth—order processes are the lowest allowed because all diagrams without the nuclear vertex are forbidden by momentum con- servation. Since deep—inelastic scattering is a second order process, we immediately expect multimuon rates from electromagnetic sources to be reduced from the single muon rates by d2, or around l0'4. The process called Bethe—Heitler trident production, or more explicitly, leptoproduction of lepton pairs in the nuclear coulomb field has been theoretically understood for several decades.32 However, the triple coincidence differential cross—section is diffi- cult to evaluate for a given experiment because the result depends sharply on kinematic acceptance, making a straightforward integration meaningless. Within the last twenty years, renewed theoretical and experimental interest in tridents has stimulated novel methods for evaluating the involved trace sums with the aid of computers.33 We have utilized these techniques in a Monte Carlo calculation of this process as will be seen in Chapter 4. However, one can get a qualitative understanding of the kinematics of these events by referring to Figure l.4 and noticing that all of the trident diagrams involve propagators like l/q2, l/qi for the photons, or l/(p2 + m2) a. Bethe-Helm c. Heavy Lepton figure l.3.--QED Ml. Fl fit] u 1 IQ bi hi hi I“ $q pi c. Heavy LeptonPair Prod. d. Deep Compton Figure l.3.-—QED Multimuon Diagrams. o.thne-m t “.1 c. space- Figure l.4.--Contri Calcul a. time- like . b. time-like c.) space-like d. space- like Figure l.4.--Contributing Diagrams to Bethe-Heitler Trident Calculations. ' for the excited mt only when at least muentun transfers at low angles will realistic calculat Carlo techniques . 35 to the sections of about l5 nb/nuc apparatus, the aco not to represent a Although the situal still not expected The Feynman pair production of is essentially the virtual photons is transfer to zero ca and therefore in re flying the bremsstr (see Appendix C for section at the aver ence work of Tsai ,3 nucleon, leading to Although this is do rates, both are com It may be that the l7 for the excited muon.34 These imply that the cross section is large only when at least two of the leptons are nearly collinear (small momentum transfers). An experiment with poor acceptance for muons at low angles will have difficulty detecting these tridents and realistic calculations of the rates are impossible without Monte Carlo techniques. However, blind extrapolation of measured cross sections35 to the E3l9 incident energy (270 GeV) gives a trimuon rate 36 with a similar of about l5 nb/nucleon. In the previous experiment apparatus, the acceptance losses were so large that tridents seemed not to represent a significant contribution to the event rate. Although the situation was somewhat improved for E3l9, tridents were still not expected to dominate. The Feynman diagram for bremsstrahlung followed by photo- pair production of muons (sometimes called the pseudotrident process) is essentially the same as that for tridents, except that one of the virtual photons is now real. This restriction of one four-momentum transfer to zero causes a large reduction in available phase space and therefore in rate. A crude rate estimate can be made by multi— plying the bremsstrahlung probability, estimated to be about 4 x l0—5 (see Appendix C for this calculation) by the pair production cross section at the average photon energy. Using the very complete refer- ence work of Tsai,37 the latter is calculated to be about 400nb/ nucleon, leading to a raw trimuon event rate of around 20 pb/nucleon. Although this is down by three orders of magnitude from the trident rates, both are completely dominated by the experimental acceptance. It may be that the kinematics of pseudotridents are more favorable than for tridents. such as target br all thought to be The same p charged heavy lept of these leptons w dimuon or even trir Tsai, the photo-pa lepton are around 7 photoproduction usi to) \J ”l =1 5) —l —. with the resulting further reduction 1‘ doubtful that such However, the striki future, high-statis Now let us or intermediate vec the weak processes ith order electroma involve particles w charged heavy pepto not in the standard if masses and cross literature that det 18 than for tridents. Note that other similar electromagnetic processes such as target bremsstrahlung and inelastic Compton scattering are 38 all thought to be negligible compared to the trident mechanisms. The same processes described above can be used to produce charged heavy lepton pairs (e.g., T+T'). Occasionally, one or both of these leptons will decay into a muon (and neutrinos) leading to dimuon or even trimuon events. Again employing the calculations of Tsai, the photo-pair production cross sections for a 2 GeV heavy lepton are around lOO pb/nucleon. This can be converted to virtual photoproduction using the well-known factor37 in Lo|\u S’le mlmm Ill with the resulting event rate being about l pb/nucleon. Given the further reduction from low branching ratios and acceptance, it is doubtful that such heavy lepton signals could be detected in E3l9. However, the striking kinematic features of such events may enable future, high-statistics muon experiments to see them. Now let us consider processes involving the weak interaction or intermediate vector bosons, as shown in Figure l.5. Note that the weak processes are second order and thus comparable in rate to the 4th order electromagnetic processes. However, all of the weak diagrams involve particles whose existence is unproven. Neutral or doubly charged heavy leptons are required in some gauge theories, but not in the standard model. Unfortunately, there is such a range of masses and cross sections quoted for these processes in the literature that detailed calculations are difficult to perform o). I Figure l.5.-—Multi Lepto wt N a). Heavy Neutral Muon Production and Decay b). Hepton Production and Decoy z° " ,,’ e’ [fl \ ‘6 F, N X c).Weok Vector Boson Production Figure l.5.—-Multimuon Diagrams Involving Production of Heavy Leptons or Weak Bosons. at present. Instc of uultirnuons pro: uill be distinct 1 A recent p mdel independent under various quar (a) only opposite around .l-.3 pb/nu energies and angle hadronic sources. to see a few such . cuts is reserved f: Heptons, or by Hilczek and Zee' electrons. Howevel could give rise to production cross se E3l9 energies, ass rates and kinemati neutral heavy lept Finally, t Vector boson 20 el the cross sections issuning Me = 5 GeV However, other expe FIIIIIIIT_____________________________________________________________________________________’_1’—" 20 at present. Instead, I have concentrated on the kinematic features of multimuons produced via these mechanisms, in the hope that they will be distinct from those seen in other processes. A recent publication by Albright and Shrock39 gives some model independent featuresof neutral heavy lepton production by muons under various quark couplings. Briefly, their conclusions are that (a) only opposite sign diumons can occur, (b) the raw rates are around .l-.3 pb/nucleon, and (c) several kinematic cuts on muon energies and angles can enhance this signal over electromagnetic and hadronic sources. While this rate is very low, it may be possible to see a few such events. A full discussion of the possible kinematic cuts is reserved for Chapter 5. Heptons, or doubly charged heavy leptons, were first proposed by Nilczek and Zee4O to allow rare radiative decays of muons into electrons. However, it is clear that the weak decay of these leptons could give rise to same-sign multimuons. A crude integration of their production cross section leads to a rate of about .2 pb/nucleon at E3l9 energies, assuming a l0% branching ratio. Clearly, both the rates and kinematic features are comparable with those from the neutral heavy lepton process. Finally, there is the possibility of producing the intermediate vector boson Z0 electromagnetically. Brown, et al.41 have calculated the cross sections for this process with several boson masses. Assuming M2 = 5 GeV, the rates for E3l9 would be about .3 pb/nucleon. However, other experiments have made it clear that the mass is much larger and so the small. No furthe the related pair For counpl hadronic sources then out kinemati lhe previous uuon isns were probabl As with the elect have been calcula be more thoroughl If the sol turned out to be t events would have of pion decay favo Shower energy, whit observed distri but rate short of Monte contributed no more experiment.30 lhe recomb‘l state can also leac have attempted to e hadron scattering c raw rates for £319 l l Zl larger and so the cross sections for this process become negligibly small. No further effort need be made to calculate this process ( or the related pair production of Ni). For completeness, it is necessary to consider the “background“ hadronic sources of multimuons in order to understand how to screen them out kinematically. Figure l.6 shows the most likely processes. The previous muon experiment had suggested that some of these mechan- isms were probably responsible for the majority of dimuon events. As with the electromagnetic processes, many of these hadronic sources have been calculated by Monte Carlo techniques and the results will be more thoroughly described in Chapter 4. If the sole source of the second muon in dimuon events had turned out to be the decay of one of the shower pions (kaons), such events would have engendered little interest. However, the kinematics of pion decay favor very low transverse momentum and large hadron shower energy, which seemed to fit very poorly with the previously observed distributions.3O There is no simple way to estimate this rate short of Monte Carlo calculations which suggested that this contributed no more than a third of the dimuons in the previous muon experiment.30 The recombination of soft quarks into muon pairs in the final state can also lead to dimuon or trimuon events. Several authors38 have attempted to estimate the contribution of this process by using hadron scattering data and vector dominance arguments. The resulting raw rates for E319 have been estimated to be about 4 nb/nucleon. ch Associated Figure l.6.——Multin _ _.__. ._.. .. ‘ 22 b). Quark Recombination cm“ 7?, Mt 1L.__<.=_ 2': i 9 t c). Associated Charm Prod. d). Vector Meson Prod. Figure l.6.--Multimuon Diagrams for Hadronic Processes. However, again th surely suffer dra Another u decays in time wi Excellent vertex low beam pion con happening. One hadror is vector meson pr acceptance of this low or high mass 0 date. Muoproducti for the ‘l’ giving a lpb/nucleon, assu Pair mass distribu if this process COl Finally, t associated product dress as mesons an Previous men“ an induction could a Process may interf multimuons due to similar kinematic Minute for charm 23 However, again these events favor low transverse momentum and will surely suffer drastic acceptance losses. Another uninteresting possibility may be that a beam pion decays in time with a scattered muon event, making an apparent dimuon. Excellent vertex resolution, good time resolution, and the inherently low beam pion contamination (5 x l0'5) make this a very unlikely happening. One hadronic process that has been studied in some detail is vector meson production. As will be obvious later, the mass acceptance of this experiment effectively prevents detection of either low or high mass objects, leaving only the W as a potential candi— date. Muoproduction cross section measurements have been published42 for the W giving a trimuon event rate at our energy of around l pb/nucleon, assuming a 7% branching ratio. Clearly, the apparent pair mass distributions for trimuon events will show a distinct peak if this process contributes significantly. Finally, there is the very interesting process known as the associated production of heavy quarks (either charm or bottom), which dress as mesons and decay semi-leptonically to provide extra muons. Previous muon43 and neutrino44 experiments have claimed that charm production could account for the majority of their dimuon events. This process may interfere with the search for leptonically produced multimuons due to the relatively higher rate expected and somewhat similar kinematic features. A recent publication38 gives a rate estimate for charmed quark associated production of 0.5 nb/nucleon and for bottom quark lations have bee distributions to sanples, hopeful] electromagnetic a Table l.4 siderations discu: istics in mind thu the experimental . cedure (Chapter 3 lations in Chapter and comparisons vi to isolate the lap tion and suggests °f the aliparatus, iii the Appendices 24 for bottom quarks of about l pb/nucleon. Again Monte Carlo calcu— lations have been made and I will rely on the resulting kinematic distributions to subtract such hadronic events from the multimuon samples, hopefully leaving those more likely to be of weak or electromagnetic origin. Table l.4 summarizes the rate estimates and kinematic con— siderations discussed in this chapter. Keeping these event character— istics in mind throughout, the next topics to be discussed will be the experimental apparatus (Chapter 2) and the data analysis pro- cedure (Chapter 3). After presentation of the Monte Carlo calcu- lations in Chapter 4, the data itself will be discussed in Chapter 5 and comparisons will be made with the calculations in the attempt to isolate the leptonic signals. Chapter 6 concludes the disserta- tion and suggests future improvements. Detailed treatment of parts of the apparatus, analysis, and theoretical calculations are reserved for the Appendices. TABLE l.4.--i’ultil -9? Process ( Bethe-Heitler ~ thou Tridents (~ Pseudo- l Tridents ( d r' 0. pair (1 production leer ~1 Doupton ~ Scattering Neutral 5 0 Heavy (3 lepton I.‘ r" Doubly- changed "tau Lepton link Bosons (lssune l= sun) issue. harmed iesuns TABLE l.4.--Multimuon Rate Estimates Process Bo (per nucleon) (event rate with perfect acceptance) Characteristics Bethe-Heitler Muon Tridents Pseudo— Tridents T+ 1' pair production Deep Compton Scattering Neutral Heavy Lepton Doubly- Charged Heavy Lepton Neak Bosons (Assume M = SGeV) Assoc. Charmed Mesons fl/K Decay up production Soft Hadron Recombinations Upsilon production 5 O ~l5000 pb (~4xlO5 trimuons) lO—3O pb (300-800 trimuons) 0.1 +1.0 pb (3-30 dimuons) ~l.5 pb (~40 trimuons) .l - 0.3 pb (3-8 OSPS) .03 - .3 pb (l-8 dimuons) ~500 pb (~l4OO dimuons) ~.85 pb (~24 trimuons) ~4000 Eb (~lxlO dimuons) ST pb (~30 trimuons) Mostly at very small angles, drastic acceptance reduction expected Also at low angles, but not so much Should give large apparent masses, transverse momenta and missing energies. Look like tridents, but at a negligible rate Only OSPs produced. Expect large p; and missing energy E1/E2 z 1 Only SSPs. Otherwise similar to neutral lepton character— istics Actually expect much larger weak boson masses making rates infini- tesimal Dominant dimuon hadronic process. Produces large apparent masses, transverse momenta and missing energies Mostly at low masses and trans- verse momenta. Should give obvious mass peak as signature. Similar to m/k results except expect lower rate Again mass peak expected. Accept- ance probably too small to see this. 2.l Overview of The purpc tape sufficient s natics of muon sc within a large ra be divided into 5 provided target In deposited in the detect beam and s chambers which me magnetic spectrom used to determine ics to record detu write the results which supply the Much of tl was constructed ft and has been full j only how this eqU'1 plete description CHAPTER 2 EXPERIMENTAL APPARATUS 2.l Overview of the Apparatus The purpose of the E3l9 apparatus was to record on magnetic tape sufficient spatial and timing information so that the kine- matics of muon scattering events could be completely reconstructed within a large range of energy and polar angle. The equipment can be divided into six types: (l) the hadron sampling calorimeter which provided target nucleons and measured the hadron shower energy deposited in the interaction; (2) scintillation counters used to detect beam and scattered muons and reject halo; (3) proportional chambers which measure the incident muon momentum vector; (4) a magnetic spectrometer with toroidal magnets and wire spark chambers used to determine the kinematics of final state muons; (5) electron- ics to record detector information, make fast trigger decisions and write the results on tape; and (6) the accelerator and muon beam which supply the incident muons. Much of this equipment (3, 4, and parts of 2 and 5 above) was constructed for use in the first generation muon experiment E26 and has been fully described in several theses.1 I will discuss only how this equipment was tested and used for E3l9. A more com- plete description of construction and operation is necessary for the 26 rest of the appar feature of this e but full detail i overview of the E New The hadron elements) of mach nucleons) sandwicl the passage of Chi hadron showers. of sampling calor‘ use in cosmic ray that when a charge iron nucleus), one teens) are produce them interact agai resulting shower l and nuclear absorp charged particles the total energy 1' hadrons has previou light proportional themwhich is, in ' ionizing charged pi converted into el et 27 rest of the apparatus. The calorimeter, which was the major new feature of this experiment, will be summarized in the next section, but full detail is reserved for Appendix A. Figure 2.l shows an overview of the E3l9 apparatus. 2.2 The Calorimeter The hadron calorimeter consisted of a long sequence (llO elements) of machined steel plates (which supply most of the target nucleons) sandwiched with plastic scintillation counters to measure the passage of charged particles and thus the energy deposited in hadron showers. The theory, design principles, and actual operation of sampling calorimeters have been adequately established by their use in cosmic ray and neutrino experiments.2 The essential point is that when a charged particle scatters off a nucleon (or the whole iron nucleus), one or more high energy hadrons (mostly pions and kaons) are produced in the re—combination of quarks. These hadrons then interact again producing more hadrons and electrons. The resulting shower length is a complex function of both the radiation and nuclear absorption lengths of iron. By sampling the number of charged particles at frequent intervals, one obtains a measure of the total energy in the shower if the response to mono-energetic hadrons has previously been determined. The scintillators produce light proportional to the amount of radiation energy deposited in them which is, in turn, proportional to the number of minimum- ionizing charged particles which have passed through. The light is converted into electrical signals by photomultiplier tubes. The 28 .Amxmpcaoo ouw> Emma ou mcwewc >m new ”mmaoumouo; cmmmwcp on“ mam um ecu .mm .wo~mc esp m? >: ”mamnEmcu chowpcoqoca Low magnum muav .mspmcmqa< mecmewcqum m_mmai._ m we: we iii'lw'lwllllllulll‘lj 25 ea :5 mm: _ 0mg. Em 1 “ nu nu "nun “ mmmnuu HH nun X wuugmw Enummin Hwy m “ll _ll“ ll lly 8%: ll 7.. ii i l .2. mm 2mm“... mm u MY . E5535 2wa {Tall ll Hi, gmmrmmmfimm hm.W:_ _ _ ll ii in l l . illi Uil jui ll ilL um mm mm l in; a me $222» @292» Ewes N2..:f s s m m e m a a mm tum; signals are then analog-to-di gi tal proportional to t non-linearities calorimeter was h target, gain shif cal interference chamber noise. Al resolved, although data taking. The tool for establish muons before and a obtained with the l uith spectrometer e level. Exhaustive provided in Appendi 2.3 E3l9 Counters Several diffe E3l9. Signals obta hudoscopes (8H) will was defined by two 1 the target hodoscopt iii of the beam at 1 target, the halo-vet hiring "live" He 29 signals are then amplified and finally converted into digital form by analog-to-digital converters (ADCs). The resulting numbers will be proportional to the number of particles in each counter assuming all non-linearities were corrected in calibration. Actual use of the calorimeter was hampered by non-containment of the shower in the target, gain shifts at any stage of the counter system, and electri- cal interference (especially with the sensitive ADCs) due to spark chamber noise. All of these problems were at least partially resolved, although the noise effects occurred through most of the data taking. The calorimeter has proven to be a very successful tool for establishing event vertices and determining the number of muons before and after the interaction. Moderate success has been obtained with the hadron energy measurement although discrepancies with spectrometer energy determination persist at the few percent level. Exhaustive detail on all aspects of the E3l9 calorimeter is provided in Appendix A. 2.3 E3l9 Counters Several different scintillation counter systems were used in E3l9. Signals obtained from the upstream experiment (E98)3 beam hodoscopes (BH) supplied beam momentum information. Beam location was defined by two sets of three counters each,labeled B and C, while the target hodoscope (TH) defined the spatial distribution and tim- ing of the beam at the front of the target. Also, upstream of the target, the halo-veto (HV) bank of counters rejected triggers con— taining ”live“ (i.e., within 25ns of a beam signal) particles outside of the b comters placed of the spark cham record of timing covered the toroi triggers with a "‘ counters provided All scintil? light, produced by scintillator, is p face of a photomul trons are focused electrons produced charge, producing was "hit." Each 5 foil and black pla tube from light. high voltage is co bases) and a plate mtil the counter tohave passed thr by the type of [tho uniformity of resp useful only for ve The actual constrU 30 outside of the beam radius defined by B and C. Trigger bank (TBC) counters placed within the spectrometer allowed flexible triggering of the spark chambers for desired event types and also provided a record of timing for final-state muons. Beam veto (BV) counters covered the toroidal holes near the back of the spectrometer to reject triggers with a ”live“ unscattered muon. Several miscellaneous counters provided efficiency checks and calibration beam definition. All scintillator counters work on the same basic principles: light, produced by the passage of a charged particle in the plastic scintillator, is piped by internal reflection to a cathode at the face of a photomultiplier tube where it ejects electrons. The elec— trons are focused and accelerated down a chain of dynodes with more electrons produced at each successive step. The anode collects the charge, producing an electronic pulse signalling that the counter was "hit.“ Each such counter must be carefully wrapped in aluminum foil and black plastic or tape to shield the scintillator and photo- tube from light. After insuring that the counter is light-tight, high voltage is connected to the phototube (via resistor chain tube bases) and a plateau curve is taken, (i e., the voltage increased until the counter sees with excellent efficiency a cosmic ray known to have passed through it.) The plateau voltage is mostly determined by the type of phototube used. Finally, if desired, the spatial uniformity of response can be mapped out by the same method. This is useful only for very large counters where light piping is difficult. The actual construction of our counters follows the general procedure described in App the function of ' for all E3l9 cour There won (two upstream and bank consisted of in the y (bend) d scopes allows beau basis, their over; our events with uu only in the final properly timed (se The three the last beam line inherently sensiti required for these counters were not which gave output 5 for such small couw (one at the front < tus) constituting 1 am of B and C ’chuS The C counters were fairly low noise 16 array of eight over 3) described in Appendix A for the calorimeter. I shall concentrate on the function of the counter systems here. A summary of the parameters for all E3l9 counters is given in Table 2.l. There were three E98 beam hodoscopes available for our use (two upstream and one downstream of the last beamline dipole). Each bank consisted of eight 0.75” wide counters, arranged with no overlap in the y (bend) direction. Although the granularity of these hodo- scopes allows beam energy determination of ~ l% on an event-by—event basis, their overall efficiency was somewhat low, leaving lO-l5% of our events with undetermined beam energy. This problem was corrected only in the final data runs when the E98 proportional chambers were properly timed (see 2.4). The three small rectangular B counters were situated within the last beam line magnets to define the beam. Since phototubes are inherently sensitive to magnetic fields, thick iron shields were required for these counters. Due to their inaccessibility, the B counters were not separately plateaued but simply set at voltages which gave output signals at levels known to represent high efficiency for such small counters. There were also three circular C counters (one at the front of the lab and two at the front of the E3l9 appara- tus) constituting the other half of beam definition. The long lever arm of B and C thus selects muons near the center of the beam line. The C counters were plateaued and showed efficiences > 99% with fairly low noise levels. The target hodoscope was a 2—dimensional array of eight overlapping rectangular counters designed to cover «memes 2: a>1 5 d5: 8m SE :3 x _.m x __m e 3:55 3.65:: -28 mcan Q>m opm> >m a>w_ awe; pmmamp to ages; m_mm .mmm xmcmaE< omh om Lm_wEEm N mpcm>m oum> >3 a><©m xUEap =w\m Ea mum; cowpmmmamm mamas .5 29; 28 stage .N E 32 .NE A m E8 232:: E pcocm ammcmkwwmu .No m> :m\_ N :P pFE cor magma—0cm Emmm mmm xmcmaEq .Nwsoa =N\_ m xcma m -wpwmwm Emuw m ao~ .mo_ a> 98%, falling to ~90% near some of the edges. Three sets of trigger banks were situated roughly in the middle of the E3l9 spectrometer. Each consisted of five (E26) counters stacked in the X (vertical) direction and five (E3l9) counters in the Y (horizontal) direction (Figure 2.2). The middle counter of each set left a hole slightly bigger than that in the magnet toroids and the overall dimensions of the banks corresponded to the size of these toroids since we wanted to trigger the apparatus only on muons scattered into the magnetic field (the triggering requirement is discussed in Section 2.6). Although the main function of the TBC‘s was triggering, the hits in each counter were recorded fimre2.2.-—Trigg were banks the s 34 Trigger Banks SA' A SB' and 80 -[T Overlap %" Counters 68" S6" 14%" wide 12” diam WWW 19.94"_ Trigger Banks SA, SB; SC [:3 Correction Counters T DZ a-e W... . ' ks Flgure 2.2.--Tri er Hodoscope Counters. (The old (unprimed).ban werggpositioned slightly upstream of the new (primed)t banks and the correction counters were used to conver the square holes to round ones on the old banks). for each event, a tion on all muon able in light of counters from tl operated during l were especially l flexibility and a similar to those pest problem bein counters in a ver 56AVP phototubes bases and cables u were three circulc than the magnet hi centered visually preventing any of from triggering 1: events to be reco crucial and each rate~dependent ef ics dead-time) we moms/Spi ll . 2.4 Pro ortional Proportion the to their wel l - 35 for each event,and this provided timing and crude position informa— tion on all muons within the spectrometer (which is especially valu- able in light of the long memory time of spark chambers). The counters from the previous experiment were simply plateaued and operated during E3l9 with efficiencies all > 95%. The E3l9 TBCs were especially built for this experiment to provide greater trigger flexibility and redundancy. The construction techniques were very similar to those used for the calorimeter (Appendix A) with the big- gest problem being support of the very large and somewhat fragile counters in a vertical position. Note that all of the TBCs used 56AVP phototubes on bgth_ends to insure high efficiency (the tube bases and cables were largely built by the E3l9 group also). There were three circular beam-veto counters (diameter slightly bigger than the magnet holes) mounted near the back of the spectrometer and centered visually on the magnets. These have the difficult task of Preventing any of the enormous number (~l05) of unscattered muons from triggering the apparatus so as to allow mostly deep-inelastic events to be recorded. Thus, the efficiency of these counters is crucial and each was plateaued to > 99.5% efficiency. Furthermore, rate—dependent effects (e.g., tube base voltage sagging or electron— 6 ics dead-time) were carefully eliminated up to intensities of TD muons/spill. 2.4 Proportional Chambers PY‘Oportional chambers were used for beam measurement in E3l9 due to their well-known high rate caPaCTty and short memory time. The principle of ope charged particle large (several k and a set of clo the wires. llhen gas further, leau of negative char! in the electric i charges even rear IProportional" tr Particle within l the particle mass problem is to des gas mixture and v caused by photons ing dead times of pulses on the wi tor level, are al electronics for t resolution of aro tional chambers u apartments (E98 able in several th minor repairs, we?“ responded and then 36 principle of operation is relatively simple:4 the passage of a charged particle in a gas produces ion pairs. Application of a large (several kV) potential difference between a high-voltage plane and a set of closely spaced wires causes the ions to drift toward the wires. When they gain enough energy,they begin to ionize the gas further, leading to the formation of an avalanche. The movement of negative charges toward, and positive charges away from, the wires in the electric field induces a current flow in them (before the charges even reach the wires). The size of the resulting pulse is "proportional" to the amount of ionization produced by the passing particle within limits (which in turn depend in a known manner on the particle mass, energy, and properties of the gas). The crucial problem is to design the geometry and use an appropriate ”magic” gas mixture and voltage such that breakdown (sparks and streamers caused by photons emitted from the ionized gas) is prevented, insur- ing dead times of less than 200ns and high-rate capacities. The pulses on the wires are amplified and, if above a pre-set discrimina- tor level, are allowed to set latches (Figures 2.3 and 2-4 show this electronics for the E319 PCS). This gives position information with resolution of around one wire spacing (l—2mm). Both sets 01: propor— tional chambers used for E3l9 were built and operated in the previous experiments (E98 and E26) with construction and test details avail- able in several theses.1’3 For our experiment, the chambers, after minor repairs, were tested in the beam to make sure all wires FeSponded and then used in the same manner as in the old experiments. i ./a\. / :3. u “no.0: ”mo-PQZzsémUm—O XQRKQIU .N_u.ou_nmiM 9.90.. 0ND. 02 ‘\_ 37 .mcmaEmao choquoé 3mm .8» 3228mm. LommEEComEi.m.m 95m; . 1' Boom 8655:35 canozo wl' >3- .mu> .e .50 060.. .54... . .omoiia s 1 . motoqndo ozq zfzza 80.02 n82. mm 0 >1 . Ye will H :1. w \Illr : _ I : Ll a . T a .. mama Econ Emu. 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UK \ Te L. no.1 gm! 5m \ $72. a $2520 u4moomm-.voomm- .lululslllluullnllllllu > ooom- .lnuunulu >oome - mammo_o> N cowgm meF Nm. comc< mung—mm + some; meF Rm. ou NmN .comg< me IIIIIIIIITIIIIII _m_>cpwz No.m + acmu330mH NON mma N :mpmmczh 1111. umpmpa urea :ogowE ON maze wsz as N_.N EEN EE N EE N mcwuwam mew: mm Nmr om? om 3mw>\mwgw3 AXN .zvv _ A>.= to zaxv N A3.>.:V m Axnxv N LwnEm;o\m3mv> w N N F mgmnsmcu .02 mom: a ‘8; mo; mLmnEmzu mmm menEmsu mpmm quwEmgma mewnEmgu _mcovoaoa0La--.N.N msmqe to produce measu disadvantage is scattering and e only muons will tected (as oppos can detect final slabs of low-car to allow for wat flowed when the provided notice 0 the magnets were In tracks to allow e Since iro lhysteresis), the taken. This was a slowly reducing tl eral hours. With: the field shape ( Since there was i their very detail Obtained for £319 Performed by windi Ieasuring the curr lilaCitor Q=f Idt [Changing the magn 42 to produce measurable bending for high energy muons. Their primary disadvantage is the limit on momentum resolution due to multiple scattering and energy loss within the iron and the fact that, since only muons will penetrate, all other final state particles are unde- tected (as opposed to E98 with an air—gap magnet and LH2 target which can detect final-state hadrons). The toroids consisted of welded slabs of low-carbon steel wrapped radially with hollow copper wire to allow for water cooling since currents of ~35 A continuously flowed when the magnets were on. Temperature monitors on each coil provided notice of overheating. As with all spectrometer elements, the magnets wereinounted on Thompson bearings which rode on railroad tracks to allow easy mobility if desired. Since iron can retain very complex magnetization patterns (hysteresis), the magnets were de—gaussed before any muon data was taken. This was accomplished by alternating the direction (and slowly reducing the amount) of current flow in many steps over sev- eral hours. Without doing this, we would have had no assurance that the field shape (when the magnets were on) was the same as in E26, since there was insufficient time and manpower available to repeat their very detailed studies of the field.1 The average field was obtained for E3l9 currents by flux loop measurements. These were performed by winding a single coil of wire around a magnet and measuring the current (or better,the total charge on an integrating capacitor Q==f Idt) induced by varying the magnetic field by AB (changing the magnet current). By Faraday's law we expect — R0 = Ad = AAB. tance in the mea the capacitor C V = Q/C So, if the field ing V gives The result of thi £26 for similar ( dependence shoulc Spark cha outgrowth of Geig principles are st noble gas mixtu pairs. Aproperl of the chamber ca hairs producing a from recombinatio the channel. Ear the position of t to rapid computer hires inside the Whom. The di FIIIIIIIIIIIIIIIII:—"T'T'T'T'T'T'T'T'T"""""TTTTIIIIIIIIIIIIIIIIIIIIIIIIIlllllllllllll"'-""§r 43 RQ = Ab = AAB, where A = area of the wire loop, and R is the resis— tance in the measuring circuit. The voltage which appears across the capacitor C is then V = Q/C = ABA/RC So, if the field is varied from 0 up to its normal value 30’ measur— ing V gives The result of this for E3l9 agreed closely with the measurements of E26 for similar currents, giving us confidence that the radial dependence should also be the same. Table 2.3 summarizes the toroids. Spark chambers, invented in the late l950's, were a natural outgrowth of Geiger and proportional counter techniques. The working principles are straightforward:5 passage of the charged particle in a noble gas mixture (standard 90% Neon, l0% Helium) creates iOn pairs. A properly shaped high voltage pulse applied between plates of the chamber causes rapid propagation and further creation of pairs producing a conducting ion channel. Aided by photons emitted from recombination of the ionized gas, a spark discharge occurs in the channel. Early spark chambers used photographic means to record the position of the sparks, but this is cumbersome and not amenable to rapid computer analysis. Placing a plane of closely—spaced fine wires inside the chamber allows electronic detection of the spark position. The discharge induces a small electric pulse in the wire — TABLE 2.3.--Ir01 --l72.7 cm outer --Lengths vary l «Saturation cur --Average field --Resi dual "dega --Each magnet = «Spectrometer = --Field measured --Radial dependen B(r) = A/r Magnet l,3,5,7 2,4,6,8 --Transverse momel -~RllS transverse l per magnet = .l 44 TABLE 2.3.--Iron Toroid Magnets -—l72 7 cm outer diameter, 30.5 cm inner diameter -—Lengths vary between 78.1 and 79.2 cm --Saturation current ~35 A, 450 turns --Average field = fB(r) dr = l7.09 Kg magnet l,3,5,7 at 34.5A Tar = 17.27 KG magnet 2,4,6,8 at 36.6A --Residual "degaussed" field = 134 gauss magnet l,3,5,7 244 gauss magnet 2,4,6,8 --Each magnet = 7.87 gm/cm3 x 80 cm = 629.6 gm/cm2 --Spectrometer = 8 magnets x 629.6 = 5036 gm/cm2 ——Field measured using (i) B—H curve was measured for a smaller toroid of the same type, and scaled up (ii) B(r) measured directly using a coil wound around one slab of the toroid; coil passed through the center of the toroid and small holes drilled in the body of the toroid slab --Radial dependence of the field known to within l% B(r) = A/r + c + Dr + Fr2 B(KG) r(cm) Magnet A C D F 1,3,5,7 12.20 19.92 -.08357 .0004346 2,4,6,8 12.07 19.71 —.0827 .0004301 --Transverse momentum “kick” due to one magnet = .4 GeV/c --RMS transverse momentum "kick" from multiple scattering Per magnet = .1 GeV/c nearest to it, w strictive wire 6 wires. In our 5 removal and is p prevent corrosio wires causes an . wire which propa edge. The change change in magneti amplifier, and 26 Along with wires Sparked every tin pulses (fiducial sent to special a which were previo Position of the f were easily conve uust be used at 9 dimensional (X-Y) dlncy, each of co oriented at 45° w Particularly usef: able in each plant heat. It is ver; Spark chambers in 45 nearest to it, which is sensed in our chambers via a special magneto- strictive wire6 (called a wand) stretched perpendicular to the grid wires. In our system, the wand is mounted separately for easy removal and is packed in a small tube, flushed with Argon gas to prevent corrosion. The electromagnetic pulse in one of the grid wires causes an acoustic stress pulse in the magnetostrictive wand wire which propagates at a known constant speed to the chamber edge; The change in permeability of the polarized wire causes a change in magnetic flux, which is sensed by a pick-up coil, pre- amplifier, and zero-crossing discriminator (Figures 2.5 and 2.6). Along with wires fired by particles, two special fiducial wires are sparked every time the chamber is triggered. Thus, a sequence of pulses (fiducial 1, up to seven fired wires, and fiducial 2) are sent to special devices called time digitizer converters (TDCs), which were previously started by the trigger. Since the spatial position of the fiducials was accurately known, the times of arrival were easily converted into spatial coordinates. Two wire planes must be used at some angle (90° in our chambers) to give two- dimensional (X-Y) coordinates for the sparks. To give added redun- dancy, each of our spark chambers had another set of two wire planes oriented at 45° with the first (measuring U-V coordinates). This was particularly useful in view of the limited number of sparks allow- able in each plane and the failure of several planes during the experi- ment. It is very important to achieve the correct gas mixture in spark chambers in order to have good spatial resolution and efficiency. 46 .mgwnEwcu.meam mpmm cow movcogpumpm LoamTFaE< new: m>~povcpmopwcmmzlu.m.N weaved SSEEIumB 8E5 op :85 95 Bo; >8 .. . >0m u1_ 3““ >9... as: cam + AAA u. m of} +1! u N U \T a: Nx u:_ . >m_+ I. >w + down xN d9 u" 3:5 me E E .. One to m.m+ O... mEIO 00. 1.53 mmmomhm omkdzimwk mad. 95an HE. 41.4 New 8> ~_+ 2. >600. mot. >509“ |/\/I -. w3<> .5 M261. ..>e cm 2 30$me ax x03, if. 00. gnun ." biz. Aspecially desi distribute the r cold traps, addi constituent (~82 spark discharge the chamber edge limits spark cur for the wands an (to prevent spur The firil ahydrogen thyra high voltage pul: break down, they unto the chamber time of these be times the chambe that more secure thyratrons for ea for £319. Since par ing a beam spill, dlSperse quickly Sharks. To keep 48 A specially designed (Berkeley) gas cart was borrowed to mix and distribute the neon-helium gas and purify the returning gases within cold traps, adding traces of alcohol and argon. Neon is the main constituent (~82%) because of its high ionization potential and spark discharge shape. The helium and argon suppress breakdown at the chamber edges and lower the high voltage needed, while alcohol limits spark currents and improves multi—track efficiency. Argon for the wands and pressurized nitrogen for the chamber spark gaps (to prevent spurious breakdown)were also dispensed by the gas cart. The firing circuit for the spark chambers (Figure 2.7) used a hydrogen thyratron which, when pulsed by the trigger logic, sends high voltage pulses to all chamber spark gaps. When these gaps break down, they switch high voltage stored in large capacitor banks onto the chamber planes, allowing spark formation to begin. The shape of the high voltage pulse is crucial and can be varied by altering the spark gap pressure or the capacitor banks (the charging time of these banks is around 30-40 ms which limits the number of times the chambers can be fired to < 50 per two—second spill). Note that more secure firing of the chambers would require independent thyratrons for each gap, but lack of money and time prevented this for E3l9. Since particles are always passing through the chambers dur- ing a beam spill, ion channels are constantly formed and would not disperse quickly enough if left alone, leading to many spurious sparks. To keep the memory time of the chamber low (~1 us), a .mcmnswgu xgmam mme soc mowcoepumrm unread new xcmqm--.N.N mczm_m conEofi fioo o. 3:82. a. 333 9.2 .N an. n N .ZN 0.6 Cognac =4 fi>om+lv .3 S. 8° 30:33.... .6. E 30 $033.. .33: $2.5 OJuE 53:36 :N\_ ‘0 to S. «5:. n r J a $100.). OFN OZ_E5: “ - Prue: so. .9 m 88+ H003 -rooon 000m 83 35+... H e xv.“ wi .rSom .0 0.4.6 xmdam 5m2 3 .. up d as. 8N. won 0504 mar/‘0 ©_m-m present (these (4) scalers to hDCs used were basic function within a short nimiber which ca was 0-256 pC (( fold overloads. pulses were not we found that s and distort the aLeCroy repres developed for a runs. Since th the gate ground Time di the start signa timed arrives. time, which is TDCs (built spe Figure 2.11) th trigger and eac sent to a shift TDCs were start (8.9., BV count late in the exp 59 present (these are used to record hit PC wires and counters); and (4) scalers to count signals for counter and logic modules. The ADCs used were LeCroy 2249A 12 channel linear response devices whose basic function is to accurately store the total incoming charge within a short gate time (100 ns) and later convert it to a channel number which can be fed to the computer. The range of these devices was 0—256 pC (Channels 1-1024) and they claimed to reject up to 1000- fold overloads. This turned out to be true only if large noise pulses were not induced in the ground lines. During the experiment, we found that spark chamber noise was able to re—open the input gates and distort the ADC digitizing for some modules. In cooperation with a LeCroy representative, special ferrite core transformers were developed for all ADC inputs to damp the noise problems for our later runs. Since the conclusion of our experiment, LeCroy has re—designed the gate grounding to avoid this difficulty. Time digitizer converters work by starting a fast clock when the start signal is received and stopping it when the signal to be timed arrives. Knowing the constant clock rate gives the elapsed time, which is converted to digital form. For the spark chamber TDCs (built specially for these chambers and schematically shown in Figure 2.11) the start comes via a special controller from the trigger and each of the up to eight sparks has its scaler reading sent to a shift register to be read later by the computer. Counter TDCs were started by a beam signal and stopped by counter signals (8.9., BV counters). These latter TDCs were not properly timed until late in the experiment so that little use has been made of them. 60 .5393 $3395 2:... L855 323m 08 059.658-- 524m $2.90 as... .0 2.0523 esteem. . Sac. emu 3.08 .o .3 zoom .8 8% .8520 m So 22208 :5 a.» mmc: now. BEEECUmG nco; Eo: 2.69: Son 0 .0 ¢\_ mac: 2:; 33220 cozoucoccucmm L £306 .925“. j .8338 00:60 09:8 48.8.0 .. ~12 ON .1... .5 Set... “ 30368 U .0 08 u 276* u _ A. [I .aa :3 .as :n [ .._.N mesm.. 25.3 .009: .cw>m ‘ The S1 every good tri clear separati state dependin are reset just to receive sig located so far latches. Thus PCS = C ~ (SA - pulser. The t‘ so far upstrear experiment, so The DCRs used 1 PC latches, all because of the particular). 1 Chapter 3. 1 experiment; the manually copied kind (LeCroy 25 redundancy was sealers is vita Furthermore, th and apparatus in The min was a DEC PDP 1 61 The status of each proportional chamber wire is recorded (for every good trigger) in a latch, which discriminates the signal for clear separation from noise and then sets itself into a ”no” or ”yes” state depending on whether the wire was missed or hit. The latches are reset just prior to the expected signal arrivals and then enabled to receive signals for 100 ns. Note that because the B counters are located so far upstream, they would arrive too late to open the latches. Thus, the strobe signal is a subset of the actual trigger PCS = C - (SA + P) where SA is the first trigger bank and P is the pulser. The timing problem is worst for the E98 PCS since they are so far upstream and, indeed, it was incorrectly done for most of the experiment, so that the wrong beam track was latched for every event. The DCRs used for latching counter signals (LeCroy 2340) work like the PC latches, although the gate width must be kept short (~40 ns) because of the very high rates in some of the counters (B and BV in particular). The list of signals latched in E319 will be shown in Chapter 3. Two sets of scalers were used to count signals for this experiment; the first kind employedan LED readout and readings were manually copied into logbook records after every run while the second kind (LeCroy 2551) were read by the computer at each event. The redundancy was necessary mostly because the flux information on these scalers is vital to determining normalization of the experiment. Furthermore, the visual scalers were the principal beam—tuning tool and apparatus monitor during data taking. The mini—computer used to control the data recording for E319 was a DEC PDP 11/45 on loan from FNAL. Equipped with 32k words of memory (core) the computer w the data onto I tasks within t1 the electronics nationally star controls the ti and crate contr electronic modu network with in transfer functir driver which cap that of a limitc would like to ha Once the store the block written per recc 350) as 9-track the format of ti analysis, with 1 Problem with the drive, requiring do to change ta Preliminary on-l the performance chamber ineffici 62 memory (core) and a specially designed disk—resident operating system, the computer was able to supervise all data recording devices, write the data onto magnetic tape, and perform some on-line monitoring tasks within the 40 ms dead time for each event. Interaction with the electronics occurs through a BDOll branch driver using the inter- nationally standard CAMAC data transfer system. The branch driver controls the timing of data flow to the computer from each CAMAC crate, and crate controllers, which reside in each crate, control individual electronic modules. These are all connected by the branch highway network with individual wires assigned to timing, power, and data transfer functions. The crates are read serially by the branch driver which can handle up to seven of them (this proved to be some— what of a limitation for us since there were other counters which we would like to have latched or scaled). Once the computer received the data, its main priority was to store the block for writing to magnetic tape. Four events were written per record, although these tapes were then copied (via an IBM 360) as 9-track tapes with two events per record. (Table 2.5 details the format of the event block.) The copies have been used for all analysis, with the actual data tapes stored at FNAL. The only real problem with the tape writing was that we had just a single tape drive, requiring a down-time of roughly five minutes every hour or two to change tapes. The second function of the operating system was preliminary on—line analysis of the data. It was essential to monitor the performance of the detection systems to spot problems like spark chamber inefficiency, dead channels in the proportional chambers or 16-87 88-179 180-215 216-220 221-228 229-456 457-454 465461 762-768 Table Words 1-15 16-87 88-179 180—215 216-220 221-228 229—456 457-464 465-761 762-768 63 Table 2.5.-— Primary data tape format Contents 1.0. block 24-bit scalers E319 PC's E398 PC's DCR's TDC's ADC's unused NSC digitizers unused Maw 15 72 92 36 5 packed 8 packed 228 packed 8 297 7 768 words/event calorimeter, e being written made for every important dUI’li computer check: and software ca 2.7 Fermilab a Law— Fennila nest of Chicago accelerators (t calling for 101 upgraded to ope protons/spill ( performance) . with the pre-ac beam of protons accelerator to for injection i reached. At thi intensity) is i circumference o to 400 GeV and, experimental ar 64 calorimeter, etc., and to get an idea of the character of the events being written to tape. Paper outputs of these on-line analyses were made for every run in the experiment. These tasks became especially important during calibration runs when time was too short for off-line A description of the mini-computer operating system and software can be found in the thesis of R. Ball.8 computer checks. 2.7 Fermilab and the Muon Beam Line Fermilab (located in Batavia, Illinois, roughly 40 miles west of Chicago) is the site of one of the world's largest proton accelerators (the other is at CERN). Built in l969 with a design 12 protons/spill at 200 GeV, the accelerator has been upgraded to operation at 400 GeV with intensities up to 2 x l013 calling for l0 protons/spill (although often at the expense of rather unstable performance). The accelerator contains four major stages beginning with the pre—accelerator, which is designed to produce a very intense beam of protons at 750 KeV. This beam is steered into a linear accelerator to boost the energy up to 200 MeV. This is sufficient for injection into a small synchrotron (the booster) where 8 GeV is reached. At the appropriate time the beam (now somewhat reduced in intensity) is injected into the main synchrotron ring, which has a circumference of over 4 km. Here the beam is boosted to energies up to 400 GeV and, every l5-20 seconds, switched out to the three main experimental areas (Figure 2.l2). During our runs, the accelerator _) _ fl) A 000.00.) l l .. 28.3.. . ll. Figure 2.12."! 6 5 lOO 000 y (feet) .._. l l t T I T l l 1 1 r i O c L noc\ Central Meson O Booster\ __ /Lob é, Area C) 11 ~ . 8 \- Neutrino " _ Proton Area _ rea ‘ Moin .. Ring ‘5 <1) )- TRUE 3: NORTH " ‘74, PROJECT .. NORTH .. I» ' 5 f“—Rbon - 1 l 1 4 A J m L 1 I 1 l I i l u: um Seam?“ m. an II“ III I in New Beam wanes :I‘l‘ g: uuon Lemmy :\ II Wanda Bumbag :lll‘ Emwkr E 5:", ' e n E I‘I‘I\ r BnomNO ll "L__/ ”1 I ~‘.‘ 1 it. a i. \ ws\_: ‘. IS‘BubeI Chum E 30' ensue Chunk '. \\ g ‘. un- -/Anunbl1 AM Lah'C' / Emmi: I W Figure 2.l2.—-Layout of Fermilab (top) and Detail of the Neutrino Area (bottom). (E3l9 was located in the Muon Laboratory). proved quite to (requiring eigl tion problems. on x to12 pre caused the elim planned with di priority at Fer order of magni t time. The muo Figure 2.l2, bo aluminum cylindi Neutrino area. kaons) is guide. magnets called ‘ beam dump. Aftr long, evacuated to yield muons ' enclosure (100) the dipoles (l again focused (l romentlum selecti bends the beam 66 proved quite temperamental with frequent main ring magnet failures (requiring eight or more hours to repair) and severe power distribu- tion problems. Suffice it to state that our promised intensity of 8—l0 x l012 protons per spill really averaged around.375 x l012. This caused the elimination of valuable calibration time and the runs planned with different target materials. However, we did enjoy top priority at Fermilab during our main data runs, which represented an order of magnitude increase in statistics on muon scattering at the time. The muon (Nl)9 and neutrino beams, schematically shown in Figure 2.l2, both stem from protons smashing into targets (a l2? aluminum cylinder for muons) in the first enclosure (99) of the Neutrino area. The resulting shower of hadrons (mostly pions and kaons) is guided through an initial set of focusing and steering magnets called the triplet train, while the protons continue on to a beam dump. After the mesons pass the triplet train, they enter a long, evacuated decay pipe where the decays m + uv and K + no begin to yield muons and neutrinos. When the beam reaches the next enclosure (lOO) the charged particles are bent (west) by main ring type dipoles (lWO), vertically trimmed (lVO), and focused by main ring quadrupoles (lFO, lDO), while the neutrinos sail on unaffected through the earth berm covering the beam lines. The m/u beam is again focused (lQl), and bent back east (lEl) in enclosure lOT, thus momentum selecting only part of the beam. Enclosure l02 trims and bends the beam back west (lV2 and lw2), again momentum selecting. At this point, ethylene blocks runs leaving a in a dispersion of halo further are obtained by The spreading bl vith quadrupole: (lF3, lDB). Th: mater randomly. enclosure l04 w‘ (Figure 2.l3 shc shirmmed main rir mhich, when push Eel muons. The the field (i.e. , time so as to mi 1e"15). However caused so we se 58V. Since the he carefully me and spatial posi (B - dl needed angle of the dip results, shown i 67 At this point, the still partly-pion beam can be filtered by poly— ethylene blocks in the beam pipe and magnet apertures to remove had- rons leaving a "pure” muon beam. This does result, unfortunately, in a dispersion (due to multiple scattering) which is a prime source of halo further downstream. Note that hadron beams for calibration are obtained by removing the CH2 blocks (a several hour exercise). The spreading beam passes through a final focus in enclosure l03 with quadrupoles salvaged from the old Cambridge electron accelerator (lF3, lD3). These magnets showed their age by overheating and leaking water randomly. Final momentum selection is performed in the last enclosure l04 with dipoles (lE4) bending the beam eastward again. (Figure 2.l3 shows the full muon beam line.) These magnets were shimmed main ring dipoles (to increase the field and bending angle) which, when pushed to their current limits, would handle up to 300 GeV muons. The normal solution employed with such magnets is to ramp the field (i.e., bring it up to maximum only during actual beam spill time so as to minimize the average current and reduce heating prob- lems). However, the shims were too unstable for the stresses this caused so we settled for d.c. running at the reduced energy of 270 GeV. Since these magnets constituted the final momentum selection, we carefully measured their magnetic field as a function of current and spatial position (so as to derive the total field integral F = f B ~ dl needed to determine momentum P = ;%§.F, where e is the bend angle of the dipoles) using an NMR probe and a gaussmeter. The results, shown in Figure 2.14, were used in our beam energy routine Enclosv 100 687 To Production Target 1W01 Enclosure l 100 1W02 ‘ 1W03 1V°}1po ' F0 '.\1Q1 ‘ l 1E1 I {E398 PWCl Enclosure BHl 103 1}Q?3,/x”//l E398 chz / , ‘7 _ B2-*' I 1E4 B3 Enclosure ! —_________ E398 PWC3 104 E398 PWC4 BHS B1 :%T{E319 pwcs E398 pwcs} c1 Muon E398 cho ‘T‘ Lab Figure 2.l3.--Muon (Nl) Beam Transport and Detectors. / \ 0 Figure 2.14 --C 69 l i r l 1 l 10 edge of the shim 8 Bow) 6 _ I=3240 amps 4 l l 2 l l l l J i I I I I o 2 4 6 8 10 12 14 2 (inches) 12. T /0 -- B: 0.114- LI + i; 4hr: : ‘ \“C 8: maahfiflc afield (KG) I: mogne'l‘ current (amps) Bus) ‘9' first‘ Ens 1,! . l=Batore 8,23,76 Z=A4i0 -2 7‘ _. 2._ y’// b .321(:.003)xl0 .33e(em03)sl0 M j*.03(t.03) "303 (1.03) o . who ' 23w . 3600 I (amps) Figure 2.l4.-—Characteristics of Dipole Magnets in Beam Enclosure El04. (Chapter 3). the extracted Neutrino depar‘ and muons down beam is monit0i bers (when the; each bend. Cor ments by remote is the beam was 0i quality were (b) minimize tt {5) achieve rea chambers, partj Themain data r the calibratior cal tune is She Althoug and balky to 0p “tense (Up to muons, then ava better muon bea new muon beam d 70 (Chapter 3). The Fermilab control room is responsible for tuning the extracted proton beam into the Neutrino area. From there, Neutrino department physicists worked with us to propagate the hadrons and muons down the Nl beam line to the front of our apparatus. The beam is monitored at each enclosure by counters and ionization cham— bers (when they work), allowing one to optimize the shape before each bend. Control of magnet settings was available to the experi- ments by remote consoles connected to a mini-computer (MAC) system. As the beam was gradually tuned toward our apparatus, three measures of quality were used: (a) maximize the rate in the B and C counters; (b) minimize the halo (monitored by the coincidence HV - S); and (c) achieve reasonable shapes and spot sizes in the beam proportional chambers, particularly avoiding scraping the beam on magnet edges. The main data runs achieved quite adequate tunes, although many of the calibration runs were sl0ppier because of lack of time. A typi- cal tune is shown in Table 2.6. Although this muon beam was old, somewhat hastily designed, and balky to optimize, it did supply a relatively small (~4” square), intense (up to l06 muons/spill), high energy (270 GeV) source of muons, then available nowhere else. CERN has since developed a much better muon beam,1O putting Fermilab muon physics in limbo until a new muon beam designed to work with the TevatronH can be build. TABLE 2.6.--Tj Magnet lg: OUT la rg 0Vl Targ UHT Targ 0Fll F ocu 0H2 Focu ODl Focu OPT Bend 0Pl3 Bend N01 Firs “(02 F i rs. W03 F i r5, W0 Vert. )FO Focus m0 Focus 10) Focus E] 2nd E lll Ver t. In 3rd 8 W2 Vert. ”3 Final 103 Final 1E4] Final lEIz Flual \ 71 TABLE 2.6.--Typical Nl Beam Line Tune for 270 GeV Magnet £55302; Location Set Value Read Back Value (mm) (mm) OUT Targeting E99 (Neuhall) 110.0 lll.2 OVT Targeting E99 (Neuhall) l5.0 15.2 0HT Targeting E99 (Neuhall) 12l.0 117.5 OFTl Focus E99 (Neuhall) 96.2 92.7 0FT2 Focus E99 (Neuhall) 95.6 92.4 ODT Focus E99 (Neuhall) 2777.0 2690 0P1 Bend E99 (Neuha11) 3102.0 2978 0PT3 Bend E99 (Neuha11) 3177.0 3060 lNOl First Bend E100 Slave 4625-4636 1W02 First Bend E100 4332.0 4180-4200 1W03 First Bend E100 4832.0 4630-4640 1V0 Vert. Trim E100 25.0 l.06 lFO Focus. Quads E100 370.0 361.5 1D0 Focus. Quads E100 370.0 353.4 101 Focus. Quads E101 4175.0 4000-4048 1E1 2nd Bend E101 3862.0 3715-3730 1V1 Vert. Trim E101 120.0 7.62 1N2 3rd Bend E102 3712.0 3550-3560 1V2 Vert. Trim El02 off 0.0 1F3 Final Focus E103 970.0 947.5 l03 Final Focus El03 1000.0 975.0 1E41 Final Bend E104 4320.0 4237.5 1E42 Final Bend E104 S1ave 4223.7 2.8 Riding ti Apparatus By way the whole appa and focused fc enclosures l03 whose signals enclosure 104, Si.lnals to the E98 detectors Supplying the Pam-“9 througl the from of ti beam PCS, as we bank (unless u this informatic triggEr 1091c, Although the pr to be deteCted muon does inter “the "‘UOH and ing the target, Dt‘opom-Ond1 Ch Chambers and ma, radiany inward 72 2.8 Riding the Muon Through the Apparatus By way of summary, let us follow the path of a muon through the whole apparatus. Born by the decay of a pion, the muon is bent and focused four times as it travels through the beam line. At enclosures l03 and 104 it registers on the E98 PCS and hodoscopes, whose signals race downstream towards the electronics. Also in enclosure l04, the B counters are hit and fast cables send these signals to the trigger logic. As the muon enters the lab, the final E98 detectors as well as our upstream PCS and counter C1 are struck, supplying the final information needed to determine the momentum. Passing through the upstream apparatus of E398, the muon arrives at the front of the E3l9 target, hitting the remaining C counters and beam PCs, as well as the target hodoscope and missing the halo—veto bank (unless this muon is outside of the beam radius). While all of this information is making its way to the recording devices and trigger logic, the muon plows into the iron target/calorimeter. Although the probability of an interaction at a large enough angle to be detected by the spectrometer is quite small, we assume our muon does interact. The calorimeter counters register the passage of the muon and the hadron shower produced in the interaction. Leav- ing the target, the now scattered muon(s) register in the hadron Proportional chambers and pass into the spectrometer with accompanying hadrons, if any, stopped in the hadron shields. Traversing the spark chambers and magnets, the muons leave ion trails, while bending radially inward (outward) if their charge is the same (opposite) as that of the b arrive at the muons sail ou‘ the spark cha: the detector ' the mini-compc display, if de next muon to c this recorded muon interacti 73 that of the beam. Eventually, trigger banks are hit, and the signals arrive at the electronic logic to complete the trigger. While the muons sail out of the end of the apparatus to decay, the logic fires the spark chambers and all recording modules are gated on to receive the detector information. For the next 40 ms, this data is read by the mini-computer, written to tape, and processed for immediate display, if desired. Then all of the electronics is readied for the next muon to come along. The next chapter will discuss how all of this recorded information is analyzed to reconstruct the physics of muon interactions. -a. The or ment with Ferm target) to be 90 GeV). The . 000 of beam I designed to el different enerr Useful in the e Also, to maxim most of the Chat ”“0” run at w h 9 beam was p( check possible runs with inCic 1‘11th 00d TIN reactions), run possible SyStem numerous mm CHAPTER 3 DATA ANALYSIS 3.l Summary of Data Taken The original plans for E3l9 (as outlined in the formal agree— ment with Fermilab)1 called for 500 hours of beam time (protons on target) to be run at three incident muon energies (240, l50, and 90 GeV). The apparatus was to be rescaled in length by /X where h = ratio of beam energies for each different energy. This scaling, designed to eliminate most systematic errors when data samples at different energies were compared, turned out to be only marginally useful in the analysis of the E26 data and was not employed in E3l9. Also, to maximize high q2 and multimuon production, we decided to run most of the data at the maximum muon energy available (270 GeV) with a short run at l50 GeV to check energy dependence. The polarity of the beam was positive for most of the runs (since the u+ beam has higher intensity) although a run with negative polarity was made to check possible weak interaction effects. Other data taken included runs with incident hadrons instead of muons (to allow study of mN + ux and mN + uux within the same apparatus as comparable muon reactions), runs with reduced (l/3) target density (to understand possible systematic effects and compare to the E26 data), as well as numerous calorimeter and spectrometer calibration runs and various 74 tests and syst data taken. 3.2 Data Deco m This s was retrieved for the comput line analysis PDP records (c records (60-bi the CDC dehinv can library u. LL1660) to yea, “0k (EVBLK) - (GETRUN) could run or event 0, 10,000 EVEnts), ”10 number ( l2) wov and words 1 data transfer 5 heme Proven to Next ir tlDiCal numbers ing. AlthOUgh of counters and 75 tests and systematic studies. Table 3.l summarizes the experimental data taken. 3.2 Data Decoding and Initial Processing This section will describe how the data taken during E3l9 was retrieved from magnetic tape and converted into a form suitable for the computer algorithms which reconstruct the events. Such off- line analysis began with software routines to decode the two event PDP records (containing 768 16-bit words) into single event CDC records (60—bit words), since all of our data has been processed on the CDC machines at MSU and Fermilab. This task was done using the CERN library unpacking routine UBYTE2 with driver routines (LLREAD, LLl660) to read the tapes and place the decoded words into a common block (EVBLK) for transfer to all other software. Another routine (GETRUN) could be used if one quickly wanted to select a particular run or event on a tape (most tapes contain a single run with about l0,000 events). 0f the first 15 words in each event block, only the run number (word 2), event number (word 3), beam spill number (word l2) and words l3~l5 (which, if nonzero, signal an error in the CAMAC data transfer system telling off—line programs to ignore the event) have proven to be useful in analysis. Next in order are the scalers listed in Table 3.2 with some typical numbers and ratios shown in Table 3.3 along with their mean- ing. Although all of these scaled numbers were valuable as monitors 0f counters and electronics during the experiment (e.g., the B/C and B/HV - 5 ratios were vital beam quality indicators) and as data TBLE 3.1.--E3 hm Numbers l-28 0-40 0- 53 0-62 63- 73 M-80 0-90 0404 05412 H3432 0344] 142446 147462 l63-l72 hem ]78-221 222-394 305426 420465 467478 473542 543-566 507.583 591-594 Tape (9_ 002-0 023-0 034-0 042-0 050-05 058-06 063-06 07l-0T 078-0E OBI-08 070 084 085-09 094-09 099-l0 lOZ-ll ll8-25 253-26 268-29 297-30 305-34 346-35 357-36 369~37l 371%]; 76 TABLE 3.l.——E3l9 Data figgbers {spes) Type of Data Beam Analysis Uses 1- 28 002-022 Equipment Tests ut None 29- 40 023-033 Hadron Calib. Tests nt None 41- 53 034-041 Hadron Calib., Full Fe mt None (E0?) 54- 62 042-049 Hadron Calib., 2/3 Fe m+ None 63- 73 050—057 Hadron Calib., l/3 Fe m' None 74- 80 058-062 Hadron Calib., 2/3 Al m+ Calorimetry Studies 81- 90 063—069 Hadron Calib., Full Al 0+ Calorimetry Studies 91—l04 07l-077 Hadron Calib., Full CH2 m+ Calorimetry Studies l05-ll2 078—080 Hadron Calib., No target 17,11"+ Calorimetry Studies 113-132 08l-084 Spark Chamber Tests 0* None l33-l4l 070 Amplifier tests —— Determines relative gains 142-146 084 Spark 0n. Batwings 0+ Alignment 147—162 085—093 KB Spectrometer Calib. 0+ Alignment l63-l72 094-098 Hadron Calib. 2/3 Fe 0+ Calorimeter Calib. 173-177 099-10l Hadron Calib., Full Fe 0+ Calorimeter Calib. l78—22l 102-117 Initial data tests 0* Few tests useful 222-394 ll8—253 270 GeV data u+ Main data runs 395-426 253-268 270 GeV, l/3 target 0* Data, but low sta- tistics 427-466 268-297 l50 GeV, l/3 target Low energy data 467-478 297-305 CCM runs u Spectrometer Calib. 479-542 305-346 270 GeV data 0' Data runs 543—566 346-356 Hadron Calib. & Tests mfim‘ Calorimeter Calib. 567-583 357-368 m + u, up runs m+ Multimuons (Vector mesons) 584-590 369—370 Calorimeter tests n+ Uniformity 591—594 37l-372 n + u,uu runs 0+ Multimuons MBLE 3.2.--EE Wrd 1647 2%23 ZAZS %-U Scaler B'BV1 (B'SD'B (B‘SL'E (B'SH-E rlllllllll——— ’TTTTTIIIIIIIIIIIIIIIIIIIIIIIIIIllllllllsr------' 77 3 TABLE 3.2.-—E3l9 Scaler Assignments Word Scaler Word Scaler Word Scaler 16-17 B-Bv1 40-41 (B-s-BVTSpg 64-65 (5L)NV 18-19 B-sz 42-43 (B-SD-BVTSpg 66-67 (s)NV 20-21 B-Bv3 44-45 (B‘SL'BV35pg 68-69 SEM (protons) 22-23 (B'BV)evg 46-47 (8~5H-BV)Spg 70—71 SPILLS 24-25 85pg 48-49 (B-BV)evg 72-73 (B104)Spg 26-27 B'ngpg 50-51 -- 74-75 cspg 28-29 Bevg 52-53 -- 76-77 B'BD60 30-31 nevg = B'B;VSA' 54-55 (B'P)evg 78-79 PCS 32-33 (8581/)evg 56-57 sSpg 80-81 (Hv-s)NV 34-35 (B'SD'BV)eVg 58—59 sospg 82-83 TRIGS 36-37 (B'SL°BV)evg 60-6l SLspg 84-85 ADC Gates 38-39 (B'SH°BV)eVg 62-63 5HSpg 86-87 PC Resets TABLE 3.3.--Sc Scaler B-S-Ev + .9V9 B'SD-BV + evg B-P BDERR B.Bvdelay 1W evg .3 . “V/Bspg B Spg/SEM BSpg/m' m(Spil s ”g/BSNT B Sl39/BSpg( 1 04) AVél‘age flux X T targets/cmz \ 78 TABLE 3.3.—-Scaler Averages for a Single Run Scaler Interpretation Average per run B-S°B\LeVg + B'SD-BVev + 9 B‘P Standard trigger 7838 BDERR Branch driver errors lll.6 __ . . . 7 . B'Bvdelay Effect1ve 1nc1dent flux 7 83lx l0 u s B-S-BV Single muon trigger 7383 evg B-SD°BVevg D1muon trnger 865 B-Pevg Pulser tr1gger 376.7 B-S-BV' _4 B—————3219 Event rate .90536 X 10 evg THV-S /B Halo l02.53% nv spg -8 B ield 5.44 x lo spg/SEM u/P y . 6 E Bspg/no. Ofspills Incident p's per sp1ll .50272 X 10 B /B Dead time 46.56% 9V9 SP9 B B Beam tune 68-38% E spg/ spg(104) I Average flux x Average luminosity 2_0 x 1035 cm'2 # targets/cm2 per run _______________________.____._._______————————————-—-—-———‘—““"“_' quality moniti line analysis dead time, the beam particle: there are seve sealers must < too, are eveni (except pulser within a singl 900d event. 1 Wei signal (3 late and defin Danied by an a my moni tore (”055 Section PFESence of in that acceptab] item trigs _ iota] wigs]. The DC where Each bit fired, and 0 1a EOU”Hrs which tion DT‘OCQSS bl spectrometer. to work Nope” 79 quality monitors in the analysis, the most important scaler for off— line analysis is the flux [(8 . BVd)evg]. In an apparatus with no dead time, the flux of incident muons would be just the count of beam particles (i e., the scaler for BEAM = B - C). In real life, there are several effects which must be accounted for: (a) the scalers must count only when the experiment is ”live” meaning they, too, are event gated (e.g., Bevg); (b) since all of the triggers (except pulser) contain EV, accidental counts or multiple beam muons within a single beam bucket (l9ns) may sometimes inadvertently veto a good event. The flux can be corrected for this by forming a delayed _Vd signal (3 beam buckets after the trigger) to sample the accidental rate and defining flux = (B - BVd)evg (i.e., all beam muons not accom— panied by an accidental beam veto signal later). Flux was so care- fully monitored because it must be known to determine absolute rates (cross sections). Further corrections to the flux account for the presence of incorrect (BDERR) and pulser triggers and the requirement that acceptable events have only one beam muon [correction factor = (total trigs - BDERR — pulser trigs — triggers with O or > 1 beam)/ total trigs]. The flux for each set of data is included in Table 3.4. The DCRs used to record counter hits are shown in Table 3.5, where each bit of the original l6-bit PDP word is 1 if that counter fired, and 0 if not. The first two latches contain the trigger bank counters which were originally supposed to aid the track reconstruc- tion process by signalling the path of the “live” muons in the Spectrometer. However, the efficiency must be very high for this to work properly and, unfortunately, there were tWO PFObiemS W‘th TABLE 3.4.--Fl Data Sample 210 GeV 11+ Full Target 150 GeV 5' l/3 Target 210 GeV Full Target \ 80 TABLE 3.4.——Fluxes for Data Samples Data Sample (Be—Vd) evg Corrected Flux 270 GeV u+ 1o 10 Full Target l.2834 x lo l.0974 x lo 150 GeV p+ 1/3 Target 1.5915 x 109 1.3772 x 109 270 GeV p' Full Target 3.4457 x 109 3.0847 x 109 TABLE 3.5.--D( Aord Bi 2T6 l- 5- ll- 2l7 1- 6- TT- 218 1 2 3 4 5 6 l4 2L9 l- 9- 220 ]_ 457 1 2- l2 l3 l4 TS 8T TABLE 3.5.—-DCR Assignments Word Bits Latch Meaning 2l6 l-5 SAV Vertically measuring (E26) 6-l0 SBV Trigger bank counters ll-l5 SCV 2l7 l-S SAH Horizontally measuring (E3l9) 6-l0 SBH Trigger bank counters ll-l5 SCH 2l8 l B°P 2 B-S-BV' Trigger Bits 3 B-SD-BV 4 B-SL-EV 5 B’SHvBV 6 11 T4 PC Reset Reset for PC Latches 2l9 l—8 E98 BH 2 E98 Beam 9—l6 E98 BH 3 Hodoscope Counters 220 l—8 E98 BH 4 457 l PC Strobe Enable for PC Latches 2—9 TH Target Hodoscope l2 STEL Efficiency Telescope l3 BV l l4 BV 2 Beam veto counters 15 BV 3 the DCRs duri criminators w seem inefficiu meaning that 1 trigger may 5' since their re used only qua' halo from live The ne and PC start 5 “GM that one selecting ever trigger banks “V3 Again, certain small Since hodoscope latc ever, were Vit information ne “0“ of DCR an Dents having least unm th (193erde in S Spark Sfihnea set. each of the 36 82 the DCRs during part of the running: (a) the thresholds on the dis— criminators were set too high for some of the DCRs making the counters seem inefficient; (b) gate widths were too wide for part of the runs meaning that muons passing through counters well after (40-50ns) the trigger may still set the latches (especially for the beam vetos since their rate is very high). Thus, the trigger bank DCRs were used only qualitatively for special (multimuon) events to separate halo from live muons. The next latch contains information on the types of trigger and PC start signals generated for the event. Initially, it was hoped that one could find multimuons, or high q2 events, by simply selecting events with those triggers, but the geometry of the trigger banks and inefficiency in the latches have made this ineffec— tive. Again, these trigger hits were used in a qualitative manner on certain small event samples. Since multiple beam events were not analyzed, the target hodoscope latch has been largely ignored. The last two latches, how- ever, were vitally important since they contain the beam hodoscope information needed to determine incident muon momentum. A combina- tion of DCR and counter inefficiency contributes to ~l0% of the events having insufficient information to determine beam momentum (at least until the E98 PCs were fixed). The algorithm for this is described in Section 3.3. Spark chamber time digitizer readings(words 465-76l) con~ stitute a set of eight integers (most of which are usually 0) for each of the 36 wands (four views for each of nine chambers). At least one (usu Hmse spatial readings were l000 triggers. propagation al the analysis r digitizer read andv=(y-x X=al R=(s f The only diffi Sparks (height Sparks being t being So Close asSlglll'ng a 51° The cc to some arbitr as the Center coordlnates mt “ted by the n and the New degaugsed (see math/e1), Unc were aligned L 83 least one (usually two) of the integers represent fiducial sparks, whose spatial position is accurately known and whose time digitizer readings were determined for each run by averaging the values over lOOO triggers. Using this correspondence (and the known speed of propagation along each wand wire if only one fiducial is available), the analysis routine (LLWANDS) must convert the rest of the time digitizer readings into spatial coordinates x, y, u = (x + y)//2, and v = (y — x)//? via the formulae: X - alignnment :_(chamber l/2 width) x (l - 2R), R = (spark integer - lst fiducial)/(2nd fiducial - lst fiducial) The only difficult part of this process is handling clusters of sparks (neighboring wires hit). Since these tend to occur due to sparks being between wires far more often than actual particle tracks being so close (.7 mm), we chose to simply average clustered sparks, assigning a single spark to the midpoint. The coordinates of the sparks were initially found relative to some arbitrary axis shifted and rotated from our true axis (taken as the center of the toroidal magnets). Thus, the spark chamber coordinates must be aligned to this magnet axis. This was compli- cated by the magnetic field and multiple scattering in the toroids and the presence of the massive iron target. So the magnets were degaussed (see Chapter 2 ) and the target removed, giving muons a relatively unobscured passage through the chambers. The front four were aligned using straightahead muons from run l30 (the proportional chambers were the back five retain memory out of the cer the front four The ac chambers rela‘ Projected intc actual and pre scattering in statistics to each chamber 1 coordinates a1 bl-view basis hatched Coord‘ See Fl’gure 3.; axis, This f. maQAEts and t' Section 3.5 a! ashift or r01 oppome QUadi Cah.bmtion r1 rotated (real‘ < final 3] lgnme. 84 chambers were also aligned with this data, see Figure 3.l). However, the back five spark chambers were deadened in the center so as not to retain memory of ”stale” beam tracks. The beam had to be deflected out of the center (by the lO4 dipoles) to align these chambers with the front four. Runs ll3-l20 provided muons for this purpose. The actual alignment procedure began by aligning all of the chambers relative to each other. Straight lines in one group were projected into another set of chambers and the difference between actual and predicted spark positions histogramed (note that multiple scattering in the magnets smears these distributions requiring high statistics to determine the mean). The means of the histograms in each chamber being aligned were then subtracted from actual spark coordinates and the procedure was iterated. This was done on a view— by-view basis. Alignment of the separate views required histogramming matched coordinates (e.g., actual x minus calculated x = (U—V)//?; see Figure 3.2). The completion of this procedure left all chambers aligned relative to each other, but still not fixed to the magnet axis. This final step exploited the cylindrical symmetry of the magnets and the full momentum fitting algorithm (to be described in Section 3.5 and Appendix B). Since the field varied only radially, a shift or rotation of axis causes momentum differences between opposite quadrants for the mono-energetic muons of the spectrometer calibration runs (also Section 3.5). Thus, the axis is shifted and rotated (really just changes in alignment constants) until the quad- rants all balance to the same mean momentum (within 2—3%). The final alignment constants are shown in Table 3.6. PCA PC3 P 85 hadron hadron magnet magnet shield shield i .\ \\\1\ MNNW P04 PC3 PczU PCl WSC9 8 7 6 Figure 3.1 Aligning PC2,PC1, and the front spark chambers /\up x \\\\\\\ looking downstream V U \} \/ Figure 3.2 Conventions for spark chamber coordinate axes west NSC on PC * 86 Table 3.6 Final E3l9 Alignment Constants in cm. 1192152. X y U V WSC l .211 .742 :953 .521 2 .324 .557 .508 .148 3 .111 .611 .663 .391 4 .341 .606 .375 .136 5 .034 .190 .429 .189 6 .140 .069 .036 -.142 7 -.124 .057 .144 .122 8 -.020 .206 .255 .316 9 -.O34 1.122 .590 .327 X Y E319 PC 1 0.637 0.688- E398 PC 1 0.0 2 0.054 3 0.476 4 0.0 5 -0.435 Sever dure. Firstl alignment am the algorithr field of 100- line of up tc reconstructic slightly diff shifts of up must be consi The l Sisted of a 5 wires, Thed the correct 0 “9T9 Unnecess the wire spac 87 Several potential problems exist with this alignment proce- dure. Firstly, the chambers worked rather erratically for the early alignment and calibration runs with extra sparks possibly misleading the algorithms. Also, the degaussed magnets still carried a residual field of 100-200 Gauss which could cause deviations from a straight line of up to 2mm if all the fields were aligned. Finally, the old reconstruction and momentum fitting routines used for alignment give slightly different momenta than the final algorithm. Thus, alignment shifts of up to 2mm are possible and their effect on data analysis must be considered. The latched proportional chamber wires (words 88-215) con- sisted of a sequence of 1's and 0's corresponding to hit and missed wires. The decoding routines index the wires to their chambers in the correct order and then search each chamber for hits. Fiducials were unnecessary here since each wire has its own unique latch, and the wire spacing is accurately known. Hit wires were converted into Spatial coordinates according to the formula: X = Alignment + (wire spacing) x (hit wire number) — PC 1/2 width ASlain, the cluster ambiguity was resolved by averaging the positions. All of the experiment's proportional chambers are handled in the same manner to this point. However, the chambers have different numbers 0f Planes, so that matching to produce x—y coordinates (only done for E3l9 PCS since the x planes of the E98 PCS were not used) was different for thermore, the difficult for were aligned with the targ alignment prc removed at ti at the front (363) with al 1E4 dipoles ( runs could al uAStream. Da timed correct The final c011 The f EaCh01c the 2 Which is a me entering the was propmio calorl'llleter c1 USEd' After . alhlication 0' logs are Store (note that the consecutiVe a1 the ADC al 90r- 88 different for each chamber (Figure 3.3 details the matching). Fur— thermore, the long distances separating the various PCs made alignment difficult for some of the chambers. The downstream E3l9 PCs (l + 4) were aligned along with the front four spark chambers using run 130 with the target removed (note that any two chambers can start the alignment process since arbitrary initial shifts or rotations were removed at the final step of pinning the axis to the magnets). PCS at the front of the Muon lab was aligned using a regular data run (363) with all E98 absorbers out of the way. Since the field in the 1E4 dipoles (and their bend angle) was accurately determined, data runs could also be used to align the E98 proportional chambers upstream. Data from the final runs when the E98 PCs were finally timed correctly, was used to align both these and the beam hodoscopes. The final constants are listed in Table 3.6. The final decoding task involves the ADCs (words 229-456). Each of the 220 ADC words contains a single integer channel number which is a measure of the total charge (pulse amplitude times width) entering the ADC during the lOO ns gate time. This charge itself was proportional to the number of particles passing through the calorimeter counter for that ADC scaled by the gain of the amplifier used. After correction for the zero (pedestal) level of the ADCs and application of muon and hadron shower calibration data, the ADC read- ings are stored in their correct order from upstream to downstream (note that the first counter uses ADC words 324,325 and the rest are consecutive around this gap on the primary tapes). Full detail on the ADC algorithms and calibration is supplied in Appendix A. mg W=(i/3X+y V:(,)I'l‘]3-X U+V+W=O 89 L r PC3 V U = -y x = (w—v)//3 W = (/3 x + y)/2 y = (V + W - U)/2 V= (y-J3X)/2 u + v + w = O x=u' AL yv—t #3 l/\ I W V PC4 if U'=x W' = (73 y - x)/2 x = (u' — v' — w')/2 v'=-(x+/§y)/2 y= (w'—v')//3 u' + v' + w' = 0 Figure 3.3.-—E319 Beam Proportional Chamber Matching Conventions. 3.3 Beam Tre and Momentum Once motion conver of the muon s momentum vect ability to de advantages en procedure beg using the e31 PTOJECted ups SCODes from w dent muon ana Given Stage, subron MKS Tn the ((116th of th AOints (1.9. 3 At least tWO 1 Points. (NOte views must be correCt-) Ali single View 01 summarizQS the 90 3.3 Beam Track Reconstruction and Momentum Once the event tapes are fully decoded and the detector infor— mation converted to usable form (spatial coordinates), the kinematics of the muon scattering event must be determined by reconstructing the momentum vector for all muons (incident and final-state). Indeed, the ability to determine the incident muon kinematics is one of the great advantages enjoyed in muon (as opposed to neutrino) experiments. The procedure begins by determining the beam track (positions and angles), using the E319 beam PCs (numbers 3 through 5). The tracks are then projected upstream through the 1E4 dipoles to the E98 PCs and hodo- scopes from which the beam energy can be found, completing the indi- dent muon analysis. Given matched points (x, y coordinates) from the decoding stage, subroutine BEAMPC attempts to form all possible straight line tracks in the beam chambers. An important factor in determining the quality of track candidates is the match code of the contributing points (i.e., the number of views which are included; see Figure 3 3). At least two views must have hits for PC3 and PC4 to form matched points. (Note that if any view has more than one hit, all three views must be used to remove ambiguity about which of the hits is correct.) Although this holds for PC5 as well, sometimes only a single view or even no hits are allowed in this chamber. Table 3.7 summarizes the method and the types of beam tracks allowed. Note that PC5 hits must lie within a window of the projected line from TABLE 3.7.—-E 2nd Pas TABLE 3.7.-—Beam Track Algorithm 91 Decode Beam PC hits l Match Views E. F“_‘_‘ E— Form x, y4 linesin PC 3 and4 1 Project lines UJPC Search for hits T1 51 ‘h'l'l ound it 3 point lines f Cut lines on X2 beam angle line parameters Search for 2 point lines in PC3 and 4 1 Fit 2 point x—y lines Cut lines on beam angle Eliminate duplicate tracks Store 2nd pass line parameters [ Store lst pass Match Code Combinations (PC3, PC4, PC5) lst (3,3,2) (3,3,1) (3,2,2) (3,2,1) Pass (2,3,2) (2,3,1) (2,2,2) (2,2,l) 2nd (3,3,0) (3,2,0) (2,3,0) (2,2,0) Pass 2 point matches allowed if 1 hit in both views the downstrer caused by the After dimensional 1 ithm, which 1 (actually in: PCs contribu‘ :lU mr) are usually app1' intercepts a1 vertex deterr finding, The allowed us U Problems in“ Now v (Which is the maBnetic fiel upstream E98 Referring to Berated bend downstream mu is Clear that R1622. e12) tonne fUllCt e :L 2 pm], 92 the downstream PCs, whose size is determined by an extrapolation error caused by the wire spacing. After all lines have been found, they are fitted in the two- dimensional planes (x—z and y-z) by a standard straight line algor~ ithm, which returns the slopes and intercepts at the z=0 point (actually inside the calorimeter) and a chi-squared (X2) if all three PCs contribute. Very generous beam cuts (XZ/DOF.: 5, beam angles i 10 mr) are made to eliminate obvious bad tracks (stricter cuts are usually applied later in analysis). The matched points, angles, and intercepts are then stored (in common blocks) for later use in vertex determination. Table 3.8 gives statistics on the beam track finding. The high rate of success in finding a single beam track allowed us to ignore other events, avoiding the difficult vertex problems involved with 0 or more than T beam muons. Now with the beam track angle and intercept in the y-z plane (which is the direction of bend in the lE4 dipoles), the measured magnetic field and position of the magnets, and the hits in the upstream E98 PCs and/or hodoscopes, the beam energy can be calculated. Referring to the geometry of Figure 3.4 (which shows a highly exag- gerated bend angle and a slightly simplified situation where the downstream muon leaves at the center of the magnet for clarity), it is clear that, for small angles, L = R(01 + 62) and h = 1/2 R(922 - 012) from trigonometry and the usual expansion of sine and cosine functions. We solve for the two unknowns h = L(%§ - 6]), 02 = %-- 0], where 01 is the measured downstream beam angle and L/R t(w+Lw+n+U ENGQII G W u.QQF 93 0.0 o m.nw mew 0.0 o on mom Eocw om m.mm vnmm v.—_ me m.mm mmmx Im mom Eccw ow m.m_ mmPF —._ mm m.m mmm Uczoe uo: om muwumwpmpm Amcwcm Emom —.m ¢w¢ m.m mmm w.¢ mmv mxumgp Emma _ A m.mm mwmw N.vm FFNw v.0m vmow xuccu Eown _ m.N mam _.N ow— m.¢ mwv xowgp Emma oz I/(l moeumaumpm xuwce Emwm w c a 2m Fmowaxk & cam _m0wazH & cam Fmoquk +1 >mw om_ 1: >mw QNN +1 >mw cum mowgmwwmum Eewm11.m.m mgm

75 cm) 5. HPCs must register if track projects through them 8. Vertex cuts (3-dimensional) l. DMIN :_ .lSr + 2.0 r §_53 cm l0 r > 53 cm 2. -250 cm :_ZMIN i 600 cm 3. IZMIN — ZADCi :_400 cm if shower found C. Track cuts l. XZ/DOF 5 l0 2. DOF_: 2 (at least l back chamber has spark) BCODE 3 2.8 boo IRAD'_>_l (:1 of the back 7 chambers out of hole) 5. At least l/2 of the chambers searched must have sparks There are line in ar combinatic intercepts struction, vertex wit approach n resulting verse DMIh are subjec the target track reco shower, a closest to are also d No bACk into Varying ma 1i0” toroi. This is a . field dist: Um probab' Sp"951d out lOl There are six view combinations (UV, YV, XV, YU, XU, XV) allowing a line in any view to participate in up to three of them. Each such combination constitutes a potential track and its line slopes and intercepts (at NSC 8) are stored. Before attempting further recen— struction, however, each candidate has its full three—dimensional vertex with the beam track calculated via the distance of closest approach method (described more completely in Appendix B). The resulting vertex consists of a longitudinal ZMIN point and a trans- verse DMIN measure of distance of closest approach. Both of these are subjected to strict cuts which insure a good vertex (located near the target) and provide a very strong rejection of halo before the track reconstruction proceeds further. When the calorimeter finds a shower, a cut is also made on ZADC—ZMIN so that the tracks pointing closest to the actual interaction point are selected. These cuts are also detailed in Table 3.9. Now the matched front line track candidates must be traced back into the magnetic spectrometer, taking account of the radially varying magnetic field and energy loss and multiple scattering in the iron toroids, in order to predict where sparks will be in the chambers. This is a very difficult problem in general, especially because the field distorts the symmetric multiple scattering distribution causing the probability of finding the track in the back chambers to be spread out asymmetrically and over a broad area. The method for tracing approximates the magnets as single bend points and uses an expansion of the complicated coordinate functions in the variable l/P up to 2nd dix B. At NSC 7 is r with all l opened abc reflecting and chambe opened in Sparks wer using the necessary Sparks can )5 availab detailEd e‘ aPpearing ifwithjn . deadened r. Hoc arWild the 1ated devig correyatior idistinctj searched ar (the aCtual lOZ up to 2nd order. This algorithm is described in detail in Appen- dix B. At each of the seven remaining spark chambers (note that NSC 7 is now properly re—considered as a true spectrometer chamber, with all lines defined at NSC 8), a spark search window must be opened about the predicted muon position, with the size of this window reflecting multiple scattering and measurement errors in all magnets and chambers upstream. Initially simple rectangular windows were opened in each chamber to obtain sparks in all four views. These Sparks were matched to form all possible three—dimensional points using the routines SMAT and UVXY2. Very complicated indexing was necessary to determine which sparks were available and how many sparks contributed to each point (the match code). Further detail is available in Appendix B. The matching window (set to l.2 cm by detailed event studies) effectively eliminates extraneous sparks appearing in only a single view. Note that sparks are matched only if within the active areas of the chambers (not within the supposedly deadened region of the last five NSCs). However, although meaSurement errorssimply contribute circles around the predicted positions, multiple scattering causes corre— lated deviations, due to the presence of the magnetic field. Such correlations dictated the formation of another, smaller window with a distinctive hourglass shape, in order to minimize the area to be searched and maximize the probability of selecting the correct spark (the actual algorithm in subroutine SELECT is again discussed in Appendix quite lar results Tl spark chai with good cuts to pi ”bad" spai down and s llSC6 was l higher rac it: My Lb) no SpE then too 5 call that behind whi Spark pass Position N an estimat tion Ptoce This momen Chamber (n magnet and The .3190”. mUItl'muons track has I T03 Appendix B.) Note that the simple rectangular windows have to be quite large to insure good spark finding efficiency and this often results in finding extraneous sparks (which are always present in spark chambers). The hourglass window rejects these incorrect sparks with good efficiency. Each selected point was subject to several cuts to protect the developing track from veering off course due to ”bad“ sparks. This was particularly important at NSC6 due to break— down and stale beam sparks primarily in the middle; so the spark at NSC6 was required to be out of the magnet holes or at least at a higher radius than that at NSC 7. Further spark search is terminated if: (a) the radius of the projected track exceeds the magnet radius; (b) no sparks were found in two consecutive chambers (because it is then too easy to mistakenly connect segments in front and back and call that a track); or (c) the track crosses the spectrometer axis beyond which the tracing routines cannot follow it. If more than one spark passed the cuts, the spark closest to the predicted track position was used. At each chamber, the single chosen point allows an estimate of the track momentum using a simple chi—squared minimiza- tion procedure (subroutine RCFIND and CHIS discussed in Appendix B). This momentum was used to update the predicted positions in the next chamber (note that the final estimate was obtained after the last magnet and used to predict positions in the back three spark chambers). The algorithms have been checked visually for many events (including multimuons) and were able to follow tracks quite closely. After the track has been located in all seven back spark chambers (or lost along the sparks we searched hrtheb fields, t multiple Points we' Although : and good < FL in Table 2 out also 1 criteria 5 Sparks agr anindicat describes bACk seven (frequentl; 9”) matchv track is Ol peter. An ”is develop Ofsinn‘lar ca"didates of frOnt li l04 along the way), the front chambers (NSC 8, 9, and HPCS), from which sparks were already found in views to give front lines, are again searched for sparks. This time the method used is the same as that for the back chambers, although now, in the absence of magnetic fields, the search windows can be simple squares consistent with multiple scattering in the hadron shields and measurement errors. Points were matched in exactly the same way as in the back chambers. Although somewhat inefficient, this procedure insures consistency and good connection between front and back parts of the track. Further cuts were then made on the complete track as shown in Table 3.9. Developed empirically to reject "junky” tracks with— out also losing good ones, these cuts all involve track ”goodness" criteria such as: (l) chi-squared, which tells how well the actual sparks agreed with predicted positions, (2) degress of freedom (00F), an indication of how many chambers contributed, (3) DMIN, which describes vertex quality, (4) BCODE, the average match code in the back seven chambers, telling how many views normally contributed (frequently tracks with mostly two point matches are halo or improp- erly matched track segments) and (5) IRAD, which insures that the track is outside of the hole (l5.24 cm) somewhere inside the spectro— meter. An overall quality factor QF = EEgQE + %%P — T5(%§E) - Q¥éfl was developed to choose the best representative of the large number of similar (x and y positions within 2 mm at half the chambers) track candidates (due to the great redundancy in matching all combinations of front lines). After the final sorting of tracks (subroutine TROUT), onto out are writ muon can event nu In the n along wi‘ ciencies each fine energy we Vector fc Squared g [momentum Ddrametri L9$0lutio toarmve T FINAL) wa Changes iv track was Very Simi‘ positions 105 TROUT), only nonidentical tracks should be left and these were written onto output tapes in the format of Table 3.l0. Note that all tracks are written out, even if they are not multimuons. Potential multi- muon candidates (more than T reconstructed track) have their run/ event numbers flagged on a separate file for later visual scanning. In the next two sections, the momentum analysis of these tracks along with the multimuon finding procedures and reconstruction effi- ciencies will be discussed. 3.5 Spectrometer Track Momentum Fitting Track reconstruction determines the position and angles of each final state muon at the end of the target. However, the muon energy was only estimated in MULTIMU. To obtain the full momentum vector for the muons requires fitting the track, by forming a chi— squared which is a function of the five independent variables [momentum p, x and y angles (6X, By) and intercepts (x0, y0)] that parametrize the muon. This chi—squared, accounting for all chamber resolution and multiple scattering correlations, is then minimized to arrive at the final values of the momentum vector. The momentum fitting program used for this experiment (called FINAL) was quite similar to that of E26, although several algorithm changes improved its range of applicability. After the reconstructed track was read from the secondary tapes, a tracing routine (TRACE), very similar to that used in reconstruction, generated predicted positions in the chambers and a momentum estimate was obtained (in TABLE 3.l .— _ Vord 4-6 PC5 7 # S' T‘ECI 8-l7 HPC‘ LB-ZO PC5- ZL Blav 22-3l HPC. 32 Blav 33-42 HPC. 43 Blar 44-45 Apt. 46 vsce if f 47 vsc7 n f 48-53 wsc 54~56 Beam L P , ox 57‘58 Beam (X0, 59‘“ Trac (Px, 62‘“ Traci (X, " \ T06 TABLE 3.l0.--Secondary Tape Format Nord Content Type Nord Content Type 1 Run x TOOOOO + Event I 64 Chi-squared x2 R 2 Track Number I 65 Degrees of Freedom R (DOF) 3 Flux I 66 ZADC (= "024 if not ) R single showers 4-6 PC5-3 x Coord. R 67 E summed over R Hadron (all showers) 7 # Sparks manually R 68—7l Track (x,y) slopes and R reconstructed intercepts 8—l7 HPC—NSCT x Coord. R 72 2nd spark chamber R pulled if necessary l8-20 PC5—3 y Coord. R 73 lst spark chamber R pulled if necessary 2T Blank R 74 # HPC hits (packed) I 22—3l HPC-NSCl y Coord. R 75 # NSC sparks (packed) I 32 Blank R 76 Match codes PCS I (packed) 33—42 HPC—NSCT x fitted R 77 # Spectrometer Tracks I 43 Blank R 78 # Beam tracks I 44-45 HPC—NSC9 y fitted R 79-83 DCRS l, 2, 3, 4, 6 I R R 46 NSC8 y fit +--l024 84 BCODE if fit failed 47 H507 y fit + 0.0 R 85 DMIN R if fit failed 48—53 NSC 6-NSC T y fitted R 86 ZMIN RS 54-56 Beam momentum R 87-88 Accepted, found lines/ I ,P , P _) view ox oy 04 57—58 Beam pos. z=0 R 89 Chamber where track I (x0, yo) leaves spectrometer 59-6l Track momentum R 90 NSC match codes I (Px, Py, PZ) (packed) 62-63 Track)pos @ Z=O R 9l-l50 Packed ADCS I x, y the same chi-squat were form (CHIF) se the weigi measureme each chah chambers initial m the deriv Ezem, detailed the momen. vaTUes of Ti lzed in AT Severed ar QVents (pa is the abi ChL‘SAUare rect Spark instead of for each 6 Ca by CMoan 107 the same manner as in MULTIMU; see Appendix B). Then the rigorous chi—squared definitions (which take full account of correlations) were formed for the back seven chambers (CHIB) and the front three (CHIF) separately (Appendix B). The total chi-squared (CHIZ) was the weighted sum of these two with weights determined by the average measurement error in front (.2 cm) versus back (.l cm). Note that each chamber should really be assigned a separate value, but the chambers are quite similar. Once the chi—squared was formed for the initial momentum guess, minimization was accomplished by calculating the derivatives of CHI2 with respect to each parameter, setting them to zero, and solving for the five parameter changes required (again detailed in Appendix B). The entire procedure was iterated until the momentum changes were less than l%. The final fitted sparks and values of the five parameters were written on the secondary tapes. The algorithm changes made in these FINAL routines (summar- ized in Appendix B) were developed by detailed study of the chi— squared and parameter varying routines for individual, difficult events (particularly extreme energies). The most important of these is the ability to remove up to two "bad” sparks from the fit if the chi—squared was too large. So even if reconstruction selects incor- rect sparks, the track was usually preserved and fit adequately instead of being cut. Sparks pulled were flagged on the output tape for each event. Calibration of the momentum fitting algorithm was determined by comparison to special data calibration runs and to Monte Carlo predicti this pur spread iv (called I beam pro; Cyclotror cases, iv these rur obstructi PCS are c determine and beam into the the targe alid energ The metho STTUCtiOn for the m, 0f the lal is possib' grammed (l Scatteyjng of the lnc the Specty TASSe dTST T08 predictions. There were two sets of data taken specifically for this purpose, in which the iron target was removed and the beam was spread into the spectrometer by upstream magnets. Runs l47-l62 (called KB runs) used special, small toroids located near the E3l9 beam proportional chambers, while in runs 467-478, the Chicago Cyclotron air-gap dipole magnet was used (CCM calibration). In both cases, incident energies ranged from 25 to 250 GeV. The analysis of these runs was complicated by energy loss and multiple scattering in obstructing material of the upstream E98 apparatus. Since the E3l9 PCs are generally not hit by the deflected beam, beam energy must be determined from the method using only the E98 proportional chambers and beam hodoscopes. A further problem is that the entrance angles into the spectrometer are much shallower than those for data with the target in place. Since the calibration is a function of angle and energy, comparison of the CCM and actual data runs is difficult. The method of analysis for these calibration runs used the old recon- struction/fitting routines (VOREP) to determine spectrometer energy for the mono—energetic muons. The muon is then traced to the front of the lab (accounting for energy loss in the E98 apparatus as well as possible; see Figure 3 5). There the variable l/E1 is histo— grammed (E1 itself is somewhat non—Gaussian because of multiple scattering which is proportional to l/E1) and compared to the mean of the incident energy l/EO. The calibration consists of shifting the spectrometer E (with a multiplicative factor PLOSS) to make l these distributions have the same mean. Note that the width of l/E1 lh I i I In IE E I I I I I l I {It mcm1\\\ £08050 AU. 2 Upwmsm COKHO~UAU iuowaw :OLUMS Nam NO“. won awn OWMUeSOv 200 :owuegnepwu swumeoeuomam map mcwgzv mzuegmagm mfimm use mmmm do p:o2ma--m.m weaned oFMUW op go: we mewZeLv m_;H Ase c? mwucmpmwuv Empmzm wocwgmemc 284 cos: cw mmpmcwucoou mew means:z 109 mmm mmu o mow: m.wau vmmfiu ommfiu _ CODE eaueepeee Apmcmmz :ocuopoxu emuweo n_m_;m N -uomaw cactus nmmmu zoo gives the sumnarize I rections, result. Carlo cal is fully Chapter 4 similar 1: the end 0 The resul data. I hf Points cise calil cdiibrativ available HLStogtdmr hives boti 3”th ea: Tables 3_] Sis, WAEre energies , TTO gives the resolution of the magnetic spectrometer. The results are summarized in Table 3.ll. Due to uncertainties in beam momentum and energy loss cor- rections, there was considerable doubt about the CCM calibration result. As a check (and refinement) of the calibration, a Monte Carlo calculation was made (using the updated E26 program MCP which 5 and briefly outlined in is fully described in several theses Chapter 4). Initially the program was run at energies and angles similar to the calibration runs and the true energy distribution at the end of the target compared to the reconstructed distribution. The results are shown in Table 3.l2 and compare well with the CCM data. The above calibrations were quite limited in range and number of points sampled in the E1-e plane. In order to develop more pre- cise calibration and resolution functions needed for the Monte Carlo calibration, MCP events were generated over the whole E1 and a plane available to multimuon events and then binned in a TD x TO array. Histogramming the quantity A=[—‘-l—l / . Efit E Efit true gives both calibration and resolution data over the whole range and allows easy application for either data or Monte Carlo corrections. Tables 3.l3 and 3.l4 summarize the results used for multimuon analy- sis, where the calibration shifts were applied to the actual data energies, but the resolutions were used in Monte Carlo calculation. L___‘ RUN N0 N0. ENi 471 1 470 1 E : 469 comb 473 474 Calibre ELMC) Table 3.ll Calibration of the Spectrometer using the CCM ABA ABBA? 6.59 “5265’ 0“ > EVENTS (Ea-E We 471 250 248.4:1.0 243.533 9.5% 3488 2.0% 470 200 200.3:0.5 199.3:.3 9.4% 5528 0.5% 468 150 149.5:0.4 149.332 8.9% 3098 0.13% 469 150 l49.1:0.4 148.613 9.1% 2954 0.35% comb 150 149.4:0.4 149.0132 9.0% 6052 0.25% 473 100 98.9:0.24 96310.2 9.4% 6055 2.6% 474 50 47.56:.14 45.89:.08 9.3% 2665 3.5% Table 3.12 Calibration of the Spectrometer using Monte Carlo Data E(MC) E(reconstructed) 0(E) EVENTS (E(MC)-E(RE))/E(MC) 250 251.831.17 1.8% 699 -0.7% 200 201.36:.21 1.6% 228 -0.7% 150 150.91:.08 1.4% 631 -0.6% 100 100. 561.08 1. 2% 223 —0.6% 50 49.51:.04 1.2% 274 +1.0% Energy (GeV ) TABLE 3 Top num Bottom Each bi 300 if 270 ———— 240 ~——— 210 ~——- —I Ln 0 __a N O 90 ~‘._ 60 -._. 30 -eez Energy (GeV) 112 TABLE 3.l3.-—Positive Muon Calibration Top number is the energy shift (in %) to be applied to data. Bottom number is the resolution (in %) used with Monte Carlo. Each bin contains 3_lO events. 300 - 9.9 - 3.5 0.1 - 6.8 —11.7 17.1 8.6 9.2 12.1 18.4 -— —— —— 270 - 4.3 + 0.2 + 1.9 + 0.6 - 7.0 — 7.5] 13.9 8.9 10.4 10.8 16 1 18.2 ——- —— 240 - 0.1 + 1.7 + 3.8 + 2.4 + 3.0 — 2.4 - 7.7 12.1 8.7 8.9 10.9 15.4 21.8 26.5 -—- 210 + 2.6 + 3.0 + 3.9 + 4.9 + 6.0 + 3.4 +13.3 10.8 8.3 8.1 10.2 17.5 22.0 20.6 -—— 180 + 3.2 + 3.9 + 6.0 + 8.0 + 8.2 +12.9 +16.0 12.3 9.0 8.1 11.4 17.4 20.4 22.0 -— 150 + 2.2 + 3 9 + 4.9 + 6.7 +10.3 +16.l +19.1 11.9 8 1 8. 11.1 18.1 23.7 25.0 ~—— 120 + 2.7 + 3.9 + 4.6 + 8.6 +13.7 +18.0 +20.9 +26.0 12.4 9.6 8.9 11.2 17.4 26.4 29.7 29.9 90 + 4.2 + 3.4 + 5.7 + 8.5 +11.2 +20.4 +27.2 +42.1 15.8 9.9 8.3 10.2 15.9 30.5 34.5 32.5 60 __ + 4.6 + 7.0 + 7.8 +10.0 +19.7 +48.1 +60.9 9.5 9.0 9.8 12.7 32.9 50.8 55.3 30 __ + 4 9 + 7.9 + 8 5 +11.5 +13.6 +17.5 +28.7 21. 12.6 10 2 12.6 15.5 25.7 38.7 0 0 16 32 48 64 80 96 112 128 Polar Angle (mr) Energy (GeV) (‘0 O TABLE 3. ———— —-————— Top numi Bottom r Each bir 300 r, 270 e—~ 240 ~ 90\ 60\ 30\ Energy (GeV) 113 TABLE 3 l4.--Negative Muon Calibration Top number is the energy shift (in %) to be applied to data. Bottom number is the resolution (in %) used with Monte Carlo. Each bin contains Z'lO events. 300 - 3.5 - 5.7 — 0.9 -10.9 -16.2 ___ ___ 11.8 l0.8 8.2 14.8 22.5 270 - 2.2 - 0.8 - 0.6 - 5.0 - 9.071 ___ ___ .__ 13.4 9.6 10.6 13.7 2l.8 240 - 1.1 + 2.2 + 2.8 + 2 4 + 1 2 - 0.5 ___ ___ 14.0 9.7 10.0 13 8 15 6 19.2 210 0.0 + 3.4 + 4.0 + 6 2 + 4.8 + 5.6 +15.6 __ 12.8 9.2 10.4 12 6 17.4 20.2 15.1 180 3.3 + 4.1 + 4.6 + 8.5 + 9 3 +11.3 +14.6 __ 10.7 9. 9.6 14.6 23 0 24.7 24.7 150 + 1 8 + 3 + 5.1 + 6 +12.2 +17 3 +21.4 __ 11 7 3 10.2 15 9 22.4 25.3 21.9 120 + 2.0 + 1 + 5.7 + 6.8 +15.9 +21 7 +26.0 +30.7 9 11.7 9 4 9.6 15.2 23.5 27.0 27.1 30.9 0 + 1.7 + 3.2 + 5.0 + 9. +12.1 +23.7 +28 9 +41.0 60 11.1 9.9 10.1 13.2 22.7 35.9 35.6 40.0 — 0. + 3.5 + 5.2 + 7 +10.4 +34.2 +47 1 +66.5 3 11.3 9.9 10.5 13 2 21.0 48.4 51.0 28.6 0.__ - + 4.7 + 7.6 + 9.7 +12.3 +16.1 +29.8 +39.6 0 21 8 11.2 12.0 15.3 21.8 23.0 34.7 35.1 0 16 32 48 64 80 96 112 128 Polar Angle (mr) 3.6 Mul was to f ples. l plished list of most are cient me cussed e cator. target, muons th- Showers 1 est, yet 4012 gray Shows any tional Cy highets. events we on 9Vents tic Pdtte hi the pr Scdnning 114 3.6 Multimuon Finding The goal of the data analysis (for this dissertation, anyway) was to find as many multimuons as possible from the E3l9 data sam- ples. The remaining discussion will focus on how this was accom- plished given the tools of the preceding sections. The end result of the track reconstruction programs is a list of event numbers, a few of which are true multimuons, although most are single muons combined with halo and extra sparks. An effi- cient method of picking out the true multimuons was needed. As dis- cussed earlier, the dimuon trigger was not a very good indi- cator. The calorimeter often indicates when two muons leave the target, but no algorithm I tried could overcome problems like two muons throughout the calorimeter (halo), noise in the ADCs, and showers near the end. The method settled upon is the oldest, slow— est, yet most reliable one; the events were displayed (on a Tektronix 4012 graphics terminal) and visually scanned. The display program shows any of the four views of the spark chambers and the propor- tional chambers, along with Options to view trigger banks, ADCs, and magnets. Paper plots can be made of any event (and all multimuon events were plotted). The reason why scanning works so well, even on events where the computer algorithms fail, stems from the fantas- tic pattern recognition ability of the human eye and brain, in spite of the presence of considerable “noise.“ However, the problem with scanning is that it takes a great deal of time (even scanning roughly 2.5% of the data took several man-years). Undergraduate college students criteria tually t deciding of the p responsi as a qua The domi: For most nificant' (eSpecia' hitting . Of the 5| low angli Causing 1 fhiding t B" X 1]” Of aPPPO) required were com; form X-Y fitting 1 Shieptit 115 students were easily trained to recognize multimuon events, given the criteria shown in Table 3.15. The more experienced scanners even- tually took over supervision of the effort, even to the point of deciding which events were worth plotting. The final classification of the plots (into eight categories shown in Table 3.l6) was my responsibility. As multimuon events were found, it became clear that as many as a quarter of them had at least one poorly reconstructed track. The dominant reasons were spark chamber inefficiency and breakdown. For most tracks, a single spark missing or incorrect does not sig— nificantly harm the reconstruction or momentum fitting process (especially with the spark pulling algorithm). However, for tracks hitting very few chambers (e.g., tracks bending quickly out the side of the spectrometer) or for tracks very near the toroid hole (mostly low angle, high energy muons), such problems can be disastrous, causing the momentum fitting to fail or give incorrect answers. To remedy this, a procedure was developed for manual spark finding by direct measurement from the plots of the events. The 8" x ll“ size plots afforded a resolution (in real spatial coordinates) of approximately 2 mm, sufficient for most tracks. Most events required the measurement of only one spark, although a few tracks were completely re-measured. The sparks are aligned and matched to form X-Y coordinates. The track can then be fed to the momentum fitting program in the usual manner. Of course, this procedure is susceptible to possible bias. To check for this, several events, N < (D "S c—o- 2A 28 TABLE 3.15.-—Scanning Criteria 116 Examine U and V views. Search for evidence of 2 or more spec— trometer tracks. If found, examine X and Y. Vertex must appear to be within the target and not change from view to view. Use trigger bank counters and beam vetoes to judge if tracks ”live." HPCs also helpful. Examine ADCS to see if 1 particle incoming and :_2 leaving target. If still in doubt, plot the event for detailed examinations. TABLE 3.l6.--Multimuon Candidate Types Type Description lA Definite trimuon. Tracks traceable. TBCs and calorimeter agree. lB Questionable trimuon. Tracks uncertain; TBC, calorimeter information not clear. 2A Definite dimuon. Two clear tracks with TBC and calorimeter consistent. ZB Questionable dimuon. One or more tracks uncertain. TBC or calorimeter inconsistent. 3 Possible dimuon but 1 track in the magnet hole region. 4 Interesting events (eg. high q2) but not multimuons 5 Not a multimuon (usually 2nd track turns out to be halo or stale beam). which ha re-fit. in all c. not be f kinemativ kinemativ lations 1 which ha‘ MSU (in ' events i1 or histog i can occur structior 01‘ by USE ”0 Ate-Sc Ale inde; the effm data Sam; F grams to SBECial h VOREP con one htogr high ()2 ( 117 which had been adequately reconstructed and fit, were measured and re-fit. The result was quite stable and accurate to within 10% in all cases. Note that some multimuon events had tracks which could not be fixed. These events are, of course, not included in the full kinematic samples to be presented in Chapter 5, although partial kinematic information is available for most of them and rate calcu- lations must count these events. The complete samples of events which have fully determined kinematics are maintained on tape at MSU (in the secondary tape format), with tracks arranged within the events in order of decreasing E]. Analysis programs to apply cuts or histogram various kinematics can be run directly on these samples. Potential losses and kinematic biases in multimuon finding can occur in both the reconstruction and scanning phases. Recon— struction problems can be checked by comparison with other programs or by use of “mass” scanning (visually examine raw data triggers with no pre—selection). Scanning losses can be understood by doing multi- ple independent scans on the same events. The following describes the efforts made to determine these losses for the main (270 GeV p+) data sample. PASSZ has been compared with three other reconstruction pro- grams to estimate its single muon efficiency; VOREP, PASSl and a special high efficiency version of MULTIMU called PASSOUT. The VOREP comparison was a visual scan study of the events missed by one program and found by the other for low q2 (:BGeVz/cz), and 2 (3 40 GeVZ/cz) regions. The results implied that the high q inefficie are lost is not hi highlight part of t similar f called PA in front applied t. extra evei the ratio 11 for @9111! extremely Slllailer 86 results 3p hULtimuong efficiency a"4 the be this using 015 GeV 1 Nu dichotomy. been re. SC Shh" in 1. 118 inefficiency of PASS2 was < 10%, except at very high q2 (where events are lost because they miss the HPCs and the front chamber efficiency is not high). The comparison with PASSl events on the other hand highlights any potential problems with reconstruction in the back part of the spectrometer, since the two versions of MULTIMU use similar front algorithms. Finally, the efficient version of MULTIMU called PASSOUT (basically the only differences are added redundancy in front lines and wider cuts making mugh longer running times) was applied to events missed by PASS2 on 28 data tapes yielding 3820 extra events with tracks (or around a 7% inefficiency). The shape of the ratio (PASSOUT—PASS2)/PASSZ is seen in Figures 3.6 and 3.7. Independent of computer algorithms, reconstruction efficiency for multimuons can be determined by mass scanning. Since this is extremely time—consuming, only two u+ tapes (runs 280 and 363) and smaller samples of u- and 150 GeV data were mass scanned. From the results shown in Table 3.11 PASS2 is clearly an efficient finder of multimuons (>92% for energies > 5 GeV). At very low energies, the efficiency falls off dramatically because of front chamber losses and the bend in the first magnet. Instead of trying to correct for this using the low statistics from mass scanning, a cut in energy of 5 GeV is imposed on all further kinematic distributions. Multiple scans were a natural outgrowth of the PASSl—PASSZ dichotomy. However, at least 30% of the PASSZ events have themselves been re-scanned. The details of the scanning efficiency checks are shown in Table 3 T7. The combined efficiency shown there is 119 .thmcm CODE AmcIumva UmLmemum .w> hucwwuwurwmcH :OwuszHWCOme Aw mmmag mzumm w DZHH4:Zvn.m.m wLmem 00"chN l' 00'? 1' 00'8 r on'it (lNEOHSd) A3NBIUIJJSNI OD'S! up» oo.w:u oo.om~ oo.mww oo.emw eo.w»u ee.om~ oe.m- eo.oo~ eo.we no.0» o _LLLLLLTB 1 o 9 e e + & % fi fi % ++++ J 0'03 _ .1 00000 c 7 0 NM 3. a . a by Bo e oocmN 00.0N Dacha oowou 6626 66... W nhzmommmo >UZMHUHLLMZH m8 A 120 09° # .00 413.00 0.00 60.00 THETH [H8903 ”0.00 3.00 20.00 3'0 igure 3.7.--MULTIMU (PASS2) Reconstruction Inefficiency vs. Scattered (Leading) Muon Polar Angle. 70.00 giving Hc mass 5 Bi co . Multih PA 8 trim PA rescan and 89 121 TABLE 3.17.—-Finding Efficiency A. Multimuon Reconstruction Efficiency Two u+ data tapes scanned represent about 1.5% of full sample. Twelve dimuons found by PASSZ and 19 found by mass scan giving only 63% efficiency. However, requiring all energies 3_5 GeV gives only 13 mass scan events making efficiency of 92.3% Broken down into components, (83 :_5)% dimuons (96 :_5)% trimuons R = Reconstruction efficiency = B. Multimuon Scanning Efficiency PASSl events not found by PASSZ scan: 25 dimuons (5.6%) and 8 trimuons (12.5%). PASS2 multiple scans: 9.5% of the total (1.61 x 104) events rescanned yielding average efficiencies of 77.8% for d1muons and 89.7% for trimuons. 83.9 :_5)% dimuons S = Scanning efficiency = (92.6 + 5)% trimuons C. Multimuon Combined Efficiency (70 :_7)% dimuons Finding Effiency E R x S = (89 i.7)% trimuons ._~_______-___¢___‘________fl____.___________‘___________._______________ necessar; lized M01 only on 1 other sah 122 necessary for all rate calculations and also to compare with norma- lized Monte Carlo predictions. Note that efficiences were obtained only on the 270 GeV u+ sample and are assumed to be valid for the other samples too. 4.1 Phi Calculat insuffic being me“ apparatus Which the ent in ti monetary aPPc‘vratus Sical mod CthTicat thei r We id) Severe dahd. witl compdl‘isor cal (Compt aSimulatE This metho ”hit (th CHAPTER 4. MONTE CARLO ANALYSIS AND MODEL CALCULATIONS 4.1 Philosophy of Monte Carlo Calculations The data taken in modern particle experiments is often insufficient for a complete description of the physical process being measured because: (a) the acceptance of the experimental apparatus (defined for each kinematic region as the ratio of events which the apparatus could detect to the total number of events pres- ent in that region)is not uniformly 100 percent, usually due to monetary and space limitations; (b) independent of geometry, the apparatus is never completely efficient (hardware failures); (c) phy- sical models, with which the data is to be compared, are often very complicated with few unambiguous features (e.g., mass peaks) and their predictions are usually greatly modified by acceptance; and (d) several physical processes are frequently responsible for the data, with separation possible only after detailed rate and kinematic comparisons. The most common solution to these problems is numeri- cal (computer) calculation of physical cross sections, folded with a simulated apparatus which accounts for acceptance and efficiency. This method, called Monte Carlo simulation,1 uses random numbers to select (throw) particle kinematics and calculates the probability 123 that the ciency), variation the magnc Although single mu tribute t Programs phi los0ph; give large Productior meson proc matic cuts 50 small t be10nd dis Th1 deve10ped 1 E26. Since described ,— employed by hliversjty models for outhhed (s. dud Chhllldre: 124 that the experiment would detect the event (acceptance and effi- ciency), if nature produced it (cross section of the model). For both single muon and multimuon parts of E319, the rapid variations in acceptance due to angular and energy limitations of the magnetic spectrometer have made Monte Carlo indispensable. Although deep inelastic scattering is known to be responsible for single muon data, all of the models discussed in Chapter 1 may con- tribute to multimuon events. The complexity and cost of Monte Carlo programs forbade any attempt to model all of these processes. Our philosophy was to simulate only those models which were expected to give large rates and nondistinctive kinematics (especially charm production, m/k decay and QED tridents). Heavy lepton and vector meson processes lead to clear experimental signatures so that kine— matic cuts would isolate these signals. Their expected rates are so small that the data probably could supply little information beyond discovery, making Monte Carlo calculations unnecessary. The main Monte Carlo computer program used for E319 was developed by A. Van Ginneken (Fermilab) for the previous experiment E26. Since some of its methods are novel, the program will be described in detail (Section 4.2). An independent program was employed by a group of theorists (represented by N. Y. Keung) at the University of Wisconsin (Madison) to calculate several different odels for comparison with our data. This method will be briefly utlined (Section 4.2). Section 4.3 describes the QED calculations nd compares the results from the two programs, while Section 4.4 does the data dis 4.2 Mon basic se cles are ciently 1 (2) Mode' different calculate be subjec ments of to data 5 0f the ev rate), an weighted among Mon- accehtancv event genv d . 125 does the same for hadronic processes. Detailed comparisons with data distributions will be made in Chapter 5. 4.2 Monte Carlo Methods All Monte Carlo simulation programs contain at least four basic sections: (l) Event generation--the kinematics of all parti— cles are selected in some pre-determined manner designed to effi— ciently sample regions of high cross section and good acceptance; (2) Model parametrization—-given the kinematics, the theoretical differential cross section (and decay distribution if relevant) is calculated; (3) Apparatus acceptance--the generated particles must be subjected to all of the important geometrical and hardware require— ments of the experiment, plus further analysis cuts for comparison to data samples; and (4) Weighting--the total weight (a l/probability of the event) is formed, summed (to keep track of total predicted rate), and binned in desired kinematic variables so as to produce weighted histograms for data comparison. Most of the differences among Monte Carlo methods can be found in the event generation and acceptance phases of the programs. There are two philosophies of event generation: a. Throw events uniformly over the available kinematic range and let the cross section and acceptance choose preferred events, or b. Pre-select regions where throwing will be concentrated and use weighting to remove the resulting bias later Method ( data com cheaper the tail weights. particle: accountir ing, etc. an attem; made on g acceptanc Predictec approach more deta because i eXPerimer detail. A llmltg’ e lnCldent tion of ,- Wltten t called be then lead 0i the ki 126 Method (a) takes much longer to achieve sufficient smoothness for data comparison and is very expensive. Method (b), which we use, is cheaper and converges more quickly, but is susceptible to spikes on the tails of distributions corresponding to rare events with large weights. There are also two types of acceptance calculation: (a) all particles are traced step by step through a simulated apparatus accounting for physical effects (e.g., energy loss, multiple scatter— ing, etc.) and hardware effects (e.g., triggering,vetoing, etc.) in an attempt to mimic treatment of data events, or (b) simple cuts are made on generated kinematics, reproducing general features of the acceptance and hoping that finer detail makes little difference in predicted rates. This second style is characteristic of a theorist‘s approach and was used by Keung and co-workers. We have employed the more detailed (and much more expensive) first method, principally because it gives more believable kinematic distributions for our experiment. The E3l9 Monte Carlo will now be considered in more detail. After initialization (of counters, histograms, kinematic limits, etc.), the main event generation loop begins by choosing incident muon kinematics (E0, ex. 8 )- To improve Simula- y’ Xo’ yo tion of incident muon distributions, the random sample of beam written to data tapes by the pulser trigger was condensed onto files called beam tapes in the format of Table 4.l. These events are then read by the Monte Carlo program with a small Gaussian smearing 0f the kinematics, because the sample of beam is not very large TABLE 4.' \ Beam available (‘18000 e\ Honis c length) x function I traCEd frr i010 ste; mmtlple s the "mUOn' Figure 4,] muon can t “Melly in l27 TABLE 4.l.--Beam Tape Format Word Beam Tape Format Run Number Event Number Fit slope of track in X-Z plane (ex) Fit slope of track in Y—Z plane (6y) Fit X at front of target (x0) Fit Y at front of target (yo) x2 of fit in x—z plane x2 of fit in v-z plane DCR3 (Triggers, PC Reset) Beam Energy (E0) OKOCXJNO‘DU‘l-wa—J ._J Beam tapes, written with l0 of the above blocks per record, are available for both 270 GeV p+ and p- data samples. (~l8000 events) and must be used repeatedly. The event vertex 2 posi- tion is chosen uniformly over the target length [i.e., z = (target length) x (random #), where the random numbers are supplied by the CDC function RANF in the open interval (0, l)]. The incident muon is traced from the front of the target to the interaction vertex in up to l0 steps, accounting for average energy loss, straggling and multiple scattering by the methods detailed in Appendix C [note that the “muon“ is really a set of three direction cosines, as defined in Figure 4.1, three spatial coordinates and an energy]. The scattered muon can then be generated at the vertex (i e., throw E], e] and a} usually in the reference frame required for cross section calculations) ccording to a desired selection function, with a weight assigned to For smal Directiol Figure 4. 128 X z/i /// l -‘ // IQ / P I a” I l G _ 1” x {)2 | l”! 2 \ l \JEY l / \\\l/ y For small angles: px = 6x pz Py = 9y PZ pz=lpI/y/l+9x2+9y2 Direction cosines: ncx=pX/Ii3! DCY = py/IPI Dcz=pZ/l'r3l Figure 4.l.--Monte Carlo Conventions. correct 1 is to be (a, b). nmnfiize (0, l). is then 5 defined a for the d CYlindric azimuthal h Virtual p duced muo tions are sECtl‘Ons “1 muons Calculate SECtion) the aCCep eVent is 129 correct for nonuniform throwing. For example, say the variable x is to be thrown by the probability density p(x) over the interval (a, b). The distribution function x P(x) = f p(x)dx a normalized by P(b) = l, can be represented by a random number r in (0, l). The integral equation is then solved for x, giving the throwing equation. The weight, defined as the inverse of the probability of the throw, compensates for the deliberate biasing of x by p(x). Note that due to the cylindrical symmetry of our apparatus and model cross sections, azimuthal angles (o) are always thrown uniformly in (0, 2n). With incident and scattered muon kinematics determined, the virtual photon (referring to EM processes) is fixed, and the pro— duced muon(s) can be generated. Usually, different selection func- tions are used here than for the scattered muon, because the cross sections and acceptance depend on produced muons differently. With all muons generated, the model differential cross section can be calculated and the event weight formed [= (throwing weights) x (cross section) x (integrated luminosities)]. The event is then passed to the acceptance and histogramming routines for judgment and the next event is generated. final-st: goals: I which wor the flbfiiél generatec end of ea (e 9., ai netic fie calculate tracing ; matics ar at the fr tion does SDark cha DMIN, ZMI the angu] mhatc (Table 3. A Veto COUn are Set, last Veto is Checke if that m l30 The main acceptance routine (called TRAMP) must trace all final-state muons from the vertex through the spectrometer with two goals: (a) deciding whether the muons generated constitute an event which would have triggered the apparatus and (b) determining what the measured kinematics of the event would be (as opposed to the generated kinematics). Constant steps of 5 cm are taken and, at the end of each step, a locating routing (HITOR) tells what material (e.g., air, iron, etc.) the muon is in and the strength of the mag- netic field. Energy loss, multiple scattering and bending all are calculated and applied to the direction cosines (Appendix C). The tracing pauses at several places in the spectrometer to store kine- matics and make cuts. The momentum and direction cosines are stored at the front of the spectrometer, since the data momentum determina- ‘tion does the same. Track positions are recorded at the location of spark chambers 9 and 8, and reconstruction cuts (maximum angle, ZMIN, DMIN, ZMIN-Z as in Table 3.9) are applied at chamber 8 along with the angular resolution of the momentum fitting. Further cuts are made at chamber 7 to simulate the reconstruction line-finding windows (Table 3.9). As the muon is traced further back, trigger bank and beam veto counter positions are reached. At each such place, indices are set, denoting which counters would have been struck. After the last veto, tracing ceases and the status of triggering and vetoing is checked. Each muon, n, has an acceptance flag NMP (n) which: = T if that muon triggered the apparatus (or at least participated in a multi-pav vetoing, it is non event haw is formed then used and TRIMU and accep their kin tum fitti the spect function 3-5). Th mOdified i Preserved distribut- smeared ea events is is a mult‘ is dlll‘dec rate, and UL and the al l3l multi-particle trigger), = 2 if that muon vetoed or cooperated in vetoing, = 3 if the muon passed through at least one magnet so that it is momentum analyzable, = 5 otherwise. After all muons of the event have been traced, an index NCODE = 25 x (NMP(l)—l) + 5 x (NMP(2)-l) + NMP(3) is formed which carries the event signature uniquely. This index is then used to determine (from the preset arrays labeled NGO, DIMU and TRIMU) whether (and what kind of) a multimuon has been generated and accepted. After all muons are traced through the spectrometer, their kinematics must be modified to simulate the effects of the momen- tum fitting algorithm and the inherent resolution and calibration of the spectrometer. Six points are chosen on the Gaussian resolution function (with standard deviation and mean as discussed in Section 3.5). These are then treated as six independent muons, with weights modified by position in the Gaussian. Thus the total weight is preserved, but resolution is naturally accounted for, and smooth distributions are obtained much more quickly than if one simply smeared each muon once. Finally, the weight for each of the smeared events is stuffed into the appropriate kinematic bins, if the event is a multimuon. At the end of each run, the total weight generated is divided by the number of thrown muons to give the experimental rate, and properly weighted histograms give kinematic distributions. Due to the limited number of multimuon events usually obtained and the already large running costs of these Monte Carlo calculations, we have g make < lC rections, errors in with diff deviation with data TI Carlo i ntv detenminec sequence ( (With n = Section). Phase Spac section is the Produc weighted h all variab the summed lot indiviv ma”) eXper- t”.glleri'ng! are its Sin 0Wl'Sconsi PluceSSes. two "‘Ethodg 132 we have generally not included physical or geometrical effects which make < 10% changes in single muon Monte Carlo (e.g., radiative cor- rections, Fermi motion of target nucleons, etc.), To estimate random errors involved in these simulations, several runs are always made with different initial random numbers and the means and standard deviations of each bin of the histograms are used for comparison with data. The ”Keung” simulation methods essentially perform a Monte Carlo integration of the model differential cross section over limits determined by features of the experimental acceptance.2 A random sequence of numbers is used to form an n—dimensional unit hypercube (with n = number of independent variables in the differential cross section). This is then mapped by a weighting transformation onto the phase space volume available (within acceptance cuts). The cross section is calculated within each bin and the final weight is then the product of cross section and the Jacobian of the mapping. Weighted histograms are formed by integration (summing weights) over all variables except the one being histogramed. The total rate is the summed weight, divided by number of events generated. Muons are not individually generated or traced through an apparatus, so that many experimental details (e.g., magnetic field bending, cooperative triggering, etc) cannot be modeled. The advantages of this method are its simplicity and low cost. We are grateful to the University 3f Wisconsin group for their willingness to simulate several difficult )rocesses. The acceptance cuts they used, and some comparison of the :wo methods will be shown in the next sections. (called l the specl lous muor be moment cal effec problems tion and events. single mu: matic rang tion 3.5, Ti‘. were those Chipter l, trimuon ev and kinema- In this so lion pi‘OCes apparatus f Monte Carl 0 The leg SUDDlie 133 Brief mention must be made of the original E26 Monte Carlo (called MCP), since it was used to obtain the energy calibration of the spectrometer. The virtue of this program is its extremely meticu- lous muon tracing and ability to write event output tapes, which can be momentum fit in the same way as the data. Furthermore, all physi- cal effects (to the 1-2% level) are included in this program. The problems with it include large cost (due to somewhat wasteful genera— tion and the detailed tracing) and the inability to generate multimuon events. Detailed comparisons of MCP with the methods we used for single muon analysis show excellent agreement over most of the kine— matic range. The use of MCP for calibration was described in Sec— tion 3.5. 4.3 Simulation of QED Processes The most important Monte Carlo calculations for this thesis were those for Bethe—Heitler tridents. As already discussed in Chapter 1, this process concentrates a potentially large number of trimuon events in a very poor acceptance region, making rate estimates and kinematic comparisons impossible without Monte Carlo simulations. In this section, the results of both Monte Carlo calculations for tridents (and the related pseudotrident and heavy lepton pair produc— tion processes) are presented with comparisons. The acceptance of the apparatus for such low angle multimuons is also shown. Hadronic honte Carlo calculations are outlined in Section 4.4. The differential cross section for our calculation of tridents - 3 was suPplied by a computer code (TRIDNT) written by Brodsky and Ting. This pro (using e' a spin-ze statistic mined by polar ang state muc then calc strained energies All of th dl can then t CC Cdl‘l‘ieg th ub/GEVZSr3 PT isthe Dhas QT 134 This program calculates four different types of elastic tridents (using electrons and/or muons as incident and final particles) in a spin-zero nucleus of charge Z and form factor F(qn2) with lepton statistics (Fermi-Dirac or Bose-Einstein) and spin (0 or l/2) deter— mined by the user. For each event, the kinematics (energy E in MeV, polar angle 9 and azimuthal angle ¢ both in radians) of the three final state muons are passed to TRIDNT and stored in arrays (4—momenta are then calculated internally). Note that the incident muon is con— strained to have 64 = $4 = O (i.e., to be along the z axis) and the energies must obey E4 = E1 + E2 + E3 because the events are elastic. All of the factors in the differential cross section dso ___‘TTTTTTTi = CCT x PT x QT x SU dE dE (d9) 1 2 1 can then be calculated as follows. The first term 10 3 ) 4 com = QLthc)2(i x lo = 5.7 x l0 2n carries the constants and conversion factors from CmZ/MeVZSr3 to ub/GeVer3. The second factor 1P2P3 P4 p PT = is the phase space factor while the third 2 2 2 2 F (on ) qn carries . transfer discusser interact‘ whole nuc good appr with indi (instead the numbe inside th deal with tion whicl using the metric ele and Dirac summing 0g and was nc resulting mental dat Th Carlo (tam rates and 1 E319, 1t . region of l malelZeS 1 135 carries all nuclear structure information (note qn is the 4-momentum transfer to the nucleus). The nuclear form factors used will be discussed in Appendix C. Of course, this description of the nuclear interaction, where the virtual photon interacts coherently with the whole nucleus, is strictly valid only for low qnz. However, to a good approximation, incoherent processes (where the interaction is with individual nucleons) can be described by using elastic nucleon (instead of nuclear) form factors, setting Z = l, and multiplying by the number of nucleons A. For still higher qn2 the interaction probes inside the nucleons and becomes inelastic. The TRIDNT code cannot deal with this because inelasticity destroys the energy balance condi- tion which allows all four diagrams (see Figure 1.4) to be calculated using the same algorithm. Finally, the fourth term SU represents the matric elements squared, calculated by numerically multiplying spinors and Dirac matrices for each helicity state, squaring the result, and summing over all helicities. The coding of this is quite complicated and was not directly checked. We relied instead on comparing the resulting distributions with independent calculations and experi- mental data. The TRIDNT routines were used in conjunction with the Monte Carlo framework described in the previous section to calculate trident rates and distributions expected from the 270 GeV u+ data sample of £319. It is particularly important since tridents occupy such a small region of phase space, to generate muon kinematics in a way that maximizes the product of cross section and acceptance. We have attem Chapt about incidi bilit muon ! SEVEFi suffiv kinema (and c 0i the howeve is cur PEP rt 10000- enougl Severe p(OdUC aCcoun accmt lteate 136 attempted to sample the four Tannenbaum4 regions (as described in Chapter l)by throwing produced muon polar angles exponentially peaked about zero. These thrown angles can be taken relative to either the incident muon, scattered muon, or the virtual photon and these possi- bilities are tried for each event. The generation of both scattered muon kinematics and produced muon energies was then optimized in several test runs to allow minimum spikiness and cost. If the product of kinematic and cross section weights is sufficiently large, a loop is set up to exploit this favorable set of kinematics by simply re-throwing azimuthal angles up to twelve times (and dividing each weight by 12). This greatly enhances the sampling of the four "good“ regions and reduces running time. The results, however, should be independent of generating functions (if weighting is correct) for high statistics runs. The number of events generated per run is set to keep the bin variations reasonably low (usually 10000—50000 events are required, with from lO-50% having weights large enough to be counted). Our trident Monte Carlo runs are summarized in Table 4.2. Several conclusions can be made: 1. The number of multimuon events expected from trident production is quite low and, as we shall show in Chapter 5, does not account for most of the E319 events; 2. Although tridents naturally lead to trimuons, the acceptance converts ~ 1/2 of these into dimuons; 3. These dimuons are primarily OSPs, because SSPs have a greater chance of the missing muon being bent into the beam veto; 137 TABLE 4.2.--E319 Monte Carlo Results for Tridents Number 2p 2p 3p 3p Run Process Generated Total 0 OSP SSP Total 0 c Fe 10000 2.0 0.7 1.8 0.2 2.9 2.4 d Fe 20000 1.4 0.4 0.9 0.5 1.3 0.3 e Fe 20000 2.5 2.5 2.2 0.3 0.4 0.1 Average Fe 50000 2.0 2.6 1.6 0.4 1.5 2.4 I p 10000 14.1 5.3 13.0 1.1 7.6 1.2 J p 10000 9.1 0.6 6.3 2.8 8.0 1.3 K p 10000 8.0 0.7 5.8 2.2 7.1 1.3 L p 10000 9.0 1.6 5.9 3.1 12.2 6.5 M p 50000 8.8 0.6 7.1 1.6 7.0 0.4 Average p 90000 9.8 5.6 7.6 2.2 8.4 6.9 Sum Fe+p 11.8 6.2 9.2 2.6 9.9 7.3 Ratio % 0.6 0.6 0.6 0.9 Ratio % 0.4 0.4 0.4 0.6 Estimated Total 21.6 11.5 16.8 4.8 22.5 17.5 F + + 9— -E e p (1 p + p) Fe = coherent tridents p = incoherent tridents q = inelastic tridents (estimated by Keung) B = pseudo tridents (estimated by Keung) 138 4. Although coherent cross sections are much larger than those from the incoherent process before acceptance, the nuclear form factor is much more strongly peaked at low qn2 than the nucleon form factor, so that incoherent tridents dominate the event rates. Histo- grams of kinematic distributions for these tridents will be compared to the data in Chapter 5. A multimuon acceptance table for the trident process was obtained in the following manner: the event generation part of the trident Monte Carlo was run without apparatus tracing or cuts, giving ran generated histograms. Then the appropriate accepted distribution was divided (bin by bin) by the generated distribution. Table 4.3 shows the acceptance as calculated in the produced muon transverse momentum relative to the virtual photon (pi) (the dimuon and trimuon accepted histograms must first be added and then divided by the purely trimuon generated histogram). Two points are clear: (1) the accep- tance is very low at small pi, which is why tridents are so greatly suppressed in our experiment, and (2) the acceptance is quite differ— ent in the low bins for the two types of tridents, illustrating the model—dependent nature of multimuon acceptance. This fact prevents the use of such a simple 1-dimensiona1 acceptance table for all processes. The problem could be avoided by forming a complete accep- tance table in all relevant kinematic variables (e.g., a nine- dimensional table would be necessary for three final state muons), but this would require prohibitive amounts of Monte Carlo computer time. In the high transverse-momentum region (>2 GeV/c), the model 1 39 TABLE d.3.—-Multimuon Acceptance in pJ for Tridents Accepted Generated Acceptance 1’1 Range (GeV/c) Fe 0 Asun Fe 0 GSUM Fe 9 23%; 0.0 - 0.3 .36 1.95 2.33 1.68 x 105 2.21 x 10‘ 1.90 x 105 2.27 x 10‘6 8.82 x 10'5 1.22 x 10‘5 0.3 - 0.6 .34 3.03 3.86 1.37 x 105 1.96 x 10‘ 1.56 x 105 6.09 x 10'6 1.62 x 10“ 2.46 x 10‘5 0.6 - 0.9 .63 2.75 3.38 2.96 x 10‘ 1.02 x 103 3.06 x 10‘ 2.14 x 10‘5 2.69 a 10‘3 1.11 x 10“ 0.9 - 1 2 30 2.39 2 77 4.50 x 102 2.03 a 102 7.33 x 102 5.36 x 10“ 0.46 x 10'3 3.75 x 10‘3 1 2 — 1.5 .20 1.74 1.94 42.19 40.50 82.68 4.70 x 10'3 4.39 x 10'2 2.35 x 16'2 1.5 — 1.8 .11 1.02 1.14 13.28 19.30 32.53 6.46 x 10'3 5.31 x 10‘2 3.49 1 10‘? 1.6 — 2.1 .06 1.09 1.14 3.74 7.04 10.76 1.71 l 10‘2 .15 .1 2.1 - 2.4 .06 .91 .97 .82 3.42 4.24 7.05 x 10'2 .27 .23 2.4 - 2.7 .03 .61 .64 .31 1.61 1.92 .11 .36 .33 2 7 - 3 o 03 4o 42 .14 00 94 20 50 44 3.0 — 3.3 .01 .25 .27 1.56 x 10‘2 .39 .41 .77 .65 .66 3 3 - 3 6 01 .21 22 1 04 x 10'2 19 20 1.17' 1 00‘ 1.03- 3.6 - 3.9 .42 x 10'? .13 .14 2.92 x 10'3 .13 .14 1.44. .99 1.00 3 9 — 4 2 .70 x 12'2 .09 .10 1.36 x 10‘3 9.56 x 10’2 9.70 x 10'2 5.15. .96 1.02- 4.2 . 4.5 .43 x 10'? .05 .06 9.24 x 10" 5.79 x 10'2 5.35 x 10'? 4.65‘ .91 .97 4.5 - 4.3 .36 x 10'3 .04 .04 1.34 x 10'3 4.20 x 10'? 4.33 a 10'2 .27 .se .35 4.9 . 5.1 .13 x 10‘3 .02 .02 5.40 x 10" 2.46 x 10‘2 2.53 x 10'2 .24 .55 .36 5.1 . 5.4 .14 x 10'2 .01 .01 7.62 x 10" 2.23 x 10‘2 2.31 x 10’2 1.64' .63 .67 5.4 - 5.7 .96 x 10'3 .01 .01 6.23 x 10“ 1.75 x 10‘2 1.31 x 10‘2 .59 .66 .65 5.7 - 6.0 .15 x 10‘3 .007 .01 5.56 x 10‘5 1.45 x 10'2 1.45 x 10‘2 2.69' .50 .52 4.21 x 104 3.78 x 105 0.24 x 10‘6 3.97 x 10" 5.16 x 12‘5 140 dependence should be a minor effect. Processes concentrated in that region could be expected to have about the same acceptance as the tridents. Using luminosities (Table 1.4) and generated event rates (Table 4.3), the total trident cross section can be calculated and compared to independent estimates, as shown in Table 4.4. The other calculations agree well with experimental data at low energies and, using the expected energy dependence, match our trident results within errors. Differences are probably due to small sampling diffi- culties and generation problems at the lowest angles, where the cross section peaks and the acceptance dips. The general agreement gives confidence in the calculated accepted trident event rates for E319. Keung has used his Monte Carlo methods and independent QED differential cross section routines to calculate rates and distribu— tions expected for tridents, as well as pseudotridents and inter- ference between the two.5 Briefly, the Feynman diagrams are all topologically converted to a general diagram, which is then reduced to algebraic form (via a trace manipulation routine similar to SCHOONSHIP). When fed event kinematics, the coded equations supply the full differential cross section. There is no restriction on nuclear recoil (unlike the Brodsky routines), so that inelastic tridents can be calculated. As described in the previous section, Keung's method requires phrasing the experimental acceptance in terms of simple kinematic cuts (integration limits). Through a series of meetings with Keung, we 141 TABLE 4.4.-—Muon Trident Total Cross Sections nb Reference Methods Used 0(nUETEEH) -- a. E319 Monte Carlo 5 b. Total generated rate - 3.8 x 10 13.5 c. Coherent and incoherent tridents Tannenbaum a. Brodsky—Ting cross section and 6.3 i 0.5 1970 FNAL Monte Carlo Integration Summer Study b. Get .075 ub per Carbon nucleus at 12 GeV. Scale using E E 3 “(E1 0‘ 1“ (6.7mu)[]n(6'._7mu)' 7] c. Coherent tridents only Russell, et a1., a. Experimentally measured to be 15.5 i 2.1 Phys. Rev. Lett. 51 i 7 nb per Pb nucleus at 26, 46 (1971) 10.5 GeV b. Calculated in manner similar 18.2 i 0.6 to Tannenbaum as 60 i 2 nb/ Pb nucleus c. Scale both in energy as above Barger, et a1., a. Keung method for E319 Preprint coo-881-83 b. Coherent, Incoherent, and 17 Inelastic tridents 142 developed such a set of simple cuts (Table 4.5) to adequately describe triggering, veto, and momentum analysis requirements. To monitor the validity of Keung's results, our trident Monte Carlo was modified by replacing the extensive apparatus section with the same simple cuts. Table 4.6 compares both simple cut results with the full cal— culation. Several conclusions are evident: (1) The agreement between simple cut versions is quite satisfactory, with the exception of SSP events which are sensitive to magnetic field bending; (2) Neither simple cut result reproduces the full calculation for the Fe process due to its extreme sensitivity to low angle geometry; and (3) Both simple cut versions agree well with the full p calculation, which is not so strongly peaked at low energies and angles. Figure 4.2 com- pares the leading and produced muon energy distributions from the Fe process for all three Monte Carlo versions. Clearly, all of the calculations populate roughly the same kinematic regions with dif— ferences attributable to resolution and spectrometer bending effects. The same distributions for the p tridents are shown in Figure 4.3, where the agreement is even better. This given us confidence in Keung's calculations for other processes (e.g., inelastic tridents (q) and pseudotridents (B))which are not too sharply peaked in low acceptance regions. Although detailed kinematic distributions are unavailable for these two processes, they appear to follow the same tendencies as the p tridents.5 Since the rates are small (Table 4.6), we include the q and B processes by simply scaling the p trident kinematics upwards with a multiplicative factor (1 + q/p + B/p), 143 TABLE 4.5.-—Simple Cut Acceptance for E319 Purpose of Cut Energy Angle l. Trigger--At least one muon must be within magnet area at the trigger banks. One 0 must satisfy (a) and one u (need not be the same one) must satisfy (b). a. E>8.5r + 4.1 b. E>8.5r + 9.0 15.3 tang > 598+738r 86.0 tane < 5981738? 15.3 tane > 1160+738r 86.0 lane < 11601738? 2. Veto-—All thrown muons must satisfy the angle cut unless they satisfy the energy lower limit to prevent hitting the beam veto counters E<8.5r + 6.6 15.9 tane> l388+738r 3. Momentum Analyzability—— To determine the momentum (ngt_necessary for total rates) the muons must penetrate 1 magnet E>8.5r + 4.1 86.0 tane< 5981738? 15.3 “W m Note: Due to the long iron target, the cuts are functions of the random number r which determines the interaction point in the target by Z = 738r. 144 TABLE 4.6.-—Simp1e Cut Trident Results and Comparison to Full Calculation OSP Calculation Process Zp OSP SSP ——- 3p SSP E 319 Simple Fe 37 27 10 2.7 61 E 319 Full Fe 2.0 1.6 0.4 4.0 1.5 Keung Fe 45 22 23 1.0 39 E 319 Simple p 11 7 4 2.0 19 E 319 Full p 9.8 7.6 2.2 3.5 8.4 Keung p 27 13 14 1.0 20 E 319 Simple Fe + p 48 34 14 2.4 80 E 319 Full Fe + p 11.8 9.2 2.6 3.5 9.9 Keung Fe + p 72 35 37 1.0 59 Keung q 16 8 8 1.0 18 (q/p) (0.6) (0.6) (0.6) -- (0.9) Keung B S 10 -- -- —- :12 (W13) (0.4) (0.6) Note: Same notation as in Table 4.2. 145 ___—E319 Simple Cut ---------- E3l9 Full Cut x 24 -----Keung “3 cu CD CD I 1 Events per 30 GeV 6 I Events per 30 GeV \. ' l r j 0 60 l20 180 240 E 3(GeV) Figure 4.2.—-Coherent (Fe) Trident Monte Carlo Leading Muon (E1) and Produced Opposite Charge Muon (E3) Energy Distributions 146 —E319 Simple Cut """" E319 Full Cut x 2.4 "---Keung Events per 30 GeV 15' __ > ’ \\ 9 / C9 \ C> I \ NiIO-l \ a -. \ .5”. ', \ c 5. , \ w o L: \ O l l L\X. l 4 0 60 120 180 240 300 E3(GeV) ' te Carlo Leading Muon (E1) and F' 4.3.—-Incoherent (p) Trident Mon lgure Produced 0ppos1te Charge Muon (E3) Energy Distribution 147 where the rate ratios are shown in Table 4.6. The systematic errors involved are estimated to be less than 20% in each bin. Distributions from the QED calculations will be compared with hadronic processes in the next section and with the data in Chapter 5. 4.4 Simulation of Hadronic Processes This section contains a brief outline of Monte Carlo calcu- lations for the hadronic processes described in Chapter 1 (a more complete discussion will be available in the thesis of J. Kiley). Our effort has been directed toward calculation of the charm and pion (kaon) decay processes, which dominated the E26 multimuon rates. Keung has studied both 03 and bb associated production, hadronic final state interactions (quark recombination), and vector meson production.5 The basic methods are the same as those described in section 4.2, with modifications for calculating cross sections in the CM reference frame and weighting procedures to account for decay branching ratios of the produced hadrons. Dimuons from the decay of one of the shower hadrons produced in the deep-inelastic scattering were the first process to be simulated for multimuon studies. The original program (called CASIM)6 was developed to-generate hadron showers (using measured hadron production cross sections and multiplicities) for use in calorimetry and shielding studies. By following each hadron until it either stops or decays, the rate of extra muons accompanying the scattered muon can be determined. Using the same program as in E267 (except for updating the geometry and flux) predicts 54 i 6 dimuons and a negligible number of trimuons 148 from n/k decay. Due to the high hadron multiplicity, none of the shower particles receives much energy so the resulting energy and transverse momentum of the produced muon are small relative to other processes, as seen in Figure 4.4. Associated charm production (and semi—leptonic decay) was the other main process considered in E26, where it was believed to dominate the dimuon sample. We have used essentially the same model8 for the production and decay of charmed mesons except that the pro- portion of the decays D + kuv and D + K+pv have been adjusted to reflect more recent data.9 Since the normalization of this phenomeno- logical model is left free, kinematic shape comparisons with data were used to establish the charm hypothesis. However, Keung's calcu- lation for associated charm production uses the photon—gluon fusion model10 which can supply rate estimates and kinematic distributions. The predicted dimuon rate after acceptance is 26 pb/nucleon, or about 730 events in the main data sample. Due to the small branching ratio (10%), the trimuon rates are quite small (about 11 events). Kinematic distributions compare closely between the two independent calculations, showing the characteristically steep fall—off in transverse momenta of all hadronic processes (Figure 4.4). A simple change in quark mass (from Mc = 1.87 to Mb = 5) in Keung's simulation allows an estimate of heavy quark production. At our incident energy, even without acceptance cuts, the rates are still very low (about 1 pb or 30 events) meaning that this process is almost certainly undetectable in our experiment. The kinematics of 149 Charm (1:319) ..... Wk (8319) ......... Hadronic Final States (Keung) —-—-Tridenis (E3l9) N O I ArbHrory Produced Muon P.L relative to virtual '7 Figure 4.4.-—Unnormalized Comparison of Transverse Momentum Distribu— tions from Monte Carlo Calculations for Several Hadronic Processes and for Tridents). 150 such events would be similar to those for charm production but scaled upwards to higher momenta and masses. Neither Monte Carlo has been used for detailed examination of vector meson (9) production and decay for £319 because: (a) The rates are known to be quite small (only 24 trimuons expected without acceptance correction), and (b) The kinematics are distinctive (i.e., the apparent mass of the produced muons should peak at Me = 3.1 GeV). Furthermore, 0 production has been thoroughly studied already in both lepton and hadron interactions. Finally, Keung has also calculated rates and distributions for the hadronic recombination process in a phenomenological manner based on hadron experiments with the results (Table 4.7 and Figure 4.4) appearing much like the m/k process. Indeed, Figure 4.4 illus— trates that all of the hadronic processes tend to lie in low transverse momentum regions, with QED spectra being much flatter. In the next chapter, we shall exploit this and other characteristics of the Monte Carlo predictions in an attempt to isolate signals from the non-hadronic mechanisms of interest. 151 TABLE 4.7.--Hadronic Monte Carlo Results Process Monte Carlo 2p 3p 1. ir/k decay E319 54 (i6) -— 2. Charm Keung 730 11 (DD) 3. "Beauty” Keung <30 (before cuts __ b5 very few after cuts) 4. p Keung Estimate <20 20-30 5. Hadronic Keung 25 8 Final States CHAPTER 5 MULTIMUON DATA AND INTERPRETATIONS 5.1 Status of Data Analysis The data taken in E319 (excluding tests and calibration) can be grouped into five chronological blocks with the following char- ]0 incident 0+ at 270 GeV on the full iron acteristics: (A) 1.1 x 10 target (the main data sample); (B) about 4 x 108 incident u+ at 270 GeV on a 1/3 density iron target with two out of every three iron plates removed; (C) 1.4 x 109 incident 0+ at 150 GeV on the 1/3 density iron target; (D) 3.1 x 109 incident 0’ at 270 GeV on the full iron target; and (E) about 2 x 109 incident n+, mostly at 120 GeV, on the full iron target. Data analysis (including PASSZ track reconstruction, momentum fitting and multimuon scanning) has been completed on all useful runs from samples A, C, and D. However, track fixing (manual reconstruction) and efficiency studies were performed only on A and calorimetry information was not available for C (due to problems with the 1/3 target arrangement) and E (rate effects from the large flux of pions). Sample E has been superficially examined to judge if the data would be useful for vector meson produc- tion studies. Data from B has not been analyzed because of equip- ment problems and the low statistics of those runs. Most of the distributions presented in the following sections came from sample A 152 153 and all Monte Carlo simulations were run with the flux and geometry of that data. Distributions from C and D will be presented only to illustrate the incident energy and incident charge dependence, respectively, of multimuon production. We group the data events from each sample into four classes on the basis of the number of final state muons: (1) Single muon (deep inelastic scattering) events, which will be discussed here only in comparison to leading particles of multimuon events (and in Appendix A as a check on missing energy determination); (2) Dimuon events which, because they are the most numerous of the multimuon types, have received the largest analysis effort; (3) Trimuon events, which are roughly an order of magnitude scarcer than dimuons; and (4) Exotic events with four (or more) final state muons. Each of these classes will be first presented in raw form, with rate esti- mates and a discussion of kinematics. Then, calculation of non- leptonic processes (backgrounds) will be subtracted and the remain- ing data compared to the simulated leptonic signals expected. When Monte Carlo predictions are unavailable, cuts on the data will be used to attempt isolation of the signal (heavy leptons). 5.2 Single Muon Events Although the track reconstruction and fitting programs are able to reject most improper triggers (e.g., live halo, cosmic rays, etc.), there are still some events on the secondary tapes which are neither deep inelastic scatters nor multimuons (principally 154 multiple scattered beam and halo events). Furthermore, some of the reconstructed tracks are not of the quality desired for the deep inelastic scattering studies. Thus, a set of geometric and kinematic cuts has been developed to further purify the sample. As detailed in Table 5.1, these cuts keep the data away from geometric (e.g., toroid holes and outer edges) and kinematic boundaries, where the apparatus and/or analysis programs are less well understood. By comparing the single muon sample thus obtained with the leading particles (those with the same charge as the beam and the highest energy) of multi- muons, the acceptance of the apparatus can be partially corrected for and multimuon rates per deep-inelastic scattering event can be obtained. For the A sample only, these rates are detailed in Table 5.2. However, these are still uncorrected for produced muon acceptance. Table 5.3 shows some single muon kinematic averages and Figure 5.1 displays kinematic distributions of single muons and lead- ing particles of dimuon events (with and without the cuts of Table 5.1). Even after cuts, the leading muons prefer higher y and W regions, mostly because the scattered muon receives less energy on 2 and low x the average if other muons are produced. Also, large q are favored, which has been interpreted as a sign of interactions with non-valence (sea) quarks in the nucleon (e.g., charmed quarks).1 However, large q2 can also be considered a sign of an interaction which is not electromagnetic (because electromagnetic cross sections are proportional to 1/q4). We have found that the leading particle characteristics are not very helpful in distinguishing among 155 TABLE 5.l.—-Single Muon Cuts % Rejected Actual % Cut Definition of Cut by This Cut by the Pro— Alone gram 1. 0 < Beam Angle (mr) < 2 .7 0.7 2. 0 < Beam Radius (cm) < 10 0.08 0.01 3. 243 < Beam Energy (GeV) < 297 0.5 0.1 4. -300 < ZNIN (cm) < 700 0.9 0.9 (Target stretches from -l67 to 567) 5. DMIN (cm) < 5 1.2 1.0 6. o (W <10 0.7 0.6 7. Require at least 7 of the 10 chambers to have sparks 20.2 18.1 8. Radius at Trigger Banks (cm) > 15.24 37.0 24.7 9. Radius at Beam Vetos (cm) > 15.88 12.3 0.3 10. 5 < 610““) < 1000 9.8 0.1 11. 10 < E(Gevl < 300 7.7 1.7 12. 1 < 02 (GeV2/c2) < 500 8.5 0.0 13. Momentum Fit Good 3.4 3.3 Total % cut 51.5% 156 TABLE 5.2.--Numbers and Ratios of Events t Number Number Ratio Multimuons Even Before After (After/ -———-——-‘- Type Cuts Cuts Before) 2. Single Muons Single Muons a. Raw 8.24 x105 3.89 x105 5 5 47.2 -- b. Corrected (for 8.87 X 10 4.18 X 10 7% of finding inefficiency”) Dimuons a. Raw 412 i 20 157 i 8 38.1 (5.9 i 0.6) b. Corrected (for 644 i 61 245 + 23 x 10-4 36% finding inefficiency) Trimuons a. Raw 36 t 6 8 i 1 22.2 (3 8 e o 7) b. Corrected (for 72 i 13 16 + 3 _5 50% losses) x 10 157 TABLE 5.3.—-Single Muon Averages (inematic Variable Average After Cuts l. kmnflmmy(%) 2. Scattered Energy (E1) 3. Scattered Polar Angle (e1) 4. 4-momentum Transfer Squared (02) 5. Energy Transfer (9) 6. Bjorken Scaling Variable (x) 7. Fractional Photon Energy (y) 8. Center of Mass Energy (W) 9. Vertex Quality (DMIN) 0. Vertex Position (ZMIN) 268.8 168.4 18.2 14.4 100.5 .09 .37 12.5 .53 115.6 GeV GeV Till” (33112 GeV C111 C111 158 npcmwc web so wpoum uvaFoELo: 65p mm: mEmLmOpm_c w—uwpeoa mcwuomp we» we :uom ._.m mFQMP mo mpso web Levee mcoze mcwnomp mpcmmmgawg Eoemoumw: uwumcm mcp m_m:3 mPQEMW cozewn F~sm mcp Eocm macse mewvmwF mpcwmmgawg EmLmOpmw; uwcmoe one .mmpmum pomF nmNTFoELo:1szLoLuwncm asp ou memwmg use _.m m_noh mo muse ms“ empem mcoze m—mCTm ovpmo—mcw gown mpcmmmeaoe Enem0pmw; nwpom mcev .mp:m>m cozswo Eocd mw_uepcoa mewcmwo use mcosz mecwm do m:0mweoquu uwpmewc_¥--.r.m mezmwa 2. >8; 0.. 03 8.0 8.0 oo 8 A V 2 oo 84 _ 1 _Lo 8- MEN: N 1 _m. 87 N _ _ _ m _ _ _ _ _ x :8 o -- No 3 oo 966 N 5 ON 0 avatar“... ON 1 p3 ON 1 . e - _ _. _m own I _ owi BM r 5 Na 87 1 um 09 H _ _ ~ _ 159 multimuon processes. In the following sections, produced muon kine- matics will be shown for the various multimuon types. 5.3 Dimuon Events Our experiment currently has the largest reported sample2 of dimuon events from muon interactions in the world (although this will soon change as more recent experiments finish their data analy- sis). Three possible mechanisms can give rise to such dimuon events with differing predictions for the expected charge types: (a) the weak production and muonic decay of neutral or doubly-charged heavy leptons leading respectively to OSPs or SSPs, exclusively; (b) the electromagnetic production of hadrons, one of which decays semi- leptonically (giving equal numbers of OSPs and SSPS before acceptance); and (c) mis-identified tridents, where one muon is undetected (and ‘the OSP to SSP ratio depends solely on the apparatus). Table 5.4 details the numbers of dimuon events (from Sample A) of various types, while Table 5.5 shows event totals from several different samples along with calculated rates, corrected for finding efficien- cies, but not for apparatus acceptance. Finally, Table 5.6 displays kinematic averages for the dimuon events (note particularly the low values of produced muon energy and transverse momentum). Since the two samples with opposite incident charges (A and 0) agree closely in rates and kinematics, we conclude that (a) the event fixing pro- cedure, done only for A, makes little impact on kinematics and can be applied to all samples and (b) weak processes, which should give sign-dependent results, do not dominate dimuon production in muon 160 mcozsve o a, Nmm 5N mom N_e oPDMNzfioe< mcozewa m mN NNe em MNm Nee Nance meozewo 8mm N m No_ _N ow e__ oraa~s_ac< mcozswo N o N__ NN om mN_ amm _aboe mcozeeo amo mcozaeo N N_ com No NMN eNm amo _aooe Logoem flexaosv “sumo; oozv cwzocm oz cocum: ewe; szogm segue: ewzo;m cognmz —mp0H 550mmpmo mwcw>m CmMPLOOCD Swrz mPCw>m mucm>m roach sow; moco>m ebb; moco>m A>_co < m—aEmmv memnE32 coaswo11.¢.m m4mgzu wsuv mucsocmxomm owcogcm: vmpm_:o—mu sow: mowumvgwpumgmzo mama cozewoii.m.m weaned 20:93; 39832 0.. vmd m _ .o Nd 1 m 9m Wm o _ _ _ _ L ‘N 1 1/ 1/ \.\ . l /./ u \\ . L/ / i .\ 1 1| / . n / \ u 1 / / \ _ / \g - / / _ / \\.\ . .x. 8 M n /l.. . n n . . S o_m+++ \ ++ m m ++ 2/ 2 2 1 /. + .\ + .1 1 ++ ./. i //o+o &\+.+ 1 1 aux o oo_ _ _ u .1. _ _ 00. A3364 EEV ad 0: wN_ an o 09 m: ma 0 _ — _ _ - 11 2 - n \\1 /u 1 m .\\. n m// \ _ fl \\ w W / / x _ l \\ 1 f . // \ M 1 \ + +1 1 . // xx \ W m n \ 1 1 / Illl . m \ + + m m 1 /1\ . m o_ n\\ +1 11.1.1 1 . n 2. ++ .\+ o_ 1 .1111 .M /. .\ 1.\\O‘++ + .1 1. /.++7fi \.\+ 1 o n /. .1. 3 .9 n .99.. 00“ n _ _ H _ _ 1 09 165 .Apxwp one use m.m mczmwd :8 may muczocmxumm uwcocuo: twee—zupmu spwz mowpmwemuomconu muon :osewo cmnuczd11.m.m wcamwd . 33823.5 383 (26 5N o 02 ON 0 _ _ .// _ N _ / _/ _ n . / L r / . 1 I. /. / I. T. / / J m f m m / / m m / m 1 m 1 .4 4 m // / _ 1 o 1 1 / 1 3 1 F .0 U n + a .1. mm m .0 m m + //. m N1N1. 9“ .7 \m m ++ 7 \mo_ 8 o /l\ .1 / /.\H¢ 11 +. / .1 H 0 ./ 1 / 1 m o/ m 1H. 9 ./ M 02m 5. .m m 3. 02 _ _ _ _ @ E _ _ _ a7 166 In Figure 5.4 and 5.5, the data left after subtraction of the hadronic backgrounds are presented, along with the QED trident Monte Carlo predictions. Some of the excess dimuons (those concentrated at moderately high apparent mass, with large momenta, and primarily quasi-elastic) can be explained by the trident mechanism. The appar- ent excess of inelastic events at low p2 (pl ) probably stems from inadequacies in the charm model and the large uncertainty in the inclusion of the hadronic recombination background. Clearly, the dimuon sample is a poor place to study tridents in this experiment due to the large charm background. Even after all of the above processes have been subtracted, there remain a few dimuons with very large transverse momenta, which constitute possible heavy lepton and/or heavy quark production sig- nals. However, since neither of these processes has been simulated for E319, we have chosen to return to the full dimuon sample and attempt isolation of heavy leptons via the kinematic cuts described by Albright and Shrock3 and shown in Table 5.7. These cuts were developed for the Berkeley-FNAL-Princeton experiment (E203).4 Although their apparatus differs from ours in several ways (which will be outlined in Chapter 6), none of the differences should pre- vent the use of these cuts for our data. Further, though the cuts were designed to select heavy neutral muon candidates, it is reason- able that they would also tend to select the kinematically similar doubly charged heptons. N9_dimuons pass all_of these cuts! However, removing the 5 energy-dependent A? cut leaves 6 OSP and 4 SSP events. This sample 167 O O S? E? _. C) E? S? __ <> 1111111 11111111 1 11111111 2 1111111 11111171 1 111111111 ..° —._.. V’ —..___. _ ——o~————— ‘9 - ‘9” ‘ 9! c>t2 1; 92 v 5; 17 v —o— < '9 —Q— _I <1 —-0— 111 .. V _ +- to; 1.0 + ‘2 + O + 11111 [11111111 4111111L 0 11111111 11111111—O——- N 9 0 111117? 11111111 1 11111111 1 Q 11 111111 _.__.__, ‘3 ——o—> ___°_—_ ——.—__——__ - LO 0 a? _._ > E 8 «5 ‘Zc <1 _.____ :L _. -O—- Q _ st: _._. -N +— _..__ +— 1L11 111111411 llllllLlJ._ 0 11111111 111111111 111111114 0 O - o 9 ._ 52 N18 52 N18 SiN3A3 SiN3A3 nic Processes lated Hadro .4.-—Dimuon Data Characteristics After Subtraction of Calcu Versus Results of QED Trident Monte Carlo (Solid Curve). Figure 5 168 .Aw>L:o vw_omv Luazm cmsuL2¢11.m mcowpmfizu_mu pcwuvch Duo 0» uwcmanu morpmwcwpumcmcu mpwa Cesare empum Ease a Agog m. 2» E o om. 8 o . _ _ _ _ n n u H 1 r 1 3 H H H u m M m m m + m N N O_ H # * m m m 0_ 18... 09 u m m “.69 _ _ _ _ _ . _ .m mcsmvu 169 TABLE 5.7.--Heavy Lepton Kinematic Cuts Kinematic Cut Meaning 1. E > 20 GeV 1 2. E > 20 GeV > 20 GeV 4. E > 20 GeV 5. Q > 10 6. Pais-Trieman 2 .48‘< E; < 2.1 7. M12 > 1.0 8. P12 > 1.0 9. A¢12 < 90° G V 2 1—3—1 w 921 C Some rejection of hadronic and EM processes Rejects hadronic processes, which favor 10w produced u energies Rejects e1astic inechanisms (e.g., tridents) Favor 1arge missing energy (i.e., decay neutrinos) Discriminate against EM processes which go 1ike 1/Q4 Characteristic of two muons from the same parent (Strong1y rejects charm) Weak rejection of n/k and hadronic back- grounds C1ear discrimination against exponentia11y fa111ng hadronic transverse momentum spectra Somewhat uncertain rejection of charm (because of broad A¢12 distributions) ______________g__________________________________________________________. 170 is expanded to 1OSSPs and 6 OSPs when the four exp1icit energy cuts are a1so removed. Tab1e 5.8 summarizes the effects of these cuts and Tab1es 5.9 and 5.10 detai1 the kinematics of the events passing the reduced cuts and which tests are fai1ed by each. If one assumes that the events which miss on1y the Ad cut are a11 heavy 1eptons, 2 cross section times branching ratio estimates of 2.1 x 10'37 cm for 37 2 SSPs (k++) and 1.4 x 10' cm for OSPs (M°) are obtained with no acceptance correction. Further, assuming that the trident acceptance app1ies in this moderate1y 1arge pl region (probab1y good to within a factor of 2 anyway), and using it to correcttheevents within the 35 bins of Tab1e 4.3, the o x BR estimates become 1.8 x 10- cm2 for k++ and 1.3 x 10'35 cm2 for M°. Perhaps more rea1istic estimates can be obtained by se1ecting a subsamp1e of events nearest the Ad bound- ary. From Tab1es 5.9 and 5.10, it is c1ear that on1y 1 OSP (299 - 4330) and 1 SSP (268 - 5907) are reasonab1y c1ose and these are a1so the events with the 1argest pl (Figures 5.6 and 5.7 disp1ay these two events). Correcting for acceptance, these sing1e events give - 0 —37 2 ++ O X BR estimates of 1 x 10 36 cm2 for M and 3 x 10 cm for k . . 6 . . The M° va1ue is consistent with the pub1ished upper 11m1t of 2.5 x 10‘36 cm2. It is c1ear, however, that our estimates are subject to much uncertainty without a c1ear heavy Tepton signa1 or Monte Car10 ca1cu1ations. The situation shou1d be c1arified substantia11y by ent muon experiments which have 1arger incident 4,7 f1uxes and better acceptance than E319. the data of more rec The few high p1 dimuons remaining after background subtrac- tion a1so did not pass the heavy 1epton cuts and Tab1e 5.11 shows why, 171 TABLE 5.8.--Effects of Kinematic Cuts Cuts App1ied (from Tab1e 5.7) #OSPS Left #SSPS Left 1 282 (94.6%) 111 (97.4%) 2 144 (48.3%) 39 (34.2%) 3 271 (90.6%) 100 (87.7%) 4 199 (66.8%) 67 (58.8%) 5 89 (29.9%) 80 (70.2%) 6 41 (13.8%) 18 (15.8%) 7 264 (88.6%) 108 (94.7%) 8 50 (16 8%) 33 (28.9%) 9 65 (21.8%) 17 (14.9%) 1+9 0 ( 0% ) 0 ( 0% ) 1+8 4 ( 1.3%) 6 ( 5.3%) 5+8 6 ( 2.0%) 10 ( 8.8%) 172 m cm. v.-p oo.m m.vm m.Pm mo.— «5. F.vF o.mN m.m— v.05 n.nw N.¢m~ ommv mam m cm. 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These events tend to be e1astic (10w EH) with negative missing energy, probab1y resu1ting from somewhat uncertain momentum fitting (especia11y on 383-3215). The e1asticity suggests these may be mis-identified tridents, a1though it is possib1e that vector meson or heavy quark production may be responsib1e. Figure 5.8 disp1ays one of these events. Fina11y, a sma11—sca1e effort has been made to examine dimuons from Samp1e E (incident pions instead of muons) with the hope of: (a) finding a p(3100) peak, to a11ow an accurate check on the ca1ibration of the experiment (the 1ower mass vector mesons give much broader peaks, amidst 1arge background, making them unsuitab1e for this purpose) and (b) comparing hadronica11y and 1eptonica11y produced dimuons within the same experimenta1 apparatus. Unfortu- nate1y, the incident hadron energy for these runs was 1imited to 150 GeV, making the rea1ization of either goa1 difficu1t. We have ana1yzed approximate1y 8% of the Samp1e E data in the same manner as the muon sampTes. Figure 5.9 disp1ays the apparent mass and azimutha1 opening ang1e distributions of Samp1e C (150 GeV muons) vs. Samp1e E (150 GeV hadrons) whi1e Tab1e 5.12 compares kinematic averages and approximate rates. C1ear1y, the apparent mass range does not extend as far as the w(3100), due to the 10w incident energy and the poor apparatus acceptance for the 1ow energy muons which resu1t from hadron interactions. Whi1e some comparison of muon and hadron induced dimuons may be possib1e, the 10w statistics a110w 178 m 92 .Aucmvwgh omo umwwwpcmuHumwz mpnwmmoav mmm 4m cmwznn.w.m mgzmvu N>m Em mm: _ __ mm 1 @352 VEmE 35> j #5 “NWT Fzm>m wdm. 2.3/m 179 .>mw of pm 20:55 @832; A 3 cos: 3.2+: cogumz U8 comCmanu--.m.m 953... + 112 ow v. 9V Nan. Q. . 00 E . \ \\ \\\ . \e \ saw \ \ JV \ 1m 3 W 1N_ mu 5 d d w 3 H 1w. 0 9w. .7 9 m. 1cm on . mo, mcanE .1 >80 098265 .8 202:6 1.: >60 omWSQo {aw m 80:66 .1 >00 098265 1_ m: 28.5“. 1.. >8 ancmao .1 1mm H m. 9 mm m m TABLE 5.12.—-Pion vs. 180 Muon Induced Dimuons Samp1e E (150 GeV n+) . Samp1e C Quantity (150 GeV u ) Sing1e Estimated Tape Tota1 Dimuons Tota1 28 76 (988) Found OSP 18 64 (832) SSP 1O 12 (156) OSP/SSP 1.8 5.3 F1ux 1.38 x 109 9.36 x 107 Luminosity 1.25 x 1036 2.39 x 1035 Uncorrected Rate/F1ux 2.0 x 10'8 8.1 x 10-7 Uncorrected Cross . Section 2.2 x 10'35 3.2 x 10‘34 Averages Leading( Partic1e Ehergy 78 GeV 24 GeV Produced( Partic1e Enérgy 20 GeV 32 GeV 4-Mom. (Q2 ) transfer squared 5.9 (ES-1)2 3.9 (2%!)2 Produced( muon transverse 0.80 ES! 0.91 fig! momentum E Energy ratio (El) 5.8 1.1 2 Po1ar Ang1e (A6 ) Difference 12 72 mr 40 mr Apparent Mass (M12) 2.6 9%! 0.9 fig! c Azimutha1 (Ao12) Ang1e 149 degrees 72 degrees Difference 181 on1y weak conc1usions. Since hadron induced dimuons have been experi- menta11y studied in detai1f3we have not pursued the ana1ysis of the Samp1e E further. 5.4 Trimuon Events Trimuons wou1d be the predominant mu1timuon type in muon scattering if: (a) such events were most1y e1ectromagnetic in origin (because the virtua1 photon has the quantum numbers of a muon pair) or (b) the semi-1eptonic branching ratios of produced hadrons (e.g., D° mesonS)were 1arge. However, trimuons are actua11y an order of magnitude scarcer than dimuons apparentTy because the pure1y QED processes are suppressed re1ative to the hadronic ones and the branching ratios of the produced hadrons are a11 :j0%. Further suppression of trimuons re1ative to dimuons arises from the occasiona1 1055 of a fina1 state muon due to the 1imited apparatus acceptance, especia11y at 10w angTes. The rates and average kinematics of trimuon events are pre- sented in Tab1es 5.13 and 5.14. The track fixing procedure has not been as successfu1 for trimuons as dimuons, due to spark chamber inefficiency and the tendency for at 1east one muon to be very near the ho1e in the spectrometer. Thus, on1y about ha1f of the trimuons found are comp1ete1y determined kinematica11y. Figures 5.10 through 5.12 disp1ay some of the kinematic distributions with curves from the QED trident ca1cu1ation superimposed. A1though the 1eading partic1e characteristics are not substantia11y different from those for dimuon events, trimuon produced muons favor 1arger momenta and 182 TABLE 5.13.——Trimuon Numbers and Rates Hadronic Hadronic Tota1 Leptonic Uncertain Category Tota1 (Not Leaky) (Leaky) Hadronic Vertex Tota1 Trimuons* 64 25 6 31 24 9 Ana1yzab1e* Trimuons 36 11 1 12 17 7 Samp1e A Samp1e D_ Samp1e C Quantity (270 GeV p+) (270 GeV u ) (150 GeV u+) Trimuons 64 18 3 Found Trimuons 36 7 0 Ana1yzab1e Trimuons 72 (:6) 20 (:5) 3 (i2) Corrected for Losses Found .143 .117 .107 (3u/2u) Corrected .112 .091 .075 (3u/2u) Found 5.9 x 10- (3u/f1uX) Corrected (6.61.8) x 10'9 (6.5i1.6) x 10' (3u/f1ux) Found 2.3 x 10- 3p “cross section: 9 9 9 5.8 x 10- 2.2 x 10' 9 9 (2.2 i 1.4) X 10— 36 36 36 2.3 X 10' 2.4 x 10- -36 -36 36 Corrected (2.61.3) x 10 3p “cross section“ (2.5i.6) X 10 (2.4i1.6) x 10‘ *Samp1e A on1y. TABLE 5.14.-—Trimuon Kinematic Averages Average Samp1e A Samp1e D Leading u Energy (E1) 152 GeV 97 GeV 4-mom. transfer squared (02) 6.7 (gig!)2 8.5 (§%1)2 Hadron Energy (EH) 22 GeV 30 GeV Produced p2 energy (E2) 43 GeV 46 GeV Produced p3 energy (E3) 47 GeV 60 GeV Transverse momentum (P12) of “2 re1ative to virtua1 photon 1.1 §%! 1.6 9%! Transverse momentum of (P13) u3 re1ative to virtua1 photon 1.1 9%! 1.0 9%! Produced Pair Mass (M23) 2.3 %§1 2.5 $31 Po1ar opening ang1e (A923) 66 mr 59 mr Azimutha1 opening ang1e (A¢23) 107 degrees 120 degrees Ine1asticity (n) .10 .24 184 10.0:- f f :2 a c (9 _ 3 C) in «a _ Lo: m, 0.1 I 1 I | I 0 60 120 130 240 300 El (69V) 10$): 1 3 I 1 g s > ‘3 ' uJ l l l 100 120 I40 I 1 l 1 20 40 60 80 E2(GeV) o '0 Figure 5.10.-—Trimuon Data Energy Distributions versus Ca1cu1ated QED Trident Resu1ts. 185 1 1 1 J 36 72 108 144 180 13%; (degrees) 1 10.0" i 100— C i E a r 3 1: _g C E g .1: F a); '9 IJJ LL! 1.0- b O 40 80 120 I60 0 Aez3(m'r.) 10.0: f E f 10.0 .‘3 ' m I c.s E s g .a - g .0 r LIJ 1.1.1 L 1.0- C L 0.: 1 1 4 4 '20 .04 .28 .52 .76 1.0 I "£105116V17 Figure 5.11.-—More Trimuon Data Kinematics M23(GeV/c2) versus Ca1cu1ated QED Trident Resu1ts (Kinematic Definitions as in Figure 1.1). 186 10.0- 1 E i . w I .2 E c c 0 :3 b o u?! 1: Q, 1 1 1 1 1 1 J 1 o .5 1.2 L8 2.4 3.0 as o .s 12 1.8 2.4 3.0 3.6 (P1): (GeV/c) 1P1.)5(GeV/c) I00:, 1 f i 10.0: i } I : V’ ' 1’ ‘ 1 1 .. c c C c .— 2 5 3‘43 I.” _ 1: 1.0:- 10— ' 1 OJ 1 1 1 1 L J o' 1 1 1 1 1 1 -I -.s -.2 .2 .e 1.0 1.4 ‘1 ‘5 ”2 1 6 1° '4 0‘13 ‘ °¢12_ Figure 5.12.--Sti11 Further Trimuon Data Comparisons with QED Trident Ca1cu1ations. 187 f1atter distributions. The ine1asticity distribution suggests an exp1anation for this; trimuons seem to be primariTy e1astic, with most of the energy avai1ab1e to the fina1 state muons, instead of the hadron shower. Another observation is that the transverse momentum distributions are much f1atter for trimuons (near1y uniform out to 2—3 GeV/c, in sharp contrast to the exponentia1 fa11-off character— istic of dimuons) which indicates that hadronic processes do not dominate the trimuon samp1e. The asymmetry distributions mere1y indicate that the 1eading muon remains genera11y more energetic than either produced muon. A c1ose examination of the produced pair mass (M23) suggests an enhancement in the bin where p(3100) wou1d be expected to appear. Given the mass reso1ution of about .3-.5 GeV/c2 in this region, one can perform a smooth fit to neighboring bins, giving a background of 3 events. This cou1d predict 6 i 3 events to have resu1ted from p(3100) production. Tab1e 5.15 shows the kinematics of the events most 1ike1y to be from this process and Figure 5.13 disp1ays one of these events. C1ear1y, e1astic production (with 1itt1e missing energy) is favored. Furthermore, the events tend to concentrate near a azimutha1 opening angTe of 180° and have 1arge produced muon energies and transverse momenta. These are a11 characteristic of the production (at rest in the CM frame) and subsequent two muon decay of a heavy partic1e. The average apparent mass of 3.1 i 0.1 for the six events is in good agreement with the accepted u mass and gives us confidence (to the few percent 1eve1) in the energy ca1ibration of 188 F.owp N.wu NF.m oo.F mm.~ ~.wp _.m— o.~m ¢.ov m.- m.mN1 m.~m u.¢vp N.okm o—Fm mum p.—o— m.~m m~.m mN.— mm.~ o.“ 1 «.mv m.o~ m.Fm m.m~ ~.¢m1 m.o~ w.mo— m.Fm~ “mmm mmm m.—m_ m.vm oo.m mo.F ww.— o.MM1 o.o e.¢m o.pm m.o v.m51 N.mm o.om_ ~.m~m mmom N—m m.on— c.0w eo.m pm.o N—.F o.wF1 0.0 m.m~ «.mm ¢.N~ m.mm1 ¢.¢P v.mmp m.o- mwom mmm m.mo— m.oo Fp.m om.— om.F N.N~ m._N ~.om m.Fm m.om N.~m1 m.m~ m.mo— p.mom mum -N m._N— m.ou c—.m o—._ _N.~ m.~1 N.N_ m.o¢ o.wv N.NF ~.m~1 m.mm «.mmr m.wm~ ommo mNN A3833 83 TM“? Ammuvmwz A>|wavmfi Aflunievmza 28sz 38$ 25mm 253 CE; 263$ A>m$~m ~3qu gwwvom ”:85 EE 38$ 9 2338.. o 28 8:32.; 8:55-225 39: .Azmumo vcm coepuzvosa 9 mFDMaogmv pcw>m cozswepi1.mr.m wczmwu m m 1 N_>m 3m “mm _ _ _ > _ _ _ _ _ 189 thw tzu>m haw 25m 190 our experiment. If we make rough corrections for finding efficiency (89%), kinematic 1osses (50%) and acceptance (estimated from the trident ca1cu1ation to be 2.5% for the pi va1ues characteristic of the w events), the tota1 cross section times branching ratio is 36 cm2, which is consistent with the ca1cu1ated to be (20 i 10) x 10' pub1ished muOrproduction va1ue9 of (49 i 14) x 10'36cm2, given the 1arge uncertainties in the corrections. After subtraction of the six events presumed to be from w production, Figure 5.14 shows some of the sensitive kinematic dis— tributions for the remaining trimuons, a1ong with estimated hadronic backgrounds from the charm and hadronic recombination processes as ca1cu1ated by Keung.10 C1ear1y, these hadronic mechanisms give tri— muons with 1ow produced muon energies and transverse momenta. A1though the norma1ization is uncertain, we can subtract this hadronic background, 1eaving the sma11 samp1e shown in Figure 5.15 again with the QED trident ca1cu1ation superimposed. The kinematics of events most 1ike1y to be tridents are 1isted in Tab1e 5.16 and one such event is disp1ayed in Figure 5.16. Sad1y, the 10w statistics prevents any attempt at extraction of trident cross sections from the data, (which wou1d be a usefu1 extension of such measurements from the 11 previous 10w energy studies at Brookhaven). PresumabTy, more recent muon experiments with improved 10w angTe acceptance and higher incident f1ux wi11 be ab1e to measure trident cross sections, if hadronic backgrounds are not overwhe1ming. 191 loo? I '9°: 1 h - - : if - C W - Q; g - \ E O 1. 1.1 I: 2 z 5 - “J5 to; \\\ 10 F \ 1- . I l 1 l 1 l 0.. OJ 1 I l [—1 o 20 40 so so 100 120 a 5 12 L8 24 so E3(GeV) P1316 eV/c) IQO— - > — 8 _ a Q ' 1 a 3 o - fl 5 c ‘E 1: E 9 3 - 3 D “J Lu “ LO:- \ n1 1 1 1 1 I 1#_1 °"_l‘— 3 .8 1.6 2.4 3.2 4.0 4.3 5.6 ° 36 72 '03 '44 "3° A15 (dagrus) M23(GeV/cz) 2’ Contributions Subtracted versus Figure 5.14.—-Trimuon Data with w . (as described in the text). Tota1 Hadronic Background 192 .mcowpmrzofimu gcwvweh omo msmew> mvczoemxoom oecoeumx pp< we cowpumcenzm empe< muon cozewch11.m_.m weaned 981m 33813 ON_ 00. om ow 9» ON 0 Qm Qm QN m._ N._ w. o . — _ _ _ — _ ”.0 — _ — — _ — _O 2 s e s . - /\ ._ L. H .7/ H {3 H .11.. . c : /IO._ / IO. 2 L L . . / L. :1 0. HA” : 1 M. w m U u w. o. - s 11.0.9 no.0. 193 o.NN N.m mm. 24. m_. 0.9 w.m m.FN m.o~ F._F o.oe- m.- o.ocp o._2~ oeme 02m e.~o_ «.08 mo.~ Nm. ON.F _.m_ 0.0 e._e w.em m.m m.m_- N.eo m.omp o.~mm mmee men _.om_ “.me mo.~ ma. em. m.~ - o.o N.Pe e.N_ _.m e.mm- F.mFF m.em~ a.me~ mmee can o.ao m.om a_.F 02. mm. 2.0 - 0.0 N.o~ m.em m.e_ m.2e- $.00 e.wme o.o- moem mwm e.mm N.~m mm._ eN. mm. «.me- 0.0 P.oo o.m~ e.a_ m.e - m.Nm_ m.mm_ m._NN coca mom m.Nw_ o.oe om._ 02. mm. e.m- o.o m.a_ m.o~ o.__ m.me- m.- m.mm_ m.me~ _mmm oew N.mw o.mm om._ me. ma. e.m 0.0 o.e_ N.we o.w m.m~- «.mm m.mo~ e.oo~ mew mNN Amooemouv m~o< AemWoa Awmez AEWMWa A>mea A>oovzm A>ouvxm Acevmo Aeevmo Acevpe A>oavmm A>ouVNm A>oov_m A>o¢vom oeo>m cam $6333 ”:83: .6» 3.595;; :o=EC._.11.2.m 53:. 194 .Aoeoeeee Duo o_eenoeav oeo>m eozeeee--.o_.m mesmea "mm _ _ m>_m N_>m Sm mm: _ _ Tofiax .9 92 02 92 32 m2 F-O _ 7>u_> f mNN 13x m v 41 om>> me o Ea 195 5.5 Exotic Events Severa1 physica1 mechanisms (inc1uding doub1e tridents, heavy 1epton combined with heavy quark production or charged heavy 1epton 12 for the pair production) have been discussed in the 1iterature production of events with more than three fina1 state muons. A1though, the improbabiTity of this has ru1ed out any systematic search for such events, ca10rimetric information fOr dimuon and trimuon events has pinpointed one event (332 - 75) which may have four fina1 state muons. However, the tracks and ca10rimeter ana1ysis are ambiguous as to whether the possib1e fourth muon penetrates into the spectro- meter. Again, the more recent, high 1uminosity experiments shou1d see these exotic events, if they are produced in muon interactions. CHAPTER 6 CONCLUSIONS 6.1 Introduction The conc1uding chapter of this dissertation has three objectives: (1) to summarize the methods and resu1ts of experiment E319 pertaining to 1eptonic sources of mu1timuon events (primariTy QED tridents and heavy 1eptons); (2) to discuss changes in the apparatus and data—taking of E319 which wou1d have improved the mu1ti- muon samp1e without substantia1 expenditures of time or money; and (3) to suggest genera1 princip1es for the design of further mu1ti— muon studies and compare these requirements with the status of third generation experiments a1ready in progress. 6.2 Summary of Mu1timuon Resu1ts A1though neither experiment was exp1icit1y designed to study events with more than one fina1—state muon, such mu1timuon events have been found, at 10w 1eve15 initia11y in E26, and in substantia11y 1arger numbers from E319. Severa1 possib1e exp1ana- tions have been proposed for the existence of muon—induced mu1ti— muons. The most 1ike1y source of such events is the virtua1 photoproduction of hadrons, either sing1y (e.g., uN + unX, n + no) diffractive1y (e.g., 1111 4 111x, 11 + 1111) or in pairs (eg. 1111 —> upobox, D0 + kip, D°~+hadrons). WhiTe a11 of these hadronic processes are 196 197 suppressed due to the 10w branching ratios of the hadrons into muons, recent mode1s (e.g., photon-g1uon fusion) suggest that they may sti11 dominate mu1ti—muon production. Associated charm pro- duction (D000) seems especia11y favorab1e. A second type of process which resu1ts in mu1ti-muon fina1 states is the weak production of neutra1 (uN + MOX, M0 + u+u'v) or doub1y charged (uN + k++x, k++ + u+u+v) heavy 1eptons. Most gauge theories which purport to combine weak and e1ectromagnetic interactions contain such heavy 1eptons (a1though the current1y favored Weinberg-SaTam mode1 does not). WhiTe such partic1es have not yet been found, the experimenta1 1imits are not particu1ar1y strict. A fina1 category of processes which may contribute to mu1ti—muon events invo1ves the direct e1ectromagnetic pair production of muons (or possib1y charged heavy 1eptons) via Bethe—Heit1er, bremsstrah1ung or Compton mechanisms. Quantum e1ectrodynamics a110ws the ca1cu1ation of these processes and indeed muon trident production has been observed at 10w energies in good agreement with the prediction. Sca1ing these resu1ts to E319 energies predicts sma11, a1though not neg1igib1e, event rates. The apparatus for experiment E319 can be functiona11y divided into three major parts; incident muon detection, interaction vertex and shower energy measurement, and fina1 state muon detection. The beam muon was detected via a system of scinti11ation counters and mu1ti-wire proportiona1 chambers which give good spatia1 (and timing) information, as we11 as a momentum ana1ysis from the 1ast beam 1ine magnet. The incident muon energy cou1d be varied from 25 to 270 GeV with a typica1 intensity of 5 x 105 muons per spi11. 198 Ha10 was vetoed at the front of the target. The event vertex and shower energy were measured via an iron-scinti11ator hadron ca10ri- meter, which a1so served as the target. Ca1ibrated with hadrons of known energy, the ca10rimeter showed good 1inearity and an energy reso1ution ranging from 5% at high energies to 25% at very 10w energies. The sampTing frequency 1oca1ized each event vertex 1ongi- tudina11y to within a few centimeters. Fina11y, the muons emerging from the interaction were detected and momentum-ana1yzed by eight toroida1 iron magnets and nine wire spark chambers. Scinti11ation counter banks provided triggering and timing information. The energy resoTution of this magnetic spectrometer averaged about 10%. Muon energies cou1d be measured with good efficiency from 5 GeV to 250 GeV and muon scattering angTes from 10 mr to 150 mr were accepted. The 10w produced muon energies and sma11 1eading muon ang1es characteristic of mu1timuons found in both experiments suggested the need for a new ana1ysis program capab1e of working from the front of the spectrometer. Deve1oped over an extended period of time with constant feedback from the growing mu1timuon samp1e, this track reconstruction program MULTIMU has become the main data ana1y— sis tooT for a11 aspects of E319. Combined with the time-consuming, but effective, visua1 scanning procedures and the vertex and muon detection capabi1ities of the ca10rimeter, this has proved to be an efficient method for finding and ana1yzing mu1timuon events. With the addition of detai1ed manua1 reconstruction of some events, the overa11 finding efficiencies were determined to be (70 i 7)% for 199 dimuons and (89 i 7)% for trimuons. Rough1y 92% (56%) of the dimuons (trimuons) were kinematicaTTy ana1yzab1e in fu11 with 1osses pri- mari1y due to poor acceptance of 10w energies and sma11 angTes. The drastic effects of experimenta1 acceptance on mode1 pre- dictions for E319 have necessitated Monte Car10 simu1ations of the dominant mu1timuon processes, inc1uding associated charm production, shower pion (kaon) decay, and QED tridents. C1ose c011aboration with theorists from the University of Wisconsin has supp1ied inde- pendent checks for these and severa1 other possib1e mechanisms. Whi1e the kinematic distributions of the Monte Car10 ca1cu1ations are genera11y be1ievab1e, abso1ute norma1ization is much more uncer- tain, especia11y for the charm mode1s. This hampers the background subtractions needed to study the sma11 1eptonic signa1s expected from QED trident or heavy 1epton production. Because of the 10w rates predicted for the heavy 1epton processes and the uncertainty in mode1 predictions, I have chosen to search for them using direct kinematic tests app1ied to the data, instead of e1aborate Monte Car10 simu1ation. The mu1timuon resu1ts presented in Chapter 5 indicate that hadronic processes (particu1ar1y charm production) account for the bu1k of dimuon events, as evidenced by the comparison of experimenta1 kinematic distributions and rates with those ca1cu1ated by the Monte Car10 simu1ation. A1though subtraction of these hadronic predictions is an uncertain proposition due to the norma1ization difficu1ties, the resu1ting distributions agree reasonab1y we11 with Monte Car10 200 predictions for QED tridents, a11owing for the acceptance Toss of one fina1 state muon. A very few 1arge transverse momentum dimuons remain, which may be from heavy 1epton (or heavy quark) production. App1ication of kinematic cuts, designed to se1ect neutra1 heavy muons (or possib1y doub1y charged heptons) out of a 1arge hadronic background, yie1ds a few candidates. However, norma1ization uncer— tainty and the 1arge over1ap between kinematics preferred by heavy 1eptons and tridents make firm conc1usions untenabTe. Accepting the hypothesis that the most 1ike1y of the candidates is tru1y a neutra1 heavy 1epton yie1ds a cross—section estimate consistent with the best upper 1imit pub1ished. Trimuons, a1though an order of magnitude 1ess numerous than dimuon events, are a1so not so severe1y dominated by hadronic pro- cesses (rough1y 50% as opposed to over 95% for dimuons). We have identified 6 i 3 events in the apparent mass distribution, which appear to derive from the production and two—muon decay of the 9(3100) meson. Subtraction of these events, and the ca1cu1ated charm and hadronic recombination backgrounds, yie1ds kinematic distributions which agree reasonab1y we11 with QED trident predic- tions, within the uncertainties. There is 1itt1e evidence for other processes in the trimuon samp1e. One exotic event with possib1y four fina1 state muons has been found, but the kinematics are not fu11y-determined, 1eaving on1y specu1ation about its origin. 6.3 Improvements in E319 E319 was origina11y proposed as a further study of deep- ine1astic muon scattering designed to extend tests of Bjorken 201 sca1ing to 1arger qz. The discovery of mu1timuon events had a con- siderab1e inf1uence on the fina1 p1anning and experimenta1 condi- tions of E319, especia11y in the p1acement and use of spectrometer detectors such as the hadron proportiona1 chambers and trigger banks. However, the need to minimize the impact on deep—ine1astic studies necessitated some unfavorabTe apparatus features for mu1timuon work, inc1uding: (1) poor detection immediate1y after the target due to the sma11 size of the hadron proportiona1 chambers and the rate 1imitations of the front spark chambers; (2) fu11 magnetic fie1d in each toroid causing 1ow—energy produced muons to be bent out of the spectrometer too quick1y or, worse, into the veto counters; and (3) inappropriate design of the trigger bank and veto counters in the h01e region favoring rejection of the typica1 10w ang1e 1eading muon. These prob1ems are most severe for QED tridents and e1ectro— magnetic processes in genera1, and 1east troubTesome for heavy partic1e production (e.g., charm or heavy 1eptons). The simp1est so1ution to a11 such difficu1ties is to take more data and attempt to work around the prob1em in ana1ysis. How- ever, due to demand for the neutrino and muon beams, this option was unavai1ab1e for E319. In the fo110wing, we detai1 some apparatus changes which wou1d have enhanced the mu1timuon aspects of E319, at minima1 expense to the deep ine1astic studies. The acceptance prob1ems cou1d have been ame1iorated by simp1y shifting some of the spectrometer detectors to different 202 positions. Given the success of the MULTIMU ana1ysis at track recon- struction from the front of the spectrometer, the back two spark chambers were unnecessary and cou1d have easi1y been shifted to the front, giving greater detection redundancy. It might have even proved feasib1e to offset some of these chambers to improve wide- ang1e muon detection. With increased shie1ding in the toroid ho1es, the 1ast beam veto (BV3) wou1d a1so have been unnecessary, and its e1imination wou1d have prevented the tendency for 1ow-energy posi- tive muons to bend back into the ho1e and veto events. Trigger bank detection cou1d have been extended further into the ho1e, a11owing a much more efficient mu1timuon trigger to be formed and great1y aiding ana1ysis of these events. Trident production, being primariTy 10w ang1e by nature: is not we11-suited to an experiment with a centra1 ho1e and veto, but heavy partic1e production cou1d have been preferentia11y se1ected by triggering on high transverse momentum ine1astic events (perhaps with the aid of the ca10rimeter). A1though 1itt1e cou1d have been done about the 10w rate capabi1ity of the spark chambers, a reduction in event rate from more se1ective triggering, or a reduction in the muon beam ha10 wou1d have great1y 1essened the effects. However, it is c1ear that the proposed heavy 1epton rates sti11 wou1d not have been substantia11y improved with— out a 1arge increase in incident f1ux. 6.4 Third Generation Muon Experiments Based on our experience with mu1timuons, I be1ieve that future experiments must emp1oy the fo11owing: (1) an improved muon 203 beam (with higher rate or at 1east 1ower ha10); (2) proportiona1 or drift chambers in p1ace of the s1ow spark chambers, especia11y to improve mu1ti-track efficiency; (3) more f1exib1e triggering schemes to enhance mu1timuon signa1s and simp1ify event finding and (4) improved acceptance, both at 10w ang1es and energies and at 1arge ang1es. Third generation muon experiments have a1ready taken considerab1e data both at Fermi1ab (E203) and CERN (NA2 and NA4). E203 has taken the nove1 approach of making the target and spectro- meter part of the same detector, giving exce11ent angu1ar accept- nce. Furthermore, they use proportiona1 chambers and emp1oy severa1 mu1timuon triggers which make use of ca10rimeter information. How- ever, they use essentia11y the same muon beam as E319. The CERN experiments have the advantage of a fantastic muon beam (107 muons per spi11 with on1y 10% ha1o), but use fair1y conventiona1 target and spectrometer arrangements, which may not represent a 1arge improvement in acceptance over our experiment. A11 of these experi- ments have rough1y an order of magnitude 1arger incident f1ux than E319, and, with the apparatus improvements mentioned, they shou1d iso1ate mu1timuons from heavy 1eptons if the cross sections are not substantia11y Tower than current upper 1imits. Shou1d these experi- ments fai1 to detect heavy 1eptons, the discovery may have to await the construction of the proposed Tevatron muon beam at Fermi1ab. APPENDICES 204 APPENDIX A THE HADRON CALORIMETER 205 APPENDIX A THE HADRON CALORIMETER A.1 Theory and Design Considerations The use of the measurement technique ca11ed ca10rimetry is conceptua11y as simp1e in partic1e physics as in its origina1 chemistry app1ications. The basic idea is to obtain a measure of the energy re1eased in a process by immersing it in a suitabTe medium which samp1es that energy in a proportiona1 manner. In p1ace of the temperature measurements used for chemica1 reactions, however, parti- c1e ca10rimeters must determine the number of partic1es produced in an interaction which can be re1ated to the energy invo1ved. Such techniques were first used in cosmic ray experiments1 where typica1 partic1e energies are often far too 1arge for conventiona1 magnetic energy measurements. More recentTy, the advent of high energy acce1erators and neutra1 beams has made ca10rimetry even more attrac- tive. A variety of forms have evo1ved depending on the energy and composition of the partic1e showers to be measured.2 Neutrino experi- ments in particu1ar have pioneered the samp1ing ca10rimeter used to measure hadron showers in which scinti11ation detectors are inter- spersed with heavy target p1ates (usua11y iron).3 The target acts as the medium with which the incoming beam interacts and the scin- ti11ators then samp1e the spatia1 distribution of the resu1ting 206 207 shower of hadrons and thus obtain a measure of the energy deposited. If the incoming beam consists of neutrinos, the hadron shower energy can be used to determine the neutrino energy. A1ternative1y, if the incoming partic1es are charged so that their energies are a1ready known, the shower energy can be used to determine if there is any "missing energy” carried away by produced neutrinos. The previous muon experiment E26 was equipped with a few scinti11ation counters in its iron target part1y for this reason. However, the sma11 size and inadequate pu1se height range of the counters effective1y pre- vented their use for ca10rimetry. From the experience gained there, and the pub1ished neutrino ca10rimeter work, came the motivation and the necessary information to bui1d a hadron ca10rimeter for the present muon scattering experiment. The E319 hadron ca10rimeter was designed with three functions in mind: (a) to improve the energy reso1ution of the apparatus for events with 1arge energy transfer to the virtua1 photon; (b) to determine the interaction point a10ng the beam direction with better spatia1 reso1ution; and (c) to measure missing energy for mu1timuon events. Achievement of these goa1s required that the ca10rimeter be made sufficientTy wide (51 cm) and 1ong (738 cm) to contain hadron showers with energies up to 200 GeV. Furthermore, the samp1ing distance (i.e., the width of the target p1ates) had to be sma11 enough (4.8 cm) to give good spatia1 and energy resqution without making the cost astronomicaT. The choice of iron for the target materia1 was a compromise between minimizing mu1tip1e scattering and 208 energy 1055 (which increase with atomic number) and maximizing the abi1ity to samp1e hadronic (re1ative to e1ectromagnetic) showers. A1uminum and p01yethy1ene targets were a1$o purchased to a11ow tests of nuc1eon number dependence for muon scattering and mu1timuon pro- duction, a1though 1ack of beam time prevented their use. The detectors in the ca10rimeter needed to respond to the anticipated 1arge range of shower hadrons with good spatia1 uniform- ity and 1inearity. The re1ative1y new p1astic scinti11ation materia1 NE110 seemed to be the cheapest way to satisfy this demand. To match the spectra1 output of this materia1, u1travio1et transmitting 1ucite was used for a111ight guides and specia1 g1ues were used to form the resu1ting counters. The choice of photomu1tip1ier tube was comp1icated by the need for a high degree of stabi1ity with time, so that constant gain checks wou1d not be needed. Most of the common tubes used in high energy app1ications were found to be rather unstab1e, especia11y at 1arge anode currents. The 1east expensive compromise turned out to be the new RCA 6342A, which tests had shown to be stab1e over suffi— cient 1engths of time and 1arge 1ight 1eve1s.4 About twice as many tubes were purchased as were actua11y used to a11ow the se1ection of on1y the ones with good signa1—to-noise ratios and minima1 instabi1— ity. The tube base e1ectronics were taken from standard designs used successfu11y on other ten stage phototubes. Direct measurement during the data runs convinced us that dynode vo1tage sagging was negTigib1e. 209 Ana1og-to-digita1 converters (ADCS) were used to convert the vo1tages from the phototubes into the digita1 form needed by the computer. Two methods were considered for achieving the 1arge dynamic pu1se height range needed: (a) use a sing1e Togarithmic response ADC for each counter, or (b) use two 1inear response ADCs each with a different amp1ifier gain,for the same counter. This second option a110ws a broader range, with the same resoTution and easier ana1ysis, so it was chosen. The fast amp1ifiers needed to take the tiny photo- tube signaIs (10 to 100 mv, 20 ns Tong) and convert them into signaTS more compatib1e with ADCs (100—1000 mv) were patterned after a work- ing design of Sippach. The actua1 choice of ADC was for a11 practi— ca1 purposes determined by the necessity of having 220 tota1 channe1s. 0n1y the new Lecroy 2249A, with 12 channe1s per modu1e, seemed feasib1e. Fina11y, a target cart had to be bui1t which wou1d a110w movement of the enormousTy heavy ca10rimeter (10.6 metric tons) a10ng a set of rai1s to give maximum f1exibi1ity in target p1ace- ment. The iron p1ates were constructed to hang free1y a10ng rai1$ in the target cart with the counters sandwiched vertica11y in between. The a1uminum frames of the counters maintained c1ose and uniform packing, minimizing air gaps which might a110w shower Teakage. A.2 Construction A11 of the scinti11ation counters, tube bases, and amp1i— fiers for the ca10rimeter were bui1t at MSU whi1e FermiTab supp1ied the ADCs and high voTtage supp1ies. Among the many prob1ems invoTved 210 in making 1arge scinti11ation counters for pu1$e height measure- ment, the worst is non-uniform 1ight attenuation from the point of passage of the partic1e to the phototube. This is rea11y a two- foId prob1em since the absorption or scattering of 1ight can resu1t either from the actua1 geometry of the counter, or from construction techniques such as poIishing and g1uing. This is further comp1i- cated by the fact that 1ight from scinti11ator is primari1y u1tra- vioTet, which is difficuTt to transmit through many materiaIS and scatters easi1y. This section describes some of the techniques used to construct scinti11ation counters for E319. The scinti11ation p1astic arrived a1ready cut to the proper size and poTished on a11 sides. Very carefu1 handTing was neces— sary to minimize crazing due to heat, stress, and chemicaTS. The 1ight pipes consisted of two pieces: (a) a trapezoida1 piece of 1ucite to funne1 the 1ight from the 20 inch scinti11ator edge to a f1at 12 inches, and (b) seven stripes of 1ucite twisted separate1y to transport the 1ight into a rough1y 2 inch circ1e which matches the phototube aperture. A11 of this 1ucite was machined and tedi- ous1y po1ished on the sides to preserve the tota1 interna1 ref1ecting qua1ity and reduce scattering of 1ight. However, the faces to be g1ued were not poTished, since a better g1ue joint resu1ts if the surface is s1ight1y rough. A counter was then put together in the f011owing way. First, the 1ucite strips were made f1exib1e by heating in an oven and care- fu11y twisted into the proper shape by a jig. They were then bonded together by a so1vent bond cement (ca11ed H94 from A1mac P1astics, 211 Co., Grand Rapids, Michigan). Next, the 1ucite trapezoid was g1ued to the strips using a specia1 non-ye110wing epoxy (ca11ed P530). The g1uing was done horizonta11y with a jig constructed to app1y some pressure to strengthen the joint and suppress air bubb1es. If the qua1ity of the joints was visua11y bad, they were easi1y broken and reformed. The scinti11ator was then attached using the Nuc1ear Enterprise optica1 cement NE580. Here the g1uing was done verti— ca11y, using gravity to squeeze out air since it was found that this pressure was crucia1 to the optica1 qua1ity and strength of the joint. Fina11y, the counter was wrapped to keep extraneous 1ight out, usinga combination of an inner 1ayer of a1uminum foi1 and outer 1ayers of b1ack viny1 p1astic and tape. The assemb1ed counter was then p1aced gent1y into its a1uminum channe1 frame and secured at the top by a c1amp arrangement to provide mechanica1 stabi1ity and a110w easy hand1ing. The phototubes were separate1y wrapped in a1uminum foi1 and b1ack tape. They were then secured to the face of the 1ight pipe simp1y by strapping tape, since it was decided that grease or g1ue coup1ings were too unstab1e. In order to shie1d the photocathode from potentia1s in the outside wor1d, the a1uminum foi1 wrapping of the tube was tied to the cathode high vo1tage via a current 1imiting resistor. Fina11y, the vita1 magnetic shie1ding was provided by commerciaI mu-meta1 shie1ds to protect the sensitive dynode chain focusing. This comp1eted the construction for one counter and the process was repeated at 1east 110 times over a space of approximate1y 6 months to bui1d the who1e ca10rimeter. 212 To conserve money, the tube base and amp1ifier circuits were a11 made in-house at MSU. The amp1ifiers were p1aced four to a printed circuit board of Camac size. This unfortunateTy contributed to some cross-ta1k prob1ems between channe1s and was not the most optimum design. However, the moduTarity and use of bussed card vo1t- ages a11owed for easy repIacement and repair. A.3 Testing Since the ca10rimeter counters were required to provide abso— 1ute pu1se height information, it was essentia1 to test their spatia1 uniformity, 1inearity with respect to energy input, and stabi1ity with time. Of course, each counter was first verified to be 1ight- tight by simp1y watching the noise signa1s under dark and 1ight room conditions and taping suspect spots. Then, using severa1 beta sources of differing energies, the uniformity of response at severa1 points on the scinti11ator was checked. The spectra1 shape of the pu1se height for each source is we11 known and degradation of that shape is usua11y a sign of poor 1ight transmission. Severa1 counters were broken apart and re-g1ued to reduce their non-uniformities to the 10—15% 1eve1 which seemed typica1 of this counter geometry. A1though techniques exist to further suppress such variance by se1ective absorption of u1travio1et 1ight, it was fe1t that this wou1d be unnecessary since ca1ibration data over the who1e face of the ca10rimeter cou1d be readi1y used to correct for non-uniformities. The next test invo1ved the use of cosmic rays to study the response of the counters to minimum ionizing muons. It was hoped 213 that this wou1d determine the voTtage and re1ative gains of a11 the counters and perhaps the singTe muon resoTution. However, the fast 2249A ADCs were not avai1ab1e at this time and the cosmic ray rate of around 10 counts/sec. was insufficient to rea11y pin down the gains. Sti11 the information obtained was a great aid in 1ater ca1ibration efforts. The first attempt to understand the energy response of these counters invo1ved the use of the 50 MeV proton beam of the MSU cyc1otron. The procedure was to varythebeam energy by using absorbers and then to p10t energy deposited in the scinti11ator versus 1ight output (measured as signa1 voItage times width). The test showed good 1inearity for absorbed energies between 10 and 30 MeV, with deviations due to stragg1ing and signa1 mismatches between counters and ana1yzers. These tests were not pursued further since the most important 1inearity curve wou1d be the response of the whoIe ca10rimeter to incoming high energy hadron beams (see section A.4). Fina11y, ha1o muon tests were made at Fermi1ab just prior to the running of E319. These muons resu1ted from an upstream hadron experiment and were used essentia11y as an intense cosmic ray test. Since the proper ADCs were now hooked up, the counter vo1tages and gains were set using these muons. To obtain the desired pu1se height range, it was necessary to make the high gain amp1ifier channe1s with a gain of around 35 and the 10w gain channe1$ with a gain around 1. Then, with counter vo1tages between 1200 and 1500 vo1ts, the 214 singTe muon peaks appeared in channe1 50 for the high gain channe1s and channe1 10 for the 10w gains. LEDs were mounted on each scinti11ator, supposed1y to pro- vide a monitor of the stabi1ity of the counters during the data taking. However, the LED signa1$ were bad1y mismatched for the ADC range and, even worse, there was no feedback to insure that the LEDs themse1ves were aTways giving the same amount of Tight. Due to severe time pressure, it was decided to use singTe muon peaks as monitors of the ca10rimeter stabi1ity. A1though somewhat broad, these peaks verified that the who1e ca10rimeter system was stab1e over the course of the data run to within 10% except for one de1iber— ate shift. During the first set of data runs, it was discovered that noise from the spark chambers was ab1e to feed into the ground paths of some of the ADCs and turn their gates back on, scrambTing some of the puTSe heights. To correct this for the 1ater data, tiny ferrite core transformers were p1aced on a11 inputs to the ADCs to absorb the spark energy induced. This had the effect of a downward shift of the ca10rimeter ca1ibration which was measured and corrected for in the ana1ysis. We understand that LECROY has since modified their design for the 2249A ADC to prevent such occurrences.5 A.4 Ca1ibration Energy caTibration of the hadron ca10rimeter was obtained by using incident hadron beams of known energy which create hadron showers at a much higher rate than incident 1eptons. The assumption in our case is that the showers deve10p in much the same manner, 215 independent of the incident partic1e type. The ca1ibration then required corre1ation of the 220 ADC readings with the number of charged partic1es present. This presumes know1edge of the response of each counter to no incoming partic1es (ca11ed the pedesta1 1eve1) and one minimum ionizing partic1e. Pedesta1s were monitored through- out the experiment by de1iberate1y writing out events when no beam was present,whi1e singTe muon peaks were obtained simp1y by trigger- ing on unscattered incident muons. In the ana1ysis, pedesta1s were determined then by averag- ing the raw ADC channeIS over the rough1y 1000 events on each of the 38 pedesta1 runs, with bad channe1s corrected from other runs. The pedesta1s range from channe1 4 to channe1 12 with the typica1 va1ue being around 7. The width of the pedesta1 peaks is usua11y 1ess than 2 channeTS. Sing1e muon peaks were partia11y obtained in the same manner for the 7 unscattered muon runs. However, in p1ace of averaging, the peaks were fit by Gaussians since stragg1ing biases the means more than the peaks of these distributions. This pro- cedure worked we11 for the high gain channe1s, but faiTed for the 10w gains, where the muon peaks were crowded into very 10w channe1 numbers near the pedesta1. However, by measuring the re1ative gains on the high and Tow gain channeTS, it was possib1e to ca1cu- 1ate the 10w gain muon peaks by the formuTa: (Low Peak) = (Low Pedesta1)-+((High Peak) - (High Pedesta1))/ Re1ative Gain 216 Now, with the O and 1 partic1e responses known, it was simp1e in princip1e to corre1ate energy with pu1se heights. The ADC channe1 numbers were first converted into equiva1ent partic1es by the formu1a: Partic1es = (ADC reading - Pedesta1)/(Muon Peak - Pedesta1) This set the sca1e for the energy ca1ibration, which is then simp1y the s1ope of a p10t of the sum of the equiva1ent partic1es in the ca10rimeter shower versus the known incident energy. Detai1ed studies of shower deve1opment have shown that the poor1y samp1ed parts of the showers do not prevent a 1inear ca1ibration a1though they do broaden the reso1ution somewhat. However, even a sma11 1eakage of the showers can significantIy a1ter the ca1ibration and we made carefu1 studies of shower containment in our data. Tab1e 3.1 summarized the hadron ca1ibration data taken for E319. The first period was essentia11y a Shakedown run for the ca10rimeter with the object being to compare its response to simi- 1ar devices and sett1e the fina1 configuration. Longitudina1 spatia1 response was of particu1ar concern, so severa1 sub—sections of the ca10rimeter were separate1y studied. Litt1e difference was detected between the response of the sub—sections and the whoTe ca10rimeter, imp1ying that even the highest energy showers were we11 contained within about one third of the ca10rimeter. This was not true of the runs made with a1uminum and p01yethy1ene targets where c1ear 1eakage effects were seen at high energies. Prob1ems with some ca10rimeter 217 channe1s, uncertain beam energy determination, and very high incident hadron rates (which give 1arge tai1s on the distributions) prevented the use of this ear1y data for actua1 energy ca1ibration. A second period of hadron ca1ibration, just before the main muon runs, focused so1e1y on obtaining a good energy ca1ibration for the fu11 iron target. A negative hadron beam was used due to its 1ower rate and the fact that it consisted primari1y of pions without the 1arge component of protons present in the positive beam. Five energies ranging from 25 GeV to 225 GeV were studied (the beam 1ine was unab1e to give reasonab1e f1uxes outside this range). Fina11y, a third set of ca1ibration runs were made near the end of the experiment in order to study how the ferrite cores affected the ca1ibration and to determine the stabi1ity of the response with time. Further tests were a1so made on potentia1 rate effects, spark chamber noise inf1uence, and spatia1 uniformity of the ca10rimeter as a who1e. The fina1 a1gorithm for determining the ca1ibration con- stants and reso1ution of the ca10rimeter began by decoding a11 high and Tow channe1 ADCs and converting the numbers to equiva1ent parti- c1es. Then a search was made for showers, with the definition being at 1east four consecutive counters with greater than 10 equiva1ent partic1es present in the high gain ADC channe1s. The vertex is then the first counter of the 1argest shower. This procedure was comp1i- cated by the presence of noise spikes and missing channe1s, with recovery methods needed to find some showers. To ca1cu1ate the energy of each shower, the equiva1ent partic1es of a11 counters 218 within the shower p1us two on either side were summed. Norma11y, the 10w gain ADCs were used, since the high gain signa1s overf1ow at around 20 partic1es. If the 1ast two counters in the target had signa1s exceeding 10 partic1es, the shower was 1abe1ed as 1eaky and its energy not trusted. Histogramming the resu1ting equiva1ent partic1e sums gives a Gaussian distribution to a good approximation. The peaks of these distributions were p1otted versus the mean inci- dent hadron energy to form the ca1ibration, whi1e the widths gave a measure of the ca10rimeter energy reso1ution. The resu1ts of this ana1ysis on the second and third sets of ca1ibration data are shown in Tab1e A.1 and in Figures A.1 and A.2. Furthermore, Tab1e A.2 com- pares our ca1ibration and reso1ution with that for simiTar ca10ri- 3,6 meters. The ca1ibration seems quite consistent with the pub- 1ished data, a1though our reso1ution is somewhat worse than might be expected. This prob1em was studied by making a whoie series of geometric and shower cuts on the hadron data, Tooking for factors which affect the widths of the distributions. It was found that showers which start 1ater in the ca10rimeter and extend over more counters have better reso1ution, as shown in Figure A.3. This imp1ies that short, e1ectromagnetic showers were often present at the front of the ca10rimeter and these seem to be inadequate1y samp1ed. A more comp1ete understanding of this prob1em wou1d have required more extensive ca1ibration data which we were unab1e to obtain. Neverthe1ess, disagreements with other experiments and pub1ished Monte Car10 ca1cu1ations7 were a11 1ess than 10% which gave us 219 4000 - 3000 - «n .2 .2 E o. E» 2000 - _‘>_’ 3 0’ 11.1 a O 5 1000 " .secpnd set of calibration runs ,ihird set of calibration runs ' 1 1 J 1 1 O 50 100 150 200 250 Incident Hadron Energy (GeV) Figure A.1.--Hadron Ca10rimeter Energy Ca1ibration. I Expect 0a (EH) ’2 so that slope would be -.5, 50... Actual slope = 255 2 .03 4o - g 30 — c .2 20- :5 8 Q) 7 9.: l0 - b V l l I 111111 I 1 IO 20 3O 4O 60 8OIOO 200 300 EH = Incident Hadron Energy (GeV) Figure A.2.--Hadron Caiorimeter Energy Resoiution {Dots are from second set of ca1ibration runs and triangles are from the third set). 221 TABLE A.1.--Summary of Hadron Calibration Resu1ts for E319 Run Incident Hadron Energy Ca1orimeter Shower Equiva1ent Partic1es Nos. Peak (9P) Reso1. (z) Peak (GeV) ResoT. (%) A B C A B C 2nd Ca1ibration, Last 2/3 Iron Target, n- incident, 01d ADC patch pane1 163, 165 228.4 0.7 3708 3796 -— 5.3 5.5 -- 166, 167 99.6 0.9 1682 1741 -- 9.2 9.5 —- 168 24.6 1.6 383 421 -- 20.1 15.7 -- 169, 170 149.5 0.8 2527 2597 2490 7.2 7.6 6.7 172 49.4 1.1 823 885 -- 13.8 13.8 —- 2nd Ca1ibration, Fu11 Iron Target, n' incident, 01d ADC patch pane1 173 224.6 0.8 4066 4079 3928 6.2 7.5 5.5 174 24.6 1.6 395 410 419 19.8 16.6 16.7 175 99.6 0.8 1832 1833 1792 9.7 10.6 8.7 176 49.5 1.2 875 894 890 14.1 14.2 12.4 177 149.8 0.8 2751 2763 2676 7.9 8.7 7.0 3rd Ca1ibration, Fu11 Iron Target, HT/p incident, new ADC patch pane1 558 101.5 1.4 1617 1663 1672 8.7 8.8 8.5 560 50.3 2.0 767 808 815 12.9 12.1 12.4 563 24.6 3.6 340 377 384 20.5 16.6 16.2 564 151.6 1.3 2454 2504 2517 7.3 7.4 6.1 ____________________________________________c________________._.________________ A = Standard shower a1gorithm with no cuts. B = A110w on1y events with sing1e shower found and not 1eaking out the back of the ca10rimeter. = A150 require that the shower start we11 into the ca10rimeter and that the first two counters are qutet. {'3 222 TABLE A.2.--Comparisons with Other Hadron Ca1orimeters Incid. CERNa CALTECHb E319C Expected E319d Hadron (t=5cm) (t=10.16cm) (t=4.76cm) o from Ener y (GeV? ep o(%) ep o(%) ep o(%) CERN CALTECH 5 18 38.4 10 53 33.1 15 234 20.3 20 106 25.3 25 419 16.7 15.7 15.1 30 496 14.7 165 19.9 50 865 11.7 269 15.8 890 12.4 11.4 10.8 75 1326 9.6 100 1725 7.8 538 11.1 1792 8.7 7.6 7.6 140 2449 6.9 150 808 8.9 2676 7.0 6.4 6.1 200 1056 7.9 225 3928 5.5 5.3 5.1 250 1287 7.3 cuts 0 is asee Reference 1. bSee Reference 2. CFrom the 2nd ca1ibration runs173-177 with the fu11 set of C 1isted in Tab1e A.1 dAssuming 0(t1) M/t] 8131:52— : FWHM(ep) the reso1ution ( equiva1ent partic1es. where t is the samp1ing thickness; /2.355 peak(ep)) and ep means 223 <\/ .Aczc mcmzogm cocvm: we cameo; use coneaz 3:598 .235 *9 £934 on nu ON 9 o. n _ _ . _ _ 8:28:86 €8.65 2. U111] 00 g 9 IO 0° hmm¢mN— OOO (°/6)U°!1nl093t1 O O (.0 [0 ¢ sapguod 1 . // l 1 l I 1 l 1 J I l I quwEZopmo .0325 *0 .258 955.63 to wocwvcwawosn (%)U°um°saa o swing-yon;- own OOO¢ sapguod 08 S o 9 ugq/sxunog O O N .m.< wcsmwd 224 confidence that the calorimeter information would be useful in the muon data analysis. A.5 Uses of Calorimeter Information In this section, I will evaluate how well the calorimeter data for the muon runs lived up to expectations, especially for multimuon events. The easiest objective was to determine, with good resolution, the event vertex along the beam direction (ca11ed ZADC). Figures A.4, A.5, and A.6 show the distributions in ZADC for single muon, dimuon, and trimuon events respectively. Clearly, the multimuons prefer more downstream vertices, mostly because the muon acceptance is better there. Also, both beam pion and shower pion decay origins of multimuons are essentially ruled out here because the events would then be strongly peaked at the front and back of the target, respectively. The ZADC vertex distributions agreed very closely with those obtained from muon track information, but supplied better spatial resolution. By averaging the high gain signals for counters well before the shower, the number of muons entering the target could be obtained. The number of muons exiting the target was available in a similar manner, as long as the shower was not too close to the end. Figures A.7, A.8, and A.9 show the distributions of these muon numbers for single muon, dimuon, and trimuon events. Although shower straggling supplies large tails on these distributions, it is clear from the ratio of leaving to entering muons that our multimuon assignments were correct. 225 000 11 .825 mewECoEo m5 59¢ 20.5.58 xwtm> p55 :0: 28505 08 00... com 08 oo. _ _ o oo.. o - 11,1141/fl/1/fi/ONO Z m—chmaiéi 9.3m; OO_ ugq 1110017 Jed siua/g 226 .Auo pco>m 503551.96. 95?... OO. o oo_- 08. o ugq ms 017 /s,iue/\3 227 .AQQ ch>m cozEwLHIl. A58 . oo La IO .. 5 .- O 21 1 I l L J 0. 1.0 2.0 3.0 4.0 5.0 Average Particles Before Shower Figure A.9.——Average Number Particles Before and After the Vertex for Trimuon Events. 231 The most difficult use of the calorimeter was the determina- tion of missing energy for multimuon events. The ADC decoding, shower location and equivalent particle summing algorithms were the same as those used to analyze the hardron calibration data except that the particle sums were converted into energies from the fits of Table A.l. At that point in the analysis then, we had the incident muon energy at the front of the target, the hadron shower energy at the interaction point, and the final state muon energies from the momen- tum fitting routines evaluated at the end of the target. A deter- mination of missing energy required that energy loss corrections be made to estimate all muon energies at the interaction point. This was done using a polynomial fit to published energy loss tables for muons in iron.8 Note that this was only an average correction which ignored straggling effects. To test the consistency of these energy measurements, the resulting hadron energy was compared with the difference between inci— dent and scattered muon energies for single muon events where the missing energy should be zero. A histogram of this comparison is shown in Figure A.lO, from which it is clear that the mean is zero within errors. Furthermore, the width of the distribution is only slightly larger than that expected from the measured calorimeter and spectrometer resolutions. Binning this missing energy versus hadron energy (Figure A.ll) shows that the only problems were at very low hadron energy (due to noise and poor resolution) and very high hadron energy (due to leakage and calibration inaccuracies). 232 Om cm can 933 .685 053:2 ON _ O _ ON: . OW- Own _ Omio 1 O Q I 1 o o 8 8 A99 ’0 Jed siuang I C) C) sf I O O In ... 00w IEOON .383 :03: 39.5 .84 33cm mcwmmwzldf,‘ 33m: 233 MISSING ENERGY Figure A.ll.--Average Missing Energy (per 25 GeV bin) versus Hadron Energy for Single Muon Events. 234 The otherwise good agreement over most of the energy range lends con- fidence in the energy calibration of both the calorimeter and the spectrometer. For multimuons, missing energy was defined as the incident energy minus the energy of all final state muons minus the hadron energy, with all defined at the interaction point. Dimuon missing energy distributions are shown in Figures A.12 and A.l3. The peak missing energy is clearly not zero, although the width is considerably larger than the distribution for single muons due to the generally poorer resolution of the extra muon. Furthermore, the missing energy also increases with the hadron energy, a characteristic feature of heavy hadron production and decay which has been shown to dominate the dimuon samp1e. Although the statistics are poor for the tri- muon sample, the missing energy distribution shown in Figure A.14 is consistent with a mean of zero. This supports the hypothesis that these events tend to be largely due to trident and vector meson pro- duction. In summary, the hadron calorimeter has contributed in a significant way to the identification and understanding of multimuon events. The missing energy distributions, in particular, tend to discriminate against some of the many possible explanations for these events. Although the construction and operation of hadron calorimeters is by no means trivial, the advantages for multimuon work are so convincing that all proposed muon and neutrino experi- ments will employ some form of calorimetry. 235 A.mpcw>m 03p mcwpcwmwcgwc cowmw>wu so mpcm>m to Logan: my onum rmowpcm> mskv >0 am we 8 a. 9%. .mp:w>m nose 91 mm cpwz :Tn >m¢ v Lma To com Amsmcm mcwmmwzii - - u . _ _ _ _ _ _ Ib\ >oom.mu1_mv 3962.. 38:2. 385 _ IIIIIArIIII Nni m4: ¢wi .N_..< 9:3: 236 32" ED- 16" L” —¢l"" Z ,_— " " w ’ fl (5) (3 i I I Z 50 100 150 200 250 EH E5; 5 '16- ‘32- Figure A.13.--Average Missing Energy (per 50 GeV bin) versus Hadron Energy for Dimuon Events. 237 A.p:w>m mco mcwpcmmmgqme cowmw>wu some spwz awn >ww ow Lon mpcw>w mo Logan: mw mFmom quvpsm> wcpv .mucm>m cosewch Low xmcmcm mcwmmwzii.¢r.< wczmwu xococm 00. om cm 0? ON 38:2 ON... 0*? 0m: Om- 00.1 q — u - u u u — APPENDIX B TRACK RECONSTRUCTION AND FITTING ALGORITHMS 238 APPENDIX B TRACK RECONSTRUCTION AND FITTING ALGORITHMS B.l Introduction This appendix is devoted to a more thorough description of the algorithms used to reconstruct and fit muon tracks in the analysis program MULTIMU. Although developed specifically for the E319 appara- tus, these methods are widely applicable to any magnetic spectrometer with toroidal symmetry about the beam axis. B.1 Vertices One of the most powerful means of rejecting halo muon and spuriously-matched tracks found in the spectrometer was to make cuts on the vertex position of the track with the beam. In MULTIMU the distance of closest approach of each line found at the front of the spectrometer to the beam track was calculated using the following method. Take any two non-parallel lines (shown in Figure 8.1) which can be parametrized as R. = F. + n.t. 1 1 1 1 The unit vector 239 240 L2 Figure B.l.--Vertex Algorithm Geometry and Conventions. 241 is then perpendicular to both lines and the distance between them is then d=(R2—R]).G This can be minimized in the standard way by taking derivatives of d with respect to each coordinate. But, for only two lines at minimum distance, the equations _; (2-R1)°n1=0 (R2'R])°n2=0 allow an easy solution for t1 and t2. Since the matched lines in the E319 coordinate system are of the form =.+. =.+.z z_t x x1 a1z y y1 B1 , we then easily obtain the 2 position of the vertex (ZMIN). This is sufficient to make cuts which insure that the tracks really come from the general vicinity of the calorimeter shower (ZADC) in the target. Then, projecting the beam to (X1, Y1, ZMIN) and the line candidate to (X2, Y2, ZMIN), the quantity 2 2 a DMIN = [(X2—X1) + (Y2-Y1) ] allows a further cut on the track quality. This method can be generalized to give the spatial position 0f the vertex for any number of lines by defining a point P = (X, Y, Z) in space. By drawing a vector R from P to line i, it is obvious that the perpendicular distance between P and the line is 242 Since this becomes analytically unmanagable for more than a few lines, the calculation is most often done numerically. B.3 Tracing Muon Trajectories in Magnetized Iron The algorithm for tracing tracks through the toroidal spectro- l meter was originally developed for the E26 apparatus and has required only minor modifications for E319. The basic approach was to treat each magnet as a set of discrete bend points for the track as shown in Figure 8.2. Then the x coordinate of the track at the nth detector (2“) can be written ) = (Slope, intercept, 2 position) just before the where (a , x0, 2 o 0 first magnet and Ax' = slope change at bend point zmi. The equation for yn is of exactly the same form due to the cylindrical symmetry of the apparatus. The slope changes can be derived from the Lorentz force equation: 243 .cocH vawpmcmmz gmzoczu mcosz mcwomch Low Acpweomwii.m.m mczmwa 252. 2.3 .335 3&3 2.3 .252: n N _ 5005050 m N _ _ .3628 244 Ax' = égx.= —kf(r)Lcos¢ Ay' = éfi¥~= —kf(r)Lsin¢. These complicated functions of k, r and p can be expanded in a Taylor series and truncated at second order in k with little loss of accur— acy. The resulting expression for the slope changes consists of a first order term, accounting for the bending due to a uniform magnetic field, and a second order term which contains the effects of field variation with radius and muon energy loss in the iron magnets. Of course, these approximations would be expected to break down at very low momenta (large k) or in regions of large field variation. They have proven quite adequate for most of the scattered muons in the E319 apparatus. Detailed comparisons of projected tracks versus actual spark coordinates have assured us that, excepting a region very near the hole in the magnets, tracks with momenta between 5 and 300 GeV are followed quite well. The above algorithm can be reversed so as to give momentum estimates for a potential track by ignoring the small second order terms and forming a pseudo chi-squared equal to the sum of the squares of the actual sparks minum predicted positions. This can be minimized as a function of k, leading to a solution for the momentum p. Although this estimate is somewhat biased at the extremes of the momentum range, it has proven useful in finding tracks. The final momentum fitting uses a more sophisticated approach as described in Section 8.5. 245 B.4 Spark Finding As described in Chapter 3, track finding in MULTIMU begins by finding x and y lines at the front of the spectrometer, forming matched three-dimensional lines, and then projecting them into the magnetic region via the algorithm described in the previous section. However, there are several reasons why the sparks will not, in general, lie along the projected track. First, the finite wire spacing of the chambers causes a Gaussian extrapolation error about the pro- jected track position downstream. This can be calculated by assuming the absence of the magnets so that the predicted position at any chamber 2 is x = a (2n — z ) + b n O with (a, b, 20) being the (slope, intercept, 2 position) of the upstream track just before entering the spectrometer. The deviations due to extrapolation error can then be written = + Axn znAa Ab with the slope and intercept changes related to the chamber resolution a by: m (4312 AaAb 2 3 7?] 2i Determinant 2 = O 1' of the AaAb (Ab) m m 2 above -2 z. Z 21 matrix i=l ‘ i=1 246 Due to the cylindrical symmetry, the extrapolation error becomes a circular spark finding window about the projected track with radius re — Axn. A much more serious source of deviation is multiple scattering of the muons in the iron magnets. The problem here is that the mag- netic field causes the positions at successive downstream chambers to be correlated with physical deviations like multiple scattering upsteam. This has the effect of offsetting the spark-finding window from the projected track position, as shown in Figure B.3. The result- ing overall shape of the spark finding window, consisting of a set of circles of increasing radii and offsets, is that of an hourglass. The radii of the multiple scattering part of the window were derived from the equations for RMS angular deviation and average linear 2 deviation = L //TT given in the particle data book. From Figure B.4, it is clear that Y‘X = + xp = [L/T +1] and similarly for ry. Defining A2 = [2n - zml, zeff = L (1//7F - l/2) gives r = [zeff + A2] th . . where 2n = nth spark chamber, zm = m magnet mid-paint. 247 m actual window Yp" * (the star marks 0' spark position) _ Yo‘ rc rrn yn-I- l t : xn XO xp wlndow rotated and translated for analytic convenience Figure B 3 --Definiton of the Hourglass Window for Track Find1ng. 248 .coLH cw mpow+wm mcwcwupmum quwupzz mcwpmraupmu Low mcowpcm>cou use Acpmeowoii.¢.m acumen omiuw 8.62% {E f. 59:3 cozomuum 86: crocooE 05 co: All-II — V M I‘ I roctotoom 23:2: I l o: 5.3 389:.— > _. 249 Thus, the mu1tip1e scattering radius rm at chamber n is The definition of the overa11 window, given the conventions used in Figure B.3 becomes: 2_ 2 2 2_ 2 2 r0 — re f rm (x/xmax) — yO + (x-xo) 2 _ 2 2 where xmax — xp + yp A spark is considered to be within the window if: (a) a reaT solu- + r ) S x s (x + , - max m max rm) The hour tion exists for x and (b) -(x giass window has proven to be a very reTiabTe and efficient aigorithm for accepting on1y sparks consistent with real tracks and inhibiting the tendency to be puiied off by bad sparks. Once sparks are found in at 1east two of the four views, they are matched to give true (x, y) coordinates with cuts made on the consistency of agreement between sparks found in x or y planes. This redundancy gives a fina1 discrimination against the inciusion of accidenta] sparks on the track. 8.5 Momentum Fitting Once the sparks on a muon track have been found, it is necessary to perform a giobai fit in order to determine the most TikeTy va1ues of momentum and upstream track parameters which wou1d have given rise tothose sparks. The resu1ts of this fit are then 250 used for a11 further kinematic ca1cu1ations. The genera1 strategy was mapped out in Chapter 3. Here I concentrate on the definition and minimization of the chi-squared function and specific improvements made to this aTgorithm for mu1timuon work. In order to achieve the best fit, chi-squared had to be defined so as to account for corre1ations of muTtipTe scattering and measurement errors between a11 of the chambers on the track. There was a naturaT distinction in the E319 apparatus between the front three chambers (TabeTed 8, 9, and TO), which were not within the mag- netic part of the spectrometer, and the downstream seven chambers (TabeTed T through 7). Therefore, chi-squared (X2) was defined as x2 = CHIF + CHIB where CHIF is the chi-squared of the upstream, and CHIB of the down— stream portions of the track. The upstream chi—squared was defined by 10 2 2 CHIF = kig {[xm - (exzk + x0)] + [ym — eyzk + yo] }/ 2 2 2 [OF + omS k ] where (xm, ym) = measured spark coordinates at chamber k, (ex,ey,xo, y ) = sTopes and intercepts of the track exiting the target, OF resoTution of the upstream chamber k and Oms = error due to mu1tipTe scattering in the hadron shie1ds at chamber k. The best fits were found with 251 0 2 { 3.6 cm for chamber 9 OF - - cm and 0ms _ T5.3 for chamber 8 The downstream chi squared is more compTicated due to muTtipTe scattering correTations: 7 7 = — ‘1 - CHIB -: § [xm xp]1 yij [ym yPJj is the matrix which correTates the positions at chambers where yij i and j and (x , y ) are the predicted positions from the aTgorithm P described in Section 8.2. The correTation matrix can be written 2 .o 8 - zmk)(zj - zmk) + 6T3 y.. = Z (2. 13 ms k=T T zmk is the 2 position of the kth magnet where o is the resoTution of the downstream chambers is the RMS muTtipTe scattering angTe ms negTecting the effect of energy Toss. This chi-squared is a function of five parameters: K =-%, the inverse momentum (e e ) the x and y sTopes at the front of the spectrometer X, 9 the x and y intercepts at the front of the spectro- (xo,y0), meter. 252 Miminizing x2 as a function of these five quantities wiTT return their best fit vaTues. This was done by expanding anaTyticaTTy in a TayTor series, keeping terms onTy through second order in k, and then differentiating with respect to each of the parameters twice to obtain the direction the parameters woqu have to be varied to reach minimum x2. SymboTicaTTy, this can be written (XX),- = ”MOW _J (zx)i. J (Ami J . . . 2 where xx = partiaT derivatives of X zx = matrix of second partiaTs with respect to the 5 parameters AP = variations in the five parameters. We then soTve for the variations (zx);1 (xx).. (Ami = J J L4. ll MU __a This requires the inversion of the 5 x 5 2x matrix, for which the CERN Tibrary routine SPXINV3 was used. The procedure was numeri- caTTy iterated untiT Ak/k s T%. We have verified that this actuaTTy does converge by pTotting the xzcurve for aTT different types of tracks. ATthough the generaT form of this fitting procedure has supp1ied by the E26 caTTaboration (as described in their status report),4 we have made severaT improvements. These incTude: 253 a. The deveTopment of a procedure to puTT bad sparks from a track and refit it. (This was essentiaT for the reTativeTy high momentum Teading partic1es of muTtimuons); b. The requirement that the tracing routines consider each magnet as three bend points, instead of just one, which greatTy improves the fits for Tow energy muons; c. Minor corrections were made to the actuaT coding which was somewhat incorrect at the extremes of the momentum range. These changes have significantTy improved the performance of the fitting procedure, especiaTTy for the typica1 muTtimuon event with a high-energy, Tow-angTe Teading muon and a Tow-energy, wide-angTe produced muon. Furthermore, this has aTTowed an extension of the kinematic range avaiTabTe to singTe muon anaTysis as weTT. APPENDIX C MONTE CARLO ALGORITHMS 254 APPENDIX C MONTE CARLO ALGORITHMS C.T Introduction This appendix describes a few usefuT techniques empToyed in the E3T9 Monte CarTo caTcuTations to simuTate the foTTowing physicaT processes: (a) muon energy Toss; (b) muTtipTe CouTomb scattering; (c) curvature of muons in the magnetic spectrometer; and (d) form factors used for coherent scattering process, such as the Bethe- HeitTer trident diagrams. This information is appTicabTe to virtuaTTy any experiment which attempts to simuTate muon kinematics. C.2 Muon Energy Loss There are four principaT mechanisms for energy Toss by charged particTes in matter: (a) ionization, or the interaction with atomic eTectrons; (b) bremsstrahTung, the radiation of reaT photons in the atomic or nucTear fiers; (c) eTectron pair production; and (d) inter- actions with the nucTeus or individuaT nucTeons. These are given in the order of their importance for the average energy Toss by muons in our energy range. However, none of these mechanisms gives a strictTy symmetricaT distribution of energy Tosses because they aTT resuTt from statisticaTTy independent scattering events. Instead, each has the usuaT Landau taiTs, especiaTTy on the Targe energy Toss end of the distribution. This l'straggTing'I is particuTarTy important 255 256 for bremsstrahTung because its differentiaT cross section is inverseTy proportionaT to energy Toss E. It is Tess reTevant but stiTT not negTigibTe for ionization, which goes Tike T/EZ. At our energies, straggTing can be ignored for pair production, since the cross section varies as T/E3 and the overaTT probabiTity is Tow. Even the average energy Toss from nucTear interactions is negTigibTe at energies Tess than about 300 GeV, so we ignored this mechanism compTeteTy. Thus, our energy Toss simuTation attempted to modeT the fuTT distribution for ionization and bremsstrahTung and incTuded the average energy Toss from pair production. The average ionization energy Toss for particTes heavier than the eTectron is given by the weTT~known Bethe-BToch equation,1 which has been modified to account for severaT smaTT atomic effects. Ioniza— tion straggTing was first studied by Landau2 and Tater by Symon.3 Their resuTts are summarized by Rossi,4 whose equations and graphs we have used. The idea is to define a most—probabTe energy Toss from the Bethe-BToch equation, and then use the distribution functions pTotted in Figure 2.7.2 of Rossi. Ne fit these functions using a centraT Gaussian section and a combination of exponentiaT and poTy- nomiaT taiTs and used this as the throwing function for the Monte CarTo. TabTes C.T and C.2 compare our simuTation with the caTcu- Tations of Theriot.5 CTearTy, the average energy Toss is weTT reproduced, aTthough he gives no information on straggTing. Muon bremsstrahTung has aTready been discussed as the first part of the pseudotrident muTtimuon process. The principTe refer— ence is the very compTete work of Tsai,6 with additionaT heTp from 257 TABLE C.T.--Comparison of Muon Energy Loss Monte Car10 CaTcuTations . Thickness of TotaT Energy Loss Inc1dent . Energy Target (GeV) Difference (GeV) (cm) (g/cmz) ”Theriot” E3T9 5 5 28.8 .054 .057 6.1 100 575.9 1.071 1.142 6.6 700 4031.3 >5.0 >5.0 —-- 10 100 575.9 1.135 1.189 4.8 20 100 575.9 1.209 1.259 4.1 50 100 575.9 1.348 1.380 2.4 100 100 575.9 1.555 1.580 1.6 150 5 28.8 .088 .085 —3.1 100 575.9 1.751 1.776 1.4 700 4031.3 12.255 12.390 1 1 270 5 28.8 .111 .110 -1.2 100 575.9 2.229 2.233 0.2 700 4031.3 15.601 15.492 -0.7 T"—————' 258 TABLE C.2.--Contributions of IndividuaT Processes to Muon Energy Loss CaTcuTations Incident Thickness of Percent of TotaT Due to: Energy Target (GeV) (cm) (g/cmz) Ioniz. Brems. Pair Prod. NucTear 5 5 28.8 98.9 0.5 0.5 <0.T TOO 575.9 99.0 0.5 0.4 <0.T 700 403T.3 99.0 0.5 0.4 <0.T TO 100 575.9 97.9 0.9 0.9 <0.3 20 T00 575.9 95.8 1.8 2.2 <0.2 50 100 575.9 89.3 4.8 5.5 <0.3 100 100 575.9 79.6 9.3 10.2 0.9 T50 5 28.8 71.8 T3.0 T4.0 T.2 TOO 575 9 7T.7 T3.T T4.0 T.2 700 4031.3 71.7 T3.T T4.0 T.2 270 5 28.8 57.6 20.2 20.6 T.6 TOO 575.9 57.4 20.2 20.6 1.8 700 403T.3 57.4 20.2 20.6 T.8 259 Rossi and Tannenbaum.7 If a muon with energy E radiates a photon of energy k, equation 111.82 of Tsai suppTies the differentiaT cross section as a function of the fractionaT photon energy y = k/E: d 3%: C; F(y) where F(y) is a very compTicated function invoTving detaiTs of the atomic properties of the target materiaT. To obtain a tota1 cross section, we cut off the spectrum at: M 4 ymax = 1 - 15' and ymin = T x TO to keep photon energies within reasonabTe bounds and prevent the cross section from diverging. Then, the probabiTity 0f bremsstrahTung is the product of the tota1 cross section and 1uminosity. The finaT aTgorithm to caTcuTate energy Toss from this process uses a poTynomiaT fit to the energy dependence of the tota1 cross section to determine when a non—zero energy Toss shoqu be generated (around 2% of the time). Then y is thrown by the differentiaT cross section to yier the energy Toss y . E. Again, the average energy Toss is shown in Tab1es C.T and C.2. At the Towest energies, the differences from Theriot grow as Targe as 20%, but the totaT contribution of bremsstrah- Tung to energy Toss is stiTT quite smaTT. The main features of eTectron pair production by high energy 7 . . muons are weTT summarized by Tannenbaum, who gives apprOXimate forms of the cross section and discusses the simiTarity with bremsstrahTung. 260 However, we have used more recent formuTae of Joseph8 and Richard- Serre9 to actuaTTy caTcuTate the average energy Toss for each energy. From TabTes C.T and C.2, it is obvious that Theriot has done the same. The overaTT energy Toss we obtain agrees with his resuTts to within 10% at aTT energies, with the Targest difference being at very Tow energies and distances. C.3 MuTtipTe CouTomb Scattering MuTtipTe scattering refers to the net change of direction of charged particTes due to many smaTT-angTe scatters from the CouTomb fiers of nucTear matter. The phenomenon has been thoroughTy 1] The resu1ting described in the Titerature by MoTiere10 and Scott. anguTar distribution is approximateh/Gaussian, but with taiTs due to straggTing just as in the energy Toss process. These represent Tess than T0% of the distribution for muons in our experiment and are ignored in the Monte CarTo. The average anguTar defTection is given .12 by 2 02 .37 = (.OT5 GeV/C) L_.=_%%§ P2 82 LR where omS is then taken to be the standard deviation of a Gaussian throwing distribution: One actuaTTy generates an angTe e in the standard manner: = _ 2 a 6 ( Tn (random #) x Oms ) within the intervaT from 0 to T. This angTe is then used to a1ter the direction cosines and the muon is traced on from there. C.4 Curvature of Muons in the Magnetic Fier Due to the smaTT step Tength (5 cm) used for tracing muons through the simuTated E3T9 apparatus, and the desire to repTace detai1ed reconstruction aTgorithms with simpTe resoTution tabTes, the method for propagating muons through the magnetic spectrometer is simpTe. Ignoring smaTT second order terms from fier derivatives and energy Toss, and using the standard formuTae for the radius of curva- ture of a partic1e of momentum p in a TocaTTy constant magnetic fier 8 yiers the change in unit momentum vector: (dX x B) Ulg-L II 2 Ir Here 61 represents the step vector and 8 the magnetic fie1d direction. Since the fie1d for E3T9 was azimuthaTTy constant, BX = Bcosa By = Bsina BZ = 0 Thus the direction cosines change in each step 0 by: ADCX = - RD sin¢ ocz ADCY = RD cos¢ DCZ ADCZ = RD (sing DCX - cosp DCY) 262 where DCX, DCY, and DCZ are the on direction cosines. The resuTts are then renormaTized to unity for the next step. Note that the apparatus resoTution was then easiTy incTuded by simpTy ”wobbTing” the generated kinematics, after each track is traced, by the actuaT measured widths of the momentum, angTe and position distributions. C.5 NucTear Form Factors In our consideration of eTastic Bethe-HeitTer tridents, we used form factors F(qg) to describe the compTex charge structure of the nucTeus as a whoTe. RecaTT that for a sphericaTTy symmetric charge density p(r), one has:13 4:. 09-58 '11 F(qz) = F o (r) sin(qr) dr where r is the radius, and q the momentum transfer to the nucTeus. In the ear1y days of eTectron scattering, the eTastic form factors T4 of nucTei were studied in detai1 by Hofstadter and many others. The form factor of the proton was fit by the dipoTe form 2 2 -2 F(Q)=(1+——CL—‘g) .7T x T0 corresponding to an exponentia1 charge density. A1though simiTar form factors have been considered for heavier nucTei, better fits are obtained by using the Fermi charge distribution 263 p0 p(r) = ____-—___?:E-—— 1 + exp (7') where c = a density radius = 1.07A1/3 b = skin thickness=4 Tn (32) =.2.4 fm 1/3 a = RMS radius = .82A + .58 . T An approximate expression for the Fourier transform gives: 6 2 2 mgr) F q ' '_-_73?_72_ 1+?q 2 2 where for iron %; = 71.6 x 10_6 —l—§, ‘%T = 24.6 x 10.6 -—l7§ MeV MeV This works weTT untiT the momentum transfer becomes so high that the individuaT nucTeons are being expTored. In that region one can revertto the form factors for the proton and neutron again. Thus, for coherent (Fe) tridents we have used the Fermi form factor, whi1e for incoherent (p) tridents, we summed the dipoTe contributions 0 from the 56 individuaT nucTeons in the iron nucTeus. REFERENCES 264 REFERENCES~-CHAPTER 1 1J. J. Thomson, PhiT. Mag. 34, 312 (1897). ATso see D. L. Anderson, The Discovery of the ETectron (Van Nostrand, Princeton, New Jersey, 1964). 2 C. D. Anderson, Phys. Rev. 43, 491 (1933). ( ) 3S. H. Neddermeyer and C. D. Anderson, Phys. Rev. 31, 884 1937 . 4w. PauTi in CoTTected Scientific Papers of Wongang PauTi (ed. R. Kronig and V. F. Weisskopf), pg. 1316. 5F. Reines and C. L. Cowan Jr., Phys. 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RusseTT et a1., Phys. Rev. Letters gg, 46 (1971); J. LeBritton et a1., preprint entitTed Trimuon and Dimuon Events Produced by 10.5 GeV/c p- on Lead to be pub1ished in Phys. Rev. TTin1980. 36K. w. Chen, Michigan State University preprint MSU-CSL—33 (May 1976) entitTed Dimuon and Trimuon Production in Deep Ine1astic Muon InteractionsatTSO GeV. 37v. s. Tsai, Rev. Mod. Phys. 46, 815 (1974). A1so see V. Ganapathi and J. Smith, Phys. Rev. 913, 801 (1979). 38V. Barger et a1., Phys. Rev. Egg, 630 (1979). 390. H. ATbright and R. E. Shrock, Phys. Rev. 019, 2575 (1979). "T 40F. Wi1czek and A. Zee, Phys. Rev. Letters 33, 531 (1977). 41R. R. Brown et a1., Phys. Rev. Letters 33} 1119 (1974). 42A. R. CTark et a1., Phys. Rev. Letters 43, 187 (1979). 43K. w. Chen and A. Van Ginneken, Phys. Rev. Letters 40, 1417 (1978). ‘_T 44L. N. Chang and J. N. Ng, Phys. Rev. 913, 3157 (1977); c. H. Lai, FNAL PUB-78/T8-THY. REFERENCES-—CHAPTER 2 1C. Chang, Ph.D. Thesis, Michigan State University (1975), unpubTished; 5. Herb, Ph.D. Thesis, CorneTT University (1975), unpubTished; Y. Watanabe, Ph.D. Thesis, Corne11 University (1975), unpubTished. 2Proc. CaTorimeter Workshop, FNAL, Batavia, ITTinois, 1975, (ed. M. Atac). 3v. K. Bharadwaj, Ph.D. Thesis, Oxford University (1977), unpubTished; S. Pordes, Ph.D. Thesis, Harvard University (1976), unpubTished. 4MuTtiwire ProportionaT Chambers (ed. M. M. Evans, Rutherford High Energy Lab, 1972). 5O. C. A11kofer, Spark Chambers (VerTag KarT Thiemig KG, MUchen, 1969). 6G. GianneTTi et a1., NucT. Instr. Methods 41, 151 (1967). 7FermiTab proposaTs £203 and £391 and CERN SPS proposais NA2 and NA4. 8R. BaTT, Ph.D. Thesis, Michigan State University (1979), unpubTished. 9Fermi1ab TechnicaT Memo TM-429 (2252). 1OCERN Report CERN/SPSC/74-12 (5.2.1974). HT. 8. w. 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Barger et a1., Charm Muoproduction with a SmaTT—AngTe Veto Univ. of Wisconsin Preprint COO-881-TOO, to be pub1ished in Phys. Rev. D in 1980. 270 REFERENCES--CHAPTER 5 1K. M. Chen and A. Van Ginneken, Phys. Rev. Letters 40, 1417 (1978). -_— 2D. Bauer et a1., Phys. Rev. Letters 43, 1551 (1979). 3c. H. ATbright and R. E. Shrock, Phys. Rev. 019, 2575 (1979). "" 4Fermi1ab proposaTs £203 and 5391. 5c. H. ATbright and J. Smith, Fermi1ab-PUB-78/92-THY, Nov. 1978. 6D. 1. Meyer et a1., Phys. Letters_193, 469 (1977). 7CERN SPS ProposaTs NA2 and NA4. 8K. J. Anderson et a1., Phys. Rev. Letters 43, 944 (1979). 9A. R. CTark et a1., Phys. Rev. Letters 43, 187 (1979). 10 V. Barger et a1., Univ. of Wisconsin Preprint COO-881-100 entitTed Charm Muoproduction with a SmaTT—AngTe Veto to be pubTished in Phys. Rev. D in 1980. 11J. J. RusseTT et a1., Phys. Rev. Letters 33, 46 (1971); J. LeBritton et a1., preprint entitTed Trimuon and Dimuon Events Produced by 10.5 GeV/c u" on Lead to be pub1ished in Phys. 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Wu, Academic Press, New York, 1961), Chapter 1. 2 L. D. Landau, JournaT of Physics U.S.S.R. 3, 201 (1949). 3k. R. Symon, Ph.D. Thesis, Harvard Univ. (1948). Aiso see gilelggggnheimer, Phys. Rev._31, 256 (1953) and Phys. Rev. 133, 4B. Rossi, High Energy Partic1es (Prentice-HaTT, New Jersey, 1952), Chapter 2. D. Theriot, NAL report TM-229, 1970. Y. S. Tsai, Rev. Mod. Phys. 43, 815 (1974). 7M. Tannenbaum, 1970 Summer Study, NAL, Batavia, ITTinois, 8P. M. Joseph, NucT. Instr. Methods 13, 13 (1969). 9C. Richard-Serre, CERN Report 71-18, Sept. 1971. C. Z. MoTiere, Z. Physik 133, 318 (1959). Hw. T. Scott, Rev. Mod. Phys. 33, 231 (1963). 12Review of ParticTe Pr0perties, Partic1e Data Group, Phys. Letters_133, No. 1, Apri1 1978, pg. 28. 13H. Frauenferer and E. M. HenTey, Subatomic Physics (Prentice-HaTT, New Jersey, 1974), Section 6.4. 14R. Hofstadfer, ETectron Scattering and NucTear Structure, Rev. Mod. Phys. g3, 214 (1956); ETectron Scattering and NuETear and NucTeon Structure (ed. R. 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