3.3.57... t a: . $.23 t .rr?‘. 1.13. 3.27). \K,Ppt.1.§\o.. . £52.}: I}... .3 2:? It: .53. h... I. : if. 5...... ..\ .l... t: .3 h :33... .‘3.~.).I.:v s...“ I . p 7... 7‘ If... .> I... v f rlv :. . ,8: 3.3 7.. \l t- at. A\: .25 v1. -“ l . I. 43 .14)....Ii. . . . .Lrgiyl. :9 .ni! J: . . . V241 4 I. ~‘rti. . . ‘.~1'l99-'.1.7,: .93.... 4.. it: I’ll...vlv.ln .Lvl. 444.. . .I. 13.--. (I 1. 11¢. 1bLO 1. fr: 1 {5' 1.1.“ I... n..v .1! nix» . NEW ERS ITY LIBRARIES IIII'IIIIIIIII’I IIIIIIII I I III 3 1293 008973 This is to certify that the dissertation entitled A COMPARISON OF HIGH TRANSVERSE MOMENTUM DIRECT PHOTON AND NEUTRAL PION EVENTS IN NEGATIVE PION AND PROTON-NUCLEUS COLLISIONS AT 31.5 GeV CENTER OF MASS ENERGY presented by David Shaw Brown has been accepted towards fulfillment of the requirements for Ph.D degree in PhySiCS 65W Major professor /§//‘;/7a? MSU is an Affirmative Action/Equal Opportunity Institution 042771 may lacuna State University PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. DATE DUE DATE DUE DATE DUE : MSU Is An Affirmative Action/Equal Opportunlty Institution cm FMS-DJ A COMPARISON OF HIGH TRANSVERSE MOMENTUM DIRECT PHOTON AND NEUTRAL PION EVENTS IN NEGATIVE PION AND PROTON-NUCLEUS COLLISIONS AT 31.5 GeV CENTER OF MASS ENERGY By David Shaw Brown A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1992 ABSTRACT A COMPARISON OF HIGH TRANSVERSE MOMENTUM DIRECT PHOTON AND NEUTRAL PION EVENTS IN NEGATIVE PION AND PROTON-NUCLEUS COLLISIONS AT 31.5 GeV CENTER OF MASS ENERGY By David Shaw Brown In 1988 experiment E706 at Fermilab wrote approximately 6 million triggered events to tape. The purpose of this was to measure the cross sections for high p i 7r° and single photon production. In addition, the cross sections were to be measured for proton and 1r‘ beams on a variety of nuclear targets. To achieve these goals the experiment had been furnished with a large liquid argon calorimeter. A magnetic spectrometer for studying the associated production of charged particles had been built as well. The purpose of this analysis is to compare the associated charged particle structure of high p i 1r° and direct photon events to see if they are indeed different. The current theory of hadron-hadron interactions, quantum chromodynamics, makes a number of predictions indicating that they are. The charged particles recoiling from a high p i 7 or 1r° trigger will be used to reconstruct the 1r° + jet and 7 + jet angular and invariant mass distributions for this study. Finally, the invariant mass distributions will be employed to study the gluon structure functions of hadrons. ACKNOWLEDGEMENTS First, I would like to extend my gratitude to all of those involved in making E706 an operational, and successful experiment. A number of these individuals are non- physicists who didn’t share in the excitement and glory of doing any physics. They worked hard within the narrow window of their specialty, often providing expert advice and getting us cocky graduate students out of numerous jams during the construction of the calorimeters. I want to express my appreciation for the efforts of all first run graduate students and post-docs. I know our relationship has been rough at times, but I am truly grateful. The validity, importance and relevance of my analysis rests on the mon- umental efforts of the photon group, and those who got the tracking code up and running. Many thanks to Marek Zielinski, Joey Huston, Phil Gutierrez, Takahiro Ya- suda, George Fanourakis, Clark Chandlee, John Mansour, Dane Skow, Eric Prebys, Amanda Lanaro, Bill Desoi, Chris Lirakis, Alex Sinanidis, Carlos Yosef, Ioanis Kour- banis, Dhammika Weerasundra, Richard Benson, Brajeesh Choudhary, Casey Hart- man, Sajan Easo, and Guiseppe Ballochi. Oh and thanks for the grapa, Guiseppe. Maybe again sometime... There are three individuals I want to single out as being instrumental in directing me along the path I took for my analysis. First, there is my advisor, Carl Bromberg. Carl has made many important contributions to the experiment, including a first rate MWPC system. He has endured many frustrations as well. I must admit I have been the cause more than once. His willingness to endure and overcome my hardheadedness has saved me much embarassment. Carl’s understanding of and experience in hadron- hadron collisions at high p I provided the subject matter for my analysis. However, I could not have completed my studies without his guidance and many helpful insights along the way. I thank him for his continual support through the years. I must also thank Sudhindra Mani for enduring so many long discussions about where to go with the charged tracking analysis. We have had many arguments, but they clarified a number of issues for me. The same goes for the noble/notorious George Ginther. He has made many extraordinary efforts, including the data summary work. Besides “canning” the data for us students, he got “canned” plenty in our sundry discussions, which more than once turned into acrimonious debate. Thank you George for your patience and help in making me an experimentalist. At least I usually look before I leap now. The collaboration’s senior members played very pivotal roles. They conceived this experiment, and used their expertise in seeing it become a reality. Thanks to the Rochester members for providing invaluable help and effort in designing the electro— magnetic calorimeter. They also kept the experiment alive at Fermilab during the many years prior to data taking. The Pennsylvania State Univeristy, University of Pittsburg and Michigan State University people were instrumental in furnishing the tracking system upon whose data my analysis depends heavily. My parents deserve special credit in providing much needed emotional support during this long ardorous venture. I have not been able to see them very much these past ten years, but thanks to AT&T and the US. mail system the lines of communication have remained open! I also want to express appreciation for their lovingkindness during my childhood years. It was they who encouraged and initially nurtured my interest in science from an early age. Last but not least I am deeply indebted to the American taxpayers, who have shelled out the better part of a million bucks so that I could get a Ph.D. in high energy physics. I hope I am worth the investment. «1|.WL ‘01 W .. “Ii“? $34311 Biasesineosa‘.......... _‘ ~,r.ma BiasesinM . . . . . ............ .. u“ 1 ' ll‘bfisOutline _ I'm-cf? rw " , Wig m“- alSetup .2' .‘LI ' .lllis [LVP‘f-fi 'lL“:‘. If. t .‘ .ol'ZSA‘ r‘Eler/ffl‘éom CCons ”Ann I traction ‘ eeeee I It“. fruit“ ' Wdéw e e e o «ms-W'flllfl 1‘1“»: 9 12:5: -_-;-. .‘l TheCerenkovDetector. . . . .‘ ‘ r1. Hadron shield and Veto Wall .‘h OIIOIOIIII 1.1.1 The Factorization Scheme .................... 1_. 1. 2 Hard-Scatter Kinematics ......... i ............ 1.13 TheMeaningofda/df ......... .......... ' 611:2 Direct Photons and QCD. ........................ 3&5.“ WIWental Considerations ...... . . . '. . . . .......... uuuuu es '0' ....... one nnnnn e or sense- Ankh“ 10 11 18 20 23 26 ? A5133 3” E706 Trigger System ........................ 64 A 32341- EMLAC p .1 System ........................ 67 . 2-3.1 Beam and Interaction Definition ................. 72 ' 3 4 2.3.3 Vetoing Elements .............. A ........... 75 l _' 2.3.4 High Level Trigger Operation .................. 77 _ 4‘ 2J4 l(Al'liairged Tracking System ........................ 78 ': A 2.4.1 SSD System ............................ 79 i" . 2.4.2 MWPC System .......................... 83 ,. __ A“ 2.4.3 MWPC Gas System ....................... 104 . . IA. 2.4.4 Tracking System Electronics ................... 107 f“ A L “A 2. 4. 5 AV MWPC Commissioning ...................... 110 A A 2. 5 The Forward Calorimeter ......................... 112 . fitztfieconstruction . 117 A g.Al EMLAC Reconstruction ......................... 117 _ iiii'i EMREC Unpacking .................... -. . . . 118 .. 'A ' 134.23.. .Showo: Reconstruction ............. . ......... 119 . ' ‘76.! i 311.3». .TrVC, Reconstruction ....................... 124 Mn; Reconstruction ......................... 126 ' .21. .A «33.3.1- . MWPC‘ Space Track Reconstruction .............. 126 " ‘: $3»? 2.881135% Reconstruction .................... 128 ,1. - ' ‘1\a if 0 1.1.“ . 1 1’ ,1‘“ i ' t a ‘5 21332 Quality of Track Reconstruction ................. 140 , J1: - '1' H - 91212 Truck Quality Cuts ........................ 142 A . , r A." .1 ‘ ‘. 31.3.4 Comparison of Data and Monte Carlo .............. 144 1 1" V‘ git Discrete Logic Reconstruction ...................... 151 ' 0*1 “pink-.11. , s1: . , ' ‘, ‘21s- that selection 153 14.1 Whole Event Cuts ............................ 153 " 4.2 Muon and Hadron Backgrounds ..................... 154 4.2 tr. Reconstruction ............................. 166 $1413.; Single Photon Reconstruction ...................... 170 4. 5 Systematics ................................ 170 ”.4 $011110 Background Calculation ........................ 172 "2 W Mums . 175 4'6?» £14: Drfi'erences Between 73 and 11’" s ..................... 175 '1 . 1"_§.2 Repidity Correlations ........................... 178 Winstruction 192 .1 j gfirfilmrithms ........... ‘ ................... 192 19,11 .1 Cone Algorithm .......................... , 193 ‘ -* 6.1.2 W470 Algorithm .......................... 194 Th! Jet Monte Carlo ........................... 195 6.4 Measurement of cos 9‘and M ....................... 212 6.4.1 cos 0‘ .......................... . . , . 213 6.4.2 Cross Sections in M .................... . 213 Final Results ' 222 7.1 1° Background Subtraction . ..................... 224 7.2 Results for cos 0‘ ............................. 229 7.3 1r° +jet and 7 +jet M Distributions .................. 237 7.4 Errors ................................... 251 Summary and Conclusion 255 Corrections to the “Kick” Approximation 257 Fake Tracks 260 Track Reconstruction Efficiency 266 Trigger Particle Corrections 272 D.1 Corrections for Cuts ........................... 272 D.2 Corrections for Inefficiencies ....................... 273 D.3 Photon Energy Corrections ........................ 276 ? 1.1 1.3 1.4 1.5 1.6 1.7 2.1 2.2 2.3 LIST OF FIGURES A hadron-hadron collision according to the factorization scheme; two partons undergo a hard scatter. ..................... All possible parton-parton scatters in first order QCD. The Mandel- stam variables are for the constituent processes. A common factor of wag/.32 has been left out .......................... lst order direct photon subprocesses in QCD. ............. Bremstrahlung contribution to direct photon production. ....... Theoretical di-1r° and single photon cos 0‘ distributions from Owens. The calculations for prompt photons are presented with and without the Bremsstrahlung contribution. The recoil jet is defined as the lead- ing hadron away from the trigger in d). ................. Scatter plot of cos 9‘ vs 1'. The region between the two horizontal lines, and to the right of the vertical line is unbiased from the trigger over the measured interval of cos 9‘. ..................... An illustration of the bias in cos 9" as a result of the detector’s accep- tance being < 41r .............................. E706 Plan View .............................. A schematic of the MWEST secondary beamline. All devices are rep- resented in terms of their optical equivalents ............... Examples of C pressure curves for both beam polarities. The peaks for each type of beam particle are labeled accordingly ............ V 17 24 25 30 31 33 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 Isometric drawing of the hadron shield, showing the central vertical slab through which the beam passes. This piece was removed during LAC calibration. ............................. 34 Sketch of the Veto Wall planes. The arrows represent the beam’s pas- sage through the counters. Each square represents one scintillation counter. .................................. 36 Layout of the calorimeters on the gantry support structure. Also shown are the filler vessel, the beam tube, and the Faraday room. ...... 39 Isometric and Cross-sectional views of an EMLAC sampling cell, show- ing the r-¢ geometry of the charge collection layers. .......... 41 Cut-view drawing of the EMLAC illustrating r-strip focusing. . . . . 42 Longitudinal segmentation as an aid to 7r° reconstruction. Showers have narrower profiles in the EMLAC’s front section, allowing both decay photons to be resolved. ........ ' .............. 47 Isometric drawing of the EMLAC with an exploded view of one quadrant. 48 Drawing of the Physical Boundaries for the sensitive area of an EMLAC Quadrant. ................................. 50 Typical layout of r and 43 strips on the readout boards for the EMLAC. 51 Signal summing scheme in the EMLAC. Signals in a quadrant are summed in the front and back sections separately. These sums are grouped into outer r, inner r, outer ¢ , and inner :13 views ........ 52 Cross-sectional view of an EMLAC cell at the outer edge of the elec- tromagnetic calorimeter. ......................... 53 Cross-sectional drawing of a quadrant support assembly for the EMLAC 55 Front and side views of the hadron calorimeter. Steel “Zorba Plates” are the absorber media. The hole, shown in the center of the front view, allows passage of beam and halo particles. ............ 57 vi 2.17 2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.2 q 2.2 on 2.29 2.30 Exploded portion of a HADLAC charge collection cell or “cookie”. . . Schematic of a LAC amplifier channel showing the Sample-and-Hold, TVC, and Fast Out circuits .................... An example of an Event Timing Sequence initiated by the BAT mod- ules. An event fires the master TVC, but fails to produce a PRE- TRIGGER signal. A short time later, an event fires the slave TVC, generating a PRETRIGGER and BEFORE pulses as well. ...... A simplified diagram for a TVC unit ................... Octant r-channel summing scheme employed by the local p 1 modules. These modules produced summed signals for groups of 8 and 32 strips. Front-back summing scheme employed by the local discriminator mod- Schematic of the EMLAC charge collection circuit (one channel). . . . The effect of image charge on the global trigger input signal. ..... The configuration of scintillation counters used the the beam and in- teraction definitions. ........................... Schematic diagram of the interaction pile-up filter, and live interaction definition circuits .............................. Schematic of the segmented target/SSD system of E706. A typical multiple event is superimposed on the planes. ............. Readout electronics schematic used to determine operating character- istics of SSD system. ........................... Arrangement of sense planes in each MWPC module. ......... Electric field equipotential and field lines in a multiwire proportional chamber. The effect on the field due a. small displacement of one wire is also shown. ............................... 58 61 65 66 69 70 72 73 74 76. 81 82 85 2.31 2.32 2.33 2.34 2.35 3.1 3.2 3.3 3.4 3.5 3.6 3.7 4.1 Principle of construction and definition of parameters in a multiw1re proportional chamber. A set of parallel anode wires is mounted sym— metrically between two cathode foils. .................. Equilibrium configuration of anode wires in a large proportional cham- ber under the influence of the device’s electric field. .......... MWPC test system used to determine latch delays. .......... A high voltage plateau curve for MWPC module 3. .......... Perspective drawing of the Forward Calorimeter with an exploded view of one of the modules. .......................... The z coordinate distribution for matched vertices within the target volume. The different target elements are clearly resolved. ...... The x2 distributions for 16, 15, 14, and 13 hit physics tracks ..... Y distribution of tracks .......................... Y-view impact parameter distribution of tracks ............ Y distributions for all tracks, and tracks passing the track quality cuts. The monte carlo result has been superimposed as a smooth curve. . . Multiplicity distributions for all tracks, and tracks passing the track quality cuts. The monte carlo result has been superimposed as a. smooth curve ................................ Momentum distributions for all tracks, and tracks passing the track quality cuts. The monte carlo result has been superimposed as a smooth curve ................................ Illustration of photon directionality and related quantities. A shower- ing muon from the beam halo will have a larger directionality than a photon emanating from the target. ................... 90 94 111 113 115 134 138 145 148 149 150 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.1 5.2 5.3 5.4 5.5 Photon p 1 vs directionality for events in which the veto wall quadrant shadowing the trigger quadrant had a hit in either wall (left), and had no hit (right). .............................. 158 TVC distributions for non-p. (left) and p. induced (right) events. . . . 160 5. vs TVC time for events with a veto wall hit (top) and without a veto wall hit (bottom). The data in the region outside the vertical lines and above the horizontal line is excluded by the directionality and timing Ar between showers and nearest tracks (left); Ar between high p 1 photons and nearest tracks (right) .................... 163 Efi-ong/Egogd for Hadron Showers (top) and Electron Showers (bottom). 164 Emu/Etc.“ for High pi Photon Showers (top) and p Showers (bottom).165 71 Mass Spectrum ............................ 168 Asymmetry distributions for 1r°s without sidebands subtracted (top) and with sidebands subtracted (bottom) ................. 169 43 density distributions for charged particles in high p1 7r° and single photon events with 5.0 5 pi < 5.5 GeV/c. ............... 179 «p density distributions for charged particles in high p 1 7r° and single photon events with p1 2 5.5 GeV/c .................... 180 q; weighted ¢ distributions for charged particles in high p J_ 71'" and single photon events with 5.0 3 pi < 5.5 GeV/c ............ 181 q; weighted qt distributions for charged particles in high p 1 1r° and single photon events with p 1 2 5.5 GeV/c. ............... 182 p ,L weighted d) distributions for charged particles in high p l 7r° and single photon events with 5.0 5 pi < 5.5 GeV/c ............. 183 fir 5.6 5.7 5.8 5.9 5.10 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 p 1 weighted 45 distributions for charged particles in high p j 7r° and single photon events with p j 2 5.5 GeV/c ................ Ay distributions for lst and 2nd highest p j recoil tracks (left), and lst,3rd, 4th, . .. highest pl tracks (right) ................. Ay between highest p _L recoil track and the trigger particle. Ay distribution of highest p J_ recoil charged pair for ISAJ ET generated data (left), and phase-space monte carlo data (right). The uncorrelated Ay distributions appear as smooth curves ................ Ay between the highest pJ_ recoil charged pair in data with the corre- sponding ISAJ ET result superimposed as a smooth curve. ...... The pl imbalance between the two hard scatter jets in ISAJET with (kl) = 0.95 GeV/c. ............................ Scatter plots of jet resolution over the acceptance for Cone (Top) and WA70 (Bottom) algorithms. ....................... 6 cos0 distributions for Cone (Left) and WA70 (Right) algorithms in- tegrated over the acceptance. ...................... Scatter plots of 6cos€ between WA70 and Cone algorithms over the acceptance for data (Top) and monte carlo (Bottom) .......... The jet finding efficiency for Cone and WA70 algorithms as a function of the trigger’s p1. Monte carlo is superimposed on the data ...... Resolution plots of the reconstructed jet momentum for 1r° triggers integrated over the acceptance. ..................... Resolution plots of the reconstructed jet momentum for 1 triggers in- tegrated over the acceptance. ...................... 63/1: resolution plots for parton momenta in high p l 1r° events, inte- grated over the acceptance. ....................... 184 188 189 190 191 197 201 202 203 207 6.9 52/23 resolution plots for parton momenta in high p _._ single photon events, integrated over the acceptance. ................. 6.1 C Effects of M and 1,3 cuts which unbias the reconstructed cos 9' distri- bution ................................. 6.11 173 for high p _L 1r°s produced via proton-nucleus collisions ........ 6.12 Reconstructed and parton level cos 9“ distributions for high pi 1r° events. The parton level distribution is shown as a smooth curve. 6.13 Reconstructed and parton level cos 0" distributions for high p j single 211 214 215 216 photon events. The parton level distribution is shown as a smooth curve.217 6.14 Reconstructed and parton level M distributions for high pj 7r° events. The parton level distribution is shown as a smooth curve ........ 6.15 Reconstructed and parton level M distributions for high p ,L direct pho- ton events. The parton level distribution is shown as a smooth curve. 7.1 Inclusive '7 /1r0 ratio for 1r‘-nucleus collisions .............. 7.2 Inclusive 1/1r° ratio for proton-nucleus collisions ............ 7.3' Scatter plots of cos 9‘ and M versus p j for 1r° events ......... 7.4 Absolute cos 0" plots for 7s and 1r°s in 1r' data ............. 7.5 Absolute cos 9" plots for 7s and 1r°s in proton data .......... 7.6 1 to 1r° ratio in cos 0' for 11" data (top) and proton data (bottom) . . 7.7 Absolute cos 9" plots for 1s and 1r°s in 1r‘ data ............. 7.8 Absolute cos 9" plots for 1s and 1r°s in proton data .......... 7.9 7 to 1r° ratios in cos 0‘ for 1r“ data (top) and proton data (bottom) 7.10 Absolute cos 0' plots for 75 and 1r°s in 1r‘ data with no 7r° background subtraction for the 1s ........................... 7.11 7 to 1r° ratio in cos 9‘ for 1r" data without 1r° background subtraction 7.12 if" + jet cross section in M for 1r" beam ................ 220 221 227 228 230 233 235 238 240 241 242 7.13 7.14 7.15 7.16 7.17 7.1 on A. H B.1 B.2 B.3 C.1 0.2 0.3 7' + jet cross section in M for 1r‘ beam ................. 1r° + jet cross section in M for proton beam .............. 7 + jet cross section in M for proton beam ............... 1r° +jet and 7+jet cross sections in M for 1r" beam. The 7 distribution is unsubtracted ............................... Ratio of absolute 7r° + jet cross sections between 7r‘ and proton beams. There is no cos 9‘ cut. .......................... Ratio of absolute 7 + jet cross sections between 1r‘ and proton beams. There is no cos 0‘ cut. .......................... Top: A track’s orientation in the bend plane as it passes through the analyzing magnet’s field. Bottom: The angles involved in magnetic field corrections ............................... Scatter plot of AX vs AY for tracks and nearest showers ....... EMLAC efficiency in P for high quality l6-hit tracks (top) and all high quality tracks (bottom). ..................... I . . . . by distribution for physics tracks that are linked in the x-view to an SSD track, assigned to the primary vertex ................ A typical relative hit multiplicity distribution for the physics tracks Relative hit multiplicity distributions of physics tracks for the four separate data sets. The monte carlo prediction appears as the dotted Relative hit multiplicity distributions for positive data (Left) and neg- ative data (Right). These plots are for tracks that do not project out- side the MWPC acceptance. Also shown is the binomial distribution for (e) = 0.92; the binomial distribution is plotted as dotted bars. 246 247 248 249 252 253 258 261 262 264 269 271 1.1 1.2 2.1 2.2 2.3 2.4 2.5 2.6 3.1 4.1 4.2 4.3 7.1 7.2 LIST OF TABLES The additive quantum numbers for the six flavors of quarks. . . . . 2 The constituent quark content of some common hadrons ....... 2 Fractions of the various particle species in the 500 GeV/c secondary beam. ................................... 32 Trigger threshold settings by run number. ............... 71 Relevant geometrical parameters for MWPC anodes (MKS units). . . 89 Electrostatic parameters for all MWPC anodes. ............ 91 Sizes of the various cathode regions in each module ........... 101 Orientation and positions of the garlands in each plane ......... 101 List of MWPC Plane Efficiencies .................... 139 E706 data divided by beam and target type ............... 154 Corrections for whole event cuts, and cuts for single photons ...... 172 False 7 fractions in p 1 for proton and 71" beams. ........... 174 Monte carlo data sets by collision and trigger particle type ....... 225 Summary of differences between 7s and 1r°s in cos 0" .......... 237 List of fake track fractions ......................... 265 Chapter 1 Motivation Over the past twenty years or so a fundamental picture of hadronic structure and collision processes has emerged. This picture is fundamental for two reasons. First, it describes hadrons as being composed of structureless or pointlike objects called partons. Second, it views a high energy. collision involving hadrons as an interaction between partons. If the collision is sufficiently violent, a simple picture of the parton level interaction emerges, which leads to predictions for absolute cross sections. There are two distinct classes of partons based on the spin quantum number. Spin-1/2 or fermionic partons are called quarks. Quarks carry electric charge such that e.l = i§|e| or eq = tile] where eq is the quark charge and |e| is the absolute value of the electron’s charge. Quarks possess two other discrete quantum numbers known as flavor and color. Six different flavor states and three different color states are possible. Flavor is important in the weak interactions involving quarks, whereas color plays a role in the strong interaction. While it is true that some quarks are known to be massive, a quark’s mass appears to be completely correlated with its flavor quantum number. Table 1.1 gives the additive quantum numbers for the six different flavors of quarks. Note that the top quark has not yet been discovered. Nucleons and pions are composed of just two kinds kinds of quarks, up (u) and down ((1). The quark content of the more common hadrons is shown in Table 1.2. The other major group of partons consists of spin-1 objects called gluons. Gluons are massless and carry no flavor or electric charge. However, they do eidst in eight different superpositions of a color and anticolor state. They are thought to play a role in confining quarks within the volume of a hadron (~ lfma), hence the name. Table 1.1: The additive quantum numbers for the six flavors of quarks. Quark Flavors Quantum Number d u s c b t Q-electric charge — .1; +§ —% +§ —% +§ I,-isospin —% +% 0 0 O O S-strangeness 0 0 - 1 0 0 0 C-charm 0 0 0 +1 0 0 B-bottomness 0 0 0 0 -1 0 T-topness 0 0 0 0 0 + 1 l Table 1.2: The constituent quark content of some common hadrons l Hadron Quark Contents p and u add 1r+ ad no mi, dd- 1r' 11d K+ 115 K" is K° d5 K0 is Sometimes a violent collision involving a quark produces a photon with a large component of its momentum transverse to the collision axis. Such photons are called direct or prompt photons. The processes responsible for their production are anal- ogous to electron bremsstrahlung in the nuclear coulomb field, electron-positron an- nihilation into gamma rays, and the Compton scattering of electrons by high energy X-rays. The study of direct photons is interesting for several reasons: 0 Prompt photons emanate from the hard scatter with no further scattering among constituents. They are thus a direct probe of the parton-parton in- teraction, and allow the kinematics to be more clearly understood. 0 Only a few subprocesses produce them so the overall interaction is easier to interpret. e A direct measurement of the gluon content of hadrons is possible. 0 It is possible to ascertain at least qualitatively the differences between quarks and gluons. Such differences, if they exist, can be compared to those expected from theory. In particular, it can be determined whether or not quark and gluon final states produce different hadronic spectra. Unfortunately, direct photon events are quite rare, representing less than .170 of the total proton cross section. One reason is that the fraction of events containing particles whose transverse momenta are a significant portion of the c.m. energy is very small. Even if the experiment selects only high p _L events online the prompt photon sample will be sparse for two reasons. First, direct photon production relative to high p ,L parton production goes as S 01m / 01.. 41cm and a. are the coupling constants for the electromagnetic and strong interactions respectively. Naively, a. S 1 so the cross section is already down two orders of magnitude. Second, there are considerably more types of processes available for producing generic hard scatters as opposed to the 4 limited number capable of generating direct photons. It is a great technical challenge indeed to collect a statistically significant and normalizable sample of these events. 1.1 CURRENT VIEW OF HADRON-HADRON COLLISIONS Before delving into the 1988 data analysis an elaboration of the high momentum transfer, Q2, scattering process is in order. This discussion will clarify the terminology used in the analysis procedure, and provide a description of the kinematics governing such reactions. As far as labelling is concerned, all hadron names and dynamical variables will be denoted by uppercase letters. Parton names and variables will appear in lowercase. 1.1.1 The Fartnrizafinn o ‘- Figure 1.1 provides a schematic illustration of a typical high p J_ collision between two hadrons, A and B. The hadrons are viewed as clouds of partons passing through one another such that a parton from A and a parton from B experience a violent scattering. Partons c and d then emerge from this collision with large components of their momenta transverse to the collision axis. Q2 refers to the momentum exchanged between a and b. While Q2 cannot, generally speaking, be expressed in terms of . experimental quantities, it is certainly true that Q2 or pi. This is because p j is invariant under Lorentz boosts along the collision axis. The interaction of hadrons A and B is believed to occur in three stages: 0 At some instant as the hadrons A and B pass through one another partons a and b have momenta pa :2 :caPA, 0 < 3., < 1 and p1, = szg, 0 < z; < 1 respectively. The probability density for parton a’s momentum distribution is denoted by G 4(za, Q2) and similarly for b inside B. c Pattons a and b interact on a time scale much shorter than the lifetime of the 5 initial parton states. da/dt denotes the constituent interaction’s cross section. 0 The final state partons, c and d, radiate additional partons, creating a cascade that results in two clusters of outgoing hadrons known colloquially as jets. This process is called fragmentation; it is assumed that c and d don’t begin radiating until they are far from the hard scatter region. The probability that hadron C is produced by parton c with a fraction, zc, of c’s momentum is given by Dc(zc,Q2). One can also construct fragmentation functions as the number of hadrons per unit z from parton i, and then sum over flavors. This 3-step process is known as the factorization scheme. The implication is that quantum mechanical interference effects between different sets of initial and final states can be ignored since they are distinguishable. Only interference effects among the processes contributing to da/df need be taken into account. The reaction has the following shorthand notation A+B—>jet1+jet2+X (1.1) where X represents all the hadrons associated with the non-interacting partons. These non-interacting partons are referred to as spectators. The hadron fragments of these constituents emerge in very narrow forward arid backward cones parallel to the colli- sion axis. These forward and backward clusters of fragments are called the beam and target jets respectively. The reader may wonder why it is assumed that partons radiate in such a way that only hadrons appear in the final state. Simply stated, no free quarks have been observed. It seems that, whatever force acts between partons, it must be strongly attractive over macroscopic distances. The current view is that hadrons represent singlet states of the field responsible for the parton-parton interaction. Mathematically factorization leads to a general expression for the hadron-hadron cross section at high Q'; it is written as a product of structure functions, and dd/df 6 asfollows: d” A B '11‘12 x- dn1dnzdpi( + 7” +1.. + l" 1 1 2 2 3110 Z// dzadsza/A(24,Q )Gb/B(zbaQ )——-.(ab—> 12) X (1.2) 115 o o 2dt 6((z. + 221)”?E — (60511171 + C051‘ "2””) x 5((311 — an)? — (sinh 171 + sinh n2)p1) This form for the cross section trivially generalizes to other processes such as deep inelastic lepton-nucleon scattering, and Drell-Yan production of high mass dilepton pairs. 1.1.2 Hard-Scatter Kinematics Equipped with this View of the collision process, the reader is now given a descrip- tion of the kinematics relevant to the analysis. At the parton level the collision is a simple 2-2 scatter with well defined initial and final states. A complete kinematical description of such a process is provided by the Mandelstam invariants s, t, and u [1]. The Mandelstam variables corresponding to the interacting partons are denoted by 3, f, and ii. They are defined in terms of the incoming and outgoing parton 4-momenta as follows: 3 = (1)., + Pb)z i: (Pa _ pa)2 1.1 : (Pa _ pd)2 (1'3) These special scalars obey the following sum rule; §+£+a=2m§ (1.4) where m.- is the mass of the ith particle either entering or exiting the interaction. For massless quarks and gluons the rule becomes 3+£+a=0 (1.5) Figure 1.1: A hadron-hadron collision according to the factor- ization scheme; two partons undergo a hard scat- ter. 8 The reader should be aware that while .9 applies to the collision at the hadron level t and u do not because the overall collision is not a simple 2-body scatter. It is important to relate experimental quantities to the underlying parton hard scatter. The hard scatter can be specified by 3 and cos 0‘; 9‘ is the angle between an outgoing parton’s 3-momentum and the beam direction in the colliding partons’ c.m. frame. If one assumes an observed jet’s direction is also the direction of the parton which produced it, then cos 9“ is the orientation of the dijet system in a frame where the jets are back-to—back. Furthermore, .13 is just the dijet system’s invariant mass squared, M2. The initial state can be specified by the variables 21 and :22. These variables represent the fractional momenta of the beam and target partons, respectively, in the hadrons’ rest frame. M, 1:1, 2:2, .9, and .3 are all related to one another by the following set of equations, A 3122.9 = s (1.6) 3 = M2 = (Rjet1+Pjet2)2 Pjeu and PM; are the 4-vectors of the hard-scatter jets. In principle, at least, they are measurable. If it is further assumed that the dijet system possesses no net p j and the jets are massless, the variable M can be expressed as follows: M = 2‘” (1.7) sin 0‘ where p j is the measured transverse momentum of one of the jets. In the context of E706 this would be the transverse momentum of a high p j_ 1r° or direct photon. The p; balancing assumption is inexact on general grounds. A simple application of the Heisenberg Uncertainty Relation between position and momentum for distances on the order of ~ 1 fm results in momenta on the order of 300 MeV/c. The variable cos 9" can be calculated from the corresponding pseudorapidity, 11'. if in turn can be obtained by solving the following set of equations, where it has been 9 assumed that the jet and corresponding parton pseudorapidities are the same. 771:1 = nj‘etl = fljeti +713 "£2 = 711212 = -nj'etl = ”jetz'tUB (1-8) . . 71' 1 —TI' 2 "p1 = _1’p2 : jet jet Clearly, the Lorentz boost to the parton-parton rest frame, 173, is nonzero whenever :31 — :c; = A2: 75 0. This method for determining cos 9' assumes that the c.m. of the colliding hadrons is related to the rest frame of the interacting partons by a boost along the hadrons’ collision axis. In other words, intrinsic transverse momentum effects is. k ,L, are ignored. The invariant cross section, expressed by equation 1.3, can also be written in terms of the parton variables. da’ __ runs 2 2 do . dzadedCOS 0' — 2 gGa/AccaiQ )Gb/B(35)Q )dt“ (ab 12) (19) Instead of .3 or M the dimensionless variable 1' = é/s can be used to represent the energy of the hard scatter. In terms of 2:1 and 1:2 T=§/s=z1:ag 0 00, a. —> 0. Thus, in the high Q2 limit the partons behave like free particles within the volume of a hadron. This property is called 9 if“: it i. . 11 asymptotic freedom. Since high p 1 implies high Q2, high p L hadron interactions may serve as an application for perturbative QCD. Gluon-gluon collisions take place also at the Born level. As a result, a large number of subprocesses can contribute to the hard-scatter cross section at lowest order. Figure 1.2 lists the various mechanisms contributing to generic parton scatters. Referring back to Figure 1.1, both the G and D functions have a dependence on Q”. In the high Q2 regime the partons behave like free particles so the structure and fragmentation functions should cease to depend on the momentum transfer i.e. they should scale. All of the p J_ dependence in the cross section would then reside in da/df, and QCD predicts that all subprocesses fall as 1/p‘1. Unfortunately, the data is observed to fall as 1/p‘_3L or faster in E706’s kinematic regime [4]. Clearly G and D have a dependence on Q2 there. This ambiguity is not as bad as might be supposed. While G and D cannot be calculated at the present time, their Q2 variation is completely predicted by the Alteralli-Parisi Equations [5]. Measuring G and/or D at some Q2 and using these equations allows one to know the behavior of these functions at any other momentum transfer where perturbation theory is applicable. 1.2 DIRECT PHOTONS AND QCD Although QCD may provide a theoretical framework that leads to predictions for absolute cross sections, the picture is nonetheless very complicated. There is little if any sensitivity in discriminating between quark and gluon effects. Worst of all is the fact that jets are fuzzy objects from an experimental standpoint. It is not straightforward to determine which jet each particle belongs to. In addition, the distinction between hard-scatter and minimum bias events isn’t always clear, especially at E706 energies. The technical difficulties peculiar to studying generic jet production can be over- come by studying only those events containing a high p L hadron i.e., a 1r°. However, -. --.., Crass muon W ifios: «'-«‘ 9--—‘, ‘ il'ev’ 1"!) __|_,_" 91—" Fl t’ T—u‘ 21 N il’ou’ d-v'l' 9—“ ‘ li'tulipv‘d-I‘ _|._u_'_ "-0" ;{ ‘X ’1 11 ll ‘ ii. a "M” 30-11 —;1v.l I' )1 I u it‘d»... 0"“ T‘4-l ’-———', 1'! .4 _J_1‘+u’ (3", z U’l | ‘1 9 ) £_.’l-.t.'— u‘“ ‘2- -1‘ 1’ u‘ 0‘ I .....L 1...... l"?' , ’ u L a 3. L 0"" 9'. 1+" 2 ‘ L 1'. "-77 3t, “4»! i I l L ' 0/ at; I, '[Ll3_ll[- H l . h _ + ”'" [Ex art. *fi- , ‘7 , +la‘u'l-elwewl-éllfi[ail-svlueuer] xileisHie-Wl-%l+*'+:*-*I-z-'l+='-:—~~l-el I-U L .. , ._| +3337": lu‘fw’ '*l'*fi"hl-él+e—*l']« -l “7' entail-1L Figure 1.2: All possible parton-parton scatters in first order QCD. The Mandelstam variables are for the con- stituent processes. A common factor of 1m: / 3' has been left out. M 13 such events are still very complicated at the hard scatter level. The large number of contributing subprocesses involve a mixture of quarks and gluons in the initial and final states. So, the ability to separate the effects of gluons and quarks is compro— mised. Direct photon events stand in sharp contrast to this rather murky situation. In lowest order only two subprocesses contribute to their production. These are illus- trated in Figure 1.3. The process involving the collision of a quark and gluon is referred to as the Compton process by analogy with the scattering of electrons by high energy photons. The other Feynman graphs describe the annihilation of a quark and anti-quark into a photon and gluon. This process is similar to e+e' annihilation into photons. The QCD formulas for the two production mechanisms are also shown, being expressed in terms of the Mandelstam variables. The Compton process is expected to dominate direct photon production in proton- nucleus collisions because to first order there are no anti-quarks in the nucleon. Being able to measure this cross section in terms of the photon and outgoing quark 4-vectors yields a direct measurement of the gluon structure function for nucleons. Only a quark appears in the final state along with the photon. Thus, direct photon production in proton-nucleus collisions should yield information on quark fragmentation. The overall dependence of da/dt on the quark charges results in an effect known as .“u- quark dominance”. It simply means that direct photon events are more likely to be produced by u-quark interactions. For the Compton subprocess, there will be an enhancement of u-quark jets in the data. In fact, one expects an 8-fold enhancement of u-quark jets over d-quark jets for pp interactions, an extra factor of two arising from there being twice as many 11 as d-quarks in the proton. The effect is diluted somewhat in this experiment because nuclear targets have been used. No such enhancement is expected for high p i 1r° production since the strong interaction is charge independent 1 9 and 1r°s contain equal numbers of u and d-quarks. f q\ JFK 9 G Am q C: V m - 2 . dc -e an, G 55 Compton Diagrams - 7:“ g #4} .,. _} A . LL 9 q—Tm, q ——'WWV W9 - 2 A 4: So can, u. Figure 1.3: lst order direct photon subprocesses in QCD. Ez' _____~\~vo’ a Annxnilauon Diagrams - ) sin ..,, 15 The annihilation process is expected to be responsible for most of the cross section at high pi in w‘-nucleus collisions. This follows from the form for da/‘df and the gluon structure function is believed to fall faster than the valence quark distributions at high x. In this regime the recoil jet is being produced by a gluon. Thus, it would be interesting to compare the hadronic spectra between proton induced direct photon events, which contain a quark generated recoil jet, and 7r‘ induced events. Generally speaking, the QCD production mechanisms for direct photons result in the photon being isolated. In other words the photon always comprises a one particle jet so there should be no enhancement of charged particles near it in phase space. This is in contrast to high p i 1r° events. There the high p 1 particle is only one of several products of a final state parton’s fragmentation. A study of the overall charged structure of high p 1 1r° and single photon events should be sensitive to such a difference between the two event types. Going back to the expressions for the production mechanisms in Figure 1.3, if one substitutes the ingoing and outgoing 4—momenta in place of the variables 3, t, and 12 they will obtain formulas with 1 / (1 :1: cos 9") terms in them. This is a general result for elementary processes containing only fermionic propagators. Among the more general subprocesses responsible for high p i 1r° production are some that contain gluon propagators. Since gluons are bosons, it follows from general considerations that do/df will have 1/(1 :1: cos 9‘)2 terms. As a result, the cos 0“ distributions for 1r° +jet events should rise more sharply than for 7+ jet events as I cos 0‘| approaches 1. Unfortunately, the picture is not quite as simple as this. Single '75 can be produced via a bremsstrahlung type mechanism illustrated in Figure 1.4. Although higher order in a., a, z .1 yields z 10% contribution. This subprocess is thought to be impor- tant at E706 energies for p l S 4.0 GeV/c, so there may be some ambiguity in the interpretation of the data. However, calculations by Owens [6] predict that the direct \ 1 ...... / q t “ .(q._q) 494) ‘W'l'rvvvvvvvv ; ‘ q Figure 1.4: Bremstrahlung contribution to direct photon pro- duction. 17 H r r I 1% r: j ”070?!“ X -—- ‘° 4 - 40 GeV u 9 l- M I 10 GOV . — — No bremsstrahiung - ......... 99"“. 3'. X L [do/d cos e'llldo Id cos 0'] case . 0.4 0.5 0.6 0.7 0.8 o: o ' 0.0 1.0 0.2 0.3 C Figure 1.5: Theoretical di-1r° and single photon cos 9' dis- tributions from Owens. The calculations for prompt photons are presented with and without the Bremsstrahlung contribution. The recoil jet is defined as the leading hadron away from the trigger in (b. photons should still be distinguishable from 1r°s as Figure 1.5 shows. The reader should be aware that Owen’s calculations involve high p _L 1r° pair production rather than generic 1r° + jet production, and there may be a larger contribution by subpro- cesses with gluon propagators in the former than the latter. The cross sections in M for high p _L direct photon and 1r° events should be different. The photon cross section should fall more slowly with M since there is no attenuation due to a fragmentation function in lowest order. It would be interesting to see if the two rates cross over within the accessible kinematic range. At higher energies direct photon production would increasingly dominate! The “hardness” of the gluon distribution can be studied by examining the ratio of 7 + jet cross sections in 7r"- nucleus collisions to proton-nucleus collisions as a function of M. In particular, it can 18 be seen how quickly this ratio rises with increasing energy. Taking the ratio cancels out a number of systematic effects, including k _L and massive jets. These effects introduce large uncertainties in a study of the cross section for proton—nucleus collisions alone because it is steeply falling in M. The physics behind this is very simple. In lowest order only the Compton sub- process is active in proton-nucleus collisions. This mechanism results in an overall dependence of the rate on a (1 — 2:)"6 factor. The cross section thus dies out at large 2:. In 1r"- nucleus interactions there is the additional contribution of quark-antiquark annihilation so the overall rate should not decrease as quickly in this case. Therefore, the larger the value of 170 the faster the 1r‘/proton ratio of '7 +jet cross sections rises with M. 1.3 EXPERIMENTAL CONSIDERATIONS A number of experiments have been performed which attempted to determine if direct photons exist and estimate the cross section. Some of them also looked for unique features in the event structure of prompt photons. An excellent review of these first generation experiments is given in the article by Ferbel and Molzon [7]. Experiment E706 is one of several second generation experiments, designed to obtain a quantitative measure of the direct photon cross section. In addition, E706 hopes to measure the gluon structure functions for protons and pions with unprece- dented precision. The rather large acceptance of the spectrometer (z 65% of the solid angle) gives it a greater sensitivity to differences in the overall event structure between single 1s and high p l single hadrons as well as between various types of direct photon events. The experiment is capable of obtaining single 1 events in the p; range of 4.0 GeV/c to 10.0 GeV/c. 19 The rarity of prompt photon events requires a detector much more efficient at selecting them than in selecting the more common hard-scatter events. There are two major steps in solving this problem. High energy photons interact with dense forms of matter, producing showers of minimum ionizing electrons. A detector is needed that is capable of measuring the electron shower energy while being insensitive to the passage of high energy hadrons. Such devices are knOWn as electromagnetic calorimeters. The second step involves implementing a special electronic circuit to sense the presence of a high p i electromagnetic shower in the detector, and to send a signal to the data acquisition system that the event information should be latched. This circuit is known as the trigger. The trigger must be capable of generating latch signals on the same time scale as the interaction rate in the target, which is 1 MHz for E706. Even for data taken using these techniques, there is still a large background to the direct photon signal. The background is produced from 1r° and 1] decays, and it is at least as large as the prompt photon signal over most of the kinematic region. 1r°s decay into two photons with a 99.9% branching fraction; 11s decay similarly 40% of the time. However, the 17 production rate is only 40% of 7r° production rate. By re- constructing the 4-vectors of these particles from their decay products, a quantitative ‘ measurement of the photon cross section is possible. However, the electromagnetic calorimeter must have a fine enough spatial granularity so that both decay photons can be reconstructed. Unfortunately, electromagnetic showers have a natural width associated with them, making it very difficult to separate showers closer than ~ 1 cm at energies typically found in the data. This difficulty can be circumvented by moving the detector farther downstream of the target, but a. price is paid in acceptance. A 65% solid angle coverage was chosen so that the two decay photons from a 100 GeV/c 1° could be separated. Such a coverage lies between $1.0 unit of rapidity and 211' in 20 azimuth. Because the acceptance is less than 41r, and the detector itself has an energy threshold (~ 5 GeV), not all neutral mesons will be reconstructed. By measuring the 1r° and 1] cross sections, the contribution of 7r° and 1) decays to the observed single photon spectrum can be calculated. This false direct photon spectrum can then be subtracted from the reconstructed single photon spectrum, resulting in the true pi spectrum for prompt photons. An experiment sensitive to the event structure associated with direct photons must have some ability to determine the 4-vectors of the recoiling hadrons. For this reason a magnetic spectrometer was used to measure the 4-vectors of charged hadrons. Although the experiment’s ability to reconstruct the neutral component of jets has been compromised, the information gained from the charged tracking system suffices for this analysis. The magnetic spectrometer provides excellent solid angle coverage, allowing containment of the recoil jet within the apparatus. This has been accomplished by using a set of silicon microstrip detectors to reconstruct the event vertex, which allows the production target to be placed right up next to the analyzing magnet’s aperture. 1.4 THESIS GOALS The major goal of this thesis is to compare direct photon and 7r° events. The asso- ciated charged particle structure of these events will be used in making comparisons. The events will be studied to see how isolated the single photons are. The angular and invariant mass spectra will also be compared between the two event types. In addition, they will be checked to see how well they conform to QCD expectations. Being able to observe all the expected differences between direct photons and 1r°s has a twoedged advantage. First, it means the experiment is capable of resolving 21 the direct photon signal from a substantial background due to neutral meson decays. Second, it further validates the QCD interpretation of hadron-hadron collisions. At- tempts will be made to see if differences between 75 and 1r°s can be found without a background subtraction. Such a finding would greatly bolster the direct photon results with a background subtraction. The conformity to QCD will be checked by comparing data distributions with those generated by a physics monte carlo. All cuts applied to the data will be applied to the monte carlo along with the p 1 balancing and massless jet assumptions. In so doing, the systematics affecting both types of data can be equalized. In addition to looking for differences between '75 and 7r°s, the ratio of absolute M cross sections between proton and 1r‘ beam data will be studied to see how hard the gluon distribution is. By “hardness” or “softness” is meant whether the value of 11a is small or large respectively. The data ratio is to be compared with monte carlo predictions, using two different sets of structure functions; the sets are distinguished by their value for 119. As a check on this method’s validity, the corresponding M ratio for high p j 1r°s will be examined and compared with monte carlo predictions. The calculation of M and cos 9‘ is straightforward as shown in section 1.1. How- ever, the M and especially the angular distributions for the E706 data sample possess large systematic biases. These biases are due primarily to the p _L cuts imposed on the trigger particle. The p _L cut is necessitated by the trigger apparatus’ p ,L threshold. In addition, the calorimeter’s limited acceptance in rapidity causes variable losses in cos 9‘ over the measured range. While these biases could be compensated for by applying corrections based on a physics monte carlo, such a procedure introduces a model dependence. Instead, cuts will be applied so that the true shapes of these distributions can be observed, albeit over a restricted range. A cut in M and 173 are required to remove the bias in the angular distributions, but cuts in M and cos 9‘ are needed for the cross sections. 22 1.4.1 Biases in cos 0" The uncut cos 0" distributions contain two sources of bias. One, triggering on events according to p j_ introduces a large artificial enhancement of events around cos 0" = 0. Second, the detector’s geometric acceptance is considerably less than 41r. These acceptance edges result in an enhancement of events around cos 9’ = 0 relative to those near cos 9‘ = :tl. The pi trigger bias can be removed by applying a cut in either 3 or 1'. Figure 1.6 shows how this cut works. In this plot cos 9‘ is plotted against 7'. The absolute kinematic boundaries are defined by cos 9' = :t1 and T = 0,1' = 1. However, the plotted points do not cover the whole region of phase space, but are constrained to lie within a region determined by the trigger threshold. The equation for this region’s boundary curve is given by 2 1 2 %.—, -r 2 —P—*— (1.13) S 7' ,/§ Note that for pith = 0 this boundary merges with the absolute one. Clearly the sin 9" = density of points is not uniform, but increases rapidly as 7' decreases towards the minimum dictated by the trigger threshold. This behavior stems from the fact that the cross section is a steeply falling function of 3. At cos 0" = 0, x/g '5 2p l but away from cos 0" = 0, J3 > 2p ,L. Events with the same p 1 may have different values of 3 depending on their orientation in cos 0’. So, selecting events according to p J. will enhance those with lower values of 3 over those with larger values. Because the cross section is so steeply falling, this artificial enhancement will completely wash out the shape of the true distribution, rendering any comparisons meaningless. Consider dividing the data in Figure 1.6 by the line 1' = run. This line intersects two points on the curve defined by Equation 1.13. The line cos 0‘ = :t cos 9;“, passing through these intersection points defines a region to the right of 1' = 11,“. unaffected 23 by the trigger bias because no points in this region lie on the boundary curve. It follows that for the data in this region each bin of cos 0' has the same :3 spectrum. Therefore, the true dependence of the cross section on cos 6‘ may be observed there. The cut in 1' only allows for an unbiased measurement of cos 0‘ within the region cos 9" = :1: cos 92“,. Increasing the 1' cut allows greater coverage of cos (9', but with a substantial loss in statistics. This analysis of the 1988 E706 data will employ T cuts yielding an unbiased cos 0' distribution out to cos 0‘ = $0.5. The acceptance bias is purely geometrical and easily understood in terms of 1].,,‘,1]",173 and 111,“; where 111,“,- represents the edge of the electromagnetic calorime- ter’s acceptance in pseudorapidity 11‘ — m: = mm, (1.14) It is easy to show that 173 = %m(32/31)- Since 3;, 2:3, and cos 9' are physically independent, the .173 distribution is the same for all 17‘. The detector’s acceptance, however, causes the boost distribution to be different for 1" near 1”,“; from 17' z 0. This is shown in Figure 1.7. There are pieces of each 1,3 distribution that are unaffected by acceptance, namely I173] < [mum —17m.,|. If a cut in 173 is imposed such that the inequality is satisfied, then there is uniform acceptance in cos 0'. The true shape of the angular distribution will then be observed. 1.4.2 Biases in M Refering again to Figure 1.6, the 1’ distribution inside the rectangle is unbiased with respect to the trigger. Including regions outside the rectangle would bias the absolute cross section in such a way that if the cross section were flat with respect to 1', the trigger would produce a cross section increasing in 1. This bias is not a problem when comparing two distributions having identical trigger thresholds and acceptances. In the case of the 1988 run of E706 though, the data can be divided into 0.8 0.6 C050’ 0 0.2 -0.4 24 Illlllllllll liIl'lllllll I 1=4p’,’/(Sin’0's) 1=4p",‘/(Sin'0‘s) l iilllllllllLLllllllllllllllllLlLLllllllllllllllll 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 Figure 1.6: Scatter plot of cos 9" vs T. The region between the two horizontal lines, and to the right of the vertical line is unbiased from the trigger over the measured interval of cos 0‘. 25 71s 1i“".— --_- , sun j 9.x“. ‘ ‘ ‘ .'__. ' ’1' it; w: . ins-111191.. ,. I ‘ the 7,. :11- ] l ”a: U. "1 butler, ith” than-2.15 f- 1- .~ 1' ' .‘ ' n ' ‘:' . .4 I "3 a I,” ”an Inn... . ’3 ' ' .- - » »‘ a .. -. .-. .- .-... /_ a J... .. . .. ,. - . ~ , L mack-ch tin;- . . . 2.. o. .. .3 2 1 , 5w :1 1;,»- 2m. " 1:?‘9 IMKE Ebllfl" -"." i ' ‘ F91. . ‘ 1.7: Anillustratiori ofthelnasmcosfi‘asaresultof ".._“ fitmaN-nm Master’s acceptance being < 411‘ ' 'i *3%’ ”‘3‘" ‘37} .‘ 11:. v»."'7. :s' 210‘ 71' ~ tf‘tf- altitfeqmtfidq i.:~’.rm::t‘iw'.:- 26 three distinct sets according to trigger threshold. Comparing a pair of cross sections in M from different threshold sets could be misleading. In addition, there are problems combining data from different threshold sets into the same distribution. For this reason, only data within the unbiased region will be used. In order to gain statistics the mass cut will be smaller than the one employed for the cos 0‘ plots. However, this means that the cos 6" limits in the M distributions are also correspondingly tighter. 1.5 THESIS OUTLINE A very brief outline of this thesis is now presented. The reader interested only in the data analysis is advised to skip the next three chapters and start with the chapter on event features. It may be wise to skim the fourth chapter in order to understand how the single photon and 11'" data samples were initially determined. The next chapter describes at considerable length the major design features of the calorimeter and its associated electronics. These features are discussed in terms of how they maximize this device’s sensitivity to direct photon events while making it as insensitive as possible to the very large background. The tracking system is dealt with also because the ensuing analysis relies heavily on the magnetic spectrometer’s ability to detect the particles recoiling from a high p j electromagnetic trigger. Following the chapter on detector hardware is a chapter about the reconstruction software, which converts the signals recorded from the detectors into photon and charged particle 4-vectors. Next comes a discussion of how events containing a high p _L 1r° or single photon are selected from the reconstructor output. There is a discussion of how the muon and 1r° backgrounds are eliminated from the single photon data set. Finally, there is a presentation of the various corrections applied to the trigger particles in order to obtain absolute cross sections. Some of these corrections are also required in obtaining the proper cos 0" and M distributions. 27 This data analysis really begins in the chapter on event features. The charged particle structure associated with the 7 and 1r° samples is examined. This study has two major goals. First, it will be shown that a difference exists between single photon and no events at high p _L without a background subtraction. Second, it must be shown that the tracking system is capable of “seeing” the recoil jet structure. Correlations in rapidity will be used to demonstrate this is so. The recoil jet reconstruction is studied in chapter 6. Much of this work depends on the output of a physics monte carlo. The aim here is to determine how correctly and efficiently the recoil jet direction is calculated over the acceptance. It will be shown that the reconstruction of cos 0‘ and M is meaningful within the conceptual framework of QCD. The reconstructed cos 0" and M distributions are presented in the last chapter. The cuts and corrections used will be elaborated upon further. A generalized method of computing the 1r° component of an unsubtracted single photon distribution is given, and the effects of 1r° background in the direct photon sample will be studied. Again, the emphasis is on comparing direct photons and 1r°s in data and monte carlo. Chapter 2 Experimental Setup The design, operation and performance of the various detector systems is now dis- cussed. The main hardware components are the beamline, the liquid argon calorime- ters, the online trigger system, the charged tracking spectrometer, and the forward calorimeter. The online trigger system consists of a set of scintillation counters, and a special high speed electronics system that analyzes signals coming from the liquid argon calorimeters in real time. The scintillation counter data can also be employed offline in whole event selection. .The analysis to be presented in the following chap- ters centers around the electromagnetic liquid argon calorimeter (EMLAC), and the charged tracking system. Consequently, only these detector components will be dealt with in great detail. Figure 2.1 shows a plan view of the apparatus. 2.1 BEAMLINE ‘ The MWEST beamline is designed to produce and transport a 500 GeV/c hadron beam. This hadron beam can be either positive or negatively charged, but different charges have to be transported at different times. The secondary beam originated in ' a 3/4 interaction length piece of aluminum, whenever 800 GeV/c protons from the Tevatron impinged upon it. One accelerator cycle occurs every 57 s. For 23 out of those 57 seconds, primary beam is available for producing the 500 GeV/c secondary beam. The period for which the primary beam is available each cycle is termed a spill. The primary beam was rotated 1.9 mrad relative to the secondary beam during positive running. This was done to prevent primary beam from entering the exper- imental hall. The two beams had no relative angle during the negative beam run- 28 29 ning. The intensities for positive and negative beam were about 6.5 x 107 / spill and 2 x 107/ spill respectively. The primary intensity delivered to the MWEST beamline was 2 x low/spill. A string of dipole and quadrupole magnets directed and focused the secondary beam unto a nuclear target in the experimental hall. The string of magnets also contained special toroids, called spoilers, which swept the halo particles out of the E706 detector’s acceptance. A set of collimators selected the beam’s momentum and regulated its intensity. The momentum spread was AP/ P = 6%. The collimators responsible for regulating the beam’s intensity were left wide Open during negative running, but had to be closed down for positive beam so that the interaction rate would be S 1 MHz. Figure 2.2 shows a schematic of the beamline. All bending and focusing elements are represented by their optical equivalents. A D or Q in the device name indicates a dipole or quadrupole respectively. An S stands for a spoiler while C designates a collimator. H or V indicates whether the device affects the beam horizontally or vertically. The primary target is designated as MW6TGT. 2.1.1 The Cerenkov Detector The positive beam contained a mixture of proton, 1r+, and K+ particles while the negative beam was composed of 1r", K", and 1‘) particles. To identify which type of particle produced a particular event, a differential C counter was installed in the beamline. The beam was tuned so that dispersion was minimized as it traversed this piece of apparatus. The C detector is 42m long and filled with helium gas, which functions as the radiator. The helium pressure varied from 4 — 6PSI over the course of the 1987-88 run. The counter’s Cerenkov angle is 5mrad. So, by varying the pressure different beam particle species could be detected and pressure curves constructed (see Figure 2.3 ) \\ so my////////////////% mu 0 O. 31 somzonm. POSITION (pm) 20 l ‘3 ‘0 3° CO 4 L 1 1 : -l CII-I—ud'flu‘f EF— H'.‘ ‘I , A u’WS-I €001 ‘--O - we! vj‘ mcm 3 «002-2 (.7 230 ‘ KMOJ la was: ; M .. —— W A "3 -i We: '3 /< mm l‘.‘ - macaz v 7— “-70. 5 600 -4 < 9 '-¢ ‘7 M1-LZ é ’% m3“ 0 u was: 3 "9 "‘ mac: 1 inns-s M03 3 —-- W806 3 3 ‘ V423 so 5:296:54 ass on vevowsnni “/4 53 ‘5“ “5° 3’ /// so so so 57 n 2 no 9 s o 5 no no an o 7 o no no no J\ /_. 22 as a so on so no/zorzn so so 27 ///// n7 no so as Figure 2.5: Sketch of the Veto Wall planes. The arrows rep- resent the beam’s passage through the counters. Each square represents one scintillation counter. 37 to minimize the number of interaction and radiation lengths between the target and the forward calorimeter. Finally, the cryostat was sealed at the top by a soft steel structure known as the top-hat. The argon was kept below its boiling point by circulating liquid nitrogen through copper cooling coils situated immediately beneath the top-hat. A layer of insulating plastic between the top-hat and these coils kept the top hat at room temperature. The calorimeters are suspended from threaded rods which are attached to a steel gantry structure. The cryostat can be moved vertically by another set of threaded rods that are also fixed to the gantry structure. The gantry itself rest on Hillman rollers which allow movement transverse to the beam direction. Such movement is used for calibration purposes and to move the calorimeters over to the service area should the need ever arise. A Faraday cage completely surrounds the top-hat structure. This cage is actually a room lined with sheet metal. The calorimeter electronics and high-level trigger system reside in a Faraday room since they are very sensitive to radio-frequency noise. In addition the room is air-conditioned in order to maintain a temperature at which the solid state circuitry can operate properly. Figure 2.6 shows the arrangement of all these modules on the gantry structure. The EMLAC measured the energies and positions of incident photons and elec- trons; this device also provided the high level online trigger signal for selecting events with high p i photons. As the name implies, a liquid argon calorimeter measures the energy of incident particles by measuring the amount of ionization they generate in liquid argon. The EMLAC is a sampling calorimeter, containing 66 ionization cells. Each cell contains, in addition to liquid argon, a 0.3 radiation length lead absorber plate and a copper-clad printed circuit board to collect the ionization electrons. The EMLAC is more than 27 radiation lengths thick longitudinally thereby insuring com- plete containment of all electromagnetic showers. This device employs a strip readout 38 scheme for recording the energy deposited by individual showers, and measuring their positions. Such a scheme is very cost-effective, and greatly simplifies the formation of a high level trigger. 2.2.1 EMLAC Design The electromagnetic calorimeter is the heart of the experiment. The data gathered from this device is used to reconstruct the high p j 7, 1r°, or 17 that triggered the events, and ultimately to measure the direct photon signal. To achieve this goal this detector had to be able to operate in a high rate environment, allow for efficient 1r° reconstruction, and contribute small systematic uncertainties to the 1r° cross section. These qualities, necessitated the following design criteria: a The detector must operate reliably with a 1-2 MHz interaction rate. 0 The device should have the ability to distinguish electromagnetic showers from those produced by hadrons. o The detector should have as large an acceptance as possible. a The energy resolution and response linearity, i. e.pulse height to energy relation, must be good enough for 1r°s and 175 to be reliably reconstructed. o The lateral segmentation of the calorimeter should be fine enough so that pho- 0 tons emanating from 1r or 1] decays can be resolved. 0 The lateral segmentation should be designed so that a trigger based on electro- magnetic p i can be easily formed. 0 The large number of channels needed to achieve the desired lateral segmentation requires the channel electronics to be stable over time, since frequent calibration would introduce unacceptable down time. 39 To storage 81“” S: dewar: ——> f rabbit crate: “199°“ roos bafflin c p :- 9 . . t Faraday room \ '1: ‘ .n‘ I. 5 I..l".-.."'.:.‘A.-,:f-r-:~Ii.‘o‘.i:" H1? la. NIH-11]] '1 2523.“ cooling coils 1,}, 4:4: beam .1- auxin-III- NIH fl Benn filler . . , vessel ”13$ ‘ , from . L l __ one: , . filler / =:== =:==: =:==-=.= =—=fl 3 "1; VCSSCl super- dewar plates ‘5.“ / ‘ aw V ‘ I ‘ ' ' ulazion g l ""l-fillman l-lAlAC EMLAC bubble rollers shield Figure 2.6: Layout of the calorimeters on the gantry support structure. Also shown are the filler vessel, the beam tube, and the Faraday room. 40 In order to have good 1r° reconstruction efficiency, reliable triggering capability and keep costs down, a sampling calorimeter design with a strip readout scheme was chosen. Liquid argon was selected for the sampling medium because of its homogene- ity, high density, and stability in a high radiation environment. The major drawback in using liquid argon is that a large cryogenics support system must be furnished, and the other materials used in constructing the device, as well as the mechanical design itself, must remain sound during and after cooldown to liquid argon temperature. The absorber material was lead. Lead is a high Z material with a radiation length of .56 cm and an interaction length of 17.1 cm, allowing good longitudinal discrimination between photons and hadrons. 27.76 radiation lengths of lead have been used in order to longitudinally contain the highest energy electromagnetic showers (z 250 GeV). To facilitate the formation of a high p i trigger an r-¢ geometry was chosen for the readout scheme. Figure 2.7 illustrates this scheme. The calorimeter consists of alternating layers of r and :1) strips, sandwiched between lead absorber plates. In between each lead plate and a neighboring charge collection or signal layer is a gap filled with liquid argon. Only the r-view pulse heights are used to form the trigger. The strips in each r layer are arranged in concentric annuli. Each layer is focused on the target 9 m away. As shown in Figure 2.8, a piece of solid angle subtending a strip in the first r layer will subtend one and only one strip in every succeeding layer. In other words, a particle trajectory emanating from the target at an angle a with respect to the beam axis will pass through a unique set of r strips. Hence, a simple sin9 weighted energy summing scheme over groups of r strips can be used to trigger on electromagnetic p ‘L. The 4} layers comprise sectors of a circle. There are two sets of (1) strips in each 4) layer. The inner-d) set divides the sector into 1r/192 subsectors while the outer (1) set divides the sector into 1r / 384 pieces. The inner-outer d) boundary occurs at r = 40 cm Exploded View 0,- EMLAC Cell / L‘“ “21.2w / ‘\\\\\\\\\\\\ 5‘ .9 \ .. \ R Mode Board a. \-l . “8°11 Gap: Cross-section“ View . of EMLAC Cell # (beam direcdon) com ‘ Cowper mm. mm on PM 532,. m a sum Figure 2.7: Isometric and Cross-sectional views of an EMLAC sampling cell, showing the r-¢ geometry of the charge collection layers. 42 46 determines the strip width on all of the r-boards EMLAC 9 III I I i . III I I I III I I I ll: : : :3 All strips on an III I 'I I I f°b03fd have 11;, ' ' the same width ._ Jug-i I I I era -r' " O Beamllna- . a e .................. Target <— 9.0m é, First R-Board Figure 2.8: Cut-view drawing of the EMLAC illustrating r- strip focusing. 43 in the first layer, and is focused in succeeding layers. Such a division corresponds to z 90° in the nucleon-nucleon cm frame. The EMLAC has a central hole of radius 20 cm. This hole allows the passage of beam particles and accompanying halo. The detector cannot reliably operate in this region of the acceptance where particle rates exceed 10 MHz. The ability to function in a high rate environment, t.e. 1MHz is primarily a function of the argon gap width [9], since this determines the rise-time of the device. A rise time of z 1 its is required for operation at a 1 MHz rate. To see how this comes about consider the following formula: tvd 1 tvd d Q“) = Nc—d— (1 - -—), t < — (2.1) where Q(t) is the charge collected in a time t off of the signal strips, 12,; is the electron drift velocity, (1 is the gap width, and N.: is the total charge deposited in the gap which can be collected by a particular group of strips. According to this formula, the maximum amount of charge that can be collected is N, / 2. If the rise-time is defined as time required to collect 90% of the charge, then (1 tri" = 0.63— (2-2) . vd Argon cannot sustain electric fields much above 10 kV / cm so this places an upper limit on the drift velocity such that 1).; = 4.5 x 105 cm/s. Therefore, a gap no larger than 7mm can be used if the detector is to function properly with a 1 MHz interaction rate. However, a small gap width decreases the signal-to-noise ratio because the chan- nel capacitance increases as more sampling cells are added. This assumes the total number of radiation lengths in the detector remains fixed. Choosing a particular gap width involves a compromise between energy resolution and rate limitations. 44 The lower limit on the gap width is determined by the intrinsic energy resolution. The energy resolution of a sampling calorimeter is limited by the fluctuations in the number of charged tracks, N, traversing the sampling gap. If the track crossings are independent, and the particles are minimum ionizing then (0(E)/E)Sampling :A'1/\/7\7 (23) There are variations in the measured energy due to path length fluctuations of showering particles, and fluctuations in the energy deposition processes themselves. The energy deposition processes for electromagnetic showers are pair production, bremsstrahlung, and multiple coulomb scattering in the absorber medium. The cor- responding fluctuations are known as Landau fluctuations and are parametrized as follows (a(E)/E)Lmdm e LNMZ/ 1210043)) (2.4) where x is in g/cmz. Therefore, the total energy resolution can be expressed in the following form: (i?)=(%)m.. c : "'""'_"’ to analog multiplexing I - t "i.___" Qi" 2 J\ z a.--" E : I . I ' Ea l l......: ’b ii 2 l [“1“ 5i— 7 l\ V SLAVE TVC signal to analog multiplexing Figure 2.20: A simplified diagram for a TVC .122. 67 circuits. There are three major portions of the trigger system. First, there are the electronics associated with the EMLAC which estimate the amount of p i deposited in the detector. Another part of the circuit provides the beam and interaction definition. Finally, there are several counters and modules that generate vetoing signals. These vetoes halt the trigger’s operation for up to 30 #5- 2.3.1 EMLAC pi System The EMLAC was used to detect local depositions of large amounts of p j. The p j deposited is obtained from the deposited energy by the following pi = Esin 9 ‘ (2.7) The detector’s focused r — 43 geometry made the formation of the trigger straightfor- ward. The r-strips were used to form a p _L sum in the following manner: pl = 2e; sin 0, I (2.8) p j is the amount of transverse momentum in a particular r-region of an octant. The sum is over the strips in the front and back sections within the region. e,- is the energy deposited in the ith readout strip in a summed region, and 0,- is the production angle corresponding to the ith readout strip. Figure 2.21 shows how the r-strips of each EMLAC octant are grouped together to form the various p _L sums. The analog summing begins by taking the sum of adjacent fast-outputs from the LACAMPs, and putting the signals into 8-bit linear attenuators. The attenuators provide the sin9 weighting of the pulse heights. The attenuator outputs are then summed in groups of 8; front and back sections are summed separately at this stage. Adjacent groups of 8 are subsequently summed into non-overlapping groups of 32 channels. The groups of 8 provided the input to the local discriminator modules, while the sums of 32 were used to form the global trigger signals. 68 The local discriminator modules are shown schematically in Figure 2.22. At this stage the sums of corresponding front and back groups of 8 are summed together on input. Furthermore, adjacent groups of 8 are summed together into groups of 16 channels, overlapping one another by 8 channels. If any sum of 16 exceeds a specxfied threshold, then a single-signal (SLOC) trigger signal is generated. There were two local discriminator modules per octant for the 1987-1988 data taking period. They produced logic signals referred to as LOCAL_PT_HI and LOCAL_PT_LO, indicating the relative magnitudes of the thresholds. The sums of 32 are discriminated in a similar fashion by a set of devices called the global p _L modules. However, the groups of 32 are summed in a different manner. There is a sum of the 3 innermost groups of 32 channels, a sum of the next 4 groups of 32, and a sum over all groups of 32 in each octant. Thus, each octant had three different global p _L sums assigned to it, and there were two global p i thresholds per octant. The three global sums are expressed mathematically as follows: 95 81Pt13 = ZPli '=o 233 glpt47 = an (2.9) {:96 233 g1pt17 = Eph- i=0 Pl; or Eisin 0,- Besides forming a global p j logic signal, the global p l sums glpt13 and glpt47 were used to generate octant PRETRIGGER signals. The generation and purpose of the PRETRIGGER signal as well as the high level interrupt signal are given in a following subsection. Table 2.2 lists the nominal thresholds for both the local and global p j trigger modules. Notice that several of them were changed from time to time during the data taking period. Ch. Clt. Ch. Ch. Ch. Ch. Ch. ' Ch. ‘ 69 O 8-bit Lines: 1 attenuator 2 > _, 8-btt linear attenuator 3 4 . >__ 8433 ltncar / attenuator 5 ' ° 8-bil linear / attenuator 7 O O O > O O C sum-of-S (0-7l sum-of-B (8- l 5) tunnel-8 (lo-23) sum-of-8 (24-31) sum-ol-BZ Figure 2.21: Octant r-channel summing scheme employed by the local p .L modules. These modules produced summed signals for groups of 8 and 32 strips. 70 {mm 91' module sum-ol-S outputs l Winston 0-7 front Ed. 0-7 back Outputs r - I q 3-l5 front 3.15 back 15.23 front >__< %___/i / 4 1 l —---—-----—-..-—-————-———-—----- 1 NJ! {rant 24°31 bacx _’ I I , . l I I I I I I - I I I I - I L' 2.3.2.5.... >_/ 248-255 back 8-bitDAC 0-2..SV Global OR (NIM dc TTL) Figure 2.22: Front-back summing scheme employed by the lo- cal discriminator modules. 71 Table 2.2: Trigger threshold settings by run number. Logic Signal Threshold (GeV / c) runs runs runs runs 1811-2292 2293-2310 2311-2904 2905-3036 LOCAL_PT_LO 1.2 LOCAL_PT_HI 4.2 3.6 3.0 GLOBAL_PT_LO 2.5 GLOBAL_PT_HI 4.0 3.6 At this point a brief discussion of the image charge effect is in order. The effect of image charge can be understood by examining Figure 2.23. As the ionization electrons drift towards the anode under the influence of the electric field between the lead plate and the grounded readout board, a current is induced. This current was originally intended to flow out through the amplifier signal cables and return to the lead plates via the high voltage ballast capacitors. However, when the EMLAC was put into operation, it was found that due to impedances in the ground path between the ballast capacitors and the amplifiers the return current flowed through the amplifiers adjacent to the ones sensing the actual ionization during the first 200 ms or so of pulse formation. The result was a signal of opposite sign and nearly equal magnitude on the channels surrounding a high energy electromagnetic shower during the time of trigger pulse formation. When summing a group of 16 channels for the local trigger, the image charge contribution is small since the typical shower width is about 16 strips. However, the global sums result in a serious loss of signal, greatly compromising the global trigger’s efficiency as Figure 2.24 illustrates. What’s even worse is that the image char e contribution rows with radius due to the r-stri s’ increasin ca acitance and 8 8 P g P a 72 Elecuon-lon Pam HV Cathode. ‘.‘ / . - Moos \ .' Liquid Argon Charge lntenation Am: ' l 1 I. I : Signal T —:——w T i L .................. .1 Figure 2.23: Schematic of the EMLAC charge collection circuit (one channel). the increase in the sin9 weighting. To alleviate the image charge problem out off diodes were installed on the inputs to the modules performing the sums of 32. These diodes shunt the “wrong sign” image charge current to ground. In addition, The outermost 32 channels were not utilized in forming a trigger. Because diodes have a characteristic turn on voltage, not all of the image current was shunted to ground, and so the global trigger’s performance was indeed compromised. 2.3.2 Beam and Interaction Definition A trigger logic signal from the EMLAC should be “in time” with a particular interaction in the target if it corresponds to an event of interest. The interaction itself should be in coincidence with the passage of a beam particle through the apparatus. To avoid pile-up effects in the calorimeter and constrain the event kinematics the interaction responsible for a high level trigger should not be accompanied by another interaction within a time window of 150 ns. Finally, it is useful to know whether image Charge (Summed over emcee o! Octant; Summed Signal for Entire Octant a ............... 7 ...... 1 l - l l l l _. I60 250 350 450 $60 660 income) Figure 2.24: The effect of image charge on the global trigger input signal. or not the beam particle associated with a given interaction was part of the beam halo since it was possible for halo particles to generate interaction signals and/or electromagnetic showers. The layout of the scintillation counters used in the beam and interaction definitions is shown in Figure 2.25. The presence of a beam particle was signalled by counters BA, BB, and BH. BH was a counter with a 1.0 cm hole to allow true beam particles to pass through it. A signal from BH indicated a halo particle’s passage. In addition, the signals from: the beam counters were put in coincidence with the RF clock and beam gate provided by the accelerator control room. The RF clock provides pulses with a period of 19.4 ns, which matches the beam’s bucket structure. The beam gate is activated when the extraction magnets are energized. The beam signal for the 1987-1988 data taking period is given by the following logical expression, BM = BA - BB - BH ~ BMGATE - RF_CLOCK (2.10) Beam signals were generated once every 19.4 ns. 74 -‘.’( "(era’s . I-'(: wfiuvhv ‘( f (~(-- I“: We‘re ‘~ ‘- w‘v Ml: \4. w :1 u d‘lv'l Z :12 *‘fisfi‘sfi: 'm': Olmvlv‘v v- ', u 3:) .\-l\rl‘:-.I(?l(obg3s: Figure 2.25: The configuration of scintillation counters used the the beam and interaction definitions. The interaction signal was formed from the coincidence of any one of the inter- action counters, SW1, SW2, SE1, or SE2 with the BM signal. Each interaction counter had a semicircular hole in it, allowing passage of the beam. Otherwise there would be an “interaction” every 20 ns and the pile-up filter w0uld veto every event selected by the EMLAC trigger electronics. The interaction pile-up filter circuit is shown schematically in Figure 2.26. The signal from each interaction is delayed 16 times in successive 20 ns intervals. The ninth delay port was defined to be t = 0, and put in coincidence with the logic signals coming from the calorimeter and vetoing el- ements. A clean interaction signal was produced if a signal exiting port nine was not in coincidence with any signals from the three adjacent ports on either side. Thus, a triggerable interaction was isolated in time from other interactions by :L-60 ns. A live interaction was defined as the coincidence of a clean interaction, the BM signal and a computer-ready gate. The computer-ready was required since the DA system had to be capable of reading out the detectors should a trigger occur; this was the quiescent 75 state of the DA system. It was the live interaction signal that was actually put in coincidence with the high level trigger from the EMLAC. 2.3.3 Vetoing Elements There are three online veto requirements. All of them have to be satisfied at the PRETRIGGER level. The first requirement is that no PRETRIGGER has occurred within the previous 300 ns of the current PRETRIGGER. The PRETRIGGER sig- nals are delayed in a manner similar to the interaction signals so that a coincidence backward in time can be made. This veto is known as the early p j kill. Its purpose is to prevent two low p _L events, separated in time by less than the LAC risetime, from satisfying the high-pjtrigger. Another veto is provided by the veto wall described earlier. The hadron shield is very effective at stopping the diffuse beam halo. However, the muon flux is so high during data taking that many halo muons penetrate the shield, and shower in the EMLAC. Enough high p _L showers could be generated this way'to seriously contaminate the single photon sample. Therefore if both veto walls register at least one hit in time with an EMLAC trigger, then a signal is produced that disables the trigger for ~ 150 ns. Finally, there was an SCR kill which disabled the trigger for 30 as. The SCR spikes are detected by a set of HADLAC channels, discriminated and then sent as a veto to ports on the trigger electronics modules responsible for the PRETRIGGER signal. SCR noise spikes are generated by the 400 Hz RABBIT power supplies inside the Faraday room. Such noise spikes induced LACAMP oscillations capable of producing false triggers. These oscillations are damped out within 30 us. 76 .J'gfiv ' I J r—--t at." a 7 ‘—T_{-\ CLCM.LAYC ]——J— F. U p— u“' ' 1N7 r 'L.‘ I 9 4‘ CLEAN.C‘3LY L—fir—thi 3 I, l #. PRCLN .5 J L“) U an ———1_ mint" J— J ————C IN! 4mm“: ‘, J 3 CLEAN.LAYE CLEAN_EARL1 PRCLN Figure 2.26: Schematic diagram of the interaction pile-up fil- ter, and live interaction definition circuits. 77 2.3.4 High Level Trigger Operation The operation of all the high level triggers is essentially the same. If the sum glpt17 for any octant has more than 1.7 GeV/c of pi then an octant pretrigger signal is generated. Provided that a live interaction signal is in coincidence with the octant pretrigger and there are is no trigger veto then a LAC pretrigger is generated. The use of zero-crossing discriminators allows a given pretrigger to be put in coincidence with the proper interaction. At this point a “load” and “event” signal are sent to the tracking system’s latches and the BAT modules respectively. In addition, the pre- trigger circuit is disabled from generating another pretrigger pulse. This guarantees that there is only one “load” signal given per high level trigger, which must be the case if the tracking system’s electronic readout system is to function correctly. If the high level trigger logic generates a signal, then the DA sends out a busy signal, suspending all further data taking. All latched information is then read by the DA and transferred to the proper PDP-ll memory. When all PDP-lls have finished reading out the detectors, the computer-ready gate is enabled, and data taking may resume. A master clear signal is also generated which resets all the electronics. The master clear prevents trigger operation for 5ps so that the trigger electronics may settle into a quiescent state. If no high level trigger is formed within 300 us of a given pretrigger, then a clear signal is sent to the tracking system electronics and the pretrigger circuit is enabled once more. Four distinct types of high level triggers were implemented during the first data taking period of E706. They were constructed from the logic signals listed in Table 2.2. e Local-GIobal—Ht', the trigger generated by a logical AND of the GLOBAL_PT_HI and LOCAL_PT_LO logic signals. This trigger indicated that a large amount of p ‘L had been deposited within an octant with a significant fraction localized 78 in a small region. Its purpose was to provide efficient detection of high pl 77 particles. 0 Single-Local, defined only by the LOCAL_PT_HI signal, signified a large local deposition of p1 within some octant (2 3.0 GeV/c). This trigger was very 0 efficient at selecting single photon and high p1 7r events. 0 Local-GIobaI—Lo, was similar to the Local-GlobaI-Hi trigger except that the GLOBAL_PT_LO signal was used instead of the high threshold global signal. Its purpose was to study the Local-GlobaI-Hi’s performance. This trigger was prescaled by a factor of 10 so it wouldn’t dominate the trigger rate. 0 Two—Gamma, defined by the logical AND of the LOCAL_PT_LO signal from one octant with the same signal from any of the three opposing octants. This trigger selected events containing massive 1r° and single photon pairs at high Pl.- Triggers based on only the beam and interaction definitions were also implemented for diagnostic purposes and various detector studies. They were prescaled by tremendous factors so as not to dominate the trigger rate. The E672 experiment also supplied a high level dimuon-muon trigger which was or’d with the E706 trigger. However, these triggers are not pertinent to this analysis. 2.4 CHARGED TRACKING SYSTEM The charged tracking system consisted of 14 planes of silicon microstrip detectors (SSDs), a dipole analyzing magnet, and 16 planes of multiwire proportional chambers (MWPCs). The SSDs are positioned upstream of the analyzing magnet. They have been used to reconstruct the primary event vertex and the beam track responsible for the interaction. The MWPCs are placed downstream of the magnet. Only the 79 MWPCs possess stereo capabilities and can therefore reconstruct tracks in space. As its name implies, the magnet was used for momentum analysis of tracks and to determine the sign of their respective electric charges. 2.4.1 SSD System The 14 planes of SSD are grouped into modules by pairs. Each pair of planes consists of an X-Plane (strips vertical) and a Y-Plane (strips horizontal). Four of these X-Y modules are positioned downstream of the target and have been used to reconstruct the primary vertex. Three of the X-Y modules are positioned upstream of the target. Their purpose was to reconstruct the tracks of the beam particles appearing within the primary interaction’s vertex. The SSD modules are composed of an aluminum plate which has the PC boards containing the SSD wafers attached to it. The plates lay in precision milled slots on a one-piece cradle. The cradle sits on an optical table which is mounted at three points to the SSD cart. The cart is a steel structure that sits on rails rigidly attached to the floor of the experimental hall. The cart has the ability to move horizontally transverse to the beamline. Figure 2.27 gives a schematic layout of the SSD system in the X and Y-Views. The three X-Y modules upstream of the target and the first X-Y module downstream of the target contain 3 x 3 cm2 wafers. The other three modules have 5 x 5 cm2 wafers installed in them. Each wafer is 250 — 300 pm thick. After the wafers are mounted onto their respective PC boards two holes are drilled in the board. The holes are on either side of the wafer 6 inches apart, centered on and parallel to the central strip. These holes mate with precision located pins in the aluminum module plates. The module plates are seated in precision milled slots on the SSD cradle. Thus, each SSD strip’s location can be known in a surveyor’s coordinate system thereby permitting an alignment of the full SSD system. A complete description of how the wafers are mounted into the modules and connected electrically strip by strip with the outside 80 world is given in a N IM article [15]. There are a total of 7120 active strips in the SSD system. Each strip is 50 pm wide and is essentially a p-i-n diode. A minimum ionizing particle that traverses one of these strips deposits (2.0 — 2.4) x 104 electron-hole pairs. The charge is collected in ~ 20 ns. This charge is picked up by a Rel-Lab IO-323-C charge sensitive preamplifier. The preamplifier output is input for the NANOMETRIC digitization system which is described in a subsequent section. The apparatus shown in Figure 2.28 was used to measure the operating charac- teristics of the SSDs. A 106Ru ,B-source with an endpoint of 3.4 MeV was used as the source of minimum ionizing radiation. 51 and S; were scintillation counters put in coincidence to form a trigger for generating load signals. The load signals were sent to the latches for the SSD plane being tested. For pulse height measurements, a post-amplifier designed to imitate the N - 277C was used to drive a LeCroy 2249A ADC. The pulse height measurements yielded a minimum ionizing peak at 71 KeV above an ADC pedestal peak. The pedestal peak had a HWHM of 3.4 KeV, which yielded a ratio of 21. A threshold study using the N — 277C amplifier yielded a plateau region between 1.5 and 2.5 volts. When normalized to the number of source electrons traversing the detector, the plateau region corresponds to an efficiency of ~ 100%. The small amount of charge produced per strip and the corresponding high gain of the amplifier stages makes the SSD system vulnerable to stray electromagnetic radia- tions coupling into the amplifier stages and dominating the signal. The SSD modules and the preamplifier stages were enclosed in an aluminum housing which formed a Faraday cage. The cables leading from the preamplifiers to the NAN OMETRIC am- plifiers passed through shielded conduits; the same is true for the cables going from the discriminated outputs of the N —277Cs to the latch modules. The power supplying the preamplifiers was passed through XENTEC isolation transformers. All amplifiers were grounded in parallel to the SSD table which was connected to the MWEST hall 81 MI(!OSTIIQ Detector x-Y Modules XY XY / / , a / / / /‘ XY XY XY XY I .y Proton a a Scam \ V 800 ” ' Cl 11 GeV/c g L1 \ 1 / 0.1 Interaction Length of Be Photon PT = 8.22 GeV/C ---~r Direct Photon I—I lcrn Jet Chorqed Particle thnI _ - .- — Spectators Troclts Figure 2.27: Schematic of the segmented target / SSD system of E706. A typical multiple event is superimposed on the planes. 82 tn! Rel Lobs .-. to 323C ...II If)“ p “TTL“‘TT 50 t '1‘ t 2‘ Threshold I ’ St I - 7 S2 5I —-t Trigger Coincidence ; 52 '- ‘‘‘‘ ‘1 r- - -, ----- ,1 LRS 2323 .-<-—-4 tags I 10 "‘ l Gote Generotor _' g I :0 _ ‘t‘ .2 l Interface 0 E z o d U l l LeCro 3500M L _. J. .. .. .J Figure 2.28: Readout electronics schematic used to determine operating characteristics of SSD system. 83 ground via a thick braided cable. 2.4.2 MWPC System The 16 planes of MWPC are grouped into 4 views (X, Y, U, and V). Each view contains 4 planes. The views are grouped into pairs with the members of each pair being mutually orthogonal. The pairs are X-Y and U-V; the U-V system is rotated about the Z-axis with respect to the X-Y system such that the intersections of X, Y, and U lines form 3-4-5 triangles, i.e. the two systems are related by the following transformation: 4 3 U = —X —Y 2.11 5 +5 ( ) 3 : ——X+5Y 5 5 In terms of hardware the MWPCs are grouped into 4 modules. Each module contains 4 anode planes, one for each view. The sense planes have independent facing cathodes for a total of twelve layers. In addition, there is a spacer layer at either end of the stack to provide clearance for the high voltage leads of the end cathodes. The sandwich is held together in compression by two massive frames. The alignment of the planes is accomplished by 12 precision steel pins which fit through bushings on each plane and precision located brass bushings in the frames. Figure 2.29 shows the manner in which the sense planes are stacked in each MWPC module. The operation of these chambers is fairly simple. Charged particles traversing the chambers ionize argon atoms in the gap between the anode and cathode layers. The cathodes are held at around —2900V while the anodes are grounded. As a result, the ionization electrons drift towards the anodes. An illustration of the electric field lines in a multiwire proportional chamber is given in Figure 2.30 [16]. The electrons drift along the field lines towards one of the anode wires. The anode planes typically consist of 800 20 um gold plated tungsten wires positioned precisely parallel 84 to and coplanar with one another. The Spacing between neighboring wires in the E706 MWPC chambers is maintained at 2.5mm. As drifting electrons get within close proximity of a wire, they acquire enough kinetic energy per mean free path to ionize other argon atoms due to the ~ 1/7‘ behaviour of the electric field near a long filamentary conductor. These liberated electrons are in turn able to ionize additional atoms, and so an exponentially increasing amount of ionization occurs as the ions drift towards a given wire. This phenomenon is called an avalanche. An avalanche generally yields a gain of 106 in the amount of ionization collected on a given anode wire over the amount originally deposited in the gap. If the wire is terminated with a resistor, then a current on the order of several pA will flow through it during the first 100 us of signal formation. The resulting voltage is detectable by a high bandwidth amplifier. The amplifier outputs were discriminated in this experiment so the only information available was whether or not a given wire had registered the nearby passage of a charged particle. By determining which wires had experienced an avalanche in an event, and knowing their positions it was possible to reconstruct the trajectories of the charged particles which passed through the system during the event. The spatial resolution of these chambers is only a function of the wire spacing. In fact, it is given simply by a' = s/\/1—2 where s is the wire spacing. The avalanche process is the basis of operation for all proportional type counters. 1 and n are the mean free path and number of It is fairly simple to quantify it. If of electrons at position 2:, then after travelling a distance As: the increase in electrons, An is given by An = na(a:)A:c (2.12) This proportionality between the incremental increase in ionization and the total amount of ionization is what gives proportional counters their name. A simple inte- 85 Cathode V-Anode .\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ othode U- Anode Wfl/WWWW Cl 08 / olho e / Y-Anode i . occlhode .1- Figure 2.29: Arrangement of sense planes in each MWPC mod- ule. X—Anoc Diffractive Region Beom Region\ (. WK ElllllllIlIlllllllllllllllllllllllllll1lIllllllllllllllllllllli!lillllll‘ 86 IIIIIIII1IIII1I1IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII 0‘ ""11"! "III IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII 11111111111111.1111 l IIIIIIIIIII1IIIII IIIIIIII IIIIIIIII IIII I IIIIIII I 11111I1I1I IIIIIIlIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII oso Illll I1 lllllllllll111lllllllllllll Illllllllll IlIIIIIIlllllIlIllllllllllll lllllllll 0,, E11111g‘gylll‘lllflfll‘lwIII} l\\ LIJIUIIIIIIIII‘ulIIIII‘uIIII/I‘IIIIIIII a‘so Viki? ‘r' :77?" 'n'J“ "A“ ’07,”? 231» «no «a» (mull? IiilIII/uml IIIllllhl IIIIIIIIIIIIItmllIImIIlllIlllttllllllflllll IIIIIIIII II IIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII1IIIIIIIIIIIIIII IIIII III IIIIIIIIIIIIIIIIII1IIIIIIII11II .3 III IIIIIIIIII IIIIIIIIII IIIII Illl IIIIIIIIIIIIIIIIIIIII|I1IIIIIIIIII111I11IIIHII IIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIII I III IIII1111 IIII11111111111111I11IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIII111I11111IIIIIIIIIIIIII11 IIIIIII IIIIII111111IIIIII11111111II III II IIIIIIIII IIIIIIIIIIIIIII IIIIIIIII II IIHII IHIII IIII1 IIIIIIIIIIIIlIlIIIIIIIlImlIIIflmllIIII III IIIIIIIII IIIIIIIII IIIIIII IIIIIlI' IIIlIIIIIIII Figure 2.30: Electric field equipotential and field lines in a mul- tiwire proportional chamber. The effect on the field due a small displacement of one wire is also shown. 87 gration leads to an expression for the multiplication factor M. M = n1 = exp1/:2 a(:c)da:1 (2.13) o 1 It is possible to determine the form of or(a:) exactly for a proportional tube counter. Such a detector is composed of a hollow conductive cylinder with a fine wire running along its axis, which is held at positive high voltage. The voltage at a distance r from the anode inside the tube and the capacitance per unit length are given by the following equations, CV0 r = - 2.14 V0.) 21reo In a. ( ) 21reo C _ ln(b/a) where a and b are the counter’s inner and outer radii respectively and V0 is the applied voltage. Generally speaking a has the form a = kpe where p is the number density of molecules in the ionizing medium, 5 is the ionization electrons’ average kinetic energy and k is a constant of proportionality. Given that an electron acquires on average a kinetic energy 6 from the applied electric field between collisions, it follows that a 1kpCVo l = _ 2.15 a(r) 21reo r ( ) If the applied voltage is much greater than the ionization potential, then the mul- has the following form: tiplication factor has the following simple form where K is another constant with dimension of charge-1. M = exp(K(CVo)) (2.16) The electric field configuration in multiwire proportional chambers is much more complex than in cylindrically symmetric proportional tube counters. However, the some simple description of the avalanche process does apply as will now be demon- strated. For a description of the parameters and coordinates used to describe the 88 field in an MWPC the reader is referred to Figure 2.31. The field, potential and capacitance per unit length have been found to be of the following form [171, E(3:Z) = 2063 V0(1+ tan2 :tanhz— 1rz ——)1/2(tan2 E + tanh2 BY“? 03 s s .9 CV 2 I V(z,z) = 411621—11 — 1n(4(sin2 7:: + sinhz $111 (2117) C = 27760 1rl/s — ln(21ra/s) These expressions are valid for the boundary conditions V(a) 2 V0, V(l) = 0. Note that a is the nominal radius of the anode wires, .9 is the wire spacing, and l is the distance between anode and cathode planes. Now, for the region very close to a given wire i.e. 2: << .9 and 2: << 3 the electric field expression reduces to the following V E(:c,z): 0 ol 1"::\/:I:2+2:2 < U C .9. '2110 , u [E 1 100 r- +4- E + + 4. so E- - I 80 :- 70 E- 4- 6° blllllLllllllllLllllllLl 2500 2600 2700 2800 2900 .3000 PWC 3 Cathode Voltage Figure 2.34: A high voltage plateau curve for MWPC module 3. 114 calorimeter was constructed. It is known appropriately as the forward calorimeter or FCAL. Figure 2.35 shows an expanded view of this device in perspective. It consists of three separate modules. Each module is 3.17 interaction lengths thick for a total of 9.5 interaction lengths. Within each module are 28 circular steel absorber plates 114 cm in diameter and spaced 6.9mm apart. 29 plexipop scintillator sheets are sand- wiched between the plates and positioned at either end of a module. The scintillator sheets are 4.6mm thick. A set of 76 holes, drilled on an 11.5 cm grid, exists in each scintillator sheet and absorber plate. 76 wave-shifter rods 1.0 cm in diameter are inserted longitudinally through the aligned holes. The wave-shifter material is an acrylic doped with BBQ which shifts the ultra violet light, produced by the scintilla- tor, into the green wavelengths so that it can be detected by phototubes. In addition, the doping absorbs UV light produced by particles traversing the length of the rods that would otherwise produce an anomalous signal. A phototube is attached at one end of each wave-shifter rod. The extinction length of the rods was short enough to make the detector’s response was very sensitive to the longitudinal shower profile, which has large fluctuations for hadronic showers anyway. To minimize the sensitivity half the rods had phototubes attached to the upstream end, and half had their phototubes attached to the downstream ends. The energy resolution could then be maximized by making corrections to the total energy based on the front-to-back ratio. The details concerning the construction and performance of this device can be found elsewhere [26] The signal from each phototube was digitized by a flash ADC clocked into a 256 x 4 bit memory at 100 MHz. The reference voltage to the ADC obeys the relation I/ref = V0 + A X Vinput (2-31) This allows the ABC’s to have a dynamic range of 8 bits for A = 3/4, but the 115 SteelAbsorber Scinullator : H... i BBQ Wave . 00. O. Shifleme'S 0.0000 ..."? i’. i" 000’: i i......[' ... . 00 000000 Figure 2.35: Perspective drawing of the Forward Calorimeter with an exploded view of one of the modules. 116 resolution of pulses near the top of the range is compromised. A 2.56 #5 history of each phototube about the trigger time can be readout. The energy resolution of the FCAL was parametrized using a monte carlo. The energy scale was determined from data taken with a 530 GeV pion beam. Unfortu- nately, the energy resolution was dominated by systematic losses in the wave-shifter rods; the resolution has a quoted value of 161%\/E. The position resolution of single showers was estimated by monte carlo to be 0.75 mm. For the actual data only the centroid of the energy flow could be determined. The reason is that several showers typically deposited energy within the device in a single event, and their energy was shared globally among the various phototubes. Chapter 3 Data Reconstruction The data for each event is collected from the detectors and written ontoimagnetic tape. This stored data must be subsequently processed to obtain the following quan- tities for every event: 1) the number, trajectories and momenta of charged particles traversing the tracking system, 2) the number, transverse positions, and energies of showers in the EMLAC, and 3) the status of the various scintillation counters, the trigger logic, and the scaler counts. The information in the HADLAC and FCAL was also processed, but the details are not pertinent here. A good discussion of how the data from these devices is analyzed can be found elsewhere [27, 28]. Each major piece of the apparatus has its own reconstruction program. The recon- structors for the tracking system, the electromagnetic calorimeter, and the discrete logic are known as PLREC, EMREC, and DLREC respectively. All of the reconstruc- tors are embedded in a larger program called MAGIC. MAGIC controls the program flow, handles I/O operations, and provides memory management via the ZEBRA package [29]. The entire data reconstruction package was written in ANSI standard FORTRAN77. 3.1 EMLAC RECONSTRUCTION During data taking the pulse heights from individual amplifier and TVC channels were written out to tape. These pulse heights have to be converted into energies and time values which are then input to a reconstruction program. This translation procedure is known generally as unpacking. The reconstructor uses the channel en— ergies to compute the energies and centroids of the electromagnetic showers. It also determines the time of arrival for the reconstructed showers relative to the interaction 117 118 responsible for the trigger. A complete description of EMREC is found in the thesis of J .P. Mansour [30]. Only the basic steps in the algorithm are given in the following discussion. 3.1.1 EMREC Unpacking The amplifier channel pulse heights are given in ADC counts. These ADC values are converted to channel energies by the formula 82' = AemGi(Ni _ N?) (31) where e,- is the energy deposited in channel i, and N,- is the raw number of ADC counts. Aem is the conversion of ADC counts to energy and represents a global energy scale factor. This factor was determined from the electron beam calibration studies; it was found to have the value of 3.1 MeV / count. The global energy scale for each octant was later modified slightly in order to reproduce the nominal 7r° mass using 2-photon combinations. G,- and N? represent the individual channel gains and pedestals respectively. The pedestals were obtained by reading out the calorimeter with pulser triggers. The gains were computed by pulsing each amplifier channel with a precision charge injection capacitor and analyzing the pulse height distribution. A correction for dead channels was made during the unpacking procedure. Some channels were known to contain strips which either had shorts or bad connections, making them unusable. Also, the amplifiers themselves occasionally developed prob- lems as revealed by the calibration tasks. Under such circumstances a channel was labelled “dead” and assigned an energy value that was the mean of the two adjacent channels. The unpacking program also performed a sum of energies for corresponding chan- nels in the front and back sections of the EMLAC. The set of summed channels was known as the summed section. The pattern recognition routines in EMREC used the 119 summed and front sections’ channels of unpacked energies to reconstruct the showers. The TVC data was unpacked in a manner similar to the amplifier channels. Recall that four amplifier channels were used to generate one channel of raw TVC data. The conversion of raw pulse height to time-of-arrival is given by the following expression: t;(in ns) = AADC(T.- — T? — C(E,)) (3.2) t; is the arrival time with respect to the triggering interaction, and T.- is the raw pulse height. T? is the channel pedestal, which represents the average time-of-arrival for in time pulses. It was determined by a special calibration task described in the thesis of E.J. Prebys [31]. Nominally, T? was half of the full scale value for a single TVC channel. The C (E,) term represents a correction stemming from the fact that smaller pulses i.e.lower energy showers, tended to trigger the TVC’s later than larger ones. 3.1.2 Shower Reconstruction The purpose of the shower reconstruction algorithm is to ascertain the energies, positions and arrival times of all photons and electrons incident on the EMLAC. EMREC reconstructs showers on a quadrant by quadrant basis. Each quadrant is divided into four views. The r channels are subdivided into men and night views; the d) channels are divided into flan" and dim“, views at the inner-outer d) boundary of the readout boards. The same pattern recognition procedures are performed on the views in the summed and front sections. This is done in order to estimate Efrong/Etotd for a shower in a particular view, and to aid in splitting showers which may have merged into a single shower in the back section, and appearing as such in the summed section. The basic program flow of EMREC goes as follows. First, individual channels are gathered into groups in each view and section. The number of peaks in each group is then computed. Each peak represents a shower whose energy, position and time—of- arrival is to be reconstructed. Second, showers are reconstructed in each view about 120 the peaks found earlier. These view showers are called “gammas”. The reconstructed “gammas” in 4) and r are then correlated by energy to obtain reconstructed photons. The arrival times are then assigned to these photons. The energy resolution function used for all weighting and decision making criteria is given by o, = \/(0.1)2 + (0.14)2o,- (3.3) where a; is the resolution of a particular amplifier channel. The 0.1 term is the incoherentnoise contribution to an individual channel. The other term is the intrinsic energy resolution due to sampling fluctuations; e,- is the measured channel energy. Four requirements must be met before a set of strips can be classified as a group. 0 For Th“, night, and (bin there must be at least three consecutive strips above threshold. Only two channels are required for 4,0,, because the readout strip widths are larger. 0 The summed channel energies must be greater than 700 MeV. e The average energy per strip must be greater than 150 MeV. e The highest energy channel must contain more than 300 MeV of energy. The peak finding procedure is straightforward. Starting at one edge of a group, the energy of each channel is examined. When a channel is found to have less energy than the preceeding one, the preceeding channel is termed a “peak”. When a channel’s energy is greater than the preceeding channel’s or the edge of a group has been reached then the previous channel is termed a “valley”. If the energy of a peak is more than 2.50’(Ep¢.k) from either valley, then the peak is flagged for reconstruction as a gamma. The gamma reconstruction algorithm is split into two parts. One set of routines is used on groups containing a single peak channel. Another set of routines is initially used on groups possessing multiple peaks. To begin with the single peak case will be 121 described. First, the position of the shower in the view is determined. The median position of the peak channel is taken and shifted by an amount depending on the relative amounts of energy in the adjacent channels. Calling this position X, two other trial positions at X $ 0.2 cm are successively chosen as the shower centroid and input to a shower shape-fitting routine. This routine compares a parametrized shower shape to the actual shape of the group energy distribution and calculates a X2 [32]. The trial centroid position corresponding to the lowest X2 is taken as the true shower centroid. Furthermore, the relative fraction of energy per channel, 2,, is computed from the fit to the shower shape. The estimated channel energy fractions relative to the full shower energy are then used to statistically determine the shower’s energy by minimization of the following likelihood function: N5 X2 = 2 $03; - Eli)2 (3.4) {:1 3 If this x2 S 5.0, then the shower energy is computed to be Ns Eshower = Etail + E: Etail : E(1_ 28°) (35) i=1 Otherwise, N5 Eshower = Z 82' (3'6) i=1 Two caveats are in order. Eng} is an estimate of the energy in the shower tails. The tail energy cannot actually be measured because of zero suppression (nominally 150 MeV), and because N3 may be less than the number of channels in the group. N; is the number of channels about the peak for which the energy measurements are not dominated by fluctuations i.e.the energy estimate is better than 50%. N5 was deter- mined from monte carlo studies, using the beforementioned shower parametrization function and measured energy resolution of the detector. For multiple peak groups, each shower’s contribution to the energy in a particular channel has to be estimated. To do this the fraction of each shower’s energy in a 122 particular channel of the group was calculated by applying the shower shape-fitting routine used in the single peak group algorithm to each peak. The shower centroids corresponding to each peak were also measured. The number of channels N 5 used for each peak was less than or equal to the number of channels between the two valleys surrounding the peak. The energy of each shower was obtained by minimizing the following likelihood function: N 28:: i=1 (8; — Z Ekfilz (3-7) 0' Here, N is the total number of channels in the group, E1. is the total energy of the kth shower, and f; is the fraction of the kth shower’s energy in the ith channel. e,- and 0'.- are the ith channel’s energy and resolution respectively. From E]. and f; the channel energies corresponding to each shower were separately computed. Each calculated distribution was then input to the algorithm implemented for the single-peak groups. The final energy and shOWer centroid estimates for each gamma were then obtained. If _a group in the front section contained two reconstructed gammas while the corresponding summed section had only one gamma, the summed section gamma was split into two. The positions of the split gammas were taken to be the positions of the front section gammas. The split gamma energies were determined from .the following condition: E1 split + E2 split = Esum (38) E1 split : E1 front E2 split E2 front Finally, all gammas reconstructed in the 1‘ view had their centroids for the back section as well as the front section calculated and assigned to them on output from the gamma reconstructor. This was done so that front and back coordinates could be assigned to the fully reconstructed photons. 123 The reconstructed gammas in the two r views are then correlated with those re- constructed in the 45 views. The gammas are correlated on the basis of their energies and front-to-total energy ratios. The interleaving of r and 43 readout layers in the electromagnetic calorimeter results, on average, in equal amounts of energy being deposited in both views. At the simplest level a gamma from the r view can be cor- related with a (I) view gamma by finding the one which has an energy and Efmm/ Etoml closest to its own. If these quantities match within the expected resolution, then a fully reconstructed photon can be formed. This simplest of correlations is called a 1-1 correlation. However, there are a number of complications which introduce ambiguities and inefficiencies into the pattern recognition for gamma correlation. One complication is the splitting of a shower in a particular view, resulting in two reconstructed gammas. Another is the loss of a gamma in a particular view, and the subsequent mismatching of the corresponding gamma in the orthogonal view. Still another problem is the presence of two showers with nearly equal energies in a single quadrant. The cor- relation routine’s performance can be optimized using monte Carlo events, but there is a physics bias due to the reconstruction efficiency’s dependence on quadrant and octant multiplicities. The basic philosophy of the correlation procedure is to divide all gammas into three groups. One group involves 43 view gammas at the inner-outer 43 boundary and the octant boundary. The second group consists of r view gammas at the octant boundary. The third group is composed of all gammas which are away from the boundaries and are not likely to suffer problems with shower splitting. The correlation algorithm first tries to match men and night gammas at the octant boundary with those from the (:5 views near the boundary. The routine first checks if an 11.3, nigh. pair can be matched with a <13 pair based on energy sums of each pair. A 124 single photon is reconstructed if a match is found; the r and 4') positions are determined from energy weighted sums. Such a correlation is termed a 2-2 correlation. After these 2-2 correlations have been found the algorithm then matches the remaining mg, mg,“ gamma pairs with single gammas from the 45 views. Whenever a match is found, a single photon is formed. This type of correlation is termed 2-1. The routine then attempts to match (pm, 430," gamma pairs near the inner-outer d2 boundary with single r view gammas. Again, if a match is found for a pair, a single photon is reconstructed. Finally, 1' and d) gammas away from boundaries are correlated. The algorithm first looks for 2-1 type correlations. Whenever such a match is found, the single gamma is split into a pair whose energies have the following relationship, E1 split + E2 split = Egamma (39) E1 split _ fl E2split E2 The positions of the reconstructed photons in the split view are both equal to the position of the unsplit gamma. This change in philosophy is due to the fact that away from boundaries such 2-1 correlations are more likely to arise from 1r° and 7] decays. All 1-1 correlations are found at the end, and the energies, positions, and Efrom/Ewml of all photons are written to output. After each correlation is found the 45 position of the reconstructed photon is re- calculated based on its r position. This is because the width of the (,6 strips increases With increasing r. So, a better estimate of the 45 coordinate can be achieved using the improved ¢ strip width. 3.1.3 TVC Reconstruction The reconstruction of the TVC data takes place at the group level. No TVC criterion is used at any stage of the shower reconstruction. Within each group of amplifier channels used to reconstruct gammas, corresponding TVC channels are 125 clustered together. The clustering involves taking each TVC channel in a group and forming a set of TVC values containing the given TVC and all other TVCs within $45 as of the given TVC’s time value. Hence, there is a one-to-one correspondence between all TVC channels belonging to an EMREC group, and the TVC time clusters associated with that group. A time value is computed for each cluster based on the energy weighted sum, - Z; tiEi T = —— 2. E; where E.- is the energy in the ith channel and t, is the TVC time value for the channel. (3.10) The clusters are then ranked in a hierarchal order according to three criteria. They are listed on the following page. 0 The number of TVCs in a cluster. 0 Clusters not ordered by the above are ordered according to the cluster energy. 0 Clusters still not ordered are ranked according to how close their times were to the time of the interaction which triggered the event. The two highest ranked times from the above set are assigned to all gammas recon- structed from the EMREC group. TVC times for reconstructed photons are obtained by ordering all clusters, as- signed to the gammas from which the photon is formed, by the same ordering criteria presented above. The photon has the two highest ranked TVC values assigned to it. If less than two TVC values get assigned to a photon, then the photon is assumed to be in time with the triggering interaction. Besides being assigned time values, a photon is also given a TVC quality value. This quality value is defined as follows, TVCquy = 103 x (# of TVCs used) + (summed energy of TVC channels) (3.11) Clearly, a photon’s TVC values have meaning only if the quality value is greater than 2000. 126 3.2 TRACKING RECONSTRUCTION The reconstruction Of tracks from raw hits is now described. The MWPC and SSD planes provide two coordinates for every track. The data is stored as a wire address, which is transformed into a real coordinate value by an unpacker program. The program responsible for reconstructing the tracking system data is called PLREC. The basic program flow is as follows. The four views in the MWPC system enable the reconstruction of tracks in space. Tracks in the SSD system are only reconstructed in the X-Z and Y-Z projections. The SSD tracks are used to reconstruct the vertex of the interaction responsible for the high p jtrigger. Space tracks are assigned X and Y view SSD tracks, taking into account changes in trajectory due to the analyzing magnet’s field. Each space track is assigned a value of momentum, and the sign of the charge which corresponds to that Of the particle responsible for the space track. All charges are assumed to be either $1. The details of the PLREC functions are given in the following subsections. 3.2.1 MWPC Space Track Reconstruction The reconstruction begins with the formation Of tracks in the X, Y, U, and V projections. Reconstruction in the various projections proceeds in the following manner for each view. First, a pair of hits is chosen form modules 1 and 4. Second, a line is constructed from the pair. Third, the points on this line that intersect planes in modules 2 and 3 are computed; the closest hits in these searched modules within 1.5 wire spacings are used to reconstruct a view track. Fourth, the program calculates the view track’s parameters via a least-squares fitting routine. The fitting procedure yields a x’; if this x2 is less than a cut value, reflecting 95% confidence, then the track parameters are retained for further processing. Otherwise, if the track contains four hits, then the hit with the largest residual is dropped and a 3-hit track 127 is reconstructed. Any 3-hit track that fails the )8 cut is dropped. PLREC performs this procedure for every pair of hits in modules 1 and 4. All 4-hit combinations for which a track was reconstructed are flagged. After all combinations in modules 1 and 4 have been checked the view track algorithm takes hit pairs in modules 2 and 3 as seeds for view track reconstruction. The purpose of this is to pick up 3-hit tracks missed during the first iteration. In fact, no 4-hit combinations from the first pass, which resulted in a reconstructed track, were reused in the second pass. Once the view tracks have been reconstructed, a cleanup procedure removes du- plicate tracks. All 4-hit tracks are grouped into sets such that each track in a set shares 3 or more hits with some other track in the set. These sets are known as global clusters. If a global cluster contains only two tracks, then the one with lowest x2 is retained. Otherwise, the two tracks with lowest x25 are saved for further processing. The same procedure culls all the 3-hit tracks as well, except that the hit sharing requirement is reduced to 2 or more hits. Finally, 3-hit view tracks that share 2 or more hits with a 4-hit view track are dropped from the ZEBRA structure. The tracking reconstructor takes the cleaned view tracks and forms tracks in space. The algorithm starts by taking all pairs of X and Y view tracks and computing the corresponding U and V projections. The intersections Of these U and V projections are determined for each U and V plane. The closest U and V hits within 1.5 wire- spacings are then used to construct a space track, provided that each view contains 2 or more hits and there are 13 or more hits in all. A space track is defined in terms of its X and Y projections, which are obtained from the following likelihood function: 1 16 23' — £5 2 2 s t = —— 3.12 {fit 2 (0,2; + (1,) cos a,- + (byz, + ay) sin a,- where b., (1., by, and a" are the space track’s parameters in the X and Y projections respectively. N denotes the total number of hits. cos a). and sin a}. project the space 128 track’s parameters into the proper view for each plane. If the ith MWPC plane has no hit for a particular track candidate then the corresponding term in the sum is skipped in the calculation. After the X and Y view track combinations have been exhausted the program goes through all U and V combinations, searching for matching hits in the X and Y views. This step recovers all those tracks which contain only two hits in either the X or the Y view, and would therefore have been missed in the first iteration. Clearly, a space track is typically reconstructed twice by this procedure. SO, another routine removes all the duplicate space tracks by the following method: 0 Any space track possessing 9 or more unique hits is always retained for output. 0 If a pair Of tracks share 6 or more hits between them, the procedure eliminates the track with fewer hits. In the event that both tracks contain the same number of hits, the selection is made according to smallest x2. 0 If a pair Of space tracks had 7 or more shared or adjacent hits, the algorithm executes the above procedure for shared hits. 3.2.2 SSD Track Reconstruction The SSD system consists of two distinct parts with separate functions. The . beam SSD system is located upstream of the target and contains three modules. The information provided by this group of planes is used to reconstruct the track Of the beam particle that produced a particular event. The vertex SSD system resides immediately downstream of the target. As its name implies, this set of planes enabled a triggered event’s vertex to be reconstructed. Before any SSD track reconstruction is performed all adjacent hits in each plane are clustered. A cluster’s position is simply the mean position of the strips comprising it; this position is the “hit” coordinate input to the reconstruction software. The hits have to be clustered for two reasons. One, the ratio of strip width to plane 129 thickness is typically 1:5 for the SSD’s. Thus, a 30 mrad track has z 25% chance of firing the discriminators of two adjacent strips. Second, the cross talk between adjacent preamplifier channels enhances the double hit count for wide angle tracks, and degrades the pair resolution for low angle tracks. The reconstruction scheme for the vertex SSD’s is identical to the MWPC view reconstruction. For the beam SSD’s, the view track reconstruction procedure is used first to find all 3-hit tracks in the beam SSD system. Afterwards 2-hit tracks are made from the unused 2-hit combinations. The XY combination Of view tracks with the smallest impact parameter about the vertex becomes the beam track for the event. 3.2.3 Linking Once the SSD and MWPC track reconstruction has been performed, an attempt is made to match each MWPC space track with an X-view and Y-view upstream track from the vertex SSD system. This requires that the effects of the analyzing magnet’s field be accounted for. Ideally, the analyzing magnet produces a uniform field parallel to the y-axis in the experiment’s coordinate system. This field is produced between zc $ L/2 where 2c is the magnet’s geometric center, and L is the length of the pole pieces. In addition, the momentum kick ~ 450 MeV/c is very small compared to typical track momenta ~ 10 GeV/c. Under these circumstances charged particles with p, < p. travel through the magnet unaffected in the YZ plane and undergo uniform circular motion in the XZ plane. Because Ap/ p < 1 for most tracks, the X-view SSD tracks intersect the X-projections of the corresponding space tracks at the magnet’s center. However, in reality the analyzing magnet’s field is asymmetric in 2 due to the up- stream and downstream apertures being considerably different in size. A measurable B. component exists also, which is non-negligible at the entrance and exit planes of the magnet. The B. component introduces pr, and pyBz couplings that produce a 130 helical motion about the beam direction. This twisting effect prevents upstream and downstream tracks from intersecting at the center Of the magnet. Also, many tracks possess a non-negligible py component so they make a non-zero angle with respect to the bend plane. In this case there is a change in the y-view slope of a track due to the change in p,, which occurs in the bend plane. Finally, for low momentum tracks the kick approximation breaks down i.e.Ap / p ~ 1, so the x-view tracks are not expected to meet at the middle Of the magnet. . The field asymmetry, produced by the difference in upstream and downstream apertures, is easily accounted for. The geometric center and length are replaced by an effective center and length. These quantities were Obtained from the field map. The corrections for the other effects involve a rather detailed analysis Of the field. They have been worked out, and are summarized in an appendix [33]. The x-view SSD tracks that projected to within $0.7 cm of a particular down- stream track are arranged in ascending order of the projection difference. The five upstream tracks with the smallest difference are retained for further processing. The y-view linking procedure imposes a cut in the slope difference between upstream and downstream tracks of $2.5 mrad. All y-view SSD tracks that match to a downstream track within this window are assigned a x”. This x2 is a weighted sum Of the slope and projection differences. The linked upstream tracks are put in ascending order of the x” parameter, and the five tracks with the lowest x2 are kept in the ZEBRA structure. 3.2.4 Event Vertex Reconstruction The event or primary vertex is formed from the vertex SSD tracks. The efficiency Of the vertex algorithm is critical since the high p [event selection involves a vertex cut. To study the nuclear A dependence of the 1r° and direct photon cross sections one must know which part of the target a given interaction occurred in. This implies 131 that the vertex finder’s 2 resolution has to be better than 1mm. The algorithm first reconstructs a vertex in the X and Y views. If view vertices are found, then the program attempts to match the vertices based on the difference in their 2 positions. When a match is found, a matched vertex is computed whose z coordinate is the weighted average of the view vertices’ z coordinates. The view vertex reconstruction algorithm first culls the SSD view tracks and takes a subset of them to construct the vertex. This procedure has three possible outcomes, 0 The subset Of vertex SSD tracks consists Of all linked 4-hit tracks. 0 If there are less than three linked 4-hit tracks in a view, then the set of all 4-hit tracks formed. 0 If there are less than three 4-hit tracks, the procedure uses the set of all 3-hit linked tracks as input to the next stage of vertex reconstruction. s In the event that all Of the above sets contained less than three tracks, no view vertex was reconstructed. A special likelihood function is used to calculate the position of each view vertex, (X0, Z0). This function expresses a track’s x2 as a Taylor series of the x2 with the vertex constraint, af‘ = X0 — bLZo. This function therefore possesses the following form, 3x’ , Bx2 X2011” bk) = Xi(ain is) +(a1. " “isla—ahlo; + (bk “ “’52:”; B’x’ , 5’x’ ‘l' (ale — (firm—la; + (bl; — lay—63?”); (3.13) 6x2 I I 'l' (“k — «0(1):: - balmlogsg + ' .. The x2 minimization condition forces the first order terms to vanish. By imposing the vertex constraint, and the additional condition that bk z b;: within the detector’s 132 resolution, one obtains the following 2nd order expression: 2 522(2 Ax: = (a. — (X0 — bozo» Fr... 67.. = WI. (3.14) (1" k Summing over all tracks in the input set gives, Ax’ = 201,. — (X0 — kao))’&,,, (3.15) I: Minimizing this likelihood function yields X0 and Z0. Once the vertex coordinates are calculated for a particular view, the algorithm checks whether or not the average impact parameter of the input tracks is greater than 20 pm, or the highest impact parameter is larger than 50 um. Should this situation arise, the track with the highest impact parameter is dropped from the input set, and the resulting set Of tracks is used to refit the vertex. The program repeats the refitting procedure until the impact parameter cuts are satisfied, or only two tracks remain in the input set. If vertices are reconstructed in both views, then a routine is called to find a matched vertex. To start with the routine takes the difference in the z coordinates of the: view vertices. If this difference is less than 3.0mm, then construction Of the matched vertex takes place immediately. Otherwise, all X-view tracks, used to re- construct the view vertex, within $1.0 cm Of the Y-view vertex’s 2 position are used to recalculate the X-view vertex’s coordinates. This assumes, of course, that two or more X-view tracks exist which satisfy the foregoing criterion. The Y—view vertex is recalculated in the same fashion. When the program fails to find a matched vertex, it assigns a nominal vertex position to the event. This nominal position is just the target’s geometric center. The vertex reconstructor was determined to be 95% efficient. It possesses a 2 resolution of 600 pm; this is sufficient to resolve the target elements as Figure 3.1 demonstrates. The quoted resolution comes from the Az distribution of X and Y- view vertices. The 2 resolution calculated from the likelihood function is 300 pm. 133 This discrepancy arises from the clustering of hits in individual planes, decay vertex tracks being assigned to the primary vertex, and secondary interactions. The vertex resolution in X and Y, estimated from the track residual distributions, is 20 pm. 3.2.5 Relinking Any time PLREC finds a primary vertex, it reorders each space track’s X and Y links. The program places all links belonging to the primary vertex at the top of each list. Furthermore, each list Of links associated with the event vertex is put in ascending order Of a x2 parameter. The parameter is the weighted sum of a link’s impact parameter and the projection difference at the center of the magnet. The calculation of the track momenta employs those links with the lowest value of this x’. In the event that a space track has no links in a particular view, the upstream trajectory is estimated by constructing a line between the vertex and the projection point at 2:. The nominal vertex position is used if an event contains no matched vertex. 3.2.6 Track Momentum Reconstruction The space track momenta are determined using the square field and p ikiCk ap- proximations with an effective length, Lo, for the magnet. The momentum calculation proceeds by solving the following three equations, P1 kick : ' 2 CB L Pis'l'P: |sina—sin,6|’ Plies]: 0 o 3 t :_ = 8:: (3.16) 1),, _ tann p, - cosa tan a and tanfl are the upstream and downstream slopes, respectively in the x-view. In addition, the sign of the particle’s charge is given by, q = sign(a - fl)sign(Bo) (3,17) 134 1000 [- 800 _ 600 - ” 400— , - l 200- - - ‘ :— ' [- O lLJllllllllllllllllllllllllllllllLllll[tilt—AL -13 -‘|2 -ll -10 —9 —8 -7 -6 -5 —4 V2 (cm) Figure 3.1: The 2 coordinate distribution for matched vertices within the target volume. The different target elements are clearly resolved. 135 It should be noted that tan 17/ sin a and tan n/ cos a are just the x and y view slopes of the upstream links reSpectively. The magnet’s momentum kick was originally estimated to be 450 MeV/c. A Subsequent analysis of the J / t1) and K5 masses indicate that the kick is 449 MeV/c instead; this data analysis will employ this p j kick value. 3.3 TRACK QUALITY STUDIES Because the ensuing analysis relies heavily on the tracking system’s data, it is important to understand its quality. The analysis uses the physics tracks, Obtained from the MWPC data, to study the charged particle structure of high p L 71'” and 7 events. Therefore, the following discussion will focus almost entirely on the quality of the physics tracks. The SSD data is relevant only in so far as linking is concerned, and with the associated systematic effects on the track momentum calculation. Several issues must be dealt with in Obtaining a quantitative understanding of track quality. First, it must be determined what fraction Of the physics tracks is false. By false it is meant that the reconstructed track does not correspond to an actual charged par- ticle’s trajectory in an event. Second, the reconstruction efficiency for true physics tracks needs to be ascertained. Third, how reliable is the momentum calculation? Fourth, can those charged hadrons emanating from the primary vertex be so identi- fied? Finally, how well do the multiplicity, rapidity, and momentum spectra of the physics tracks compare with the monte carlo simulation used in comparing data with theory? 3.3.1 Alignment and Plane’s Efficiencies To guarantee the highest quality tracks possible the various modules in the track- ing system had to be aligned relative to one another, and to a universal coordinate system. Aligning things to a precision better than the spatial resolution of the track- ing system insures that the reconstruction program is limited in principle only by the 136 device’s inherent resolution. The alignment procedure consists Of two steps. To begin with a survey is performed. The survey establishes a universal coordinate system for the entire experiment, including the beamline, with I‘CSpeCt to a US. Geological Survey marker. The survey had a precision of < 1mm. The universal coordinates of a point on the SSD cart was established by the survey. A transit, whose position was known relative to this point, was then used to locate the transverse positions of all SSD modules. The modules’ positions along the beam direction are known from the SSD cart’s dimensions. The MWP C modules were leveled square with the beam direction i.e.the z-axis, and plumbed vertical. The transverse y-position was determined by measuring the bottom center pins’ height above the floor, which was assumed to be flat. The transverse orientation in x was found by centering a plumb bob about a survey line on the floor parallel to the z-axis. The plumb line hung from a rod which passed through the top center pin on each chamber. Another vertical plumb line was dropped which passed across the face of the top and bottom center bushings. A tape measure was then placed between the survey plug (2 = 0), and the plumb bob, yielding each chamber’s z-position. From the known positions of each anode plane within a module stack, the position of every anode wire was determined in the universal coordinate system. A computer program was used to reduce the uncertainties in the transverse align- ments to a negligible level. It systematically centered all residuals between track projections and hits about 0. In addition, a relative alignment between SSD and MWPC systems was performed so that the linking procedure could be optimized. The SSD system was moved relative to the MWPC system, and then each sense plane in the tracking system was transformed back to the universal coordinates as established by the point on the SSD cart. Both non-interacting beam and minimum bias events were processed by the alignment program. The data was taken at low in- tensity with the analyzing magnet’s field off. The algorithm found no rotations about 137 the z-axis, but small shifts in 2 were detected. However, these shifts were so small that their effect on the reconstruction was negligible. Besides residual distributions, the x2 distributions provide some information on alignment quality. Figure 3.2 shows x2 distributions for 16, 15, 14, and 13- hit tracks. The 16-hit distribution provides the best indication since it involves all planes. The 13-hit distribution looks rather poor, but this is because PLREC did not utilize the narrowest window cuts possible. This was so that the reconstruction efficiency would be maximized. The measurement of individual MWPC sense plane efficiencies is important in understanding the reconstruction efficiency. Even if the reconstruction program gen- erated no losses, the reconstruction efficiency is ultimately limited by the efficiencies of the various planes. The method used tO determine the planes’ efficiencies was as follows. The hit information for a given plane was not used to reconstruct tracks, and only 15-hit tracks were reconstructed. The fraction of times there was a hit within a one wirespacing window of a projected track’s intersection with the given plane was computed; this fraction is the given plane’s detection efficiency. This method takes into account all equipment effects, including the readout electronics. Efficiencies have been determined for the three separate cathode regions, using low intensity minimum bias data. The reader should be aware that under standard running conditions the beam region is essentially off. Table 3.1 provides a complete list of all MWPC plane efficiencies [34]. 0.05 0.04 0.03 0.02 0.01 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 138 lllrl—IIIIITTIIIWTIYYIIII llllllLllllll Illl 1 2 3 x216-hit ITFIIIIIIUIIUIIlIIITIIIIUIIIIUIIIIIIIIIUI Illllllllllll Illl 1 2 3 x’14-hit 0.045 0.04 0.035 0.0.3 0.025 0.02 0.015 0.01 0.005 0.06 0.05 0.04 0.03 0.02 0.01 lLlLlllLlllll O "IIIIIIIITIIIIIIIIIIIIIIIIIiIIITIIIIIIIIIIIIW 1 2 x2 151—hit IIVUIIIIIIIIII‘ITIIIIIIIIITTTTI llllllllllll Figure 3.2: The x2 distributions for 16, physics tracks 1 2 X2 131—hit 15, 14, and 13 hit 3 Table 3.1: List of MWPC Plane Efficiencies 139 Plane Efficiency Diffraction Main 1 0.8862 0.9365 2 0.9463 0.9565 3 0.8751 0.9450 4 0.9233 0.9488 5 0.9488 0.9455 6 0.9168 0.9338 7 0.9395 0.9488 8 0.9134 0.9263 9 0.9483 0.9603 10 0.9822 0.9594 11 0.9726 ’ 0.9463 12 0.9799 0.9470 13 0.8405 0.9008 14 0.9535 0.9327 15 0.9127 0.8998 16 0.9340 0.9167 140 3.3.2 Quality of Track Reconstruction The fraction of fake tracks in the data summary output has been estimated using the data itself. Various distributions have been studied which are sensitive to misre- constructions. From these studies two techniques have been developed for measuring the fraction of fake tracks. These two techniques involve different cuts and track selection criteria, although there is a significant amount Of overlap between the two sets. A common assumption for both techniques is that all high quality 16-hit tracks are real. The definition Of high quality implies that a given track has a x2 g 1, a y-view impact parameter ,] by I, of S 1cm, and is linked in the x-view to an SSD track, belonging to the primary vertex. The first technique is known as the LAC method because it considers the matching of tracks (or the lack thereof) to showers in the electromagnetic calorimeter. The high quality 16-hit tracks are used to estimate the device’s efficiency for detecting charged particles impinging upon it as a function of their momenta. The number of generic tracks, which failed to match with a shower, can then be corrected for those real tracks that failed to match because Of inefficiency. The second method utilized the y-view impact parameter distributions for physics tracks that linked in the x-view to a matched vertex. It is known as the by technique. The basic idea here is that such physics tracks with high impact parameters are suspect because the linking information indicates they are associated with the primary vertex; a high y-view impact parameter indicates otherwise. Of course, there may be some real tracks in the tails Of the by distribution due to improper linking. The fraction of such tracks has been estimated by studying the corresponding distribution for the high quality 16-hit tracks, and the tails of the generic by distribution have been corrected accordingly. The LAC method used only those tracks with | y [S 0.7 while the by 141 technique used tracks between $1.5 units Of rapidity. The reader interested in the exact details of the two methods, and all the selection criteria for the tracks should consult the appendices. Both techniques have been found to yield consistent results. The LAC method gives a higher estimate for fake tracks than the by one, but the variation is also considerably larger and overlaps with the results of the impact parameter study. It appears that the fraction Of fake tracks is S 1% for | by Is 1cm and S, 2% for all impact parameters. The reconstruction efficiency can be estimated from a study of the relative 16, 15, 14, and 13-hit multiplicity distribution. If the reconstruction program results in miniscule losses, then the shape of such a distribution is governed by the individual planes’ efficiencies and the geometric acceptance. A monte carlo study has been done using the output from ISAJ ET. The charged particles generated by the IS AJ ET monte carlo are projected through a simulation of the analyzing magnet’s field. The altered trajectories are subsequently projected through the MWPC acceptance to determine the number of intersections with active regions of the sense planes. In addition, an intersection with a particular active region is considered to be a “hit” only a certain fraction of the time; this fraction or probability is just the measured efficiency for that active region. The monte carlo result yields a relative multiplicity distribution corresponding to a higher reconstruction efficiency than the data. However, data and monte carlo are close. An effective planes’ efficiency has been determined for each data distribution. This efficiency corresponds to a reconstruction efficiency of 96% or better for the data; the monte carlo distribution yields an efficiency of 98%. Again, the reader interested in the details of this analysis, and the exact means by which these two numbers were arrived at should consult the appendices. 142 3.3.3 Track Quality Cuts These results indicate that the quality Of the track reconstruction is very high. The physics tracks almost always represent an actual charged particle’s trajectory in the MWPC system, and only a few trajectories are missed. It can be inferred that the reconstruction program, PLREC, introduces a very small inefficiency and that the pattern recognition is almost always reliable. However, the momentum calculation does rely on the linking of upstream and downstream tracks. In the event that a space track is improperly linked a spurious momentum may be assigned to it. This systematic effect can be overcome by recalculating the track momentum, using only the vertex position and the space track parameters. What one does is project the space track to the magnet’s center in the x-view. One then calculates the slope of the segment between the vertex point and the projected point. The difference in slope between this segment and the space track is used to calculate the momentum in the manner dictated by equation 3.17. The eXpected statistical variation between recalculated and PLREC momenta, 6P, is given by the following expression, 6’P = (.002P;§,,,,)2 + (.001P,3,,,,EC)2 (3.18) If the two momenta differ by more than 36P, the recalculated value is used. Note that the above expression ignores a constant multiple scattering term. Such a contribution is negligible above 5 GeV / c. This technique has two underlying assumptions. First, the event contains a re- constructed primary vertex, and second, the space track corresponds to a particle produced at the main vertex. All of the data used in this analysis is required to have a primary vertex. The second assumption can be satisfied by applying a selection criterion. Such a cut is indeed necessary for this analysis since only charged hadrons emanating from the primary vertex are of interest. 143 A set Of track quality cuts has been develOped for preferentially selecting those MWPC tracks produced by hadrons coming from the vertex, and rejecting those which do not. An additional cut in p j_ of 300 MeV/ c selects out the jet candidate tracks, used by the jet reconstruction algorithm. The first cut requires | y IS 1.5. This cut can be better understood by examining the rapidity distributions Of tracks shown in Figure 3.3. This distribution is asymmetric due to the effect of the magnet and the MWPC acceptance. Such an asymmetry will produce a systematic uncertainty in the pseudorapidity, 17, distribution of reconstructed jets. A cut of I y [S 1.5 prevents this. Furthermore, the quality of reconstruction beyond rapidities Of 1.5 is compromised by the beam region’s inefficiency, and there is a degradation in momentum resolution due to a constant wire spacing. Because no change in trajectory occurs in the YZ-plane as a particle passes through the analyzing magnet’s field, a cut in the y-view impact parameter ,Of the physics tracks will select only those coming from the primary vertex. The by distribution of all tracks is shown in Figure 3.4. There is a dominant peak between $1.0 cm on top of a fairly flat tail. Therefore, a quality cut of | by [S 1.0 cm is imposed On all charged tracks. The flat tails Of the by plot contain tracks from strange decays (Kos and As), muon halo and fake tracks. All such tracks would not have a correct momentum assigned to them by either method employed by this analysis. The impact parameter cut guarantees that the momentum recalculation is valid within its resolution, and so all tracks satisfying the track quality cuts will have the recalculated momentum as- signed to them, if it differs significantly from the value assigned by the reconstruction program. Finally, the foregoing cuts do not discriminate between electrons and hadrons. Electrons can arise from photon conversions in the target, and by certain heavy quark decays. The decay electrons are effectively removed by the impact parameter cut, but the vast majority arise from photon conversions. A detailed study concerning electron 144 identification has been carried out [35]. This study resulted in an electron identify- ing algorithm, which was implemented during the reconstruction pass through the data. Those tracks so identified as being electrons will be removed from the sample satisfying the track quality criteria. 3.3.4 Comparison Of Data and Monte Carlo The data and monte carlo will be compared by studying the rapidity, multiplicity, and momentum distributions Of tracks. Separate data distributions have been con- structed for all tracks, and those satisfying the track quality cuts. The monte carlo results are superimposed on the data as smooth curves. Since it is the shapes of these distributions that are of interest, all plots have been area-normalized. The studies of fake tracks and reconstruction inefficiencies, presented earlier, in- dicate that the track reconstruction code for the MWPC’s does not introduce any major systematic effects. Such a result allows for a great simplification to the detec- tor portion of the monte carlo with a great saving in computer time. The monte carlo used for this study takes the ISAJ ET output for high p 1 1r0 and single photon events and projects the charged particles through a simulation of the analyzing magnet and MWPC system only. The magnet is assumed to be a simple dipole, and the p _L “kick” approximation is used. The slight change of slope in the y-view is accounted for also as well as the acceptance at the entry and exit apertures. Tracks that project into the iron yoke are dropped from further consideration. A track is considered to have produced a “hit” in a given MWPC sense plane in the same manner as it was in the study of track reconstruction efficiency. Only the main and diffractive cathode regions are considered active. Those tracks that produce 13 or more “hits” are used to generate the various monte carlo distributions. The reader should be aware that in addition to 0.05 0.04 0.03 0.02 0.01 145 1 l l J l l l L 1_J J 1 Y,,,,,,.,, Plrec Figure 3.3: Y distribution of tracks 146 [Illl 1O Illll'l l I 10 IIIIUI] -4 10 LiJJllLLllllllllllllllLlllLlllllllllllllllLLlllll -25 -20 —15 -10 —5 O 5 10 15 20 25 by Figure 3.4: Y-view impact parameter distribution of tracks 147 ignoring PLREC effects this monte carlo does not account for secondary interactions and nuclear rescattering effects. The rapidity, multiplicity, and momentum distributions are displayed in Fig- ures 3.5 through 3.7 respectively. The rapidity distributions agree very well although the backward acceptance seems to have been underestimated in the monte carlo. Overall, the data possesses higher multiplicity than the monte carlo, and an excess Of low momentum tracks. These discrepancies are reduced in the sample Of tracks that meet the track quality criteria. Such behavior is expected, indicating the cuts are doing their job. The discrepancy in the rapidity distributions may in fact be due to an excess of low momentum tracks in the data. A similar study has been carried out for the jet candidate tracks (p _L 2 0.3 GeV/c) with the same trends and discrepancies present. The discrepancies are reduced only slightly over those in the set for which the track quality cuts have been applied. While the observed differences in multiplicity and momentum may be due secondary interactions, nuclear rescattering, and/or prompt strange decays, the fact that they appear in the jet candidate sample with its substantial p 1 cut indicates that the monte carlo fragmentation may be too stiff. Additional evidence is provided by the jet reconstruction efficiency as a function of p j, which is presented in Chapter 6. The efficiency is about 10% higher in the monte carlo than real data. While there are systematic discrepancies between data and monte carlo, they are only at the 10% level. They are not due to PLREC effects. Therefore, the simple monte carlo should suffice for the more sophisticated comparisons and distributions studied in Chapters 5, and 7. In particular, the :7-7ro comparison should not be. compromised. The 1r° + jet and 7 + jet cross sections can be affected, but their ratios should be insensitive to the observed discrepancies. These systematic effects are negligible compared to the statistical uncertainties as shall be seen. 0.06 0.05 0.04 0.03 0.02 0.01 148 _ pi All Tracks 0.06 0.05 0.04 0.03 0.02 0.01 TkQuol Cuts 1-- Figure 3.5: Y distributions for all tracks, and tracks passing the track quality cuts. The monte carlo result has been superimposed as a smooth curve. 149 0.2 0.2 c t 0.18 L AllTrOCkS 0.18 :_ TkQUOICUtS C i r _ 0.16 — 0.16 e- C I 0.14 _ 0.14 l 0.12 :- 0.12 L— 0.1 L 0.1 L +2.“: I I E + +2 I g I . §+ 0.08 — 2:4 0.08 — §+ ’ 4. + ' 2+ .. + _ .. +2 __ t 0.06 — ‘1' 0.06 - 5+ 4' .- + + '- + l" + " 0.04. f _,_ + 9.04 L-+ + . + l. + .5“ + + 5;" 0.02 :- + 0.02 L * ti * *2 q -§ '2 B.‘ s *m... i ... o [’1' l l I l Lira-.1 I l 1__1 1 T-l 0 TI 1 i i l 1 :l"---Ll “7.111 1 l 10 20 30 10 20 30 Multiplicity Multiplicity quuol Cuts Figure 3.6: Multiplicity distributions for all tracks, and tracks passing the track quality cuts. The monte carlo result has been superimposed as a smooth curve. 10 10 10 10 150 t PLREC P )- - m<1.5 E - s-e' [ .. ; .. k + ....... b '0‘- ......ug r _._. ............. E .. —+— l l l 1 l l l l l l l l l l I l L l l l l l l l o 20 4o 60 so 100 P (GeV/c) 10 10 10 ” PLRECP - quuolCuts )_ *2 n - C [- —O— —4— E’ —+— l- )- r- —l—41 llllLlLlllllllllllllllll O 20 40 60 80 P(CeV/c) Figure 3.7: Momentum distributions for all tracks, and tracks passing the track quality cuts. The monte carlo result has been superimposed as a smooth curve. 100 151 3.4 DISCRETE LOGIC RECONSTRUCTION The latching of various logic levels took place during the 1987-1988 data taking period. These latched outputs are represented as specific bit patterns in a portion of each event word known as the event header. The offline analysis of these bit patterns has two major purposes. One is to accumulate and interpret the information from those detectors which provided only discrete logic output. The other purpose is to ascertain the types of high level triggers associated with a given event, and to determine whether or not any inconsistencies in the outputs Of modules, used to construct the high level trigger, occurred. The following detectors yielded only discrete logic data: 0 The veto wall a The beamline Cerenkov (C) counter 0 The beam and interaction counters. The accumulated information from these counters provides absolute normalization of cross sections, and live-time esti- mates. The interaction counter data included a bit which was set if the clean interaction definition had been satisfied. All of these counters had their information stored in the Minnesota latch modules. These modules latched data at a clocked rate. Each latched word gets stacked into a buffer, capable of storing up to 255 consecutive words. If a buffer overflowed, only the most recent words with respect to a given pretrigger remained. The clock stopped whenever a trigger signal arrived from the Faraday room, and the buffers were read out. Only the information latched on the 15 clock pulses centered about the interaction time are available to the offline analysis. 152 The C counter’s data allows one to know what type of beam particle interacted in the target by determining which differential and anticoincidence counters had fired. The counter configuration is represented by dNM where N and M are the minimum and maximum number Of anticoincidence and differential counters, respectively, that fired. For data taken with positive beam the combination d23 indicates a 11"” produced a particular event. Otherwise, one should assume a proton has interacted in the target. The veto wall data is checked to see if either wall contains a hit. If a hit exists, then the veto wall quadrant possessing the hit is determined. A bit is set whenever a veto wall quadrant, containing a hit, shadows an EMLAC quadrant that produced a trigger. For reasons discussed in the next chapter, all events having this bit set, are cut from the DST level analysis. An examination of the beam and interaction counter data shows one if the beam and clean interaction definitions used in the online trigger have actually been satisfied. A set of scalers ascumulated the beam and interaction signals during each spill. The total beam count, corrected for the fraction of time the detector was incapable of taking data, is used to normalize all cross sections. Scalers also counted how many times the C detector satisfied the online d23 requirement. The EMLAC’s trigger logic formed a tree structure with a LeCroy 4508 pro- grammable logic unit (PLU) at each branch point. The 4508 units can latch'the input signal configuration upon being strobed. All 4508 units at the pretrigger and higher levels had this feature enabled. Every time an interrupt occurred, these units were read out. The trigger logic can then be analyzed Offline to see whether or not the 45088’ logic states were consistent with the logic state corresponding to the high level trigger signal. Besides this diagnostic role, the 4508 data also tells one which octants triggered and what type of trigger they contained. Chapter 4 Event Selection The reconstruction of high p _L 7, 1r”, or 17 events from the compressed data sum- mary tapes is the subject of this chapter. The selection Of events containing high p j triggers, and the filtering out of muon induced triggers will be described. A discussion of the cuts pertaining to the direct photon sample, and their systematic effects is presented. The 1r0 background to the direct photon signal is also dealt with. However, the analysis of the recoil features and the problem of jet reconstruction are discussed in the next two chapters. The major subsamples Of the data used are given in Table 4.1. 4.1 WHOLE EVENT CUTS Each reconstructed event was subjected to a series of general cuts in order to obtain a sample of enhanced high p J_ events containing a non-muon induced electro- magnetic trigger. These cuts are listed below: There was no hit in either veto wall corresponding to a trigger quadrant. There was a single-local trigger. e The event contained a matched vertex The event contained physics tracks, and reconstructed photons. The veto wall cut provided an excellent filter for removing muon induced events from the sample. The performance of this device is the subject of the next section. The vertex cut insures that an interaction in the target is associated with the event. This helps cover for inefficiency in the veto wall, and the possibility of upstream 153 154 Table 4.1: E706 data divided by beam and target type. Set Beam Polarity Target Run Interval Triggers A Negative Cu-l-Be 2852-3036 786K B Positive Cu-l-Be 2588-2670 440K C Positive Cu+Be 2387-2586 1225K D Negative Be 2062-2382 1247K E Positive Be 1728-2007 1508K F Positive C 2588-2670 161K and downstream interactions contributing to the sample. The latter possibility could result in a compromise of the raw data reconstruction. The single local trigger requirement was necessary for two reasons. First, the events’of interest are those containing a high p j_ 7, 1r“, or 17 so a high threshold trigger from the LAC is necessary. Second, the single-local trigger is the only high- level trigger for which reliable corrections exist. The global triggers experienced problems in their turn on characteristics due to image charging effects, and these effects are still not completely understood. Hence, no corrections exist. 4.2 MUON AND HADRON BACKGROUNDS The veto wall is sensitive to beam halo particles which penetrate the hadron shield. Clearly, the only particles capable Of traversing the shield and forming high p j showers in the electromagnetic calorimeter are muons. In this section the efficiency of the veto wall in rejecting muon background is explored. There are actually two veto wall requirements. The online veto wall requirement was part of the trigger. If the same quadrant in both walls had a hit in coincidence with a LAC pretrigger, the event was vetoed. The offline requirement is just the veto wall cut described 155 above. The offline requirement is necessary because of inefficiency, gaps in the two- wall coincidence, and the fact that the online veto signal window was not centered in time about the pretrigger signal as shall be seen. Besides the veto wall there are two other ways of identifying muon events. The first one involves studying the directionality of a high p j shower in the LAC. The directionality of a shower is defined as follows 6;- : R4 _ ZfrontR'b (41) Zback R4- and R1, are the r coordinates of the shower at the beginning Of the front and back sections of the LAC respectively. The quantities Zfront = 900cm (4.2) mek = 918.5 cm are the positions of front and back sections of the LAC along the beam direction relative to the target center. Particles which travel parallel the beamline, i.e. muons, will tend to have larger values of 5,. than those which emanate from the target. In fact, particles coming from the target are expected to have directionalities distributed about zero. This effect is illustrated in Figure 4.1. In the left half of Figure 4.2 the p .L distribution of the highest p _L photon is plotted against its directionality for all events containing a hit in either veto wall quadrant that shadows the trigger quadrant. Two bands of directionality are easily distin- guished. The high directionality band dominates the high p j spectrum indicating a large muon background. The band of low directionality is centered about 6,. = 0 as is expected for photons originating from interactions in the target. A similar plot appears in the right half of Figure 4.2, but with the requirement that neither veto wall contains a hit in the quadrant corresponding to the LAC trigger quadrant. Very little is left of the high directionality band, while the band corresponding to photons 156 originating in the target is intact. In fact, the remaining distribution is quite sym- metric about 6, = 0 except at very high P1- Thus, the online veto wall requirement in the trigger should predominately reject muon induced triggers. Imposing an offline veto wall or requirement is necessary in direct photon candidate events because of the high muon background. The loss of true direct photons due to the offline cut can ° events. be investigated with high p j_ 1r The other quantity of interest is the time at which a shower’s energy was deposited in the LAC relative to the time the interaction for a particular event occurred. Muons are expected to have a time distribution that is considerably broader than for show- ers truly associated with a particular interaction. This is because there is no a priori correlation between the muon shower and the interaction which was detected in co- incidence with it by the trigger logic. In reality the muon showers are peaked before the interaction due to the online veto wall requirement being shifted such that an event having a LAC pretrigger was vetoed if there was a hit in both walls from ~ -—20ns to 120ns about the interaction time. The timing information was provided by the TVC circuits described in chapter 2. There were two factors which, unfortunately, hindered the performance of these de- vices. One, the TVC’S were susceptible to firing by high frequency noise, which i ’ blocked real signals from being timed. Evidence for this effect occurs in the TVC efficiency curve as a function of energy; the efficiency flattens out at about 90%. The other problem is that the TVC efficiency was lower in earlier runs due to malfunction- ing units and threshold problems. A complete description of TVC calibration, and reconstruction of TVC data is given in a thesis [36]. The time distributions for the highest p J_ photon in each event with and without the offline veto wall hit requirement are shown in Figure 4.3 . When there is no hit in the veto wall, a distribution sharply peaked at zero emerges with only a slight forward skew. On the other hand, the time 157 _________________ ”(:‘_ _— // // / ’I" /—” ”’___.——’ 6,=0 // ’” é¢ // // // // ZM=900.0 cm Zu=918.5 cm Figure 4.1: Illustration of photon directionality and related quantities. 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I -2 -1 O 1 2 -2 -1 6 cm 6 cm Prvstss '( ) P,vs<5, '( ) Figure 4.2: Photon p _L vs directionality for events in which the veto wall quadrant shadowing the trigger quad- rant had a hit in either wall (left), and had no hit (right). 159 distribution without the offline veto requirement is broadly peaked at ~ —40ns. There is also a large flat tail extending forward in time, which reflects the inefficiency in the online veto requirement. One expects the Offline veto to be more efficient and the evidence for this is the much smaller tail in the non-p induced distribution. At the t0p Of Figure 4.4 the photon directionality is plotted against the TVC time for events containing a veto wall hit. Two distinct regions of clustering exist. In-tiine photons strongly populate the low directionality region, while those that are early cluster in the high directionality region. The flat tail of the time distribution, having only the online veto requirement, also has high directionality, indicating the presence of muons missed by the online requirement. The lower plot in Figure 4.4 results when there is no hit in the veto wall. The highly clustered region of in-time photons with good directionality remains with small uncorrelated tails extending vertically and horizontally. The in-time tail extending towards negative directionality is assumed to be entirely due to single photons. The other tails are a mixture of single photons and muons, resulting from TVC inefficiency and ambiguity in directionality on the inner part of the EMLAC. A discussion of the systematic effect of TVC and directionality cuts on the single photon distribution is given in a following section. The muon cuts are very effective. However, charged and neutral hadrons as well as electrons can also contribute to the direct photon signal. It is imperative to at least ascertain the magnitude of their effect. Two quantities enable discrimination against hadrons. One is the front to total energy ratio of EMLAC showers. The other quantity is the distance of a charged track to a shower as seen by the MWP C system. A proximity distribution for showers and nearest tracks appears in Figure 4.5 for the hemisphere opposite a high p j_ trigger. There is a very sharp peak for Ar < 2.0 cm, demonstrating a clear signal for showers produced by charged particles. Figure 4.5 also contains the corresponding distribution for high p1 photons where directionality and Events/2ns N u‘ C o 2000 1 600 1 200 800 400 160 I I I I—5 T I I b l- L lLllllJJllllll Lil t ns Photon Arrival Time (w/out VW(Hit)) -80 -40 0 40 80 Events/2ns O) O O 500 400 300 200 100 llllllllLlJlllllllLllllL —80 — 40 0 40 80 t Photon Arrival Time (w VW Hil Figure 4.3: TVC distributions for non-p. (left) and 4‘ induced (right) events. 3’” 161 ? 2 h u 1.6 E.- V E «6‘ 1.2 :7 :'= {2,91, , 0.8 E .."-.'I__-;..:.'.:"" ‘ 0.4 E.— :pi.’ o :— '~ -o.4 :- -o.s E- -1.2 :— -1.6 E- , . _2 :llllllLlllLl—LLIJ’lL-[llLlllJJ_lll_illlllllLLllllllle -100 -80 - 60 - 40 - 20 0 20 4O 60 80 100 t (ns) 6, vs TVC Time ’s‘ 2 = 3 1.6 E- ' 6‘ 1.2 :— 6 -- 0.8 :— '.°- - 0.4 :— ' O :- .’. ' if i —o.4 .- -o.s :— ’ Hi" E -1.2 .— -1.6 :— .. . .2:LJIIllillllllllLllllel'fii'l-‘llllll-l'lIllllllllllllLLl -100 -80 -GO -40 -20 0 20 40 60 80 100 t (ns) 6, vs TVC Time Figure 4.4: 6,. vs TVC time for events with a veto wall hit (top) and without a veto wall hit (bottom). The data in the region outside the vertical lines and above the horizontal line is excluded by the direc- tionality and timing cuts. 162 timing cuts have been imposed as outlined in Figure 4.4. Again there is a sharp peak at small Ar, but it is narrower than for showers that don’t possess a high trigger bias. In addition, we expect direct photons to be more isolated because they can be pro- duced without accompanying hadron fragments. To eliminate the charged hadron background an isolation cut will be imposed on all direct photon candidates. Generally speaking, showers in the EMLAC can be hadronic or electromagnetic in origin. The electromagnetic showers associated with charged tracks are due to electrons (positrons), generated from 1r° decay photons that have converted in the target. Detailed studies of conversion pairs have been performed, and a method exists for identifying them, using only the charged tracking system. This method relies on the fact that the mass spectrum of conversion pairs peaks sharply at zero since the photon has no rest mass. For this reason a pair of conversion electrons is referred to as a zero-mass-pair or ZMP for short. The reader who is interested in the details of this procedure should consult the thesis by Hartman [37]. The EMLAC’s response to electromagnetic energy can be studied quite well with these reconstructed ZMPs. The front-to-total ratios for showering electrons from conversion pairs are plotted in Figure 4.6. The Ebom/Etom distribution for hadron showers is also shown. For the conversion pairs a large peak at high Egan/Eta“; dominates, and only a small tail extends to 0. The non-conversion plot contains a dominant Efrem/Emu peak below about 0.2 with a tail extending to 1.0. Clearly electromagnetic and hadronic showers have very different longitudinal characteristics in the EMLAC. The Efrem /Em.1 plot for photons that are in time and have low directionality appears in Figure 4.7. This distribution is similar to the one for the electrons, possessing only a slight hump at Emu/Egog‘l z 0. The plot for the muon showers, selected by requiring a veto wall hit, and an out-of-time shower with large directionality, is completely different. The 9000 8000 7000 6000 5000 4000 3000 2000 1 000 163 vIIll 1000 — 800 - 600 - 400 [IFTIIIrIIIIII%IIII;1' 200 Illl llll l “LlllJ_JL llllllllllLLUlllll 0 0 20 40 60 80 1 00 0 20 40 60 80 Ar for Showers (cm) Ar for 7 Events (cm) Figure 4.5: Ar between showers and nearest tracks (left); Ar between high p ,L photons and nearest tracks (right) 100 164 1600 1400 1200 1000 800 600 400 II'IIIIVIIIIIYUIUIIIIIIII‘IIUIIII' 'IT M llllLJlLdlllllllllllllllllLLlllllllLllllllllLllL OJ (12 045 (14 (15 (16 057 (18 (19 1 200 o 11" E,/Em for Hadrons 70 60 50 40 30 20 10 HillllllllllllllJlJLLlJ 0 Oil (12 (13 (14 (15 (16 (17 (18 (19 1 E,/Em for Electrons Figure 4.6: Emu/Etogd for Hadron Showers (top) and Elec- tron Showers (bottom). 2400 2000 1600 1200 800 400 450 400 350 300 250 200 150 100 50 0 165 OJ (12 023 (14 111111]llllllJllllllllllllllllllllllllL (15 (16 (17 (18 09 EF/Em for 7 Events I 0 LilJllllllllllllllllllllllllllLJlllllllllLJllllLL GA (12 (13 (14 raj—J— (15 (16 (17 (18 (19 E;/Em for p Events Figure 4.7: Efrem/Egogd for High p _L Photon Showers (top) and p Showers (bottom). 1 166 flatness is expected, however, because muons can penetrate considerably into the EMLAC before emitting a hard bremsstrahlung photon. In order to eliminate neutral hadrons and compensate for inefficiencies in the tracking reconstruction, a cut on the Egan/Etc“; ratio will be imposed on all direct photon candidate events. 4.3 1r° RECONSTRUCTION For the highest p i trigger octant all 2-photon mass combinations were used to ob- tain a mass distribution. This distribution is shown in Figure 4.8 for all asymmetries and for asymmetries less than 0.75. Asymmetry is defined as A __ IE1 —E;| _ 4.3 E1 + E: ( ) where E; and E; are the energies of each photon. The 1ro and 1) peaks .at ~ 135 MeV and ~ 550 MeV respectively are clearly visible above the combinatorial background. The uncut distribution has a considerably larger low mass region below 110 MeV than the plot with the 0.75 asymmetry cut. In fact, the cut plot has a pretty symmetric background around the 11'" peak. The low mass pairs have been studied extensively [38]. The majority of them are produced from single high energy showers that hap- pen to fluctuate into two showers. The systematic loss of 1r°s due shower energy . fluctuations is very small. The mass region from 110 — 160 MeV has been designated as the 1r° mass band. An event is labelled a 1r° event if it satisfies the following criteria: 0 All whole-event cuts are satisfied 0 An octant has a diphoton pair with 110 MeV < Mpg, < 160 MeV o The diphoton pair has A < 0.75 167 Similarly, if the diphoton pair has a mass between 500 - 620 MeV, the event is labelled an 1) event. Otherwise, the event is considered a direct photon candidate. The 11'" sideband regions have been designated as 75 — 100 MeV and 170 — 195 MeV . These regions are used to estimate the combinatorial background underneath the 1r° peak. Any 1r° distribution i.e. A, Mass, E, is made for the peak and sidebands separately. The sideband distribution is then subtracted from the peak distributions. The 1r° mass has been studied as a function of radius and azimuth in the octants. The sundry distributions show a number of dips in the mass, indicative of energy losses. These losses occur near the various boundaries. Such losses can result from only part of the shower being contained in an active region. They can also arise from the reconstruction program incorrectly splitting showers in multiple peak groups, and/ or failing to properly correlate showers between views. For this reason, a set of fiducial cuts have been imposed on all photons used to reconstruct a high p 1 1, 1r°, or n: o A photon must have its r coordinate in the interval 24 cm _<_ R, __<_ 138 cm. 0 A photon must lie more than 2.0 cm away from any radial boundary of an octant. The asymmetry distributions for 1r°s with' and without sideband subtraction are displayed in Figure 4.9. There is no asymmetry cut so that the roll-off at high asym- metry can be observed. Ideally, one expects a flat asymmetry distribution because the 1r° is a spin 0 particle undergoing a two-body decay to photons. In the rest frame of the 1r° the photons emerge back-to-back isotropically. Consequently, the A distri- bution should be flat in any frame for which the motion of the 1r° is very relativistic. However, the plots of Figure 4.9 are fairly flat out to .75 after which significant losses of 1r°s occur with increasing A. Such behaviour is due to the increasing inefficiency of the LAC for photon energies below 10 GeV. This is the reason for the .75 A cut on reconstructed 1r°s. All 27 masses above .75 A are classified as direct photon candi- Events/SMeV 10 168 E P, > 3.5 GeV/c : A < 1.0 ’ ................ A < 0.75 : 10 .- 3 3'3} 3:5" * " 10 :- 5’ .5 —4 10 d’ HIIIIIIIJIIILLIlllLlllUllllllllllllllllllllllllll 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 M Moss (GeV) 77 033 Figure 4.8: 71 Mass Spectrum 2400 2000 1 600 1200 800 400 2400 2000 1600 1200 800 400 O 169 =_ +_._ I - —+— —+-— I —+— _+_ r ‘*‘ +—+— I _+_ E _,_ L —+— E -*— L —+——-+-— bllllIllllll141111111llllllLLlllllllllll[111111111 0 0.1 0.2 0.3 0.4 0.5 0.5 0.7 0.8 0.9 1 A E e +++ | I :- —+— . —+— I _1_ L —+— E. —+— : ""— .- _._ :lllllllllllLlllilllllllllllllllllIlllJllllllFrr-J—L 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 A Figure 4.9: Asymmetry distributions for 1r°s without side- bands subtracted (top) and with sidebands sub- tracted (bottom). 170 dates if the highest p ,L photon passes all other direct photon criterion. It is these 1r°s with A > 0.75 that are the source of direct photon background after cuts. 4.4 SINGLE PHOTON RECONSTRUCTION An event is classified as a direct photon event if it meets the following conditions: 0 All whole event cuts were satisfied. N o diphoton pair formed a mass in the 1r° or 1] mass bands The highest p i photon had 5,. < 0.4cm If timing information was available, then —15ns. < TVC“me > 40ns 0 There was no charged track within 1.0 cm of the highest p 1 shower . Ebont/Etotal_> 02 The octant multiplicity distribution for the single photon sample shows that about 30% of the events have more than one photon in the octant, containing the recon- structed single photon. This indicates that 1r°s, which decayed asymmetrically, are present. However, even the events with only one photon contain 1r° background from decays in which a photon was lost due to acceptance or inefficiency. 4.5 SYSTEMATICS Both the whole event cuts and the single photon cuts resulted in losses of recon- structed 1, 1r°, or 1] that must be accounted for. The 1r°s are affected only by the whole event cuts. The direct photon candidates also have to be corrected for timing, directionality, track isolation, and E50,“ /EM.1 losses. Furthermore, the direct photon 171 events must in principle be corrected for residual muon background. However, stud- ies indicate that this background is consistent with zero, given the available statistics [39]. Table 4.2 summarizes the corrections for the whole event and muon cuts. Besides correcting for cuts, corrections must also be applied to compensate for trigger inefficiency, reconstruction losses, and conversions Of high p i photons in the target material. The correction for reconstruction inefficiency is different for 1r°s and single photons because 1r° s are also affected by geometric acceptance losses as well. Studies have been done to determine these corrections, and routines exist in the library of data summary programs to compute them on an event-by-event basis. The analysis presented in the following chapters utilizes these standard routines in making the various corrections as they are currently available. There is still one very important correction, which is critical in Obtaining absolute cross sections. This is the correction to individual photon energies that takes into account the electromagnetic calorimeter’s response (energy scale), and the energy loss due to the three radiation lengths of material in front of the detector. This energy correction is critical because the cross sections fall steeply with p 1- This systematic uncertainty must be known to better than 1% if the cross sections are to be known to better than 10%. The localization of shower energies in liquid argon sampling ' calorimeters, and the ionization mechanism’s stability makes these device capable of such precision. It is thus imperative to understand the energy loss in the material between the vertex and the calorimeter. Studies have been done using the ZMP’s reconstructed from the tracking system to determine the photon energy correction. The correction is also available in the data summary library, and has been used in the following analysis. If the reader is interested in the details of how all the corrections were obtained, he will find a summary of them in an appendix. 172 Table 4.2: Corrections for whole event cuts, and cuts for single photons. Cut Correction Negative Beam Positive Beam Veto Wall 1.111 :1: .033 1.099 :1: .006 Vertex and“ = 1.0019 - 0.0079 x Vz Track 1301. 1.043 :1: .002 Timing 1.034 :1: .004 Directionality 1.005 1 .001 Erma/Ema 1.015 :1: .001 2“,, (total correction) 1.230 :1: .007 1.216 :1: .009 4.6 To BACKGROUND CALCULATION After muons the major source of direct photon background is the decay products of highly asymmetric 1r°s. Because of the asymmetry cut of 0.75 on reconstructed 1r°s, 25% of all triggering 1r°s could contribute. The p i distribution of fake direct photons has to be calculated, and for this task a monte carlo program was developed. The monte carlo used events from the DST stream. as input. The input set con- sisted of all events with a high p l diphoton pair in the mass range 0 — 175 MeV. The diphoton pair must have sufficient p i so that a reliable trigger correction exists, and each member of the pair must reside in the same octant. However, no asymmetry cut is applied to the pair of photons. All of the extra photons in the octant containing the high p ,L pair are also included. Relaxing the mass and asymmetry cuts on the 7r° candidates allows the simulated energy fluctuations to reproduce the actual 27 mass spectrum obtained from the data. This provides yet another check on the monte carlo. 173 Each event is processed through a GEAN T simulation of the detector a total of 5 times. On each successive generation the entire event is rotated by 1r / 4 into a neigh- boring octant. Since the 1r° decay is uncorrelated with the underlying event topology, the 11’" is redecayed with a new asymmetry and rotation of the decay photons about the direction of motion on each generation. The simulated raw data is then processed by EMREC and a binary DST output file is written. The monte carlo DST is then processed by the high level reconstructor and the p 1 distributions of 1r°s and fake direct photons are generated. Each entry in these distributions is corrected by the event weight of the corresponding input event and the acceptance, reconstruction, and conversion weights corresponding to the generated event. The quotient distri- bution yields a set of numbers in p 1 which are used to correct the direct photon p 1 distribution. The bin contents of the quotient distribution are the so called f, numbers in p l. These numbers have been computed separately for the proton and 1r" data sets. Although the f, numbers from both sets are statistically consistent, the ensuing analysis will use the set of f, numbers that corresponds to the beam type used to generate a specific data set. Table 4.3 gives the fake gamma, f.,, numbers for both types of beam together with their uncertainties. While the background from asymmetric 1r° decays is dominant, there are measur- able contributions from 17, 17’, and w decays into two photons. The calculation of these contributions to the direct photon background was performed in the same manner as for wos. The same input data was used in each case, but the 17, 1”, or w mass was assigned to the diphoton pair instead before redecaying it. In addition, these events had an additional weight factor assigned to them, which accounts for their respective production rate and branching ratio relative to 1r°s. The relative production rate for as was obtained from the world data. The world data is consistent with an 17/1r° ratio of 0.45. Based on results for the relative rate of high p _L K to 1r production [40], the other relative production rates were assumed to be the same as for the 17. 174 Table 4.3: False 1 fractions in p _L for proton and 11" beams. p ,L (GeV/c) fgam Numbers Proton Beam 1r‘ Beam 4.375 .169 j: .006 .192 i .006 4.625 .162 :t .006 .185 :1: .006 4.875 .156 i .006 .178 :1: .006 5.250 .146 :1: .006 .166 :1: .007 5.750 .133 :1: .008 .152 :1: .008 6.500 .113 :1: .011 .129 :1: .010 7.500 .087 :1: .016 .099 :1: .013 9.000 .048 :1: .023 .055 :1: .018 Chapter 5 Event Features Attention is now turned to the charged particle structure of high p J_ 1r° and single 7 events. The distributions of charged particles in both the recoil and same-side hemispheres will be examined. One purpose of this study is to determine if there are any differences between high p _L single 7 candidates and 1r° events. Another purpose is to demonstrate the existence of jet structure in the recoil hemisphere. The results presented in this chapter are qualitative in nature. Nevertheless, it will be shown that a direct photon signal exists in the data without the application of a 1r° background subtraction, but employing all of the selection criteria described in the previous chapter. The existence of dynamical correlations among the recoil charged particles will also be investigated. 5.1 DIFFERENCES BETWEEN 7S AND 1r°s The azimuthal distributions of charged particles with respect to the trigger axis have been used to find differences in the overall features of 1r° and single 7 events. Sets of distributions have been made for different trigger p ,L intervals. These intervals ' are 5.0 S p; < 5.5 GeV/c, and pl 2 5.5 GeV/c. The only cuts made on the charged particles, besides the general track quality cuts discussed in chapter 3, were p L cuts. and a rapidity cut of I y |< 0.7. The rapidity cut was intended to cut down on the background from spectator jet fragments. The spectator fragments emerge in narrow cones about the beam axis, the particle density having an exp’api dependence. This cut should not compromise the comparison of 7 and 1r° events. Sets of plots were made for each of the following p ,L intervals: p i(tracks) > 0.05GeV/c, p_,_(tracks) > 0.3 GeV/c, pi(tracks) > 0.5 GeV/c, and pJ_(tracks) > 175 176 0.75 GeV/c. This was done in order to minimize the spectator jet background. The particles emanating from the hard scatter should be enhanced in p J_ while those produced by the other “sof ” part of the interaction should be strongly suppressed with respect to this variable. More importantly, however, was to check the stability of any Observed trend in the 45 distributions as a function of p i. The plots presented here correspond to the 0.3 GeV/c p J_ cut. The features appearing in this data set are present in all of the others as well. The azimuthal plots have been constructed over the interval 0 _<_ 45 3 1r. If the Acfi value computed for a track fell outside this interval, it was transformed into the corresponding value lying within the interval. All plots have been normalized to the corresponding number of 1r° or single 7 triggers. The corresponding plots for proton and 1r‘ beam appear in the same figure. The 7 and 1r° distributions for the same data set and cuts appear superimposed in the same plot to facilitate the comparison. Three different types of azimuthal distributions have been constructed. First, there are the simple number density distribution of charged particles about the trigger axis. These are shown in Figures 5.1 and 5.2. The 1r‘ beam data gives reveals an unambiguous difference between single photons and 1r°s for p 1 2 5.5 GeV/c. Here the photons appear more isolated within the trigger hemisphere than do the 1r°s. Such an effect is expected since direct photons are produced in lowest order with no accompanying hadrons whereas high p ,L 1r°s are just one of several hadrons resulting from the hadronization of the hard-scattered parton in the trigger hemisphere. The proton data shows a similar trend in both p i intervals, but it isn’t as significant. Another type of d) distribution is one in which each entry is weighted by the p i of the corresponding track. Such a weighting has a sensitivity to jet structure in so far as jet particles tend to have more p _L than non-jet particles. The p l weighted plots appear in Figures 5.3 and 5.4. Again the 11" data shows the 73 as being definitely more isolated than the 1r°s for p ,L 2 5.5 GeV/c. In addition, the same trend appears 177 for the lower p 1 interval although it is confined to the bin closest to the trigger particle. The proton data follows a trend consistent with the direct photons being isolated but again it is not very significant statistically. A third type of distribution arises by weighting the entries by the quantity <11 defined as follows, ‘11 = PJ-(traczk)..pj_(tngger) (5.1) pr(tnsser) pJ_(track) 05 A45 p i(trigger) This quantity is similar to a p L weighting, but it also takes into account the expected spatial orientation of the jet in azimuth. Such a weighting is useful in conjunction with a p _L weighting since systematic effects due to misreconstruction of track mo- menta enter differently. Consistency with the p 1 weighted plots indicates that this systematic effect is not determining the observed features. The q 1 weighted plots are shown in Figures 5.5 and 5.6. They display the same trends observed in the p 1 weighted distributions. In summary all of the 11'" distributions show a clear and consistent difference between 73 and 1r°s above 5.5 GeV/c in p _L. The p _L and q 1 weighted plots show the isolation of direct photons at lower p J_ but the (,1) density distributions do not. The trends in the proton data are consistent with this observed difference, but have little statistical significance. This could be due to a greater relative amount of background from 1r° and n decays in the reconstructed photon sample than is present in the negative data. Such an effect is expected from naive QCD considerations. There are two direct photon production mechanisms in 1r‘ data, but only one in proton. While the annihilation process can contribute to high p _L 1r° production in the negative data as well, it makes a much smaller relative contribution because the overall number of contributing subprocesses is much larger than for direct photons. Finally, a set of d: 178 distributions was made for 4.5 S p L < 5.0 GeV/c. N o differences between 75 and 1r°s were Observed. Besides finding a difference between reconstructed photon and 1r° events in at least some portion of the data, all of the azimuthal distributions show a dominant peak Opposite the trigger. This peak begins near 21r / 3 away from the trigger particle and has its maximum at 1r. Furthermore, these 43 plots possess only two peaks; a dominant peak at 1r and a small bump about the trigger particle’s direction. Such behavior is consistent with a 2-body hard scattering among pointlike constituents, i.e.partons. This recoil feature will be utilized in the following chapters to ascertain the direction Of the jet recoiling from either a high p l 1r0 or single photon. Similar analyses of charged particles associated with single high p l particle production have been done at the ISR [41]. 5.2 RAPIDITY CORRELATIONS The azimuthal distributions showed a very strong clustering of particles opposite the trigger in the plane transverse to the beam. If jets indeed exist, then correlations should also exist in the plane defined by the beam axis and the transverse axis of the hard scatter. Orientation in this plane can be measured as a function of cos 6 where 0 is the polar angle. However, a more desirable quantity is the rapidity, y. A particle’s rapidity has very simple Lorentz transformation properties along the z- axis. In addition, differences in the rapidities of a pair of particles are invariant under Lorentz boosts parallel to the beam direction. Ay distributions are the same whether they are constructed in the lab frame, the beam-target cm frame, or the rest frame of the colliding partons. The difference in rapidity between recoiling charged particles will be used to see whether or not they are dynamically correlated. If this experiment is sensitive to jet structure, then one would expect the highest p .L charged particles to cluster together . FEM 1 main/ago) (rod") 179 - Proton Beam _ O 75 : 0 71's _ 5.0 a P, < 5.5 GeV/c " Track P, 3 0.3 GeV/c 3:111+i F #1 l L l l I l I l l 4 l l l L 1/N(dn/d¢) (rod") 0 1 2 3 Arp n' Beam Oys 011’s _. 5.0 5 P, < 5.5 GeV/c - Track P. 3 0.3 GeV/c I + IrTj FTTH + l —.- *1 11+ Tfi '0". P lLJiJlllllllllL 0 1 2 3 Aso Figure 5.1: ()5 density distributions for charged particles in high p _L 1r° and single photon events with 5.0 S p; < 5.5 GeV/c. 1/N(dn/d¢) (rad") 180 - Proton Beam 0 78 : 0 71's ._ 5.5 5 P, GeV/c - Track P, i 0.3 GeV/c LlLllLlllllllLl 1/N(dn/d¢) (rod") 0 1 2 3 Av - n' Beam 073 011's ._ 5.5 s P, GeV/c '- Track P, 3 0.3 GeV/c 1. 7. I I T *- I TfTfi —O——O— I j 1 I ...— H1 1 bill] lllllilllllllll I .0— r b 0 1 2 3 Ago Figure 5.2: 4: density distributions for charged particles in high p i 1r° and single photon events with p j 2 5.5 GeV/c. 1 /N(dq,/d¢) (rod" GeV/c) 1.4 1.2 0.8 0.6 0.4 0.2 181 l l U T l l I I I I r T IITTUIrTTrTTTUTTrTIIII Proton Beam 0 3 o a. (I 5.0 s P, < 5.5 GeV/c Track P, E 0.3 GeV/ c 1.4 1.2 0.8 0.6 1 /N(dq,/d¢) (rod" GeV/c) 0.4 ’ 0.2 .s o 1 : ¢i03 O Jlllll'l‘lllJlll 0 0 1 2 AP Figure5.3: lTIIlfIrTrTTIlTFfilerrTTrTTTTIIT T T O '0- r 11‘ Beam 0 V m 0 1r°s 5.0 § P, < 5.5 GeV/c Track P, E 0.3 GeV/c 3', ’ a I 111—Lijl_.l.lillLll 0 1 2 3 Av q _L weighted 4) distributions for charged particles in high p _L 1r° and single photon events with 5.0 _<_ p; < 5.5 GeV/c 1/N(dq,/d¢) (rod" GeV/c) 1.4 1.2 0.8 0.6 0.4 0.2 182 IIrW‘lfiIjIIII I I r I I I l I I I I I I I I I I I I I Proton Beam - n' Beam 07$ 1.4 : 073 In‘s P .n’s 5.5 s p, GeV/c ; 5.5 s p, GeV/c ‘ Track P, 2 0.3 GeV/c 1 .2 —- Track P, 2 0.3 GeV/c 1 _. 1 L- 0.8 0.6 1/N(dq,/d¢) (rod" GeV/c) IIo-IIIIHIIIIIIIIIII 0.4 0.2 :1 i I o . ’ 8 9 a ' 1L10119.1.lllj 0 311315.101 0 1 2 0 1 Aw Aw Figure 5.4: q j weighted d) distributions for charged particles in high p l 1r° and single photon events with p 1 2 5.5 GeV/c. 1/N(dp,/dp) (rod" GeV/c) 183 8 Proton Beam n' Beam 0 73 O 75 O 1r°s 7 O n“: 5.0 E P, < 5.5 GeV/c 5.0 5 P, < 5.5 GeV/c Track P, a 0.3 GeV/c Track P, z 0.3 GeV/c 6 1/N(dp,/d¢) (rod" GeV/c) 45 .. C .- h— .- .. .. .- 1— 7.. - .— .— ... 1. [- .— .. .— - .. .. .- ... - ,. .- .. _- .. [- .. 1' ... IIIII'III’TIIIIIIIIIIIIIIIIIITIIIIII + 2 , 1 1 . . 1’. ['0 . o8 .. a .itloii 33.38:] lllllllllllllLl OPPLIIIL4111114LL1 o 1 2 3 o 1 2 3 M Aw Figure 5.5: p _L weighted 4: distributions for charged particles in high p _L 1r° and single photon events with 5.0 S p; < 5.5 GeV/c. 1 /N(dp,/d¢) (rod" GeV/c) 184 lIIIIrIrrIlIIIIIIIIIIIIIIIITjleIII —.- 1 I I I Proton Beam 0 18 I n's 5.5 s P, GeV/c Track P, E 0.3 GeV/c «o—o—— o. -O-.— 1/N(dp,/d¢) (rod" GeV/c) O IIITTIin—IIIIIIITIIIIIITIIIIIIIIIII n" Beam 075 O «‘3 5.5 i P, GeV/c Track P, a 0.3 GeV/c O — 1 -1 O Q P o t 3 ’ 3 l l l l I l J J J_l l 1 l 1 2 Av Figure 5.6: p i weighted ¢ distributions for charged particles in high p ,L 1r° and single photon events with p ‘L 2 5.5 GeV/c. 185 in rapidity producing a peak in the Ay distribution about 0. Of course, some of the clustering around zero can be due to accidental coincidence. Even perfectly flat rapidity distributions will produce a Ay distribution peaked at 0. It is important therefore, to compare any observed correlation in rapidity against that which is at- tributable to random coincidence. The degree of random coincidence is governed by the shape of the particles’ rapidity distributions; these are in turn governed by the physics of the hadron-hadron collisions as well as the acceptance and overall efficiency for finding tracks. The Ay plots appearing in the following figures have the uncorrelated background superimposed as a smooth curve. The uncorrelated Ay distributions are constructed by choosing values from the rapidity distributions of those particles used in mak- ing the corresponding data plots. The values are chosen such that if plotted the shape of the parent distribution is preserved. As with the azimuthal, distributions, a set of selection criteria have been applied to the tracks used in this study. These criteria are essentially the same as for the 4) distributions except that the rapidity cut was extended to :1:1.5 in the beam-target center of mass, and only p _L cuts of 0.3 and 0.5 GeV/c were applied. The results from the two sets in track p _L are the same, and so only the study employing the low p i cut will be discussed. Finally, the plots have been folded into the interval from 0 to 3.0 units of rapidity, the data for 1 different trigger particle’s and beam types have been combined, and all plots are area normalized. Figure 5.7 shows the rapidity differences between the two highest p l tracks in the recoil hemisphere, and between the highest p ,L track and all other tracks besides the second highest which pass the selection criteria. Both plots show a definite correla- tion above the level of accidentals. The correlation is strongest between the highest p .L tracks. This is probably due to a larger fraction of non-jet tracks in the other distribution. Such a correlation has also been reported by the AFS collaboration [42]. 186 Before the observed correlations can be interpreted as dynamical in origin it has to be demonstrated that they are not an artifact of phase space. In particular, it could be argued that the enhancement around Ay = 0 is due to longitudinal momentum, p., conservation and/ or energy conservation. If p, conservation is responsible for the correlation, then the highest p L recoil particle should be correlated in rapidity with the trigger particle. Figure 5.8 clearly shows this not to be the case; all correlation is merely accidental. Such a result is consistent with a hard-scattering of nucleon constituents in relative motion. The colliding partons’ rest frame does not generally coincide with the rest frame of the colliding hadrons. To understand the effect of energy conservation on the correlation one must resort to a phase space monte carlo. Such a monte carlo produces a spectrum of particles, governed only by the constraint of energy-momentum conservation. The phase space monte carlo GENBOD was chosen for this study. It exists in the CERN library of FORTRAN callable routines. Events were generated in which all particles were assumed to be pions with equal numbers of 7r+,1r‘, and 1r°s present; the conservation of electric charge and isospin was thus automatically insured. The data presented here was generated with 30 particles per event. Parallel studies in which the multiplicity varies from 20 to 50 tracks have yielded the same result. A generated event was selected for output, provided it contained a high p 1 1r° with p ,L 2 4.0 GeV/c and l y I< 0.7. The Ay histograms were filled in accordance with the same selection criteria as used on the charged tracks in the data. The effect of the analyzing magnet’s field together with the MWPC’s geometric acceptance, and the effect of the planes’ eficiencies have also been accounted for. Figure 5.9 shows the phase space result for the two highest P1 tracks recoiling from a 1r°. No correlation above the accidental background is observed! Also shown is 187 a plot from the ISAJET monte carlo where each event contains a high p i no. The ISAJET result is very similar to the real data. In fact, Figure 5.10 shows the data Ay distribution with the ISAJET prediction superimposed. Although this physics monte carlo differs from the data in the tails, there is good agreement near Ay = 0. The ISAJET data has been subjected to the same cuts, track selection criteria, and detector effects as the GENBOD generated set. It appears that the observed correlations in the data are artifacts of the underlying collision dynamics. They are consistent with those observed in the ISAJ ET generated distributions. If one interprets the Ay and 45 correlations in the recoil hemisphere as arising from the presence of jets in the high p _L data, then these correlations can be utilized on an event by event basis to ascertain the direction of a recoiling jet in the apparatus. This is the subject of the following chapter. (1/N)dn/dy 188 P,> 4.5 GeV/c I IIIII I 16 — I— p b 'O b I fl? Track P, i 0.3 GeV/c 162:- - 1 r IOJP I r y. y. 16‘ lllllllllllULLllllJllll 0 0.4 0.8 1.2 1.6 2 1AY|12 (1/N)dn/dy P,>4.5 GeV/ c Track P, i 0.3 GeV/c _ - D - b h 1. -2 10 __— -3 10 :- ,. 16‘ LlALlllllllLlllllllllllll O 0.4 0.8 1.2 1.6 |AY113,4,5... Figure 5.7: Ay distributions for lst and 2nd highest p 1 re- coil tracks (left), and lst,3rd,4th, . .. highest p 1 tracks (right). 2 (1/N)dn/dy 189 1.. ",2 P,>4.5(3eV/c : Track P, 2 0.3 GeV/c —1 10 C— p- I. -2 10 r I -:s 10 r l 16 llllLLlllllIlllllllllJ_LlLllllllllll_LLlJlllllIllll o 0.2 0.4 0.6 0.8 1 1.2 1.4 1.5 1.8 wmml Figure 5.8: Ay between highest p J_ recoil track and the trigger particle. 2 (1/N)dn/dy 190 - r- : P,> 4.5 GeV/c : P,>4.5 GeV/c I Track P, a 0.3 GeV/c I Track P, a 0.3 GeV/c ' ISAJET “ GENBOD I I 16 >\ U -2 F -2 10 _— 210 L— .- Z .- p- \ .. 1- :, - r- . - b 9 .. [- .- -3 -3 10 :- 10 :- 3 K " 1' 16‘ LlljllllllLlJlllllllllll 164 llLlllllllllllllllllllll 0.4 0.8 1.2 1.6 2 O 0.4 0.8 1.2 1.6 2 1AY|12 1AY|12 Figure 5.9: Ay distribution Of highest p ,L recoil charged pair for ISAJ ET generated data (left), and phase-space monte carlo data (right). The uncorrelated Ay distributions appear as smooth curves. 1 h I P,>4.5 GeV/c I Track P, .2. 0.3 GeV/c '- ............ lsMET -1 10 _- r: .............. ;° ' ”"o' ............. o ----- 1" o "...”. .. ".o_ >~ _ ..o“ . a ............ . 0 . c _2 .......... ‘O 1 __ ---------- 9 9 A .. '°-. 2 - --------- t > : ------- ., t + :- ... + -3 10 :- 16‘ LLLllllllllllllllllllllllllllllllllllllllllilllll 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 1AY|12 191 Figure 5.10: Ay between the highest p 1 recoil charged pair in data with the corresponding ISAJET result su- perimposed as a smooth curve. 2 Chapter 6 Jet Reconstruction The previous chapter contained a study of the correlations associated with jet structure. The study revealed that the recoil jet is contained within the tracking system’s acceptance a fair fraction of the time. This chapter focuses on the recon- struction of the recoil jet’s 4-vector. The goal is to show that cos 0" and M 7J3 are measurable quantities within the realm of a physics monte carlo. If the corresponding distributions in the data are similar, then one might be inclined to believe the data distributions are meaningful as well. Achieving this goal requires several intermediate steps. First, the jet axis must be reconstructed with some reasonable efficiency, and the resolution estimated. This task is accomplished by implementing a jet reconstruction algorithm. Second, the recoil jet’s momentum must be computed, and values of z, and as; obtained. The sources of systematic uncertainty in these variables have to be understood, and their magnitudes estimated. Understanding the origin of these effects allows one to decide if meaningful cos 9" and M distributions can be constructed. 6.1 JET ALGORITHMS Two jet algorithms will be studied and compared against one another. A cone type algorithm, familiar to collider experiments, has been chosen since it is directly sensitive to the jet correlations described in the previous chapter. The other algorithm has been used by the WA70 [43] collaboration in their study of jets recoiling from high p 1 single photons and 1r°s. Use of the WA70 procedure allows the results from this analysis to be compared directly with those of another experiment in a similar kinematic regime. 192 193 Both algorithms only make use of the charged tracking data. They utilize the same initial set of jet candidate tracks, and employ the leading charged particle as the initial or “seed” jet direction. The input set of tracks is defined by the following criteria: 0 All tracks must be more than 1r / 2 radians away from the trigger particle (Hemi- sphere Cut). 0 All tracks must have pl 2 0.3 GeV/c. o All tracks must have n S 1.5. The last cut is intended to provide a symmetric acceptance, but it also removes tracks belonging to the forward spectator jet. Such tracks can have considerable momentum and as a result, bias the jet reconstruction. In addition to these criteria, two additional constraints are imposed on the leading charged particle. One, the leading charged track must have p i 2 0.5 GeV / c, and two, this track must be more than 271' / 3 radians from the trigger particle in azimuth. 6.1. 1 Cone Algorithm The cone algorithm selects tracks from the input set based on the value of AR associated with them. This quantity is defined as follows: AR = ,/A2, + A243 (6.1) where A17 and A45 are the differences in pseudorapidity and azimuth, respectively, between the candidate jet track’s orientation and the jet axis’s direction. Of course, on the first iteration the jet axis is just the direction of the leading charged track. The A45 and A31 plots, presented in the last chapter, indicate that strong correlations exist between particles in the recoil hemisphere for A¢ S 1r/ 3 and Ay S 1.0. For this reason a cut value of 1.0 has been chosen for AR. While not all jet tracks will 194 be included by this procedure, it is expected that the fastest jet tracks will be and that most spectator tracks will be excluded. After making a selection based on AR the momentum vectors of the tracks as- signed to the jet are summed, and the jet axis’s direction computed. The new estimate for the jet direction is used to make another AR selection on the initial input set of tracks. Another jet axis is calculated from the second set of jet candidate tracks. This process is repeated until a maximum number of tracks are assigned to the recoil jet, or the algorithm oscillates between a solution containing N tracks and one possessing N + 1 tracks. In the latter case the solution with N + 1 tracks is chosen. A final check is made on the jet axis calculation. First, a reconstructed jet must have two or more tracks assigned to it. Second, the reconstructed jet axis must be more than 21r/ 3 radians from the trigger in ()5. These cuts on the reconstructed jet reduce the number of jets biased by spectator fragments and insure that the events represent true 2-2 hard scatters rather than multi-jet events, which are difficult to interpret. 6.1.2 WA70 Algorithm The algorithm developed by the WA70 group is based on an e+e‘ sphericity algorithm. The routine has been modified for use in a hadrO-production environment by including a means of discriminating between particles belonging to the recoil jet and those belonging to the spectator jets. Furthermore, the sphericity tensor is not actually used in calculating the jet axis because the trigger and recoil jet axes are not generally back-tO-back in the rest frame of the colliding hadrons. The WA70 routine is the same as the cone algorithm except that instead of making a jet track selection based on AR, a selection based on the probability, P, that a track belongs to the recoil jet as opposed to the spectator jet is performed. P is calculated 195 from weights w, and 102. These weights are formulated mathematically as w, = Ell—:DE exp(—3.0p_LJET) 10: = W exP(-3-OP.LBEAM) (62) P P = L, P > 0.5 (cut criterion) (wl + 102) The subscript, JET, refers to the momentum component parallel or transverse to the current estimate of the jet direction. The subscript, BEAM, has an analogous meaning for a track’s momentum components with respect to the beam direction, taken as the z-axis in the experiment’s coordinate system. In addition, the same pair of cuts are applied to the final estimate of the jet axis. 6.2 THE JET MONTE CARLO The monte carlo used to study jet reconstruction and resolution has two distinct parts: an event generator that produces simulated events according to the current understanding of hadronic interaction, and another program which simulates the de- tector’s response to the passage of high energy particles. The ISAJET monte carlo was chosen as the event generator. Version 6.36 has been used since it allows for effi- 0 cient generation Of high p _L 11' events. All events were generated on the VAX family of computers, possessing 32 bits of precision. 6.2.1 Implementation of ISAJ ET The physics monte carlo employs the independent fragmentation model, and the factorization scheme outlined in the introduction. The results from perturbative QCD are used to simulate the high Q2 parton-parton scatter. It should be noted that the event generator for direct photons contains only the Compton and annihilation subprocesses; there is no bremsstrahlung component in the direct photon monte carlo 196 data. Unless otherwise stated, the events were generated with the default set of parameters. This implies a 6GeV/c radiative cutoff and a (k,) of 0.95 GeV/c. As described in the chapters on the experimental apparatus and event selection, the type of trigger utilized in detecting high p i 1r°s and single photons relied on only one large deposition of p ,L in the electromagnetic calorimeter. There is then the possibility of a net p _L for the trigger+recoil-jet system in the direction of the trigger particle due to fluctuations in the transverse momenta of the colliding partons. Recent results from the WA70 group indicate a rather substantial (k _L) of 0.95 GeV / c [44]. This explains the value currently implemented in ISAJ ET. In order to take into account the effects of the single-local trigger, the p 1 thresholds for jets 1 and 2, produced by the monte carlo, were set at different levels. Jet 1 was re- quired to have pl 2 4.0 GeV/c while jet 2 was only required to have p, 2 3.0 GeV/c. The plot in Figure 6.1 reveals a significant spread in Api with a mean of ~ 1.0 GeV/c. As a matter of fact, there is evidence in the E706 data sample for such a p j imbal- ance in the direction of the trigger particle. This imbalance represents the minimum imbalance in the acceptance for tracks and showers outside the beam halo region of the LAC [45]. 6.2.2 Detector Simulation Ideally the ISAJET generated data would be input to a full detector simulation program. The simulation used by the E706 collaboration is an implementation of the GEANT monte carlo package. The output from GEANT would be run through the same chain of reconstructor code used on the real data. Finally, a compressed DST is made from the reconstructor output, and the monte carlo DST’s are subsequently processed by the high level DST reconstruction code. The advantage of this method is that the systematics associated with data reconstruction, e.g. “bugs” in the code, are duplicated in the monte carlo. (109 (108 (107 (106 (105 (104 (103 (102 0TH 0 197 IIIIIIIII'ITII'IIII'IIIIlIIII'IIfiIlIIITjTrIW—r I I LJ iII LI 1 I I I I l I I I I [J I I I l I I l I l I I I I I I I I -5 -4 —3 —2 -1 o 1 2 3 4 k, GeV/c Figure 6.1: The p l imbalance between the two hard scatter jets in ISAJET with (kl) = 0.95 GeV/c. 198 Unfortunately, such a thorough procedure represents a huge investment of com- puter time. A more expedient solution was used in this analysis. A simplified detec- tor simulator was written which takes into account the acceptance of the magnet and MWPC system, the efficiencies of the individual chamber planes, and the effects of the analyzing magnet’s field on charged tracks that traverse it. The field is modeled as a simple dipole with an effective length as measured from the data. This same magnetic field model, incidentally, is used by the GEAN T monte carlo as well. All charged ISAJET particles within the fiducial volume of the detector are projected through the magnet into the MWPC system. A detailed description of this simple monte carlo for the tracking system is found in chapter 3. In addition, the interested reader will find a comparison of this monte carlo with data. Except for the trigger particle, no neutral particles from the monte carlo were analyzed by the DST level reconstruction routines. No simulation of the calorimeter’s response to the high p _L trigger particle was implemented here. Such a response was modeled, however, for the no background calculation to the direct photon signal; the details of this monte carlo procedure are given in the next chapter. The acceptance cuts in rapidity that were applied to the real data have also been imposed on the high p .L single photons and 1r°s generated by ISAJET. 6.3 JET ALGORITHM PERFORMANCE The performance of the Cone and WA70 algorithms is summarized in this sec- tion. There are three basic performance characteristics relevant for later studies. First, there is the question of how well each algorithm can determine the recoil jet’s direction. Second, does the jet reconstruction algorithm find the recoil jet a substan- tial fraction of the time. While the results for cos d’and M do not depend critically on the reconstruction efficiency, a low efficiency means a loss of statistics. The third issue concerns the precision and accuracy with which 2:, and 2:; are calculated. Of 199 immediate concern is the issue of jet axis resolution since this determines if cos 9‘and M are measurable. In addition, it can provide a measure of how often the jet is misreconstructed. All subsequent studies of reconstructed jets will involve a pseudo- rapidity cut of [17] S 1.0. Such a cut is necessary because of the pseudorapidity cut on individual tracks ([17] _<_ 1.5). 6.3.1 Jet Axis Resolution The previous work with the 11> distributions indicates that things are alright trans- verse to the collision axis. The particles clearly recoil from the trigger. The events are not expected to always be planar, but the (1) variable plays no role in determin- ing 2:, or 23. What is of great interest is how well a jet’s longitudinal direction is ascertained. A number of variables can be used to express the longitudinal direction. cos 0 and 17 in the rest frame of the colliding hadrons are the most relevant for this study; all results will be expressed in terms of them. Figure 6.2 plots the difference, 5cos 9, between the reconstructed and generated directions in c089 as a function of the sum cos HALO + cos OGEN for each algorithm. This particular choice of variables allows for a symmetric distribution of points centered about 5 cos 9 = 0 over the entire acceptance. Such a plot has absolute boundaries formed by the intersection of lines through the points (—2,0), (0,2), (2,0), and (0, —2). The allowed region of scatter is therefore a square. However, the plots in Figure 6.2 appear bounded by a parallelogram with the extrema in 6 cos 0 shifted away from cos 9“,; + cos BMC = 0. This effect is due solely to the pseudorapidity cut on the reconstructed jet axis. By inspection one can see that both algorithms yield very similar results. There is a dense band of points, centered about 6 cos 9 = 0, extending across each plot with an absolute width of about 0.3. In addition, there is a sparse uniform scatter of points away from the band in each plot. The dark band represents the resolution of each jet algorithm, while the diffuse scatter indicates the frequency at which the jet is 200 misreconstructed. Fortunately, the fraction of misreconstructed jets is rather small. A projection of each plot into 6 cos 9 appears in Figure 6.3. The HWHM indicates a uniform resolution in cos 9 of 0.1 for both algorithms. An estimate of the misreconstruction frequency can be obtained by measuring the fraction of each distribution in Figure 6.3 comprised by the tails. Out to [6 cos 9| = 0.3 the jets should be deemed properly reconstructed. Outside this interval there is a mixture Of correctly and incorrectly reconstructed jet axes with the relative fraction of misreconstructed axes increasing with increasing [6 cos 9]. By deeming all jets for which [6 cos 9] > 0.5 as improperly formed, and using this fraction to determine the “wrong” jet contribution between 0.3 and 0.5 in 6cos 9, the misreconstruction frequency has been found to be about 7% for the Cone and WA70 algorithms. It is also interesting to know how well the jet reconstructors track each other event-by-event. An advantage in studying the difference in cos 9 between the two algorithms versus cos 9cm“; + cos owns is that the monte carlo can be compared with the data! Such a study appears in Figure 6.4. It is easy to see that the data and monte carlo are similar and that the algorithms track each other very well. The dense band about 6cos9 = 0 is much narrower than in Figure 6.2, implying the reconstructors do not differ significantly in their estimates of the jet’s longitudinal orientation. Such a systematic correlation between the two algorithms is expected because they both rely on the same input track set. The diffuse spread of points in the Figure 6.4 represents the frequency for either one or both algorithms to misreconstruct the recoil jet direction. However, the central band contains those events for which both routines either correctly or incorrectly de- termined the recoil jet axis. The fraction of those events for which the “wrong” jet was reconstructed represents the frequency for which the input track set contains insuffi- cient information. A study has been done in which the difference between both jet al- gorithms is plotted against the difference between each algorithm and the monte carlo GCOSG GCOSG 1.6 1.2 0.8 0.4 -0.4 -0.8 -1.2 -1.6 1.6 1.2 0.8 0.4 -0.4 -0.8 -1.2 201 ISAJ ET MC - |- 1— b _ . I- .~ - D . I, |- — | V I- . ‘. I .. - , o z . ‘ — , . v- .. . _‘.' '- - . .’ .". '0 _ .. ‘- ' i' , .. '. h ‘ . ~ ' ‘ 1:65.“: ":2."':‘.'".I. -. " 1 J” 5‘."- . “...-'1 .‘...;..; — ‘ \ 2'? '. .'.'..~;'\'.-:': .L '- .:\"i. .‘ . ‘3’ ._._-l ‘5.‘ ,‘. . I- . . '1: ‘2: J -‘.P ~j', H. I} 5‘: l “):_?s\_-.-.‘. )\',~"$',6 Ci“- "'1in“ ,_,‘;.:~'-‘~I .. .; . : ”.... ..v '5'}- "‘fi' .2 ‘I._ a 9" ‘w;.‘"r 1.. 0:32;" s'ufl.‘ 3521'. V"d"“§<}"{§"‘i' .."...'J..;" 1.12)). ' w -- 1 - - - _ A, v 4 w x: t - . V. s “s‘,.- ‘5' _, ,‘_;1X \' 7‘0,‘ " '12:“: ‘ . \' .-.‘ ,;‘,-- , 'Cv’b-if . 1 . T — - n ' . ,-' '-" ' I-—-.* .'~ 'e; 4. 5" 1-’“‘ ‘- D‘ ‘ r " "-' .e- " 1"; 1’51 3- ‘ , ‘v’ 3' ‘7 ' '. )x’u‘ffif 35R 34'- '—.\‘L.Za'°'-.“' ..1’ '2 .' 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' ' - :.1 " , - '~ ' ._ I ‘. . ‘ o I . . . .I UIIIJIIILIIIJJIIHILIIIlIIIIlIILlllILIfIlIIlIllI l N -1.6 Figure 6.2: Scatter plots of jet resolution over the acceptance —1.2 -0.8 -0.4 0 0.4 0.8 1.2 CosOm+Cosem for Cone (Top) and WA70 (Bottom) algorithms. 1.6 2 202 CONE Algorithm WA70 Algorithm 0.2 0.2 I I 0.18 —- 0.1a _ 0.16 - 0.16 _- Z I - P 0.14 - 0.14 r- 0.12 L mg L t : 0.1 :- 0.1 — " "‘ L 0.08 — 0.08 — C I 1 0.06 b 0.06 r I I 1 0.04 - 0.04 _ '- T 1. i 1 0.02 — 0.02 r- ; I o 0 I J I I I l I I I Al -2 —2 -1 0 1 6CosO 6COSO Figure 6.3: 6 cos9 distributions for Cone (Left) and WA70 (Right) algorithms integrated over the accep- tance. 1.6 1.2 0.8 0.4 6Cos® o -0.4 -0.8 -1.2 -1.6 1.6 1.2 0.8 0.4 60030 c -O.4 —0.8 —1.2 -1.6 203 E _r Doto IL I? E. E. EIJIIIIIIIIJIIIIIIIIIlIIIIIILIIllIIIAIIIIIlllILlII -2 —1.6 —1.2 -O.8 -O.4 O 0.4 0.8 1.2 1.6 2 Cosem+CosGwo ;- MonteCorlo EIILIIIIIIIIIIIIIIIIIIIIIIIIIIIILIIIJIIIIIIIIIIIII -2 -1.6 -1.2 —O.8 -0.4 0 0.4 0.8 1.2 1.6 2 CosOm-t-Cosewo Figure 6.4: Scatter plots of 6 cos 9 between WA70 and Cone algorithms over the acceptance for data (Top) and monte carlo (Bottom). 204 The abscissa in each plot is projected out for I5 cos 6| < 0.2. Again, the technique of measuring misreconstruction by examining the tails of these distributions is used to determine the fraction of “wrong” jets beyond Icos 9AM; — cos OMCI = 0.3. This fraction is 5%. Clearly, it is the input track set which is responsible for most of the jet misreconstruction. Comparing one reconstruction technique against another also allows one to study the variation in resolution as an algorithm’s parameters are varied. Such a study has been done rwhere AR was allowed to vary between 1.0 and 2.0, while the factor in the exponential terms for 1111 and w; was varied between 2.0 and 5.0. No significant changes in resolution were observed for either jet reconstructor. This indicates that the systematics associated with jet axis reconstruction are not critically dependent on the reconstruction technique. 6.3.2 Jet Finding Efficiency There are a number of viewpoints concerning the jet finding efficiency. In the previous discussion, inefficiency was viewed in terms of how often the recoil jet axis is formed incorrectly. There is also the question of how frequently a jet is found given that an event contains a high p i w° or single photon. One expects that within the hard-scatter picture any event possessing such a high p i object will have a recoil jet. However, the limited acceptance of the experiment’s spectrometer, the p L cuts on the jet candidate tracks, the leading charged particle cuts, and the selection criteria of the jet algorithms all conspire to produce a jet finding efficiency substantially less than one. The jet finding efficiency can be estimated by taking the trigger’s p L spectrum for those events with a reconstructed jet, and dividing it by the inclusive p ‘L spectrum. This method has the advantage of being able to compare the monte carlo with data. 205 The jet finding efficiencies for both jet algorithms are plotted in Figure 6.5; the data is plotted with error bars and the monte carlo is superimposed as a dashed line. All plots show an increase in efficiency with p _L. This is due to kinematics, which favors the trigger and recoil jet to be at 90 degrees in the nucleon-nucleon rest frame at high p _L, and the scaling of the fragmentation functions. The WA70 algorithm appears to be more efficient than the Cone algorithm, implying the AR cut is a bit more selective. The greatest source of inefficiency are the leading particle cuts, which represent a 20% loss. Overall the monte carlo data is 10% more efficient at low p L with the data and monte carlo coming into agreement above 5GeV/c p i. This effect is not due to hardware or PLREC systematics since they should possess no p j dependence. Rather, this difference stems from the fragmentation functions being steeper, and/or the structure functions peaking at lower x values in the data than the monte carlo. 6.3.3 Parton Variables Before :1 and 2:; can be calculated the recoil jet’s momentum must be determined. This analysis makes an estimate based on the assumption that p i is balanced between the trigger particle and the recoil jet. It is important to see how well this premise works when intrinsic k Land fragmentation effects are present. Figure 6.6 illustrates the difference between generated and reconstructed jet momenta as a fraction of the reconstructed momentum. Both algorithms give consistent results. The peaks are centered about zero with HWHM’s of 25%. From the expression for the momentum of the recoil jet, PJET = pi/ sin 933T (6.3) and the estimated resolution for the reconstructed jet axis one can easily calculate the contribution to the smearing of Pm over the acceptance. This contribution alone 206 represents 2 80% of the total observed smearing in the peak of 6P/P! In Figure 6.7 the corresponding plots for single photon events are shown. By inspection the reader can see they yield slightly better estimates of the jet momentum resolution. All of these plots have an asymmetric tail extending towards increasing (SP/P. This tail is a combination of events with misreconstructed jets, and those containing a large kjenhancement in the direction of the trigger. No correlation between the frequency of jet misreconstruction and large 6P/ P values has been found. So, the right hand tails of the 5P/ P plots indicate the magnitude of the effect intrinsic kjhas on the misreconstruction of jet momenta. By subtracting the left portion of each histogram from the right half one determines the fraction of incorrect momenta to be 15%. Although the contribution of jet axis misreconstruction to the tails of the 5P/ P distributions is quite small, it does bring into consideration the application of general kinematical cuts, i.e. PJET < fi/Z, and 21,32 < 1. ' The resolution for 2:1 and z; is estimated from the monte carlo by computing 63/2; Recall that in addition to the p L balancing assumption, the trigger and recoil jets are assumed to be massless in calculating 2:1 and 22. Figure 6.8 and Figure 6.9 diSplay the parton a: resolution functions for 1r° and single photon events, respectively. Once, again both jet reconstruction algorithms yield consistent results. The asymmetric tails in the momentum resolution plots do not, however, carry over into these distributions. The 62/2: distributions for 7 events are centered near 0 with a HWHM of 10%. Unfortunately the 11’" plots are smeared about twice as much and are systematically shifted below 0 Z 10%. This systematic shift arises because 1r°s are usually only one of the trigger jet’s fragments. This difference between single photons and 1r°s implies that the kinematic regions for both classes of events, used to construct the cos 6‘ and M distributions do not coincide exactly. In summary, both jet algorithms have yielded consistent results as far as the resolution of various quantities is concerned. It is expected that the same behaviour 0.9 0.8 0.7 0.6 6 0.5 0.4 0.3 0.2 0.1 O 207 CONE Algorithm WA70 Algorithm 1 t i h- l- — 0.9 ~— - l- : t _ 0.8 — L 0.7 L .... 0.6 H‘ll : r 50.5 - r a l. 0.4 #- o.3 — C 0.2 - o.1 L P l. ILIIIILIIIIIIJJILLL OPIIIIIIIIIJIIIIIIII 4 5 s 7 a 4 5 6 7 s P, (GeV) P, (GeV) Figure 6.5: The jet finding efficiency for Cone and WA70 al- gorithms as a function of the trigger’s p j. Monte carlo is superimposed on the data. 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 208 High PT 1t° Events 0.1 rIfIIlIUr'III][FF—FTIIIIUIT'rIlIIIUrIIIIIIIIIIII—II l- 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 It‘ll[IIIIIIITTIIIIIIIIIIIIIIITIIIIII'TIIIIIIITTII (SP/P for Cone (SP/P for WA70 Figure 6.6: Resolution plots of the reconstructed jet momen- tum for 1r° triggers integrated over the acceptance. 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 209 IIlll'llTlerI'erIIIIlIllIIIIIIIIIIIIIIIIIIIIIII - High P, yoEvents .1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 IIIIIIIIIIIIII'1IT1TIIII[jIIITTITIIITIIlTTIIIIITT O l- l— 6P/P for Cone (SP/P for WA70 Figure 6.7: Resolution plots of the reconstructed jet momen- tum for 7 triggers integrated over the acceptance. 210 High P, 1T° Events 0.25 0.25 ~ + " l' 0.225 - 0.225 — 0.2 — 0.2 r— : E 0.175 — 0.175 - . L - l- . l- 0.15 '- 015 '- 0.125 *— 0.125 —- P I- 0-1 - 0.1 - I I 0.075 - 0.075 — I . t- i— 0.05 '— 0.05 '- P l- h l- 0.025 - 0.025 — - 1- - 1- bIlIJ LIIIIILI IJJIII_I oblIlII IIIIIIII LLllIlI—I -0.8 -0.4 0 0.4 0.8 -0.8 -0.4 0 0.4 0.8 6x/x (fix/x Figure 6.8: 62 / 2 resolution plots for parton momenta in high p _L 1r° events, integrated over the acceptance. 0.25 0.225 0.2 0.175 0.15 0.125 0.1 0.075 0.05 0.025 211 rTIIIIIIl—F‘FijTrTFIIIITIIIIIIIII{III—rillfij‘rliil IIIIII IIIlIlI -0.8 -0.4 0 0.4 6x/x High P, zzEsvents IIJIIII [Illl C 0.225 '- 0.2 - l. i- 0.175 l— r 1- Z 0.15 r- 0.125 -- 0.1 — l. C 0.075 r- 0.05 — 0.025 — i- l. t 1 . o I Illl 0.8 -0.8 —0.4 0 6x/x 0.4 Figure 6.9: 62/2 resolution plots for parton momenta in high p ‘L single photon events, integrated over the ac- ceptance. 0.8 212 will be observed in cos 9‘ and M as well. From the lack of sensitivity to a particular jet algorithm, even under a reasonable variation of its parameters, it can be concluded that the information required for this analysis is contained in the leading jet particles. This property is an artifact of the independent fragmentation scheme, but it appears to adequately represent the data for the task at hand. 6.4 MEASUREMENT OF cos 6’AND M For the studies of cos 9" and M only the Cone algorithm will be utilized. There is still the issue of what it means to measure these quantities. By measuring the cos 9" and M distributions for the 7 + jet and 11'" + jet systems it is hoped that one is essentially reconstructing the same distributions for the final state partons. To check whether or not this is indeed the case the angular and invariant mass distributions at the parton level will be compared to those reconstructed from the complete event generation. The parton level distributions will be constructed from ISAJ ET data . generated without any evolution (k l smearing, underlying event) or hadronization processes activated. There are several general kinematical cuts that will be applied to the monte carlo data in performing this study, and in subsequent studies with the real data. Because . the possibility exists for misreconstructing the recoil jet’s direction, unphysical values for the jet’s momentum and/or the parton momentum fractions may occur. By defi- nition 2, and 23 can never be negative, but they can exceed 1. Such misreconstructed events will be eliminated from consideration by imposing the following kinematical constraints 3 PJET S ‘12.: 23 _<_ 1 213 6.4.1 cos 0* Figure 6.10 illustrates the effects of applying those cuts in succession that provide uniform acceptance in cos 9“. Clearly the edges of the reconstructed distribution rise relative to the central region in accordance with the discussion presented in the first chapter. The smearing observed in the reconstructed parton momentum fractions is also present in M. In addition, this smearing is different for 7s and 1r°s. This doesn’t compromise the M cut’s effectiveness, however. M is proportional to the P1 of the trigger particle, and it is the p i cut on the data which introduces the bias in cos 0"“. So, if M is cut on accordingly, the bias is removed. Figure 6.11 shows the 1,3 distribution generated by ISAJET, and the interval of 173 for which there is uniform acceptance in cos 0“. Any smearing in this variable will tend to “feed” down from bins of smaller 113 to bins of larger 1,3. Hence, the smearing may produce a net loss of events, but it will not affect the reconstructed distribution’s shape provided the smearing is uniform over the acceptance used in constructing cos 9". The absolute cos 9" distributions for 1r°s and direct photons are shown in F ig- ures 6.12 and 6.13 respectively. The cos 9“ distribution for 1r°s agrees vary well with the one corresponding to just 2-2 parton scatters. The parton distribution is plotted in Figure 6.14 as a smooth curve. All of the parton level distributions are referred to as the generated distributions. The parton level distribution for direct photon events, however, appears to rise faster than the reconstructed distribution. The effect is not very large, and the ability to discriminate between the two types of events in cos 6" is not compromised. The reconstructed monte carlo cos 9" distributions will be used in comparing these results with the actual data. 6.4.2 gross Sections in M Reconstructed invariant mass cross sections for high p ‘L 1r° and direct photon events are displayed in Figures 6.14 and 6.15 respectively. Again the corresponding (l/N,,,)dn/dCosO° 214 CONE Proton Beom MC n° Events T>O.310 |n.l<0.301 ........ No Cuts - _ _ No lml Cut 1 + +1 + \ \ \ + ,, +9: IIIIjIUIUlUIITTTfiTIIIIIIIIIIUIIIIIIIIIF IJIIIIIIIIIIIJIIIIIIIIJIIIIIIlIILIlgLIIILIIlllIlII -1 —0.8 -0.6 -O.4 -0.2 O 0.2 0.4 0.6 0.8 1 CosO' Figure 6.10: Effects of M and 17;; cuts which unbias the recon- structed cos 0“ distribution. 0.07 0.06 0.05 0.04 0.03 0.02 0.01 215 T111]IIIUIIIIUIIIIIlIIlIlIIITIIUIIIIT IIIIIIIIIIIIIIIIIIIIIIIIlLIIIlJI_IlIIIII L I -O.8 -O.5 -O.4 -0.2 O 0.2 0.4 0.6 770 Figure 6.11: 1,3 for high p 1 1r°s produced via proton-nucleus collisions. 0.8 (1 /N.),)dn/dCosO° 216 CONE Proton Beom MC n" Events T>O.310 I17.l<0.301 Duke-Owens l + + + $101+; ++++ TIIIIIIIIIIIIIITTFIIIIIIIIIITIIIT1IIjI IIIIILIIIIILLIIIIIIlIIIIIIILIlIIlIllIIILLlIllIIII -1 -0.8 —0.6 —0.4 -0.2 0 0.2 0.4 0.5 0.8 CosG' Figure 6.12: Reconstructed and parton level cos 6“ distribu- tions for high p 1 1r° events. The parton level dis- tribution is shown as a smooth curve. 1 (1/N,,,)dn/dCosO' 217 CONE TIT! [FTIrrITIIIYITIlIIIIIIIfIITYIIlIrlI Proton Beom MC 7 Events T>0.310 |1).| 9.82 GeV I ....... 001 T _ _ 0011 C. r 1- , I”IIIIIIJIIIIIIIIILJIIII_IEII 0 0.2 0.4 0.6 0.8 1 CosO' (1/N.,,)dN/dCosO' 4.5 3.5 2.5 0.5 II—IlIIIIIIIIIIIITTIlT—ITIIIIIlIIrTIlIIfI T—I—IIIIII ,‘11 Single 7 Events (subtracted) 11" Beam M > 9.82 GeV IIIIILIIIIIIIIIIIIIIIIII 0 0.2 0.4 CosO' 0.6 0.8 Figure 7.4: Absolute cos 6" plots for 7s and 1r°s in 1r" data 1 (1 /N.,,,)dN/dCosO° 4.5 3.5 2.5 1.5 0.5 _ Single n‘Events .... Proton Beam 2 M > 9.82 GeV I ....... 001 .— _ - .0011 C" 7- P E 1- I. P 1. I.- L I-JIIIJIIIIlIIIIIIIIIIIIII 0 0.2 0.4 0.6 0.8 1 0030' 234 (1 /N.,,)dN/dCos0° 4.5 3.5 2.5 1.5 0.5 .. Single 7 Events : (subtracted) _— Proton Beam I ~— M > 9.82 0111/ : ....... 001 _— - _ 0011 1. 1— l- "' / n— ’3' 1— ’3'. 1- {1" —-1-- {.- l' 5.?- ’ " —‘-7--“‘ -—11—-"“'. PIIII ILJ IIILIIIIIIIIIII 0 0.2 0.4 0.6 0.8 1 CosO' Figure 7.5: Absolute cos 6" plots for 7s and 7r°s in proton data (dN,/dCos®')/(dN./dCosG‘) (d N,/dCosO')/(dN./dCosG') 1.8 1.6 1.4 1.2 0.8 0.6 0.4 0.2 1.8 1.6 1.4 1.2 0.8 0.6 0.4 0.2 O O nu 235 III‘IIIIIIIIIIIIIIIIIIIIIIII ++_1_ IIIIIIIIIIIIIIIII 11‘ Beam M > 9.82 GeV ............................................................................................................................................ I I I I l I I I I I I I I I I l I I I I I I I I I I I I I I I I 1 I I I I I I I I I I 1 I I I I I 0 0.1 0.2 0.3 0.4 0.5 CosO' 0.6 0.7 0.8 0.9 1 Proton Beam M > 9.82 GeV ....................... IIIIIIIIII'IIIIIIIII IIIIIIIIIIIIIIIIIIIIIIII I I I I I, I I I I I I I.I .L_I I I I I I I I I I I I I I I I I I,.L I l I I I I I I I I I I I I I L 0.1 0.2 0.3 0.4 0.5 CosO' 0.6 0.7 0.8 0.9 Figure 7.6: 7 to 1r0 ratio in cos 6“ for 71" data (top) and proton data (bottom) 1 236 Figures 7.7 through 7.9 display another set of cos 6" plots for pi 2 5.0 GeV/c. The 1r‘data shows the same trends as the low p .1. sample albeit with greater significance. The proton data is quite different though. At high p j it has the same behaviour as the negative data! These trends are expected from QCD as well. Of course, the observed change is due entirely to a change in the shape of the direct photons’ angular distribution. An explanation for this change is that there is less 7r° background at high p ‘L. The difference between 7s and 1r°s in the high p _L proton data is not as significant as it is for the 11" sample, but the 7 /1r° ratio doesn’t rise as fast for protons either. The high p _L sample exhibits a direct photon signal without background subtrac- tion as Figure 7.10 and Figure 7.11 reveal. Only the 1r‘ data shows such an effect. This behavior is consistent with that observed in the A43 distributions, presented in Chapter 5. What appear to be definite differences between the 7 + jet and 11" + jet systems by visual inspection are quantified below. A simple way to do this is to compute the x2 difference between corresponding angular distributions as follows, 1 1 ( (cos 6;,—cos6;o,.)z ) 2 — _ XPDF _ 4 E; 62 cos 6;,- + 62 cos 6:0,. (7.4) The x2 is for four degrees of freedom because the central bins have no information content. Note that the 11’" distributions have been rebinned for this operation. The observed differences in the angular distributions are summarized in Table 7.2. The meaning of % confidence in the table’s last column is the percent chance that the computed difference ()8) is not due to a statistical fluctuation. A simple linear fit has been applied to the various 7/1r° ratios. Except for the low p _L proton data, the results are consistent with a 1 — cos 6' dependence at > 30 significance. The ratio plots are inconsistent with a constant value of 1, which is expected in the case of no difference between 75 and 1r°s. Indeed, the 7 /1r° ratio for the proton data with a p J_ cut of 4.25 GeV/c is consistent with 1 across the whole 237 Table 7.2: Summary of differences between 75 and 1r°s in cos 6‘ Beam p1 Cut (GeV/c) X1230? % Confidence Proton 4.25 0.583 >324 Proton 5.0 2.93 > 98.0 Proton 5.0 (Unsubtracted) 1.31 > 73.2 1r“ 4.25 2.45 > 95.4 1r“ 5.0 5.15 > 99.9 1r" 5.0 (Unsubtracted) 2.83 >975 accessible range of cos 6" (see Figure 7.6). 7.3 1r° + jet AND 7 + jet M DISTRIBUTIONS The invariant mass distributions are presented as absolute cross sections, and as ratios of absolute cross sections. The 1r° + jet and 7 + jet cross sections are given by, 1 dd _ NEvents C (7 5) 2M 11M 11 cos 6* d4) - NB,mm 21rAM2MA cos 6' ' NEvents = the number of reconstructed events N13,“, 2 the number of incident beam particles AM = the bin size in M A cos 6‘ = interval of cos 6" integrated over C = the trigger particle corrections 1/(211'AM2MA cos 6") = normalization to an element of phase space The calculation of Ngem is essentially just the total beam particle count, corrected for the time the apparatus could not take data. There are additional corrections for inefficiencies in the discrete logic as well as beam absorption in the target. The details involved in calculating the live-triggerable-beam (LTB) are found in Chris (1/N.,,)dN/dCosO' 4.5 3.5 2.5 1.5 0.5 238 _ Single 11' Events :— 11' Beam )— . M > 11.5 GeV 1- ....... DOI - _ _ DOII : 1 __ 44 1 : —1— I P i L l 3 . ' i ,- ' :' I S C I :‘ _ 1 ,- - 1'? . 1 1— ...11...‘ I g. .. I . _ I j - I : I.-" _. I." D ’0... - ‘5" 50 —11— fi' .' ..IIIIIIIIJIIIIIJIIJIIIIII 0 0.2 0.4 0.6 0.8 1 0050' (1 /N.,,)dN/dCosG' 4.5 3.5 2.5 0.5 1 Single 7 Events : (subtracted) ; 11‘ Beam : M > 11.5 GeV I ....... 001 .— - _ Don P P 1- 1- ' / — [‘0' .. /.,-’ 1- ’o'. 4" 1- "_"'— l.’ ’- p.031. _IIIIIIIIII IIIIIIIIIIIII 0 0.2 0.4 0.6 0.8 1 CosO' Figure 7.7: Absolute cos 6" plots for 7s and 1r°s in 11‘ data (1/Nm)dN/dCosG)' 4.5 3.5 2.5 1.5 0.5 O Single 11' Events Proton Beam M > 11.5 GeV ....... DOI IIIIIIIIIIIIIIIIIIjTI—FTTIlI'IIIIIIITl IIIIIIIILI_IILIIIIIIIII ojIIIlIT 0.2 0.4 0.6 0.8 CosO' 1 239 (1/N.,,)dN/dCosO' 4.5 3.5 2.5 1.5 0.5 1. Single 7 Events I: (subtracted) L. Proton Beam I 1.4 > 11.5 GeV : ....... 001 :— _ _ 0011 P— )— L - / — -—1r—- ’3’ 1— I." 1— In" .’ ’- "fipflI' 1. _IIIIIIIJJIIIIIIIIIIIIIII 0 0.2 0.4 0.6 0.8 1 CosO' Figure 7.8: Absolute cos 6* plots for 7s and 1105 in proton data (dN,/dCosB')/(dN./d0050') (dN,/dCosB')/(dN./dCosB') 1.8 1.6 1.4 1.2 0.8 0.6 0.4 0.2 1.8 1.6 1.4 1.2 0.8 0.6 0.4 0.2 240 IIII IIII IIII IIII IIII IIII IIII IIII IIII I I I I I I I I 11' Beam M>11.SCeV :IIIIIIIIIIIILIILIIILILLIIIIIIlIIlIIIIIIIIIIIIIII 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 CosO' E... Proton Beam : :_ M > 11.5 GeV ELIIIIIIIIIIILIIIIIIIIIIIIIIIIlIIIIILIIlIIILILJILI 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 CosO' Figure 7.9: 7 to 11° ratios in cos 6* for 11‘ data (top) and pro- ton data (bottom) (1/NdeN/dCose' 4.5 3.5 2.5 1.5 0.5 IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII Single 11' Events 11' Beam M>11.SCeV IIIIIIIIIIJLLIIIIIIIIJII O 0.2 0.4 0.6 0.8 0030' 1 241 (1/N.,,)dN/dCosG)° 4.5 3.5 2.5 1.5 0.5 IIIrlIIIIIIIIITIIIIIIIIIIIIIITIIITIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIII Single 7 Events (unsubtracted) 11' Beam M>11.SGeV O 0.2 0.4 0.6 0.8 CosO' Figure 7.10: Absolute cos 6" plots for 7s and 1r°s in 11‘ data with no 11° background subtraction for the 7s 1 1.8 '01 1s ix: (dN,/dCosO‘)/(dN,./dCosO‘) .0 m .1 .0 m .0 4's -O.2 242 IIIIIIIIIIITIIIIIIIIIIIF 11’ Beam M > 11.5 GeV 75 Unsubtracted IIIIIIIIIIIIIIIIIIIIIIII + IIIIIIIIIILIILIIIILIIIIIIIIlLIIIIIIIIlIIIILIIII O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 CosO' Figure 7.11: 7 to 2° ratio in cos 6" for 1r' data without 1ro back- ground subtraction 1 243 Lirakis’ thesis [48]. Absorbed into Nana“, is the number of target nucleons per unit area. The conversion factor from events to nucleons per unit area is given by, NoALp C 7.6 MW 7 ( I N0 = Avogadro’s number A = the atomic mass number L = the target length p = the target's density MW = the atomic weight in g / mol C = conversion from cm"2 to mb All cross sections in M are given in units of mb/GeVz. The target was composed of copper and beryllium elements; the configuration did change to just beryllium for certain data sets. NEW,“ has been computed for the whole target in accordance with the actual copper-beryllium configuration on a run-by-run basis. A cut in cos 6" is necessary for the absolute M distributions because different trigger threshold sets are to be combined. A cut in 113 is not required as long as the monte carlo data is processed in like fashion. The reason is that the geometric acceptance in 1,3 is the same for all M. The results of the ISAJ ET analysis are superimposed on the data as parametrized fits. The absolute M cross sections for 1r° events have been parametrized as ex- ponentiated linear fits. Those for direct photon events have been parametrized as exponentiated quadratic fits. The results from both the DOI and DOII structure function sets will be presented. Figures 7.12 through 7.15 show the absolute M cross sections for 11° + jet and 7 + jet events. It is clear from inspecting all four plots that the data is tracked by the DOI and DOII monte carlo sets. There does not seem to be a great deal of preference for one set of structure functions over the other, particularly in the direct photon data. 244 More statistics are required. However, the 7 + jet cross section for 11‘ data definitely has a shallower slope than the corresponding 11° + jet distribution. It appears that the two mass distributions cross over, i.e. 7/11° 2 1 at 18 GeV. This corresponds to a p 1 of 9 GeV at 90°. The shape difference is also present in the unsubtracted 7 + jet cross section as Figure 7.16 clearly shows. Note how the unsubtracted distribution turns up at low M indicative of a substantial 11° background there (low p j). Unfortunately, the 7 — 11° difference is not very significant in the proton data. This is mainly due to a lack of statistics as is evident from the size of the error bars. Part of the problem may also be that the low M region rises too steeply because of residual 11° background. Such behavior is consistent with earlier results in Act and cos 6" at low pi. The absolute M cross sections are plagued by a number of large systematic effects. Most notable is the smearing that results from the assumptions of massless jets, and p _L balancing between the trigger particle and recoil jet. There is the uncertainty in the electromagnetic calorimeter’s energy scale too (~ 1%); this effects the trigger par- ticle’s reconstructed four-vector. These effects are very substantial because the cross sections are so steeply falling. In fact, there is already a 25% systematic uncertainty on the inclusive cross sections alone! Besides~these experimental uncertainties there are theoretical ones as well. They are the value of AQCD, the definition of Q2 and the amount of primordial k _L. High p _L 1r°s suffer an additional uncertainty due to an incomplete knowledge of the z-distribution or fragmentation function. All of these problems can be minimized, even cancelled, by studying the ratio of corresponding cross sections for 11’ and proton data. The variation of these ratios in M is dependent on the hadrons’ internal structure, if any, and the behavior of 7s and 1r°s should be different. For direct photon events, the ratio is particularly sensitive to the value of 173. In principle it should be able to discriminate between the DOI and DOII sets. The physics da/ZMdM (mb/GeV’) 245 : "'-.11° Events '- \ '1_ + 1- \ . - .. \ 11 Beam \ . \ 2..._ lCosO'l<0.4 \ ’1, :- \ \—*-+— ............. DOII F- \ 3.. : \ \ - - _. _ DOI 1- \ \ _ 7*.— \ 1— ‘ ' .. \ \ ".. — \ ..I I— \ ... 2 fi— 1- \ 3". "’ \ ,. \ - x F- \ .... \ ‘. E \ "... \ ‘.. \ ‘. t \ \ ’- \ I- \ 0. b \ 'I.. \ I- \ l \ -\ .o r \ Z \ " \ '- \ '- \ \ '- \ L'— 1. J 1 I 1 I 1 I 1 I I I 8 I O I 2 1 4 1 6 1 8 M (GeV) Figure 7.12: 11° + jet cross section in M for 11“ beam 20 da/2MdM (ms/Gev') 246 I Ij IIII I IIIIIII I I IIIIIII I I IIIIII' I I I I IIIII' I I IIIIIII 7 Events Subtracted 11' Beam ICosG‘l<0.4 ......... DOII I 1 I 1 I 1 I 1 I 1 I 8 10 12 14 16 18 M (GeV) Figure 7.13: 7 + jet cross section in M for 11" beam 20 I'r-‘r-Fe-“g da/2MdM (mb/Gev‘) 247 E 11° Events : \\ Proton Beam \ In. . \ \ lCosO'l<0.4 __ DOII 1101 ,. E E— 1- \ C [- I 4 I 1 I m I 1 I 1 I 8 I O I 2 I 4 I 6 18 M (GeV) Figure 7.14: 11° + jet cross section in M for proton beam 20 da/ZMdM (mb/oev’) 248 E 7 Events : Subtracted ' Proton Beam __ ICosO'I 1r° +jet + X) =a+exp(b+CoM) (7.7) The bin-by-bin uncertainties in the fit are insignificant compared to those in the data. One can see by inspection that the ratio is greater than 1, being centered around 1.5. Such a trend is expected since the pion contains half as many partons on average as the proton, and the beam energies were the same. Thus, the value of 2 is typically larger for a pion than for a proton, and M is the proportional to the geometric mean of 21 and 23. It is fair to say that the DOI and DOII sets merely bracket this sample. The ratio for 7 + jet events appears in Figure 7.18. The general trend here is for a larger ratio at high M than for 1r°s. Although the error bars are quite large, such an effect is consistent with an additional enhancement over parton counting due to a larger relative contribution of the annihilation mechanism in 11" data for direct photons as opposed to 1r°s. Most dramatic of all is the difference between the DOI and DOII predictions with the data clearly favoring DOII. If the low point at small 251 M is ignored, a x2 difference between the monte carlo curves and the data shows the DOI prediction to be inconsistent. Some qualifications are in order. The major contribution to the )8 occurs in the last bin and the statistics are pretty low. While tantalizing to say the least, this result can only be of a preliminary nature. Five events from the 11" data and two events from the proton data contribute to the last point. The error bars have been calculated using the assumption of Gaussian statistics. The proton data events are all above 7GeV/c in pj_, while those from the 11‘ data are all above 6GeV/c. The trigger particle rapidities are all within y = :I:0.7, which is the range used in the inclusive analysis. The acceptance and reconstruction efficiency corrections are well understood within this region. Finally, the ISAJET rapidity distributions for high p _L single photons are in agreement with the subtracted data distributions, especially for p j 2 5.0 GeV/c. There is therefore no apparent systematic bias in the last data point. However, the issue of just what the value of 716 is needs to be resolved with a higher statistics sample, whose systematics are better understood than at present. 7.4 Ennons A few comments about errors are in order. The error bars on the data distribu- tions are the statistical errors multiplied by the systematic corrections to the trigger particle. All corrections currently available in the data summary library of E706 anal- ysis code have been applied. The shape of the cos 6““ distributions could in principle be driven by the corrections. However, studies of cos 6* versus the various corrections have been done and it has been determined that they are not responsible for the observed shape differences between the two types of events. As mentioned earlier, the absolute cross sections possess large systematic uncer- tainties. The uncertainty from the inclusive analysis is 25 %. This number was arrived at from a careful study of the data and varying the input parameters to the data driven 252 do(11'N —> 11°+Jet+X)/d0(pN —> 11°+Jet+X) . F 11° Events : l P A 7+Jet+X)/da(pN —) 7+Jet+x) 10 253 : I’ 7 Events L 1I Subtracted _ I C I’ NO CosO', 17. Cuts _— 1’ ............ DOII - I - ’ - - - _ DOI '- I ’- I _ I I. I _ I .- I .- I [— I i / r I ’- I ’- I _ / - / ' l ' I - I I e _ ..1' r F -.-'-‘—‘— - 1 I 1 1 1 4 I 4 1 6 1 8 M (GeV) Figure 7.18: Ratio of absolute 7 + jet cross sections between 11‘ and proton beams. There is no cos 6“ cut. 20 254 background monte carlo over known limits [49]. Unfortunately, the systematic error arising from the jet reconstruction technique cannot be determined in any absolute sense, but is inherently model dependent. No physics monte carlo corrections have been applied to any of the results presented in this chapter. Rather, cuts have been applied to unbias the data as much as possible, and the monte carlo data has been subjected to the same jet reconstruction procedure and cuts. Finally, the 7 /1r° ratio in cos 6" and the ratios of cross sections in M minimize the effects of smearing on the result since numerator and denominator are similarly effected. Chapter 8 Summary and Conclusion This analysis represents a logical extension of the inclusive 11° and direct photon analysis. After selecting a high p j sample of 11° and single 7 candidate events atten- tion turned towards the associated event structure. In particular, the charged particle structure has been used to establish the existence of jets in these events. The pres- ence of jets is manifested in the correlations found in the A45 and Ay distributions presented in chapter 5. These correlations are consistent with a 2-2 hard scattering mechanism, acting among hadron constituents. Furthermore, these correlations have been utilized by a jet-finding algorithm to reconstruct the recoil jet’s spatial orien- tation event-by-event. The recoil jet’s direction together with the trigger particle’s four-vector have subsequently been used to reconstruct the cos 6" and M distributions of the 2° + jet and 7 + jet systems in their rest frames. The principle thrust of these studies has been to determine if 7 and 11° events are different from one another as QCD predicts they are. The 11‘ data has proven very fruitful in this regard. The shapes of the Ad), cos 6“ and M distributions for single photons are all significantly different from those for high p l 1r°s. In addition, the 11' data above 5.0 GeV/c in p ‘L reveals these differences without any 1r° background subtraction, and at a high degree of significance. Unfortunately the proton beam data’s results are not very convincing. No direct photon signal was found below 5.0 GeV/c in p _L even with a background subtraction. Above 5.0 GeV/c however, the angular distributions do show the expected difference. The differences observed in cos 6* have also been seen by the high energy collider experiments CDF and UA2 [50, 51]. The M distributions reveal only a slight difference in slope. Finally, the ratios of 7 + jet and 11° + jet cross sections in 11' and proton beams are different, but the error bars are large. Nevertheless, there is a definite trend for the 7 + jet ratio of 255 F. —_" a 256 cross sections in a" and proton beams to be larger than the corresponding ratio of 11° + jet cross sections as M increases. The ISAJ ET generated data possesses similar jet correlations to the real data. The agreement between data and monte carlo is very good for the angular distributions. The DOI and DOII sets of structure functions allow ISAJ ET to bracket the data’s M cross sections. The ratios of these cross sections in 11‘ and proton beam also track well, especially for the direct photons. Indeed, the 1988 data supports a “low” value of 11¢, implying a “hard” gluon distribution for hadrons. The DOII prediction is consistent with the 1r" to proton beam ratio of direct photon cross sections in M while that for DOI is not. However, the statistics are rather poor, and all the errors have been assumed to be Gaussian. One can look towards the new higher statistics data sample, and an improved tracking system simulation to ascertain the value of 113 with better confidence. Hopefully, a direct photon signal before background subtraction will emerge for p ivalues above 6.0 GeV/c in the new proton beam data. APPENDICES Appendix A Corrections to the “Kick” Approximation The following is a summary of the various corrections to the p j “kick” approx- imation. These corrections are important in obtaining the correct matching of up- stream and downstream tracks. Consequently, the momentum calculation becomes more reliable. The corrections described below take into account the non-negligible z-component of the analyzing magnet’s field, the change in the y-view slope of a track as it traverses the magnetic field, and the momentum dependence of the intersection point in z of corresponding upstream and downstream tracks. All of the field corrections can be expressed in terms of the angles of tracks, a and ,6 at the entrance and exit planes of the magnet, the angle of the track with respect to the bend plane, 1), and the effective length, L0. The reader is referred to Figure A.1 for an illustration of these quantities. The effect for a 7‘- fl and Ap / p ~ 1 in the x-view is given by Lo 2 6x1: —;(a + 911a — 11) (1.1) The shift due to the p,BI coupling is L0 . . . 2 6x; = ——2-(81na — smfl) smn (A.2) There are three shifts in the y-view. First, there is the effect of the Psz coupling tann 2 6y, = — (sina — sin ,6)[Ao(tana + tan 6) + Lo tan 6] (A3) where A0 is the distance from the vertex to the entrance plane of the magnet. The correction for p. changing in the bend plane is split into two pieces. The track inside the magnet follows a spiral path while the kick approximation assumes straight lines. Hence, the real downstream track is too high by 257 258 $2 ‘\ ‘R \ \ \I 'x \ \. \ Y x , A ‘. ’\ 1 \ . - \ l \ . I '\\. l '\\ l " 1 -‘I- X1 I 'J >2 Figure A.1: Top: A track’s orientation in the bend plane as it passes through the analyzing magnet’s field. Bot- tom: The angles involved in magnetic field correc- tions. 259 53’: = tanfllR(a " 16) — L0! a - 13 = Lo tann[sina _ sinfl — 1] (A.4) 2 563(1):2 + a6 + 33)tan17 (A.5) where R is the track’s radius of curvature in the bend plane. The change in the x-view slope produces an offset at zc because the apparent slopes, tan n/ cos a and tan 11/ cos 6, rather than the actual slope out of the bending plane. Thus, Lo 1 Lo )2 + (1 — cosfl)_2_l (A6) 6Y3 = tan](1 — C08 (1 The linking procedure is different for the X and Y projections of the space tracks. However, both methods project the upstream view tracks to the center of the magnet and attempt to match them with the proper space track projection via separate selection procedures. All of the above corrections are applied before matching is attempted. Appendix B Fake Tracks The following is a description of the two methods used in estimating the fraction of fake tracks in the data. Both methods assume that the high quality 16-hit tracks are all real. Recall that a high quality track is one with x2 S 1, |by| S 1cm, and is linked in the x—view to an SSD track belonging to the primary vertex. The first technique is known as the LAC method. As its name implies, it utilizes the data produced by the electromagnetic calorimeter. Scatter plots of the differences in X (AX) and Y (AY) between each track and the nearest electromagnetic shower was constructed. The tracks used in making the plots had to have momenta greater than 5GeV/c, the LAC’s “ turn on” point, and |y| S 0.7, the LAC’s acceptance. Two scatter plots were used. One was for all tracks satisfying the momentum and rapidity cuts, and the other was for those tracks that, in addition, had |b,,| S 1 cm. The absolute limits of each plot are 0 to 10 cm. Those tracks with AX,.AY S 2.0 cm were deemed to have been “seen” by the LAC. Figure B.1 displays one of these scatter plots. In order to correct for the LAC’s inefficiency the detection efficiency for all high - quality 16-hit tracks as a function of their momenta was measured. The detection efficiency for all high quality tracks was measured also. Plots of these efficiencies appear in Figure B.2. Those scatter plot entries for which AX, AY S 2.0 cm were then corrected by the appropriate {(P) for high quality 16-hit tracks. A second study performed the correction using the £(P)s coming from all high quality tracks. The ratio of weighted contents in the region AX, AY S 2.0 cm to the total contents (weighted and unweighted) yields the true track fraction. The fake track percentage is just this number subtracted from 1. 260 10 AY (cm) 01 261 '] I I II 'I .l I I I I l I I I I' I I If I I47] I II’I Ii 1’ I I’ I I' I I I ’I I. I II ITTI' I l I I' I I I .0 -J'\ ' . .0 ' 5'73: '7 I .- .' ... ..t-I.rIIIIL.IIII.I°I-IIIIIIIIIIIIIIIII'IIIII'IIIIIIIII'IIIIIIII 0 1 2 3 4 5 6 7 8 AX (cm) Figure B]: Scatter plot of AX vs AY for tracks and nearest showers 9 10 1.4 1.2 0.8 0.6 0.4 0.2 1.4 1.2 0.8 0.6 0.4 0.2 O o IIIII—IIII4FLII'IIIIIIITIIITIIIIIIIlII + + + 262 + ++++++++++++TL++‘_ F' e _r —s._ O IITIIIWITITIIIIIIIIIIIIIIII'I Figure B.2: P (GeV/c) EMLAC efficiency in P for high quality 16-hjt tracks (top) and all high quality tracks (bottom). 263 The second method employs the y-view impact parameter distributions for physics tracks that are linked in the x-projection to an SSD track belonging to a primary vertex. It is known as the by method. Such an impact parameter distribution is shown in Figure B.3. Clearly, tracks that are linked in x to an SSD track associated with a reconstructed vertex should have small lbyl; those which do not are suspicious. Those tracks for which Ibyl 2 2.0 cm have been deemed fake; a flat contribution under the peak in the by distribution has been assumed. To account for improper linking of real tracks in the tails a similar by distribution was made for the high quality 16-hit tracks. The ratio of entries for lbyl 2 2.0 cm to those inside |b,,| S 1.0 cm was used to subtract off a portion of the tail in the distribution for all tracks. The fraction of fake tracks, including the contribution under the peak was then estimated from the subtracted distribution. The results of these studies are summarized in Table B.1 for all by and for Ibyl 5 1.0 cm. LACl and LACZ refer to the separate studies using efliciency corrections for 16-hit high quality tracks and all high quality tracks respectively. Notice that the impact parameter method yields very small fractions while those measured via the LAC technique are considerable. However, the results of the LAC method, using the efficiency corrections for all high quality tracks appear consistent with the by method based on their variation. In addition, the error bars on the plots of Figure B.2 indicate that both sets of efficiency corrections yield consistent estimates for the percentage of fake tracks. From these studies it appears that the tracking data contains fake MWPC tracks at the S 1% level for Ibyl S 1.0 cm and S 2% overall. 10 264 I IIIIII] I I IIITTI IIIIIIII I IIIITIII I I P p JlJllllLLliLLJJllLllJllllllll l 111 IllllllllJlllLLJ -25 -20 —15 -1O -5 O 5 10 15 20 25 b,linked Figure B.3: b, distribution for physics tracks that are linked in the x-view to an SSD track, assigned to the primary vertex. 265 Table 3.1: List of fake track fractions. Beam Method IbyISl.0cm(%) anb,(%) LACl 2.97 9.39 + LAC2 -.946 1.32 + b, .0592 1.39 - LACl 2.92 9.41 - LAC2 .208 3.32 - b, .0586 1.41 Appendix C Track Reconstruction Efficiency The issue of track reconstruction efficiency will now be addressed. This efficiency can be estimated by studying the relative multiplicities of 13, 14, 15, and 16-hit tracks. Such a distribution appears in Figure 0.1 along with the MC prediction. The monte carlo prediction uses the ISAJET monte carlo’s output, and projects the charged particles through a simulation of the magnet and MWPC system. Such a simulation takes into account the effects of the analyzing magnet’s field, the geometric acceptance of the wire chambers, and most importantly, the planes’ efficiencies on the relative multiplicity of 13, 14, 15, and 16-hit tracks. However, it completely ignores the effects of noise and the reconstruction program. Figure C.2 shows four plots of relative hit multiplicities. Each plot is for one of the separate sets of data used in the analysis. The sets are distinguished by the time at which they were accumulated, and by the sign of the beam used to generate them. The sets are time ordered with set E being the earliest, and set A the latest. Sets A and D were generated with negative beam; sets C and E were generated with positive beam. Each of the plots has the monte carlo result superimposed on it. It is clear by inspection that the shape of the distribution has a time dependence. It also looks as though PLREC might be reconstructing 14-hit tracks in favor of 15-hit tracks because the l3-hit and 16-hit fractions are closer to the monte carlo result. This effect should not degrade the reconstruction efficiency though. Overall'the monte carlo distribution does have a greater efficiency for seeing tracks than the data, except possibly for set E. Nevertheless, all the distributions are quite similar, implying that the reconstruction efficiency for the data is close to that predicted by the monte carlo. The monte carlo reconstruction efficiency can be calculated explicitly from the plane’s efficiencies. The result is 98%. One can average the efficiencies and use the . 266 267 binomial probability distribution to calculate the reconstruction efficiency as well. The binomial probability distribution i.e.hit or no hit, is given by NI 13”“): k!(N ; k)! < e>"(1— < e>)N"‘ (C.1) where N = 16 and k is the number of hits on a track. < e > is the average plane efficiency. The reconstruction efficiency is obtained by summing the probabilities corresponding to k = 13, 14, 15, andl6. Again the answer is 98%. A similar procedure can be applied to the data by finding a number 6 such that the corresponding binomial distribution matches the data. The number 6 takes into account PLREC inefficiencies, the effect of geometric acceptance on event topology as well as the planes’ efficiencies. There is reason to believe that a major portion of the difference between data and monte carlo is due to variation in the actual planes’ efficiencies over the course of the run. One reason is the observed set dependence of the relative hit multiplicity distributions. Another is that the measured efficiencies were obtained using low intensity minimum bias data over a short time period. The effect of geometric acceptance on event topology can be removed by using only tracks that do not project outside of the acceptance at the z-position of any plane. The resulting relative hit multiplicity distributions for positive and negative beam are shown in Figure C.3. Note that the reconstruction efficiency for the monte carlo, calculated earlier, is not affected by the acceptance in this manner since the “true” efficiencies for the planes are known a priori. In other words a relative hit multiplicity histogram was not used to determine < e >. A value of < 6 >= 0.92 yields a binomial distribution which is skewed to a lower overall efficiency than the data as Figure 0.3 illustrates. Here, one observes the 16-hit fraction to fall below the data while the 13, 14, and l5-hit fractions are larger. Such a value of < e > corresponds to a reconstruction efficiency of better than 96%. Since the fraction of fake tracks is very small, it can be concluded that this number is representative of 268 the real tracks. It is clear from this discussion that the reconstruction program has a very small adverse affect indeed! 0.36 0.32 0.28 0.24 0.2 0.16 0.12 0.08 0.04 269 IIIIIIIIITIIIIIrIIlIIIIlIIIIIIIIIIIIIIIIIIIrII llllllllllilllllll [Jlll llllLLllllllllllll lllll 12.4 12.8 13.2 13.6 14 14.4 14.8 15.2 15.6 Hits Figure C.1: A typical relative hit multiplicity distribution for the physics tracks 16 (L5 (L45 (L4 (L35 043 (L25 (L2 0J5 OJ (L05 (L5 (L45 (L4 (L35 (L3 (L25 (L2 0J5 OJ (L05 270 IIIIIIIIII‘IIIIIIIIIIIIII'IIIIIIIIIIIIIIIIIII IITI y- SEDA .......... Illlllllilllll 1511151 Iijl 13 14 15 16 Hits lIIIIlIIII'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIII p- SETC I, El, 1 I I I I l IE I I I l I: I I 5I l 13 14 15 16 Hits (L5 0A5 (L4 (L35 043 025 02 GAS OJ (L05 (L5 (L45 (L4 (L35 053 (L25 02 0J5 OJ (L05 IIIIIIIIIIIIIIIIIIIIIIIIIIIIII'IIIIIIIIIlIIII IIII oooooooooo ......... l - #Iilllillilllillilllilliil 13 14 15 16 Hits IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIPIIIIIIII SETE cccccccccc ' ' - i ; l : Lilllljlilllijlfllliljijll 13 14 15 16 Hits Figure C.2: Relative hit multiplicity distributions of physics tracks for the four separate data sets. The monte carlo prediction appears as the dotted bars. (L5 0A5 0A- 0.35 03 025 0.2 0.15 GA 0.05 271 0.5 P P _ 0.45 L. P 0.4 r 0.35 _. —‘— 0.3 _ A“ """"" 0.25 )- _ 002 E _ 0.15 5 s s s s — :———: °-‘ — 0.05 '..§.1.§.1i.11§..§.1.§..§11 0 13 14 15 16 Hits in Acceptance ......... ooooooooooo IIIIIIIIIIIIII'IIIIIIIIIIIIIIIIFIIIIIIITerlllI—II .. O I 11.11151151l1511311LiL1iJl 13 14 15 16 Hits in Acceptance Figure C.3: Relative hit multiplicity distributions for positive data (Left) and negative data (Right). These plots are for tracks that do not project outside the MWPC acceptance. Also shown is the bi- nomial distribution for (e) = 0.92; the binomial distribution is plotted as dotted bars. Appendix D Trigger Particle Corrections The following is a brief summary of the methods employed in determining the various corrections to high p j 7, 1r°, or 1] events. These corrections involve those asso- ciated with the whole event and muon cuts described in Chapter 4, those for trigger and reconstruction inefficiencies, and the energy correction for individual photons. This last correction is both an energy scale correction, and an energy loss correction that takes into account all (the material in front of the electromagnetic calorimeter. D.1 CORRECTIONS FOR CUTS The correction for vertex finding efficiency has been parametrized as a function of the 2 position in the target. It has the following form [52]: 5",.th = 1.0019 — 0.0079 x Vz (D.1) This correction was obtained by studying the behaviour of the vertex finding algo- rithm on a sample of events which had been visually examined via computer graphics to see if they should have satisfied the vertex criterion. This correction is applied to each reconstructed event individually. The 6,. correction was obtained by assuming that the true directionality distri- bution of photons emanating from the target was symmetric about 0. The fraction, f5,<_o,4 of photon events with 5, < -0.4 cm relative to the total number passing the directionality cut was computed. The correction is then expressed as follows. 56, = 1 + f6.<-o.4 (D.2) All the other cut corrections are obtained by studying the 1r° mass distribution with sidebands subtracted . For the offline veto wall and track isolation cuts all that is 272 .—._z.—_z- ...- 273 necessary to do is see how many good 1r°s remain after each cut is applied individually. The correction is just the ratio of good 7r°s without the cut to good 1r°s remaining after the cut is applied. The timing and Efmnt/Etom corrections are obtained by ex- amining the tails of these distributions. The timing and Efrong/Etotd distributions for 1r°s in the mass band and the sidebands are constructed. The sideband distributions are subtracted from the mass band distribution. The ratio of the total entries in each distribution to the number satisfying the cut divided by 2 constitutes the correction. Note that the track isolation correction for 1r°s is twice that for direct photon candi- dates. The corrections for all cuts that are applied to the reconstructed direct photon sample are summarized in Table 4.2, along with a total correction. D.2 CORRECTIONS FOR INEFFICIENCIES There are additional corrections to the data. First, the trigger inefficiency has to be taken into account. Second, there are the acceptance and reconstruction efficiency corrections’for 1r°s and photons. Third, the loss of photons and 1r°s through photon conversion in the target material has to be accounted for. All these corrections, along with the vertex correction, are applied to each event individually while it is being reconstructed from the DST stream. The trigger efficiency consists of two parts. There is the efficiency of the high threshold SLOC relative to the TWOGAM trigger, and there is the pretrigger effi- ciency. The overall efficiency is just the product of the individual efficiencies. This breakdown of the trigger analysis is due to the fact that there are two independent hardware mechanisms responsible for producing a high p _L trigger. To simulate the hardware response to p _L deposited in the EMLAC, the actual energy of a triggering event is reconstructed by EMREC. The energy deposited in the individual r-view strips is then estimated from the reconstructed showers, and the simulation of the hardware summing schemes is performed. Thus the actual p ,L as seen by the hardware 274 can be determined. Pedestal shifts, gain variations and discriminator thresholds can be taken into account with this method. However, no reliable model of image charge effects exists at this time. The turn on curve for the SLOC was done using the TWOGAM trigger, which was known to be fully efficient at a pj_ of 1.8 GeV/c. Recall that the TWOGAM trigger is a special coincidence of low threshold SLOC triggers. The ratio SLOC o TWOGAM/TWOGAM is plotted as a function of p _L. The calculation of p _L is done by using the reconstructed energy to estimate the energy in the r strips. The summing of overlapping groups of 16 strips is simulated and the value of p _L determined. The efficiency curve was fitted to a function of the following form: P(r, pi) = ——L +00 dx6(pj_ + x — 7(1)) exp(—x2/202(r)) (D.3) \/2—7‘l’0'(1') -oo where P(r, p .1.) is the probability a trigger was satisfied which deposited transverse momentum p i at the position r. The integral is a convolution of a step function and a gaussian which represents an ideal discriminator affected by gaussian noise. The parameters 1' and a' are the threshold and smearing respectively. Each octant is divided into five regions on the basis of statistics. The r dependence of the trigger is determined by taking the eight strips with the highest p _L and assigning that as the triggering p _L. The pretrigger turn-on curve was made using events with SLOC triggers, and examining the octant opposite the trigger octant. The energy of the octant was reconstructed using EMREC and the strip energies estimated. The global summing scheme was simulated and a value of triggering p _L assigned. A p _L distribution for events with a pretrigger and an unbiased p j distribution were made. The quotient distribution is the pretrigger turn-on curve. To accommodate the summing scheme each octant was divided into two regions, corresponding to inner and outer r. A fit was done to the turn-on curve for each octant, using equation D.3, although the r 275 dependence was simply averaged over each region. Due to a lack of statistics the outer regions’ results were averaged over all octants. There is an additional trigger correction of a purely geometrical nature. The cor- rection is for dead octants and dead regions of octants. It is computed by dividing the number of octants by the number of active octant regions corresponding to the region that triggered the event. This correction is necessary for calculating the abso- lute cross sections, but can be ignored when making relative distributions i.e. 7-to-1r" ratios. To find the acceptance and reconstruction efficiency for 1r°s a monte carlo gener- ation of events with a single 1r° was performed. The w°s were generated uniformly in a grid from 3.0 - 10.0 Gev/c in pl with 0.5 GeV/c bins and —0.85 — 0.85 in Y with 0.2 bins. 1000 events were generated per unit mesh in the grid. The 1r°s were required to have asymmetry less than 0.75 on input to a GEANT simulation of the LAC. EMREC was run on the GEANT output and the number of 1r°s reconstructed per unit mesh was determined, yielding the correction eax(y,pj). The acceptance and reconstruction efficiency for direct photons was determined in a similar. fashion. The inefficiencies for photons occur at the inner-outer ¢ boundary. and near the edges of fiducial regions. A 1r° can be lost if one of its decay photons converts in the target material. The conversion probability is a function of the vertex 2 position in the target. A photon can be assigned a probability that it did not convert in the target material. The conversion correction for 1r°s is the square of the reciprocal of this probability, while for direct photons it is just the reciprocal 276 D.3 PHOTON ENERGY CORRECTIONS Photons impinging on the front face of the EMLAC typically lose energy in the material between the event vertex and the calorimeter. In fact, there are nearly three radiation lengths of material between the outside surface of the dewar vessel and the upstream face of the electromagnetic calorimeter alone! One would therefore expect a net energy loss as a function of photon energy, which manifests itself in a systematic shift in the calorimeter’ s energy scale. By studying the energy scale one can determine a single function of energy which will compensate for this systematic effect on the measured photon energies. There are other systematic effects on the energy scale, namely ambiguities in the amplifier gains, the ADC pedestals, and energy losses near the fiducial boundaries. In order to simplify the monte carlo simulation of the detector, used in this study, the pedestal shifts and gain variations were determined using the calibration procedures available during data taking. In addition, the energy losses around fiducial boundaries were compensated for by adjusting the energies of photons used in reconstructing 1r°s. This was accomplished by fixing the reconstructed 7r° mass at its nominal value. Only photon pairs with a separation greater than 5.0 cm were used for this procedure. By using separated photons one is guaranteed that no systematic correlations due to reconstructed energy sharing between the two photons occurs. The absolute energy scale was then set with the electron calibration beam data as will be described shortly. The corrections for these effects are applied to the DST data so that the energy loss corrections are independent of them. The solution to the energy loss problem has required many months of work on the part of several individuals [53]. Only the highlights will be presented here. To start with conversion electron pairs were reconstructed from the tracking system data. 277 Those conversion or zero mass pair (ZMP) tracks that matched to EMLAC showers within the fiducial region of the detector were used to compute the ratio shower energy to tracking momentum. These E/ P ratios were then plotted as a function of shower energy. The point at 100 GeV was determined from the calibration data, which used a 100 GeV electron beam. This was done because the track momentum resolution begins to suffer systematic uncertainties greater than 1% at momenta ~ 100 GeV/c. The E/ P ratio was set to one for the calibration data point, thereby establishing the absolute energy scale for the EMLAC. This calibration factor was then applied to the E/ P ratios for the ZMP data. An E/ P ratio was constructed for each octant. The values of E/ P thus determine an energy loss correction for electron showers as a function of their measured energy. The corresponding correction for photons was obtained by running a monte carlo simulation of the calorimeter apparatus, including the inactive material between the target and photon detector. The mean energy loss per unit solid angle in the interval E —+ E + AE was used to estimate the actual energy loss of photons and electrons in the inactive material. This mean energy loss is obtained from well known formulas governing the behaviour of minimum ionizing radiation [54]. The alternative to this approach is to implement a full showering scheme in the monte carlo; such a scenario was unrealistic for the computing power then available to the collaboration. The photon and electron shower energies were reconstructed by EMREC and the ratio of photon to electron energies computed as a function of the reconstructed photon energy. This ratio can then be used together with the E / P ratio obtained for showering electrons to determine the EMLAC energy scale for photons as a function of their reconstructed energy. This method for ascertaining the reconstructed photons’ energy scale was checked by calculating the 7e+e" mass spectrum, using the reconstructed electron track mo- menta. By utilizing the tracking information the width and position of the mass peak 278 for the 11'” would be determined solely from the photon energy resolution and energy scale uncertainty. The peak revealed that the energy scale uncertainty is within the required tolerance and the width is consistent with an energy resolution of 18% / x/E. 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