a: : t: ..o.,(. mm 5 .5 x A». «.35 '74.“..33 .if «out: . :- .. .:I.. It! t 1:; :1. :1 .3“? 2 a! V'. any-1', 05‘1”“!!“5 an It. I x‘ ‘ 1!. 1 L. . .51.... i. 3.3.... .. :51...,.$_..an1~}; a: .ézauazmfi 3.? I; ‘5 | .IL... ? 63% lirlle/ LIBRARIES NIICHIGAN STATE UNIVERSITY EAST LANSING, MICH 48824-1048 This is to certify that the dissertation entitled High Transverse Momentum Direct Photon Production at Fermilab Fixed-Target Energies presented by Leonard Apanasevich has been accepted towards fulfillment of the requirements for the Ph.D. degree in Physics Mace/14524 q Major Professor’s Sign flag 7/ £00-xg’”. 0 Date MSU is an Affirmative Action/Equal Opportunity Institution PLACE IN RETURN Box to remove this checkout from your record. To AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE # 2/05 c:/ClRC/DateDue.ind¢p.15 HIGH TRANSVERSE MOMENTUM DIRECT PHOTON PRODUCTION AT FERMILAB FIXED-TARGET ENERGIES By Leonard Apanasevich A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics and Astronomy 2005 Abstract HIGH TRANSVERSE MOMENTUM DIRECT PHOTON PRODUCTION AT FERMILAB FIXED—TARGET ENERGIES By Leonard Apanasevich This thesis describes a study of the production Of high transverse momentum direct photons and no mesons by proton beams at 530 and 800 GeV/c and Tr- beams at 515 GeV/c incident on beryllium, copper, and liquid hydrogen targets. The data were collected by Fermilab experiment E706 during the 1990 and 1991- 92 fixed target runs. The apparatus included a large, finely segmented lead and liquid argon electromagnetic calorimeter and a charged particle spectrometer featuring silicon strip detectors in the target region and proportional wire chambers and drift tubes downstream of a large aperture analysis magnet. The inclusive cross sections are presented as functions of transverse momentum and rapidity. The measurements are compared with next-to—leading order perturbative QCD calculations and to results from previous experiments. Acknowledgments I would like to take the opportunity to thank some of the people who helped make this dissertation possible. Foremost, I thank my adviser, Carl Bromberg, for his guidance and support over these many years. His insights and enthusiasm for the subject have been a continuing source Of inspiration for me and I feel lucky to have had him as my adviser. The analysis presented here is built upon the work of many collaborators who invested significant time and effort into making this experiment a success. I thank them for their dedication and hOpe this thesis reflects their work in a positive light. There are several collaborators I would like to thank in particular. George Ginther has been a mentor and a second adviser to me. I am grateful for his advice and encouragement more than he could possibly know. I thank Paul Slattery for his heroic efforts in keeping the analysis moving forward, for standing by me, and for providing financial support in the end. I would also like to thank Marek Zielir’iski and Joey Huston for their always valuable comments and suggestions. I thank Michael Begel for many spirited and enlightening discussions over the years and for his technical assistance in putting this document together. Finally, I’d like to thank Steve Blusk, Casey Hartman, Chris Lirakis, Rob Roser, Nikos Varelas and all the other students and post—docs on E706 for their help during the early years of my involvement with this experiment. The road to this Ph.D. has been a long one and I would like to thank some people outside of the experiment who have helped me along the way. I thank iii Walsh Brown, Stacey Hamlin, Rick Kwarciany, Noah Wallace and Steve Worm for helping keep me sane during the pursuit of this degree. I especially thank Kate Frame and Jordan Poler for their constant support and encouragement. It has meant a lot to me. And also thanks to Larry Servidio. There are not too many people in this world who would be willing to spend their Saturday afternoons in a dingy bar on the lower east side of Manhattan. For those Saturdays and for everything else, I am eternally grateful. Finally, I would like to thank my parents and my brother. Without their love and support, I could not have completed this thesis. iv Table of Contents Abstract ii Acknowledgments iii List of Tables x List of Figures xiv Chapter 1 Introduction 1 1.1 Overview ............................................................. 1 1.2 Quantum Chromodynamics ........................................... 1 1.3 Phenomenology of High Transverse Momentum Interactions ........... 4 1.4 Direct Photon Physics ................................................ 7 1.5 Experimental Challenges and Techniques ............................. 10 1.6 Nuclear Effects ...................................................... 17 1.7 Initial State Parton Transverse Momentum Effects ................... 18 1.8 Recent Experiments ................................................. 21 Chapter 2 The Meson West Spectrometer 23 2.1 Overview ............................................................ 23 2.2 Beamline ............................................................ 23 2.3 The Target .......................................................... 30 2.4 The Beam and Interaction Detectors ................................. 32 2.5 The ’Il‘acking System ................................................ 34 2.5.1 Silicon Strip Detectors ......................................... 34 2.5.2 Analysis Magnet ............................................... 35 2.5.3 Proportional Wire Chambers ................................... 37 2.5.4 Straw Tube Drift Chambers .................................... 40 2.6 Liquid Argon Calorimeter ............................................ 43 2.6.1 Electromagnetic Calorimeter ................................... 45 2.6.2 Hadronic Calorimeter .......................................... 50 2.7 Forward Calorimeter ................................................. 53 Chapter 3 Trigger and Data Acquisition 55 3.1 Overview ............................................................ 55 3.2 Trigger System ...................................................... 55 3.2.1 Beam and Interaction Requirement ............................. 57 3.2.2 Pretrigger Requirement ........................................ 61 3.2.3 The Local Triggers ............................................. 63 3.2.4 The Global Triggers ............................................ 64 3.2.5 The Two GAMMA Trigger ...................................... 65 3.3 Overview of the DA system .......................................... 66 Chapter 4 Event Reconstruction 69 4.1 Overview ............................................................ 69 4.2 Charged "Hack Reconstruction ....................................... 70 4.2.1 Downstream Tracking .......................................... 71 4.2.2 Upstream View Tracking and Linking .......................... 74 vi 4.2.3 Vertex Finding and Relinking .................................. 78 4.2.4 Beam Tracking ................................................ 80 4.2.5 Charged Track Momentum Determination ...................... 81 4.3 Electromagnetic Shower Reconstruction .............................. 84 4.3.1 Unpacking ..................................................... 85 4.3.2 Group and Peak Finding ....................................... 88 4.3.3 GAMMA and PHOTON reconstruction ............................ 91 4.4 Discrete Logic Reconstruction ........................................ 94 Chapter 5 Data Analysis 97 5.1 Overview ............................................................ 97 5.2 Target F iducial Requirement ......................................... 98 5.3 EMLAC Fiducial Requirement ...................................... 101 5.4 Hadron Rejection ................................................... 104 5.5 Rejection of Beam Halo M uons ..................................... 107 5.5.1 Veto Wall Requirement ....................................... 110 5.5.2 Directionality Requirement .................................... 110 5.5.3 x2 Requirement ............................................... 113 5.5.4 Balanced pr Requirement ..................................... 114 5.5.5 Corrections for Muon Requirements ........................... 116 5.6 no and 7] Energy Asymmetry Requirement .......................... 118 5.7 Photon Conversion Correction ...................................... 119 5.8 Electron Studies .................................................... 121 vii 5.9 EMLAC Energy Scale Calibration .................................. 125 5.9.1 Calibration Procedure ........................................ 127 5.9.2 Results and Linearity ......................................... 129 5.10 ’Il‘igger Analysis ................................................... 132 5.10.1 Trigger Corrections ........................................... 135 5.10.2 Trigger Selection .............................................. 138 5.11 no and 77 Signal Determination .................................... 140 5.12 Direct Photon Candidate Definition ................................ 141 5.13 Beam Normalization .............................................. 147 Chapter 6 Monte Carlo Simulation 150 6.1 Overview ........................................................... 150 6.2 Parameterized Monte Carlo Studies ................................. 151 6.2.1 EMLAC Resolution Effects .................................... 159 6.3 The Detailed GEANT Simulation .................................... 162 6.3.1 Event Simulation ............................................. 163 6.3.2 Simulation of Detector Response .............................. 169 6.3.3 Monte Carlo Spectrum Weighting ............................. 176 6.3.4 Monte Carlo and Data Comparisons ........................... 178 6.3.5 Evaluation of Reconstruction Efficiencies ...................... 185 6.3.6 Vertex Reconstruction Efficiency .............................. 197 6.3.7 Background Photon to no Ratio ............................... 201 Chapter 7 Results and Conclusions 211 viii 7.1 Overview ........................................................... 211 7.2 Cross Section Calculation ........................................... 211 7.3 no Cross Sections ................................................... 212 7.4 Direct Photon Cross Sections ....................................... 213 7.5 Summary of Systematic Uncertainties ............................... 224 7.6 Nuclear Dependence ................................................ 233 7.7 Comparisons with NLO Calculations ................................ 237 7.7.1 Evidence for Initial State Parton kT ............................ 243 7.7.2 Comparisons with kT-enhanced N LO Theory .................. 251 7.8 Comparisons Between Other Experiments and NLO Theory ......... 257 7.9 Conclusions ........................................................ 266 Appendix A Tabulated To Cross Sections 270 Appendix B Tabulated Direct Photon Cross Sections 284 Appendix C 17 Results 293 Cl 1] Cross Sections ................................................... 293 REFERENCES 304 1.1 1.2 1.3 2.1 2.2 2.3 2.4 2.5 2.6 3.1 5.1 5.2 5.3 6.1 6.2 7.1 7.2 A.1 A.2 List of Tables Properties Of the quarks. ................................................ 2 Valence quark content of some common hadrons. ......................... 3 Recent direct photon experiments. ...................................... 22 Beam composition Of the secondary beams. ............................ 27 SSD beam chamber geometrical parameters. ............................ 36 SSD vertex chamber geometrical parameters. ........................... 36 PWC geometric parameters. ............................................ 40 Orientation and positions of the garlands. The positions are relative to the center of the chamber. Note that within a chamber, the garlands are arranged in pairs, separated by z5 cm. .......................................... 41 Straw geometrical parameters. .......................................... 44 Trigger characteristics during the 1990 fixed target run. Many events satisfied more than one trigger. Some prescale factors changed during the run. . . . 58 Data summary for the 1990 and 1991-92 fixed target runs. .............. 98 Peak and sideband mass regions used in the 7r0 and 77 meson analysis. . . 141 Average values Of the beam absorption correction. ..................... 149 Number of generated HERWIG filter 2 and filter 3 direct photon background Monte Carlo events (in thousands) as a function of the pTGEN threshold. 175 Number of generated HERWIG Monte Carlo direct photon events (in thousands) as a function of the pram threshold. ................................... 175 Average value of corrections applied to the data. ....................... 213 Measured a values for no and direct photon production as determined from the fits shown in Figure 7.19. .......................................... 236 Invariant differential cross sections per nucleon for 7r0 production by 530 and 800 GeV/c proton beams and 515 GeV/c 7r‘ beam on Be targets, for 1.0 < pr < 4.0 GeV/c. ................................................. 271 Invariant differential cross sections per nucleon for no production by 530 and 800 GeV/c proton beams and 515 GeV/c 7r“ beam on Be targets, for pr > 4.0 GeV/c. ....................................................... 272 X A.3 Invariant differential cross sections per nucleon for n0 production by 530 and 800 GeV/c proton beams and 515 GeV/c n’ beam on Cu targets. ...... 273 A4 Invariant differential cross sections for n0 production by 530 and 800 GeV/c proton beams and 515 GeV/c n“ beam on proton targets. ............. 274 A5 Invariant differential cross section per nucleon for n0 production by 530 GeV/c proton beam on a Be target as a function Of pr and rapidity. ........... 275 A6 Invariant differential cross section per nucleon for n0 production by 800 GeV/c proton beam on a Be target as a function of p]. and rapidity. ........... 276 A.7 Invariant differential cross section per nucleon for n0 production by 515 GeV/c n" beam on a Be target as a function of [1,. and rapidity. ............... 277 A8 Invariant differential cross section for n0 production by 530 GeV/c proton beam on a Cu target as a function of pr and rapidity. ........................ 278 A9 Invariant differential cross section for n0 production by 800 GeV/c proton beam on a Cu target as a function of pr and rapidity. ........................ 279 A.10 Invariant differential cross section for n0 production by 515 GeV/c n’ beam on a Cu target as a function of pr and rapidity. ........................ 280 All Invariant differential cross section for n0 production by 530 GeV/c proton beam on a p target as a function of pr and rapidity. .......................... 281 A. 12 Invariant differential cross section for n0 production by 800 GeV/c proton beam on a 19 target as a function of pr and rapidity. .......................... 282 A.13 Invariant differential cross section for n0 production by 515 GeV/c n" beam on a p target as a function of pr and rapidity. .......................... 283 El Invariant differential cross sections per nucleon for direct photon production by 530 and 800 GeV/c proton beams and 515 GeV/c n" beam on Be targets. 285 B2 Invariant differential cross sections per nucleon for direct photon production by 530 and 800 GeV/c proton beams and 515 GeV/c n‘ beam on Cu targets. 286 B3 Invariant differential cross sections for direct photon production by 530 and 800 GeV/c proton beams and 515 GeV/c n‘ beam on proton targets. .. 287 B.4 Invariant differential cross section per nucleon for the inclusive reaction pBe —> 7X at 530 GeV/c as a function of rapidity for several pr bins. . . 288 B5 Invariant differential cross section per nucleon for the inclusive reaction pBe -r 7X at 800 GeV/c as a function of rapidity for several pT bins . . . 288 xi B.6 Invariant differential cross section per nucleon for the inclusive reaction n‘Be —> 7X at 515 GeV/c as a function Of rapidity for several pT bins . 289 B7 Invariant differential cross section per nucleon for the inclusive reaction pCu —+ TX at 530 GeV/c as a function of rapidity for several pr bins. . . 289 8.8 Invariant differential cross section per nucleon for the inclusive reaction pCu —t 7X at 800 GeV/c as a function of rapidity for several pr bins. . . 290 B9 Invariant differential cross section per nucleon for the inclusive reaction n‘Cu —> 7X at 515 GeV/c as a function of rapidity for several pr bins. 290 8.10 Invariant differential cross section for the inclusive reaction pp —> 7X at 530 GeV/c as a function of rapidity for several pr bins. ..................... 291 8.11 Invariant differential cross section for the inclusive reaction pp —> 7X at 800 GeV/c as a function of rapidity for several pT bins. ..................... 291 8.12 Invariant differential cross section for the inclusive reaction n‘ p ——> 7X at 515 GeV/c as a function of rapidity for several pr bins. ..................... 292 CI Invariant differential cross sections per nucleon for 17 production by 530 and 800 GeV/c proton beams and 515 GeV/c n‘ beam on Be targets. ...... 297 C2 Invariant differential cross sections per nucleon for 77 production by 530 and 800 GeV/c proton beams and 515 GeV/c n‘ beam on Cu targets. ...... 297 C3 Invariant differential cross sections for 1) production by 530 and 800 GeV/c proton beams and 515 GeV/c n‘ beam on proton targets. ............. 298 C4 Invariant differential cross section per nucleon for 7) production by 530 GeV/c proton beam on Be target as a function of pr and rapidity. ............. 299 C5 Invariant differential cross section per nucleon for 17 production by 800 GeV/c proton beam on Be target as a function of pr and rapidity. ............. 300 C6 Invariant differential cross section per nucleon for 77 production by 515 GeV/c n" beam on Be target as a function of pr and rapidity. ................. 301 C7 Invariant differential cross section per nucleon for 17 production by 530 GeV/c proton beam on Cu target as a function of pr and rapidity. ............. 302 C8 Invariant differential cross section per nucleon for 17 production by 800 GeV/c proton beam on Cu target as a function of pr and rapidity. ............. 302 C9 Invariant differential cross section per nucleon for 7) production by 515 GeV/c n‘ beam on Cu target as a function of pr and rapidity. ................ 302 xii C.10 Invariant differential cross section for 17 production by 530 GeV/c proton beam on p target as a function of pr and rapidity. ............................ 303 CH Invariant differential cross section for 17 production by 800 GeV/c proton beam on p target as a function of pT and rapidity. ............................ 303 C12 Invariant differential cross section per nucleon for 17 production by 515 GeV/c n‘ beam on p target as a function of pr and rapidity. .................. 303 xiii List of Figures 1.1 Schematic illustration of a high pr hadronic interaction. ................. 5 1.2 Left: Parton distribution functions for the proton as a function Of :13. Right: Probability that a parton will fragment into a n0 as a function of z. ..... 8 1.3 Lowest order Feynman diagrams for direct photon production. ......... 10 1.4 Relative contribution Of the annihilation and Compton diagrams to the leading order direct photon cross section for n‘ and proton beams as a function of the photon pr. GRV92 LO parton distribution function is used for the n" calculation, and CTEQ6.1L is used for the proton calculation. The theory calculation is provided by [15]. ........................................ 11 1.5 Top: Gluon distribution uncertainty as characterized by the CTEQ6.1M eigenvector basis sets. Bottom: Ffactional uncertainty in the N LO prediction for direct photon production in pBe interactions at 530 GeV/c due to the uncertainty in the PDF. ............................................... 12 1.6 Top: Definition of n0 energy asymmetry, A. Bottom: no opening angle in the lab frame versus energy asymmetry. ................................... 14 1.7 Average pr of muon, photon, and jet pairs produced in hadronic collisions versus ,/§. ............................................................ 20 2.1 Schematic view of the Meson West spectrometer. ...................... 24 2.2 Schematic view of the Fermilab Tevatron. .............................. 26 2.3 A schematic drawing of the beamline Cerenkov counter. Each ring of photomultiplier tubes is labeled according to the particle it was designed to tag. ................................................................... 28 2.4 Pressure curves for the proton, kaon, and pion tags with incident +530 GeV/c beam. Peaks/ plateaus are labeled by the associated particle type. The solid vertical line represents a typical Cerenkov operating pressure. .......... 29 2.5 Layout of the target region during the 1990 and 1991-92 runs. ........... 32 2.6 Exploded view Of a single PWC chamber. .............................. 38 2.7 Relative chamber efficiency versus distance from the center of a garland pair for (a) zero voltage applied to the garland wire, and (b) 1500 volts applied to the garland wire. ...................................................... 42 2.8 A bundle of straw tubes. .............................................. 45 2.9 Side view of the LAC gantry and cryostat. ............................. 46 2.10 Detailed view of the electromagnetic calorimeter. ...................... 49 2.11 Schematic diagram of a single LACAMP module. ....................... 51 2.12 Exploded view of a HALAC cookie. .................................... 52 2.13 The forward calorimeter. .............................................. 54 xiv 3.1 3.2 3.3 3.4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 5.1 5.2 5.3 5.4 5.5 5.6 Sums-Of-8 signal formation. ............................................. 57 Number of photon pairs with mass in the n0 region per pr bin versus pr for several different trigger types. No corrections have been applied to the data in this plot. .............................................................. 59 Block diagram of a local discriminator module. ........................ 65 Block diagram of the E706 DA system. ................................ 67 Distribution of PWC hits per space track. ............................. 73 AX, AY, and AYSL linking resolution as a function Of the track momentum. The dotted lines indicate the functions used to determine the size of the linking window. .............................................................. 77 AZXy distribution for vertices in the 1990 n" data. ................... 80 Reconstructed K 2 and J / "(/J masses. The means are within 0.1% Of the world averages. .............................................................. 83 Schematic drawing of R and q5-boards showing the left-right R and inner-outer d) boundaries. ......................................................... 85 Energy deposition in the EMLAC. The dotted lines in the R view (<75 view) plots indicate the location of the inner-outer ¢ (left-right R) boundary. The pair of high energy depositions in the left R and outer (7) views are most likely from an 17 -—1 ’77 decay. ................................................ 86 Time dependence of the response of the EMLAC. ...................... 89 Another example of energy deposition in the EMLAC. The high energy deposition in the right R view and the pair of high energy depositions in the outer <75 view are most likely from a n0 -—> '77 decay. .................... 94 7'7 invariant mass distribution in the 530 GeV/c proton data. .......... 99 Z position Of vertices in the 1990 515 GeV/c n‘ and 1991 800 GeV/c proton data for events containing '77 pairs with invariant mass within the n0 signal region and pr > 4 GeV/c. The events are corrected for beam absorption and losses due to photon conversions. ..................................... 100 X -Y distribution of vertices in the Copper and Beryllium targets in the 1990 515 GeV/c n" data and the 1991 530 GeV/c proton beam data for events containing '77 pairs with invariant mass within the n0 signal region and with pr > 3.5 GeV/c. The vertices outside the Cu and Be target area in the 1990 data are primarily due to interactions in the Rohacell target stand. . . . . 102 X -Y position of photons contained within the EMLAC fiducial volume. The photons are from '77 pairs with invariant mass within the n0 signal region and pT> 5 GeV/c in the 1990 n‘ data. .................................... 104 Geometric acceptance for single photons, nO’s, and 17’s versus ylab for several different 77,. bins. ........................ ' ............................. 105 The distance to nearest track distribution for showers reconstructed in the EMLAC with pr > 1.0 GeV/c. ....................................... 107 5.7 E fmm/ E70707 distributions for electromagnetic showers and hadronic show- 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17 5.18 ers. .................................................................. 108 The effect of the muon rejection requirements on the ’77 invariant mass distribution in the vicinity of the n0 for 515 GeV/c n" beam data. Each subsequent plot includes all the requirements from the previous plots. . 111 Use of focusing of the EMLAC radial strips to discriminate against showers induced by muons from the beam halo. ............................... 112 Directionality distributions for beam halo muons and photons in the 1990 515 GeV/c n’ data for showers with pT > 5 GeV/c. The beam halo muon sample was obtained by requiring the veto wall requirement to fail in the quadrant of the reconstructed shower. The photon sample was obtained by imposing all the muon rejection criteria on the showers, with the exception of the directionality requirement. ......................................................... 1 14 x23/ E distributions for beam halo muons and photons in the 1990 515 GeV/c n" data for showers with 77,. > 5 GeV/c. The beam halo muon sample was obtained by requiring the veto wall requirement to fail in the quadrant of the reconstructed shower. The photon sample was obtained by imposing all the muon rejection criteria on the showers, with the exception of the X2 requirement. ......................................................... 1 15 Pgway/pr distributions for beam halo muons and photons in the 1990 515 GeV/c n“ data for showers with pr > 5 GeV/c. The beam halo muon sample was obtained by requiring the veto wall requirement to fail in the quadrant of the reconstructed shower. The photon sample was Obtained by imposing all the muon rejection criteria on the showers, with the exception of the balanced pr requirement. ...................................................... 117 The 77 invariant mass distribution in the region of the n0 for several energy asymmetry ranges. The number of nO’s was obtained using the sideband subtraction technique described in Section 5.11. ....................... 120 Average value of the photon non-conversion probability versus Z for the 1990 (top) and 1991 (bottom) fixed target runs. Superimposed on the figures are the corresponding primary vertex distributions for these runs. ......... 122 Effect of ZMP cuts on the A5,, and Z Xi,“ distributions of oppositely charged track pairs. The ASy cut is $3 mr and the ZXint cut is :l:10cm from the magnet center. ....................................................... 124 EMLAC efficiency for reconstructing an electron as a function of electron momentum. The solid curve represents a fit to these data. ............ 125 The resultant systematic uncertainty in the n0 cross-section due to a 0.5, 1.0, and 2.0% uncertainty in the energy scale. This is for n‘Be interactions at 515 GeV/c. .............................................................. 126 The '77 mass distribution in the region of the n0 and 17 and the n07 mass distribution in the region of the w for mass combinations with p], > 5.0 GeV/c. The mean values for these masses agree with the world values to better than 0.5%. ................................................................ 128 xvi 5.19 Average energy lost in the material upstream of the EMLAC for photons and electrons as a function of reconstructed energy. ....................... 129 5.20 Radial dependence of the reconstructed n0 and 17 masses (normalized to their world values) and the E / P ratio for ZMP electrons from the 1991 data sample. Inset: Radial dependence of the reconstructed nO mass for several choices of charge integration time. .............................................. 130 5.21 The mean 17 mass (relative to the world value) as a function of the 17 energy (top) and pr (bottom) from the 1991 data sample. .................... 131 5.22 The 76+6‘ mass distribution from the combined 1990 and 1991 data samples. ............................................................. 133 5.23 Ratio of the reconstructed 76+e' (o) and 77 (o) masses to the n0 world value versus the number of radiation lengths traversed in the target. The lines are fits to the data. ....................................................... 134 5.24 Ratio of the reconstructed ye+e‘ mass to the 17 and n0 world values versus the energy of the unconverted photon. ..................................... 134 5.25 LOCAL_HI and LOCAL_LO discriminator turn-on curves for typical discrimina- tors in the inner and outer regions of the EMLAC versus trigger-pr for the 1991 data. ................................................................ 137 5.26 Composite trigger maps used for the 800 GeV/c proton beam data. . . . 139 5.27 Invariant mass distributions for '77 pairs in the region of the n0 for several pr bins. ................................................................. 142 5.28 Invariant mass distributions for cry pairs in the region of the 17 for several pr bins. ................................................................. 143 5.29 Invariant mass distributions for 77 pairs with pr> 3.5 GeV/c in the region of the n0 and 17. The arrows indicate the boundaries of the peak and sideband regions. .............................................................. 144 5.30 Illustration of the various fits and fit ranges used extract the signal in the bin 1.0 < pr < 1.2 GeV/c. The resultant fits are drawn over the fit range of the histogram. ........................................................... 145 5.31 Asymmetry distributions for '77 mass combinations in the n0 signal region, sideband region, and for the sideband subtracted n0 signal. ........... 146 6.1 The n0 cross section versus pr and rapidity (inset) for 530 GeV/c proton beam incident on beryllium. The error bars are statistical only. Overlaid on the plots are the results of the fit used in the PMC (solid curve) and a fit to Equation 6.1 (dotted curve), integrated over the appropriate pr and rapidity ranges. 153 6.2 Background subtracted n0 (left) and 17 (right) mass distributions from the data compared to the energy resolution smeared n0 and 17 distributions from the PMC. Here, and in future plots where the y-axis values are unspecified, the histograms are normalized to unity. ................................... 155 6.3 Comparison between the sideband subtracted 1r0 energy asymmetry distribu- tion in the data and the energy smeared PMC. ........................ 157 xvii 6.4 Left: Contribution to 7b/n0 from n0 decays in the 75S candidate photon definition. Also shown is the contribution from each of the sources described in the text. Right: Contribution to 712/770 from no’s, 17’s, w’s and 17”s. In these curves, the background photons have not been corrected for effects due to energy resolution. ................................................. 158 6.5 Illustration showing the effect of energy resolution on a steeply falling pr spectrum. For any given reconstructed p1, bin, the number of entries entering from bins with lower true pr outnumber the losses out of the pr bin, leading to a net shift in the observed uncorrected pT spectrum. ................... 160 6.6 a) Esmem. / E versus pr in the PMC before rescaling the photon energies and b) after rescaling the photon energies. ................................... 161 6.7 Comparison between the number of reconstructed photons in the triggering octant and the total number of reconstructed tracks in PYTHIA, HERWIG and the data for events containing no’s with pr > 3.5 GeV/c. The triggering octant is assumed to be the octant containing the no. ........................ 164 6.8 Comparison of E / P distributions in the data and the Monte Carlo. . . . 171 6.9 Comparison between the the total number Of reconstructed tracks and the number of reconstructed photons in the triggering 1/2 octant in the 515 GeV/c n“ beam data and the 530 GeV/c proton beam data for events containing no’s with 797. > 3.5 GeV/c. ................................................ 177 6.10 Comparison between the weighted and unweighted HERWIG n0 pr spectra for the 721.013”: 3.0 GeV/c n“ sample. The weighting surface is normalized to unity at pr = pTGEN, ycm = 0. ............................................... 179 6.11 Ratio of the measured 17 to n0 production cross sections versus pr for 515 GeV/c n’ beam and 530 and 800 GeV/c proton beams. The error bars represent only statistical errors. ..................................................... 180 6.12 Comparison of n0 energy distributions in the data and the DGS. The solid ' points are the DGS and the histogram is the data. ..................... 182 6.13 Comparison of ER — E¢ distributions in the data and the DGS for the 530 GeV/c proton beam. The black dots are the DGS and the histogram is the data. ................................................................ 183 6.14 Comparison of the n0 and 17 mass distributions in the data (histogram) and the DGS (o) for the 800 GeV/c p beam. ............................... 185 6.15 Comparison of E from / Etotal distributions in the data and the DGS for the 515 GeV/c n" beam. The histogram is the data, and the points are the DGS. 186 6.16 Comparisons of background subtracted n0 energy asymmetry distributions in data (histogram) and the DGS (0). Comparisons are shown for two pr intervals, 4.0 < p]. < 5.5 GeV/c and 5.5 < pr < 7.0 GeV/c. Also shown are energy asymmetry distributions from the PMC (dotted curves). ............... 187 6.17 Comparison of background subtracted n0 energy asymmetry distributions in the data (histogram) and the DGS (o) for backward, central, and forward rapidity ranges. ...................................................... 188 xviii 6.18 6.19 6.20 6.21 6.22 6.23 6.24 6.25 6.26 6.27 6.28 6.29 6.30 7.1 Comparison between the number of reconstructed photons in half-octants containing a n0 candidate with pr > 3.5 GeV/c in the DGS and the data. 189 7r0 reconstruction efficiency for the 530 GeV/c proton beam as a function of for several rapidity ranges. The dotted curves in the figure indicate the contribution from EMLAC resolution smearing alone. ................. 193 17 reconstruction efficiency for the 530 GeV/c proton beam as a function of p]. for several rapidity ranges. The dotted curves in the figure indicate the contribution from EMLAC resolution smearing alone. ................. 194 SINGLE LOCAL HIGH direct photon reconstruction efficiencies for the 90N, 75N and 75S candidate definitions as functions of pr for several rapidity ranges. The dotted curves in the figure indicate the contribution from EMLAC resolution smearing alone. ...................................................... 195 Reconstruction probability for no’s as a function of the number of generated photons in the 1 / 2 octant of the generated no. The curves represent fits to the Monte Carlo points. No trigger requirement has been placed on the Monte Carlo data. ........................................................... 198 Comparison between reconstruction probabilities obtained using HERWIG and DATA-DRIVEN input to the DGS. ....................................... 198 Comparison between the Z positions of primary vertices in the DGS (points) and the data (histogram) for events containing a n0 candidate with pr > 4.0 GeV/c. .............................................................. 200 The ratio 712/ n0 for each direct photon candidate definition for the three major beam types as functions Of pr. The dotted curves represent the results of the background fits integrated over the indicated rapidity ranges. ......... 203 The ratio 711/ n0 as a function Of pr for backward, central and forward rapidities for the 530 GeV/c proton beam. The dotted curves represent the results of the background fits integrated over the indicated rapidity ranges. ..... 204 Difference between vb/no in copper and beryllium versus pr for the 1991 800 GeV/c p beam data. Also shown is the difference between cyb/no in hydrogen and beryllium. The dotted lines represent fits to the differences, integrated over the rapidity range —1.0 < y < 0.5. .................... 205 Ratio of background photons to charged pions for the 515 GeV/c n“ data. The background photons are from interactions in the EMLAC by charged pions. The dotted line represents a fit to the Monte Carlo data. (Note cyb/ni is g 0.1%.) ............................................................... 207 Comparison of 712/ n0 from the PMC and the DGS simulations for the 75S photon candidate definition. ................................................. 208 Comparison of 7b/n0 from the DGS using input events from HERWIG (o) and from data (0) for 90N, 75N and 758 photon definitions. ............... 209 n0 production cross sections per nucleus as functions of pT for 530 GeV/c proton beam on copper, beryllium, and hydrogen targets. .................... 214 xix 7.2 n0 production cross sections per nucleus as functions of pT for 800 GeV/c proton beam on copper, beryllium, and hydrogen targets. .................... 215 7.3 n0 production cross sections per nucleus as functions of pr for 515 GeV/c n" beam on copper, beryllium, and hydrogen targets. .................... 216 7.4 n0 cross section per nucleon as a function of rapidity for 530 GeV/c proton beam on beryllium for several pT intervals. ............................ 217 7.5 n0 cross section per nucleon as a function of rapidity for 800 GeV/c proton beam on beryllium for several pT intervals. ............................ 218 7.6 n0 cross section per nucleon as a function of rapidity for 515 GeV/c n’ beam on beryllium for several pr intervals. .................................. 219 7.7 Single (unsubtracted) photon to n0 ratio for 530 GeV/c proton beam on beryllium. The error bars represent the statistical uncertainties only. Also shown is 712/ n0. ...................................................... 221 7.8 Single (unsubtracted) photon to n0 ratio for 800 GeV/c proton beam on beryllium. The error bars represent the statistical uncertainties only. Also shown is orb/n0. ...................................................... 222 7.9 Single (unsubtracted) photon to n0 ratio for 515 GeV/‘c n~ beam on beryllium. The error bars represent the statistical uncertainties only. Also shown is 7b/n0. ............................................................... 223 7.10 Direct photon cross sections per nucleus versus pT for 530 GeV/c proton beam on copper, beryllium, and hydrogen targets. .......................... 225 7.11 Direct photon cross sections per nucleus versus pT for 800 GeV/c proton beam on copper, beryllium, and hydrogen targets. .......................... 226 7.12 Direct photon cross sections per nucleus versus pT for 515 GeV/c n" beam on copper, beryllium, and hydrogen targets. ............................. 227 7.13 Direct photon cross section per nucleon as a function Of rapidity for 530 GeV/c proton beam on beryllium for several pT intervals. ..................... 228 7.14 Direct photon cross section per nucleon as a function of rapidity for 800 GeV/c proton beam on beryllium for several pr intervals. ..................... 229 7.15 Direct photon cross section as a function of rapidity for 515 GeV/c n‘ beam on beryllium for several pr intervals. .................................. 230 7.16 Relative systematic uncertainties for direct photon (top) and n0 (bottom) production at 530 GeV/c versus pr. ................................... 232 7.17 Ratios of direct photon and n0 production cross sections by 515 GeV/c n" beam on Be obtained from the 1991-92 fixed target run to those obtained from the 1990 run. The error bars reflect statistical uncertainties only. ...... 233 7.18 Ratio of 90N to 758 and 75N to 75S direct photon cross sections for the 515 GeV/c n“ and 530 and 800 GeV/c proton beams. ................ 234 7.19 The nuclear dependence parameter a measured using Cu and Be targets versus pr for direct photon and n0 production by incident 530 and 800 GeV/c proton beams and incident 515 GeV/c n‘ beam. ............................. 237 7.20 The ratio of inclusive n0 production cross sections per nucleon on Cu to those on Be as functions Of n0 pr. Also shown are shape comparisons with HIJING. The error bars represent only statistical uncertainties. ................. 238 7.21 The ratio of inclusive direct photon production cross sections per nucleon on Cu to those on Be as functions of direct photon pT. Also shown are shape comparisons with HIJING. The error bars represent only statistical uncertainties. ........................................................ 239 7.22 The ratio of inclusive n0 cross sections per nucleon on Be target to those on p target as functions of n0 pr. Also shown are shape comparisons with HIJING. The error bars represent only statistical uncertainties. ................. 240 7.23 The ratio of inclusive direct photon cross sections per nucleon on Be target to those on p target as function of direct photon pr. Also shown are shape comparisons with HIJING. The error bars represent only statistical uncertainties. ........................................................ 241 7.24 Direct photon cross section versus pr for 515 GeV/c n“ beam on beryllium compared to NLO pQCD results for several choices Of scales. Also shown is the n0 comparison (scaled down by a factor of 1000). ................. 244 7.25 Comparison between a threshold resummed pQCD calculation and NLO pQCD for scale choices of $77,. and 2721.. Figure from Ref. [31]. ................. 245 7.26 Direct photon and n0 cross sections versus p]. for 530 GeV/c proton beam on beryllium compared to NLO pQCD results for several choices of parton distribution functions. ................................................ 246 7.27 Direct photon and n0 cross sections versus pr for 800 GeV/c proton beam on beryllium compared to NLO pQCD results using MRST2001E PDF. The shaded band indicates the uncertainty associated with the PDF. ....... 247 7.28 POUT, Act and QT distributions for high-mass direct photon pairs in the 515 GeV/c n' data. The data are compared to NLO pQCD (dashed), resummed NLO (solid) and kT enhanced PYTHIA (dotted) results. Figure from Ref. [27]. ....................................................... 249 7.29 POUT distributions for high-mass '77, nOnO, 7n0, and non pairs in n‘Be interactions at 515 GeV/c. Figure from Ref. [27]. ..................... 250 7.30 Away-side fragmentation function for jets recoiling against isolated 7’5 with pT> 5.5 GeV/c [108]. ................................................. 252 7.31 Di cross section per nucleon versus for 515 GeV/c n'-Nucleon collisions compared to NLO calculations with and without kT. .................. 253 7.32 Direct photon cross section for pBe collisions at 530 GeV/c compared to N LO (dotted), threshold resummed (dashed) and joint threshold and recoil resummed (solid) calculations. Figure from [111]. ..................... 255 7.33 kT-enhancement factors for direct photon and n0 production cross sections by 530 GeV/c proton beam for several values of (k7). .................... 256 xxi 7.34 Direct photon and n0 cross sections for 530 GeV/c proton beam on beryllium compared to kT-enhanced N LO pQCD calculations. Also shown is the quantity (Data — Theory) / Theory for the direct photon cross section. .......... 258 7.35 Direct photon and n0 cross sections for 800 GeV/c proton beam on beryllium compared to kT—enhanced N LO pQCD calculations. Also shown is the quantity (Data — Theory) / Theory for the direct photon cross section. .......... 259 7.36 Direct photon and n0 cross sections for 515 GeV/c n‘ beam on beryllium compared to kT-enhanced N LO pQCD calculations. Also shown is the quantity (Data — Theory) / T heory for the direct photon cross section. .......... 260 7.37 Data/ Theory for proton induced direct photon data from various experiments as a function of :rT. The theory calculations use CTEQ5M PDF and scale 71 = 2131“ ............................................................. 261 7.38 Data/Theory for proton induced n0 data from various experiments as a function of TT. The theory calculations use CTEQ5M PDF, KKP FF, and scale 71 = épr. ........................................................ 262 7.39 Direct-photon and n0 cross sections from experiments WA70 and UA6, compared to [CT-enhanced N LO calculations. .......................... 264 7.40 Isolated direct photon cross sections from CDF and DO at ,/5 = 1.8 TeV (top) and \/§ = 0.63 TeV (bottom) compared to NLO predictions. The predictions for CDF (DO) use CTEQ5M (CTEQ4M) PDF. The solid curves represent the expected enhancement to the predictions from parton-kT. The data from CDF at \/s = 1.8 TeV have been scaled up by 10% to facilite a shape comparision. ................................................... 265 7.41 Isolated direct photon cross section from ZEUS. The NLO predictions are by Gordon (LG) and by Krawczyk and Zembruski (K&W). ............... 267 7.42 The ratio between 530 GeV/c and 800 GeV/c p beam direct photon cross sections as functions Of pr. Overlayed on the plots are N LO predictions with and without supplemental kT. ........................................ 269 Cl 17 production cross sections per nucleus as functions of pr for 530 GeV/c proton beam on copper, beryllium, and liquid hydrogen targets. .............. 294 C .2 17 production cross sections per nucleus as functions of pr for 800 GeV/c proton beam on copper, beryllium, and liquid hydrogen targets. .............. 295 C3 17 production cross sections per nucleus as functions of pr for 515 GeV/c n— beam on copper, beryllium, and liquid hydrogen targets. .............. 296 Chapter 1 Introduction 1 . 1 Overview This thesis describes a study of the production of high transverse momentum (72,) direct photons by proton and n' beams on beryllium, copper, and liquid hydrogen targets. The data were recorded by F ermilab experiment E706 during the 1990 and 1991-92 fixed target runs. The results presented here have been published previously by the author [1—3]. Presented here is a compilation of these results and of the various methods used to extract the direct photon production cross sections. To achieve the smallest possible systematic uncertainty, which limited the direct photon measurement, extensive detector evaluations were required and alternative analyses were explored. This necessarily led to a relatively long document. In this chapter, the motivations for investigating direct photons, the experimental techniques and challenges associated with this study, and an overview of other experiments that have reported direct photon results are presented. 1.2 Quantum Chromodynamics In 1969, a deep inelastic scattering experiment performed at the Stanford Linear Accelerator Center (SLAC) [4, 5] provided the first direct evidence that hadrons, the particles which experience the strong force, are comprised of pointlike constituents called partons [6, 7]. Partons have since been identified as massive spin 1/2 fermions, quarks, and massless spin 1 gauge bosons, gluons. There are six Table 1.1 Properties of the quarks. Generation 1 2 3 I Quark u(up) d(down) C(Charm) s(strange) t(t0p) b(bottom )| Electric Charge +2/3 —l/3 +2/3 —1/3 +2/3 —1/3 I Mass (MeV/cz) ~300 ~300 ~1500 ~500 ~175000 ~5000 | types (or flavors) of quarks and eight gluons. Table 1.1 lists some of the physical properties of the quarks. The interactions of quarks and gluons are described by a non-Abelian gauge theory called Quantum Chromodynamics (QCD) [8, 9]. In QCD, quarks are assigned a quantum number called color charge, which is analogous to the electric charge in quantum electrodynamics. Color charge has three degrees of freedom. Gluons also carry color charge and can consequently interact with each other. Colored objects are not expected to exist as free particles. This is called color confinement and is manifested in high energy scattering experiments by the outgoing partons fragmenting into collimated jets of particles traveling in roughly the same direction as the scattered partons. The hadrons are colorless combinations of bound quarks. Until recently, only two classes of bound quark states have been observed: mesons and baryons. Mesons are formed from quark—antiquark pairs and baryons are formed from three quark (or antiquark) combinations.1 The quarks which form these combinations are called the valence quarks. The valence quarks in a hadron describe gross features such as the hadron charge and spin. However, the interactions of these valence quarks give rise to a 1 Evidence for pentaquarks, hadrons comprised of 4 quarks and one antiquark, was first reported by the LEPS collaboration in 2002 [10]. 2 dynamic sea of quarks and gluons within the hadrons as well. The valence quark content of some common hadrons are listed in Table 1.2. Table 1.2 Valence quark content of some common hadrons. I Hadron I p n n+ K +l IQuark Contentluud udd ud ugl One important result from QCD is that the strong coupling constant, as, becomes weaker as the momentum transfer, Q2, of the interaction between partons increases. In the literature, this is commonly referred to as the running of the coupling constant. The dependence of as on Q2 is given, in the leading log approximation, by [11] 12n 1 1 (33 — 2nf)ln(Q2/A2)’ ( ' ) 03(Q2) : where nf is the number of quark flavors, and A is a constant. Equation 1.1 indicates that as Q2 ——1 00, as ——> 0. This phenomenon is known as asymptotic freedom. If the momentum transfer in an interaction is large enough, as may be sufficiently small to allow the effective application of perturbative methods to make quantitative calculations about the interaction. Conversely, for Q2 ~ A2, as becomes large, and the suitability of perturbative techniques becomes questionable. The parameter A may be regarded as the limit where the “strong interactions become strong” [12]. This is also thought to be the region where the confining forces Of QCD set in. 1.3 Phenomenology of High Transverse Momentum Interactions Consider the inclusive reaction A + B —> C + X, where A and B are colliding hadrons, C represents the outgoing observed hadron of interest, and X represents everything else produced in the reaction. This process is shown schematically in Figure 1.1. If emerging hadron C has large transverse momentum (high pr), it is likely that the underlying partonic subprocess, a + b —1 c + (1, involved a large Q2, and thus the use of perturbative techniques to evaluate the cross section for the subprocess may be justified [13]. However, although the cross section for the partonic hard scatter may be properly evaluated, the challenge of relating this quantity to the experimentally measured hadronic cross section remains. This challenge is addressed via the ansatz of factorization [14]. Factorization asserts that the cross section calculation can be separated into a short-distance, or high momentum transfer, piece describing the partonic subprocess, and long- distance pieces describing the momentum distributions of partons within hadrons and the fragmentation of partons into hadrons. Assuming the initial state partons are traveling collinearly with their respective hadrons, the cross section for particle production can be written as [15]: d3o s EC'C-l—E-(A + B —'> C + X) = Z/diliadflfbd206(§ + Z + [(1)2271- pC abcd C (1'2) do >< Git/Mira, Qzle/B($b1Q2)d—i(ab -*> “000/ch, Q2), where s, t and a are the parton level Mandelstam variables, defined as § = (1711+pb)2 t 2 (pa - ps)2, and a 2 (pa - pd)2; p.- being the 4-momentum of parton i, I 4 A / “ c \ G: Parton Distribution D: Fragmentation Functions Functions \ . . / B Figure 1.1 Schematic illustration of a high pr hadronic interaction. %i’-(ab —+ cd) is the parton level hard scattering cross section, Gi/I(xs,Q2/u%) represents the probability of finding parton i with fraction $7 of the longitudinal momentum of hadron I, and DC/C(zs, 6.22/m3?) represents the probability of finding hadron C with the fraction 2s of the momentum of the outgoing parton c. G (:13, Q2 / 71%) is called the parton distribution function (PDF) and D(z, Q2/m}) is called the fragmentation function (FF). The variables 71}: and m F are called the factorization and fragmentation scales, respectively. These scales are arbitrary, non-physical parameters which serve to define the separation between long and short-distance phenomena. Typically, the values chosen for these scales are related to some experimental observable such as transverse momentum, although other, more sophisticated choices are sometimes made [16, 17]. Note that the cross section, being a physical quantity, cannot depend upon these arbitrary parameters. Therefore, any significant scale dependence in the prediction is usually taken as an indication of the need for higher order diagrams in the perturbative calculation. As the C(T, Q2/ 71%) and D(z,Q2/m§) functions describe the long-distance interactions of partons bound within hadrons, perturbative techniques cannot be used to calculate them, and thus these functions are presently determined from experimental data. However, they are universal in the sense that they are presumed to be independent of the process used to measure them. Furthermore, although these functions have an explicit Q2 dependence, this dependence is calculable using perturbative QCD (pQCD).2 Thus it is possible to evaluate 2 Typically, the distribution or fragmentation function is extracted at some scale, Q0, and then evolved to a different scale using DGLAP [20], or their equivalent, equations. C(x, 622/713,) or D(T,Q2/m}) from some process at some Q3 and use it in the calculation of the cross section for other processes at other Q2 values. Graphs of proton PDFs (as determined by CTEQ [18]), and n0 FFs (determined by KKP [19]), are shown in Figure 1.2. Calculations for the parton level hard scattering matrix elements have been carried out to next-tO—leading order (NLO) precision for many processes, including direct photon and n0 production. At NLO, another scale is introduced into the perturbative calculation, the renormalization scale up. This scale is used during renormalization, which is a technique used to regulate divergences encountered while evaluating diagrams containing loops. It is typical in practice to choose the scales 713, up, and mp to be equal to each other, though they need not be equal in general. 1.4 Direct Photon Physics The study of direct photon production has attractive aspects from both experimental and theoretical viewpoints. Direct photons are photons produced in parton interactions, rather than as the result of the electromagnetic decay of hadrons. At leading order, they emerge carrying the full pr of the hard scatter, and thus offer a clean probe of the underlying quark-quark and quark-gluon dynamics. Although the study of jet production also offers this opportunity, the 4-momentum of the parent parton may be difficult to reconstruct accurately since there are many particles that must be simultaneously detected and measured. There are also experimental and theoretical ambiguities present when assigning 7 xG(x) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 IIIWTIITIIIITITI l- [ Proton PDF r CTEQ6.1M pdf - Q2 = 5 GeV2 in " -‘\ t 7 ‘. - - - Up (valence) :- 7' t. ------ Down (valence) P i |“ . . - Up (sea) . j K - 1 - Down (sea) :— ." ‘.‘ — Gluon i; l' ,' ', l— I 1 L ,’ ’. r- , \ I50. “ 55“.... “‘ .\O ...o “‘\ 0" O. \\‘ "S .0 .3 ‘\‘ . \:~ . ' ....... ‘o . 5.. 0 0.2 0.4 0.6 0.8 L l l l l l I l l l l l l l l l LilliLlllllLllllllllll zD(z) 10 10 1O 10 I l I I I I l I I I I T .7 no Fragmentation I KKP ff 1 1- .~\“ 2 2 'l . Q = 5 GeV -1 t l' l. -2 7- q -3 :- --- UporDoanuark -; : - - Strange Quark : ” — Gluon ‘ .4 l 1 l l l J l l 1 4L L14 0.2 0.4 0.6 0.8 2 Figure 1.2 Left: Parton distribution functions for the proton as a function of 1:. Right: Probability that a parton will fragment into a n function of z. 0 8.88. final state particles to particular jets. With direct photons, there is only one particle to measure, and the measurement can be made with good accuracy using electromagnetic calorimeters. It has been proposed [21, 22, 23] that the study of direct photon production can provide important information about the partonic structure of hadrons. At leading order, only two processes contribute to direct photon production in hadronic interactions. These processes are illustrated in Figure 1.3. In proton-proton (pp) reactions, the cross section is expected to be dominated by the Compton process since there are no valence anti-quarks present. This is shown quantitatively in Figure 1.4. Note that since the Compton process is initiated by quark-gluon scattering, direct photon production in pp interactions is sensitive to the gluon content of the proton. Consequently, direct photon data have been anticipated to provide constraints on the gluon distribution function which, particularly at moderate to large values of :17, is not very well determined. To illustrate, gluon distributions at Q2 = 5 GeV2 for the 40 CTEQ6.1M eigenvector basis sets are shown at the top of Figure 1.5. These sets represent the positive and negative displacements, within some allowed tolerance, about each of the 20 independent parameters used in the determination of the PDF. The spread in these distributions gives some measure of the gluon uncertainty. The uncertainty in the NLO prediction for direct photon production at 530 GeV/c due to the PDF uncertainty is shown at the bottom of Figure 1.5.3 As expected, the uncertainty in the prediction, which is dominated by the uncertainty in the gluon distribution, is large. 3 The uncertainty is calculated using Eq. 2.5 of [18]. 9 q H Y q E Y g Cl g q Compton Diagrams a . 1 a g Annihilation Diagrams Figure 1.3 Lowest order Feynman diagrams for direct photon production. 10 1-0 r ' T . f r l T t: O .8 [- .7 g 0.8 - 4 Annihilation , 0.6 7- ~~~~~~~ .. 0.4 - ~~~~~~~~~ T .......... Compton 0.2 - .......... _ 0 O 1 L n . 1 . 1 . ' i ' l ' l ' I ‘ 0.8 F """"""""""""""""""""""""""""""""""""""" _ Compton r pp —> 'yX at 530 GeV/c ‘ 0.6 - _ L -1 0.4 - 'l l. . Annihilation 0.2 i- .. \ ' l 0 O 1 . 1 . 1 4 1 . 4 6 8 10 12 pT (GeV/c) Figure 1.4 Relative contribution of the annihilation and Compton diagrams to the leading order direct photon cross section for n‘ and proton beams as a function of the photon pr. GRV92 LO parton distribution function is used for the n‘ calculation, and CTEQ6.1L is used for the proton calculation. The theory calculation is provided by [15]. 11 xG(x) _L 0 Fractional Uncertainty Figure 1.5 Top: l I lllIIll Gluon Distribution Q2 = 5.0 GeV2 CTEQ6.1M pdf .2 _ 3 f . . 1 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 x : ' ' ' I ' ' ' l ' l I i ' ' r : I pBe —> yX at 530 GeV/ I ~ CTEQ6.1M pdf Q=pT / 2 l l l l L A 41 l l I l l 1 J J l l l I l l I 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Photon x.r Gluon distribution uncertainty as characterized by the CT EQ6.1M eigenvector basis sets. Bottom: Fractional uncertainty in the NLO prediction for direct photon production in pBe interactions at 530 GeV/c due to the uncertainty in the PDF. 1.5 Experimental Challenges and Techniques Due to the weakness of the electromagnetic coupling constant relative to the strong coupling constant, the direct photon cross section is z 10'3 times smaller than the jet cross section. Thus the electromagnetic decay of hadrons in jets can become significant sources of background to the direct photon signal. The biggest contributor to this background comes from the decay of n0 mesons. no’s are produced copiously in hadronic reactions and decay to two photons nearly 100% of the time. Because of the small n0 mass, the opening angle in the laboratory between the photons from the n0 decay tends to be small. This is shown in Figure 1.6, where the opening angle is plotted as a function of the energy asymmetry of the photons from the n0 decay; A E ——————|El —E2[, E1+E2 (1.3) where E1 and E2 are the energies of the photons. Unless the photon detector has sufficient granularity, the two photons often appear as a single shower in the detector, mimicking the direct photon signal. Also, even for detectors with enough transverse segmentation to efficiently resolve the photons from n0 decays, substantial background may result from highly asymmetric decays in which the detector failed to detect the low energy photon. After the no, the next leading contributor to the direct photon background comes from 17 meson decays. The 17’s contribution is roughly 20% that of the no’s, since the production rate of the 17 is approximately half that of the n0 and the only decay mode that significantly contributes is 17 —> 717 which has a 39% branching 13 lEl'Ezl * = A : ______._. BCOSO E1+E2 E20 I I l I . H ® P — E 0:50 GeV : 15 — 1: H r """" 13“.: 100 GeV :é .. ............. En°=200 GCV :1 10 [— i l' d l- 3‘ 5 *- j r. _________________________________________________________ 1 .................................................................................................................... , 0 7 l 1 1 l l m J 1 1 L 1 1 '1 ° 02 0.4 0.6 08 1 no energy asymmetry Figure 1.6 Top: Definition of n0 energy asymmetry, A. Bottom: n0 opening angle in the lab frame versus energy asymmetry. 14 ratio.4 As will be shown later, the n0 and 17 decays contribute nearly 100% of the direct photon background. Although the overall signal-to-background ratio may be small, it is expected to increase with 72,. The chief reason for this increase is attributed to the fact that at leading order, direct photons emerge from the hard scatter carrying off the full momentum of the collision, while nO’s and 17’s are fragments of jets. At medium to large values of :r, the fragmentation functions get softer as the Q2 of the interaction increases5 [24], which leads to a steepening Of the n0 and 17 pr spectra 0 relative to the parent jet pr spectra. Therefore, there are fractionally fewer n ’s and 17’s contributing to the background at high pr than at low pr. There are several experimental techniques used to statistically separate the direct photon signal from the background. The most common of these techniques are described below. Reconstruction 0’s and 17’s are identified and eliminated from In this method, photons from n the direct photon sample through the measurement of the two photon invariant mass. The remaining background, resulting from inefficiencies in identifying photons from these decays, as well as background from other sources, is usually evaluated using Monte Carlo simulations and then statistically subtracted from the direct photon sample. To minimize the background contributions, the photon 4 Contributions from decay modes such as 17 —1 3n0 are automatically included in the n0 contribution. 5 In other words, the momentum fractions carried off by the jet fragments shift to lower values as the pr of the hard scatter increases. 15 detector should have good spatial resolution in order to separate the two photons from the n0 decay and should be able to efficiently reconstruct low energy photons. This is the method used by E706. Isolation From the first order diagrams, it is expected that direct photons should emerge from the hard scatter unaccompanied by other particles. nO’s and 17’s come from jets, and are usually accompanied by other particles. Therefore, a significant reduction of the background can be obtained by imposing some isolation requirement on the direct photon candidates. One drawback to this method is that in higher order production diagrams, such as the quark bremsstrahlung diagram, direct photons are no longer expected to appear as isolated particles, and therefore a portion of the cross section is excluded from this isolated cross section measurement. The theoretical expectations must be adjusted accordingly to make meaningful comparisons with the data. Shower Profile For detectors whose granularity is too coarse to efficiently resolve the individual photons from n0 decays, some background discrimination is still possible through a comparison of transverse and/or longitudinal electromagnetic shower profiles. 0’5 are expected to be broader in the transverse view and to Showers resulting from n peak sooner in the longitudinal view than showers from direct photons. Typically, shower profiles for no’s and direct photons are determined using Monte Carlo simulations. Then, by comparing shower profiles in the data with Monte Carlo 16 profiles containing both no’s and direct photons, the fraction of direct photons in the data can be evaluated. Conversion The conversion method relies on the fact that it is more probable to observe + 0 a photon conversion into an e e" pair from a n or an 17 than it is for a direct photon (simply because there are two photons in the final state rather than one). Typically, a thin piece of material, called a converter, is positioned upstream of an electromagnetic calorimeter and scintillators are placed immediately upstream and downstream of the converter. The scintillators are used to count the number of photon conversions in the converter. By comparing the conversion fraction in the data to the fraction expected from a pure n0 and sam 1e, the fraction of 77 P direct photons in the data can be extracted. 1.6 Nuclear Effects E706 is one of relatively few high energy experiments to use multiple targets. Data were taken on beryllium, COpper, and liquid hydrogen targets. Thus the nuclear dependence of the direct photon and n0 production cross sections may be studied. In a simple view of high pr particle production using nuclear targets, the observed high pr particle is believed to result from a single hard-scatter between the beam and target nucleon constituents. Consequently, the cross-section per nucleus is expected to be proportional to the number of nucleons in the target. This can be expressed mathematically as 0A :UOAQ, (1.4) 17 where as is the cross section for a free nucleon, A is the atomic mass of the nuclear target, and a is a parameter which is equal to one in this naive view. However, as early as 1975, it was discovered that this simple view of hard scattering within nuclei did not explain the experimental data, and that the parameter a is a function of pr and for meson production is somewhat larger than one at high pr [25]. This nuclear enhancement is presumed to be due to the multiple scattering of partons as they travel through nuclear matter. In high-pr hadron production, multiple scattering may take place in the initial and/or final states. However, in direct photon production, multiple scattering is expected to occur only in the initial state since direct photons do not interact strongly. The nuclear targets employed by E706 were copper and beryllium. Since the Z /A ratio (Z is the atomic number) is similar for these materials, the parameter a can be extracted for direct photon production as well as for meson production. As E706 is the only direct photon experiment that used more than one nuclear target, its data provides a unique measurement of a for direct photon production. In addition, a theoretical calculation for the nuclear enhancement of direct photon production is available [26] and can be compared to the E706 measurement. 1.7 Initial State Parton Transverse Momentum Effects In the theoretical description of high pr particle production presented thus far, the effects of transverse motion in the initial state partons were assumed to be negligible. However, measurements of the average pr ((pr)) in dimuon and diphoton pairs indicate instead the presence of significant initial state parton transverse 18 momentum (117) A collection Of these measurements spanning a wide range of center Of mass energies is presented in Figure 1.7 [27—30]. The amount of kT 6 and is significantly larger than that expected from hadron confinement alone, is currently attributed to soft-gluon emissions prior to the hard scatter. Also shown in Figure 1.7 is the (pr) of dijet pairs, (p1,)psir. Note that (pr)ps,',. in these measurements is somewhat higher than corresponding (pr)ps,-r measurements for dimuon pairs. This is expected because in dijet production soft-gluon emissions can occur in the final state as well. Theoretically, soft—gluon emissions have been treated formally for certain processes using Sudakov resummation calculations.7 However, for inclusive direct photon production no such calculation currently exists, although progress in this area is being made [31—34]. In lieu of a rigorous treatment of soft-gluon radiation, the effects of kT can be approximated by assuming a Gaussian kT distribution and convoluting it with the cross section either analytically [35], or through Monte Carlo methods [15]. The width of the Gaussian is usually obtained through the measurement of kinematic distributions sensitive to initial state .117. It is expected that the inclusion of parton kT will enhance the predicted single inclusive differential cross section. This can be understood qualitatively through the following argument. On an event by event basis, kT can either add to or subtract from the pr from the underlying partonic interaction. If the cross section 6 Since partons are confined within hadrons, the uncertainty principle dictates that they have an intrinsic transverse momentum spread of order 0.4 GeV/c (assuming a hadron size of order 0.5 f m). This is commonly referred to as Fermi motion. 7 For example, in Drell-Yan [36, 37] and diphoton production [38, 39]. 19 A 7 r I I II I I T r I I I I] T I Ifi‘r III I Q 2 I I 1 I I l I I if, _ - g Plon Data a _ . q] - _ 13 + l- _ \9‘ 1 .— 0 8° —- 5 t— 4) ¢ 0 ’7 4 — 1 — O L l l l l l l _ ’0 ‘18 (GeV) 7 3 — . s 1- * - 2 — ¢ + “ . Ill 4; - O 1 a). 0% O Diphoton ¢ 3’ Proton Data 0 Wm, ' I Dijet ’ l l I ll 1 l l l I. l I 11 L l l l 1 J4]. l 0 1o 102 103 \/s(GeV) Figure 1.7 Average pr of muon, photon, and jet pairs produced in hadronic collisions versus ,5. 20 for particle production was a flat function of pr, then for any given value of observed photon pr, the number of instances in which there was a net pr gain will cancel with the number of instances with a net pr loss. However, the cross section for particle production is a steeply falling function Of pr, falling roughly an order of magnitude per 1 GeV of pr at fixed target beam energies. Therefore, there will be many more cases of interactions with lower partonic pr receiving a [CT boost than vice versa, leading to a net increase in the differential cross section at high pr. 1 .8 Recent Experiments Direct photon production in hadronic collisions has been studied extensively over the past 20 years. The earliest results came from the CERN ISR machine [40—44]. Though the results were subject to large statistical and systematic uncertainties, they provided clear evidence for the existence of direct photons. A review of the early experimental results can be found in [45]. Table 1.3 shows a summary of recent experiments that have published results on direct photon production. Note that the E706 data, in addition to spanning a wide range in :rT, explores the largest xT values of any direct photon experiment. 21 Table 1.3 Recent direct photon experiments. . . v? .. Experiment Beam Target Machine (GeV ) Method (: ”TA/5) _ _ 546 Isolation, .006 —1 .17 UAI [46] p p SW3 630 Shower Profile .005 —+ .29 546 Isolation, NA UA2 [47] T) p SppS 630 Conversion .04 —1 .26 Isolation, CDF [48] '1') P Tevatron 1800 Conversion /Profile .01 —1 .13 Isolation, DO [49] 1'? P Tevatron 1800 Conversion,PrOfile .01 -1 .11 R108 [43] p p ISR 63 Conversion .16 -1 .38 R110 [44] p p ISR 63 Conversion .14 -+ .32 31 .05 —-> .32 R806 [50] p p ISR 45 Reconstruction .05 -1 .32 63 .12 -> .37 R807 [51] p p ISR 63 Reconstruction .15 —1 .33 R808 [52] p, 1') p ISR 53 Reconstruction .11 -1 .23 E629 [53] p, n+ C Tevatron 19.4 Reconstruction .25 —+ .5 E704 [54] p Be Tevatron 19.4 Reconstruction .25 —1 .4 UA6 [55] p, 1'1 p SppS 24.3 Reconstruction .34 —1 .50 NA3 i Conversion/ [56] p, n C SPS 19.4 Reconstruction .30 —) .52 NA24 [57] p, ni p SPS 23.7 Reconstruction .27 —1 .50 WA70 [58, 59] p, n:b p SPS 22.9 Reconstruction .36 —1 .54 p Be, Cu, H2 38.8 .18 -> .53 E706 p, 7,: Be, Cu, H2 Tevatron 31.1, 31.6 Reconstruction .22 __) .65 22 Chapter 2 The Meson West Spectrometer 2.1 Overview The Meson West spectrometer was designed and built to perform experiment E706. The spectrometer was located in the Meson West experimental hall at the Fermi National Accelerator Laboratory (Fermilab). This spectrometer was also used for experiment E672, a dimuon experiment which ran concurrently with E706. The physical layout Of the Meson West spectrometer is shown in Figure 2.1. The experiment used a right-handed coordinate system. The Z-axis was oriented along the nominal beam direction and pointed away from the source of the beam and the Y-axis pointed upward. The X -axis therefore pointed to the left when viewed from along the Z-axis. The origin of this coordinate system was located approximately 9 cm downstream1 of the spectrometer target and was roughly centered on the beam. Various elements of the Meson West spectrometer are described in this chapter. A description of the downstream dimuon identifier can be found elsewhere[60]. 2.2 Beamline During the 1990 and 1991-92 fixed target runs, the Fermilab Tevatron (Figure 2.2) operated on a 58 second cycle. During the first 35 seconds of the cycle, protons were accelerated to an energy of 800 GeV. The remaining 23 seconds constituted the spill, during which time the beam was extracted and directed to the 1 The term downstream means along the direction of increasing Z. 23 WT... eslllvm . . nan—8:9: beam—25 " "9888: 8388 new: . . 33th. 8: 3.2..an 3.5: . an?! . Dwarf—.1 1.95%. 1.33.3..— 26265 m ”an...“ m_m.m_a:< m ohm», " u . . n . — Illllll his: 5325.310 DmQ «ON—ah. .5532 303a no; Owl-“35% Bass—Mm 90>?— :23: Figure 2.1 Schematic view of the Meson West spectrometer. 24 various fixed target experiments. Within each spill, beam particles were bunched within 1 ns buckets separated by 19 ns. The 19 ns period was a consequence of the accelerator’s RF frequency. During normal operation, the Tevatron beam intensity was z 1013 protons per spill. Beam particles were transported to the experimental hall via the Fermilab Meson West (MWEST) beamline. The beamline was designed to transport negative or positive charged beams, with momenta ranging from 25 to 1000 GeV/c. During the 1990/91 runs, the beamline delivered three types of particle beams to the experiment: an 800 GeV/c primary proton beam, a 515 GeV/c secondary negative beam (primarily n"s), and a 530 GeV/c secondary positive beam (primarily protons). For each of these beams, the beam intensity at the spectrometer target was about 2 x 108 particles per spill. The intensity limit was set by radiation safety requirements and by the rate limitations of the data acquisition system of the experiment. To generate the secondary beams, a beryllium production target was inserted into the beamline z 300 m upstream of the spectrometer target. The production target was 1.14 interaction lengths in 1990, and 0.75 interaction lengths in 1991- 92. A dipole magnet was located just downstream of the production target. By adjusting the current and polarity of the dipole magnet, a beam of secondary particles with the desired charge and mean momentum was directed down the beamline. To obtain the desired secondary beam intensity, the Tevatron beam intensity at the production target was attenuated to 5 x 1012 protons per spill for the negative beam, and to 2 x 1012 protons per spill for the positive beam. The 25 Linac Cockcroft-Walton Antiproton / 7 ‘ Booster Accumulator Tevatron Extraction for Fixed Target Experiments r 4' : MR PI 'ecti m °n Tevatron Main Ring CDF Tevatron Injection DO Figure 2.2 Schematic view of the Fermilab Tevatron. 26 beam attenuation was accomplished using two long pinhole collimators located in the beamline, and monitored using two Secondary Emission Monitors (SEMs). The particle content of the secondary beams was evaluated using a 43 m long helium filled Cerenkov counter located z 100 m upstream of the spectrometer target. A spherical mirror at the downstream end of the counter was used to reflect the light emitted by the beam particles back to an array of photomultiplier tubes located at the upstream end of the counter. This array consisted of three concentric rings of photomultiplier tubes, with each ring containing six tubes. A schematic diagram of the Cerenkov counter is shown in Figure 2.3. Various logical combinations of signals from the photomultiplier tubes were used to identify, or tag, the incident beam particles. For example, the n2P2 pion tag required signals from two or more n-ring phototubes along with NOT two or more signals from the p—ring phototubes. In Figure 2.4, the tag probability is shown as a function of pressure for three incident particle tags. The solid vertical line in the figure represents a typical Cerenkov operating pressure. Note that this line passes through the desired peaks for tagging n+, K 1‘, and protons with the appropriate coincidence logic, thus enabling the counter to tag these three particles simultaneously. From a study of these curves, the secondary beam composition was extracted [61]. The secondary beam composition for the 1990 and 1991-92 runs is shown in Table 2.1. Table 2.1 Beam composition of the secondary beams. Beam —515 GeV/c +530 GeV/c Particle Type n‘ K " p n+ K+ p Beam Fraction 97% 2.9% 0.1% 2.8% 0.5% 96.7% 27 <——— 43.4 m > + a \ a Photomultiplier Tubes /‘Z Spherical Mirror Figure 2.3 A schematic drawing of the beamline Cerenkov counter. Each ring of photomultiplier tubes is labeled according to the particle it was designed to tag. 28 t ooooooolooooooocmfintmun l I l l I 3 C _ MN ' . . ' ' ' ' : — r 0 92019 P °o a!” 4 3:3 _ °o .v'" P ~ m u . K41r2P2 °° 'v" - 3 10" .. 0_ r y n2P2 '9; T: o C :' 00 P : < l— 'v 00 d '— [. "v 'fioo . .r r n ”g .- o, . - 0 ° ' r ."1 - °°.. ' i r (K) - °- -2 'v o q 10 E. v: . "1% ‘21 7: v' . ' ° : _ TI 0 ° 0 o o a v . o o 10" fi- ° L— ' o o 1 : , ' . j : ' v ' O ’5‘ K . : __ v v ' b. .. ' v v ' V O. . L 0 .~: _’ 10" _ - __ ; 3 l- . . 0 Q 1 7 '1 -5 o o o 0 9 ° . . . 10 l l l l l l 5.2 5.6 6.0 6.4 5.8 7.2 7.6 PRESSURE (PSIA) Figure 2.4 Pressure curves for the proton, kaon, and pion tags with incident +530 GeV/c beam. Peaks/plateaus are labeled by the associated particle type. The solid vertical line represents a typical Cerenkov operating pressure. 29 The beamline was equipped with a series of dipole and quadrupole magnets to focus and direct the beam onto the spectrometer target. The beam position and X and Y profile was monitored using a series Of Segmented Wire Ion Chambers (SWICs) positioned at various locations along the beamline. The beamline also contained a series of spoiler magnets which were designed to sweep away beam halo particles.2 A 4.3 x 4.7 x 3.7 m3 hadron shield composed of steel was installed at the end of the beamline to further reduce the number of halo particles incident on the spectrometer. A tank of distilled water was located at the downstream end of the shield to absorb neutrons produced in interactions in the hadron shield. Finally, charged particles not absorbed by the shield (muons) were detected by arrays of scintillation counters called veto walls. During the 1990 run, there were three veto walls, one located just upstream of the hadron shield, and two located just downstream. For the 1991-92 run, a fourth wall was constructed and placed adjacent to the veto wall upstream of the hadron shield. 2.3 The Target During the 1990 run the experiment used two beryllium and two copper targets. The beryllium targets were cylindrical in shape, with radii of 1 cm. The upstream beryllium target had a length of 3.7 cm, while the downstream target had a length of 1.1 cm. The copper targets were located upstream of the beryllium targets. The COpper targets were 0.08 cm thick. They were formed from 2.54 cm diameter 2 Beam halo particles are particles produced in conjunction with the secondary beams that travel alongside and approximately parallel to the beam. They are mainly hadrons produced at the production target, and muons, which arise from the subsequent in-flight decay of these hadrons. 30 cylindrical disks that had two diametrically opposite arcs sliced off. This gave the targets a cross-sectional shape that was circular on top and bottom and rectangular in the middle. In the rectangular region, the copper targets were 2 cm wide in the X view. In 1991, the target configuration was changed to include a liquid hydrogen target. The liquid hydrogen was contained in a 15.3 cm long mylar flask. The flask was cylindrical with tori-spherical endcaps. It had a diameter of 6.4 cm, and each endcap had a crown radius of 6.4 cm and a knuckle radius of 1.6 cm. The flask was housed within a stainless steel vacuum shell. The vacuum shell was cylindrical in shape and was oriented with the cylindrical axis along the Z axis. At the upstream and downstream ends of the vacuum shell were beryllium windows. The upstream window was 8.25 cm in diameter and 0.25 cm thick while the downstream window was 9.52 cm in diameter and 0.28 cm thick. The 1991-92 target configuration also included two 0.08 cm thick copper targets and a 2.54 cm thick beryllium target. The copper targets were located approximately two centimeters upstream of the vacuum shell. The copper targets were cylindrical in shape with diameters of 2.5 cm. The beryllium target was placed adjacent to the downstream end of the vacuum shell. This target was also cylindrical in shape and had a diameter of 2.54 cm. The physical configurations Of the target during the 1990 and 1991-92 runs are illustrated in Figure 2.5. Also shown in the figure are the positions of the silicon strip detectors, described in Section 2.5.1. 31 3x3 cm wafers 50 um pitch l l B 5x5 cm wafers ' cm 3 25/50umpirch 3.7 cm Be 5x5 cm wafers 50 um pitch 0.8 mm Cu +8 cm => M ‘ 111 =A '30!“ = +2cm =2: +i3cm == E E E E U U U U .9. as a 9 5x5 cm wafers 0- ‘6 m C“ 25150 tun pitch 0.2 cm Be 3x3 cm wafers 2 8 B 5115 cm wafers 50 um pitch ' m e 50 um pitch 15 cm H 2 V Beam ilil E E E E E U U U U O \O ("I N w M ' ' + + 1' -l30 cm -61 cm -34 cm Figure 2.5 Layout of the target region during the 1990 and 1991-92 runs. 32 2.4 The Beam and Interaction Detectors Beam particles were detected using the beam hodoscope. The beam hodoscope consisted of three planes of scintillators and was located #15 m upstream of the target region. Each plane contained 12 scintillator elements. Each element was 2 mm thick and 35 mm long. The width of the elements varied depending upon their location relative to the center of the hodoscope plane. The central eight scintillator elements were 1 mm wide, the elements adjacent to the central eight were 2 mm wide, and the outermost elements were 5 mm wide. The hodoscope planes were arranged in X, Y and U views, with the U view making a 45 degree angle with the horizontal. A second scintillating plastic device, called the beam hole counter, was used to help ensure that the beam was incident on the target, and to help eliminate interactions from particles belonging to the beam halo. In the 1990 run, the beam hole counter was simply a 4 x 4 x % inch3 piece of scintillator with a 3/8 inch diameter hole in the center. In 1991, the single scintillator was replaced by a set of four 2,5; x 23- x % inch3 scintillators. Each scintillator had a circular piece removed from of one its corners. The piece was 3/ 8 inch in diameter and centered on the corner. When installed, the four counters formed a square with a 3 / 8 inch diameter hole in the center, essentially reproducing the geometry of the single counter used in the 1990 run. An interaction was detected through the use of two sets of two scintillation counters, one set located a few centimeters upstream of the magnet, and the other 33 set located a few centimeters downstream of the magnet. The upstream counters measured 3 x 6 x 1% inch3 while the downstream counters measured 4 x 8 x T16 inch3. Each counter had a circular piece removed from it whose center was located at the middle of the edge of one of the longer sides. The diameter of the hole was 3/ 4 inch in the upstream counters, and 123; inch in the downstream counters. When installed, the upstream counters formed a 6 x 6 inch2 square with a 3/ 4 inch hole in the center. The downstream counters formed a 8 x 8 inch2 square with a 1% inch diameter hole in the center. 2.5 The ”hacking System Charged particles were detected using sixteen Silicon Strip Detectors (SSDS), four sets of Proportional Wire Chambers (PWCs) and two sets of Straw Drift Tubes (STRAWS). A large aperture analyzing dipole magnet was used to evaluate the momenta of the charged particles. The following sections briefly describe each of these elements. 2.5.1 Silicon Strip Detectors The SSD system consisted of 16 planes of silicon wafers. The planes were arranged in 8 modules. Each module contained two planes, with the strips on the upstream plane oriented along the Y direction (X -plane) and the strips on the downstream plane oriented along the X direction (Y—plane). Three of the eight modules were located upstream of the target and were used to measure the position and trajectory of the beam particles. These were called the beam chambers and they contained wafers measuring 3 x 3 cm2. The five modules located downstream 34 of the target were called the vertex chambers and they contained wafers measuring 5 x 5 cm2. All the silicon wafers were z 300 pm thick. On 7 of the 8 modules, the width of the individual strips on the planes was 50 pm. On the other module, located just downstream of the target, the strips were 25 mm wide in the central region, and 50 um wide in the outer region. The geometric parameters of the SSD system are given in Tables 2.2 and 2.3. The SSD system had an angular resolution Of 1:10.06 mr. The angular acceptance of the SSD system was zi125 mr. The signals from each strip were amplified by Rel-Lab IO 323-C charge sensitive pre-amplifiers. The outputs from the pre-amps were then transported via z20 feet of twisted pair cable to Nanometeric[62] N-277 amplifier cards for further amplification and discrimination. The outputs from the amplifiers were then transmitted to Nanometeric N-278 latches, which were housed within standard CAMAC[63] crates. These latches stored the hit status of each strip in a buffer while awaiting a trigger decision to be reached3. In all, the SSD system included 8192 instrumented channels. Detailed information regarding the SSD electronics can be found in [64]. 2. 5.2 Analysis Magnet The analysis magnet used in this experiment was a 350 ton iron core dipole electromagnet whose aperture measured 127.0 x 91.4 x 167.64 cm3. At the upstream and downstream ends of the magnet 20 cm thick iron mirror plates were installed to reduce the fringe field. The upstream mirror plate had a 35.6 x 25.4 cm2 3 The trigger system is described in Chapter 3. 35 Table 2.2 SSD beam chamber geometrical parameters. Number of Active Region Z Position (1990) Z Position (1991) Module Instrumented Strips (cm) (cm) (cm) 1X 256 1.28 -130.2 -130.5 11’ 256 1.28 -129.3 -129.6 2X 256 1.28 -34.2 -61.8 21’ 256 1.28 -33.3 -60.9 3X 256 1.28 -19.2 -34.4 3Y 256 1.28 -18.3 -33.5 Table 2.3 SSD vertex chamber geometrical parameters. Number of Active Region Z Position Module Instrumented Strips (cm) (cm) 1X 640 2.08 -6.3 lY 640 2.08 -5.3 2X 512 2.56 -3.7 21’ 512 2.56 -2.8 3X 704 3.52 1.8 31’ 704 3.52 2.7 4X 832 4.16 7.3 4Y 832 4.16 8.2 5X 1000 5.00 12.8 SY 1000 5.00 13.7 36 hole in its center while the downstream plate had a 127.0 x 91.4 cm2 hole. A helium filled polyethylene bag was placed inside the magnet aperture to help minimize the effects of multiple scattering. The magnetic field was mapped using the ZIPTRACK[65] system developed at Fermilab. At an operating current of approximately 1050 amperes, the maximum field strength was 6.2 kilogauss. This field imparted a 450 MeV/c momentum impulse in the horizontal plane to charged particles. 2.5.3 Proportional Wire Chambers The PWC system consisted of 4 modules, with each module containing 4 planes of anode sense wires. In each module, the anode wires in each successive plane made the following angles with the horizontal: —90° (X plane), 0° (Y plane), 369° (U plane), -53.1° (V plane). Each anode plane was sandwiched between two sheets of graphite coated mylar, which served as cathode planes. The distance between the anode and cathode planes was 5.74 mm. The cathodes had three electrically independent regions, referred to as the beam, diffractive and main regions. The main and diffractive regions were held at a high negative voltage of z 3000 volts. In the beam region, current limiting resistors were installed between the cathode and the voltage supply. These resistors reduced the voltage on the cathode by an amount proportional to the beam current in that region. This desensitized the beam region, and thus prevented wires intersecting the beam region from continuously registering hits. An exploded view of a PWC chamber is shown in Figure 2.6. 37 Y—Anode % [ i F ///////////////////// X‘An‘x’elllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll Diffractive Region Beom Region \ \EN Cathode WWI/Ill ? Cathode Figure 2.6 Exploded view of a single PWC chamber. 38 The PWC modules varied in size in order to maintain an approximate constant solid angle acceptance. The first module measured 1.63 x 1.22 m2. The second and third modules measured 2.03 x 2.03 m2. The fourth module measured 2.44 x 2.44 m2. Table 2.4 gives the number of wires, wire orientation, and nominal Z position for each of the 16 PWC planes. The sense wires were made of 20 um diameter gold-plated tungsten wires. In each plane, the wires were spaced 2.54 mm apart and were strung to a tension of 40 grams prior to being fastened into place. To help maintain a constant distance between the anode and cathode planes, zigzagged strips of Kapton, called garlands, were installed in pairs at various positions along the length of the cathodes. Table 2.5 shows the location and orientation of the garland supports. The presence of these garlands disturbed the electric field locally. To compensate for this, an insulated field-restoring wire was strung along each garland on the side adjacent to the anodes. Figure 2.7 shows how the efficiency of the plane varies with respect to distance from the the center of a garland pair for two cases: (a) with no garland voltage applied, and (b) with the operating voltage of 1500 V applied to the garland wire. In all, the PWC system contained 13,440 instrumented channels. The readout electronics for the PWC system was the same as for the SSD system with the exception that the preamp boards were unnecessary, and therefore not used. For a detailed description regarding the construction of the PWC chambers, the reader is referred to [66]. 39 Table 2.4 PWC geometric parameters. Module Number of Wires Angle (degrees) Z Position (cm) 1X 640 -90.0 379.0 11’ 480 0.0 380.8 IU 704 -53.1 382.5 IV 672 -36.9 384.2 2X 800 —90.0 472.3 2Y 800 0.0 474.0 2U 896 -53.1 475.8 2V 896 -36.9 477.5 3X 800 -90.0 567.4 31’ 800 0.0 569.1 3U 896 -53.1 570.9 3V 896 -36.9 572.6 4X 960 -90.0 660.1 4Y 960 0.0 661.9 4U 1120 -53.1 663.7 4V 1120 -36.9 665.4 40 VII In ilflllu \f... Table 2.5 Orientation and positions of the garlands. The positions are relative to the center of the chamber. Note that within a chamber, the garlands are arranged in pairs, separated by z5 cm. Module View Orientation Positions (cm) 1 X,U Horizontal 2122.54, i381, 21:43.2 1 Y,V Vertical i178, i229, i584, $63.5 2,3 X,U Horizontal 21:12.7, $17.8, 21:43.2, $48.3, 21:73.7, i787 2,3 Y,V Vertical i127, i178, 21:43.2, 21:48.3, 21273.7, 21278.7 4 X,U Horizontal 2l:15.2, 21:20.3, i508, :t55.9, 21:86.4, 3291.4 4 Y,V Vertical 2l:15.2, 21:20.3, i508, 21:55.9, 21:86.4, 21:91.4 2.5.4 Straw Tube Drift Chambers Two straw chambers were installed downstream of the magnet prior to the start of the 1990 fixed target run to improve the resolution of the downstream tracking system. The first chamber was located in between the first and second PWC modules. The second chamber was located just downstream of the last PWC module. Each chamber consisted of eight planes of straw tubes; four in the X view, followed by four in the Y view. The tubes in each view were placed adjacent to one another and glued together to form a bundle. The first two planes in each view were offset by 1/2 of the straw tube diameter and glued together. The last two planes in each view were glued together in the same manner. These two pairs of planes were then glued to opposite sides of a thin sheet of mylar and offset with respect to each other by 1 / 4 of the straw tube diameter (see Figure 2.8). This offset helped minimize the number of left/ right hit ambiguities4 in the straw tubes. 4 This is discussed in the straw tracking portion of Section 4.2.1. 41 100 [I ll Efficiency (%) 60 40 20 a) 0 Volts lllllLLLlLLiillLJlllll —4 —1 d .— d _ -l ——4 -l —l —1 — - a—q _ — .l d .1 l l .IIITIIITIIIIITI—ITITITIrIII 100 80 60 40 20 b) 1500 Volts o . 1 . 1 . 1 . 1 E 1 A 1 1 1 . 1 . 1 . -1O -8 -6 -4 -2 O 2 4 6 8 10 Distance from Garland Pair (cm) llll‘lllllllLllllllilll TrIIIIITIjIIIjIIIIIIIII Figure 2.7 Relative chamber efficiency versus distance from the center of a garland pair for (a) zero voltage applied to the garland wire, and (b) 1500 volts applied to the garland wire. 42 H1135 that 2.6 The diameter of the tubes in the first chamber was 10.3 mm, while in the second chamber, the diameter of the tubes was 15.9 mm. Each tube was constructed from two spiral wrapped layers of 75 pm thick mylar. The inner surface of each tube was coated with a 8 pm thick layer of aluminum. In addition, the central four tubes in each plane had 7.5 cm long mylar inserts glued to their inner surfaces at the midpoints to desensitize the tubes in the beam region. The tubes in the upstream chamber were 1.67 m long in the X view, and 1.26 m long in the Y view. The downstream Chamber’s tubes were 2.80 m long in both views. The STRAW chambers geometric parameters are given in Table 2.6. The anode wires were made from 20pm diameter gold plated tungsten wire, and were strung at a tension of 50 g. During Operation, the anodes were held at a voltage of z1800 V. The signals from the straw tubes were amplified and discriminated using N277 amplifier cards. The signals from the cards were then sent to time-to- digital converters (TDCs) [67] via z 23m of twisted pair cable. From the time measurement, a drift-time to drift-distance conversion was determined. The straw chamber resolution was @250 um per tube. 2.6 Liquid Argon Calorimeter The Liquid Argon Calorimeter (LAC), refers collectively to two independent calorimeters, an electromagnetic calorimeter (EMLAC) and a hadronic calorimeter (HALAC). These were sampling calorimeters that used liquid argon as the ionizing medium, and lead (in the EMLAC), and steel (in the HALAC), as the absorber. The EMLAC and HALAC were housed in a common steel cryostat, which was 43 Table 2.6 Straw geometrical parameters. Module Number of Wires Tube Diam. (cm) Z Position (cm) 1X 160 1.04 426.2 1X 160 1.04 427.1 1X 160 1.04 428.1 1X 160 1.04 429.0 ' 11’ 128 1.04 434.0 IY 128 1.04 434.9 11’ 128 1.04 435.9 11’ 128 1.04 436.8 2X 160 1.59 743.9 2X 160 1.59 745.3 2X 160 1.59 747.0 2X 160 1.59 748.4 21’ 160 1.59 750.3 21’ 160 1.59 751.8 21’ 160 1.59 753.4 2Y 160 1.59 754.8 44 Anode wire ....... . N I I M y l C r Y Y Y Y Y Y Y Y Y Y A A A A A A A A A A 0000000000 Cathode Figure 2.8 A bundle of straw tubes. suspended from a movable gantry, as shown in Figure 2.9. The cryostat was made of 1.6 cm thick stainless steel and held m 17,000 gallons of liquid argon. The cryostat was encased in z 25 cm of fiberglass and polyurethane foam for thermal insulation. A low density filler vessel was placed between the cryostat wall and the front face of the EMLAC to help minimize the development of electromagnetic showers before the EMLAC. This vessel had 1.6 mm thick steel walls and was filled with Rohacell foam. 2.6.1 Electromagnetic Calorimeter Photons were detected by the EMLAC, a large lead and liquid argon sampling calorimeter. A sampling calorimeter was chosen because it offers fine position resolution at an affordable cost. Liquid argon was used as the sampling medium because it can sustain relatively high interaction rates and has good energy 45 gantry To storage 1 fl 1 dewars _. rabbit crates support rods O Axawaxaxaxx Vaxaxaxax IIIIII '''''''''''' r l l l l I j l l l I j I l l _ .44-711..,. _[, 53 filler "' Beam vessel 1’ \ Eh ’ \ ; front . .1 Q gr... II .;E Ivessel '3“; HALAC EMLAC insulation é Figure 2.9 Side view of the LAC gantry and cryostat. 46 resolution. Lead was used as the absorber because it has a relatively small radiation length and a relatively large interaction length. These properties allow electromagnetic showers to develop relatively early in the calorimeter, while minimizing the development of hadronic showers. For a detailed discussion of the design criteria of the EMLAC, the reader is referred to [68]. The front face of the EMLAC was located approximately 9 meters downstream of the target. The EMLAC was cylindrical in shape, with the cylindrical axis oriented parallel to the beamline. It had an inner radius of 20 cm and an outer radius of 150 cm. The hole at the center contained a second filler vessel filled with gaseous helium to minimize the interactions beam and forwardly produced particles in this region. The filler vessel was 40 cm in diameter, and was made from stainless steel. In the case of the 530 GeV/c proton beam, the angular coverage of the EMLAC was from 40° to 138° in the center of mass frame, corresponding to z77% of the total 471’ solid angle. The EMLAC was divided into four independent quadrants. Each quadrant was divided longitudinally into 66 layers of alternating lead absorber sheets5 and copper clad G-106 boards. The lead absorber sheets were 2 mm thick while the G-lO boards were 1.59 mm thick. They were separated by 2.5 mm gaps filled with liquid argon. The width of the EMLAC was 71 cm, or z26.5 radiation lengths. The lead absorbers also served as high voltage cathode planes. During Operation, the cathodes were maintained at a voltage of —2.5 kV. The G-lO boards 5 To be precise, the absorber sheet in the first layer was made from aluminum. 6 G-lO is the industrial name for a type of fiberglass-epoxy laminate. 47 served as the anodes. The anodes were segmented into electrically isolated strips of either constant radius (R-board) or constant phi (gt-board). The strips on the R boards were split azimuthally down the center of each quadrant, effectively dividing each quadrant into two electrically isolated octants. The R and (,25 boards were interleaved, with the first board being an R-board. The structure of the EMLAC with an exploded view of one of its quadrants is shown in Figure 2.10. On the first R—board, the inner boundary of the first r-strip was located 20.3 cm from the cylindrical axis. The strips on this board were 0.55 cm wide. On each successive r-board after the first board, the strip width increased slightly, as did t he distance from the cylindrical axis to the first strip. The strip width increased in such a manner that the line of flight of photons emanating from the target region intersects the same sequential r-strip on each R-board. This is referred to as the focusing of the EMLAC. The ¢-boards were divided into two sections, called inner and outer (23. The boundary between the two sections occurred at a radius of 40.2 cm. The inner <15 strips each subtended an angle of 7r/ 192 rad, while the outer (:5 strips subtended an angle of 7r/ 384 rad. The EMLAC was read out in two sections, a front and a back section. COI‘I‘esponding strips from first 11 R-boards were ganged together along the quadrant boundaries with braided copper wire connector strings. Similarly, the first 11 inner (outer) (b-boards were ganged together along the inner (outer) edge of the Quadrants. The connector strings were then attached to one of several readout 48 Vertical Tapered Plate Sections ‘1) -Boar - h - - - - ’ — - _ _ - ————————— ’ ‘k \‘\ i ’0 \\\ \\\ § — — — — — - - — — n — — \\ ‘ kt: 4'Jid’ \\\ I, \\\ ’ \\\ ” \\\ ‘- d - _ ————— - - — - \\\ \\\ \\\ 11:11:: I \‘\ [11111111 \\\ \ 'IIII‘ IIIIIIIII 'l/IA (cunt: 'l/II4 'IIIA -———— mn --- J - —————— - u ‘ ‘ — - d - ' '1/1/4 'lllh ' fill/4 VIII/4 \ fill! E _ - M R-Board ‘— Capacitor Bank Spacers 54““ fi 5 Slotted Spring plate Front G-10 plate ¢ Support Ring Figure 2.10 Detailed view of the electromagnetic calorimeter. 49 boards located at the front of the calorimeter. This formed the front section. The back section was formed by applying a similar wiring procedure to the last 22 R and d) boards, but in this case running the connecting strings to readout boards located at the back of the calorimeter. The signals from the readout boards were transmitted through the top of the cryostat via low impedance cable to specially designed LAC amplifier cards, called LACAMPS. The LACAMPS were designed to operated within the RABBIT[69]7 system, developed at Fermilab. Each LACAMP card handled 16 detector channels. The LACAMPS provided three types of output: a fast estimate of the energy based upon a z 180 ns charge integration time, a more precise energy measurement based upon a longer (z 800 ns) charge integration time, and a time-of—arrival measurement. A schematic diagram of a LACAMP card is shown in Figure 2.11. 2- 6.2 Hadronic Calorimeter The HALAC was located directly downstream of the EMLAC. It consisted 0f 53 sampling cells, or cookies, separated by 2.54 cm thick steel plates. The Cookies consisted of four layers of 0.8 mm thick copper clad G-10 boards. The tW0 outermost layers of G-10 had copper cladding on both sides. The outsides of these two layers were held grounded, while the insides were held at high voltage and served as the cathode planes. The inner two G-IO boards were the anode planes. They were copper clad on only one side, the side nearest the cathode plane. Etched in the copper were horizontal rows of equilateral triangles that ~7\ RABBIT stands for Redundant Analog-Bus Based Information Transfer 50 Calibration Before After \ V 1 F ost Output x1 6 180 ns top _1_ {>— LAC —1 >——l >— Amp 800 no delay I V L > Amp fl Master TVC I m: ______l Slave TVC ——l x4 x1 6 Top Bus (__ , Analo Multi Iexers Bottom Bus \ g p Figure 2.11 Schematic diagram of a single LACAMP module. served as the readout pads. The signals from the readout pads were channeled to the edge of the plane via signal traces that ran horizontally between the rows. The anode and cathode planes were kept separated by 3 mm thick strips of G-10. These strips were oriented along the direction of the readout pads, and covered the area. in between the readout pads. The G-lO spacer strips also displaced the liquid argon in front of the signal traces which preventing any current from being induced directly on the signal traces. The height of the rows containing the readout pads Was equal to the height of the rows containing the signal traces, so that only half of each anode plane was instrumented. The two anode planes were aligned so that the rows of readout pads on one anode shadowed the rows of signal traces on the 51 other, so that when taken together, the two anodes left no area uninstrumented. The size of the triangular readout pads increased in each successive cell. This served to focus the pads on the target. The height of the rows ranged from 11 cm to 14 cm. An exploded view of a cookie is shown in Figure 2.12. Tongue plate EOORiC §\\ ;\ “9P0“ ‘ .«\ " Headers 32:- \‘é High \bltage G-lO Ribs 3.0mm Thick 2.5cm Thick G- 10 ships Steel Plate Ground Cu Shorting 11cm Tall Anode Stub Pads Planes EJOCtor/Fastener Ears ' Card Edge Connector Figure 2.12 Exploded view of a HALAC cookie. As with the EMLAC, the HALAC was divided longitudinally into a front and a back section. The front section consisted of 14 sampling cells, while the back section consisted of 39 cells. Corresponding pads in the front section were C01111ected together and read out into the same amplifier channel. The back section 52 ml phi; HUI 5h‘lt'l was read out in a similar manner. The HALAC employed readout electronics similar to those used for the EMLAC. 2.7 Forward Calorimeter The forward calorimeter, or F CAL, was designed to measure the energy and mean 1971 of the beam jet. It was located downstream of the LAC gantry, approximately 15 meters from the target. The FCAL consisted of three nearly identical modules. Each module was composed of interleaved sheets of 1.9 cm thick steel absorber and 4.8 mm thick acrylic scintillator and measured 114 cm in diameter, with a 3.2 cm diameter hole in the center. The upstream and middle modules contained 28 steel plates and 29 scintillator sheets, while the downstream module contained 32 steel plates and 33 scintillator sheets. These three modules gave the forward calorimeter a thickness of 10.5 interaction lengths. To collect the light produced by the scintillator, 60 1.0 cm diameter wave Shifter rods, arranged in a 11.5 cm grid, were placed through each module. A Photomultiplier tube was located at one end of each rod. The signals read out from the photomultipliers were proportional to the light collected by the wave Shifters, which in turn was proportional to the energy deposited in the scintillator Sheets. A more detailed discussion of the FCAL can be found in reference [70]. 53 Steel Absorber Scintillator——-> BBQ Wave S a ifter Bars Figure 2.13 The forward calorimeter. 54 Chapter 3 Trigger and Data Acquisition 3. 1 Overview The primary physics goal of this experiment was to study the production of direct photons at high pr. However, since the majority of strong interactions are soft (i.e. produced at low pr), an online trigger system was developed that predominately selected the high pr interactions, or events, of interest for further study, and rejected the rest. This trigger system selected approximately 1 out of every 105 interactions that occurred in the data. Once an interaction was selected by the trigger system, a signal was sent to the data acquisition (DA) system, and the event was read out and written to 8 mm magnetic tape. This chapter provides a brief description of the E706 trigger and DA systems. For a complete discussion of the trigger system, the reader is referred to [71]. Complete discussions of the DA system can be found in references [72, 73]. 3.2 Trigger System The signature of an interaction containing a high pr direct photon is the localized deposition of high pr electromagnetic energy in the EMLAC. To select such events, the trigger used a dedicated system of electronics, called the “pr system”. The 111. system, which operated within the RABBIT standard, used the fast output lines from the r-view LACAMPs to form fast estimates of the pr in the EMLAC. To form these fast estimates, the signals from the fast outputs of adjacent r-strips were added together and attenuated by a factor proportional to 55 sin (0;), where 0,- was the angle between the ith r-strip and the beam direction. The attenuated signals from groups of eight consecutive r-strips were summed together to form sums-of-8 signals (see Figure 3.1). Because of the sin(6) weighting, these signals represented, to a first approximation, the pr deposited in a given radial region of an octant. These sums-0f—8 signals formed the basis from which most of the trigger decisions were made. Since the n0 and direct photon pr spectra fall rapidly with pr, the experiment used several different trigger definitions to populate different pr regions. To populate the low end of the pr spectrum, simple triggers based upon the detection of beam particles and interacting beam particles were used. To keep these triggers from overwhelming the DA system, only a certain fraction of them were selected for further processing. This is referred to as trigger prescaling. At moderate values of pr, LAC-based prescaled triggers with relatively low thresholds were used, and at high pr, LAC-based triggers with relatively high thresholds were used. In Table 3.1 the primary trigger definitions used by the experiment, the fraction of events selected by these triggers, and the prescale factors associated with these triggers is shown. The pr regimes of these triggers is illustrated in Figure 3.2. At this point, no corrections have been applied to the data. The formation of the trigger took place in a series of three increasingly complex steps. The first step is the beam and interaction determination. This was followed by a preliminary pretrigger determination, and finally, the trigger determination. In the following sections, these steps are described. 56 Ch. 0 8-bit linear Ch.l attenuator 7 Ch. 2 ‘ 8-bit linear Ch. 3 attenuator ‘ H sum-of—8 Ch. 4 ’ (0-7) 8-bit linear Ch. 5 attenuator - Ch. 6 8-bit linear Ch. 7 attenuator 7 x O C 0 # sum'Of'S /’ 1 (8-15) sum-of-8 (16-23) 0 o % > Ch. 30 o o o > sum-of—8 01.31: >‘—f (2431) sum-of—32 Figure 3.1 Sums-of-8 signal formation. 57 Table 3.1 Trigger characteristics during the 1990 fixed target run. Many events satisfied more than one trigger. Some prescale factors changed during the run. Prescale Fraction of 'Irigger Factor Events (%) BEAM 156 2 INTERACTION 155 3 PRETRIGGER 2925 7 SINGLE LOCAL Low 40 18 SINGLE LOCAL HIGH 1 4O LOCAL GLOBAL Low 40 2O LOCAL GLOBAL HIGH 1 35 TWO GAMMA 1 20 DIMUON 1 2O 3.2.1 Beam and Interaction Requirement The lowest level of the trigger formation is the beam and interaction ‘ requirement. The beam hodoscope planes (Section 2.4) were used to detect beam particles. If at least two hodoscope planes registered at least one hit cluster eachl, then a BM signal was produced. If in addition, not more than one hodoscope plane identified two or more hit clusters, then a second signal, called BMl was produced. To ensure that these signals were produced in phase with the bucket structure of the beam, two timing signals from the main accelerator were used to form the final beam definition. These were BMGATE, which was a @23 sec pulse generated during the spill cycle of the accelerator, and RF_CLOCK, which was a 252 MHz pulser signal that produced a train of 1 as wide pulses in phase with the bucket 1 A cluster is defined as one hodoscope element registering a hit or two adjacent elements registering hits. 58 11 1O IIIIITIIITIIIIIIIIIIIITIIIlleIIIIITTIIIIIIIll E-‘ a. E ”a % 101° 0.. pBe at 530 GeV 9 Doc, 10 ”0,, 0 Interaction 8 a q: I Pretrigger High 10 -....-- A Single Local Low or A Local Global Low 10 7 .i 0 Single Local High pew-2'. 0 Local Global High W 10 6 _ .m E 10 5 a: 4 .m’?‘ 103 {"93 102 . Pit-ff" + +—+— 10 + 1 ll1111llllJlIlllLlilLllilllllll]ILL11141llllll 1 2 3 4 5 6 7 8 9 410 pT (GeV/c) lllllfll 1 Lllllul l llll|||l | |||||||l Figure 3.2 Number of photon pairs with mass in the r0 region per pr bin versus for several different trigger types. No corrections have been applied to the data in this plot. 59 structure of the beam. With these signals, the following beam definitions were made: BEAM E BM (8 BMGATE ® RF_CLOCK (3.1) and BEAMI E BMl ® BMGATE ® RF_CLOCK, (3.2) where ® is the symbol for the logical AND. The BEAMl definition was the definition primarily used by the experiment since it guarded against the presence of multiple beam particles within the same RF bucket. The indication of an interaction came from the interaction counters. An INTERACTION signal was generated when at least two of the four interaction counters fired in coincidence with the BEAM signal. However, before an interaction could be considered for triggering purposes, there were several additional criteria imposed on the event. To ensure that the interactions occurred within the target region, a veto was imposed on signals from the beam hole counter, BE. In addition, a CLEAN signal, which was generated when there was no INTERACTION signal within i3 RF buckets of the current RF bucket, was required. This was necessary because the pretrigger logic units needed time to reset themselves after receiving the final interaction signals. Also, since the tracking electronics had a timing gate of z100 ns, this helped eliminate overlapping events in the tracking system. Finally, a signal from the DA system, CMPRDY, was used to indicate that the DA system was ready to accept data. The final interaction signal, LIVE_INT1, was given by LIVE-INT1 2 INT ® BEAMl ® fi 8) CMPRDY ® CLEAN. (3.3) 60 3. 2.2 Pretrigger Requirement The next step in the formation Of the trigger was the pretrigger requirement. The pretrigger was designed to quickly reject the bulk of the low-pr interactions. To form the pretrigger signal, the sums-of—8 signals from each octant were sent to specially designed biased pr adder cards. There were two such cards for each octant, one for the inner 128 r-strips and one for the outer 128 r-strips. The biased pr adder cards added together the signals from the sums-of-8 to produce an output corresponding to the total p, in each half octant of the EMLAC. These cards only summed signals from the sums-of—8 that were above a certain thresholdz. This was done to suppress the effects Of image-charge induced signals on strips located in regions of the EMLAC that did not have any associated shower activity [71]. To temporally match the signals from the biased pr adder cards with the signals from the beam and interaction counters, the outputs from the pr adder cards were sent to two sets of zero-crossing discriminators. One set had a higher threshold than the other, and was used to produce the PRETRIGGER HIGH signal. The other set was used to produce the PRETRIGGER LOW signal. In the 1990 run, the PRETRIGGER HIGH threshold corresponded to z2 GeV/c pr deposited in a half-octant. The PRETRIGGER LOW threshold was 20.5 GeV/c lower than the PRETRIGGER HIGH threshold. In the 1991-92 run, the corresponding thresholds were somewhat higher. Once the pretrigger pr requirement for a given octant was met, several other conditions had to be satisfied before a PRETRIGGER HIGH or PRETRIGGER LOW 2 The threshold was of the order of a few hundred MeV. 61 signal was sent to the next level of the trigger system. A LIVE_INT1 signal was required to ensure the presence of a usable interaction. In addition, to protect against triggers resulting from interactions Of beam halo muons in the EMLAC, the status of the veto wall quadrants shadowing the pretrigger octant was checked. If an event satisfied the following logic: (VW1 63 VW2) ® VVV3 (3.4) in 1990, or (VWI GB Vl/Vz) ® (VW3 {B VW4) (3.5) in 1 991, where VW, indicates that veto wall i registered a hit within i3 RF buckets of the current RF bucket in the quadrant shadowing the pretrigger octant and EB and (3 are the symbols for the logical OR and AND respectively, then the event was rejected. Also, since the signals from the EMLAC have a rise time of the order of 300 ns, signals from interactions occurring in close time proximity may overlap, creating the impression of a high—pr event. To avoid these “pile-up” events, the pretrigger vetoed events in which the pretrigger octant had significant pr in one Of its half-octants within the previous @300 ns. This was called the early- pr re(lliirement. Finally, the power supplies for the LAC electronics generated a CharElcteristic 400—Hz noise spike. These noise spikes affected the signals from the LAC AMPS, and therefore events occurring in time coincidence with these noise Splkes were vetoed. 62 nei 3.2.3 The Local Triggers The local triggers were designed to select events that deposited large amounts of pr over relatively confined regions of the EMLAC. This made them well suited for efficiently selecting events containing high-pr direct photons or Ito’s. There were two local triggers, one with a relatively high pr threshold called the SINGLE LOCAL HIGH, and one with a lower threshold called the SINGLE LOCAL LOW. To keep the SINGLE LOCAL Low trigger from dominating the data sample, the SINGLE LOCAL LOW trigger was prescaled by a factor of 40 during the 1990 run. During the 1991 run, the prescale factor was 200 for all but the last part of the run, where the prescale factor was 280. TO form the local triggers, the sum-Of-8 signals from each octant were sent into local discriminator modules. There were two modules for each octant, one for the SINGLE LOCAL HIGH and one for the SINGLE LOCAL Low. In these modules, overlapping sums-0f-16 were formed by combining the signals from neighboring sums-of-8 (see Figure 3.3). This summing eliminated the likelihood of inefficiency in the trigger due to showers that were centered near the boundaries of neighboring sums—of-S’S. If the signals from any of the sums-of—16, called the trigger-pr, exceeded the modules threshold, either a LOCAL_HI or LOCAL_LO logic signal was produced (depending on the module). The final local triggers were then formed from the logical AND of the LOCAL-HI or LOCAL_LO signals with the PRETRIGGER HIGH signal, viz. SINGLE LOCAL HIGH 5 LOCAL_HI ® PRETRIGGER HIGH (3.6) 63 and SINGLE LOCAL Low E LOCAL-LO <8) PRETRIGGER HIGH. (3.7) 3.2.4 The Global Triggers Although the local triggers were well suited for selecting events containing high pr direct photons and Ito’s, they were not well suited for selecting events containing other high 17,. particles such as the w and 77, since the showers resulting from the decay products Of these particles are typically separated by distances greater than the width of a Single sum—of-16. For this reason, the experiment also used another class of triggers, called global triggers. The global triggers were formed from the analog sum of the Signals from the inner and outer biased pr adder cards in an octant. AS with the local triggers, there was a high threshold global trigger, called the GLOBAL-HI, and a low threshold GLOBAL..LO trigger. TO suppress global triggers due to coherent noise in the EMLAC and / or image charge effects, the final global trigger definitions also contained a LOCAL_LO requirement: LOCAL GLOBAL HIGH 5 GLOBAL_HI <89 LOCAL-LO ® PRETRIGGER HIGH (3.8) and LOCAL GLOBAL Low E GLOBAL_LO ® LOCAL_LO ® PRETRIGGER HIGH. (3.9) During the 1990 and 1991 runs, the LOCAL GLOBAL LOW triggers were prescaled by various amounts ranging between 10 and 70. 64 from p sum-01$ 0.? 55-15 M.‘ 16-33 163? Ml 24.31 248.13: 25-154 from pT module sum-of.8 outputs * discriminators 8-bit DAC ma... ____\__/o-2.5V l ECL 0-7 back '\ Outputs 8 15 r I ' I - rout / | : 2 l ' 8-15 back I I 16-23 front ‘ / I : I 16-23 back ‘F : E J\ . I > | 24.31 front >_< / i : 4 ' I 24-31 back 2 ' I / l\ 7 L: ' l t / i : ' I ' l 8-bit DAC : . a25v ' i ' l l : . ' I ' I \ ' | \ : I 248-255 front I: - i 248-255 back 8-bit DAC O—2.5V Global OR (NIM & TTL) Figure 3.3 Block diagram of a local discriminator module. 65 3.2.5 The TWO GAMMA Trigger In addition to studying the inclusive production Of direct photons, the experiment also sought to study the production of high-mass pairs of direct photons. The signature Of such a pair is significant pr deposition in Opposite hemispheres of the EMLAC. The TWO GAMMA trigger was used to select such events. This trigger was formed by coincidences of the LOCAL_LO and PRETRIGGER LOW logic signals from a given octant and in one of the three octants Opposing it. There was no need for a prescale factor for the TWO GAMMA trigger, since it is relatively rare for Opposing octants to have pr depositions satisfying the LOCAL_LO requirement 3.3 Overview of the DA system Data acquisition was controlled by a DEC3 aVAX computer. Linked to the aVAX were three DEC PDF-11 computers, referred to as ROCH, NEU, and MU, and a F ASTBUS[74] system. Each of these systems was responsible for the readout of one or more of the experiment’s detectors. ROCH and MU read out the CAMAC crates connected to the forward calorimeter and the E672 downstream dimuon system, respectively. NEU read out the CAMAC crates connected to the SSD’S and the PWC’S. This PDF-11 also recorded the state of the trigger logic and the Cerenkov information. The FASTBUS system read out the STRAW TDC’S and the LAC RABBIT crates. A block diagram of the DA system is Shown in Figure 3.4. 3 Digital Equipment Corporation 66 Downstream Trigger Muon PWC (E672) F CAL Cherenkov STRAWs it \ 4x 4‘ WOLF CAMAC CAMAC CAMAC TDCS ICBM MU ROCH NEU PDP PDP PDP FASTBUS 11/34 11/34 11/34 T T l T HOST . TAPE nVAx DRIVE Figure 3.4 Block diagram Of the E706 DA system. (57 Once a trigger was satisfied, an INTERRUPT signal was sent to each of the front-end systems indicating that the data were to be read out. While the data were being transmitted from each system to the host aVAX, a BUSY gate was generated which remained enabled until all the data had been read out. Once all the BUSY gates were disabled, a CMPRDY signal was sent tO the trigger, indicating that the DA system was ready to accept more data. The complete readout of a typical event took z8 ms. The software used for data acquisition was VAXONLINE [75], a DA software package deveIOped at Fermilab. The VAXONLINE package consisted Of 4 major components: EVENT_BUILDER, OUTPUT, RUN_CONTROL, and BUFFER_MANAGER. EVENT.BUILDER was responsible for the concatenation of the data received from each subsystem. The data were checked for consistency and collected into a single event buffer. The size Of an event was z25 kilobytes. OUTPUT was responsible for writing the buffered events to the output media. During normal running conditions, events were written to a pair Of 8 mm tape drives, with events being sent to each drive in alternating order. Events were written out in sets known as runs, with each run containing $365000 events. RUN-CONTROL managed the above processes, and also performed any initialization necessary tO begin the data acquisition. BUFFEILMANAGER was used to send a COpy Of some of the events to various computers for online monitoring of the data. 68 Chapter 4 Event Reconstruction 4.1 Overview Over the course Of the 1990 and 1991 fixed target runs, E706 recorded z71 million events onto @1250 eight mm magnetic tapes. To reconstruct this large data sample, the experiment used a number Of SGI1 computer farms located at the Feynman Computing Center at Fermilab. Each farm consisted Of a cluster Of le central processing units (CPU’S). Within each farm, one CPU was the host, or I/ O node, while the other CPU’S were the worker nodes. The host node read events from the raw data tapes, and distributed (farmed) single events to the worker nodes. The worker nodes reconstructed the events, and then returned the results to the host node, which then wrote these results to eight mm tape. These tapes were called Data Summary Tapes, or DST’S. The raw data were reconstructed using a software package called MAGIC [76]. MAGIC was written in FORTRAN 77 and utilized the ZEBRA [77] memory management system. Technically, the main source code was not written in proper FORTRAN, but was converted into FORTRAN through the use of the PATCHY [78] code management package. The use of the PATCHY package allowed essentially the same piece Of computer code to produce executable programs on a variety of system platforms. MAGIC was successfully run on DEC VAX, SGI INDIGO, and IBM2 RISC machines. 1 Silicon Graphics, Inc. 2 International Business Machines 69 The various detectors of the spectrometer had their data reconstructed through calls to their respective reconstruction subroutines. These were: 0 PLREC — Charged Track Reconstruction; o EMREC — Electromagnetic Shower Reconstruction; o DLREC — Discrete Logic Reconstruction; o HCREC — Hadronic Shower Reconstruction; o FCREC — Forward Calorimeter Reconstruction. In the following sections, a brief description Of PLREC, EMREC, and DLREC will be provided, as they were the reconstructors Of most direct relevance to this analysis. Readers interested in the details Of the HCREC and FCREC reconstruction programs are referred to [79] and [70], respectively. 4.2 Charged Track Reconstruction The planes reconstruction subroutine, PLREC, was responsible for reconstruct- ing the positions and momenta Of the particles detected by the charged particle tracking system, and for finding the location of the primary interaction vertex. The trajectories Of the charged particles, called tracks, were determined indepen- dently upstream and downstream of the magnet. The upstream and downstream tracks were then linked together, and the track momenta were calculated. The major elements Of PLREC are highlighted below. For a more complete discussion, see [80]. 70 4.2.1 Downstream Tracking The paths Of charged particles downstream Of the magnet were reconstructed using information from the PWCS and straw drift tubes. View tracks were formed from the wire locations with a latched signal (hits) Observed in each PWC view (X, Y, U or V). The view tracks were then correlated to form three dimensional space tracks. Space track parameters (slope and intercept) could then be improved using information from the straw drift tubes. Because Of the high efficiency, redundancy, and low noise in the PWC system, and in Spite of the high average track multiplicity (about 30), tracking was rather straightforward in all but a small region surrounding the beam trajectory. Since the direct-photon, dimuon, and heavy-quark production physics Of the experiment did not rely on tracking in this region, the tracking hardware and software were not intended to be used for these very forward tracks. Nevertheless, attempts were made to handle this region and complicated the details Of the tracking code. These complications will largely be omitted in the discussion below in order to focus on the features of the tracking code relevant to the physics of the experiment. PWC Tracking In the high multiplicity environment Of this experiment, Monte Carlo studies Showed that the highest efficiency for finding true tracks while keeping the number Spurious tracks to a minimum, was Obtained not by a simple cut on a fit X2 (per degree of freedom) but by cuts on the nature of the track constraint class, i.e., the number of hits or hits shared with another track. For example, outside of 71 the forward region, it was rare for more than two tracks to Share a large number Of hits between them. Therefore, the first level of the tracking code performed a search for four hit tracks with a straight line fit x2 < 3.0, in each Of the four views. Hits were assigned to tracks if they were contained within a window of i1.0 wire spacings. If two or more tracks shared three hits, only the lowest x2 solution was retained. Also, if two or more tracks Shared one or two hits, only the two tracks with the lowest X2 solutions were retained. This was followed by a pass searching for three hit tracks with a straight line fit x2 < 2.0, that Shared at most one hit with a four hit track. These were then subjected to sharing cuts to select one or two tracks from a cluster. Using the view tracks as a guide, space tracks were identified that had at least 13 hits (out Of the 16 possible hits in the four views) and were consistent with a straight line fit to a common track with appropriate X2 cuts. A hit-Sharing cut removed tracks that shared nine or more hits with another track of higher hit count. TO capture tracks with large X2 due to multiple scattering or other anomalies, hits not used in the tracks found above were searched for tracks with 12 hits if they projected through all four PWC modules, or 10 hits if they projected through only three modules. To further increase the acceptance for low momentum particles, wide-angle tracks that lay outside of the acceptance Of the last two PWC modules were identified. These tracks had tO have at least 6 hits and Show correlated activity in the X view Straw Drift Tubes and point back to the target in the Y view. 72 g l I l ‘ l r l ' T ‘ l T l r l I l ' l ' l ' 1 “+3 0'5 P 800 GeV/c p beam —0— 8 E 0.4 — — c: . g _.._ m 0.3 — ~— 02 — T l —o— I 0.1 - - , _._ o L i ‘—‘1‘ Mi 44 n L i A 5 6 7 8 9 1o 11 12 13 14 15 16 Hits per Track Figure 4.1 Distribution Of PWC hits per space track. Figure 4.1 Shows the number of hits per Space track from a representative sample Of the 800 GeV/c data. Assuming all losses Of hits are due to the intrinsic efficiency of the PWC planes, such a hit distribution implies an average PWC plane efficiency of A9670. Note that this is a lower limit, since losses can result from multiple scattering within the PWC planes and from biases in the track reconstruction algorithm. Track Parameter Improvement using Straw Drift Tubes The downstream tracking system included two modules of straw drift tubes, with each view containing four X and four Y planes. Since the drift tubes have a spatial resolution approximately 3 times smaller than that of a PWC, the drift 73 tube hits were used to improve the PWC track parameters. Closely spaced drift tubes, however, have a weak pattern recognition capability. Therefore, previously found PWC space tracks were projected to the straw drift tubes, and the tubes searched for hits (both left and right solutions for each) within a 3.5 mm window. In a number of iterations straw tube hits were removed that were not consistent with the PWC track parameters. As a final step, hits in the straws (minimum Of four hits with at least one in each straw drift tube module) and those of the PWC were used in a combined fit of the space tracks. Space tracks using only PWC information were called PWC tracks, while space tracks incorporating both PWC and straw drift tube information were called STRAW tracks. Approximately 75% of the space tracks were STRAW tracks. 4.2.2 Upstream View Tracking and Linking Charged particle trajectories upstream Of the magnet were reconstructed using the SSD vertex chambers3. Note only X and Y View tracks were found, Since the SSD vertex chambers did not have a rotated view with which to correlate the View tracks. The SSD view tracking was carried out in two stages. In the first stage, only four and five hit view tracks were found. The procedure for finding view tracks was analogous to the PWC view track finding. Two planes were chosen as seed planes, and the three remaining planes were used as search planes. The window for finding hits in the search planes was 75 mm wide. TO find all possible track 3 These were the five SSD X -Y modules located downstream of the target. 74 combinations, two passes were made through the SSD hits, using different planes as the seed planes in each pass. View track candidates were fit to straight lines, and only view tracks with xz’s of 5 or less, for the five hit tracks, and 4 or less, for the four hit tracks, were saved. Any pair Of view tracks was allowed to Share a maximum of three hits between them. If a pair shared more than three hits, then the track with the fewer number of hits was dropped. In cases where both tracks had the same number of hits, the track with the larger X2 was dropped. Once all the four and five hit view tracks were found, they were then correlated, or linked, with downstream Space tracks. To link the tracks, each downstream space track was projected to the center of the magnet in the X and Y views. The upstream view tracks were also projected to the center of the magnet, and the difference between these projections in each view, AX and AY, as well as the difference in the slope in the Y view, AYSL, was calculated. Corrections to AX, AY, and AYSL were included to account for the effects of the magnet on the trajectories Of charged particles[81]. If these quantities fell within their respective linking windows, the SSD view track was considered linked. TO determine the size of the linking windows, the widths of the AX, AY, and AYSL distributions were determined as functions of the track momentum. Separate functions were determined for PWC and STRAW tracks. These distributions are shown in Figure 4.2. The broadening of the resolution at low momentum is due to the increased importance Of the effects of the magnet’s fringe field and multiple scattering on the particle trajectories in this regime. A width of 3.3 0 was assigned to the linking window for each of these distributions. Also, an additional 0.1 mm, 75 for the AX and AY windows, and 0.015 mr, for the AYSL window, was added to the linking windows to accommodate small variations in the alignment of the PWC and STRAW chambers over the course of the run. Often, several SSD tracks would link to a given downstream space track (particularly in the case Of PWC Space tracks). TO determine the best link in these situations, a “linking x2” was defined: X2 = (AX/(fax)2 (4-1) in the X view, and X2 = (AY/UAYl2 + (AYSL/UAYSLl2 (4-2) in the Y view, where oAx, 0A)», and OAYSL were the expected uncertainties in AX, AY, and AYSL, respectively. The link with the smallest linking X2 was called the best link to the downstream track. In addition, up to four extra links were stored for each downstream track. In cases where the downstream track had more than five links, the five links with the lowest linking x2 were saved. After the linking, all unlinked SSD view tracks, with the exception of isolated view tracks“, were removed. Isolated view tracks were generally formed by low momentum particles that were swept out of the acceptance of the downstream tracking system by the magnet. These were saved to aid in the finding of the primary interaction vertex in cases where there were few linked tracks. In the second stage of SSD view tracking, three hit view tracks were found. In this stage, all the hits associated with previously found view tracks were removed 4 These are tracks that did not share any hits with other tracks. 76 A r I I I I I I T I l I If I I I T I T I l I T I I l I I I I 6 ht o o o —‘ E [.1 o pr Tracks AX Llnklng Resolution - e "4* o STRAW Tracks 4 ’13) _ _ 38 fl 2 - Q — A 1 fl' r l I T1_l—l"—f_l—l—l'—l_l—I—"l—1'_T_T— 6 1 . . . ‘ g AY Linking Resolutlon _ o 4 3 _ _ g . a- a... 1 o. l M 4 ‘ -[ 0 _L_4_L.4_J_I_I_.L4_L4_4_4_I_L_L_L_l__l__L_L_I__l__l__L_J_L.J_I_ A rI—W—F—T—r-W—F—I—Tfi—T—T—Ij—Ifi—T—ITT—IW g 3 :‘g AYSL Linking Resolution 0 h 2 F”. I S lllllllilljljll A v I l 1 l I 1 l l I Y 1 J l l i O 1 0 20 3O 40 50 60 p (GeV/c) {‘0’ 0]) Figure 4.2 AX, AY, and AYSL linking resolution as a function Of the track momentum. The dotted lines indicate the functions used to determine the size Of the linking window. 77 from consideration. To find all possible combinations of three hit tracks, there were four passes made through the SSD hits, with each pass using a different set of SSD seed planes. The tracks were fit to straight lines, and only tracks with x2 values of less than 2.0 were saved. To save these tracks, it was also required that they linked to downstream Space tracks that were previously unlinked. 4.2.3 Vertex Finding and Relinking The location of the interaction vertex (primary vertex) was reconstructed using the SSD view tracks. Vertices were found in the X and Y views independently. At first, only SSD tracks that were best links to downstream tracks were used by the vertex finding algorithm. If no vertex was found, then SSD tracks that were extra links, and, if necessary, unlinked were used. The vertex finding algorithm was based upon an impact parameter minimization (IPM) scheme which is described in detail in reference [82]. For a given vertex position, a X2 was defined, it x2 = Z bk/ok. (4.3) k=1 where bk is the impact parameter Of track k5, and 0k is the projection uncertainty of track k. The vertex position was found by minimizing this X2- Once the minimum was found, the vertex algorithm calculated the average impact parameter of the input tracks. If the average impact parameter was less than 20am, or the largest impact parameter was less than 50am, the vertex candidate was retained. Otherwise, the track with the highest impact parameter was excluded from the fit and the vertex position was re-evaluated. 5 The impact parameter is defined as the Shortest distance between the track and the vertex. 78 After the view vertices were found, they were correlated based upon the difference in the Z positions, AZ Xy, of the vertices. View vertices with AZXy < 5mm, or with oAz/AZXY < 8, where 0A2 was the estimated uncertainty in AZ Xy, were called matched vertices. In cases where multiple combinations Of view vertices satisfied the matched vertex criterion, the view vertices with the smallest AZXy became matched vertices. The Z position Of the matched vertex was then given by the weighted average Of the Z positions found in the two views. Finally, in cases where several matched vertices were found, the matched vertex located furthest upstream was assumed to be the primary vertex. The difference AZ Xy provides a measure of the vertex resolution in Z, since the view vertices are determined independently. The AZ Xy distribution is shown in Figure 4.3 for the 1990 7r' data. The half width at half maximum (HWHM) 0.6 mm.6 Given that the uncertainties in the Z position in the two views are approximately equal, the uncertainty in Z for a given view is HWHM/J2, or 0.4 mm. Once the location Of the primary vertex was established, the assignment Of the best SSD links to the downstream space tracks was performed again using the position Of the vertex as an added constraint. The linking X2 was redefined to include terms proportional to the SSD track’s impact parameter with the 3 primary vertex. The SSD track with the smallest “relinking X2, was subsequently reassigned as the best link. 6 The HWHM is being used to characterize the width of the distribution, Since the distribution is non-Gaussian. 79 x103 IIIIIIIIiIITIIIIIIIIfT fiIIIITIIIIfiIIIITI E 40 :- j —l _"'... Q . .. . o : - : \ .. 3 3° - ‘ i E - " - . t: _ a m . ’ - . 20 — - _ a _ -l l - '_ . 10 " _" .. m 0 m1 1 l #1 l l 1 L1 1 1 l J l 1 L LL 1 L l l l .1 -0.4 -0.3 -0.2 -O.1 0 0.1 0.2 0.3 0.4 AZ (cm) Figure 4.3 AZ Xy distribution for vertices in the 1990 17‘ data. 4.2.4 Beam Tracking The SSD planes located upstream of the target were used tO measure the trajectories of the incoming beam particles. There were six SSD planes upstream of the target—three in the X view and three in the Y view. Beam view tracks were reconstructed in each Of these views. To reconstruct the view tracks, two passes were made through the hits in the SSD beam planes. In the first pass, beam tracks were reconstructed requiring hits in all three SSD view planes. Two planes were chosen as the seed planes. Candidate beam tracks were constructed by forming all possible combinations of pairs Of hits from the two seed planes. These tracks were then projected to the third (search) plane, and if the search plane contained 80 a hit within 75 pm (1.5 strips), a least squares straight line fit was performed. If the X2 Of the fit was less than 3.0, then the three hit combination was considered a beam view track. In the second pass, all SSD hits used to make tracks in the first pass were removed from consideration. The remaining hits were used to form two hit view track candidates. These candidates were retained if their slopes were less than 2.0 mr. The closest beam track within 100 am of the primary vertex in each view was assumed to be the trajectory of the beam particle that produced the event. If no view track was found within 100 am of the primary vertex in either, or both views, then the interacting beam particle was assumed to travel parallel to the Z—axis. In later stages of the analysis, the measurement Of pr for each particle was made with respect to the direction of the interacting beam particle. 4.2.5 Charged Track Momentum Determination The determination Of the charged particle momenta required a knowledge Of the particle trajectories upstream and downstream of the magnet. The downstream trajectories were Obtained from the downstream space tracks. The upstream trajectories were Obtained from the best linked SSD view tracks. For downstream tracks that did not contain a link in the X -view, the upstream X -view trajectory was obtained by construction, assuming that the particle originated at the primary vertex. For downstream tracks that did not have a link in the upstream Y-view (~ 5%), the upstream Y-view trajectory was assumed to be the same as it was downstream. 81 The track momentum was calculated using the effective field approximation. In the effective field approximation, the real magnetic field is replaced by a dipole field with an effective field strength, Bo, and an effective length, L. The track momentum, p, and charge, g, were then calculated from the following equations: = sign(01 — 02) - sign(Bo) (4.4) kick . 193,. + p; = sindfir— sin02’ 12’le]: = qBOL (4'5) Et- 2 tandl (4.6) pz 5% = tandy (4.7) where 191 is the angle between the charged particle trajectory in the X view and the Z axis upstream Of the magnet, 62 is the angle between the charged particle trajectory in the X view and the Z axis downstream of the magnet, and 0,, is the angle between the charged particle trajectory in the Y View and the Z axis upstream of the magnet. The nominal value Of 121/“bk was 450 MeV. After studying Signals in the data, this value was adjusted slightly so that the reconstructed K3 and J / w masses measured via the tracking system were consistent with the world values. In Figure 4.4, the n+7r‘ and a If invariant mass distributions in the regions of the K? and J/w are Shown. The mean value of the peaks in these distributions are within 0.1% Of the accepted world average Of the K2 and J /w. Note that in these samples, the momenta Of tracks from J / w decays tended to be much larger than the momenta Of tracks from K? decays. 82 "o :al., I ,.l.,,2.r-.l.,.l.,.l.,.,.,.l.,.j S 500 :- a) MK =497. 65:0. 07 MeV/ c2 1 - 1 0 ~ 1 2 400 _— l 1 "‘ : ll 1 b - + . @300 :' l ‘1 a: - [ [ .1 .g : l + 1 a 200 : + l f m : i [i : 100 :— Hi ++ : l: ++,+1+ 53W g "Wt +++ Hm, + H++++++,+,,++ m + MTV o-.l.i.l.l....++il._Lll.i.l.|.l.i.l.l.l:i.l.+1 0.45 0.47 0.49 0.51 0.53 0.5 n+1t' Mass (GeV/ c2) NU ,_ I '1‘ I ' l ' l I l I I a l. 'lfi rI ' l2 : 3 400 —— b) MW = 3. 097i0. 002 GeV/ c2 — o I I 2 : : 3 30° F I“ '5 *6 - 1 3200 "— l ll — .0 I i J, I s - , - s: - + 1+ - m 100 — + , -— t + “++ l++++++ : 5”?” If. ”f “f. . l . . ”+1”? MT an.” : Figure 4.4 Reconstructed K? and J / w masses. The means are within 0.1% Of the world averages. 02.4 2.6 2.8 3.0 32 3.4 3.6 3.8 4.0 it It Mass (GeV/ c 2) 83 5 The momentum resolution for charged particles was measured using the Monte Carlo simulation of the spectrometer described in Chapter 6. For particles produced in the target region, the average momentum resolution was found to be Op/p 2: 0.0076 + 0.0026p, (4.8) where p is the momentum measured in GeV/c. 4.3 Electromagnetic Shower Reconstruction Showers in the electromagnetic calorimeter were reconstructed using the EMREC subroutine package. EMREC reconstructed showers on a quadrant by quadrant basis. Within each quadrant, showers were reconstructed independently in the R and (15 views of the EMLAC. Furthermore, in each quadrant, the R view was subdivided into left and right R views, and the 05 view was subdivided into inner and outer (0 views. The boundary between the R views occurred at ¢ = 45", while the boundary between the 05 views occurred at R = 40.2 cm (see Figure 4.5). The showers reconstructed in each of these four views were called GAMMAS. An example of the energy deposition and the associated GAMMAS in an EMLAC quadrant for a typical high pr event is shown in Figure 4.6. The GAMMAS from the different views were correlated based upon their energies and positions to form the final reconstructed showers, which were called PHOTONS. In the following sections, the major features of the EMREC reconstruction algorithm are described; a more complete description can be found in reference [83]. 84 \\ ll /uter ‘1’ _____— Inner (D Figure 4.5 Schematic drawing of R and qb-boards showing the left~right R and inner-outer <15 boundaries. 4.3.1 Unpacking The first task of the reconstructor was to convert the digitized pulse heights recorded for each EMLAC channel into units of energy. The energy of the 1"" strip, E, was given by Ei = AemGi B(t)lNi - N29] (49) where: 0 Am, was the factor used to convert ADC counts to energy (determined from electron data to be 33.1 MeV/count); o G,- was the relative gain of the amplifier for channel 2'; 85 Run 14876 Event 15777 Quadrant 3 A j II I I T I I I I I I II I I I I I I I I I >2115 :- : l ' '2 10 e 5 a 0: ea 2- s 2 -: .4 s ___< >.17.5 '— 5 —‘ 8 L 5 J E,=15.7 5312.5; E J 6* 5 453:1.38 10 :— 5 .: r E 1E4=21.72 : : : 4 — i — _ 7.5 __ E1 __ . E 1 135- 1.17 5 E— I _: 2 ... I _ E6=20.6 2‘5 :_ E _: _| E _ E7: 15.61 0 .h ' LLL l [‘4‘ 1 l J J -‘ O . Lgl-l L L...L._L‘_Al__..l-A.L E8=40'78 0 100 200 0 100 200 59: 126 Left R strip Right R strip 8 . TI I ITI—IT I IIIIIII I I I I II . 14 __I I I I I I I I I I IEII I I I I I I I I I-‘ 7 ' 6 r 8 E ‘ 1 12 _ I .— 6 : - : - l 10 '—' I —‘ 5 E - E 1 l l— 1 —1 4 5 8 _ : _ : L 7 : ._ 3 : 6 . . - 2 4 — i " ‘ i 2* 0? - : - 9 : r 0 ll _ .l 1 -- I 1L .1 .J ‘ III 0 [A L l A 1.14;] All-.1 J .1 LA I 0 20 40 60 80 0 40 80 120 160 Inner (I) strip Outer (I) strip Figure 4.6 Energy deposition in the EMLAC. The dotted lines in the R view (05 view) plots indicate the location of the inner-outer d) (left-right R) boundary. The pair of high energy depositions in the left R and outer (,0 views are most likely from an n —-> 77 decay. 86 o B (t) was a correction factor for the observed time dependence of the response of the EMLAC; o N,- was the ADC pulse height in channel 1'; o Nf’ was the pedestal (in ADC counts) for channel 1'. The channel pedestal was the mean response of a channel when there was no energy deposited into the EMLAC. Initial values of the channel pedestals (mean and RMS) were calculated and stored between spills during data acquisition at z8 hour intervals. These values were later modified offline using prescaled beam triggered events[73]7. The channel gains were also measured between spills during the data acquisition phase of the experiment. Each LACAMP channel was equipped with calibration hardware that included a charge injection capacitor. This provided the means for each channel amplifier to be pulsed with a known charge distribution and then read out. The channel output was then plotted as a function of the input charge and fit to a straight line. The slope of the line was the gain. The gains were found to be very stable over time, typically varying by less than 0.2% over the course of each of the 1990 and 1991 fixed target runs. Although the response of the EMLAC electronics appeared to be stable over time, the overall response of the EMLAC was observed to change with time. This time dependence is illustrated in Figure 4.7, which shows the dependence of the 7 Prescaled beam events were used since they are expected to have a minimal amount of shower activity in the EMLAC. Channels associated with reconstructed showers were excluded from this offline analysis. 87 mean uncorrected no and 17 masses on the number of beam days. Days in which the EMLAC high voltage was turned off8 are not included in the beam day count as the EMLAC response did not appear to change during these periods. Possible sources for this behavior, such as impurities in the liquid argon, have been investigated, but no satisfactory explanation for this behavior has been found. For a detailed discussion regarding this effect, the reader is referred to [84]. 4.3.2 Group and Peak Finding After the ADC to energy conversion, the energies from corresponding channels in the front and back sections of the EMLAC were added together to form the summed section. The reconstruction algorithm began by searching the summed section in each View for contiguous clusters of strips with energies above 80 MeV (95 MeV in outer (b). If such a cluster satisfied the following additional requirements: 0 It was at least 3 strips (2 strips in outer 05) wide; 0 It had at least one channel with energy greater than 300 MeV (350 MeV in outer (15); 0 Its total energy exceeded 600 MeV. then that cluster was identified as a group. After the group finding was done, each group was searched for peaks. This was done in an effort to resolve showers in close spatial proximity to one anotherg. 8 Generally, the high voltage was turned off during periods of extended accelerator down time. 9 E.g., the two showers resulting from the decay no —> 77. 88 2 I I I I I I I f I I I I I I I I I I I I I I I I I I I a o _ _ m E T 0 — 33 1 8 ._ 0. 3 . ° — I: . a, I-I-l .— .. 08 —1 U 9 <9 < — ° ‘ ..J 1991 a * -‘°° ‘ 1 6 — '0 — g o .5 ._ _ .53 o _ __ 0!. F— A _ 1.4 —— — _. g — 8 F— 0 _ 1.2 — 1990 o 0 0 no mass relative to PDG — —- 088 O 1] mass relative to PDG 4 _ 08 ' A Calibration electron energy - -— . ° relative to 50 GeV/c — 1.0 F— A '— 4L 1 l l l l l l l l l I l l l 1 #1 l l L l l I l I l 0 40 80 120 160 200 240 Number of Beam Days Figure 4.7 Time dependence of the response of the EMLAC. 89 To find the peaks, each group was scanned from left to right for local minima and maxima. If a local maximum was found bounded by two minima, a peak candidate was obtained. To eliminate peaks found due to simple energy fluctuations within the strips, the significance of the peak was evaluated using the nominal EMLAC energy resolution function, 02(E) = A2 + B2 E + 02 E2. (4.10) where A = 0.22 GeV, B = 0.16 GeVl/z, and C = 0.01. If the height of the peak relative to the minima was consistent with energy fluctuations to within 2.5 a, then the candidate was discarded and the search continued for another peak. If a peak was considered significant, initial estimates of its energy and position were made. The peak energy was given by the sum of the energies of the strips between the peak minima, while the peak position was given by midpoint of the peak strip offset by an amount determined by the energies in the two strips adjacent to the peak strip. Once a peak was found in the summed section, the strips in the group in the front and back sections were searched for corresponding peaks. Often, two showers which had coalesced to form a single peak in the summed section were resolved into two peaks in the front section. (This is because the shower profiles in the front section are narrower than the corresponding profiles in the summed section.) In these cases, the summed section peak was split in two and energies were assigned to the new peaks according to the relative energy fractions seen in the front view. The positions of the new peaks were assigned the corresponding positions of the front view peaks. 90 4.3.3 GAMMA and PHOTON reconstruction After the peak finding was completed, a more precise calculation of each peak’s position and energy was made by fitting the peak to a parameterized shower shape [72]. The fitted peaks were referred to as GAMMAS. The shower shape was parameterized as a function of the radial distance from the shower centroid. To determine the shower shape, a sample of single photon showers emanating from the target region was generated using a Monte Carlo simulation of the EMLAC’S response to photon showerslo. This shape was compared to the shape derived from isolated photons in the data and the two were found to be consistent. The fitting procedure is simplest to describe in the case of single peak groups in the R view. In this case, the fit energy was given by the energy, E, that minimized the X2, x2 = 2 (E I :i EV. (4.11) i 01’ where E.- is the energy in strip 2', z, is the fraction of energy in strip i predicted from the shower shape, and 0,- is the standard deviation of the energy for the ith strip (Equation 4.10). After the fit energy was determined, the energy in the tails of the shower was calculated from Eta“ = E(1 — Z 2,). (4.12) If the X2 was less than five, then the energy stored for the GAMMA was the fit en8rgy. However, if the X2 was greater than five, then the sum energy was stored, Esum = Z Ei + Etail- (413) i 0 The details of this Simulation are given in Section 6.3.2. 91 In the case of the single peak 03 groups, the situation was complicated by the fact that distance from the strip to the shower centroid is not well known due to the radial dependence of the strip width. To proceed, an estimate of the radial position of the shower was made based upon the energy and width of the peak. Later, when the radial position of the shower was better determined, the 6’) peaks were refit. Once all the GAMMAS were reconstructed, the next task was to correlate the GAMMAS from the different views to form PHOTONS. The correlation routines looked to match GAMMAS from the R and ¢ views based upon the difference in 11. To illustrate the general procedure GAMMA energies and Efmnt/Etotal ratios for correlating GAMMAS, consider the event shown in Figure 4.6. In the quadrant shown, there are nine reconstructed GAMMAS. Based upon the similarities in GAMMA energies, GAMMAS 1 and 7, 2 and 8, 4 and 6, and 3 and 9, all appear to be good candidates for correlation. Note that GAMMAS 3 and 5 are not considered for correlation since their respective locations are not compatible; GAMMA 3 is located on the outside of the detector (large R), while GAMMA 5 is located on the inside of the detector (inner 0’) view). To correlate GAMMAS, the differences between the R and 43 view energies and E from / Etotal ratios were calculated in units of a, where a was the standard deviation of the total energy (Equation 4.10). If these differences fell within a preassigned window, the GAMMAS were considered correlated and a PHOTON of energy E = E, + E¢ was obtained. 11 Recall that the EMLAC’S R and 65 boards were interleaved. Therefore, the energy and longitudinal development of correlated GAMMAS in the R and 03 views should be nearly equal. 92 Often, two showers would overlap in one view to form a single GAMMA (this happened frequently in 710 —-> 7')! decays). An example of such an occurrence is shown in Figure 4.8. In this event, the energy of R view GAMMA 5 is roughly equal to the sum of the energies of 66 view GAMMAS 9 and 10, which implies that GAMMA 5 was comprised of two showers that strongly overlapped in the R view. EMREC contained specific routines designed to correlate GAMMAS in these situations. In this case, the two R view GAMMAS were summed together and compared to the (15 view GAMMA. If the differences in energies and E from / Etotal ratios were within the correlation window, then two PHOTONS, with relative energies assigned according to the relative energies of the 45 view GAMMAS, were obtained. Note also a similar situation involving GAMMAS 3, 4 and 6, although in this case, the overlapping showers occurred in the 63 view. EMREC also contained a set of routines designed to correlate showers that developed near the view boundaries. In such cases, the showers were often split into multiple GAMMAS, with each GAMMA located in a different view. For example, a shower that develOps near the inner-outer (15 boundary can result in three reconstructed GAMMAS—one in the R view and two, one in inner d) and one in outer (b, in the (15 View. To correlate these GAMMAS, the inner and outer (15 view GAMMAS were summed together and compared to candidate R view GAMMAS. The correlation process was repeated twice. After the first pass, the 05 view GAMMAS that were correlated were refit to obtain a better measurement of their energy. A second correlation pass was then performed. 93 Run 9411 Event 101 Quadrant 4 9 I TI I I I I I I I I I I T ' I I I I T I I I I I -‘ 0 2.4 l 2 10 T i 5 _ E(GCV) ‘3 i . i 4m is 2 5 8 — E - 1" ' as . I : . E,=5.15 1: 1.6 ' : m . 6 — i 1 53:4.75 1.2 I 5 1 54:2.03 E 4 : - E,=31.71 0.8 : : .. : : E6=7.36 0.4 . E 2 E ja=0.93 0 .. 1. ,. _ . o 1 E8=4.58 o 100 200 0 100 200 . 59:21.75 LeftRstrip RightRstripE _1135 TI I I I IIII Ij IIIIIVIIIIIII 9 ). IIIIIII IIIIII I I I I—IIIII .1 10- . 1'6 5 6 8 r E 9 " 1.4 E 7 E- 5 —f 1-2 l 6 E- l —f 1 5 5 E— 5 —: 0.8 E 4 E 5 1° —3 0.6 i 3 :— E —: 0.4 5 2 :— j —; 0-2 . . I 1 :— ‘2 0 ‘l 1““ lb Llhll lulL fl. .- O .: o 20 40 60 80 0 4o 80 120 160 Inner (D strip Outer (I) strip Figure 4.8 Another example of energy deposition in the EMLAC. The high energy deposition in the right R view and the pair of high energy depositions in the outer <23 view are most likely from a 7rO —-> 77 decay. 94 4.4 Discrete Logic Reconstruction The discrete logic reconstructor, DLREC, was used to reconstruct the status of the trigger, veto wall elements, Cerenkov counter, beam counters, interaction counters, beam hodoscope elements, and the hole counter. With the exception of the trigger, the status of these devices was latched and read out using custom made CAMAC modules called “Minnesota Latches”. The Minnesota Latches stored information in a buffer at the RF_CLOCK rate, thus storing the status of the counters for each beam bucket. When an event was selected, an INTERRUPT signal was sent to the latches, and the information stored in the 15 RF buckets centered roughly on the time of the triggering interaction were read out. The status of the trigger for each event was latched by LeCroy 4508 Programmable Logic Units and Nanometric N278 latches. The 4508’s stored the status of the PRETRIGGER HIGH, PRETRIGGER LOW, LOCALJII, LOCAL_LO, GLOBALJII, and GLOBAL-LO logic signals for each octant. The Nanometric N278 latches stored the status of each of the local discriminators. DLREC provided two main summary banks of information regarding the state of the discrete data. This information was stored in the bits of integer words. The first bank contained four words of quality information. In these words, a summary of the status of the trigger, veto walls, and Cerenkov elements was contained. In addition, bits were set that indicated if there were CAMAC readout failures, and/ or inconsistencies in the trigger logic. The second bank contained z40 integer words. These words stored the status of each of the triggers for each octant and the status of each of the trigger 95 discriminators. From these words, the efficiency for each trigger could be evaluated. The bank also contained a summary of the data from the Minnesota Latches, from which the time history of the various counters could be obtained. 96 Chapter 5 Data Analysis 5.1 Overview The data used in this analysis, sorted by beam and target type, are summarized in Table 5.1. To facilitate the analysis of this large data sample, object oriented ntuples1 were created from the DST tapes and stored on disk. Independent ntuples were written for the direct photon and neutral meson (no and 7]) analyses, as well as for most other analyses. The direct photon ntuples stored information on a 0’s and 77’s were reconstructed per photon basis. In the neutral meson analyses, 7r via their decay into two photons. Therefore, the neutral meson ntuples stored information on a per 77 basis. Most of the data analysis was based upon the information stored in these ntuples. This chapter describes the various requirements on the events and showers used in the direct photon and neutral meson analyses. As an illustration of the effect of these requirements, a 77 invariant mass spectrum for photon pairs with total p, > 3.5 GeV/c that landed in the same EMLAC octant is shown in Figure 5.1. The solid line shows the spectrum for all photon pairs, while the dashed line shows the spectrum after applying the photon and photon pair requirements. Although the 7rO and r) signals are clearly evident in both cases, the background is significantly reduced after the requirements are applied. 1 Ntuples are n x m arrays, where n is the number of objects stored and m is the number of variables stored for each object. 97 Table 5.1 Data summary for the 1990 and 1991-92 fixed target runs. Run Interaction Beam Momentum Number of Recorded Events Sensitivity (GeV/c) (millions) (events/pb) 7r"Be 8.6 1990 7r'Cu 515 30 1.4 pBe 7.3 pCu 800 23 1.8 pH 1.5 (p,7r+)Be 6.4 1991 (p,7r+)Cu 530 14 1.6 (p,7r+)H 1.3 7r‘Be 1.4 7r_Cu 515 4 0.3 7r“H 0.3 98 pT > 3.5 GeV/c Entries / 10 MeV/c2 —- A11 W pairs After cuts 0.6 0.8 1 2 w Mass (GeV/c ) Figure 5.1 77 invariant mass distribution in the 530 GeV/c proton data. 5.2 Target Fiducial Requirement Figure 5.2 shows the reconstructed Z position of vertices for events containing 77 pairs with invariant mass within the no signal region (defined in Section 5.11) and p,. > 4 GeV/c in the 515 GeV/c 7r' (1990) and 800 GeV/c proton (1991) beam data. From plots such as these, target locations were determined and longitudinal fiducial regions for each target were defined. The events used in this analysis were required to have a reconstructed primary vertex within the fiducial region of the Be, Cu, or Liquid H2 targets. Transverse target fiducial volumes for the Be, Cu, and Liquid H2 targets were also defined. The transverse location of vertices with Z position inside the Cu and 99 (x103) Events/0.05cm T I I I I I I I I I I—I I I I I I I I I I I ICI I Ifi—I I I I I I I I I I I _. r- u - I - ,0 :- 1990 -; Z 1 r- -l 7.5 :- j I Vertex j 2.5 :- SSDS 1 )- -1 0 l I I I I I I I I I I I I I T 1 I r f I Ifi ‘r T I r I I I I I r T I I I 1 I I 8 T 1991 Cu I _ Be , 6 r _. 4 ; Be Vertex —: : SSDs _ Figure 5.2 Z position of vertices in the 1990 515 GeV/c 7r’ and 1991 800 GeV/c proton data for events containing 77 pairs with invariant mass within the it0 signal region and pr > 4 GeV/c. The events are corrected for beam absorption and losses due to photon conversions. 100 Be fiducial regions is shown in Figure 5.3 for the 1990 515 GeV/c 7r" beam data and the 1991 530 GeV/c proton beam data. The transverse positions of the Be and Cu targets are indicated by the solid line. Also shown are the boundaries of the instrumented regions of the upstream SSD wafers (dashed line segments) and the location of the beam hole counter during the 1990 run (dotted circle). Note that in the 1990 run, the beam was not centered on the target.2 To account for the fraction of the beam that missed the Cu and Be targets, corrections were determined using interactions in the upstream SSD wafers. These corrections were evaluated as the fraction of vertices contained within each target’s transverse fiducial volume. 5.3 EMLAC Fiducial Requirement It is difficult to accurately measure the energy and position of photons near the quadrant boundaries of the EMLAC since portions of the resultant electromagnetic showers are deposited in non-instrumented regions. An EMLAC fiducial volume was defined for this reason. The boundaries of the fiducial volume were located far enough away from the EMLAC’S physical boundaries that such losses were minimal. Figure 5.4 shows the X—Y position of photons contained within the EMLAC fiducial volume. Note that a small region between octants within a quadrant was also excluded from the fiducial volume, even though it was fully instrumented. This was done to simplify the trigger analysis. Recall, the trigger selected events based upon the energy deposited in individual EMLAC octants. 2 This offset was caused by a manufacturing flaw in the target stand used during the 1990 run. 101 I I I I I I I T I I I I I I I I I I 3 1990 Cu _2 4| I_l I_l l 41 I L I 14 l 141 l 1 4|. 1 l l l l I I l l I I l I h l 41 J L l l l -2 -1 O 1 -2 -1 0 1 X(cm) Figure 5.3 X -Y distribution of vertices in the Copper and Beryllium targets in the 1990 515 GeV/c 7r‘ data and the 1991 530 GeV/c proton beam data for events containing 77 pairs with invariant mass within the no signal region and with pr > 3.5 GeV/c. The vertices outside the Cu and Be target area in the 1990 data are primarily due to interactions in the Rohacell target stand. 102 By cutting away from the octant boundaries, the trigger analysis did not have to account for energy leakage into other octants. An additional fiducial requirement was placed upon the contributing photon pairs in the neutral meson analysis—both photons were required to land inside the same EMLAC octant. Again, this requirement was imposed to simplify the trigger analysis. The correction for the fiducial requirement was called the EMLAC geometric acceptance correction. The EMLAC’S geometric acceptance was determined from a simple geometrical Monte Carlo simulation. For 7r0’s, a sample of 7r0 —-> 77 decays was generated on a pr and rapidity3 grid. Only 7r0’s whose photons had decay energy asymmetry (Equation 1.3) less than 0.75 were included in the simulation.4 The photons from the 7r0 decay were projected to the front face of the EMLAC and checked to see if they satisfied the EMLAC fiducial requirement. The ratio of the number of 7r0’s in which both photons passed the fiducial requirement to the total number of generated 7r0’s is the EMLAC’S geometric acceptance. An analogous procedure was used to evaluate the geometric acceptance for 77’s and single photons. The geometric acceptance for 7r0’s, 77’s, and single photons is shown in Figure 5.5 as a function of ylab for several pr intervals for the 800 GeV/c p beam data. The acceptance is similar for the other data samples. 3 The rapidity, y, is defined as y E %ln(%%:—), where E is the particle energy and p is the momentum. In this thesis, unless otherwise specified, y refers to the rapidity in the center of mass frame of reference. The relation between the rapidity in the center of mass and laboratory frames of reference is given by y = ylab —yboost, where yboost = 3.50, for the 515 GeV/c 7r‘ beam, and 3.51 (3.72), for the 530 (800) GeV/fl beam. " ‘ivation behind this asymmetry requirement is discussed in Section 5.6. 103 A v I I I v I r I I | v E 3 >_' i- . 100 r — l . 50 L. .— 0 - _ -50 — _. -100 _ _ . 1 . 1 . 1 a ' l . 1 . -100 -50 0 50 100 X (cm) Figure 5.4 X -Y position of photons contained within the EMLAC fiducial volume. The photons are from 77 pairs with invariant mass within the 1ro signal region and pr> 5 GeV/c in the 1990 7r" data. 104 Geometric Acceptance Figure 5.5 Geometric acceptance for single photons, 7r 0.8 0.6 0.4 0.2 0.8 0.6 0.4 0.2 I ' I ' I I I I __ i; ;" --------------------- - -------------- 7— :' - :- ".. uuuuuuuuuuuuuuuu yo .5 «hr 5 — , : 1|: ., _: . P- . ________ ‘ l' 'l ‘1" 11 if: i -l -i h .. .: . I: .. 3.5 < Pr < 4.0 GeV/c .t. 4.0 < pT < 5.5 GeV/c . __. _ l l l . l J A l l r 1 . I I I ' I ‘ . ' T I fl I ‘ .. N P H u ....... 4 u I .......................... a p a“ -------------------- J . :J ----- |._' .4 - .-l -"_: r : '4 q l- — T .a, rt .: LE _ LE - E‘ 5.5 < pT < 7.0 GeV/c T. 7.0 < pT < 8.5 GeV/c 1 1 4 I A l l . I 1 l 3 3.5 4 several different pr bins. 105 2.5 3 3.5 4 ylab 0’s, and 77’s versus ylab for 5.4 Hadron Rejection Background contributions to the direct photon signal due to interactions of charged hadrons (and electrons) in the EMLAC were suppressed by imposing a distance to nearest track (DTRK) requirement on direct photon candidates. The DTRK distribution for reconstructed showers with pr > 1.0 GeV/c is shown in Figure 5.6. Showers with DTRK < 1.0 cm were considered to be likely from charged particles and were excluded from the direct photon candidate sample. The correction for the DTRK requirement was evaluated using the no signal, since any losses resulting from the application of the DTRK requirement can be attributed to incidental track and shower overlap. The ratio of the 7r0 cross section measured with the DTRK requirement to the cross section measured without it provided the correction factor for 7r0’s. This ratio varied with rapidity, since the Spacial density of particles increases as the rapidity increases. In backward regions 0f rapidity the correction fractor was z 2%. At forward rapidity, it increased to a 4%. The correction for the losses incurred to direct photons was taken as the Square root of the correction for 7r0’s. Information on the longitudinal development of the shower was used to Suppress the background from long lived neutral hadrons such as neutrons and Kg’s. The ratio of the energy in the front section of the EMLAC to the total energy due to an individual incident particle, E from / Etotag, is shown in Figure 5.7 for electromagnetic showers and for hadronic showers. The electromagnetic showers are from a sample of electrons.5 The hadronic showers were selected by using \ 5 The identification of electrons in the data is described in Section 5.8. 106 IIIIIIIIIITIIIIITITTIIITWIIIIITTIITTIIIIT Entries/0.05 cm : I L— .. L— .. 1— —< 1. .. +- .4 0 P 1 1 1 l 1 r L l 1 1 1 l r J_1 l 1 1 1 J 1 1 1 l 1 1 1 l 1 1 1 l—1— 1 1 1 1 1 .. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 cm Figure 5.6 The distance to nearest track distribution for showers reconstructed in the EMLAC with pr > 1.0 GeV/c. the signal Kg —> n+7r‘, where the Kg was identified through the invariant mass Of'the 7r+7r’ pair as measured by the tracking system. The tracks were then Projected to the EMLAC and spatially matched with showers. Candidate photons Contributing to the direct photon and neutral meson analysis were required to have Efrem/Eton” > 0.2. The correction for this requirement was determined using a dEtailed Monte Carlo simulation of the EMLAC response (Section 6.3.2) and was found to range from 211%, at moderate values of pr, to z1.5%, at high values 0f 12,. This correction was absorbed into the direct photon and neutral meson l”(econstruction efficiencies (Section 6.3.5). 5.5 Rejection of Beam Halo Muons 107 0-25firrlrlllllrlrllllll[IfirITIIIITIIII Ill 0 Electromagnetic showers : O Hadronic showers _ 0.20 — __ _ ++ — —- a 0.15 — _ _ _¢_ ._ _ -¢- a 0.10 — 0 t 1— -O— _O_ -’— —4 _ 0 + _ 0.05 — -O- -O- __ ._ _0_ —O—- '0— —1 0 o _ 0 0.0—0+ 0g _ _. : +—.— '0' _ r + 0‘ O'CO‘WMIIJLIIIIIIIIIIJJL 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 EFRONT/ETOTAL Figure 5.7 E from / Etotal distributions for electromagnetic showers and hadronic showers. 108 A major source of background to the direct photon signal in the 515 GeV/c 7r" and the 530 GeV/c proton beam data was due to bremsstrahlung radiation from beam halo muons. These muons were typically produced far upstream of the target region and tended to travel approximately parallel to the beam. Therefore, when they interacted in the EMLAC, they were often misidentified as high pr showers, since the pr calculation assumed that the particle that produced the shower emanated from the target region. Beam halo muons were also a source of background in the 7r0 analysis. The reason for this follows. Since beam halo muons do not emanate from the target region, muon induced showers are distorted relative to showers from the target region. Due to this distortion, muon showers were occasionally split by EMREC into two closely separated GAMMA’s, which tended to form low mass 77 pairs. Although the Meson West beamline was equipped with spoiler magnets to deflect muons, and the pretrigger logic used the signals from the veto walls to reject events associated with beam halo muons, additional measures were required in the offline analysis to completely eliminate beam halo muons from the data sample. In Figure 5.8, the low mass region of the 77 invariant mass spectrum is shown both before and after the application of these measures. Figure 5.8a shows the 77 invariant mass distribution in the region of the 7r0 for 77 mass pairs satisfying the target and EMLAC fiducial requirements, with energy asymmetry less than 0.75, and with p]. in the range 7 < pr< 10 GeV/c. There is a large peak at low mass and the 7rO mass peak is barely discernable. However, as the beam halo muon rejection criteria are applied (Figures 5.8b-f), the low mass peak disappears 109 and a very significant no mass peak is revealed. These muon rejection criteria are described below. 5.5.1 Veto Wall Requirement Although the pretrigger vetoed events in which the veto walls registered coincidences in the triggering quadrant (Section 3.2.2), there was some inefficiency in the online veto wall requirement due to the relatively tight timing windows imposed on the coincidence of the signals from the veto walls (and the challenge of establishing the proper timing). Therefore, to improve the rejection efficiency, the veto wall requirement was recreated offline to allow for a i1 RF bucket jitter between the signals from the veto wall elements. In addition, it was found that further beam halo muon rejection was possible if the timing window for the veto wall signals with respect to the interaction time was expanded from the online requirement of :tB RF buckets to if) RF buckets. 5.5.2 Directionality Requirement The separate readout and offline reconstruction of the signals from the front and back sections of the EMLAC was used to discriminate against showers produced by beam halo muons. Because the radial strips of the EMLAC are focused upon the target region, showers resulting from particles emanating from this region will be roughly centered on the same sequential radial strip in the front and back sections. This is not expected to be the case for showers from beam halo muons, since their trajectories do not follow the focusing of the EMLAC radial strips (see Figure 5.9). 110 (x102) (x102) 01 O Entries / 5 MeV/c2 8 0.05 0.1 0.15 0.2 0.25 N 0.05 0.1 0.15 0.2 0.2 Mass (GeV/c) Figure 5.8 The effect of the muon rejection requirements on the 77 invariant mass distribution in the vicinity of the 7r0 for 515 GeV/c 1r" beam data. Each subsequent plot includes all the requirements from the previous plots. 111 Trajectory of a u from the beam halo — -- _¢ -_--- - -— _-- _- -— _— —a— _' -— ------ .- - -.- YT EMLAC Figure 5.9 Use of focusing of the EMLAC radial strips to discriminate against showers induced by muons from the beam halo. To quantify this characteristic, a directionality parameter was defined, zLAC (I E Rf — Rb, (5.1) ZbLAC where Rf (Rb) is the radial position of the shower as measured in the front (back) section, and Z fLAC (ZbLAC) is the Z position of the first EMLAC cell in the front (back) section. Showers produced by particles coming from the target region are expected to have distributions in 6 centered about zero, while showers produced by beam halo muons are expected to have distributions in 6 centered about a value of delta greater than zero. Directionality distributions for two classes of showers with pr > 5 GeV/c are shown in Figure 5.10. One class is a beam halo muon enriched 112' sample, which was obtained by requiring the veto wall requirement to fail in the quadrant containing the sample. The other class of showers is a photon enriched sample. It was obtained by applying all the muon rejection criteria, except the directionality requirement, on the showers. The directionality requirement was a function of radius. Showers with directionality 6 > 0.193 for R < 40.175 cm, or 6 > 0.0048 x R for R 2 40.175 cm, were considered to be likely from beam halo muons, and thus were excluded from the direct photon and neutral meson candidate samples. 5. 5. 3 X2 Requirement The fact that beam halo muons do not emanate from the target region can be exploited further. The electromagnetic shower shape was determined for photons coming from the target region. Consequently, showers resulting from beam halo muons are poorly fit by the shower shape, particularly in the R-view. The x2 of the fit in the R-view therefore provided further discrimination against beam halo muons. Figure 5.11 shows the xi/ E distributions for a muon rich sample and a photon rich sample for three rapidity ranges. Candidates with X:/ E > 0.1 were attributed to beam halo muons and were rejected. 113 Entries 0110’) Halo sample Beam 0.5 - 1 I 4.. I I I T T I T I I < y <—.30 —.75 -.30 < y < .30 30 5 GeV/c. The beam halo muon sample was obtained by requiring the veto wall requirement to fail in the quadrant of the reconstructed shower. The photon sample was obtained by imposing all the muon rejection criteria on the showers, with the exception of the directionality requirement. 114 (x103)‘ Beam Halo sample Entries IIIrIrIIIIlIITIfII —.75 < y < -.30 1 5 _ I I I I I i I O FT—I—f—I—I—I'fi—T—I—I—Tfi I I I Ifi .. » 30 5 GeV/c. The beam halo muon sample was obtained by requiring the veto wall requirement to fail in the quadrant of the reconstructed shower. The photon sample was obtained by imposing all the muon rejection criteria on the showers, with the exception of the x2 requirement. 115 5.5.4 Balanced pr Requirement The last requirement used to reject beam halo muons from the direct photon and neutral meson data samples was the balanced pr requirement. In real high pr interactions, the net pr in the trigger hemisphere of the EMLAC should be roughly balanced by the net pr in the opposite, or away-side, hemisphere. However, for events triggered by beam halo muons, the p, in the trigger hemisphere is expected to be much larger than the pr in the away-side hemisphere, since the event accompanying the beam halo muon is typically a soft (low pr) interaction uncorrelated with the beam halo muon responsible for generating the trigger pr. away The away—side pr, PT , was calculated by summing the [Jr’s of all the reconstructed tracks and photons which landed inside a 120° cone opposite the direct photon 0r meson candidate. The reconstructed tracks and photons used in this calculation were required to have [21. > 0.3 GeV/c. The reconstructed tracks were also required to have total momentum < 250 GeV/c. The fraction filmy/pr, where pr represents the 12, of the direct photon or meson candidate, should be near zero for triggers induced by beam halo muons, and should be near one for triggers induced by real direct photons or mesons. Figure 5.12 shows the Pygmy/pr distribution for a muon rich sample and a photon rich sample for three rapidity ranges. Candidates where Filmy/pr < 0.3 were considered likely to be beam halo muons and were rejected. 5. 5.5 Corrections for Muon Requirements The application of the beam halo muon rejection requirements also resulted in rejection of some real direct photons and neutral mesons. To account for these 116 (x103) Beam Halo sample b Entries o_I_I'—1'—T'1"-I—"I_f'_1"IIIIIIIIII OWIIIIIII ‘— 30 5 GeV/c. The beam halo muon sample was obtained by requiring the veto wall requirement to fail in the quadrant of the reconstructed shower. The photon sample was obtained by imposing all the muon rejection criteria on the showers, with the exception of the balanced pr requirement. 117 losses, a separate correction factor was determined for each of the muon rejection requirements. In the case of the veto wall requirement, the same correction was used for single photons and neutral mesons. Each EMLAC quadrant had its own veto wall correction factor, and these factors varied somewhat for each data sample. For the other requirements, separate corrections for single photons and neutral mesons were necessary. These corrections were determined from a “pure” single photon or neutral meson sample which was obtained by applying harsh versions of all the muon rejection requirements except for the requirement in question. The fraction of signal lost by the application of the requirement was taken as the correction for that requirement. These corrections were functions of the single photon, or neutral meson, pr and rapidity. In the case of neutral mesons, the product of the corrections for the muon rejection criteria was 2 1.08 at W = 4 GeV/c and increased to z 1.10 at pT = 7 GeV/c. For single photons, the product of the corrections was z 1.08 at pr; 2 4 GeV/c and decreased to z 1.02 at pp = 7 GeV/c. 5.6 7r0 and 77 Energy Asymmetry Requirement The no and 77 are pseudoscalar mesons. As such, they decay uniformly in cos 9*, where 0* is the angle between the line of flight of one of the photons from the meson decay in the rest frame of the meson and the line of flight of the meson (Figure 1.6). At high energy (5 z 1), this implies that the energy asymmetry distribution of the two photons from the decay is flat. However, experimentally it is difficult to measure 7rO’s and 77’s over the entire energy asymmetry range because of the 118 difficulty of efficiently detecting extremely low energy photons (see Figure 5.16). To illustrate, Figure 5.13 shows the 77 invariant mass in the region of the n0 for several energy asymmetry intervals. The number of reconstructed nO’s is fairly constant over the energy asymmetry range 0.0 < A < 0.8. However, for energy asymmetries above 0.8, the number of reconstructed no’s drops substantially. In addition, for A > 0.8, the n0 mass peak is significantly broader and the signal-to- background ratio is considerably diminished. At large radius, the degradation of the n0 signal begins at A > 0.75. For this reason, photon pairs were required to have an A < 0.75 to be considered as n0 or 77 candidates. Because of the flatness of the energy asymmetry distribution, this requirement has a simple 1/0.75 correction factor. 5.7 Photon Conversion Correction Photons with energy above 2mg, where me is the mass of the electron, can convert into an electron-positron pair in the presence of matter. The probability for conversion, Pam”, is approximately constant for photon energies above 1 GeV and is given by [85] Pconv = 1 _ e—7X/9, (5'2) where X is the thickness of the material in radiation lengths. This formula was used to correct for losses resulting from photon conversions. For each photon used in the neutral meson and direct photon analyses, the amount of material (in radiation lengths) the photon passed through was calculated. The probability of non-conversion, 1 — Pmnv, was then calculated. The average value of the non- conversion probability for photons versus the Z location of the photon production 119 (x103) N . I . . n f 1 Q : 0.0 - 1 ’ ‘ a g 20 — — 1 '0. j N“. = 13911103 j N“. = 137,1103 « m - . i \ _ q . 8 10 — — 4 — .5 . It Be at 515 GeV/ _ . c: » pT>4.O GeV/c - . U1 I —.75 5.0 GeV/c. The mean values for these masses agree with the world values to better than 0.5%. 128 A 5 I I I I I I j I I I I I I I I I I I I I I I I I T I I I I I I I I I I I I I I I I I I q > : | l 1 r l J (5’ ‘ 1 " '1 v 4 :— ...... j 3 ~ _________ 1 3 : .......... 1 3 — ......... Electrons 1 > ; ......... 1 :4 : ----------- . c: 2 L— ,,,,, .2 m r Photons ; a t - c0 1 tr” ._ I-t l- .. Q) .. > t - < o I I I I I I I I I I I I J I I I I I I I I I I I I L I I I I I I I I I l I I I I I I LI I I I I d 20 40 60 80 100 120 140 160 180 200 Energy (GeV) Figure 5.19 Average energy lost in the material upstream of the EMLAC for photons and electrons as a function of reconstructed energy. gross effect was strongly correlated with the choice of charge integration time for the LAC amplifiers, as shown in the inset of Figure 5.20. The radial dependence of the response observed from each octant was parametrized using the reconstructed mass from low pr 7r0 ——+ 77 decays. These parameterizations were then used to correct individual photon energies. 5. 9.2 Results and Linearity The calibrated masses of the 7r0, n, and to have been shown in Figure 5.18. The linearity of the energy scale is illustrated in Figure 5.21, where the reconstructed mass from 17 —> 77 decays is shown as a function of the 77 energy and pr. ZMP electrons were used extensively to cross-check the calibration procedure. Figure 5.22 shows the 7e+e" mass distribution. The momenta of the e+e‘ pair 129 .2 I I I I I I I I I I I I I I I I Ir T T I I I T I I {a : .9 1.12 I l I I I I r I 1 I I I .— : 0‘ _ 5 110C 0 1991 with AT=840ns I _ 1.10 +— v, — I 1990 with AT = 790 ns — - F 31083 A l988withAT=640ns — ‘ '_ U ' = _ '— V CZ 1.06 33 1990 Wlth AT 400 ns _ _ 1.08 — I: 433) —- fi 1 04 — a .0 ‘ .—I % —. —‘ 1 2 —' - 1.06 3 0 — “—1 _ i . -1 _ 4.? 1.00 : : d — dj _ 4 1.04 _ 0.98 ft fi_ I I 0.96 F - I ’— flp- 1 l 1 1 1 l 1 1 1 l 1 1 " 1 02 P 0 40 80 120 S 1 3% la _. %§D +$q 1.00 :- WOI + {if —: 0 98 :_ O 1:0 mass ratio with pT > 3.0 GeV/ c _j ' - O 1] mass ratio with pT > 4.5 GeV/ 0 ~ I 0 ZMP E/P ratio with 15 < P < 25 GeV/ 0 i 0.96 — _ _ I I I I I I I I I I I I I I I I I I I J I I I I I .1 20 40 60 80 100 120 140 Radius (cm) Figure 5.20 Radial dependence of the reconstructed it0 and 17 masses (normalized to their world values) and the E / P ratio for ZMP electrons from the 1991 data sample. Inset: Radial dependence of the reconstructed 7r0 mass for several choices of charge integration time. 130 .2 I I I _I I I I I I I I h I I r I I I I I I I I I I l I I I I I 161.04 L — a: __ _ a «31.02 ._ — 2 _ _ s:- 1.00 — "+‘*o*—o——o———o—_"—_ l — 0.98 - _ 0.96 — _ L I J I I I I I I I I I I I I l I L J J I I l I I I I I I L I 50 100 150 200 250 300 E(GeV) .2 j I 1 I I I I I I I I I I I If I I I I I I I I I I 281.04 — — 04 _ 3:) 1 «$1.02 -— _ E __ _. =' 1,00 - H—O— . —O—-——O—+——.—— ¢ ~ 0.98 r- — r __ 0.96 - _ I I I I I I I I l I I I l I I I I I I I L I I I I 3 4 5 6 7 8 9 PT (GeV/ c) Figure 5.21 The mean 17 mass (relative to the world value) as a function of the 77 energy (top) and pr (bottom) from the 1991 data sample. 131 was measured by the tracking system. The mean 7r0 and 77 masses measured in this mode are z1% lower than their respective world values. This drop, however, is expected since the conversion electrons lose energy as they travel through the target material via bremsstrahlung. This energy loss is demonstrated in Figure 5.23, 0 mass measured in this mode is shown as a function of the where the mean 7r number of radiation lengths traversed through the target. The e/e+e‘ mass ratio approaches unity in the limit of zero radiation lengths traversed, and drops uniformly with the amount of target material traversed. For comparison, the '77 mass ratio, which is not expected to show any radiation length dependence, is also shown. The 7€+€_ sample also provides another important cross-check on the energy scale calibration. The unconverted photon in the 76+6' sample is typically isolated from the electrons since the electrons are deflected away from the photon by the magnet. Therefore, by plotting the 76+8‘ mass relative to the 17 and II0 world values versus the energy of the unconverted photon, the isolated photon energy scale is investigated. This is shown in Figure 5.24. The ratio is flat versus energy and z 1% low, as expected from Figure 5.22 5.10 Trigger Analysis The events used in this analysis were selected by the SINGLE LOCAL HIGH and SINGLE LOCAL LOW triggers in 1991, and the SINGLE LOCAL HIGH and LOCAL GLOBAL LOW triggers in 1990.7 To correct for losses near the trigger threshold 7 The LOCAL GLOBAL Low trigger was used in 1990 because the SINGLE LOCAL LOW was only available during the later part of the run. 132 2 N 8 C Entries per 5 MeV/ c 61‘ 8 1000 500 I I I I j I I I I I I I I Ifi I I I I I I I I I I I I I I IT I I P _ I I I I I I I I I I I I I I I I _ .. _ pT>3.O GeV/C - PT>O-8 GeV/c- + ’ ~ Mn=133.8i0.1MeV/c2 : i ‘ _ on212.0i0.lMeV/c2 . * — 4ooo — - — I L : Mn=542i2MeVlc2 j F _ on=28i2MeVlcz - - 2000 P — . I. _ ._ L _ - _ O .- I I I I I I I I I I I I I J I I 4 ‘ 0.2 0.4 0.6 0.8 Mn = 134.0 i 0.2 MeV/ c2 on = 13.0 i 0.2 MeV/ 02 M = 543 :1 MeV/c2 n 2 on=22i1MeVlc I I I I I I I I I I I I I I J_L I I I PI L I I I I I 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 J 0.9 y e+e’ Mass (GeV/ cz) Figure 5.22 The 76‘“? mass distribution from the combined 1990 and 1991 data samples. 133 o 52 1.04 — 0 no _, W ‘ a I 0 11’, ——> w I :61 02 — L) e+6 - o _ _ l:1 00 =G====£:_.:. v WWW -------- ,. ------- — .— - -- . "'.1.-+“ _______ ‘ V .— 0.98 — -- H ----- .. 0.96 - _ I I I I I I I I 0.00 0.05 0.10 0.15 0.20 Target Radiation Length Figure 5.23 Ratio of the reconstructed ye+e‘ (o) and 77 (o) masses to the 7r0 world value versus the number of radiation lengths traversed in the target. The lines are fits to the data. .2 I I I I I I I I I I I I I I I I I I I I I I I—I I Ifi I I I I I I I I I Ifi' I 51.04 — <> nOpT>0.8 GeV/c — a — O n pT>3.0GeV/e - €31.02 — '— 2 _ _ 1.00 — o i + ‘ MM ---------- . ------ + .................................... . 0.98 r '- 0.96 — - I I I I I II I I I I I I I I I I I I I I I I I I PI I J I I I I I I I I I I 0 20 40 60 80 100 120 140 160 180 200 7 Energy (GeV) Figure 5.24 Ratio of the reconstructed 76+e‘ mass to the 1) and 7r0 world values versus the energy of the unconverted photon. 134 (see Figure 3.2), trigger corrections were determined for each trigger on an event by event basis. The determination of these corrections is described below. 5.10.1 Trigger Corrections The efficiency of the local triggers was determined by the performance of the thirty-one (one for each sum—of-16) local discriminators in each octant. Ideally, these discriminators only issued a logic signal if the input signal (the trigger-pr) exceeded the discriminator threshold. However, in practice, each discriminator had a small transition, or turn-0n, region where the probability for the discriminator to fire changed from zero to one. Turn-on curves were measured as functions of the trigger-pr for each local discriminator. In addition, separate curves were measured for run regions in which the trigger response differed due to changes in the discriminator thresholds, replacement of hardware modules, etc. To measure the turn-on curve for a given discriminator, a data sample that is unbiased with respect to the status of that discriminator must be chosen. For the LOCAL_HI discriminators, this sample consisted of events which satisfied the TWO GAMMA trigger (in the 1990 data), or the SINGLE LOCAL Low trigger (in the 1991 data), in the octant of the given LOCAL-HI discriminator. These lower threshold triggers were generally fully efficient in the turn-on regions of the LOCAL_HI discriminators, and thus provided an unbiased sample. For the LOCAL_LO discriminators, an opposite octant sample was chosen. To obtain this sample, events that satisfied the SINGLE LOCAL HIGH trigger were selected, and the seven octants other than the octant that satisfied the SINGLE LOCAL HIGH 135 trigger were ordered according to their respective pr depositions. The octant with the largest pr deposition was deemed the opposite octant and used to measure the LOCAL_LO turn-on. Once the appropriate sample of events was selected, the turn-on curve was measured by taking the ratio of the trigger-pr distribution for the sample which fired the local discriminator to the trigger-pr distribution for the entire sample. The trigger-pr for a given sum-of—16 was calculated offline by taking the energy deposited in each strip, weighing it by the appropriate trigger gain, and then taking the sum of these weighted energies. Importantly, the energy in the strips were not corrected for the time dependence of the EMLAC response, as the discriminator thresholds did not scale with time. In Figure 5.25, typical LOCAL_HI and LOCAL..LO discriminator turn—on curves are shown for the 1991 data. Once the turn-on curves were determined, the probability for the LOCAL-LO or LOCAL_HI Signal to be issued in a given octant can be obtained from 31 P =1— I10 — p.) (5.3) i=1 where p,- is the probability that discriminator 2' fired. The probabilities, pi, were determined on an event-by-event basis by calculating the trigger-pr for each discriminator and obtaining the corresponding probability from the appropriate turn-on curve. The efficiency of the GLOBAL_LO and PRETRIGGER HIGH discriminators was determined in a similar manner using the opposite octant event sample. However, the offline calculation of the input trigger-pr to the discriminators was more difficult 136 ) .5 k 0 120 Efficiency (% a s a s a O If I I T I I I I I fi @140 ’- I I I jiI I I I r I I A _ —- Z120 - 4 P I 8 P LII I I—- + w) —-1 .2 100 -- +17 I I '1 —1 n- + —1 2 I- —I I — 8: 80 ~— J, — _ - m I _ _ — 60 »— -— I. + _. P _ _ — 4o - — L (Inner) _‘ 20 _ + (Outer) _‘ I , LOCAL_ LO _ _ LOCAL_LO _ I l I l I L 1 I l 0 I l +1 l g l 4 l l l I 0 4 6 8 10 12 0 2 4 6 8 10 12 Trigger pT Trigger pT I I f; 140 I I I If Ti I I T I T _ 5 l. _ _ _ V120 _ LOCAL_HI _ — « 5‘ » (Outer) ' « r— . I fl E, 100 — + L r -( 2 r- + 1 _ _ a: 80 _ _ ~ 4 LL] » A _ L 60 _ I _ _ + - _ . _ 4 4o _ a + 20 - - r I , + _ l l LII l I l I l I 0 I l I l + l I l I l 1 0 4 6 8 10 12 0 2 4 6 8 10 12 Trigger pT Trigger pT Figure 5.25 LOCAL_.HI and LOCAL.LO discriminator turn-on curves for typical discriminators in the inner and outer regions of the EMLAC versus trigger-pr for the 1991 data. 137 due to the small threshold applied to the signals sent into the pr adder cards and the large number of strips contributing to the input. In addition, these efficiencies were found to be dependent upon the number of photons in the octant. Therefore, separate efficiency measurements were made depending upon the number of sums- of-eight contributing the trigger-pr. For more details on the these analyses, the reader is referred to [71, 88]. 5.10.2 Trigger Selection The photons used in the final direct photon and neutral meson cross section analyses were required to land in octants where the trigger had a probability of firing of at least 10% to avoid excessively large trigger corrections. The corrections for losses below this cutoff was calculated by the Monte Carlo and was absorbed in the reconstruction efficiencies (see Section 6.3.5). However, at sufficiently low pr the correction for a given trigger becomes unreliable, and it becomes necessary to use a lower threshold trigger. The transition point between triggers was determined by comparing fully corrected cross sections measured using high and low threshold triggers in the turn-on region of the high threshold trigger. The point where the two measurements agreed was deemed the transition point. The transition point was different for 7rO’S, 17’s and direct photons, since a particular trigger’s response is different for different particles.8 A composite trigger map was determined for each of these particles, and the transition point was rapidity dependent. The composite 8 For example, the large separation of photons from n decays relative to photons from no decays (at a given pr) tends to make the SINGLE LOCAL HIGH trigger less sensitive to 77’s. 138 £3, wGeV/c p data : h _ - Q: / 1 .\ ?\ _ Pretrigger High % 2 I ALI/J; I I I / I 4 1 l I -O.5 0 0.5 -1 -0.5 0 0.5 y / I A Figure 5.26 Composite trigger maps used for the 800 GeV/c proton beam data. 139 trigger map is shown for the 800 GeV/c proton beam data in Figure 5.26. The transition points for the other data samples are similar. 5.11 7r0 and 1) Signal Determination Invariant mass distributions for 77 pairs in the regions of the no and 77 are shown in Figures 5.27 and 5.28, respectively, for several bins in 7'7 1),. All meson candidate criteria have been applied to the showers contributing to the figure. For the "w pr bins where the background is linear (pr > 2.0 GeV/c), the background underneath the 7,0 and 77 peaks was determined using a sideband subtraction technique. In this technique, a peak region was defined for each meson. To each side of the peak region, sideband regions were defined. The range in mass spanned by the two sideband regions was chosen to be equal to the mass range spanned by the peak region. The physics distributions of interest (e.g. pr, y) were made for 77 mass combinations in both the peak and sideband regions. The no and 17 signal distributions were then obtained by simply subtracting the sideband region distributions from the peak region distributions, since the combined width of the sideband regions is equal to the width of the peak region. The no and 17 peak and sidebandregions used in this analysis are defined in Table 5.2. They are also shown graphically, in Figure 5.29. For the 77 pr bins below 2.0 GeV/c, a fitting procedure was used to evaluate the background. The 77 mass distributions were fit using Gaussians for the signal, and second or third-order polynomials, depending upon the pr bin, for the background. The background was evaluated using the resultant fit parameters and subtracted 140 Table 5.2 Peak and sideband mass regions used in the no and 17 meson analysis. Peak Sidebands (MeV/c2) Meson (MeV/c2) Low Mass High Mass 7r0 100-180 70-100 190—240 72 450-650 350—450 650-750 from the 77 mass distributions. The signal was then obtained by adding the counts within the peak region of the subtracted distribution. The peak regions for these low pr mass bins were defined to be somewhat wider than the peak regions used for the sideband subtraction techique to account for the wider signals in this regime. Several fits were performed for each 77 p, bin in which the mass range of the fit and/or the order of the polynomial was varied. Examples of these fits are shown in Figure 5.30. The result for the signal was taken from the average of the fits. 5.12 Direct Photon Candidate Definition Only photons that passed the aforementioned hadron and muon rejection requirements and fell within the EMLAC fiducial volume were included in the direct photon candidate sample. Furthermore, to reduce the direct photon background resulting from the two photon decay modes of the no and 77, photons were rejected from the candidate sample if they combined with another photon in the same EMLAC octant to form a 77 pair with invariant mass in the 7,0 or 77 peak region and energy asymmetry less than some specified value. The specific value for the asymmetry cut depended upon the direct photon candidate definition. Three 141 (x102) (x103) (x102) ‘5 T 1.0 3.5 GeV/c E sob pT > 3'5 GeV/c. - - F' o ‘ C I ?- Signal Region ”‘5’ .- I: LL} \ 800 GeV/c p beam J § -1.0 < y < 0.5 1 0.08 _ 10.12 10.14“ lo.16L 0.181 I 0.2 0.22 0.242 W Invariant Mass (GeV/c ) Figure 5.29 Invariant mass distributions for 77 pairs with pr> 3.5 GeV/c in the region of the no and 77. The arrows indicate the boundaries of the peak and sideband regions. 144 x107 m _I I I I . I I I‘r I ~.I r __I I I T ' I I 7 I I I I 1— ,__,I I I .I I I I I fl I g 15 _ a) Quadraiic backgrouhd m 7 _ b) Quadralic backgrodnd fit 4 _ c) Cubic black round fit — ’ _, .- ct - C'. - - ~ 1 - Lu - - - 1 - 1o — - — — — i- -I v- - :- ~ i -+ - : « ~ ~ ......... - ......... . - 5 r . ' fi Ts ' :++t r t 5 § 4 L 5 — - . a”; 1.0 < pT < 1.2 GeV/c i h; ‘ u; g A I 1 L I 1 l 1 1 I 1 1 1 1 r- I 1 1 I I 1 J J 1 I I 1 1 J 1.1 1 1 1 1 1 1 I T I I I I I I I Ifi—r _r I I I I I I I I I I J- I I I I I I I I 1 d) Cubic liack round fit I _ e) Quadraiic backgroulnd fit _ LDCublC back round ill _ I- -1 - .. L- a l— -1 r- u b q 10 »- - — "l - - _ . i I . _ ........ 3 —+ l- ........ ;J 7. ......... ‘ 5 —: . .‘PH ’— 0 . _ . 5+” ’ . : 1 l' :1 “2 " : = : : .2 E: :2 : _"§ ‘ _"’ E ‘ _. . g I I I l I 1 1 1 1 I 1 l l 1 1 I 1 1 I l 1 1 l I 1 I 1 .1 1 l l I l l 1 1 I I 1 l ,_r I I I I I I I I I I L 1 b g) Cubic liack roun fit ‘0 0'1 0'2 O 0'1 0'2 >- -I o .- f I I I I I I I I I I - " 1 '51.4 — - r ‘ a: I 2 10 b .1 _ - . - 1.2 '_" "_ : 1 E if i + i I i -1 5 r- ...... : I I 1 0.8 r 1 v- : -1 _ _ O ‘ a, - 06'— nBe—HtXatSlSGeV/c ; 0 T1. J 4 LL1 1 L 1 I 1 1 1 1‘ . I. 1 l I 1 1 1 1 l l l l d 0 0.1 0.2 b c d e f 9 W Mass (GeV/c2) Figure 5.30 Illustration of the various fits and fit ranges used extract the signal in the bin 1.0 < pr < 1.2 GeV/c. The resultant fits are drawn over the fit range of the histogram. 145 (x103) 8 . ' l ' T I ' ‘ E " —o—+—o— . [E *h— . h.“ '.'" ' . W“ ' I _. 4 _ + _ ; 4.0 < p, < 5.5 GeV/c 0 . _ 7: signal region . 2 _ —l.0 < y < 0.5 __ “ 515 GeV/c 1t- beam 2 b 1 l I 4 A l 1 l I * o I I I T I I I I I -l ~ i 4 - -1 " —o— "l *' 0 . , —o— 1 » 7t SIdeband re glon - 2 — + _ l' -o— 1 I. J I - - ”*fii-l -o-1 A—:—_;_: :1: c—r4—tfi;: r: vlf', , o I l r I l I r I I L—HW+++ 3 ; ; -O— : 4 _ —0— — .- . 0 -4 - SIdeband subtracted 1t . 2 ” asymmetry distribution * ‘_ - —O— 1 0 L l I l l l I L I o 0.2 0.4 0.6 0.8 1 Asymmetry Figure 5.31 Asymmetry distributions for 77 mass combinations in the no signal region, sideband region, and for the sideband subtracted no signal. 146 formed a 77 pair with another photon in the same octant with invariant mass in the 77 peak region and the pair had energy asymmetry less than 0.8. The third definition, 753, rejected the same photons as the 75N definition, but differed in that it also attempted to correct for losses due to true direct photons making accidental 77 mass combinations in the no peak region. In this definition, photons that formed mass combinations with other photons in the no and 77 sideband regions were weighted doubly—once for being outside the peak region and a second time to account for losses due to accidental combinations underneath the mass peaks. Each of these definitions have relative strengths and weaknesses. The 90N definition rejects the most background. However, the residual background in this definition, which must be determined from the Monte Carlo simulation, is sensitive to how well the Monte Carlo reproduces the high end of the 7r0 energy asymmetry distribution (Figure 5.31). In addition, losses of true direct photons are greatest in this definition, which again must be accounted for by the Monte Carlo simulation. The 75N and 758 definitions are less sensitive to the Monte Carlo simulation of low energy photons from no decays, but have higher background contamination. The use of all three of these definitions provides a measure of the systematic uncertainties associated with the direct photon cross section measurement. 5.13 Beam Normalization The number of beam particles incident on the target during the time in which the trigger and data acquisition system were ready to record data must be counted 147 #I‘ I in order to calculate an absolutely normalized cross section. This quantity, called the live triggerable beam (N LTB), can be written as NLTB = NBEAMl-ITH— x (LiveFractz'on), (5.4) where NBEAMl-fi is the number of isolated beam particles incident on the target that did not strike the beam hole counter and LiveFraction is the fraction of time the trigger and DA systems were live, or ready to take data. The LiveFraction can be expressed as: LiveFraction 2: (CompLiveFractz'on) X (CleanIntFractz'on) x (5.5) (PretLiveFraction) x (VetoLz'veFraction), where: o CompLz'veFractz'on is the fraction of interactions for which the data acquisition system was ready to accept data; 0 CleanIntFraction is the fraction of interactions not vetoed by the CLEANINT trigger requirement; 0 Preth’veF motion is the fraction of time the PRETRIGGER logic was not busy evaluating another interaction; 0 VetoLiveFractz'on is the fraction of interactions not vetoed by the presence of a signal in the veto wall, or a power supply noise spike, or early pr. To determine these quantities, the trigger system contained a number of electronic scalar units which counted various signal coincidences on a spill by spill basis. 148 Table 5.3 Average values of the beam absorption correction. Energy Beam (GeV) Be Cu H2 1990 7r‘ 515 1.06 1.02 —- 7r‘,'rr+ 515 1.06 1.01 1.03 1991 p 530 1.08 1.02 1.04 p 800 1.08 1.02 1.04 The live triggerable beam count obtained from the scalers must be corrected for beam absorption in the target. This correction was calculated on an event-by-event basis from the formula: Cabs = Hell/Xi, (56) i where the product runs over the materials between the beam hodoscope and the interaction vertex, A, is the absorption length of material 2', and 27 is the amount of material upstream of the interaction vertex.9 Average values for the absorption correction are tabulated in Table 5.3. Corrections were also applied to the live triggerable beam count to account for muon contamination within the beam [91], and for the fraction of beam incident on the target (Section 5.2). The cross section normalization can be cross-checked using prescaled BEAM and INTERACTION trigger samples. In these samples, the normalization can be obtained independently of the scalers simply by counting events in the sample. Comparing the results using the two different normalization methods yielded a systematic uncertainty in the overall normalization of le%. 9 For the nuclear targets, the values for A were obtained from [89]. For the liquid hydrogen target, A was obtained from [90]. 149 Chapter 6 Monte Carlo Simulation 6.1 Overview Monte Carlo computer simulations play an important role in the analysis of data from experiments investigating high energy particle interactions due to the complexity of these interactions and of the devices used to detect them. Typically, Monte Carlo simulations are used to evaluate, among other things, corrections for the detector acceptance and the detector response, particle reconstruction efficiencies, and backgrounds to the signals the experiments are attempting to extract. In this experiment, because the direct photon background can be ' substantial compared to the signal, significant effort was expended to ensure that the computer simulation provided precise and accurate information related to the direct photon background. Technically, the Monte Carlo was used to calculate the production of photons from background sources, 7b, relative to 7rO production. The direct photon background was then obtained by multiplying the ratio 7b/7r0 by the measured 7r0 cross section. Two different approaches were used to evaluate 7b/7r0. In one approach, a highly parameterized single particle Monte Carlo simulation (PMC) was used. Only contributions from the major sources of background were evaluated in this simulation. Wherever possible, simple parameterizations were used to describe the effects of reconstruction and to evaluate contributions to 7b/7ro. In the other approach, a more complicated Monte Carlo simulation was used. Multi-particle events from high 72, hadronic interactions were generated and then processed 150 through a sophisticated GEANT [92] simulation of the E706 spectrometer. This simulation modeled the interactions of the particles as they traveled through the spectrometer, as well as the response of the sensitive detector elements. The results of the detector simulation were written to output tapes in a format similar to that of the unpacked data. These output tapes were run through the same reconstruction software as the data, so any biases or inefficiencies introduced to the real data by the reconstruction programs and/ or algorithms should also be represented in the simulated data and accounted for in the resulting corrections. This simulation is referred to as the detailed GEANT simulation (DGS). This chapter presents a comprehensive description of both Monte Carlo simulations. Comparisons are shown between the real and simulated data for a variety of important distributions. Direct photon, 7r0, and 77 reconstruction efficiencies are presented. Also, a detailed analysis of 7b/7r0 is given. 6.2 Parameterized Monte Carlo Studies The PMC calculated the direct photon background resulting from the following 0 —> 77, 7r” —> 76+6‘, 77 -+ '77, w —> 707, 77’ -> 77, and 77’ -+ 7007- decays: 7r These are expected to be the primary sources of direct photon background at high pr. The contributions from other sources, such as from 7ri interactions in the EMLAC, neutrons, radiative decays of other hadrons, etc., were evaluted using the full shower Monte Carlo. 0 Parameterizations of the inclusive 7r cross section as measured by the experiment were used to generate input pr and rapidity spectra for the PMC. 151 A common expression used to fit inclusive hadronic cross sections is the phemomenological form [56, 93]: where: as. = [no.2 + (x. — 2207211”, x. = 2am. as. = mum/«5, and C, m, n, 3:0 are free parameters and Pllcm is the component of the 7r0 momentum parallel to the beam direction in the center-of-mass frame of reference. However, it was found that this form did not provide a satisfactory fit over the full kinematic range spanned by the data. Therefore, the sum of two such forms was used to fit the measured 7r0 cross sections. As shown in Figure 6.1, this provides a reasonable parameterization of the data. 1r0’s, 77’s, w’s, and 77”s were all assumed to have the same input spectra, but were normalized so that 77/7r0 in the PMC matched what was observed in the data (Figure 6.11), W/Wo was 1.0 [94, 95] and 77’/7r0 was 0.85 [95]. The absolute 7r0 normalization is unimportant, since only the ratio of background photons to 7r0’s is of interest. Once the above particles were generated, they were allowed to decay via the modes listed above according to their respective branching ratios [87]. The energies and positions of the resultant photons were then smeared using Gaussian distributions with widths determined from measurements of the EMLAC’S intrinsic energy and position resolutions [27]. In Figure 6.2, the smeared 77 invariant mass distributions from 7r0 and 77 decays in the PMC are compared to the background subtracted 77 mass distributions from the data. The good agreement shows that this procedure yields a reasonable representation of the effects of the EMLAC resolution. 152 ”E 8 TS 1o6 5 C it 61> 105 0 CD '8. 104 v m 8‘ \ mg 103 102 1o 1 —1 1o -2 1o ,,,,,,T r- IIIIITI l I II I I II '1 L’ 60 ‘5‘ = a : 4 4o E 20 i E t ,3 ’ til. I 1 .—- -O.7571 +Xat530GeV/c 5 FIIlmumml.IIIIIIIIIIIIIIIIIIIIIIIIII‘ ‘ 3 4 5 6 7 8 9 10 pT(GeV/c) Figure 6.1 The 710 cross section versus pr and rapidity (inset) for 530 GeV/c proton beam incident on beryllium. The error bars are statistical only. Overlaid on the plots are the results of the fit used in the PMC (solid curve) and a fit to Equation 6.1 (dotted curve), integrated over the appropriate pr and rapidity ranges. 153 After the energies of the resulting photons were smeared, the photons were tested to see if they would contribute to the direct photon background. For 0 photons from 7r -—> 77 decays, the background contributions can be divided 0 into two categories: background from 7r ’3 with energy asymmetry greater than Acut, where Amt is the value of the asymmetry cut used for a given direct 0 photon candidate definition, and background from 7r ’3 with energy asymmetry 0’s with energy asymmetry greater than Acut were less than Amt. Photons from 7r automatically considered as background to the direct photon signal since these photons would not be eliminated from the candidate sample via reconstruction of the no mass with another photon. For 710 —> 77 decays with energy asymmetry less than Amt, direct photon background candidates result from the failure to simultaneously detect both photons from the no decay. In the PMC analysis, the following possibilities for such failures were considered: 0 one of the photons landed outside the EMLAC fiducial volume while the other photon landed inside it; o the photons landed in different EMLAC octants; 0 one of the photons converted into an 6+6“ pair; 0 one of the photons was lost due to detector inefficiency; o the photons coalesced to form a single reconstructed shower. The contribution to the direct photon background from the first two items listed above was straightforward to evaluate. The photons were projected to the 154 IIIIIITIIIITIIIjTIIII p.r > 5.5 GeV/c ‘ I I I I I r I I I I ‘ I I I I I I I r 7 I I a .— Entries per 2 MeV/c2 Entries per 10 MeV/c2 ImIIJuImlI 0.3 0.4 0.5 0.6 0.7 0.8 w Invariant Mass (GeV/c2) Figure 6.2 Background subtracted 7r0 (left) and 77 (right) mass distributions from the data compared to the energy resolution smeared 7r0 and 77 distributions from the PMC. Here, and in future plots where the y- axis values are unspecified, the histograms are normalized to unity. front face of the EMLAC and checked to see if they fell within the EMLAC’S fiducial volume. If one of the photons was inside the fiducial volume while the other photon was outside outside it, then the photon inside the fiducial volume became a direct photon background candidate. If the photons landed in different octants, then each became a candidate unless it landed outside the fiducial volume. If both photons landed within the same octant and satisfied the EMLAC fiducial requirement, background to the direct photon signal could result from photon conversions, detector inefficiency or photon coalescence. The contributions 155 to the direct photon background from these sources were determined using a weighting procedure. This procedure is outlined below. The background from conversions were obtained by assigning a weight to each photon based upon the conversion probability of the other photon. The conversion probabilities were determined using Equation 5.2. To ensure that the photons in the PMC traversed the same amount of material as in the data, starting locations for the photons were assigned according to the observed primary vertex distributions in the data. Similarly, the background contributions due to detector inefficiency were obtained by weighing each photon from the no decay by the non-detection probability of the other photon. The detection probabilities were determined using the efficiency function shown in Figure 5.16. The contributions from photon coalescence were obtained by assigning each generated 7r0 a weight based upon its coalescence probability. This probability was determined using the DGS, since coalescence is dependent upon many factors, including the relative geometry of the two photons, the total and relative energies of the photons, and the reconstruction algorithm’s ability to resolve the two photons. The probability of coalescence was significant in a very limited region of phase space, namely pr ,2 7 GeV/c and Mob 2 3-8- It is possible to verify that the function shown in Figure 5.16 is a reasonable representation of the true detection efficiency by comparing 7r” energy asymmetry distributions in data and the PMC. This comparison is shown in Figure 6.3. If the detection efficiency was perfect, this distribution would be flat. However, due to losses of low energy photons, the distribution falls at high asymmetry. The 156 IIIIIIIIIIIIITTIIITTTTII‘IITTIIrrIIl’I‘ITiIIIIiIrITTrI _+_ + 3.5 < pT < 4 GeV/c _ + + + j - —— PMC _ 0 Data _ : 530 GeV/c p Beam —0.75 < y < 0.75 . an 1 Entries per 0.04 IllllllLlllllJllllllllJlllllLllllllIllllllllll O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Asymmetry Figure 6.3 Comparison between the sideband subtracted no energy asymmetry distribution in the data and the energy smeared PMC. good agreement indicates that the losses of low energy photons are adequately represented by the efficiency function. 0 —-> 77 decays to generated 7r0’s The ratio of background photons from 7r is shown (without corrections for the effects of the EMLAC energy resolution (Sections 6.2.1 and 63.5)) on the left hand side of Figure 6.4. Also shown is the contribution from each of the sources described above. From the figure, it is evident that photons resulting from highly asymmetric 7r0 decays are the dominant contributors to the direct photon background, although at very high 1.1,, the contribution due to photon coalescence becomes fairly significant. 157 1" o I. r I fir I I I I -’- I I I I I —[ I I I q E ~ —- a >~ -_ -4 g 1; \ “F" 10 r "I ' """"" ---------- —.-.— """""""""""""""" :5 go 3 — Total no contribution “"55 — All sources 3 .3 Z---- Asymmetry ...... Z: ---- no ---' u), I a : ........ Coalescence .0. ...... ::.............................::::::::...n. n : _2 Conversions ............................ , 10 F“-.. Fiducial " '3; 1 I Efficiency i: .......... 1 n- ..' d5 ............. '1 "~': - .. ii ""°- -..'2' ~~~~~~~~ i -3 . pBe at 530 GeV/c ' ' - -':-.~ 10 E . - . 4% —o.75 77 decays was calculated in an analogous manner, except that in this case, Amt = 0.8 for both photon definitions, and the background from coalescence could reliably be assumed to be negligible. For the background contribution from the decays 7r0 —) ye+e‘, w —> Nov, and 77’ -—> p07, the photon emanating directly from each of these decay vertices was automatically considered a direct photon background candidate, as no attempt was made to identify photons from these decays through reconstruction of the invariant mass. Photons arising from the subsequent decay of the no in the case of 158 the w and the p0 —> 7r07r0 decays are not considered in the direct photon background candidate sample, as their contribution to the background was already accounted for during the explicit consideration of the no. The contribution to the background 0 —+ 7e+e‘ decays was deemed to be negligible for two from the e+e' pair in 7r reasons: first, most of the electrons are removed from the candidate sample by the DTRK requirement, and second, since the energy of the e+e‘ pair is, on average, the same as the energy of one of the photons in the 7,0 —> 77 case, the electrons from these decays typically have much less energy, and hence 70,, than the parent no. Because of the steeply falling pr spectra, the background contributions from photons with pr significantly less than that of the parent no are generally dwarfed in comparison to other contributions. On the right hand side of Figure 6.4, 7b/7r0 (again without energy resolution corrections) in the PMC is shown. Also shown is the contribution to 7b/7r0 from each of the particles considered in the PMC. The contribution from 17 decays is z 20% that of 7r0 decays, which is roughly what is expected from simple considerations of the relative 17 and 7r0 production rates and their two photon branching ratios. 6.2.1 EMLAC Resolution Efiects The energy resolution of the EMLAC affects the measurement of the inclusive cross section. The mean reconstructed pr tends to be shifted high relative to the true mean pr, due to the steep pr dependence of the cross section. This effect is illustrated in Figure 6.5. In this section, the PMC is used to investigate how the EMLAC resolution smearing affects the analysis. 159 PT PT Figure 6.5 Illustration showing the effect of energy resolution on a steeply falling pr spectrum. For any given reconstructed pr bin, the number of entries entering from bins with lower true 72,. outnumber the losses out of the pr bin, leading to a net shift in the observed uncorrected pr spectrum. In Figure 6.6a, the ratio of the EMLAC resolution smeared 7r0 energy, Esmear, to the unsmeared, or generated, energy, E, is plotted as a function of the smeared and unsmeared pr. When plotted as a function of smeared p1,, Esmear / E is greater than one, as expected from Figure 6.5. However, when plotted as a function of unsmeared pr, Esme“, / E is equal to one, since the unsmeared 77,. is unaffected by resolution, and the energy is smeared symmetrically about the mean. Resolution smearing affects the EMLAC energy calibration. Since the measured quantities are all smeared, the mean 7r0 and 77 energies, and hence the mean 7r0 and 77 masses, are shifted high relative to their true values. However, in 160 1.04 1.03 1.02 1.01 0.99 0.98 0.97 0.96 0.95 1.04 1.03 1.02 1.01 0.99 0.98 0.97 0.96 0.95 IIIIII IIIIIIIIIIIIIIIII IIITITTIIIIIIIIIIIIIIIIII I I I I I I I I I 41 I I r I I I l — Esm/E vs. Smeared pT Emu/E vs. Unsmeared pT l I I I I I I I I I I I I I I I I I II I II I IIII IIIIIIIIIIIIIIIIJJI IIIIIIIIIIIIIIIIIIIIIIII IIIIII IIIIIIIIIIIIIIIIIIIII I IIIIIIIIIIIIIIIIIII .1 l l I I Ah I I I I I r I I -q n— I I I I 41 I441 I u b) / I I I Iinl, I 14,1 I I J I I I a n d:— 47- .1.- I I I I I I I I I I I I 4,.4 I, I I I L IL, I I I I J I I I I IIIIIIIIIIIIIIIIIII‘IIL IlIIIIIIIIlIJIIIIIIIIJII I I I 414,1 I 4I4,I I I I I I L, I I I (JD 4 5 6 7 8 9 pT (GeV/c) .A 0 Figure 6.6 a) Esmear / E versus pr in the PMC before rescaling the photon energies and b) after rescaling the photon energies. 161 if the calibration procedure, the photon energies are set so that the mean 7r0 and 77 masses equal their world values. This procedure can be mimicked in the PMC 0 mass after by lowering the energies of the smeared photons so that the mean 7r energy resoluton smearing equals the world value. Once done, Esmear/ E plotted versus smeared pI is now 21, as shown in Figure 6.6b. However, Esme” / E plotted versus unsmeared pr is now shifted low. This means the mean reconstructed pr is shifted low relative to the true 9, and hence the measured cross section is low. The DGS simulation of the detector was calibrated in the same manner as the energy scale in the data. Therefore, this feature is present in the Monte Carlo events, and was thus accounted for in the reconstruction efficiencies, which are described in Section 6.3.5. 6.3 The Detailed GEANT Simulation The PMC evaluated 7b/7r0 based upon relatively simple considerations of how direct photon background candidates may arise. However, only the major sources of background were evaluated by the PMC. In addition to contributions from decays other than those included in the PMC, the other particles created in these high pr interactions, as well as particles created from subsequent interactions within the detectors themselves, may effect 7b/7rO by confusing the reconstruction algorithms, affecting the trigger response, etc. Although these background contributions are expected to be minor, the detailed GEANT simulation (DGS) provided the means by which to fully evaluate their effects. The DGS was also responsible for the determination of the direct photon and neutral meson reconstruction efficiencies 162 and the vertex reconstruction efficiency. Presented below is a description of the DGS. 6.3.1 Event Simulation HERWIG [96] and PYTHIA [97] are two of the most frequently used generators of hadronic events. To choose between the two, a sample of events containing high 721. 7r0’s was produced using each of these generators. These samples were processed through the detector simulation, and then through the MAGIC reconstruction program. The outputs were compared to events containing high pr 7r0’s in the data. In Figure 6.7, the number of reconstructed photons and charged tracks per event is shown for the data, the PYTHIA DGS, and the HERWIG DGS.1 Since the events generated by HERWIG match the data in these distributions better than those generated by PYTHIA, HERWIG was chosen as the primary event generator for the DGS. A second sample of DGS events was also created to cross-check the HERWIG results. In this simulation, the reconstructed output from a selected sample of data events used as input to the GEANT simulation. This was called the DATA-DRIVEN Monte Carlo. The simulation of electromagnetic showers in the EMLAC is highly CPU intensive. Therefore, several event selection algorithms were developed in order 1 Note that here and in future comparisons with the DGS, the data are represented by the histogram and the Monte Carlo by the points; Opposite to the sense shown in the comparisons with the PMC. This is done so that the error bars are shown on the statistically limited sample. 163 Entries ' _¢_ — 7 - n Be at 515 GeV/c + ’ -— Data ‘ L o PYTHIA DGS - — o HERWIG DGS ‘ : _._ pT > 3.5 GeV/c j ._ ++ _. I _._ i 1- + —1 1 1 1 I 1 {—9— k w 1 I L 1 1# 1 1 1 I 1 o 2 4 6 8 1o 12 14 Number of Photons in 71:0 Half Octant per Event .g ’- T I T I I I I I I I I I I I I I I I I I I I I I I I I I I I r I I I I I I I I I I T I I I I I I 1 c: - l u: +++ _ -¢- -¢- I L I I L I __ . MPE—-——h—u‘_i. .- - O 5 10 15 20 25 30 35 40 45 50 Number of Charged Tracks per Event 0.... Figure 6.7 Comparison between the number of reconstructed photons in the triggering octant and the total number of reconstructed tracks in PYTHIA, HERWIG and the data for events containing 7r0’s with pr > 3.5 GeV/c. The triggering octant is assumed to be the octant containing the 7r". 164 to reject uninteresting events before they entered this time consuming stage of the detector simulation. These algorithms typically required that the generated event contain at least one user-defined particle with pr above some specified generation threshold, called pTGEN. Since the pr spectra of particles produced in strong interactions fall rapidly, several Monte Carlo samples were generated, each with a different value of pTGEN. This allowed the full range of pr spanned by the experiment to be adequately sampled, without investing huge amounts of resources populating the lower end of the pr spectrum. A description of the selection algorithms used by the DGS is presented below. HERWIG Event Selection Algorithms For the purpose of the evaluating 7b/n0, HERWIG was instructed to generate 2 —> 2 QCD hard parton scatters.2 It is important to note that in these interactions, HERWIG does not generate any direct photons. Therefore, after processing the Monte Carlo data, any photons which satisfy the direct photon candidate criteria can be automatically considered as background to the direct photon signal. Also, since neutral mesons are natural products of these interactions, these samples were used to determine the n0 and 77 reconstruction efficiencies. For the evaluation of the direct photon reconstruction efficiency, a dedicated sample of HERWIG direct photon events was used.3 There were three different selection algorithms, or filters, used to select events for the evaluation of 7b/n0. These were called filters 3, 2, and 6. The filter 2 2 —+ 2 QCD hard scatters can be specified by setting the process identification number, variable IPROC in HERWIG, to 1500. 3 Direct photon events are generated by setting IPROC equal to 1800. 165 3 algorithm proceeded as follows. After HERWIG generated a hard scattered interaction, a search was made over the final state particles in the interaction for either a n0, 7, ei, or Kg with pr > 72,03”. These particles were chosen because either they themselves or their decay products readily produce electromagnetic showers in the EMLAC (and hence, background to the direct photon signal). If the search was successful, then the event was accepted and processed through the full detector simulation, otherwise the event was rejected, and another hard-scattered interaction was generated. Although no’s and Kg’s are typically not considered final state particles, they were made final state particles by declaring them stable during the initialization of HERWIG. The decay of these particles was then handled during the detector simulation. The n0 was explicitly held stable in HERWIG to ensure that the DGS also contained an unbiased sample of nO’s for the evaluation of 7b/n0 and n0 reconstruction efficiency calculations.4 The Kg was held stable in HERWIG for a different reason. Due to its relatively long lifetime, the pr of the photons from the Kg decay5 tends to be mis—measured since the pr is calculated under the assumption that the photons originated at the primary vertex. By allowing the detector simulation to take care of the decay, this effect is included in the DGS. In general, short-lived particles such as the 77 and the (.0 were decayed by HERWIG, while long-lived particles such as the K g were held stable and then decayed during the detector simulation. 4 Otherwise, this filter would preferentially select events containing no’s in which the no decayed into a highly asymmetric photon pair. 5 These photons arise primarily from the decay chain Kg —> non0 —-> 7777. 166 1:? Filter 2 was more sophisticated than filter 3. In addition to selecting events based upon particle pr, it also selected events based upon the pr deposited in localized regions of the EMLAC. By selecting events in this manner, events in the data where multiple particles contributed to the satisfaction of a particular trigger definition were also included in the Monte Carlo simulation. In the final analysis, both filters were found to give consistent results for the ratio 77,/n0 and as a result, events from both filters were combined and used in the overall 7b/nO determination. The filter 2 algorithm proceeded in two stages. The first stage was similar to the algorithm used by filter 3, i.e., there was a search over the final state particles in the event for a high pr particle. However, in this case, the 77, 77’, and to were also declared stable in HERWIG, and the search for a high pr particle was over all final state particles with the exception of charged pions, protons, and anti-protons. Also, during this stage, the minimum particle pr requirement was set at 0.5 GeV/c below the prN threshold. If the search was successful, then the first stage of the filter algorithm was satisfied and the event was sent to the detector simulation for the second stage of the filter algorithm. In the second stage of filter 2, the generated particles in the event were tracked by the detector simulation up to the ARMCO fire curtain, located just upstream of the LAC dewar.6 All the photons and electrons produced up to this point in the event were projected to the front face of the EMLAC, and “sums-of-8”7 6 The tracking of particles up to this point in the detector simulation is not prohibitively time consuming. 7 These sums-of-8 are analogous to the sums-of—8 used by the trigger (see Section 3.2). 167 were calculated using the generated energies. Overlapping sums-of—16 were then calculated, and if the pr in any of the sums-of-16 was greater than 72193”, or if the triggering particle was a n0, 7, 77, 77’, w, K2, Kg, ei, or neutron and the total pr from photons and electrons in the trigger quadrant was greater than pTGEN, then the second stage of the filter was considered satisfied, and the detector simulation of the event was continued to completion. Note that events containing high pr charged pions are not selected by either of the filters described above. These particles occasionally interact in the EMLAC and mimic an electromagnetic shower. Although this background is expected to be small since charged pions rarely deposit significant energy in the EMLAC, and the distance to nearest track and E from / E70707 requirements imposed on direct photon candidates (see Section 5.5) will reject most of those that do, a sample of events containing high pr ni’s was generated to explicitly evaluate this background. The filter used to produce this sample was called filter 6. The filter 6 algorithm was very simple—requiring only that a n+ or a n“ with pr > prN be found among the final state particles. Data-Driven Event Selection Algorithm Events from the data that contained either a high pr n0 or 77 candidate were used as input to the DATA-DRIVEN Monte Carlo. Two samples were generated, one with a low 7), threshold and one with a high threshold. The low threshold sample consisted of events that satified the LOCAL GLOBAL LOW trigger and contained at least one n0 or 77 candidate with pr > 3.0 GeV/c. The high threshold sample used 168 events that fired the SINGLE LOCAL HIGH trigger and had a n0 or 77 candidate with pr > 3.5 GeV/c. Photons which formed high pr n0 or 77 candidates were removed from the input particle list. Substituted in their place was the reconstructed 4-vector of the meson candidate. In addition, photon pairs judged to be ZMP’s were also removed and replaced by a single photon with the ZMP’s 4-momenta. Photons that spatially matched with reconstructed tracks were replaced as either electrons, if they had high Efrem/E70707, or as pions. Finally, since the data also contain true direct photons, any remaining photons that had pr greater than the generation threshold were removed from the input sample. 6.3.2 Simulation of Detector Response The simulation of the spectrometer was performed using the GEANT software package developed at CERN. This is a package specifically designed to simulate the interactions of elementary particles with the detectors used in high energy physics experiments. GEANT provides a set of generic subroutines that enable the user to describe the shapes and prOperties of the various devices used by a given experiment. In addition, utilities are provided that allow the user to store various information during the simulation. This information can then later be used to digitize8 the Monte Carlo data. Understanding the response of the EMLAC to electromagnetic showers is critical in the study of direct photon and neutral meson production. The DGS 8 Digitization refers to the process of taking the Monte Carlo event information and converting it into the hits registered by the various active detector elements. 169 played a large role in developing this understanding and so it was important to verify that GEANT accurately simulated the development of electromagnetic showers in the EMLAC. To this end, simulations of the development of electromagnetic showers in the EMLAC due to single electrons were performed, and the output was compared to a sample of high quality electron showers extracted from the 515 GeV/c n‘ data. The input momentum spectrum of the Monte Carlo electrons was chosen to be the same as that observed for the electrons extracted from the data to eliminate ambiguities in the results due to differences in momenta spectra. The ratio of the electron energy measured in the EMLAC, E, to the electron momentum measured by the charged particle tracking system, P, is shown in Figure 6.8 as a function of E for Monte Carlo and data. This distribution is sensitive to the electromagnetic shower shape, as well as to the amount of material in front of the EMLAC. The distribution from the Monte Carlo is in good agreement with the distribution from the real data. The falloff in the E / P distribution at low energy is attributed to differences in the shower shape between electrons and photons. Electron-induced showers tend to be broader than photon-induced showers. However, the shower energies were determined from fits to shower shapes optimized for photon-induced showers (Section 4.3.3), which resulted in the underestimation of the energy of showers induced by low-energy electrons. The tracking of the photons and electrons produced during the development of the showers in these simulations continued until their energies reached 1 MeV. Once this energy threshold was reached, the tracking of the particle stopped, and its 170 .7 1.1 r r r I r r I I r r r I r r r I 1 r E/P 1 .075 IIIIFI I I 0 Data 0 DGS 1.05 1 .025 I I I I T I I I I I I I I I I 0.975 0.95 0.925 0.9 o ITTI I IIT Ii‘l’III‘IIIII Figure 6.8 Comparison of E / P distributions in the data and the Monte Carlo. 171 remaining energy was deposited at that location. However, tracking photons and electrons in the EMLAC down to energies of 1 MeV is a time consuming process. For example, using this energy cutoff, a single 70 GeV photon shower took, on average, z3 minutes of CPU time to fully develop on an SGI 4100 computer. Given the CPU resources available to the experiment, it was necessary to simulate electromagnetic shower development more efficiently. Two important time-saving measures were taken. The first was to reduce the number of volumes9 needed to define the liquid argon calorimeter. In GEANT, a non-negligible fraction of time is spent calculating the probabilities for various physics processes to occur each time a particle encounters a new volume. A significant reduction of CPU time was achieved by combining several volumes into a single volume whose properties reflected the average of the combined volumes. To illustrate, in the original detector simulation, three volumes were necessary to define a copper clad G-10 board: two copper volumes and one G-10 volume. These three volumes were combined into a single homogenized volume of equivalent radiation length. In all, over 200 volumes were eliminated from the original GEANT simulation, and the CPU processing time per event was reduced by a factor of two. The second measure taken was to increase the tracking cutoff energy from 1 MeV to 10 MeV. This reduced the CPU time per event by a factor of 5. Unfortunately, the generated shower shape suffered as a consequence. To rectify this, a simple model of electromagnetic shower development was implemented to continue the tracking after the 10 MeV cutoff was reached in GEANT [72]. This 9 In GEANT, the term volume refers to the separate elements of the detector. 172 model provided for photon conversion into 6 6' pairs and energy loss due to ionization. Effects due to multiple scattering were also included in this model. The showers produced using this model and GEANT run with 10 MeV energy cutoffs were found to be in reasonable agreement with the showers in the data in the transverse view. However, the longitudinal shower shape required additional tuning to reproduce the shower shape seen in the data. Once this tuning was completed, the experiment generated the large sample of events needed to evaluate the direct photon background. These events were generated using several SCI and IBM computer clusters at Fermilab, and a cluster of SGI machines at the Physics Detector Simulation Facility (PDSF) in Dallas, Texas. At the time of generation, the spectrometer elements were treated as “perfect” detectors—perfect in the sense that all channels were considered to be instrumented, fully efficient, and noiseless. Detector effects were then implemented prior to event reconstruction through the use of a preprocessing program called MCPREP. Among the detector effects modeled by the preprocessor were: noise and dead channels in the EMLAC; o variations in the LACAMP gains; 0 the intrinsic efficiency of the tracking system detectors; noise hits in the tracking system. As many of these effects varied over time, MCPREP assigned run numbers from the data to the Monte Carlo events. The assignment of run numbers also allowed 173 the simulation to account for the time dependence of the EMLAC response. The number of Monte Carlo events assigned per run number was proportional to the number of high pr triggers per run number in the data. This ensured the correct averaging of the run dependent effects. In all, approximately 7.5 million HERWIG and DATA-DRIVEN Monte Carlo events were generated for the direct photon analysis. The breakdown, by beam type and 12,03” threshold, of the HERWIG filter 2 and filter 3 direct photon background and HERWIG direct photon statistics is given in Tables 6.1 and 6.2, respectively. In addition, 55,000 filter 6 HERWIG events were generated for the purposes of evaluating the contribution from charged pions to 77,/n0. The DATA-DRIVEN Monte Carlo statistics numbered 0.3 million 77,05" 2 3.0 GeV/c and 1.0 million prN = 3.5 GeV/c 1990 n“ beam events. It may be noted that the Monte Carlo statistics for the analysis of the 1991 n“ and secondary proton beam data are very limited, particularly at low 72,. Time limitations prevented the generation of independent Monte Carlo statistics for these samples. Therefore, to obtain corrections for these beams, the 1990 n‘ beam Monte Carlo was rerun through MCPREP and the reconstructor using 1991 run numbers. In Figure 6.9, the number of charged tracks and the number of photons t10 per event are compared for the 515 GeV/c n‘ beam in the triggering half-octan data and the 530 GeV/c proton beam data. Since these multiplicities do not differ significantly, using the n‘ beam Monte Carlo to simulate the event structure 10 In these comparisons, octants were divided into two at the inner-outer (75 boundary (R = 40.2 cm). 174 G E” threshold. Table 6.1 Number of generated HERWIG filter 2 and filter 3 direct photon background Monte Carlo events (in thousands) as a function of the pr 1990 1991 72,015” 530 GeV/c 800 GeV/c 530 GeV/c 530 GeV/c (GeV/C) 7’- beam p beam p beam n‘ beam 0.5 210 95 - - 1.5 220 330 - _ 2.25 305 - - - 2.5 - 195 - _ 3.0 495 185 - - 3-5 - 850 — - 4.0 235 — - _. 5.0 200 265 110 95 6.5 160 150 - .. 7.0 - - 100 _ 8.0 65 115 50 - ' 9.0 40 35 25 - Table 6.2 Number of generated HERWIG Monte Carlo direct photon events (in thousands) as a function of the prN threshold. 1990 1991 17,053” 530 GeV/c 800 GeV/c 530 GeV/c 530 GeV/c (GeV/c) n‘ beam p beam p beam n" beam 3.0 440 347 - - 3.5 - 437 - - 5.0 203 210 - - 7.0 91 83 - - 8.5 10 48 - - 175 in the secondary proton beam data is reasonable. Although the input particle spectra generated by the n“ beam HERWIG Monte Carlo are not appropriate for the 1991 secondary proton beam data, this problem was corrected through the use of special weighting functions that adjusted the input particle pr and rapidity spectra to the spectra observed in the data. These functions are described in the next section. Also, contributions to the direct photon background due to conversions were improperly calculated for these data samples, since the target configuration was different in the 1990 and 1991 runs. The PMC was run using the two target configurations to obtain a correction for this. 6.3.3 Monte Carlo Spectrum Weighting The generated Monte Carlo n0 pr spectra were weighted to reproduce the spectra observed in the data, since the slope of the pr spectrum had effects on several aspects of the analysis (e.g. EMLAC calibration, evaluation of reconstruction efficiencies). The ratio 77,/n0 depends upon this s10pe also, since the number of background photons at a given 72, depend upon the number of mesons at higher pr. The weighting functions were obtained through an iterative process. Originally, n0 reconstruction efficiencies were determined and applied to the data with no weighting function. A weighting function was then determined, and applied to the Monte Carlo data. The reconstruction efficiencies were reevaluated, and updated cross sections were determined. This in turn led to new weighting functions and new efficiencies. This process was iterated several times until the results stabilized. 176 IIIIIIIIIIIIIIIIIIIIIIIW—rfTIWIIjIIIIIIIIIIfiWTTIT Entries 0 n’Be at 515 GeV/c 0 pBe at 530 GeV/c IIIIIIIIII1IIIIII IIIIIIIIIIIIJJIII o n Pr > 3.5 GeV/c L I J J I I I I IJI I I I I J I I I I I L I I I I I I L I I I I L J I J I I L d 0 5 10 15 20 25 30 35 40 45 50 Number of Charged Tracks per Event .8 _'I I I I T I I I I Ifi I Ij I I I I I I I I 1 I I I I I I I I I I Ij T I I I I I I I I I I I I I E l + . Lu 7 "'0'“ ~ , . .. --. J I I I I m I I J I J4 I l I I I I I I I I I I -‘-‘-‘_-‘-l .1 L LA I l I I I I I I I I o 1 2 3 4 5 6 7 8 9 10 Number of Photons in n0 Half Octant per Event Figure 6.9 Comparison between the the total number of reconstructed tracks and the number of reconstructed photons in the triggering 1 / 2 octant in the 515 GeV/c n‘ beam data and the 530 GeV/c proton beam data for events containing nO’s with pr > 3.5 GeV/c. 177 A separate function was determined for each pTGEN sample in the DGS. For p195" thresholds below 6.5 GeV/c, the weighting functions were functions of pr and rapidity. For prGEN thresholds 2 6.5 GeV/c, the weighting functions were functions of pr only, due to limited statistics at high pr in the data. A comparison of the weighted and unweighted generated nO pr spectra for the 1990 pTGEN = 3.0 GeV/c sample is shown in Figure 6.10. The DGS was also weighted so that 77 / n0 was consistent with what was observed in the data, since 77’s contribute significantly to the direct photon background. In Figure 6.11, the observed 77 to n0 production ratio is shown for the 515 GeV/c n— beam and the 530 and 800 GeV/c proton beams. 77/n0 in HERWIG was adjusted to obtain this value. In principle, w/n0 should also be weighted. However, in this case, the ratio was found to be consistent with data [94]. For other sources of direct photon background, it was assumed that HERWIG reproduced the ratio of these sources to no’s correctly and therefore they were given the same weight as 07 7I'S. 6.3.4 Monte Carlo and Data Comparisons A variety of comparisons were made between the data and the DGS to verify that the E706 Monte Carlo provided an adequate simulation of the events seen in the data, and that it properly modeled the detector characteristics. These comparisons are discussed below. As a cross-check of the DGS pr and rapidity weighting functions, comparisons 0 were made between n energy spectra in the DGS and data for each of the Monte 178 Entries per 0.1 GeV/c 8 4 1—4 1° F 1 _ l 10 3:- -. C I 7- a _ —O.75 < y < 0.75 +1 . 41‘ I I I I I I I I I I I I I I I I I I I I I I I I 3 3.5 4 4.5 5 5.5 pT (GeV/c) 515 GeV/c n— Beam 0 Data — Default HERWIG Weighted HERWIG Figure 6.10 Comparison between the weighted and unweighted HERWIG 7r0 pr spectra for the prGEN= 3.0 GeV/c n‘ sample. The weighting surface is normalized to unity at pr 2 179 GEN pr ,ycm=0- I I I I I I I I I I I r I I l I I IfiIIIIIIIIjI é : 0 2 n: 0.8 _— n/n = 0.48 i 0.01 -: °s I i I j c 0.6 PI . . Q .. ‘ ¢ + + : :""" """" " """ "' """""""""""""""""" '4 o 2 7 n_Be at 515 GeV/c j ' E —0.75 < y < 0.75 : 0 P I I L LI I I I I I I I I I I 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 L IL‘ 1- T I I I I I I I I I I I I I I I I I I I I I I I I I I I I I Ifi I I I I I I I I I I I:1 . 0 ., 0-8 P 71/71: = 0.45 i 0.01 ‘: 0.6 1 -§ :. -- ...... -- --.’.---¢---9.--i_ ..... -- m] ................... _: 0-4 r I . I I I I I I 1 0 2 i pBe at 530 GeV/c + j ' E —0.75 < y < 0.75 : O IJJ LI LLLJ IL I I I I I J J I LJ 1 J LIJ LI I I I I I I I I I I I I I I l J "1 I I j T I I I I I I I II I IT fiI I I I I I I I I I I I I I I I I I I I I I I I I I I II . 7- 0 .1 0-8 7 71/7: = 0.42 i 0.01 1 0.6 {— + + 3 : ¢ + : 0.4 f""¢"'¢"';"t"* """" I“ """ I """"""""""""""""" =3 0 2 -_+ pBe at 800 GeV/c + j ' : —1.0 3.5 GeV/c in the 530 GeV/c proton data. The good agreement between the Monte Carlo and the data indicates the Monte Carlo pr and rapidity weighting function was appropriately evaluated. It is important to verify that the DGS reproduces the resolution of the EMLAC. Since the EMLAC’S R and d5 boards are interleaved, the energy reconstructed in each view should be roughly equal, with the difference in energies due to fluctuations in the amount of deposited energy in each view. Hence the difference, ER —— E¢, provides a measure of the EMLAC’S resolution. In Figure 6.13, E R — E¢ is plotted for data and the DGS for several reconstructed energy intervals. The agreement is excellent over a large range of photon energies. Another distribution sensitive to the detector resolution is the reconstructed '77 mass distribution. Figure 6.14 shows a comparison between the reconstructed no and n masses in the data and the DGS. The width of these distributions is sensitive to both the position and energy resolution of the EMLAC. Also of interest in this plot is the amount of background underneath the 7r0 and 17 mass peaks. The good agreement between the backgrounds in data and the DGS indicates that the DGS is providing a reasonable representation of the underlying event structure. The longitudinal development of electromagnetic showers can be checked by comparing distributions in Efr0,,t/Et0taz for photons in the DGS and the data. These distributions are also sensitive to the amount of material located in front of the instrumented portion of the EMLAC. A comparison of E from / Etota; 181 > ,...,...,,.r,...,.... . o . 3 __ pBe at 530 GeV/C _- 3.5 .1 Q - .8 _ + —- Data j g f + ODGS j : _ pT>3.5 GeV/c j _— + -0.755'5 GCV/C 4 NL pT>4GeV/C §_ 4 j *9.“ t ‘ s L §~ ‘ . " 0 a . a . LL] m f— —+ J O DGS _ — Data , pBe at 800 GeV/c ' —l.O < y < 0.5 o t o _.____ _____ .I 1 I I 1 “ ' °_‘ __.__._.._ 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 .25 W Mass (GeV/c ) Figure 6.14 Comparison of the no and 77 mass distributions in the data (histogram) and the DGS (o) for the 800 GeV/c p beam. 185 I I l I l l T l I T I l 103.5 GeV/c -- - r- II!- II )- -II- 1 ~ «- -I b uF 1 - —I— I- ‘F 1 : e DGS I: I )- -I- -( f -—Data 1: 1 C. .2; J r ‘- 1 - —1.0 3.5 GeV/c in the DGS and the data. 189 6. 3.5 Evaluation of Reconstruction Efficiencies The DGS was used to evaluate the neutral meson and direct photon reconstruction efficiencies. These efficiencies, in addition to correcting for detector losses, also provided corrections for EMLAC resolution smearing effects (Section 6.2.1), the photon E from / Etotal requirement (Section 5.4), and the trigger probability requirement (Section 5.10.2). The reconstruction efficiencies were evaluated as functions of pr and rapidity, and were defined to be the ratio of the number of reconstructed particles to the number of generated particles.11 The reconstructed particles were binned according to their reconstructed pr and rapidity, while the generated particles were binned according to their generated pr and rapidity. By binning in this manner, the reconstruction efficiencies corrected for the effects of resolution smearing in the EMLAC. The reconstructed photons used in the evaluation of the neutral meson and direct photon efficiencies had the E from / Emmi cut imposed on them to correct for the E from / Etotal requirement. Also, reconstructed entries were only included if the octants they landed in had at least a 10% probabilty of firing a given trigger. This corrected for the minimum trigger probability requirement. Note that this implies each trigger definition had its own reconstruction efficiency function. 11 For the neutral meson efficiencies, the number of reconstructed particles was determined using the sideband subtraction technique described in Section 5.11. 190 In addition, the following requirements were placed upon both the recon- structed and generated entries: a reconstructed vertex in the target region; the photons landed within the EMLAC’S fiducial volume; the photons did not convert into ei pairs; for the neutral meson efficiencies, the energy asymmetry of the decay was less than 0.75. Each requirement listed above had its own independent correction. Imposing these requirements on both generated and reconstructed entries ensured the reconstruction efficiency did not correct for these requirements as well. Also, in order to fully reproduce the effects of resolution smearing, the reconstructed and generated particles were required to have pr at least 0.5 GeV/c above the value of the prN threshold of the DGS sample. Reconstruction efficiencies for 7r0 mesons for the 1991 530 GeV/c proton beam are shown in Figure 6.19 for INTERACTION, SINGLE LOCAL Low, and SINGLE LOCAL HIGH triggers. The falloff at low 1),, in the SINGLE LOCAL Low and SINGLE LOCAL HIGH trigger efficiencies are due to the trigger probability requirement. The falloff at high pr and forward rapidity is due to the coalescence of the two photons from the 770 decay. Real detector losses are seen at low pr and backward rapidity in the INTERACTION trigger efficiency. Also shown in the figure is the contribution to the efficiency from EMLAC resolution smearing. Note that away 191 from the regions described above, resolution smearing is the dominant contributor to the inefficiency. In Figure 6.20, corresponding efficiencies for the r] are Shown. Note that in the case of the 17, trigger effects are present at significantly higher pr’s than for the 7r”, Since the wider separation of the photons from the 77 decay makes it more difficult to satisfy the trigger-pr threshold for a given sum-of-16. In addition, there is little evidence of coalescence at high pr. The SINGLE LOCAL HIGH direct photon efficiencies for the 1991 530 GeV/c proton data for the 90N, 75N, and 758 candidate definitions are shown as functions of pr in Figure 6.21. The 758 definition has the highest efficiency Since, in this definition, losses due to direct photons making 77 mass combinations in the no signal region with random photons in the octant are compensated for (Section 5.12). These losses are greatest at low pr, and are fractionally larger in the 90N definition than in the 75N definition since the combinatorial background underneath the r0 grows with energy asymmetry (recall Figure 5.13). As was the case for the no, the majority of the direct photon inefficiency is due to energy resolution smearing. Systematic Uncertainties in the Reconstruction Efficiencies The main contributors of systematic uncertainty in the reconstruction efficiencies were: statistical limitations in the Monte Carlo data, dependence of the efficiency on the modeling of the detector response, detector environment, and trigger response. To assess the systematic uncertainty arising from the Monte Carlo 192 8‘. .- T T T T I T T T T I T T T T I T T T T I T T T T r T T T T I T T T T I T T T T l T l T fr T T T T .4 {3' 1 L 530 GeV/c p beam q 2 r‘ ................................... ' Id: '- 8 b . . ‘ . "ns....u‘ ..... .. ..... . ..... h ..... .. ..... ¢ ..... ¢ ............. om * l 4 ° i ‘ r- O -4 g 0.5 —‘ — I- II I- . -I * —O.75 < y < —0.25 i I ° , o I l l I I l l I J 1 £1 1 I I l I j I I 1 I 1 1 I I I .1 l I l I l L I I l l J J. I I l I I l I I I T T T T I T r T TT T T T T I T T T T I T T T ITITT T T T T T r T T I T T1 T I T T T T I T T T T 1 - 1 1 _ —-4 + ‘ ..... .6. ...... i ..... .. ..... '...... ..... .. ..... .. ..... . ..... . ..... .............‘ ..... . ...... . ............. ; cos-loouue: - ‘ d O 0.5 — ._ . O 4 : a —0.25 < y < 0.25 j o 1.4 J .1 I l i I I L LJ #1 I I J I I I I L I I L l I J l L l l I I I 141 Ll I I l I 1 I l l l T T T T I T T T j I T T T T I T T T T I T T Tfi' I T T T T I T T—r T l' T T T T I T T T71 l T T T T d 1 w ................................................................... T l: A T 9 . a . . .. . . """" .- ----- -.- ............................. 4 + + 4? ' ‘ * r A INTERACTION ' ¢ 1 0.5 r- 0 ¢ + _. r 0 SINGLE LOCAL LOW , ’ 0 SINGLE LOCAL HIGH + i I . 0.25 < y < 0.75 ‘ - -1 o l I J l I I I I Li I I l I I I J I I I l I l I I I I L 1 I I I I l I I I I 1 I I I l l I 1 I J I 1 2 3 4 5 6 7 8 9 10 11 pT (GeV/c) Figure 6.19 7r0 reconstruction efficiency for the 530 GeV/c proton beam as a function of pr for several rapidity ranges. The dotted curves in the figure indicate the contribution from EMLAC resolution smearing alone. 193 5‘ b T T T T 1—r T T T I T T T T I T T T T I T—T T T I T T T T I T T T T r T T T T I T T T T - 5 1 L 530 GeV/c p beam j —1 o . ..................... + 4 _, ................................................................ a P * 1 ¢ . : v .......... t .................................... . Lu . . . :- " -+ 0.5 _ ¢ — L. é . t —O.75 < y < -0.25 * 0 I I I I I I I.I I I I I I I I I I I 44 I I I I I I I I I I4 I I I I I I I I J I l I I P T T T I T T—T T I T T T T I T T T T I T T T T I T T T T I T T T T I T T T T I T T T T ‘ 1 _ .— C + 6 ........ $ ............... : .............. ' ............... 3 ............... . .............. ¢ ............... +. ...... 4 0.5 t“ ¢ ¢ "‘ L 1 Z . -O.25 < y < 0.25 ‘ 0 I 1‘1 1 L I I I I I l I I I I I I I I 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 T '- TT T T I T T T T I T T T T I T T T T I T T T T I T T T T I T T T T I T T T T I T T j T _ _- ..................... ¢ ............... 4, .................................... 7 b I t I ------ .. .............. I ..................... ‘ I + + A INTERACTION ..: 0.5 : . 0 SINGLE LOCAL LOW — . 0 SINGLE LOCAL HIGH ‘ : 0.25 < y < 0.75 3 0 1 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 l 1 1 1 1 I 1 1 1 1 I 1 l 1 1 I 1 1 ‘ ‘ l 1 l ‘ l 2 3 4 5 6 7 8 9 1o 11 pT (GeV/c) Figure 6.20 77 reconstruction efficiency for the 530 GeV/c proton beam as a function of pr for several rapidity ranges. The dotted curves in the figure indicate the contribution from EMLAC resolution smearing alone. 194 5‘ ’- TTTI T l I T T T T I T T T T T T T T T I T T T T I T T T l I T T T -1 § 1 L - ha I ............................... . ....... . . ._ + t + J _ .i .............................. . ...... g ............................................ :5 p. § I I I I I o I I ‘ v i 1 + + + "-‘ 1 0 _ 8 0.5 . .1: D‘ 1. t3 : 530 GeV/c p beam —0,75 < y < —(),25 . I I I4 I I I I I I I _I_I I I I I I I I I I I I I I I J I I I I I I I I I a o ’- T I T T T T I T T T T I T T T T I T I T T I T T T T I T T T T I T T T T .‘ 1. a 1 e - L. ......................................................... , ........ I ............ I I . 1. g g n g . . . h . | . . . . ...... ......................... . .3 + + 1 _ I .1 0.5 - _ r . : —O.25 < y < 0.25 : o I I I I I I I; I I I I I I I I I I I I I J I I I I IA I I I I I I I I I ”T T I T T T I T T T TTI T T T T I T T T T FT T T T I T T T T I TI T T q » 4 1 _. —l :c..."i...i...o‘....‘....‘....n.;...'...'..............‘...‘u*...‘.....u..............’. ................. +. nu { : 1. ‘ I I + +. ................ . 0.5 - 0 758 Definition I I C o 75N Definition C I 9ON Definition 0.25 < y < 0.75 o 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 I I J ;I I I I I I 4 5 6 7 8 9 1o 11 pT (GeV/c) Figure 6.21 SINGLE LOCAL HIGH direct photon reconstruction efficiencies for the 90N, 75N and 758 candidate definitions as functions of pr for several rapidity ranges. The dotted curves in the figure indicate the contribution from EMLAC resolution smearing alone. 195 statistics, closure tests were performed in which the ratio between the efficiency— corrected number of reconstructed entries and the number of generated entries was calculated. These ratios were consistant with unity within :l:1%. To assess the uncertainty in the efficiency due to the modeling of the detector response, the smearing contribution to the efficiency was evaluated using the PMC and compared with the result from the full shower Monte Carlo. Comparisons 0’s and 77’s and the results were typically found to were made for direct photons, 7r agree to within i570. Therefore, a i570 systematic uncertainty was assigned for the modeling of the detector response. The uncertainty in the efficiency due to the modeling of the detector environment was assessed by examining the reconstruction probability12 as a function of the number of generated photons in the 1/2 octant containing the generated direct photon, 1r”, or n. This is shown for 7r0’s in Figure 6.22. At low pr, the reconstruction probability drops by <2% for each additional generated photon in the 1 / 2 octant. Since the mean number of reconstructed photons in the data and the DGS agree to better than 0.25 photons (recall the discussion in Section 6.3.4), a systematic uncertainty of :l:1% was assigned to account for the modeling of the detector environment. Another measure of the uncertainty in the modeling of the detector environment can be obtained by using the DATA-DRIVEN DGS to evaluate the reconstruction probability and comparing it to the reconstruction probability evaluted using the HERWIG DGS. This comparison is shown for both the LOCAL 12 The reconstruction probability differs from the reconstruction efficiency in that the effects of smearing are removed from the reconstruction probability by binning the reconstructed entries according to their generated pr’s and rapidities. 196 GLOBAL Low and SINGLE LOCAL HIGH triggers in Figure 6.23. For the LOCAL GLOBAL LOW trigger, these probabilities are within :l:1% of each other. For the SINGLE LOCAL HIGH trigger, these probabilities also agree to within :l:1% for pr’s above 4.0 GeV/c. However, at lower pr, the agreement is worse. This discrepancy between the two triggers is most likely due to the effect of the detector environment on the trigger response. To assess the uncertainty in the trigger response near the trigger threshold, the ratio of the no cross section measured using the SINGLE LOCAL HIGH trigger to the cross section measured with the SINGLE LOCAL Low trigger (LOCAL GLOBAL Low trigger in the 7r‘ beam data) was examined. Because the low threshold triggers have relatively low statistics in the region of the SINGLE LOCAL HIGH turn-on, fits of the low threshold trigger data in the region of the turn-on were used. To constrain the fits at high pr (prz 5.0 GeV/c), SINGLE LOCAL HIGH data was used. The transition point for the SINGLE LOCAL HIGH trigger, and the lower limit of the fit was varied in the fits to test sensitivity. In these ratios, the results were found to differ from unity by no more than z 2%, and thus a 2% uncertainty was assigned for the trigger response. 6.3.6 Vertex Reconstruction Efficiency The DGS was also used to evaluate the primary vertex reconstruction efficiency. For this study, Monte Carlo samples were generated using HERWIG v6.1 [98], as the vertex distributions generated with this version were found to give much better agreement with the data than the samples generated with HERWIG v5.6. The 197 Reconstruction Probability ‘ .0 to .0 co .0 x: .0 a: .0 m L TT T T T I T7 T j T I T T T T I T T T T I T T T T I T T T T I T T T T C I gen . . o . _ A Nzen=5 pN —> n: x at 800 GeV/c _ - —1.0 < y < 0.5 ~ ’- L I I_ g L I 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 L I d 3 4 5 6 7 8 9 1o pT (GeV/c) Figure 6.22 Reconstruction probability for 7r0’s as a function of the number of Reconstruction Probability A .0 to P on .0 x: .0 a: 9 a: generated photons in the 1/2 octant of the generated 7r”. The curves represent fits to the Monte Carlo points. No trigger requirement has been placed on the Monte Carlo data. '- T fi T T I T T T T I T T T T I T T T T I T T T T I T T T T I T T q I ------- :: -:::- -.-.-.- -.-.-.- ”55$:5-s 555 5555 5525 5552 5355 a =:t—---+ 1 .. :1 +1 + 1 f . ::=" 7 L «a o DATA-DRIVEN input events} GLOBAL LOW _‘ t o HERWIG input events . C .C" I DATA-DRIVEN input events} SINGLE LOCAL HIGH I :45 1:1 HERWIG input events '2 ;’ n‘N —> nOX at 515 GeV/cl 3 —0.75 < y < 0.75 - '- L I I I I I I I I I I I I I 1 IL I I I I I I I I I I J I I I I I.| 3 5 4 4 5 5.5 6 6.5 pT (GeV/c) Figure 6.23 Comparison between reconstruction probabilities obtained using HERWIG and DATA-DRIVEN input to the DGS. 198 transverse positions of the vertices in the DGS were chosen according to beam profiles observed in the data. The longitudinal positions were assigned using Monte Carlo methods based upon the absorption lengths of the materials in the target region. This approach gives rise to a number distribution for each target that varies approximately as 142/3, where A is the atomic mass of the target. However, as described in Section 1.6, at high pr (pr 2, 3.0 GeV/c) the number distribution is found to vary as A“, where a is around one. Therefore, for the purposes of evaluating the vertex efficiency, the vertices in the DGS were weighted to reproduce the values of a observed in the data. A comparison between the weighted DGS vertex distribution and the data is shown in Figure 6.24. Separate reconstruction efficiencies were evaluated for the Be, Cu, and H2 targets. The reconstruction efficiency was defined as the number of reconstructed vertices divided by the number of generated vertices in each target’s fiducial volume. The reconstructed entries used the reconstructed vertex position to determine if the vertex was in the fiducial volume while the generated entries used the generated vertex position. This allowed the efficiencies to also correct for resolution smearing of the reconstructed vertex positions. The reconstruction efficiencies for the Cu and Be targets for the 1990 target configuration and the H2 and downstream Be targets for the 1991-92 configuration were unity. The Cu and upstream Be efficiencies for the 1991-92 target were 0.96 and 0.97, respectively. Additional beam particles occasionally interacted in the target material during the time the tracking system was sensitive to charged particles. For data taken using the relatively long target configuration of the 1991-92 run, such situations 199 l T T T T I T T T T I T T T T I r T T 1' I T j fl T l T T F 800 GeV/c p beam - pT > 4.0 GeV/c L L I I 17 I Entries per 0.1 cm i l I I I I I414 I I LJ I I I -11 ~10 -9 -8 ZVER'I’EX (cm) Figure 6.24 Comparison between the Z positions of primary vertices in the DGS (points) and the data (histogram) for events containing a 7r0 candidate with 12, > 4.0 GeV/c. 200 induced a reconstruction bias which favored interactions in the downstream target material over interactions in the upstream material. This bias was studied by comparing cross section measurements on the upstream and downstream pieces of Be, and with a dedicated DGS sample which included additional minimum bias interactions. The number of upstream Be and Cu vertices were corrected for this misreconstruction due to this confusion. The correction was 1.04 for the 1991—92 1r“ sample, 1.06 for the 530 GeV/c p sample, and 1.12 for the 800 GeV/c p sample. The systematic uncertainties in these corrections were dominated by the statistical uncertainties in the upstream Be cross section measurements. They were :l:2% for the 515 GeV/c 7r“ and 530 GeV/c p beam samples, and i3% for the 800 GeV/c p beam sample. 6.3.7 Background Photon to no Ratio After all the cross section corrections were evaluated, the filter 2 and filter 3 DGS Monte Carlo samples were run through the same analysis code as the real data, and 7b and no “cross sections” were obtained. By dividing these cross sections, the nominal 7b/7r0 were obtained. These ratios were fitted to surfaces in p, and rapidity. In Figure 6.25, yb/Tro are shown as functions of pr for the three major incident beams on beryllium. The fit results, integrated over the appropriate rapidity ranges, are indicated by the dotted lines Figure 6.25. The ratio 7b/7r0 for the 515 GeV/c 7r’ data and the 800 GeV/c proton data at low to moderate values of pr are very similar. This is due to the fact that the slopes of the no pr spectra in these data are very similar. At high pr, 7b/7r0 is 201 larger for the 800 GeV/c proton data than it is for the 515 GeV/c 7r" beam data. This is because the 800 GeV/c 7r0 cross section is peaked more forward in rapidity than the 7r“ cross section, which allows for a larger background contribution from coalescence in the 800 GeV/c data. The 530 GeV/c proton beam 717/770 is smaller than in the other two beams. This is attributed to the slope of the 7r0 pr spectrum being significantly steeper in this sample. Also, 712/ 7r0 does not rise as sharply at high pr as in the other samples, since the 7,0 rapidity distribution in this sample is the least forward. In Figure 6.26, 7b/7r0 is shown for the 530 GeV/c proton data for several rapidity intervals. The background levels are quite similar in the backward and central rapidity regions. However, the background levels are significantly greater at high 12, in the forward rapidity region due to contributions from coalescence. Fits to 7b/7r0 were only made for the beryllium target simulations due to the relatively poor full shower Monte Carlo statistics for interations in the c0pper and hydrogen targets. However, 7b/7r0 is expected to be slightly different for each target due to the different amounts of target material the photons must traverse. Therefore, corrections to ’yb/7r0 for the copper and hydrogen target data were calculated using the PMC. In Figure 6.27 the differences between 7b/7r0 in COpper and beryllium and between hydrogen and beryllium are shown for the 800 GeV/c proton beam configuration. The differences for the other incident beams are similar. The difference is greater than zero at low pr, which is expected since there should be more background photons resulting from 'y —-> e+e— conversions in interactions in the copper target. However, at high pr the correction becomes 202 Background 'y/1t0 .0 s: N (D _o —b O 0.3 0.2 0.1 0.3 0.2 0.1 p.17 T I T T T T I f T T T I T T T T j T T T T I T T T T I T T T T .4 Z ‘ 75S n—Be at 515 GeV/c j g‘ 0 75N —o.75 < y < 0.75 j : I 90N j :t-gu-‘Z::81111311:-:l-$u.........'..‘..'..'.r.. .‘..‘.P.:'.+nnnr. uuuuuuu .b ““““““““““““ '. aaaaaa j i" """ I ----- I ..... ’ ..... g ..... I ..... . ..... I ........ I .............. I ----- 1 : I 3 I I I L I I I I I I I I I I I I I I I I I I I I I I I I I I I " : T I T T T T I T T T T I T T T T I T T T T I T T T T I T T T T :4 : pBe at 530 GeV/c : ; —0.75 < y < 0.75 ; :'"8"7‘:1:81:17°78".-7-7-T.8.3....r.:.e:.:..-,.-,,-°,-__..,.,.‘,.na“...n nnnnnn .‘ ____________ _. ______ _; : ' - ---- I ----- - ..... I ..... I ..... l ..... I ..... l ........ I .............. I ....... -: C I .- I l I l I I I I I I I I I I I L I I I I I I I I I I I I J A :T I T T T T I T T T T I T T T T I T T f T Iifi r T T I T T T T : : pBe at 800 GeV/c 1 ; —L0 n X g - 1 E 0 § 1- E 0 pBe —) 7t X i .1 - < 10 .r 0 pp —> “OX ? l 1. _2: : 10 E- I 4 J. P A I I I I I I I I I I AL I; J I I E 2 4 6 8 1o pT (GeV/c) Figure 7.1 71'0 production cross sections per nucleus as functions of pr for 530 GeV/c proton beam on copper, beryllium, and hydrogen targets. 214 a : I I I I I I r I I I I I I I I I I I I I :4 31010’ a Q 3 gr . u 800 GeV/c p Beam = ' . : G ' _ H109? o. D 1.010 ! u E 0 I 9.. [J I O 7' 0. 1: 91° F 0. D E 8 5 o '. DD : n . - «9106:— 00 0.. an 1‘ E E o .. U E . . . b . o 0. DD . '0 105-— 0 .0. El 1 LL] o o a a : o ‘0. an : 4 O .0. D ‘ 10 r 0 o n E o '0 D ‘3 2 o .9. D I 3’ 0° - [In 1 10 :r 00 .. El E E 00 o I 1025— 00 . . a g E 5 0° 0 E 10 g- 0 0 g ‘5 E 0 a E - CI pCu—>1: X - 1 r 0 9 1- s 0 pBe—>11: X a .1 - O . 1o 5 o pp—>1t X E _2: : 10 =r . . 1 i . i 1 . . . 1 . . . l . . L 2 4 6 8 10 pT(GeV/c) Figure 7.2 7r0 production cross sections per nucleus as functions of pr for 800 GeV/c proton beam on copper, beryllium, and hydrogen targets. 215 Eda/d3p (pb GeV'2 per nucleus) Figure 7.3 7r _A o .a O _A O (D _| O 03 g’ ” 515 GeV/c 1f Beam ‘5 ' a —0.75 < y < 0.75 ‘ 5 - 1: E o D E E g .0 ”a 1: E 0. 1:1 5 0 Cl ' E i '0. an 1. E '0 n : E‘ .. an 1 E o "-. an I O .0. D . E- 0 o ...°o Dan E : o '0. 1:1 3 E‘ 0 '0... an E E o :1 5 - D .1 L o o ‘0. 1:1 1:1 1 o s. u E : O o 2 - o o . 0 El 1 ; ° 1 : .r ° ' '5 E _ Q E - D R Cu ——> TEOX ° I - E — 0 E E 0 1: Be —> n X I f : g 0 112-p —> 1:0X a: 5 . . 1 . . . 1 . . . 1 . . . 1 1 1 . 1 l ‘5 2 4 6 8 10 pT (GeV/c) 0 production cross sections per nucleus as functions of pr for 515 GeV/c 7r‘ beam on copper, beryllium, and hydrogen targets. 216 E. ' 1 ' ' ' ' I ' ' ' 1 1 'fiq % pBe—)TEOX at 530 GeV/c “a pTRange E ' ' ' " "‘ " 1 (GeV/c) g- ; £1.0 ‘5‘ L5 i l I i l l o 2.0 1tI at 800 GeV/c . -= P1 Range 3 ' ' " ' g (GeV/c) II-I NE i i i i i as 1.O 01 o "<.° 01 Figure 7 .5 7r0 cross section per nucleon as a function of rapidity for 800 GeV/c proton beam on beryllium for several pr intervals. 218 I I I I I I I I I I H109 T I I I I :1 S — o O ' ‘ ' . ‘ g 108 I _: (GeV/c) L. E 8. 1 a: l.0

a 8 I I I I g j C 2.0- >- ' pBe at 800 GeV/c 25” —L0 yX j i 0 pp —> YX a: c 1 r I I I I L4 I I I I I_I I I I I I L I I I I I I L I I I I I I I L I I I ‘l. I 4 5 6 7 8 9 10 11 PT (GeV/c) Figure 7.10 Direct photon cross sections per nucleus versus pr for 530 GeV/c proton beam on copper, beryllium, and hydrogen targets. 225 Eda/d3p (pb GeV”2 per nucleus) .5 O N 10 10 1O 10 :I I I I I I I I I I r I I I I I I I I I I I I r I I I I I I I I I I I I II I a : 9 800 GeV/c p Beam : :r ‘3 a —1.0 < y < 0.5 1 : 1' ° C, : _ 9 n _ I a E ’ n E . o a 1 ¢ , o r o '3 ‘= E 0 o E I o ' o o I :- o . D ”E 5 o ’ 5 _ o 1 E ° ‘ 1 1 E - 3 F 9 ‘ E” i 1 C Q 1 D pCu —-> yX 3 O pBe —>yX I E” 0 pp -+ YX E E i L I I I I I I I I I L L I I I L I I LLIL J I JL I J I I I I I I I I I J I I I 4 5 6 7 8 9 1o 11 pT (GeV/c) Figure 7.11 Direct photon cross sections per nucleus versus pr for 800 GeV/c proton beam on copper, beryllium, and hydrogen targets. 226 Eda/d3p (pb GeV”2 per nucleus) {:3m 8‘ ES _L o N 10 1O 10 10 : r r I I I I I I I I I I I 1 I I I I I I I I I I I I I I I I I r I I I I I I E : 515 GeV/c n” Beam : 5— ° I3 —0.75 yX i F 0 n”Be —> yX 3 E” 0 n”p —> yX 1 I I I I L I I I I l I I I I I I l I I l l I I I l I I I I J I I_ L I I I I I 4 5 6 7 8 9 1o 11 pT (GeV/c) Figure 7 .12 Direct photon cross sections per nucleus versus pr for 515 GeV/c 7r“ beam on copper, beryllium, and hydrogen targets. 227 _b O (a) Eda/d3p [pb/(GeV/c)2 per nucleon] 8 8 1O 10 10 l. b )- § 4 H-o 4? § I“ p— . ' I l I T t r l 1 E pBe —9 7X at 530 GeV/c *9 +111 I I IIIIIII I IJIIIIII I IJIIIJII I I lIIlII '9 I? > I 0 > O I I IllIIII I IIIIlllI pT Range (GeV/c) 3.5 < pT < 4.0 4.0 < pT < 4.5 4.5 < p1. < 5.0 5.0 < pT < 5.5 5.5 < pT < 6.5 6.5 < pT < 8.0 8.0 < pT < 10.0 Figure 7.13 Direct photon cross section per nucleon as a function of rapidity for 228 530 GeV/c proton beam on beryllium for several pr intervals. '— ‘ r ' ' l 1 ' 1 r I ' ' T ' - E, _ pBe —>yX at 800 GeV/cg g pTRange é _ § § ¢ § - (GeV/c) c 1an § + _ o 3.59 1 - - - Photon Background '5 0.15 - ------ Beam Contamination - .9. ' ------------- Misc. Other Sources ‘ o r ‘ a: : : 0.1 1— fl ..1' 0.05 — ............ .1 0*...-J°"'1"°“1. 1 1 1 1 1 1 1 1 1 1 1 ‘ 4 5 6 7 8 9 10 1 1 pT (GeV/c) 5.0 25 1 I r 1 1 I f—l 1 1 0' l ' 1 1 1 1 l ' . g t n production at 530 GeV/c . 8 0.2 :- —— 1:: - - D f ‘ 3 ~ ‘ '3: 0.15 _ '2 " -1 o - .1 D4 : - 0.1 e ______ .1 r -;"_':._”_”.. .. .. .5 0,05 l ...................... J O'H'JU'I'HlnT. 1 1 1 1 1 L 1 1 1 1 1 1 1 1 1 ‘ 1 2 3 4 5 6 7 9 1O 1 1 pT (GeV/c) Figure 7.16 Relative systematic uncertainties for direct photon (top) and no (bottom) production at 530 GeV/c versus pr. 232 8 2 b I I T I — I ‘l I I I I I I I l T j’ d g . 515 GeV/c 1: Beam . q—q ’ d v 1- - S C 11 2 3 L. 0.. .0 Q $ + L . 1 ---- ---1 ------------- a. -- -- -- --------------------- -< v 1. J 1. . 1 . 0.5 :- . no '1 : o y 2 o b 4 l I l 1 I I I l 1 I l I L I L I q 2 4 6 8 1O pT (GeV/c) Figure 7 .17 Ratios of direct photon and 7r0 production cross sections by 515 GeV/c 1r" beam on Be obtained from the 1991-92 fixed target run to those obtained from the 1990 run. The error bars reflect statistical uncertainties only. by examining the ratio of the cross sections obtained using the different direct photon candidate definitions. The ratio of the 90N to 758 and the 75N to 758 direct photon cross sections is shown for the three incident beams in Figure 7.18. These ratios differ from unity by z 5%, again well within the quoted systematic uncertainty. 7 .6 Nuclear Dependence As stated in Section 1.6, the cross section per nucleus for high-pr particle production is often parameterized as proportional to A“. The parameter a can be extracted from the Cu and Be cross sections per nucleon, ac“ and age, using the 233 1.4 Ratio 1.2 0.8 0.6 1.4 1.2 0.8 0.6 1.4 1.2 0.8 0.6 .- . 90N/7SS . ._. . . fl 1 , , , . 7 1: Be —> yX at 515 GeV/c —‘ —0.75 yX at 530 GeV/c 1 I —0.75 < y < 0.75 I .1 ------ 1 ----- 1 ----- W11 ----- 1 --------------------------- — i j -I L l I I I l I J l I I I L 4 l I I I I l I J 4 1“ I T fi I T j I I I I I I I I I I I I I .. _- pBe —-> 7X at 800 GeV/c ? : —l.0 < y < 0.5 - E'+ """ 9 """ 9 ----- G ----- +----+ ..... +m+ ........ + ___________ -: :- 1 1 1 Stalt uncertainties only — 4 5 6 7 8 pT (GeV/c) Figure 7 .18 Ratio of 90N to 753 and 75N to 758 direct photon cross sections for the 515 GeV/c 1r” and 530 and 800 GeV/c proton beams. 234 relation _ ln(OCu/UBe) 0‘ ‘ mam/AB.) + 1' (7‘4) The nuclear dependence parameters a for direct photon and no production are shown as functions of pr for the three incident beams in Figure 7.19. Most of the experimental systematic uncertainties cancel in the ratio of the Cu and Be cross sections. The remaining uncertainties, indicated by the bands in the figure, are dominated by the target-related systematics described in Section 6.3.6. At low pr, the values of a for no production are below one—consistent with expectations that at low pr the interactions are occurring at the nuclear level rather than at the parton level. As the pr increases, the a values rise to, and exceed, one; the value expected for scatters occurring between the beam and target constituents. The excess above one is interpreted as due to multiple scattering of the partons in the nucleus. The values of a for direct photon production are clearly below the corresponding values for no production, which may be expected since multiple scattering is limited to the initial state in the case of direct photon production. The solid lines represent fits to constants over the ranges indicated by the lines. The resultant values for a are presented in Table 7.2. In the table, the first uncertainty is statistical and the second is systematic. The dotted line overlaid on the 515 GeV/c 7r‘ beam data represents a theoretical prediction for a in direct photon production from Guo and Qiu [26]. Also shown are 0 measurements for charged 7r production by 200 GeV/c 7r" beam by Fermilab experiment E258 [100]. The measurements are in good agreement with the a results for no production at 515 GeV/c. 235 Table 7.2 Measured a values for 7rO and direct photon production as determined from the fits shown in Figure 7.19. Beam 7r0 530 GeV/c p 1.123 i 0.007 i 0.011 1.060 i 0.015 :t 0.011 800 GeV/c p 1.129 :1: 0.011:t 0.017 1.028 :1: 0.016 i 0.016 515 GeV/c 7r’ 1.109 i 0.007 :1: 0.011 1.044 :1: 0.011i 0.011 Direct photon The results for the nuclear dependence of direct photon and no production can be compared to theoretical expectations from the HIJING Monte Carlo—a program designed to simulate particle production in pp, pA, and AA collisions [101]. However, at these beam energies the normalization of the cross sections from HIJING are sensitive to the choice of the hard scatter pr threshold, and thus, only shape comparisons are possible. Comparisons for the ratio of 7r” and direct photon production cross sections on Cu target to those on Be target are shown in Figures 7.20 and 7.21, respectively, for the three incident beams. The HIJING normalizations were obtained by fitting the shapes obtained from HIJING to the data over the range indicated by the dashed lines. The shapes from HIJING for the incident proton beams are in good agreement with the data, while the shape of the HIJING prediction for the incident 7r‘ beam has a bigger slope than is seen in the data. Similar comparisons can also be made for the ratio of the inclusive 7r° and direct photon cross sections on Be target to those on p target. These are shown in Figures 7.22 and 7.23. In these comparisons, the shapes from HIJING are seen to be in relatively good agreement with the data for all the data samples. 236 o I I I I I fI I I I I I I I j I I I I I I I _I' I I II I I I I I f g 1 2 ’ 530 GeV/c pbeam i j :5 ' . 1 1 1 .. ................................................. ‘E ....... l "i ....... l---.. 1 . ,1 . 0.8 - o _ L L 1 Y 1 lSystematic uncertailnty band 4 iiiiIiiiiIiiiijiiiiIIiiiI§§§§IL4ii 12 L 800 GeV/c p beam _‘ ° . 1 ¢ . + A. o 1 4> - 1 — -------------------------------- I ---------- v ------------------------ 1m— . + I 0.8 ~1 — A. I I L l I I I I I I I I I l I I I I I I I I I l I I I LL I I I I I fiI I I I I I I I I I I T T I I I I I I I I I I I I T I 12 *_ 515 GeV/c1: beam 11 _‘ 1- . -1 _ I . “TAN-fi_ -4 u- ‘ ¢ 3‘} I ‘ + I A _ ........‘r. ......................................... 1 5+ ------------------------ :1 --------- 1-..-1 ------------ «1+ ------- 1----; A. O L d ............ X. Guo and J. Qiu i1 -1 1- + | .1 0.3 f 51' ;.}200 GeV/c n“ beam (E258) ~ L I I I l I I I I 1441 I J l I I I I l J I I I l I I I I I L L I I 1 2 3 4 5 6 7 8 pT (GeV/c) Figure 7.19 The nuclear dependence parameter a measured using Cu and Be targets versus pr for direct photon and no production by incident 530 and 800 GeV/c proton beams and incident 515 GeV/c 7r“ beam. 237 0 2 ' 1 ' r T 1 ' ' ' 1 CO . E 1:0 production by 530 GeV/c p beam 1 5 . * I g 1 b *4-$-¢".‘.".'.".'".".“.'" ----------------------- 1 --------------- I 1 _. ¢ ¢ + + —1 C -------- HIJING . I 1 o t I : IL L I t + t I : t 1:0 production by 800 GeV/c p beam . _ I, + . {1.1.111-1..-.---.-.._¢.-..,1 ++---i _____________________ 1 1 ~ _, + 1 o t I : t : I : i : I : 1 no production by 515 GeV/c 1t- beam . L . 1-‘u;-.‘-6.‘-.'.‘.‘-.--..-._._.._.._-..-?--+-- -+ ----------------- q 1 — f f ""‘-1 1 . 1- . r 1 1 l 1 1 1 l 1 1 I l 1 o 4 6 8 pT (GeV/c) Figure 7 .20 The ratio of inclusive 7r0 production cross sections per nucleon on Cu to those on Be as functions of 7ro pr. Also shown are shape comparisons with HIJING. The error bars represent only statistical uncertainties. 238 2 W F I T V I V I j V *T I I r Y 1 r l : 7 production by 530 GeV/c p beam i'"“+'"+""r"0---¢---$--+ ------ .+.----i ------- +- ------------------ ‘ oICu/ 686 F : -------- HIJING + 0 l L l l l L l l l l l l l l l 1 l l l l l l 17 T l I I I I l T I l I I I i I V y production by 800 GeV/c p beam ++1119 ....... 1 ........... + ....... e y production by 515 GeV/c 1t- beam #- ”WW3 ------- -3. + ‘ 1;+ 1 1 ---.---¢ ......... 1 ....... i ............ t _______ j . J 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 o 4 5 6 7 8 pT(GeV/c) Figure 7.21 The ratio of inclusive direct photon production cross sections per nucleon on Cu to those on Be as functions of direct photon pr. Also shown are shape comparisons with HIJING. The error bars represent only statistical uncertainties. 239 a. l ' ‘ r l l D \11 no production by 530 GeV/c p beam - om - é i j 't- 4- --'-. .l- 1 _ i " ""0-o-t-.--‘-¢--¢--+-+-+--- -------------------- u I -------- HUING + i o s I I . . I I I I I 1:0 production by 800 GeV/c p beam 1 3..-?-+.*'.".‘.".-.--?-‘-¢..¢-i_.___+_ _____ +_ ________________ + .4 t ¢ + + - o a I ' . If k I I I I I _ no production by 515 GeV/c 1F beam 1 ’- ‘i‘+-i-.-‘-“_.._._*_¢_.§-+.+.-+.-*-- ---+--__________________;- o l L l 1 l 4 6 8 pT (GeV/c) Figure 7.22 The ratio of inclusive no to those on p target as functions of 71'0 cross sections per nucleon on Be target Also shown are shape comparisons with HIJING. The error bars represent only statistical uncertainties. 240 7 production by 530 GeV/c p beam 036/ 6p .1 1 +- +§O£t¢¢++ ------------ + ------------------- '7 b q -------- HUING #- .1 L . y production by 800 GeV/c p beam 1 =----------+----.---.---.---¢---Q---¢---+------* ------- § ------------ + ------- : I l fl I I I I fl T I I I I I I I I I I I f 7 production by 515 GeV/c 1t- beam 1 +1. ....... 1 ............ . ....... 3 b a . 1 o l l l l l l 1 l 1 l 1 l l 1 1 J 1 l 1 l l j 4 5 6 7 8 pT (GeV/c) Figure 7.23 The ratio of inclusive direct photon cross sections per nucleon on Be target to those on p target as function of direct photon 12,. Also shown are shape comparisons with HIJING. The error bars represent only statistical uncertainties. 241 7 .7 Comparisons with NLO Calculations In this section, direct photon and no cross section measurements are compared with perturbative predictions calculated to next-to-leading order precision. The NLO predictions for direct photon production are from Ref. [102], while the predictions for 1r0 production are from Ref. [103]. In these comparisons, the theoretical scales, ,uR, up, and mp (for the 7r0 prediction), are all chosen to be equal. Also, for the n0 comparisons, the calculations use KKP [19] fragmentation functions (FF). Although the theoretical calculations account for the numbers of protons and neutrons in nuclear targets, they do not account for nuclear effects. Therefore, the theoretical calculations for the beryllium target have been adjusted using results from HIJING (Section 7.6). In Figure 7.24, inclusive direct photon and 7r0 cross sections per nucleon for 515 GeV/c 7r‘ beam are compared to NLO pQCD results with scale choices of ,u = lgpr, %pT, and pr.5 The discrepancy between the theory and the data is significant. Analogous comparisons between NLO calculations and the 530 and 800 GeV/c p beam data show similar discrepancies. In addition, the theory shows significant dependence on the scale choice. However, recent calculations which include the effects of soft-gluon resummation in direct photon production near the threshold limit (:1: —> 1) [31] have significantly reduced scale dependence and, at E706 beam energies, are comparable to the bare NLO prediction with a scale choice 5 The theoretical prediction for 7r0 production with ,u = §pr is not shown below pr: 4.25 GeV/c because the scale is below the starting scale for the KKP fragmentation function. 242 of u = épr (see Figure 7.25). This scale choice is employed in the following NLO comparisons with the data. In Figure 7.26, the direct photon and 7,0 cross sections for 530 GeV/c p beam are compared to NLO calculations using CTEQ5M[104], CTEQ6.1M[18] and MRST2003C[105] parton distribution functions (PDFs). Although the calculations show sensitivity to the choice of PDF, none of the PDF’s bring the predictions into agreement with the data. PDF’s from CTEQ6.1 and MRST2001E[106] also provide additional PDF sets which can be used to assess the uncertainty in the calculation due to the PDF uncertainty. In Figure 7.27, the direct photon and 7r0 cross sections for 800 GeV/c p beam data are compared to N LO calculations using MRST2001E PDF. The uncertainty in the calculation from the PDF is indictated by the shaded band in the figure. The uncertainty in the PDF is not large enough to account for the difference between the data and the theory. 7. 7.] Evidence for Initial State Parton kT As stated in Section 1.7, a possible cause for the large discrepancies between data and NLO calculations may lie in the effects of soft-gluon radiation in the initial state. Such soft—gluon emissions may not be fully accounted for in the NLO theory and may generate substantial amounts of transverse parton momenta (kT) in the initial state. Evidence for such kT can be found through the analysis of distributions of high-mass direct photon pairs in the data [27]. Distributions sensitive to [CT include: the total pr of the two photons (QT), the azimuthal angle between the photons (Ad), and the out-of-plane momentum (pOUT), which is 243 I I I I I I I I I I I I I I l I I I I I I I I r I I I I I I T—I I I I I I I I 0.1 E 3 .26 ; _ 5 B 103: , 1!: Be at 515 GeV/c . LB 1“. _ u y [pb/(GeV/c)2] 1 - _ :1 11° [nb/(GeV/c)2] 3 -0.75 < y < 0.75 .uL N . I? I 1 I IIIIII .0 .. .. .. . . I I . I '0‘, I. ’ .. ’ -. ’ ‘ I I l l 1 11111] I IIIIIIII [I Ill 0 I I d 1 =- _. 1- I : : : '--‘.,~ - :1 b ' ‘..‘l.‘ ‘ '4 o 'o.‘ h ‘ °.\ -1 - C C..‘. 1 ‘ . ‘ ,".s 10 :— . ‘ ....-\ l 1 1. \ °0f~ : E 52%... 5 — 0 ~ i’.’.’ 4 I» ~ 0 ".§ q '2 \ ' ' s 10 L— ‘ "I": :- ~ I . " 1 - . ‘? .1 : l . O... ‘ . ‘2’lai : I- . .0. ~ .\ q .. s '0. \ ' °§q ' O \ o . -3 . NLO Theory ~— ~ . .'I.~‘D 10 5:. ‘ . "a s ‘1 : GRV92 ._ = h \ . .0. ‘~ :1 - ~ we ~ '- ....... u = p l 3 . \ . '0.. ‘ .1 h- ‘ '0. \ " .4 T o . I...‘ I I IIITIII .............. “=pT/2 ."‘.....":“f -5 - ....... p. = p1. ~...‘.-... 1..“ O \ '0. \ o . ‘ \ ' § 1: uses KKP fragmentation . L1 1 llllll .5 o I IITIITII I I I I o I o. I .' I ”W p. I ”I I l l lllllll 1O #1111111]lllIlllllLllJ_lllllllllll.:°-l 4 5 6 7 8 9 10 11 PT (GeV/c) (a) Figure 7 .24 Direct photon cross section versus pr for 515 GeV/c 7r“ beam on beryllium compared to NLO pQCD results for several choices of scales. Also shown is the no comparison (scaled down by a factor of 1000). 244 4 lo I ‘l I I I I I I I I n [ I I I I T I I I I \ Solid: Resummed — 2 \ Dashes: NLO ‘6‘ 10 — \ _ % \ g — ‘ \ - a \ \ Upper: 11=p1/2 : 100 ”‘ \ \ Lower: p.=2pT — Q1 \ N _ \ .. Q Ebeam=530 GeV \ \ 3 10-2 __ Proton—Nucleon \ _, \ _ Catani, Mangano, Nason, \ \ q Oleari and Vogelsang \ \ \ 10’4 F PRELIMINARY \ \ "r \ \ I 1 l 1 1 J 1 J I 1 J 1 l I 1 1 1 l 1 1 1\ L\ 4 6 8 10 12 PT (GeV) Figure 7 .25 Comparison between a threshold resummed pQCD calculation and NLO pQCD for scale choices of %pr and 212,. Figure from Ref. [31]. 245 a I I T T I I I I T I I j I I I j T I I I I I I I I r I I I I 1 I T I I I II I I : M'U 2 B 3 1 pBe at 530 GeV/c - 10 4 2 '31 3 ~. 1 A 'yo[pb/(GeV/c) 2] 5 a, . 2 ‘ 1 A n [nb/(GeV/c) 1 q 10 ‘~.. _: AA ‘\ ‘ —0.75 < y < 0.75 a 1141‘ \ ‘ ‘ : 5AA A d I) A ‘5 : §> AA '~..~ ‘ .1 '3‘ A fl“: - *«AA elm, ‘ 1 *4» AA ‘91:". '3 .R'AA ”‘55,. .. "Q. A ‘c """"" i " In A ‘; n. '4 ‘i’oAA ‘s . 10 "';..AM “1: ..... I _E “file-A A ‘.~‘.“ """""" E -2 2;...“ ‘2‘ . 10 "~33. “~2~. ‘2 {ft-f :‘ t i 10 _3 NLO Theory “1. A ”a. 1i . ll = pT / 2 "a “K: E 4 ------- CTEQSM 132;. ~. 3 \ 5.. \z‘ 10 .............. CTEQ6. 1M \E'“. l I ‘s Z .5 ------- MRST2003C ~,.-.._,_. 10 no uses KKP fragmentation fit. 1 10 1 l I I I l l l l l l l l l l l l l l l l l l l l 1 l L i l l l L 1x1..." 1 1 J 3 4 5 6 7 8 9 1O 1 1 pT (GeV/c) Figure 7.26 Direct photon and no cross sections versus pr for 530 GeV/c proton beam on beryllium compared to NLO pQCD results for several choices of parton distribution functions. 246 Edo/d3p Figure 7.27 Direct photon and 7r0 cross sections versus 10 10 1O 10 10 10 10 : T I I I I I I I I I I I fi' I I I I I f] I I I I I f I I I I I I I I I I I I I 1- ’ -1 t , pBe at 800 GeV/c 3 :— '3 ’ , . y [pb/(GeV/c)? coo ..... ’ . o no [nb/(GeV/c) ] - ri': o E""3°° ......... . . —1.0 < y < 0.5 E ; «“300 .......... g :1 O """" o E” "-..°o ''''''' 1: : “30° ...... o : ~ o 3 - -. o o " "-.f’oo ------ ‘ :- .". O ..... . 1 E "~..°o ...... E E "-5900 ......... g 5 ,. “3&0 ......... .1 _ °°°° °o """" _ ...... o ------ f : ...... o ........ :1 I ----- o ------ I o '- é' ..o ........... —§ 5 .......... P 5 ; .. ...... " .............. NLO Theory an : l1 = 91‘ l 2 §'- L MRSTZOOIE .......... * 1:0 uses KKP fragmentation ....... j .- 1 1 1 1 I 1 1 1 1 1 1 1 1 L; 14 1 14 L 1 1 L l 1 1 1 1 l 1 #1 1 l 1 l l 1 I 3 4 5 6 7 8 9 1o 11 pT (GeV/c) for 800 GeV/c proton beam on beryllium compared to NLO pQCD results using MRSTZOOIE PDF. The shaded band indicates the uncertainty associated with the PDF. 247 defined as the component of the momentum of one of the photons perpendicular to the plane formed by the incident beam direction and the direction of the other photon. These distributions are shown in Figure 7.28. Overlayed on the data are results from NLO pQCD (dashed) [107], resummed NLO (solid) [38], and [CT-enhanced PY’I‘HIA6 (dotted) calculations. The shape of the NLO prediction is inconsistent with the data. The resummed calculation, which accounts for multiple soft gluon emission, provides a reasonable match to the shape of the data. The shape of the [CT-enhanced PYTHIA distribution is also in good agreement with the data. Similar com arisons can be made for hi h-mass 7r07r0, 7r0 , and 7r0 airs. P g 77 7 P In Figure 7.29, POUT distributions are shown for these, as well as for 77, pairs. The 77 results are compared to NLO pQCD (dashed line), resummed NLO (solid line) and [CT enhanced PYTHIA (dotted line) calculations. The now0 and 77r0 distributions are compared to L0 theory with several choices of supplemental- kT. Although fragmentation also contributes to the width of these distributions, the theoretical comparisons are greatly improved when kT effects are incorporated into the theory. The (kT) values that provide the best agreement with the data are comparable to the (hp) measured for 77 pairs. Also shown in the figure is the POUT distribution for 7r017 pairs. Theoretical curves are not shown for this distribution, 0 as fragmentation functions for 77 production are not available. Therefore, the non distribution has been overlaid on the 7r°17 distribution for comparison. 6 The effects of kT are approximated in PYTHIA using a Gaussian smearing prescription similar to the one described in Section 7.7.2. 248 110-6 IF71:‘ l ' 70-15 _1'1'1'; Q 5 : ’8‘ 7t Be—wa at 515 GeV/c: > i E H pl' .0 GeV/c E (“5 ;' : fig” fim‘kgso v 0.4 — = ': —-vo.1o — A¢>105 2 - £3 ' - e M>10 GeV/c a E 2 a '8 0.2 90.05 g ._. 0.0 0.00 ......v-_' _________ 150 160 170 180 A4) (degrees) UT 1.00 : I I I I I I If j I ’5‘ : Resummed (RESBOS) g '. ----- NLO (Bailey et al.) (3075 __'; ---------- PYTHIA (<1c,>=1.1GeV/c)_ {- '. 0’ ': €0.50 — - -o b \ "0.25 0.00 """""" 0 1 2 3 4 5 QT (GeV/c) Figure 7 .28 pOUT, A45 and QT distributions for high-mass direct photon pairs in the 515 GeV/c 7r" data. The data are compared to NLO pQCD (dashed), resummed NLO (solid) and k7 enhanced PYTHIA (dotted) ‘ results. Figure from Ref. [27]. 249 (l/o) do/dpom. (GeV/Cy‘) 0.6 I I ' I . I T r I T T T l§”'NL0 O O n LOTheory 0 5 - W E : —Resummed 1- Tc Tc :' ‘.‘ -- - «9:00 GeV/c- 5 5 ------ PYTHIA 5 3 ------ «9:12 GeV/c O4 _ E E (=l.l GeV/C)q_ 5 E——=1.4 Gequ 0.3 _ : 0.2 ~ .' 1 0.1 - ,-' l,‘ 0.6 1 " "1’" 1 E“ . O {x LO Theory 0 - — - nono data 05 * YTE :' ‘.‘---=0.0GeV/c+ TITE . 5 '. ------ =l.2 GeV/c 04 - f '1..——<1cr>=1.4 GeV/c.- J 0.3 " .5 .3 I‘m..." qr- f: ." '. - .. 0.2 - :-: in. . 0.1 - + + _ 0.0-:9-51 1 . m- -4 -2 0 2 4 -4 -2 0 2 4 pOUT (GeV/c) Figure 7 .29 pan distributions for high-mass 77, 7r07r0, 7710, and won pairs in 7r'Be interactions at 515 GeV/c. Figure from Ref. [27]. 250 The presence of significant [CT is also expected to affect other aspects of the data. In particular, consider the fragmentation of jets recoiling against high-pr photons. The fragmentation variable z is defined as the longitudinal momentum fraction of the recoil jet momentum carried by particle '1', z E p} - 13'th / ”5,642. As the total recoil jet momentum is difficult to measure accurately, the momentum of the away-side direct photon can be used in its place. However, if the (by) is not negligible, such a procedure will affect the 2 distribution. This is seen in Figure 7.30 [108], where the 2 distribution of charged particles in jets recoiling against isolated photons in the 800 GeV/c proton data is compared to theoretical expectations [15] for several choices of (kT). The calculation with (kT) comparable to the values found using the kinematic distributions discussed earlier is in good agreement with the data. Finally, this experiment has also measured the cross section for the production of charm mesons at high pr [109]. Figure 7.31 shows the differential Di cross section compared to results from N LO pQCD calculations with and without supplemental- kT [110]. Again, the kT-enhanced calculation accommodates the data better than the calculation without 1%. 7. 7.2 Comparisons with [CT-enhanced NLO Theory Higher-than-NLO calculations for direct photon production are currently being developed which simultaneously incorporate the threshold corrections cited earlier with corrections for the recoil from soft radiation before the hard scatter[111]. Such calculations are expected to account for the gluon emissions responsible for 251 fl r I I I I I I I I I I I I I a .................. -1,0 isolated y + X at 800 GeV/c Owens LO * BKK fragmentation -1 Inf : u = pT / 2 10 _- -------- (kT)=O.O GeV/c — * (kT)=O.9 GeV/c ~ — (kr>=1-3 GeV/c 1 1 1 1 4 1 1 1 1 l 1 a 1 1 l 1 0.3 0.4 0.5 0.6 0.7 2 Figure 7 .30 Away-side fragmentation function for jets recoiling against isolated 7’8 with pr> 5.5 GeV/c [108]. 252 c o l - :t .02 - 7tN—>D X otSlSGeV/c o ........... 10 ~ ' g 0 Data 5 --— NLO QCD: Frog. + =2.o Gev’ o. ------ - NLO QCD: Frog. + =o.o GeV2 A > 1 - <1) 0 1 \ . 13 1 3 —1 10 r p— » Q_ I “O C \ . b . '0 -2 10 g —3 10 g —4 10 g L —5 1O 1 1 O 1 Figure 7.31 Di cross section per nucleon versus pr for 515 GeV/c 7r‘-Nucleon collisions compared to N LO calculations with and without hp. 253 the generation of hp. Although this work is still in its preliminary stages, early results are encouraging (see Figure 7.32). Until these calculations are fully developed, kT effects may be implemented into NLO calculations using an intuitive phenomenological approach. An outline of this approach follows. A LO pQCD Monte Carlo calculation [15] imparts an effective [CT to each of the colliding partons assuming a Gaussian [or distribution, [2; e—kT/(k’f‘) 9( T) — W1 (7.5) where (19%) is the square of the 2-dimensional (2D) RMS width of the hp distribution for a single parton. It is related to (kT) by the relation (1:31) 2 4 G §“‘ . fig 11 usesKKPfragmentation ‘~~.‘ .~ 5 1 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 1 1 1 1 I I 1 1 1 1 l 1 1 1 1 I 1 11s ‘1 d D10 II IIIIIIIIII—rI—fiIIIIIIIIfiIIIIIIIIIIIIIIII o . 0.) 4 >— § 1 A _ t» _ 8 2 - E, t I S F «1 F C: 0 ‘ v t 1 1 l 1 1 I l l 1 1 l l 1 1 L l 1 1 1 l l 1 l 1 1 1 1 l 1 1 l 1 1 1 1 1 1 1 1 1 3 4 5 6 7 8 9 1o 11 pT (GeV/c) Figure 7 .36 Direct photon and no cross sections for 515 GeV/c 7r‘ beam on beryllium compared to [CT-enhanced NLO pQCD calculations. Also shown is the quantity (Data — Theory) / Theory for the direct photon cross section. 260 ry Data/Theo 8 10 I IIIIII iD<><>1<« I IIIIII I I rIIIIII I I I E704 Vs=19.4 GeV ‘ r E629 1s=19.4 GeV NA3 \(s=l9.4 ch WA70 11:23.0 GeV NA24 \ls=23.8 GeV UA6 \(s=24.3 GeV E706 ‘(s=3 1.6 GeV . E706 45:38.8 GeV R806 1s=63 GeV 111111 R807 Js=63 GeV R110 ~1s=63 GeV PHENIX 1s=2oo GeV CDF 1s=630 GeV Dz \/s=630 GeV CDF «13:1300 GeV Direct photon production D25 Vs=1800 GeV by proton beams 1 11L1L 1 1 l 1 1 11 l 1 “‘ r “—fl—r" 1" 1‘1 1 l '_"'"_"—"'— T '_' 'TI‘T—‘l—"TT‘I-l ”'11 _‘-' " "m1" 10'2 10 Figure 7 .37 Data/Theory for proton induced direct photon data from various experiments as a function of asT. The theory calculations use CTEQSM PDF and scale ,1 = %pF. 261 IIIIII I I I IIIIII I I I I I E706 ‘/s=31.6 GeV ‘ ry 8 E704 11:19.4 GeV .5 0 E629 \/s=l9.4 GeV I E706 \ls=38.8 GeV g <1: NA3 Js=19.4 GeV <1- R806 \/s=44.8 GeV «,1 ° 5‘ 0 E268 \/s=l9.4 GeV 1' R806 1s=52.7 GeV 4 ‘3 Q - 1 5300 15:19.4 GeV 7 R806 \/s=63 GeV + 4 j 1:1 WA70 13:23.0 GeV 1 R807 \(s=63 ch j A - *1 NA24 \/s=23.8 GeV E300 ‘(s=23.8 GeV PHENIX ‘/s=200 GeV 31: 31‘“ A UA6 \ls=24.3 GeV ‘1' :1 + I +— 1 1 E300 15:27.4 ch R806 \/s=30.6 GeV o . A UAl 1s=5000ev - . 1- o UA1\/s=630 GeV . 7‘ PTOdUCUO A UA2 \Is=630 GeV .1 by proton beams o UAl Vs=900 GeV 10 1 1 1 1 1 1 .2 11 1 J 1 1 1 l .1 1 1 1 1 1 10 10 Figure 7 .38 Data/Theory for proton induced 7r0 data from various experiments as a function of 177' The theory calculations use CTEQSM PDF, KKP FF, and scale )1 = %pr. 262 from these experiments are compared to NLO expections with and without kT enhancements. The choice of (hp) values shown in the figure is motivated from a study of kinematic distributions of direct photon pairs by WA70 [28], which measured an (kT) of 0.9 GeV/c in their 7r’ p interactions. W ith the exception of the WA70 p beam direct photon result, which appears to be reasonably represented by the bare NLO prediction, the measurements are better represented by kT-enhanced calculations. Direct photon cross sections were also measured for pp collisions at \/E = 1.8 TeV and fl = 0.63 TeV at the Tevatron collider by the CDF [48] and DD [49] collaborations. Comparisons of data from these experiments to NLO QCD calculations are shown in Figure 7.40. Also shown are curves representing the expected enhancement to the predictions from initial state parton-kT effects. The enhancement is only significant at the low end of the 12, spectrum, where the (IQ) is comparable to the pr. The result from CDF at \/E = 1.8 TeV has been scaled up by 10% to facilitate a shape comparison to the theory at low pr7. The data from CDF and D0 at both center-of-mass energies show an excess at low pr compared to bare NLO calculations, which is reasonably described by the kT-enhanced calculations. The choices for the (197) are motivated by the measurements shown in Figure 1.7. A related process to the hadroproduction of direct photons is the photopro— duction of direct photons at electron-proton (ep) colliders. The cross section for this process has been measured at the HERA ep collider by the ZEUS collabora- tion [112]. In Figure 7.41, results from this collaboration are compared to NLO 7 A shift of this magnitude is accommodated within the systematic uncertainties quoted for this measurement. 263 I I I I I I I I I I I I I pp at 280 GeV/c (WA70) '5 ......... —O.35 < xF < 0.45 . ' Y [Pb/(GeV/C)2] '1' 3.35.1": 0 11° [nb/(GeV/cf] \ '0. s 0.. NLO Theory (11 = pT / 2) ' 42911... CTEQSM PDF '~ . :53," 1:0 uses KKP FF ‘ ' 3.41%.. fi I I I I I I I ITI l I I I I fl I n'p at 280 GeV/c (WA70) —0.35 < X}, < 0.45 0.. ~a s . .- Qi'.’ Q '0. ‘go‘.. o ~~.d. O~¢‘. ‘ d . ‘1- s.‘ 5‘ ‘ I ‘ ‘9 '5‘? s ‘ ‘° ~‘ . ' 31:. ‘5'»? I's..\°' ‘. 'e. ': ~59 \.\.o.. \ ‘0. 0 “2:0,. . .... (15> = 0.9 GeV/<5 a - - - (k1): 0.7 GeV/c '35':-;.. - . - (1%) = 0.0 GeV/c "‘53"- Sltat and sys uncerfainties combinedl ‘ ' 3.1" FRV92 PDF 1 1:33;... 1 J 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 J1. ”.011 1 I I I I I I I I I I I I I T I I I I I I I I I I- I I I I I I I I I I I pp at 315 GeV/c (UA6) pp at 315 GeV/c (UA6) -O.l S y S 0.9 ~ §;o..' Q .~.I. a o 2. ~ I ‘ ...o 5. ~ ~"l.. ‘ 0 ~ Q o. o ‘i. o §~ . 5 ~ ‘0 ' o . Q ‘ .' ~. \‘u 0 ~ .'. . ~9 ~ . ~.- I '0 Q ‘ ‘ O a ‘mu. ~ 0 .§ ‘0'. . o §.¢~.o.. ‘ § ' I 0 ~:?;'-. ~".. \ .- o —0.lSySO.9 \ ‘0. s‘ . o ‘.. 0". \‘o \ o .s . \‘° .\ 1'. o ‘1' ‘1“ ‘ \..o CTEQSM PDF .‘~. '0 111L11111111111‘11411 4 5 6 7 8 pT (GeV/c) Figure 7 .39 Direct-photon and 1r° cross sections from experiments WA70 and UA6, compared to kT-enhanced N LO calculations. 264 b 1 _ ' l ' ' r l ' ' ' l ' ' ' l r I ' r ' ' ' 4 8 : f ppatVs=1.8TeV : g g % -0.9Sy$0.9 A 0.5 < E r: o S a . v-o.5 — (I) ggféxf) _ (kT)=3.5 GeV/c j - . . (kT)=O.O GeV/c _ Stat uncertamtles only _1 r L . . 1 L . . . L m 1 . 1 1 . . 1 . 20 4o 60 so 100 pT(GeV/c) b1 'I"'*I""I"" 8 pp at \/s=0.63 TeV % 0.5 —0.9SySO.9 g l l 1 i . 0 " """"""""""""""" f"? """""""""""""""""" " l T l ‘ : v-05 :- NLO Theory -- (kT)=2.5 GeV/c : t },t=pT (kT =0.0 GeV/c _1b..1111L11L.11111.LL.IL111..IJJ.. 1o 15 20 25 30 35 4o pT(GeV/c) Figure 7.40 Isolated direct photon cross sections from CDF and D0 at \/s = 1.8 TeV (top) and \/§ = 0.63 TeV (bottom) compared to NLO pre- dictions. The predictions for CDF (D0) use CTEQSM (CTEQ4M) PDF. The solid curves represent the expected enhancement to the predictions from parton-kT. The data from CDF at \/E = 1.8 TeV have been scaled up by 10% to facilite a shape comparision. 265 predictions with and without kT enhancements. The choice of the (by) value is motivated by measurements of kinematic distributions made by this collaboration [113]. Note that in this reaction, the kT-enhanced predictions are only @10% larger than the bare NLO predictions over most of the kinematic regime explored by the data. This relatively small enhancement, combined with the current level of ex- perimental uncertainty, make it difficult to ascertain whether or not the data are better described by the kT-enhanced predictions. 7 .9 Conclusions Differential cross sections for direct photon and no production have been measured for 530 and 800 GeV/c proton beams and 515 GeV/c 7r‘ beams on beryllium, copper and hydrogen targets. NLO theoretical calculations for these cross sections with conventional scale choices lie significantly below the measured results. Many corresponding comparisons with other experimental results show similar disrepancies. A phenomenological kT model has been shown to improve these comparisons for many of the experimental results. Many experimental and theoretical uncertainties cancel in a ratio between direct photon cross sections in proton-induced reactions at 800 and 530 GeV/c. A comparison of this ratio to kT-enhanced predictions using MRST2003, CTEQSM and CTEQ6.1M PDFs is shown in Figure 7.42 as a function of pr. The CTEQ6.1M PDF has a gluon distribution that is much harder than the gluon distribution in the other sets; a result of the inclusion of inclusive jet results from Tevatron Run I in the global fit. However, the use of these data introduce the possibility that 266 do/de (pb/GeV) I I I I I I I I I I I I I I I T I ZEUS 1996-97 —O.7 < y < 0.9 stat and sys uncertainties combined — \“ : i _ NLO Theory Upper: LG ~. Lower: K&Z .. GRV pdf “ — (k1): 1.5 GeV/c (kT) = 0.0 GeV/c l 4 1 1 l l 1 n l l 1 l l L 4 1 7 6 8 1o 12 14 Figure 7 .41 Isolated direct photon cross section from ZEUS. The NLO predictions are by Gordon (LG) and by Krawczyk and Zembruski (K&W). 267 effects due to new physics phenomena may be contained within the current fit uncertainties and absorbed within the resultant PDFs. The E706 data, which appear to favor the calculations using the softer gluons, suggest such a possibility. 268 81o_"‘l""lr"'l“"l"fifl'fi"l'"T 55 C pBe—)yX at 800 GeV/c >3 9 :- pBe—)yX at 530 GeV/c 8 - 1°, C 8 :- I NLO Theory (p.=pT/ 2) L. 7 f ——CTEQ5M t ----- MRST2003C 6 E. .......... CTEQ61M 5 4 3 ........... .t 2 35:5 """ _.l .......................... < > 1.3 GeV/C(SOO GeV/C) : 1 - k7 — 1.2 GeV/c (530 GeV/c) -§ o'....1....1.1J.1..4.1.4L.L..r11....1 3 4 5 6 7 8 9 10 pT (GeV/c) Figure 7 .42 The ratio between 530 GeV/c and 800 GeV/c p beam direct photon cross sections as functions of pr. Overlayed on the plots are NLO predictions with and without supplemental kT. 269 Appendix A Tabulated #0 Cross Sections This appendix contains the measured 7,0 cross sections in tabular form. The results are presented in the form A :t B :l:C, where A is the measured value, and B and C represent the statistical and systematic uncertainties, respectively, on the value. For those cases where the systematic uncertainty is not given, the statistical and systematic uncertainties have been combined because of the large correlation between them (Section 5.11). 270 Table A.1 Invariant differential cross sections per nucleon for 7r0 production by 530 and 800 GeV/c proton beams and 515 GeV/c 77‘ beam on Be targets, for 1.0 < [1, < 4.0 GeV/c. Eda M310 (Mb/(GeV/C)2) p Range 7 pBe at 530 GeV/c pBe at 800 GeV/c 1r‘Be at 515 GeV/c (GeV/C) —0.75 < y < 0.75 —1.0 < y < 0.5 —0.75 < y < 0.75 1.00 — 1.20 550 :l: 66 706 i: 95 258 :l: 36 1.20 - 1.40 223 :1; 28 301 a: 41 98 i 14 1.40 — 1.60 72 :t 11 125 :l: 18 39.9 :5 6.0 1.60 - 1.80 32.7 :1: 5.3 54.3 :t 8.4 20.0 :1: 2.6 1.80 — 2.00 15.3 :1: 2.7 23.9 :1; 4.1 9.6 :l: 1.3 2.00 - 2.20 6.9 :t 1.3 :l: 0.7 7.4 :t 1.7 a: 0.8 3.68 d: 0.36 :t 0.43 2.20 - 2.30 3.00 :l: 0.15 a: 0.32 3.95 a: 0.24 :t 0.44 2.134 :t 0.054 :t 0.25 2.30 - 2.40 2.02 :t 0.13 :l: 0.22 2.69 :l: 0.22 :t 0.30 1.475 i 0.038 3: 0.17 2.40 - 2.50 1.38 a: 0.13 a: 0.15 1.78 :l: 0.14 :t 0.20 0.964 :t 0.027 :1: 0.11 (nb/(GeV/c)2) 2.50 — 2.60 982 :t 87 :t 100 1221 :t 96 i 140 681 :5 17 :5 79 2.60 - 2.70 614 :l: 17 :i: 65 825 :t 46 :l: 91 502 :t 14 :l: 58 2.70 - 2.80 388 :5 10 :l: 41 653 :t 33 :1: 72 318.9 :5 9.7 a: 36 2.80 — 2.90 291.1 :t 9.2 :5 31 452 :l: 10 :l: 50 246.4 a: 7.3 :l: 28 2.90 — 3.00 196.5 2}: 7.2 :l: 21 319.8 :h 7.3 4: 35 172.1 a: 4.3 a: 20 3.00 - 3.10 141.0 i 3.2 :t 15 223.7 :t 5.3 :l: 25 128.8 :l: 3.3 a: 15 3.10 - 3.20 100.8 :t 2.8 :t 11 163.2 :t 4.6 :t 18 91.8 i: 2.6 :t 10 3.20 — 3.30 75.7 i 2.4 a: 8.1 117.2 :t 3.3 :l: 13 72.9 :1- 1.9 a: 8.2 3.30 - 3.40 49.6 :t 1.5 :l: 5.3 92.4 :l: 3.2 :1: 10 48.8 a: 1.3 :l: 5.5 3.40 - 3.50 37.2 d: 1.5 :l: 4.0 62.6 :1: 2.2 :5 6.9 35.7 :t 1.0 :1: 4.0 (pb/(GeV/C)2) 3.50 - 3.60 26800 i 1000 a: 2900 44200 a; 1800 :t 4900 26810 :t 660 :t 3000 3.60 — 3.70 18650 :5 840 :L- 2000 33800 9; 1600 a: 3700 19940 :t 500 i 2200 3.70 — 3.80 13800 i 520 :t 1500 26600 d: 1200 a: 2900 15030 :i: 360 :5 1700 3.80 — 3.90 10560 a: 300 i 1100 20800 :1: 1000 :l: 2300 11260 :l: 300 i 1200 3.90 — 4.00 7637 a: 57 :t 820 14680 :t 770 :t 1600 8370 a: 110 :1: 920 271 Table A.2 Invariant differential cross sections per nucleon for no production by 530 and 800 GeV/c proton beams and 515 GeV/c 7r’ beam on Be targets, for 12, > 4.0 GeV/c. Eda/(1312 (pb/(GeV/C)2) p Range 7' pBe at 530 GeV/c pBe at 800 GeV/c 7r'Be at 515 GeV/c (GeV/C) —0.75 < y < 0.75 —1.0 < y < 0.5 —0.75 < y < 0.75 4.00 — 4.10 5613 i 42 j: 600 10940 :1: 450 :t 1200 6286 i 40 :1: 690 4.10 — 4.20 4203 :1: 33 j: 450 8660 :1: 120 j: 960 4820 :1: 34 :1: 530 4.20 — 4.30 3177 i 27 :1: 340 6500 :t 97 :1: 720 3642 :1: 27 i 400 4.30 - 4.40 2318 :1: 22 i: 250 4746 :1: 73 :1: 530 2855 :t 23 :1: 310 4.40 — 4.50 1748 :1: 18 :1: 190 3687 :1: 68 :1: 410 2189 :1: 19 :1: 240 4.50 - 4.60 1327 :1: 15 j: 140 2856 :1: 54 :1: 320 1672 d: 15 :1: 180 4.60 - 4.70 1005 :1: 12 d: 110 2178 i 46 :t 240 1290 :t 13 :1: 140 4.70 - 4.80 762 :1: 10 :1: 83 1741 :1: 38 :1: 190 1000 :1: 11 :1: 110 4.80 — 4.90 577.2 i 8.6 :1: 63 1353 :t 25 :1: 150 764.5 :1: 9.6 :h 84 4.90 — 5.00 443.2 :E 7.4 :t 49 1057 :1: 22 :1: 120 612.2 :1: 8.6 :1: 67 5.00 — 5.10 348.0 :1: 6.5 :t 38 817 :1: 18 :h 92 480.9 :1: 7.3 :1: 53 5.10 -— 5.20 263.1 :1: 5.4 i 29 664 :t 17 :1: 75 370.0 :1: 6.1 :t 41 5.20 - 5.30 205.1 :t 4.9 :1: 23 490 :1: 16 :t 55 301.3 :1: 5.5 :1: 33 5.30 - 5.40 156.0 :t 4.0 i: 17 415 :h 13 :1: 47 240.2 :1: 4.9 :1: 27 5.40 - 5.50 121.2 :1: 3.5 :t 14 315 :t 10 :1: 36 193.4 :1: 4.3 :1: 21 5.50 - 5.60 92.2 :1: 3.0 :1: 10 246.4 :1: 7.9 :1: 28 152.9 :1: 3.7 :1: 17 5.60 — 5.70 64.7 i 2.6 :1: 7.3 209.1 :1: 6.9 :1: 24 117.7 :1: 3.2 :1: 13 5.70 — 5.80 57.7 :t 2.4 :1: 6.5 160.8 :1: 6.2 i: 18 92.0 :1: 2.8 :1: 10 5.80 - 5.90 45.1 :t 2.1 i: 5.1 130.0 :t 5.7 :1: 15 78.0 :1: 2.6 :1: 8.7 5.90 — 6.00 36.4 :t 1.8 :1: 4.1 104.2 :t 5.4 :1: 12 57.9 :1: 2.2 :L- 6.5 6.00 - 6.25 23.28 :1: 0.89 :1: 2.7 74.9 :1: 2.1 :t 8.6 41.7 :1: 1.2 :1: 4.7 6.25 - 6.50 12.53 :1: 0.63 :1: 1.4 44.2 :1: 1.6 :1: 5.1 25.57 :t 0.91 :t 2.9 6.50 - 6.75 6.11 :1: 0.43 :1: 0.71 23.8 :1: 1.1 :t 2.8 15.43 :1: 0.68 :1: 1.8 6.75 — 7.00 4.49 i 0.36 :b 0.53 15.68 :1: 0.84 :1: 1.8 8.80 :1: 0.50 :1: 1.0 7.00 - 7.50 1.74 :1: 0.16 d: 0.21 7.37 :1: 0.40 :1: 0.88 4.53 :1: 0.25 :1: 0.53 7.50 — 8.00 0.353 :1: 0.069 :1: 0.043 2.58 :1: 0.25 :1: 0.31 1.32 :1: 0.13 :1: 0.16 8.00 - 9.00 0.105 :1: 0.025 :1: 0.013 0.73 :t 0.11 :1: 0.09 0.370 :1: 0.050 :1: 0.046 9.00 - 10.00 0.0082 :1: 0.0058 :1: 0.0011 0.068 :t 0.024 :1: 0.009 0.045 :1: 0.022 :1: 0.006 10.00 — 12.00 — 0.020 :1: 0.019 :h 0.003 0.0031 :1: 0.0031 :t 0.0005 272 Table A.3 Invariant differential cross sections per nucleon for n0 production by 530 and 800 GeV/c proton beams and 515 GeV/c n’ beam on Cu targets. Eda/r1319 (#b/(GeV/CV) p Range T pCu at 530 GeV/c pCu at 800 GeV/c n" Cu at 515 GeV/c (GeV/c) —0.75 < y < 0.75 —1.0 < y < 0.5 -0.75 < y < 0.75 1.00 -— 1.50 252 :1: 40 246 :1: 55 135 :1: 26 1.50 - 2.00 29.9 3: 6.2 51.9 :1: 10.0 25.0 :t 4.2 2.00 — 2.50 4.1 :1: 1.2 :1: 0.5 3.2 :t 1.7 4: 0.4 2.409 i 0.067 :t 0.29 (nb/ (GeV/6)?) 2.50 - 2.75 920 :1: 57 :1: 99 1260 a: 110 :1: 140 673 :1: 29 :t 79 2.75 - 3.00 319 :1: 13 a: 35 516 :1: 15 a: 59 268 d: 12 :1: 31 3.00 — 3.25 135.7 a: 4.2 a: 15 212.2 :1: 6.9 a: 24 128.3 :1: 5.1 :1: 15 3.25 — 3.50 62.7 :t 2.4 :1: 6.8 109.4 :1: 4.2 :t 12 58.8 :1: 2.3 :1: 6.7 (pb/(GeV/C)2) 3.50 — 3.75 26500 :1: 1300 :1: 2900 50200 :1: 2600 :1: 5700 26400 :t 1000 :1: 3000 3.75 - 4.00 12240 :1: 400 i: 1300 24700 :1: 1500 :1: 2800 13410 :1: 410 :t 1500 4.00 — 4.25 6028 :1: 57 d: 660 11930 :1: 550 :t 1400 6555 :1: 66 :1: 730 4.25 — 4.50 2881 :1: 33 :1: 320 5700 :h 120 :1: 660 3310 i 40 :1: 370 4.50 — 4.75 1424 :1: 21 :1: 160 2976 :1: 83 :t 340 1742 :1: 25 :1: 190 4.75 — 5.00 690 :t 13 :t 77 1594 :1: 40 :1: 180 946 :1: 17 :1: 110 5.00 — 5.25 360.4 :t 9.1 :1: 40 887 :1: 27 :1: 100 488 :1: 12 :1: 55 5.25 — 5.50 187.1 :1: 6.3 :1: 21 485 :1: 19 :1: 57 282.5 :1: 8.6 :1: 32 5.50 — 5.75 92.0 :1: 4.3 :1: 10 305 :1: 13 :1: 36 158.6 :1: 6.6 :1: 18 5.75 — 6.00 47.1 :1: 3.0 :1: 5.4 154.4 :1: 9.2 :1: 18 83.6 :1: 4.3 :1: 9.5 6.00 ~ 6.50 20.9 :1: 1.3 :t 2.4 71.3 :1: 3.2 :t 8.5 39.6 :1: 2.0 i 4.5 6.50 — 7.00 4.99 d: 0.63 :L- 0.59 26.4 :1: 1.8 :1: 3.2 12.4 :1: 1.1 :1: 1.4 7.00 - 8.00 1.25 :1: 0.21 :L- 0.15 5.78 :1: 0.56 :1: 0.71 3.08 :1: 0.39 :1: 0.37 8.00 — 10.00 0.074 :t 0.030 :1: 0.010 0.49 :t 0.15 :1: 0.06 0.244 :1: 0.088 :1: 0.031 273 Table A.4 Invariant differential cross sections for n0 production by 530 and 800 GeV/c proton beams and 515 GeV/c n" beam on proton targets. Edd M31? (#b/ (GeV/012) pf Range pp at 530 GeV/c pp at 800 GeV/c n‘p at 515 GeV/c (GeV/C) —0.75 < y < 0.75 —1.0 < y < 0.5 —0.75 < y < 0.75 1.00 - 1.40 355 1 63 630 :1 110 164 :1: 70 1.40 - 1.80 68 91 14 124 1 23 33 :1 16 1.80 - 2.20 17.5 :1: 3.7 9: 2.0 27.6 9 5.5 :1 3.3 4.4 9: 3.2 :1 0.6 2.20 — 2.40 3.54 1 0.84 9: 0.40 3.44 1 0.45 1 0.40 — (Db/(GEV/Cl2) 2.40 — 2.60 1220 1 150 :1: 140 1410 1 230 9: 170 290 1 32 1 35 2.60 — 2.80 479 :1 23 9: 54 732 1 60 :1 86 351 d: 31 :1: 43 2.80 — 3.00 219 9 16 :1 25 334 1 14 9. 39 153 :1: 14 9: 18 3.00 — 3.20 104.6 1 4.8 :1 12 181.6 :1 8.2 9: 21 103.0 :1 9.7 1 12 3.20 — 3.40 56.0 :1 3.5 1 6.4 97.1 :1: 4.9 :1 11 48.6 :1 5.7 9: 5.8 (Pb/ (GeV/6)?) 3.40 — 3.60 27300 9: 1900 1 3100 50200 :1 3700 1 5900 24500 9: 3600 1 2900 3.60 — 3.80 13400 1 1000 1 1500 27300 1 2500 9: 3200 18300 1 2500 1 2200 3.80 - 4.00 7660 :1: 250 9: 880 15500 :1 1400 9: 1800 7600 1 1300 1 890 4.00 — 4.20 4427 9: 63 :1 510 9710 1 690 :t 1100 5040 9: 150 1 590 4.20 — 4.40 2398 1 39 :1 280 5320 :1 160 :1 630 3170 1 100 :1 370 4.40 — 4.60 1357 :1 29 :1 160 3080 :1 100 1 360 1786 1 72 1 210 4.60 - 4.80 803 :1: 19 1 93 1785 9 68 :1 210 1134 9: 48 1 130 4.80 — 5.00 477 1 14 1 56 1118 9.: 38 1 130 637 1 35 1 74 5.00 - 5.20 297 :1 10 :1 35 635 :1: 29 :1 76 417 1 28 :1 49 5.20 — 5.40 173.5 :1 8.0 :1: 20 423 1 22 9: 51 251 :1 20 :1 29 5.40 - 5.60 107.4 9: 5.7 1 13 271 9: 18 :1 33 177 9: 16 1 21 5.60 - 5.80 63.2 :1 4.2 1 7.5 172 :1 11 :1 21 112 9: 13 1 13 5.80 - 6.00 41.2 :1 3.5 1 4.9 104.3 1 8.4 1 13 66.4 1 9.9 :h 7.9 6.00 — 6.25 23.8 1 2.2 9: 2.9 80.2 1 5.6 9: 9.8 34.8 1 6.0 :1 4.2 6.25 - 6.50 12.0 :1 1.6 :1 1.5 36.1 :1: 3.2 1 4.4 29.9 9: 5.8 9: 3.6 6.50 — 6.75 5.87 :1 1.00 :1 0.72 29.3 1 2.7 9: 3.6 17.4 1 4.0 :1 2.1 6.75 - 7.00 4.39 9: 0.84 :1 0.55 13.0 1 2.0 :1 1.6 5.2 1 2.1 :1 0.6 7.00 - 7.50 1.43 9: 0.33 9: 0.18 8.7 1 1.2 1 1.1 4.6 :1 1.4 9: 0.6 7.50 — 8.00 0.75 :1: 0.25 :1 0.10 3.55 1 0.70 1 0.45 2.9 1 1.0 1 0.4 8.00 - 9.00 0.199 1 0.100 9 0.027 0.71 i 0.20 1 0.09 — 9.00 — 10.00 — 0.09 :1 0.10 9: 0.01 — 10.00 - 12.00 — 0.017 1 0.017 :1 0.003 — 274 Table A.5 Invariant differential cross section per nucleon for 7rO production by 530 GeV/c proton beam on a Be target as a function of p1. and rapidity. —0.375 — —0.250 83.8 :1: 3.3 :1: 8.9 17.7 :1: 1.1 :1: 1.9 3.743 :1: 0.053 :1: 0.40 9,. (GeV/C) Rupidity 1.00 — 1.50 1.50 — 2.00 2.00 — 2.50 2.50 — 3.00 pb/(GeV/c)2 115/(own)2 ub/(GeV/c)2 nb/(GeV/c)2 -0.750 — —0.625 600 :1: 190 :t 60 4.625 _ —0.500 350 1 57 27.9 1 8.7 0.7 11.7 1 0.7 425 1 89 1 45 —0.500 - —0.375 514 :t 24 :1: 55 _0.375 _ _0‘250 303 :1: 52 26.4 :1: 6.8 2.9 :1: 1.2 :t 0.3 512 :1: 15 :1: 54 —0.250 — —0.125 532 :1: 12 :1: 57 4.125 _ 0.000 364 1 51 31.2 1 7.2 4.3 1 1.2 1 0.5 609 113 1 65 0.000 - 0.125 547 i 10 :1: 58 0.125 _ 0.250 289 1 43 34.1 1 6.9 5.3 1 1.3 1 0.6 520.4 1 8.5 1 55 0.250 — 0.375 471.4 1 7.9 1 50 0.375 _ 0.500 308 :1: 44 32.6 :1: 6.1 2.8 :1: 1.4 :1: 0.3 443.2 :1: 7.7 :t 47 0.500 — 0.625 401.2 1 8.3 1 43 0625 _ 0.750 359 1 48 17.3 1 5.5 2.4 11.0 1 0.3 353.8 1 8.0 1 38 3.00 - 3.50 3.50 - 4.00 4.00 - 4.50 4.50 — 5.00 nb/(GeV/c)2 nb/(GeV/c)2 nb/(GeV/c)2 pb/(GeV/c)2 —0.750 — ——0.625 71.8 :1: 4.8 :t 7.6 9.96 :t 0.68 :1: 1.1 2.624 :1: 0.068 :h 0.28 607 :t 21 d: 66 —0.625 - -0.500 88.6 :1: 5.7 :1: 9.4 14.4 i 1.3 i: 1.5 2.982 :t 0.064 t 0.32 703 :t 20 d: 77 -0.500 — -0.375 81.9 :1: 5.3 :1: 8.7 14.9 :t 1.1 :1: 1.6 3.383 :1: 0.055 :t 0.36 812 :1: 18 i 89 943 :1: 19 :1: 100 -0.250 - —0.125 93.2 :1: 3.4 :1: 9.9 18.4 :1: 1.1 :1: 2.0 4.014 :t 0.043 :1: 0.43 999 :1: 17 :1: 110 —0.750 - —0.625 -0.625 — -—0.500 150.0 :1: 7.9 :t 17 210.3 :1: 8.9 :1: 23 25.8 :1: 2.1 :l: 2.9 29.9 :1: 2.0 :1: 3.4 1.59 :1: 0.23 :1: 0.19 —0.500 - —0.375 —0.375 - —0.250 224.3 :t 8.0 :1: 25 246.1 :1: 8.1 :1: 27 41.6 :1: 2.1 :1: 4.7 45.5 :t 2.3 :1: 5.2 2.11 i 0.24 :1: 0.25 —0.250 - —0.125 -0.l25 - 0.000 263.4 :1: 8.2 :t 29 278.9 :1: 8.5 :l: 31 50.2 :t 2.3 :t 5.7 52.2 :1: 2.4 :1: 5.9 3.43 :t 0.31 :1: 0.41 0.000 — 0.125 0.125 - 0.250 260.5 1: 7.6 :1: 29 278.7 :1: 7.9 :1: 31 47.8 :1: 2.1 :t 5.4 47.2 i: 2.2 :1: 5.4 3.17 :1: 0.28 :1: 0.38 0.250 - 0.375 0.375 — 0.500 238.8 :1: 7.5 :1: 27 189.8 :1: 6.9 :1: 21 44.3 i 2.1 :1: 5.0 36.0 :1: 1.9 :t 4.1 2.78 :1: 0.29 :1: 0.33 0.500 - 0.625 0.625 - 0.750 169.6 :1: 6.8 :t 19 114.9 :1: 5.9 :t 13 25.8 :1: 1.9 :1: 2.9 16.3 :1: 1.5 :1: 1.8 1.63 :I: 0.24 :1: 0.19 275 -0.125 - 0.000 94.9 :t 3.4 :t 10 20.7 :1: 1.2 :1: 2.2 4.350 :1: 0.043 :1: 0.47 1078 :1: 18 :1: 120 0.000 — 0.125 91.8 :1; 3.0 :t 9.8 17.94 i: 0.99 :t 1.9 4.151 :1: 0.040 :1: 0.45 961 :1: 16 :t 110 0.125 — 0.250 80.4 :t 2.5 :t 8.6 16.04 :1: 0.75 :t 1.7 3.864 :t 0.036 :1: 0.42 965 :t 16 :t 110 0.250 — 0.375 81.9 :1: 2.6 :h 8.7 17.40 :1: 0.88 :t 1.9 3.549 :1: 0.033 :1: 0.38 905 :1: 15 :1: 99 0.375 - 0.500 77.4 :1: 2.6 :1: 8.2 13.62 :t 0.79 :1: 1.5 3.268 :1: 0.035 :1: 0.35 769 :t 15 :1: 84 0.500 — 0.625 67.7 :t 2.7 :1: 7.2 14.4 i: 1.1 :1: 1.5 2.769 :1: 0.034 :1: 0.30 650 :1: 14 i 71 0.625 - 0.750 57.5 :1: 2.7 d: 6.1 10.52 :1: 0.92 :1: 1.1 2.238 :t 0.032 :1: 0.24 486 i 13 :t 53 5.00 — 5.50 5.50 — 6.50 6.50 - 8.00 pb/(GeV/c)2 pb/(GeV/c)2 pb/(GeV/c)2 Table A.6 Invariant differential cross section per nucleon for 7r° production by 800 GeV/c proton beam on a Be target as a function of 121. and rapidity. p, (GeV/c) Rupidity 1.00 - 1.50 1.50 — 2.00 2.00 - 2.50 2.50 - 3.00 115/(own)2 pb/(GeV/c)’ 115/(own)2 nb/(GeV/c)’ —1.00 — -0.875 479 1 87 1 53 4.875 _ 4.750 464 1 88 37 112 6.6 11.9 1 0.7 850 1 180 1 90 -0.750 - --0.625 621 :1; 56 :1: 69 _0.625__0.500 469183 601 11 5.91 1.8107 690150176 —0.500 — —0.375 615 1 51 1 68 _0.375_-0.250 419176 581 12 1.21 1.8101 712152179 —0.250 — —0.125 765 :1: 45 :1: 85 _0.125_0.000 457:1:74 56:1:11 4.2116105 737146181 0.000 - 0.125 773 :1: 48 :1: 85 0.125 _ 0.250 423 :1: 66 46.2 1 9.4 5.5 d: 1.6 :1: 0.6 730 :1: 100 :1: 80 0.250 - 0.375 757 :1: 49 :1: 84 0.375 _ 0.500 495 1 71 32.0 1 8.6 4.5 1 1.5 1 0.5 597 1 43 1 66 3.00 - 3.50 3.50 - 4.00 4.00 - 4.50 4.50 — 5.00 nb/(GeV/c)2 115/(own)2 nb/(GeV/c)’ pb/(GeV/c)’ —1.oo — -—0.875 101.1 1 8.1 1 11 20.1 1 2.0 1 2.2 4.03 1 0.28 1 0.45 1046 1 36 1 120 -0.875 - —0.750 125.4 :t 7.7 :1: 14 22.5 :t 2.2 :1: 2.5 4.75 :1: 0.37 :1: 0.53 1190 :t 37 :1: 130 -0.750 - -0.625 —-0.625 — —-0.500 103.2 :1: 6.2 :t 11 119.3 :1: 5.2 :1: 13 25.9 :1: 2.5 :t 2.9 25.4 :t 1.9 :1: 2.8 5.63 :1: 0.31 :1: 0.62 7.68 :1: 0.45 :l: 0.85 1525 i- 38 :1: 170 1801 :h 43 :t 200 —0.500 — --0.375 —0.375 - —0.250 144.1 :1: 6.5 i 16 145.6 :t 5.8 :1: 16 30.2 :t 2.1 :t 3.3 32.6 :t 2.1 :t 3.6 7.47 :1: 0.40 :1: 0.83 8.06 :1: 0.36 :1: 0.89 2046 :t 37 :1: 230 2120 :1: 35 :1: 240 —0.250 — —0.125 150.5 i 5.8 d: 17 28.3 :t 2.2 :1: 3.1 7.97 :t 0.32 :1: 0.88 2187 :1: 36 i: 240 2211 :t 38 :1: 250 2145 :k 87 :t 240 2040 :1: 100 :t 230 1896 :l: 87 :1: 210 1842 :1: 85 :t 210 -0.125 - 0.000 145.6 :1: 5.9 :1: 16 30.1 i 2.3 :1: 3.3 7.84 :1: 0.38 :1: 0.87 0.000 - 0.125 143.3 :h 4.8 :1: 16 32.4 :1: 1.9 :1: 3.6 8.01 :t 0.29 :1: 0.89 0.125 — 0.250 144.4 :1: 4.6 :1: 16 29.8 :1: 1.7 :1: 3.3 7.68 :1: 0.29 :1: 0.85 0.250 - 0.375 130.6 :1: 4.9 i 14 29.7 :t 1.8 d: 3.3 6.95 d: 0.22 :1: 0.77 0.375 - 0.500 128.6 :1: 5.6 :1: 14 29.3 :1: 2.1 :t 3.2 6.81 i: 0.24 :1: 0.75 5.00 — 5.50 5.50 - 6.50 6.50 — 8.00 IJb/(GeV/C)2 pb/(GeV/C)2 Pb/(GeV/C)2 —1.00 - —0.875 270 :t 25 :t 30 54.7 i 3.7 :h 6.3 —0.875 - -0.750 329 :1: 16 :1: 37 68.6 :1: 4.3 :t 7.9 3'58 i 0'42 i: 0.42 -0.750 - -0.625 415 i 16 :t 47 83.5 :t 4.2 :t 9.6 -0.625 - -—0.500 509 :h 19 :1: 57 110.3 :I: 5.7 :l: 13 7'58 i 0'64 i- 0‘90 —0.500 - —0.375 —-0.375 - —0.250 600:1: 18 i68 642 :1: 17 21:72 121.5 :1: 4.9 :1: 14 142.7 :1: 5.3 :1: 16 11.25 :1: 0.70 :1: 1.3 —0.250 - —0.125 651 1 18 1 73 143,5 1 5,1 1 16 —O.l25 - 0,000 646 i 19 :1: 73 136.7 :1: 5.3 :1: 16 12.81 :1: 0.75 $1.5 0.000 — 0.125 650 1 28 1 73 139.1 1 6‘2 1 16 0.125 - 0.250 652 1 38 1 74 134.0 1 7.4 1 15 “'08 i 0‘78 i 1-7 0.250 — 0.375 588 1 29 1 66 134.9 1 6.5 1 16 0.375 - 0.500 531 1 27 1 60 108.0 1 6.0 1 12 10"” i 0'74 i 1'2 276 Table A.7 Invariant differential cross section per nucleon for no production by 515 GeV/c 7r" beam on a Be target as a function of pr and rapidity. —0.375 — -0.250 69.4 :t 3.4 :1: 7.8 15.11 :1: 0.57 i: 1.7 3.706 :t 0.041 :1: 0.41 er (GeV/C) Rapidity 1.00 — 1.50 1.50 - 2.00 2.00 - 2.50 2.50 - 3.00 ub/(GeV/c)’ ub/(GeV/c)’ ub/(GeV/c)’ nb/(GeV/c)’ —0.750 — —0.625 377 1 26 1 43 4.625 _ 4.500 123 1 29 11.2 1 3.8 1.87 1 0.86 1 0.22 404 1 24 1 46 —0.500 - —0.375 370 d: 24 :t 42 4.375 _ 4.250 189 1 30 25.2 1 3.8 2.577 1 0.083 1 0.30 339 116 1 39 -0.250 — —0.125 380 :t 16 :1: 44 41125 _ 0.000 178 1 28 21.7 1 3.3 2.555 1 0.055 1 0.30 408 1 15 1 47 0.000 - 0.125 414 1 14 1 47 (“25 _ 0.250 195 1 29 17.4 1 2.9 2.554 1 0.045 1 0.30 396 112 1 45 0.250 - 0.375 398 1 12 1 46 0375 _ 0.500 155 1 24 19.7 1 3.5 2.430 1 0.049 1 0.28 358 1 12 1 41 0.500 — 0.625 372 1 13 1 43 0.625 _ 0.750 179 :h 26 16.3 :1: 2.5 2.267 :t 0.052 :1: 0.27 338 :1: 12 :t 39 3.00 - 3.50 3.50 — 4.00 4.00 - 4.50 4.50 — 5.00 nb/(GeV/c)2 nb/(GeV/c)2 nb/(GeV/c)2 pb/(GeV/c)2 —0.750 - -0.625 61.4 1 5.7 1 6.9 10.48 1 0.98 1 1.2 2.221 1 0.072 1 0.24 620 1 22 1 68 -0.625 — —0.500 61.6 1 5.8 1 6.9 11.71 1 0.96 1 1.3 2.795 1 0.057 1 0.31 778 1 19 1 85 —0.500 - —o.375 74.1 1 4.1 1 8.3 14.42 1 0.47 1 1.6 3.343 1 0.045 1 0.37 872 1 16 1 96 965 11:17 :1: 110 —0.250 - —0.l25 —0.125 - 0.000 78.0 :1: 2.9 :1: 8.8 84.1 :1: 2.4 :1: 9.4 17.49 :1: 0.66 :t 1.9 18.75 :1: 0.53 :1: 2.1 4.109 :1: 0.038 :1: 0.45 4.609 :t 0.040 :1: 0.51 1129 :1: 18 :1: 120 1242 :t 19 :1: 140 0.000 — 0.125 0.125 — 0.250 87.5 :1: 1.7 :1: 9.8 85.5 :1: 1.7 :1: 9.6 18.33 i: 0.54 :1: 2.0 18.77 :t 0.61 :t 2.1 4.582 :t 0.038 :1: 0.50 4.574 :1: 0.038 :t 0.50 1258 :1: 18 :1: 140 1231 :1: 17 i 140 0.250 — 0.375 0.375 - 0.500 85.4 :1: 1.7 :t 9.6 82.6 :1: 1.9 :1: 9.3 18.84 i 0.61 :1: 2.1 17.71 :k 0.63 :1: 2.0 4.723 :t 0.040 :1: 0.52 4.578 :1: 0.041 :1: 0.50 1276 i: 18 :1: 140 1255 d: 19 :t 140 0.500 - 0.625 0.625 - 0.750 78.9 :1: 1.8 i- 8.9 70.9 :1: 1.8 :f: 8.0 18.72 :t 0.58 :h 2.1 15.11 :1: 0.51 :1: 1.7 4.307 :t 0.041 :1: 0.47 3.861 :t 0.040 :1: 0.42 1171 :t 19 :t 130 1016 :1: 18 :t 110 5.00 - 5.50 pb/(GeV/c)2 5.50 — 6.50 lib/(GeV/C)2 6.50 - 8.00 pb/(GeV/c)2 -0.750 - --0.625 —0.625 - --0.500 177.2 :1: 8.5 :1: 20 213.0 i 7.5 :1: 24 31.8 d: 2.121: 3.6 44.1 :t 2.2 :h 4.9 2.08 :1: 0.26 :t 0.24 -0.500 - —0.375 -0.375 - -0.250 253.5 :h 8.2 :t 28 306.6 :1: 9.0 :t 34 52.1 :1: 2.3 i 5.8 65.3 :t 2.6 :t 7.3 4.47 :l: 0.35 i 0.52 -0.250 - -0.125 -0.125 - 0.000 326.9 :t 8.8 :1: 36 356.2 :1: 9.0 :1: 39 73.4 :1: 2.8 :1: 8.2 75.8 i 2.8 :1: 8.5 6.84 :t 0.43 :1: 0.79 0.000 - 0.125 0.125 - 0.250 381.2 d: 9.0 :1: 42 383.9 :1: 8.9 :1: 42 88.5 :1: 2.9 :1: 9.9 82.5 :1: 2.8 :h 9.2 8.44 :t 0.46 :1: 0.98 0.250 — 0.375 0.375 - 0.500 387.9 :1: 9.2 :1: 43 375.3 :1: 9.6 :t 41 83.2 :t 2.8 :t 9.3 72.0 i 2.9 :1: 8.1 7.42 :1: 0.46 :1: 0.86 0.500 - 0.625 0.625 — 0.750 343.7 :1: 9.4 :t 38 299.5 :1: 8.9 :1: 33 76.1 :1: 2.9 i 8.5 57.0 :t 2.6 :l: 6.4 6.49 :1: 0.49 :t 0.75 277 Table A.8 Invariant differential cross section for 7r0 production by 530 GeV/c proton beam on a Cu target as a function of pr and rapidity. p1. (GeV/C) Rapidity 1.00 — 2.50 2.50 — 3.00 3.00 - 3.50 ub/(GeV/c)’ nb/(GeV/c)’ nb/(GeV/c)’ -0.750 - -0.625 710 1 240 1 80 83 1 12 1 9.0 —0.625 - -0.500 90 i 31 i 9'0 990 1 240 1 110 109 1 13 1 12 —0.500 — —0.375 545 :1: 54 :1: 58 98.3 $ 8.5 :1: 11 112 $ 29 :1: 12 —0.375 - —0.250 614 $ 38 $65 99.6 $ 7.6 :1: 11 —0.250 - -—0. 125 91 $ 24 $ 10.0 604 $ 26 $ 64 111.1 $ 8.0 $ 12 —0.125 — 0.000 737 :1: 36 $ 78 120.5 $ 7.8 :1: 13 0.000 - 0.125 652 1 24 1 69 107.0 1 7.1 1 11 0.125 — 0.250 90 i 22 it 9'0 621 1 20 1 66 97.8 1 6.4 1 10 0.250 — 0.375 551 1 20 1 59 110.3 1 6.7 1 12 0.375 — 0.500 71 i 23 i 7'0 511 1 18 1 54 92.1 1 6.8 1 9.8 0.500 — 0.625 491 1 21 1 52 77.9 1 6.8 1 8.3 0.625 - 0.750 78 i 19 i 8'0 404 1 19 1 43 84.0 1 7.5 1 8.9 3.50 - 4.00 4.00 — 4.50 4.50 — 5.00 nb/(GeV/c)’ nb/(GeV/c)’ pb/(GeV/c)’ —0.750 - —0.625 -—0.625 - —0.500 15.6 $ 2.4 $ 1.7 19.1 $ 2.2 $ 2.0 3.44 $ 0.17 $ 0.37 4.06 $ 0.15 $ 0.44 780 :1: 45 $ 85 961 $ 54 $110 —0.500 - -0.375 —0.375 - —0.250 18.3 $ 2.4 $ 2.0 24.8 $ 2.8 $ 2.7 4.32 :1: 0.13 $ 0.47 5.07 $ 0.13 $ 0.55 1070 $ 44 :1: 120 1227 $ 47 $ 130 -0.250 - —0.125 22.6 :1: 2.6 :1: 2.4 5.39 $ 0.11 :1: 0.58 1258 $ 43 $ 140 —0.125 — 0.000 23.4 1 2.9 1 2.5 5.70 1 0.11 1 0.62 1325 1 45 1 150 0.000 - 0.125 20.8 1 2.4 1 2.2 5.475 1 0.099 1 0.59 1191 :1 39 1 130 0.125 - 0.250 22.9 1 2.2 1 2.4 5.037 1 0.092 1 0.54 1258 1 41 1 140 0.250 — 0.375 19.5 1 2.0 1 2.1 4.507 1 0.083 1 0.49 1108 1 38 1 120 0.375 - 0.500 20.3 1 2.1 1 2.2 4.094 1 0.090 1 0.44 1049 1 38 1 120 0.500 — 0.625 13.6 1 2.3 1 1.5 3.614 1 0.088 1 0.39 795 1 35 1 87 0.625 — 0.750 11.7 1 2.2 1 1.2 2.748 1 0.080 1 0.30 665 1 33 1 73 5.00 - 5.50 5.50 - 6.50 6.50 — 8.00 pb/(GeV/C)2 pb/(GeV/C)2 pb/(GeV/C)2 -0.750 - -—0.625 237 1 21 1 26 25.9 1 4.7 1 2.9 -—0.625 — —0.500 200 1 18 1 22 34.2 1 5.3 1 3.9 1'62 i 0'65 i 0'19 —0.500 - -0.375 257 1 20 1 29 55.0 1 5.9 1 6.2 —0.375 — —0.250 297 1 20 1 33 43.7 1 4.7 1 5.0 3‘17 i 0'65 i 0'38 -0.250 — -o.125 343 1 20 1 38 53.8 1 5.3 1 6.1 —0.125 — 0.000 328 $ 21 $ 36 68.7 :1: 6.1 $ 7.8 4.23 :l: 0.76 $ 0.50 0.000 - 0.125 0.125 — 0.250 361$ 20$40 337 $ 20$ 37 63.8 $ 5.6 $ 7.2 57.3 $ 5.2 $ 6.5 3.53 $ 0.68 $ 0.42 0.250 - 0.375 0.375 - 0.500 301 $ 19$ 33 234 $ 17$26 56.2 $ 5.3 $ 6.4 38.6 :1: 4.6 $ 4.4 1.45 $ 0.53 $ 0.17 0.500 - 0.625 0.625 - 0.750 228 $ 17$25 164 $ 15 $ 18 28.5 $ 4.1 :1: 3.2 17.2 $ 3.4 $ 2.0 0.97 $ 0.40 $ 0.12 278 Table A.9 Invariant differential cross section for 770 production by 800 GeV/c proton beam on a Cu target as a function of pr and rapidity. 1a,. (GeV/c) RApidity 1.00 - 2.50 2.50 — 3.00 3.00 — 3.50 1.5/(own)2 nb/(GeV/c)’ nb/(GeV/c)’ —1.00 — —0.875 390 1 170 1 40 90 1 16 1 10.0 —0.875 — -0.750 103 i 49 i 11 860 1 290 1 100 158 1 17 1 17 —0.750 — —0.625 840 1 210 1 90 117 1 13 1 13 -—0.625 - —0.500 66 i 45 i 7'0 870 1 110 1 100 184 1 15 1 20 —0.500 - -0.375 600 1 110 1 70 159 1 13 1 17 —0.375 - -0250 100 i 39 i 11 673 1 78 1 74 187 1 13 1 21 —0.250 - —0.125 950 1 150 1 100 186 1 15 1 20 —0.125 — 0.000 146 i 37 $16 920 :1: 120 :1: 100 174 $15 $ 19 0.000 - 0.125 1030 :t 110 :1: 110 196 :1: 13 :t 22 0.125 - 0.250 93 i 32 i 10 1050 1 140 :1: 120 167 :1: 11 :l: 18 0.250 — 0.375 1520 i 420 :t 170 158 :1: 12 :t 17 0.375 — 0.500 206 i 31 i 23 940 :1: 120 :1: 100 153 :1: 13 :1: 17 3.50 - 4.00 4.00 - 4.50 4.50 — 5.00 115/(own)2 115/(own)2 pb/(GeV/c)2 -1.00 — —0.875 16.1 1 3.4 :1: 1.8 4.00 :1: 0.42 :t 0.44 1390 :1: 110 :h 160 -—0.875 — -—0.750 26.6 $ 4.6 $ 2.9 5.61 $ 0.50 $ 0.62 1530 $ 110 $ 170 -0.750 - —0.625 —0.625 - —0.500 40.4 $ 5.8 :1: 4.5 41.0 $ 5.9 $ 4.5 9.3 $ 1.8 $ 1.0 8.67 $ 0.64 $ 0.96 1855 $ 88 $ 210 2350 $ 110 $ 260 —0.500 - —0.375 -0.375 — —0.250 39.0 $ 5.6 $ 4.3 46.5 :1: 5.8 $ 5.1 11.0 $ 1.1 $ 1.2 10.6 $1.2 $1.2 2447 $ 88 $ 270 2721 :1: 91 :1: 300 -0.250 - —0.125 35.2 $ 5.2 $ 3.9 10.1 :1: 1.2 $ 1.1 2753 $ 92 $ 310 —0.125 — 0.000 43.0 $ 5.7 $ 4.7 10.9 $ 1.4 $ 1.2 2796 $ 96 $ 310 0.000 - 0.125 45.4 $ 5.0 $ 5.0 9.43 :1: 0.56 $ 1.1 2670 $ 230 $ 300 0.125 — 0.250 42.2 $ 4.4 $ 4.6 8.19 $ 0.59 :1: 0.91 2630 $ 280 :1: 290 0.250 - 0.375 , 36.8 :1: 4.6 $ 4.0 9.14 :1: 0.59 $ 1.0 2150 $ 220 $ 240 0.375 — 0.500 36.9 :1: 5.4 $ 4.1 8.78 $ 0.59 $ 0.97 2130 :1: 220 $ 240 5.00 — 5.50 5.50 - 6.50 6.50 - 8.00 Pb/(GeV/C)2 pb/(GeV/c)’ pb/(GeV/C)2 —1.00 - -0.875 310 $ 34 $ 35 67.7 $ 9.9 :1: 7.8 —0.875 - —0.750 322 $ 29 :1: 36 99 $ 12 $ 11 3.38 i 0‘79 21: 040 —0.750 - —0.625 547 :1: 43 $ 62 107 $ 11 $ 12 -0.625 - -—0.500 575 $ 47 $ 65 120 $ 15 $ 14 8'3 32 1'7 i 1‘0 —0.500 - —0.375 768 $ 47 $ 87 144 $ 13 $ 16 —0.375 - —0.250 792 $ 46 $ 89 200 $ 14 $ 23 13.8 :t 1‘8 i 1.6 —-0.250 - —0.l25 844 $ 47 $ 95 175 $ 14 $ 20 20.0 $ 2.0 $ 2.4 —0.125 - 0.000 883 $ 49 $ 100 204 $ 13 $ 23 0.000 — 0.125 931 $ 75 $110 191 $ 17 $ 22 0.125 - 0.250 756 $ 87 :1: 85 187 $ 20 :1: 21 16.8 i 1'9 i 2'0 0.250 — 0.375 878 :1: 80 $ 99 167 $ 18 $ 19 0.375 — 0.500 622 :1: 73 $ 70 145 $ 16 $ 17 13'7 i 1'9 i 1'6 279 Table A.10 Invariant differential cross section for 7r0 production by 515 GeV/c 7r“ beam on a Cu target as a function of pr and rapidity. pr (GeV/C) Rapidity 2.50 - 3.00 3.00 ' 3.50 3.50 — 4.00 4.00 - 4.50 nb/(GeV/c)2 nb/(GeV/c)2 rib/(GeV/c)2 nb/(GeV/c)2 -0.750 - —0.625 2.77 :t 0.21 i 0.30 -0.625 _ _0.500 497 i 55 :1: 57 82 i 11 $ 9.0 10.7 :1: 1.6 :1: 1.2 351$ 0.16 :1: 0.39 -0.500 - —0.375 4.02 i 0.13 :1: 0.44 _0.375 _ _0.250 426 :1: 39 i 49 77.0 :t 7.0 :1: 8.6 20.2 :1: 1.4 i 2.2 4.66 i 0.12 :1: 0.51 -0.250 - -0.125 5.07 :1: 0.11 :1: 0.56 _0.125 _ 0.000 492 :1: 28 :1: 56 105.7 $ 5.6 :t 12 22.9 $1.2 i 2.5 5.93 i 0.12 :1: 0.65 0.000 - 0.125 5.56 :1: 0.11 i 0.61 0.125 _ 0.250 502 i 26 i 58 99.9 :1: 3.5 i 11 22.1 :1: 1.2 :1: 2.5 5.74 :t 0.11 :1: 0.63 0.250 - 0.375 5.98 It 0.11 i: 0.66 0.375 _ 0.500 413 i 21 :t 47 100.0 :1: 3.7 21:11 21.0 21:1.2 :1: 2.3 5.73 i 0.12 :1: 0.63 0.500 - 0.625 5.47 :1: 0.12 i 0.60 0.625 _ 0.750 390 i 23 $ 45 91.6 :1: 3.9 :t 10 21.6 :1: 1.2 :1: 2.4 4.72 :1: 0.12 i 0.52 4.50 - 5.00 5.00 - 5.50 5.50 - 6.50 6.50 - 8.00 Pb/(Gev/012 pb/(GeV/c)’ pb/(GeV/c)2 pb/(GeV/c)2 —0.750 - —0.625 634 i 48 :t 70 234 :1: 25 :1: 26 43.7 i: 6.1 :1: 4.9 -—0.625 - —0.500 899 :1: 48 :t 99 262 :1: 22 :1: 29 50.7 d: 7.7 i 5.7 2.05 i 0.69 i 0.24 -—0.500 - -0.375 1078 :1: 48 :1: 120 332 i 26 :1: 37 68.4 :1: 7.3 :1: 7.7 -0.375 - -0.250 1218 :1: 48 i 130 350 :1: 23 :1: 39 72.5 i 7.0 :1: 8.1 4.91 i 0.97 i 057 --0.250 - -0.125 1426 :1: 51 :1: 160 412 :t 25 i 45 84.0 :t 7.8 :1: 9.4 -0.125 - 0.000 1634 :1: 55 :t 180 380 :1: 24 :1: 42 86.4 $ 7.8 :t 9.7 7.3 i 1.1 i 0.8 0.000 - 0.125 1655 :1: 52 :1: 180 488 :1: 27 :1: 54 99.2 :1: 7.7 :1: 11 0.125 - 0.250 1518 $ 50 :1: 170 439 :1: 25 :1: 48 120.3 :1: 8.5 :1: 14 8.2 i 1.2 i 1.0 0.250 - 0.375 1685 :1: 55 :1: 190 521 :1: 27 :1: 57 98.6 :1: 8.1 :1: 11 0.375 - 0.500 1593 i 55 :1: 180 465 :1: 28 :1: 51 85.7 :1: 7.7 i 9.6 7.7 i 13 i 0.9 0.500 - 0.625 1523 :1: 57 i 170 400 :t 27 :1: 44 79.5 :t 7.8 d: 8.9 0.625 - 0.750 1265 :1: 51 :1: 140 315 :t 23 :1: 35 73.0 :h 7.8 :1: 8.2 5.9 i 1.3 i 0.7 280 r1 , ll 1 4 -2- -1 .1 2.4. . 1 1- 54 l x .. .1- 3.. 61119.11 .- .7 ._ -- ._—.»——-—-: ~-~4>~.«-—-‘- , . . «- : m 091 i - 1“" . 3’ . '_' : I‘n.‘ .1 ' '::§111'l‘l9mb ‘Ll.’ '1 ‘ -:,11.u.1fl-') B a " ”I , 1' 1". . .169 “L, ' -1 - -- -_‘...._...... “H" ' .‘:~.' 1'1:H*“ ' . 1-._-.. I“, . 1 9'1“ 2" ‘l ; " I i--‘—I.— 4.. VI I" | ”"83“: ' J.” ' '1 1“ ' 1 '15 1. I t“ . .‘1' _ .. L ‘._~_ ‘ r... .19 ! T11 ttéwt.‘ ' '1 i do 1485*? ~ .-... ._... - - ... ; 71:14 on." 1 ; I 1;)1r ‘ht‘hfl .1 My ' 1 1' . 1111541 ._ .. .1"; a t 0“ . ‘1 * ' .. 7 7711-9161 Affi- “1 1 “* ..' . $771.. 171611181- .0.) ‘ mu’ .1—9‘1 971105;" 001 2 58*" 30' '5 - 90151151". ”75:11:“ i cut“ _,_ ‘TR ‘ If L’V‘Jfi'm '\1 I “1.5/r“ 0):" {i ' 3&‘.r11 -1. ~ Table A.11 Invariant differential cross section for 770 production by 530 GeV/c proton beam on a p target as a function of pr and rapidity. PT (GeV/C) Rapidity 1.00 — 2.50 2.50 — 3.00 3.00 — 3.50 115/(own)2 nb/(GeV/c)’ nb/(GeV/e)2 —o.750 - —0.625 450 1 210 1 50 72 1 11 1 8.0 -0.625 — -o.500 186 i 41 i 20 1000 1 340 1 110 69 1 16 1 7.0 —0.500 - —0.375 390 $ 43 $ 41 66 $ 11 $ 7.0 —o.375 — —0.250 124 i 35 i 13 466 1 41 1 50 69.2 1 7.6 1 7.4 —o.250 — -0.125 484 1 28 1 52 81.0 1 7.3 1 8.6 —o.125 — 0.000 79 i 33 i 8'0 566 1 34 1 60 87.1 1 7.7 1 9.3 0.000 - 0.125 484 1 21 1 51 83.0 1 6.8 1 8.8 0.125 — 0.250 121 i 28 i 13 449 1 20 1 48 71.9 1 5.7 1 7.6 0.250 - 0.375 420 1 19 1 45 67.6 1 6.1 1 7.2 0.375 - 0.500 111 i 28 i 12 390 $ 18 $ 42 67.6 $ 6.3 $ 7.2 0.500 - 0.625 366 1 19 1 39 60.6 1 6.5 1 6.4 0.625 — 0.750 138 i 29 i 15 319 1 19 1 34 52.1 1 6.2 1 5.5 3.50 — 4.00 4.00 — 4.50 4.50 — 5.00 nb/(GeV/c)2 nb/(GeV/c)’ pb/(GeV/c)2 -0.750 - —0.625 9.2 1 1.4 1 1.0 2.14 1 0.15 1 0.23 652 1 66 1 71 -0.625 - —0.500 10.6 1 1.5 1 1.1 2.60 1 0.15 1 0.28 544 1 49 1 59 —0.500 — -0.375 13.1 $ 2.9 d: 1.4 2.91 :1: 0.12 :1: 0.31 686 $ 39 $ 75 -—0.375 — —0.250 15.8 1 2.4 1 1.7 3.54 1 0.13 1 0.38 886 1 48 1 97 -0.250 - —0.125 16.4 $ 2.6 $ 1.8 3.518 $ 0.096 :1: 0.38 858 $ 40 $ 94 —0.125 — 0.000 15.5 1 2.6 1 1.7 3.78 1 0.10 1 0.41 974 1 42 1 110 0.000 — 0.125 14.5 1 2.4 1 1.6 3.780 1 0.097 1 0.41 857 1 36 1 94 0.125 — 0.250 14.3 1 1.8 1 1.5 3.512 1 0.088 1 0.38 896 1 39 1 98 0.250 — 0.375 11.9 1 1.7 1 1.3 3.153 1 0.077 1 0.34 767 1 35 1 84 0.375 - 0.500 15.0 1 2.1 1 1.6 2.958 1 0.083 1 0.32 723 1 35 1 79 0.500 — 0.625 11.8 1 2.3 1 1.3 2.501 1 0.080 1 0.27 659 1 36 1 72 0.625 — 0.750 8.2 1 1.7 1 0.9 2.037 1 0.073 1 0.22 476 1 31 1 52 5.00 - 5.50 5.50 - 6.50 6.50 - 8.00 1'1b/(GeV/C)2 Pb/(GeV/C)2 pb/(GeV/C)2 —0.750 - —0.625 110 1 13 1 12 29.2 1 4.9 1 3.3 -0.625 - —0.500 175 1 23 1 19 22.2 1 4.4 1 2.5 2'12 i 0'60 i 0‘25 —0.500 - —0.375 —0.375 - -0.250 219 $20$24 204 $ 18$ 23 43.0 $ 5.7 $ 4.9 42.4 $ 5.2 $ 4.8 2.77 $ 0.70 $ 0.33 —0.250 - —0.125 245 1 19 1 27 43,3 1 5,5 1 5_0 —0.125 — 0.000 252 1 20 1 28 66.4 1 6.8 1 7.5 3'16 i 0‘73 i 0'38 0.000 - 0.125 282 1 20 1 31 55.0 1 5.8 1 6.2 0.125 - 0.250 265 1 19 1 29 55.3 1 5.9 1 6.3 3'84 1' 0'74 i 0'46 0.250 - 0.375 249 1 19 1 28 40,3 1 5,1 1 4.6 0.375 - 0.500 211 1 18 1 23 33.0 1 4.6 1 3.7 1'79 3‘ 0'52 i 0"“ 0.500 — 0.625 189 $ 18 $ 21 26.8 :1; 4,4 $ 3;o 0,625 _ 0.750 124 it 15 i 14 23.1 :1: 4.3 :1: 2.6 0.96 :1: 0.43 :1: 0.11 281 Table A.12 Invariant differential cross section for 770 production by 800 GeV/c proton beam on a p target as a function of pr and rapidity. 9T (GeV/C) Rapidity 1.00 — 2.50 2.50 - 3.00 3.00 — 3.50 1.6/(own)2 nb/(GeV/c)2 nb/(GeV/c)2 —1.00 — —0.875 1060 1 630 1 120 87 1 17 1 10.0 —0.875 - —0.750 159 i 65 i 18 430 1 120 1 50 115 1 15 1 13 —0.750 — —0.625 444 1 66 1 49 106 1 15 1 12 —0.625 — —0.500 238 i 62 i 26 610 1 110 1 70 117 1 13 1 13 —0.500 — —0.375 600 1 120 1 70 153 1 15 1 17 —0.375 - —0.250 286 i 57 i 32 640 1 100 1 70 138 1 14 1 15 —0.250 — —0.125 800 1 180 1 90 123 1 15 1 14 —0.125 — 0.000 265 i 52 i 29 680 1120 1 80 124 1 13 114 0.000 — 0.125 707 1 100 1 78 134 1 11 1 15 0.125 — 0.250 199 i 44 i 22 760 1110 1 80 137 111 115 0.250 - 0.375 540 1 88 1 60 122 1 12 1 13 0.375 - 0.500 236 i 43 i 26 740 1 100 1 80 108 1 13 1 12 3.50 - 4.00 4.00 - 4.50 4.50 — 5.00 nb/(GeV/c)2 nb/(GeV/c)’ pb/(GeV/c)’ —1.00 — —0.875 20.2 1 7.8 1 2.2 3.20 1 0.26 1 0.36 1250 1 130 1 140 —0.875 — —0.750 19.8 1 4.3 1 2.2 4.92 1 0.69 1 0.55 1015 1 77 1110 —0.750 - —0.625 —0.625 — -0.500 38.8 1 7.2 1 4.3 19.0 1 3.8 1 2.1 9.0 1 2.3 1 1.0 7.8 1 1.6 1 0.9 1427 1 90 1 160 1590 1 98 1 180 -0.500 — -0.375 —0.375 - —O.250 28.2 1 5.8 1 3.1 39.2 1 6.3 1 4.3 6.75 1 0.65 1 0.75 7.27 1 0.65 1 0.81 1911 1 92 1 210 2013 1 86 1 230 -0.250 - —0.125 32.9 1 5.5 1 3.6 6.34 1 0.21 1 0.70 2075 1 87 1 230 -0.125 - 0.000 21.8 1 4.4 1 2.4 6.49 1 0.37 1 0.72 1984 1 86 1 220 0.000 — 0.125 25.1 1 4.8 1 2.8 8.7 1 1.1 1 1.0 1580 1 140 1 180 0.125 - 0.250 27.9 1 4.3 1 3.1 6.55 1 0.60 1 0.73 1810 1 230 1 200 0.250 — 0.375 23.8 1 3.8 1 2.6 7.49 1 0.60 1 0.83 1770 1 210 1 200 0.375 — 0.500 23.7 1 5.4 1 2.6 6.01 1 0.54 1 0.67 1920 1 220 1 210 5.00 — 5.50 5.50 - 6.50 6.50 - 8.00 pb/(GeV/c)2 pb/(GeV/c)2 pb/(GeV/c)2 —1.00 - —0.875 297 1 49 1 33 32.1 1 5.5 1 3.7 —0.875 - -0750 229 1 27 1 26 73 1 14 1 8.0 4'4 i 1'1 i 0'5 —0.750 - —0.625 350 1 36 1 39 63.8 1 8.8 1 7.3 -—0.625 — —0.500 448 1 38 1 51 105 1 12 1 12 9'3 i 1'7 i 1'1 —0.500 — —0.375 507 1 44 1 57 90 1 10 1 10 -0375 — —0.250 547 1 41 1 62 132 1 12 1 15 ”'8 i 2'0 i 1'7 —0.250 - —0.125 629 1 43 1 71 117 1 11 1 13 —0.125 - 0.000 585 1 41 1 66 148 1 14 1 17 ”'6 i 1'8 i 1‘7 0.000 — 0.125 643 1 72 1 73 159 1 18 1 18 0.125 — 0.250 600 1 93 1 68 118 115 1 13 13'4 i 2'2 i 1'6 0.250 - 0.375 487 1 65 1 55 103 1 13 1 12 0.375 — 0.500 530 1 67 1 60 138 1 18 1 16 10.2 i 1‘9 i 1'2 282 Table A.13 Invariant differential cross section for 7r° production by 515 GeV/c 77‘ beam on a p target as a function of pr and rapidity. p, (GeV/C) Rapidity 2.50 - 3.00 3.00 - 3.50 3.50 - 4.00 4.00 — 4.50 nb/(GeV/c)2 nb/(GeV/c)2 nb/(GeV/c)2 nb/(GeV/c)2 —0.750 - —0.625 1.97 1 0.29 1 0.22 —0.625 _ _0.500 293 1 711 34 51115 1 6.0 5.7 1 3.7 1 0.6 2.96 1 0.34 1 0.33 —0.500 - —0.375 3.61 1 0.35 1 0.40 _0.375__0.250 300162134 51.119.51 5.7 4.012.910.4 38510291042 —0.250 - —0.l25 3.61 1 0.29 1 0.40 _0.125 _ 0.000 297 1 32 1 34 77 112 1 9.0 16.2 1 3.0 11.8 3.911 0.21:}: 0.43 0.000 - 0.125 4.66 1 0.23 1 0.51 0.125 _ 0.250 3511 311 40 77 110 1 9.0 22.9 1 4.0 1 2.5 4.10 1 0.211 0.45 0.250 — 0.375 4.26 1 0.20 1 0.47 0.375 _ 0.500 373 1 26 1 43 68.11 9.3 1 7.7 20.9 1 3.3 1 2.3 4.02 1 0.22 1 0.44 0.500 -— 0.625 3.92 1 0.25 1 0.43 0.625-0.750 291128133 73111180 16.814.611.9 3.3410.2410.37 4.50 — 5.00 5.00 — 5.50 5.50 - 6.50 6.50 - 8.00 r>b/(G€V/C)2 r>b/(GeV/C)2 Pb/(GeV/C)2 Pb/(GeV/C)2 -0.750 — —0.625 493 1 91 1 54 119 1 30 1 13 46 1 15 1 5.0 —0.625 - —0.500 680 1 110 1 70 263 1 68 1 29 69 1 l8 1 8.0 3.2 i 19 i 0.4 —0.500 - -0.375 910 1 100 1 100 322 1 55 1 36 77 1 l7 1 9.0 —0.375 - -0.250 905 1 95 1 99 279 1 46 1 31 72 1 l7 1 8.0 2.2 i 1.3 It 03 -0.250 - —0.l25 1129 1 96 1 120 368 1 50 1 41 62 1 15 1 7.0 —0.125 - 0.000 1170 1 100 1 130 410 1 55 1 45 62 1 l3 1 7.0 7.5 i 2.5 i 0.9 0.000 - 0.125 1122 1 95 1 120 326 1 46 1 36 89 1 16 1 10.0 0.125 - 0.250 1450 1 110 1 160 342 1 49 1 38 70 1 14 1 8.0 9.3 i 2.7 i 1'1 0.250 - 0.375 1290 1 100 1 140 382 1 51 1 42 103 1 18 1 12 0.375 - 0.500 1107 1 100 1 120 362 1 51 1 40 59 1 15 1 7.0 7.6 i 2.4 i 09 0.500 - 0.625 1100 1 110 1 120 255 1 48 1 28 57 1 14 1 6.0 0.625 - 0.750 930 1 110 1 100 224 1 47 1 25 59 1 16 1 7.0 7'7 i 2.7 i 0.9 283 Appendix B Tabulated Direct Photon Cross Sections In this appendix, the measured direct photon cross sections are presented in tabular form. The entries in the tables are given in the form A 1 B 1 C, where A is the cross section measurement, and B and C represent the statistical and systematic uncertainties, respectively, on the measurement. 284 Table B.1 Invariant differential cross sections per nucleon for direct photon production by 530 and 800 GeV/c proton beams and 515 GeV/c 7r‘ beam on Be targets. Eda/6131D (pb/ (GeV/CV) p1. Range __ pBe at 530 GeV/c pBe at 800 GeV/c 7r Be at 515 GeV/c (GeV/c) —0.75 < y < 0.75 —1.0 < y < 0.5 —0.75 < y < 0.75 3.50 — 3.75 1860 1 170 1 370 3070 1 240 1 640 1810 1 100 1 340 3.75 - 4.00 1010 1 10 1 190 1540 1 10 1 290 935 1 10 1 160 4.00 - 4.25 484 1 10 1 82 927 1 10 1 163 511 1 1 1 81 4.25 — 4.50 254 1 1 1 40 492 1 10 1 80 292 1 1 1 43 4.50 — 4.75 135 1 1 1 20 273 1 1 1 42 175 1 1 1 24 4.75 - 5.00 76.4 1 2.1 1 10.8 165 1 1 1 24 109 1 1 1 14 5.00 — 5.25 41.7 1 1.4 1 5.6 100 1 1 1 14 71.2 1 1.8 1 9.0 5.25 — 5.50 24.6 1 1.0 1 3.2 64.7 1 2.3 1 8.5 42.9 1 1.3 1 5.3 5.50 — 5.75 15.3 1 0.7 1 1.9 38.3 1 1.6 1 4.9 30.8 1 1.0 1 3.7 5.75 - 6.00 8.67 1 0.55 1 1.08 27.1 1 1.3 1 3.4 20.1 1 0.8 1 2.4 6.00 — 6.50 4.00 1 0.25 1 0.49 13.0 1 0.5 1 1.6 10.4 1 0.4 1 1.2 6.50 - 7.00 1.80 1 0.15 1 0.22 5.43 1 0.30 1 0.64 4.75 1 0.23 1 0.55 7.00 — 7.50 0.72 1 0.09 1 0.09 2.54 1 0.19 1 0.29 2.12 1 0.15 1 0.25 7.50 — 8.00 0.33 1 0.05 1 0.04 1.12 1 0.12 1 0.13 1.15 1 0.10 1 0.13 8.00 — 9.00 0.08 1 0.02 1 0.010 0.42 1 0.05 1 0.05 0.45 1 0.04 1 0.05 9.00 — 10.00 0.008 1 0.005 1 0.001 0.09 1 0.02 1 0.01 0.08 1 0.02 1 0.01 10.00 — 12.00 0.001 1 0.001 1 0.0002 —— 0.006 1 0.003 1 0.0008 285 Table B.2 Invariant differential cross sections per nucleon for direct photon production by 530 and 800 GeV/c proton beams and 515 GeV/c 77‘ beam on Cu targets. Eda/63p (pb/(GeV/c)2) pr Range _ pCu at 530 GeV/c pCu at 800 GeV/c 7r Cu at 515 GeV/c (GeV/C) —0.75 < y < 0.75 -1.0 < y < 0.5 —0.75 < y < 0.75 3.50 — 3.75 3110 1 450 1 630 3010 1 590 1 630 1840 1 280 1 340 3.75 — 4.00 1210 1 150 1 220 1870 1 230 1 360 1070 1 23 1 180 4.00 — 4.25 583 1 23 1 10 989 1 23 1 176 585 1 23 1 93 4.25 — 4.50 282 1 23 1 45 523 1 23 1 87 361 1 23 1 54 4.50 — 4.75 152 1 2 1 23 299 1 23 1 47 178 1 2 1 25 4.75 — 5.00 86.5 1 5.2 1 12.3 182 1 23 1 27 112 1 2 1 15 5.00 — 5.25 50.2 1 3.5 1 6.8 111 1 2 1 16 81.0 1 4.8 1 10.4 5.25 — 5.50 27.7 1 2.5 1 3.6 59.9 1 5.5 1 8.1 40.4 1 3.4 1 5.0 5.50 — 5.75 15.6 1 1.8 1 2.0 37.0 1 4.1 1 4.8 32.3 1 2.7 1 3.9 5.75 — 6.00 11.2 11.3 11.4 21.4 1 2.9 1 2.7 23.1 1 2.11 2.8 6.00 — 6.50 4.99 1 0.62 1 0.62 15.4 1 1.3 1 1.9 9.74 1 0.95 1 1.15 6.50 — 7.00 1.93 1 0.34 1 0.24 5.43 1 0.72 1 0.66 5.30 1 0.60 1 0.62 7.00 — 8.00 0.28 1 0.09 1 0.04 2.01 1 0.27 1 0.24 1.84 1 0.23 1 0.22 8.00 — 10.00 0.09 1 0.03 1 0.01 0.14 1 0.06 1 0.02 0.20 1 0.05 1 0.02 286 Table B.3 Invariant differential cross sections for direct photon production by 530 and 800 GeV/c proton beams and 515 GeV/c 7r- beam on proton targets. Eda/(1319 (pb/(GeV/C)2) pr Range _ pp at 530 GeV/c pp at 800 GeV/c 77 p at 515 GeV/c (GeV/c) —0.75 < y < 0.75 —1.0 < y < 0.5 —0.75 < y < 0.75 3.50 — 4.00 1200 1 200 1 240 2020 1 320 1 410 1750 1 420 1 320 4.00 — 4.50 388 1 42 1 66 642 1 42 1 112 500 1 42 1 79 4.50 — 5.00 111 1 4 1 17 241 1 42 1 37 168 1 42 1 24 5.00 - 5.50 34.6 1 2.2 1 4.8 87.5 1 4.7 1 12.3 65.6 1 6.0 1 8.6 5.50 - 6.00 11.8 1 1.2 1 1.5 37.2 1 2.6 1 4.9 25.8 1 3.5 1 3.2 6.00 — 7.00 3.53 1 0.38 1 0.46 10.4 1 0.8 1 1.3 9.03 1 1.26 1 1.11 7.00 - 8.00 0.43 1 0.12 1 0.06 1.83 1 0.30 1 0.22 2.83 1 0.62 1 0.35 8.00 - 10.00 0.010 1 0.02 1 0.001 0.36 1 0.07 1 0.04 0.31 1 0.14 1 0.04 10.00 - 12.00 — 0.02 1 0.01 1 0.002 — 287 Table B.4 Invariant differential cross section per nucleon for the inclusive reaction pBe —> 7X at 530 GeV/c as a function of rapidity for several pr bins. Table 3.5 Invariant differential cross section per nucleon for the inclusive reaction pBe —1 7X at 800 GeV/c as a function of rapidity for several pr bins Pr (GeV/c) Rapidicy 3.50 - 4.00 4.00 - 4.50 4.50 — 5.00 5.00 — 5.50 pb/(GeV/c)2 pb/(GeV/c)2 pb/(GeV/c)2 pb/(GeV/c)2 -0.75 — —0.50 1200 1 230 1 220 352 1 14 1 59 91.1 1 4.4 1 13 23.3 1 1.9 1 3.1 —o.5o - —0.25 1530 1 220 1 280 396 1 12 1 67 109.4 1 4.6 1 16 29.2 1 2.1 1 3.9 —0.25 — 0.00 1450 1 220 1 270 380 1 11 1 64 109.5 1 4.8 1 16 37.7 1 2.4 1 5.0 0.00 — 0.25 1570 1 200 1 290 386 1 10 1 65 111.3 1 4.4 1 16 38.6 1 2.3 1 5.1 0.25 - 0.50 1630 1 160 1 300 381.9 1 9.5 1 64 115.6 1 4.3 1 17 38.1 1 2.2 1 5.1 0.50 — 0.75 1170 1 270 1 210 302 1 53 1 51 90.4 1 4.1 1 13 29.1 1 2.0 1 3.9 5.50 - 6.50 6.50 - 8.00 8.00 — 10.00 pb/(GeV/c)’ pb/(GeV/c)’ pb/(GeV/c)2 —0.75 - —0.50 5.35 1 0.50 1 0.67 0.63 1 0.11 1 0.08 0.020 1 0.016 1 0.003 -0.50 — —0.25 7.65 1 0.62 1 0.95 1.00 1 0.14 1 0.12 0.034 1 0.019 1 0.005 —0.25 — 0.00 8.54 1 0.70 1 1.1 1.24 1 0.17 1 0.15 0.039 1 0.021 1 0.005 0.00 — 0.25 9.26 1 0.67 1 1.2 0.88 1 0.14 1 0.11 0.056 1 0.025 1 0.007 0.25 — 0.50 8.47 1 0.65 1 1.1 1.10 1 0.16 1 0.14 0.042 1 0.021 1 0.006 0.50 — 0.75 7.67 1 0.62 1 0.96 0.64 1 0.13 1 0.08 0.039 1 0.023 1 0.005 3.50 — 4.00 pb/(GeV/c)2 pT (GeV/C) 4.00 — 4.50 pb/(GeV/c)2 4.50 - 5.00 Pb/(GeV/C)2 5.00 - 5.50 pb/(GeV/c)’ 1260 1 320 1 240 2050 1 320 1 390 526143192 511144189 131.7 1 7.5 1 20 160.5 1 8.2 1 24 44.9 1 3.8 1 6.1 65.5 1 4.1 1 8.9 2070 1 320 1 390 3770 1 420 1 710 718 1 44 1 130 807 1 39 1 140 223.4 1 9.0 1 34 239.3 1 8.6 1 36 79.4 1 4.6 1 11 97.0 1 4.6 1 13 2740 1 250 1 520 1940 1 250 1 370 916 1 38 1 160 779 1 35 1 140 302112 146 255 112 1 39 102.2 1 5.5 1 14 105.2 1 5.6 1 l4 5.50 - 6.50 pb/(GeV/C)2 6.50 - 8.00 pb/(GeV/C)2 8.00 — 10.00 pb/(GeV/c)2 10.51 1 0.94 1 1.3 18.7 11.3 1 2.3 1.36 1 0.19 1 0.16 1.96 1 0.24 1 0.23 0.170 1 0.045 1 0.020 0.171 1 0.046 1 0.020 23.7 1 1.5 1 2.9 27.6 1 1.4 1 3.4 3.44 1 0.33 1 0.40 3.81 1 0.33 1 0.45 0.328 1 0.070 1 0.038 0.151 1 0.054 1 0.017 Rapidity —1.0 -- -—0.75 —0.75 - -O.50 —0.50 - -—0.25 -0.25 - 0.00 0.00 — 0.25 0.25 - 0.50 -1.0 — —0.75 —0.75 - —0.50 —-0.50 — —0.25 -0.25 - 0.00 0.00 - 0.25 0.25 - 0.50 31.11 1.6 1 3.9 25.6 1 1.6 1 3.2 4.25 1 0.37 1 0.50 3.34 1 0.37 1 0.39 0.286 1 0.076 1 0.033 0.41 1 0.10 1 0.05 288 Table 3.6 Invariant differential cross section per nucleon for the inclusive reaction 7r‘Be -—+ 7X at 515 GeV/c as a function of rapidity for several pr bins Rapidity 3.50 - 4.00 pb/(GeV/c)’ 9T (GeV/C) 4.00 — 4.50 lab/(GeV/C)2 4.50 - 5.00 pb/(GeV/C)2 5.00 — 5.50 Pb/(GEV/C)2 -0.75 — —0.50 -0.50 — —0.25 1260 1 220 1 210 1160 1 100 1 200 373115158 346111 154 81.2 1 5.0 1 11 125.3 1 4.7 117 30.9 1 2.2 1 3.9 48.3 1 2.5 1 6.1 -0.25 — 0.00 0.00 - 0.25 1329 1 88 1 230 1690 1 120 1 290 406111163 441111169 138.6 1 5.1 119 164.0 1 5.11 23 54.9 1 2.7 1 6.9 64.5 1 2.7 1 8.1 0.25 — 0.50 0.50 — 0.75 1510 1 100 1 260 1258 1 67 1 210 449111170 392111161 176.6 1 5.4 1 24 166.8 1 5.4 1 23 73.6 1 2.9 1 9.2 69.5 1 3.0 1 8.7 5.50 — 6.50 Pb/(GeV/C)2 6.50 — 8.00 pb/(GeV/c)2 8.00 - 10.00 Pb/(GeV/C)2 —0.75 - -—0.50 —0.50 — —0.25 8.66 1 0.64 1 1.0 12.86 1 0.79 1 1.5 0.96 1 0.14 1 0.11 1.77 1 0.19 1 0.20 0.060 1 0.029 1 0.007 0.159 1 0.040 1 0.019 -—0.25 — 0.00 0.00 - 0.25 18.59 1 0.93 1 2.2 21.81 1 0.95 1 2.6 2.85 1 0.24 1 0.33 3.23 1 0.25 1 0.37 0.294 1 0.056 1 0.035 0.425 1 0.065 1 0.051 0.25 - 0.50 0.50 - 0.75 23.38 1 0.99 1 2.8 22.0 1 1.0 1 2.6 4.10 1 0.29 1 0.48 3.10 1 0.28 1 0.36 0.367 1 0.068 1 0.044 0.238 1 0.053 1 0.029 Table B.7 Invariant differential cross section per nucleon for the inclusive reaction pCu —-) 7X at 530 GeV/c as a function of rapidity for several pr bins. Rapidity 3.50 - 4.00 Pb/(G'BV/C)2 2T (GeV/C) 4.00 - 4.50 lab/(GeV/c)2 4.50 — 5.00 [Db/(GNBV/C)2 —0.75 - —0.50 -0.50 — —0.25 1990 1 640 1 370 2780 1 620 1 510 466 1 35 1 79 426 1 311 72 1001 11 115 126 1 12 1 19 -0.25 - 0.00 0.00 - 0.25 2200 1 560 1 410 2180 1 540 1 400 426 1 28 1 72 444 1 25 1 75 126112119 141 111121 0.25 — 0.50 0.50 - 0.75 1110 1 310 1 200 2720 1 740 1 500 465 1 24 1 79 370 1 130 1 60 141 1 11 1 21 80.1 1 9.8 1 l2 5.00 - 5.50 lab/(GeV/C)2 5.50 — 6.50 Pb/(Gev/C)2 6.50 — 8.00 Db/(GeV/C)2 —0.75 - —0.50 —0.50 — -—0.25 27.1 1 4.3 1 3.6 45.2 1 5.4 1 6.0 5.8 11.2 1 0.7 8.4 1 1.5 1 1.1 0.39 1 0.20 1 0.05 0.58 1 0.27 1 0.07 --0.25 - 0.00 0.00 - 0.25 39.7 1 5.8 1 5.3 42.8 1 5.6 1 5.7 10.1 1 1.7 1 1.3 8.8 1 1.6 1 1.1 1.18 1 0.39 1 0.15 1.37 1 0.38 1 0.17 0.25 - 0.50 0.50 - 0.75 49.7 1 5.6 1 6.6 29.2 1 5.1 1 3.9 12.4 1 1.7 1 1.5 9.6 1 1.6 1 1.2 0.66 1 0.28 1 0.08 0.78 1 0.32 1 0.10 289 Table B.8 Invariant differential cross section per nucleon for the inclusive reaction pCu —) 7X at 800 GeV/c as a function of rapidity for several pr bins. PT (GeV/C) Rapidity 3.50 — 4.00 4.00 - 4.50 4.50 — 5.00 pb/(GeV/C)2 pb/(GW/C)2 pb/(GeV/C)2 —1.0 — —0.75 1600 1 570 1 300 768 1 79 1 130 143 1 19 1 22 —0.75 - —0.50 1280 1 790 1 240 440 1 150 1 80 206 1 20 1 31 —0.50 - —0.25 1860 1 810 1 350 500 1 130 1 90 261 1 22 1 40 —0.25 — 0.00 4500 1 1000 1 900 800 1 140 1 140 257 1 21 1 39 0.00 - 0.25 2700 1 680 1 510 1105 1 83 1 190 284 1 33 1 43 0.25 — 0.50 2660 1 650 1 500 929 1 90 1 160 294 1 31 1 44 5.00 — 5.50 5.50 — 6.50 6.50 — 8.00 Pb/(GeV/C)2 lib/(G'BV/C)2 139/((3917/0)2 —1.o - —0.75 49.5 1 7.3 1 6.7 12.7 1 2.5 1 1.6 1.62 1 0.43 1 0.19 -0.75 — —0.50 85 1 10 1 12 17.3 1 2.9 1 2.2 2.83 1 0.63 1 0.33 —0.50 — —0.25 84 1 11 1 11 23.9 1 3.5 1 3.0 3.26 1 0.73 1 0.38 —0.25 — 0.00 93 1 11 1 13 30.3 1 3.6 1 3.8 2.29 1 0.72 1 0.27 0.00 - 0.25 109 1 14 1 15 23.8 1 3.8 1 3.0 3.69 1 0.83 1 0.43 0.25 — 0.50 91 1 14 1 12 25.8 1 4.0 1 3.2 5.24 1 0.99 1 0.61 Table 3.9 Invariant differential cross section per nucleon for the inclusive reaction 7r‘Cu ——> 7X at 515 GeV/c as a function of rapidity for several pr bins. PT (GeV/c) Rapidity 3.50 — 4.00 4.00 — 4.50 4.50 — 5.00 pb/(GeV/c)’ pro/(GeV/c)2 nab/(GeV/c)2 —0.75 — —0.50 2180 1 590 1 370 459 1 42 1 72 124 1 l3 1 17 —0.50 - —0.25 820 1 280 1 140 427 1 30 1 67 142 1 13 1 20 —0.25 - 0.00 1580 1 270 1 270 450 1 30 1 70 142 1 l4 1 20 0.00 — 0.25 1410 1 290 1 240 552 1 30 1 86 150 1 l4 1 21 0.25 — 0.50 2020 1 260 1 340 468 1 31 1 73 166 1 15 1 23 0.50 — 0.75 1030 1 210 1 170 461 1 32 1 72 143 1 14 1 20 5.00 — 5.50 5.50 — 6.50 6.50 — 8.00 pb/(GeV/c)2 pb/(GeV/c)2 pb/(GeV/c)2 —0.75 — -0.50 37.9 1 6.0 1 4.8 9.4 1 1.8 1 1.1 1.20 1 0.38 1 0.14 -0.50 — -0.25 39.5 1 6.3 1 5.0 15.8 1 2.2 1 1.9 2.03 1 0.51 1 0.24 -0.25 — 0.00 64.0 1 7.3 1 8.0 18.7 1 2.4 1 2.2 2.48 1 0.58 1 0.29 0.00 - 0.25 65.8 1 7.3 1 8.3 19.7 1 2.5 1 2.3 4.90 1 0.73 1 0.57 0.25 — 0.50 63.4 1 7.6 1 8.0 20.1 1 2.5 1 2.4 3.44 1 0.69 1 0.40 0.50 — 0.75 89.6 1 8.3 1 11 26.8 1 2.8 1 3.2 3.57 1 0.71 1 0.41 290 Table B.10 Invariant differential cross section for the inclusive reaction pp —> 7X at 530 GeV/c as a function of rapidity for several p1. bins. p7. (GeV/c) Rapidity 3.50 - 4.00 4.00 - 4.50 4.50 — 5.00 pb/(GeV/c)2 pb/(GeV/c)2 pb/(GeV/cf —0.75 - —0.50 2350 1 600 1 430 378 1 34 1 64 98 1 12 1 14 —0.50 - -—0.25 1250 1 510 1 230 385 1 29 1 65 118 112 1 17 —0.25 - 0.00 900 1 440 1 160 437 1 27 1 74 135 1 12 1 20 0.00 - 0.25 1170 1 410 1 210 336 1 24 1 57 116 1 11117 0.25 — 0.50 850 1 250 1 150 348 1 23 1 59 110 1 10 1 16 0.50 — 0.75 590 1 550 1 110 410 1 170 1 70 77.9 1 9.7 1 12 5.00 - 5.50 5.50 — 6.50 6.50 - 8.00 pb/(GeV/c)2 pin/(GeV/c)2 pb/(GeV/c)2 —0.75 — —0.50 26.0 1 5.3 1 3.5 5.9 1 1.2 1 0.7 0.26 1 0.21 1 0.03 —0.50 - -0.25 37.7 1 5.2 1 5.0 9.7 1 1.6 1 1.2 0.89 1 0.34 1 0.11 -0.25 — 0.00 40.2 1 5.8 1 5.4 7.3 1 1.7 1 0.9 0.93 1 0.36 1 0.11 0.00 - 0.25 38.0 1 5.6 1 5.1 11.0 1 1.8 1 1.4 1.06 1 0.37 1 0.13 0.25 —- 0.50 35.2 1 5.3 1 4.7 10.6 1 1.7 1 1.3 1.75 1 0.43 1 0.22 0.50 — 0.75 25.7 1 5.0 1 3.4 4.2 1 1.4 1 0.5 0.63 1 0.29 1 0.08 Table B.1] Invariant differential cross section for the inclusive reaction pp —> 7X at 800 GeV/c as a function of rapidity for several pr bins. pr (GeV/C) Rapidity 3.50 — 4.00 4.00 — 4.50 4.50 — 5.00 pb/(GeV/c)’ pb/(GeV/c)’ pb/(GeV/c)2 —1.0 — —0.75 2140 1 920 1 400 516 1 76 1 90 174 1 21 1 26 —0.75 — —0.50 1430 1 830 1 270 160 1 210 1 30 225 1 21 1 34 —0.50 — —0.25 1080 1 830 1 200 796 1 87 1 140 234 1 22 1 35 —0.25 - 0.00 2460 1 860 1 460 855 1 54 1 150 223 1 20 1 34 0.00 - 0.25 2670 1 600 1 500 860 1 110 1 150 351 1 28 1 53 0.25 - 0.50 2350 1 580 1 440 666 1 84 1 120 237 1 31 1 36 5.00 — 5.50 5.50 — 6.50 6.50 - 8.00 pb/(GeV/c)2 pb/(GeV/c)2 pb/(GeV/c)2 —l.0 - —0.75 47.0 1 8.1 1 6.4 13.5 1 2.4 1 1.7 1.78 1 0.52 1 0.21 -0.75 - -0.50 84 1 10 1 11 22.1 1 3.2 1 2.7 2.32 1 0.68 1 0.27 -0.50 —- —0.25 89 1 11 1 12 26.5 1 3.5 1 3.3 3.21 1 0.84 1 0.38 —-0.25 - 0.00 90 1 11 1 12 32.3 1 3.7 1 4.0 3.97 1 0.84 1 0.46 0.00 - 0.25 118 1 l4 1 16 33.4 1 4.0 1 4.1 5.6 11.0 1 0.7 0.25 - 0.50 97 113 113 25.11 4.1 1 3.1 4.44 11.00 1 0.52 291 Table 3.12 Invariant differential cross section for the inclusive reaction 7r’p —+ 7X at 515 GeV/c as a function of rapidity for several pr bins. p7 (GeV/C) RApidity 3.50 — 4.00 4.00 — 4.50 4.50 — 5.00 pb/(GeV/c)2 pb/(GeV/c)2 pb/(GeV/c)2 -0.75 - -0.50 -999 1 790 1 40 483 1 76 1 75 158 1 26 1 22 —0.50 - ——0.25 4100 1 1300 1 700 460 1 80 1 72 160 1 27 1 22 -0.25 - 0.00 4300 1 1600 1 700 575 1 71 1 90 192 1 30 1 26 0.00 - 0.25 730 1 770 1 120 521 1 64 1 81 139 1 26 1 19 0.25 — 0.50 880 1 490 1 150 551 1 57 1 86 210 1 29 1 29 0.50 - 0.75 240 1 710 1 40 409 1 67 1 64 147 1 29 1 20 5.00 — 5.50 5.50 - 6.50 6.50 - 8.00 pb/(GeV/c)2 pb/(GeV/c)2 nab/(GeV/c)2 —0.75 - —0.50 43 1 l2 1 5.0 6.7 1 3.5 1 0.8 2.2 1 1.0 1 0.3 —0.50 - -—O.25 52 1 14 1 7.0 14.3 1 4.7 1 1.7 2.9 1 1.2 1 0.3 —0.25 - 0.00 74 1 16 1 9.0 20.8 1 5.1 1 2.5 4.0 1 1.5 1 0.5 0.00 — 0.25 66 1 14 1 8.0 26.1 1 5.4 1 3.1 4.7 1 1.6 1 0.5 0.25 — 0.50 85 1 16 1 11 25.4 1 5.5 1 3.0 4.7 1 1.6 1 0.5 0.50 - 0.75 73 1 16 1 9.0 19.9 1 5.5 1 2.4 5.0 1 1.9 1 0.6 292 "‘1. Appendix C 77 Results 0.1 77 Cross Sections In Figures C.1, C2, and CB, inclusive 7] cross sections per nucleus are shown as functions of pr for 530 and 800 GeV/c proton beams and 515 GeV/c 7r“ ‘1 .' 'trl beam, respectively, incident upon copper, beryllium, and liquid hydrogen targets. Since the cross sections fall steeply, the data are plotted at abscissa values which correspond to the average values of the cross section in the apprOpriate pr bins assuming exponential pr spectra[99]. These results are also presented in tabular form in Tables C.1 — C.3. In addition, the cross sections as functions of rapidity for several pr intervals are presented in Tables (3.4 — CH. 293 ? 7 I I I I l I I T I l I f T T l I I I I I I I I I I j r I I I I T I I 10 —: 3 a 73 g 530 GeV/c p Beam : S 5 106 -0.75 11X 5 -2 P ‘ 10 F 0 pp —9 nX -= q 10.3 Pl 1 l l l l l 1 l l l l l l l l l l l l L L l 1 J J 1 L J L L l 3 4 5 6 7 8 9 10 PT (GeV/c) Figure C.1 77 production cross sections per nucleus as functions of pr for 530 GeV/c proton beam on copper, beryllium, and liquid hydrogen targets. 294 ? 7 I r I I I I I I I I I I I Fl I I T I T I— I—I rrfT I I l I I I I 3‘0 : ‘3‘ 73 59 800 GeV/c pBeam 5 g 61 -—10nX 3 .2 ' '1 10 1 ° [DP—“1X ‘3 I 1 10-3 1 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 _1 1 1 3 4 5 6 7 8 9 1O pT (GeV/c) Figure 0.2 17 production cross sections per nucleus as functions of pr for 800 GeV/c proton beam on copper, beryllium, and liquid hydrogen targets. 295 Eda/d3p (pb GeV'2 per nucleus) ESm a; 8m 89 84 .5 O N 10 1 -1 10 -2 10 -3 10 J I I T I f I I I I I I I I I I I I T I I I I I I j I I T I 7 I I I g 515 GeV/c 11:- Beam ; -0.75 < y < 0.75 1 U I Q E . a _ E- 0 I D E . . . F f a i E ' a 5 L Q ' 9 _' t E : Q : ’ r I .3 l i D 11; Cu —> 71X 1 . 0 n‘Be —> nX : 0 up —) 11X 1: 1 L #1 l 1 l l l l l 1 l 1 l 1 l l 1 l l l l l 1 l 1 1 l l l l l 1 q 3 4 5 6 7 a 9 1o pT (GeV/c) Figure C.3 7] production cross sections per nucleus as functions of pr for 515 GeV/c 7r‘ beam on copper, beryllium, and liquid hydrogen targets. 296 Table C.1 Invariant differential cross sections per nucleon for 7) production by 530 and 800 GeV/c proton beams and 515 GeV/c 7r‘ beam on Be targets. p Range Edd/<13? (Pb/(GeV/C)2) T pBe at 530 GeV/c pBe at 800 GeV/c 7r‘Be at 515 GeV/c (GeV/c) -0.75 < y < 0.75 -1.0 < y < 0.5 -0.75 < y < 0.75 3.00 - 3.50 34800 1 4300 1 4200 54800 1 8000 1 6800 35300 1 3500 1 4400 3.50 - 4.00 7810 1 890 1 900 8760 1 1800 1 1000 8290 1 660 1 990 4.00 - 4.50 1480 1 66 1 170 2700 1 160 1 320 1810 1 16 1 210 4.50 - 5.00 379 1 16 1 44 761 1 16 1 90 537 1 16 1 62 5.00 — 5.50 105 1 l 1 12 248 1 l6 1 29 154 1 l 1 18 5.50 - 6.00 27.4 1 2.6 1 3.2 83.0 1 7.1 1 10.0 51.9 1 2.8 1 6.1 6.00 - 6.50 7.52 1 1.01 1 0.91 26.5 1 3.6 1 3.2 20.3 1 1.5 1 2.4 6.50 - 7.00 2.74 1 0.45 1 0.34 10.6 1 1.8 1 1.3 6.30 1 0.73 1 0.76 7.00 - 7.50 0.21 1 0.24 1 0.03 3.93 1 1.07 1 0.49 1.59 1 0.38 1 0.19 7.50 - 8.50 0.19 1 0.07 1 0.02 2.15 1 0.51 1 0.27 0.53 1 0.13 1 0.07 8.50 - 10.00 — 0.26 1 0.23 1 0.03 0.11 1 0.04 1 0.01 10.00 — 12.00 — 0.07 1 0.05 1 0.01 —- Table C.2 Invariant differential cross sections per nucleon for 7) production by 530 and 800 GeV/c proton beams and 515 GeV/c 7r“ beam on Cu targets. p Range Eda/d3? (Pb/(GeV/C)2) T pCu at 530 GeV/c pCu at 800 GeV/c 7r’Cu at 515 GeV/c (GeV/C) —0.75 < y < 0.75 —1.0 < y < 0.5 —0.75 < y < 0.75 3.00 - 3.50 53400 1: 12000 1 6500 81800 1 25000 1 10000 44500 1 12000 1 5700 3.50 - 4.00 7880 1 2200 a; 920 9900 1 5100 1 1200 10600 a: 1600 1 1300 4.00 — 4.50 1680 1 170 a: 200 4780 3: 470 a: 580 2210 a: 170 1 260 4.50 — 5.00 434 1 17 a: 51 1060 :1: 120 1 130 730 :1; 12 1 86 5.00 — 5.50 120 1 12 1 14 274 1 12 1 34 203 1 12 1 24 5.50 - 6.00 41.0 1 6.6 1 4.9 123 5: 12 1 15 56.6 3: 8.0 1 6.7 6.00 — 7.00 7.48 1 1.42 1 0.92 15.8 1 4.7 1 2.0 18.2 1 2.3 a: 2.2 7.00 — 8.00 1.01 1 0.35 1 0.13 3.02 a: 1.46 1 0.39 2.66 1 0.76 1 0.33 8.00 — 10.00 0.09 1 0.08 1 0.01 0.15 1 0.41 1 0.02 0.29 1 0.16 1 0.04 297 Table C.3 Invariant differential cross sections for 17 production by 530 and 800 GeV/c proton beams and 515 GeV/c 7r‘ beam on proton targets. Eda/(1312 (pb/(GeV/C)2) p Range 7 pp at 530 GeV/c pp at 800 GeV/c 7r"p at 515 GeV/c (GeV/C) —0.75 < y < 0.75 -—1.0 < y < 0.5 —0.75 < y < 0.75 3.00 - 3.50 24100 1 10000 1 3100 53400 1 18000 1 7000 72200 1 65000 1 9500 3.50 — 4.00 8030 1 2000 1 980 12200 3: 3900 1 1500 9350 1 3900 1 1200 4.00 - 4.50 1270 :2 150 3: 150 2250 1 360 1 280 1780 3 310 1 220 4.50 — 5.00 329 1 31 1 40 717 1 31 1 89 407 1 108 3: 50 5.00 — 5.50 82.3 3: 12.7 3: 10.2 232 1 10 3: 29 124 3: 10 1 15 5.50 — 6.00 25.5 1 5.3 3: 3.2 114 3: 10 1 14 19.5 3: 17.6 3: 2.4 6.00 - 7.00 2.54 1 1.33 1 0.32 21.8 1 5.1 3: 2.8 7.88 1 4.79 1 0.99 7.00 — 8.00 0.44 3: 0.33 1 0.06 4.68 1 1.93 1 0.61 0.38 1 0.97 1 0.05 8.00 — 10.00 — 1.12 1 0.76 3: 0.15 — 298 Table C.4 Invariant differential cross section per nucleon for 17 production by 530 GeV/c proton beam on Be target as a function of pT and rapidity. p, (GeV/C) Rapidity 3.00 - 4.00 4.00 - 4.50 4.50 - 5.00 nb/(GeV/c)2 nb/(GeV/c)2 pb/(GeV/c)2 —0.750 - -0.625 1.09 :1: 0.32 :1: 0.12 256 :t 64 :l: 29 -0.625 - —0.500 15.4 i 94 i 1.8 1.00 i: 0.33 :t 0.11 329 :1: 91 :l: 38 -0.500 - -0.375 1.47 :1: 0.29 :l: 0.17 390 :l: 70 :t 45 -0.375 - —0.250 25.6 i 52 i 30 1.80 :l: 0.30 :l: 0.21 440 :1: 63 :1: 51 -0.250 - —0.125 1.98 :1: 0.26 :1: 0.23 503 :1: 59 :h 58 -0.125 - 0.000 22.1 i 4.0 i 2.6 1.80 :1: 0.21 :1: 0.21 534 :t 58 2t 62 0.000 - 0.125 1.38 :t 0.18 :i: 0.16 502 :l: 53 :1: 58 0.125 — 0.250 27.4 i 3.5 i 33 2.14 :l: 0.17 :1: 0.24 379 :1: 47 :1: 44 0.250 - 0.375 1.53 :t 0.12 :1: 0.17 345 :t 41 :1: 40 0.375 - 0.500 23.5 i 3.4 i 2.8 1.45 :l: 0.11 :t 0.17 354 :1: 37 :1: 41 0.500 - 0.625 1.27 :1: 0.11 :1: 0.15 334 :t 37 :i: 39 0.625 — 0.750 13.9 i 4.2 i 1.6 0.863 :t 0.077 :t 0.099 193 :l: 29 :1: 22 5.00 — 5.50 5.50 - 6.50 6.50 — 8.00 pb/(GeV/cf pb/(GeV/cf pb/(GeV/cf -0.750 - —0.625 66 j: 26 d: 8.0 4.8 :l: 7.2 :t 0.6 -0.625 — —0.500 99 :1: 21 :i: 12 14.0 :1: 4.1 :l: 1.7 0.37 i 034 i 005 -0.500 - —0.375 104 :1: 27 2h 12 7.9 :l: 7.1 :1: 0.9 -0.375 - -0.250 112 :l: 18 :1: 13 16.9 :h 4.5 :t 2.0 1.07 i 0.48 i 0.13 —0.250 - —0.125 139 :1: 20 :1: 16 21.8 :1: 4.8 :1: 2.6 —0.l25 - 0.000 129 :1: 18 i 15 20.2 :1: 4.6 :t 2.4 1.65 i 0.48 i 0.20 0.000 - 0.125 126 :t 19 :t 15 22.4 :1: 4.4 :t 2.7 0.125 - 0.250 102 :t 15 :t 12 20.9 :1: 4.1 :l: 2.5 1'74 i 0'47 i 0'22 0.250 - 0.375 133 :l: 21 :t 15 24.6 :1: 4.0 :t 2.9 0.375 — 0.500 97 :1: 15 :1: 11 20.7 :t 4.0 :l: 2.5 0.85 i 0.42 i 0.10 0.500 — 0.625 94 :1: 15 :l: 11 19.2 :1: 3.4 :l: 2.3 0.625 - 0.750 57 :h 12 :1: 7.0 15.0 d: 3.3 :1: 1.8 0.71 i 035 i 0.09 299 Table C.5 Invariant differential cross section per nucleon for 17 production by 800 GeV/c proton beam on Be target as a function of pr and rapidity. pT (GeV/C) Rapidity 3.00 - 4.00 4.00 - 4.50 4.50 — 5.00 nb/(GeV/c)2 nb/(GeV/c)2 pb/(GeV/c)2 —1.00 - —0.875 0.92 :i: 0.58 :t 0.11 —0.875 - -0.750 13 i 16 :1: 20 1.36 :l: 0.63 :1: 0.16 500 :l: 240 :t 60 —0.750 - -0.625 2.00 :1: 0.64 i 0.23 560 :1: 130 :1: 70 —0.625 - —0.500 47 It 11 i 60 1.27 :l: 0.58 :t 0.15 560 :l: 160 :l: 70 —0.500 - -0.375 2.35 :l: 0.55 :1: 0.27 640 :l: 120 :1: 80 —0.375 — —0.250 17.6 i 81 i 2'1 3.88 i: 0.54 :1: 0.45 710 :1: 150 d: 80 —0.250 — -0.125 3.54 :i: 0.57 :l: 0.41 570 :1: 130 :1: 70 —0.125 - 0.000 48.5 i 8'8 i 5'9 4.17 :t 0.52 :t 0.49 950 :t 140 :1: 110 0.000 — 0.125 4.10 :1: 0.60 :1: 0.48 1200 :1: 160 :t 140 0.125 - 0.250 35.2 i 68 i 4'3 2.86 d: 0.52 :i: 0.33 1240 :1: 190 :1: 150 0.250 — 0.375 3.71 :1: 0.35 :1: 0.43 1180 :i: 130 :h 140 0.375 — 0.500 29.3 i 7'1 i 36 2.25 :t 0.26 :1: 0.26 1090 :i: 110 :i: 130 5.00 - 5.50 5.50 - 6.50 6.50 - 8.00 pb/(GW/C)2 Pb/(G-e'V/C)2 Pb/(GeV/C)2 —1.00 — —0.875 115 :t 47 :1: l4 9 2t 10 21:10 -0.875 - -0.750 88 :l: 52 :t 10 22.5 :I: 9.1 :l: 2.7 -0.750 - —0.625 159 :t 44 i 19 52 :l: 16 :t 6.0 —0.625 — -0.500 260 :t 48 :1: 31 41 :1: 11 :l: 5.0 68 :1: 20 i 08 —0.500 - -0.375 302 :t 49 :1: 36 34 :l: 12 :1: 4.0 —0.375 — -0.250 255 :1: 56 :l: 30 51 :1: 11 :t 6.0 4‘3 i 1'6 i 0'5 —0.250 — —0.125 240 :f: 48 :t 28 87 :t 16 :1: 10 —0.125 — 0.000 293 :t 54 i 35 80 :i: 13 :1: 10.0 6'5 i 1'5 i 0'8 0.000 — 0.125 315 :t 64 :l: 37 94 :l: 17 :f: 11 0.125 - 0.250 390 :l: 76 2t 46 71 :t 19 :l: 9.0 8.3 i 22 i 1.0 0.250 — 0.375 277 :1: 58 :l: 33 62 :t 15 :l: 7.0 0.375 —- 0.500 284 :t 49 :t 34 54 :1: 13 :t 6.0 7'5 2!: 18 i 0'9 300 Table 0.6 Invariant differential cross section per nucleon for 17 production by 515 GeV/c 1r“ beam on Be target as a function of p7 and rapidity. p, (GeV/c) Rapidity 3.00 - 4.00 4.00 - 4.50 4.50 - 5.00 nb/(GeV/c)2 nb/(GeV/c)2 pb/(GeV/c)2 -0.750 - -0.625 0.69 :t 0.26 :1: 0.08 290 i 89 :l: 34 —0.625 - —0.500 14.2 i 63 i 1.7 0.89 :1: 0.23 :1: 0.10 281 i: 62 :l: 33 -0.500 — -0.375 1.31 :l: 0.18 :t 0.15 343 :l: 52 :1: 40 —0.375 - —0.250 17.2 i 5.7 i 2.1 1.83 :t 0.18 :h 0.21 461 :t 45 :1: 53 -0.250 - —0.125 1.73 :l: 0.15 :1: 0.20 587 i 53 :1: 68 -0.125 — 0.000 27.4 i 46 i 3'4 2.23 i 0.14 :1: 0.26 562 :1: 47 :l: 65 0.000 - 0.125 1.77 :b 0.13 :1: 0.21 584 :l: 47 :l: 68 0.125 - 0.250 27.8 i 2.4 i 3.4 2.43 :t 0.14 :l: 0.28 657 :1: 55 :h 76 0.250 - 0.375 2.39 :1: 0.15 i 0.28 690 :l: 52 :1: 80 0.375 - 0.500 239 i 2.5 i 2'9 2.30 :1: 0.14 :1: 0.27 695 :t 51 :1: 80 0.500 - 0.625 2.05 :l: 0.12 :l: 0.24 657 :1: 47 :1: 76 0.625 - 0.750 18.3 i 22 :1: 23 2.09 :1: 0.12 :t 0.24 601 :1: 44 :1: 70 5.00 - 5.50 5.50 - 6.50 6.50 - 8.00 Pb/ (GeV/C)2 Pb/ (GeV/C)2 Pb/ (GGV/C)2 -0.750 - -0.625 37 :1: 15 :1: 4.0 6.9 :1: 4.6 :l: 0.8 -—0.625 — -0.500 79 2t 22 :t 9.0 23.1 :1: 4.9 :t 2.7 049 i 049 i 0'06 —0.500 - -0.375 142 :t 22 :l: 17 18.7 :1: 4.3 :l: 2.2 -0.375 - -0.250 126 :t 17 :1: 15 32.5 :1: 5.7 :t 3.8 1.32 i- 049 i 0.16 —0.250 - —0.125 158 :1: 17 :l: 18 37.0 :t 4.5 :1: 4.4 -0.125 - 0.000 145 :f: 20 :1: 17 43.0 :t 5.6 :1: 5.1 3.67 i 0.72 i 0.44 0.000 - 0.125 139 :t 19 :l: 16 33.7 :t 5.3 :1: 4.0 0.125 - 0.250 200 :1: 22 :1: 23 46.1 :1: 5.5 :1: 5.4 3.60 i 0.78 i 0.44 0.250 - 0.375 227 :1: 22 :l: 26 48.4 :1: 5.4 :1: 5.7 0.375 — 0.500 220 :i: 23 :1: 26 46.5 :1: 6.5 :1: 5.5 440 i 0.86 i 053 0.500 - 0.625 186 :1; 21 :1: 22 41.9 d: 5.9 :1: 4.9 0.625 - 0.750 175 :t 18 :1: 20 36.2 :1: 5.2 :l: 4.3 390 i 0.78 It 047 301 Table C.7 Invariant differential cross section per nucleon for 17 production by 530 GeV/c proton beam on Cu target as a function of pT and rapidity. p, (GeV/c) Rapidity 4.00 — 5.00 5.00 - 6.00 6.00 — 8.00 pb/(GeV/c)2 pb/(GeV/c)2 pb/(GeV/c)2 —0.75 — —0.50 580 :l: 300 :1: 70 58 d: 18 :l: 7.0 -0.50 - -0.25 1190 :t 290 :l: 140 86 i 21 i 10 3.6 d: 1.5 i 0.4 -0.25 - 0.00 1390 :1: 230 :l: 160 95 :t 18 :l: 11 0.00 - 0.25 1320 :1: 170 d: 150 112 :1: 18 :1: 13 3.7 i 1.1 i 0.5 0.25 — 0.50 1170 :l: 110 :l: 130 72 :1: 19 :l: 8.0 0.50 — 0.75 710 :t 90 :l: 81 59 :l: 12 i: 7.0 5'4 i 1'2 i 0'7 Table C.8 Invariant differential cross section per nucleon for 17 production by 800 GeV/c proton beam on Cu target as a function of pr and rapidity. p, (GeV/C) Rapidity 4.00 - 5.00 5.00 - 6.00 6.00 - 8.00 pb/(GeV/c)2 pb/(GeV/c)2 pb/(GeV/c)2 -1.0 - -0.75 3240 :l: 950 :h 380 47 :1: 31 :l: 6.0 -0.75 - —0.50 2460 i 580 :t 290 136 :l: 49 :1: 16 9.7 d: 4.1 i 1.2 -0.50 - -0.25 2550 :1: 480 :1: 300 233 :1: 45 :l: 28 -0.25 - 0.00 3490 :1: 570 :l: 410 235 :1: 52 2t 28 6.6 i 3.6 i 08 0.00 - 0.25 3170 :h 520 :l: 370 310 :l: 78 :h 37 0.25 - 0.50 2600 :l: 320 :1: 300 230 :l: 54 :t 27 11.8 i 5.1 i 1.4 Table C.9 Invariant differential cross section per nucleon for 1) production by 515 GeV/c 1r" beam on Cu target as a function of pp and rapidity. p, (GeV/C) Rapidity 4.00 - 5.00 5.00 — 6.00 6.00 - 8.00 Pb/(GeV/C)’ pb/(GeV/C)2 pb/(GeV/C)2 -0.75 - -0.50 630 1 350 1 70 47 1 24 1 5.0 —0.50 - —0.25 1350 1 260 1 160 74 1 20 1 9.0 6'8 i 1’9 i 0'8 -0.25 - 0.00 1770 1 170 1 210 134 1 20 1 16 0.00 - 0.25 1560 1 160 1 180 156 1 24 1 18 13'0 i 2'3 i 1‘6 0.25 — 0.50 1960 1 170 1 230 187 1 23 1 22 0.50 — 0.75 1520 1 140 1 180 174 1 23 1 20 “‘7 i 2'2 i 1‘4 302 Table 0.10 Invariant differential cross section for 7] production by 530 GeV/c proton beam on p target as a function of pT and rapidity. pr (GeV/C) Rapidity 4.00 - 5.00 5.00 - 6.00 6.00 - 8.00 pb/(GeV/c)2 pb/(GeV/c)2 pb/(GeV/c)2 -0.75 - -0.50 580 :t 270 :1: 70 31 :l: 20 :l: 4.0 -0.50 - —0.25 750 :t 240 :1: 90 56 :l: 17 :l: 7.0 1'7 i 1'1 i 0'2 —0.25 — 0.00 1230 :t 200 :t 140 62 :l: 17 :1: 7.0 0.00 — 0.25 780 :t 160 :l: 90 74 :l: 19 :1: 9.0 1'4 i 1'1 i 0'2 0.25 - 0.50 850 :1: 110 :l: 100 49 :l: 13 :1: 6.0 0.50 — 0.75 600 i 77 :l: 69 52 :t 14 :t 6.0 1'4 i 1'3 i 0'2 Table 0.11 Invariant differential cross section for 1) production by 800 GeV/c proton beam on p target as a function of pr and rapidity. p, (GeV/C) Rapidity 4.00 — 5.00 5.00 - 6.00 6.00 — 8.00 pb/(GeV/C)2 pb/(GeV/C)2 pb/(GeV/C)2 —1.0 — —0.75 1120 1 460 1 130 76 1 53 1 9.0 -0.75 - —0.50 380 1 550 1 40 102 1 51 1 12 6'3 i 4'2 i 0'8 —0.50 — —0.25 2040 1 440 1 240 206 1 42 1 25 —0.25 - 0.00 2000 1 470 1 230 271 1 50 1 32 19'5 i 5'1 i 2‘4 0.00 - 0.25 2090 1 500 1 240 174 1 58 1 21 0.25 - 0.50 1290 1 260 1 150 208 1 53 1 25 13’9 i 4'8 i 1’7 Table C .12 Invariant differential cross section per nucleon for 7) production by 515 GeV/c 7r- beam on p target as a function of pr and rapidity. 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