J/Psi $ Yield Modification in 200 Gev Per Nucleon Au+Au

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2016 J/# Yield Modification in 200 GeV Per Nucleon Au+Au Collisions with the PHENIX Experiment at RHIC Jeffrey Klatsky

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COLLEGE OF ARTS AND SCIENCES

J/ψ YIELD MODIFICATION IN 200 GEV PER NUCLEON AU+AU COLLISIONS WITH

THE PHENIX EXPERIMENT AT RHIC

JEFFREY CURRY KLATSKY

A Dissertation submitted to the Department of Physics in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy

2016

Jeﬀrey Curry Klatsky defended this dissertation on April 7, 2016. The members of the supervisory committee were:

Anthony Frawley Professor Co-Directing Dissertation

Volker Crede Professor Co-Directing Dissertation

Tim Cross University Representative

Susan Blessing Committee Member

Simon Capstick Committee Member

The Graduate School has veriﬁed and approved the above-named committee members, and certiﬁes that the dissertation has been approved in accordance with university requirements.

ii To my parents, without whose constant love and support I would have quit long ago.

iii ACKNOWLEDGMENTS

I want to say something like, “Wow, I honestly don’t know how I made it this far.” But that would be a lie, because there is no doubt in my mind that I’ve only made it this far because of the countless people that have helped me in one way or another during my time as an FSU grad student. I have eight years worth of people to thank, so if a momentary lapse in my failing memory has caused me to forget you, I deeply apologize. I’ve got a lot to cover here, so bear with me. First and foremost, I thank my advisor, Tony. For showing me what it means to be a scientist, and how to pick apart a problem at the finest scale. For being willing to help me with even the most trivial of questions at a moment’s notice, even when they are about things I should know. For setting the bar high, so that I always tried to do better. And for sticking with me, even when things looked not so promising. To my committee, I realize that this may be the longest you’ve ever been on a Ph.D. student’s committee. Thank you for being patient with me as I wrapped things up and being understanding about last minute problems that seem to always find ways to emerge. To the FSU physics department, thank you for allowing me to stay as long as I did. Thank you for the opportunity to teach classes, which ended up being one of my favorite things about graduate school. To the PHENIX collaboration, especially those I sat shifts with, thank you for the good mem- ories, whether at BNL, workshops or at overseas conferences. Eastern Long Island is a pretty forgettable place, but those I’ve met have made the trips there unforgettable. Special thanks to Mihael and Ermias for their help with HBD-related issues. To the students who came to FSU physics department in the Fall of 2008, thanks for being a family during what was a difficult transition for everyone. That first semester was no doubt the hardest academic semester of my life, and I could not have made it through those courses without the help of everyone. I remember we would discuss things like, “Who is going to be the last one of us to graduate?”. Well guys, it’s me! To my fellow FSU nucs, including but not limited to Bemder, Smitch, Bookvalter, Dmac, Tony K, Pim, Turn-the-Tacos-into-Chili, Rutger and JP, thank you for making a building as ugly as

iv NRB feel like home. Thanks for all the Momo’s Fridays, Panda Wednesdays, Dirac Lunch and the short-lived Voodoo Dog Thursdays and all our group lunches a thing. Thanks to Drs. Anthony Kuchera and Chris Levi Duston for Mega After Eight. We came, we saw, we rocked. MA84L. To my outside-the-field family, Azúcar Dance Company, thank you for the amazing experiences and the chance to be involved in something I never thought I’d do. If someone had told me I’d end up performing and teaching salsa before I came to FSU, I’d have laughed in their face. Showing up to that first class in 2010 was one of the best decisions I’ve ever made. Special thanks to Dave, Daniel, Yingxue, Jeni, Mobes, Tayonce, VV and Deb for the incredible dances, support and friendship. To JB, Natty and Laura, thank you for always believing in me and supporting me, even after seeing me at my worst. To Arien, thank you for convincing me to stay in Tallahassee and not give up, even though I was at an all-time low my first semester. I know I would have left Florida if not for that phone call, so thank you for talking some sense into me. To Anthony, thanks for an awesome five and a half years. Our experiences with the struggles of grad school, exploring a new city and doing stuff like soccer, running and music together has really made me feel lucky to have had you as my friend. I really can’t imagine grad school being as memorable as it has been without you. To Dmac, thanks for not only being a friend, but also for your unending help with my work. I constantly badgered you while you worked 6 feet from me, and I badgered you when you moved 1600 miles away to Boulder, CO. You never ceased to lend a helping hand, and for that I am eternally grateful. Celeste, thank you for being so good to me as I got through the last leg of this thing. Your support means more to me than you know. Last but certainly not least, I thank my family: Mom, Dad, Gander, Maya and Bozo. Thank you for everything.

v TABLE OF CONTENTS

ListofTables...... ix ListofFigures ...... x List of Abbreviations ...... xvi Abstract...... xvii

1 Overview 1

2 Motivation 2 2.1 RelevantAspectsofQCD ...... 2 2.1.1 Conﬁnement ...... 2 2.1.2 Quark Gluon Plasma ...... 4 2.2 Relativistic Heavy Ion Collisions ...... 5 2.2.1 Elliptic Flow and Quark Scaling ...... 5 2.2.2 Jet Suppression in Au+Au Collisions ...... 6 2.2.3 Small η/s andNear-PerfectFluidity ...... 7 2.2.4 ChemicalEquilibrium ...... 9 2.2.5 Hard Probes ...... 9 2.3 Charmonium in Nuclear Collisions ...... 10 2.3.1 TimeScales...... 12 2.4 What Can We Learn from Charmonium? ...... 12 2.5 Motivation for this Analysis ...... 13

3 Charmonium in Nuclear Collisions 14 3.1 Observables...... 14 3.2 Brief Overview of J/ψ Measurements...... 15 3.3 Cold Nuclear Matter Effects ...... 16 3.4 Hot Nuclear Matter Effects ...... 18 3.4.1 SPSResults...... 18 3.4.2 RHICResults...... 19 3.4.3 ALICE Results ...... 22 3.4.4 Comparison of Heavy Ion Data at Different Energies ...... 22 3.4.5 Models for Hot Nuclear Matter Effects ...... 24 3.5 Motivation for this Analysis ...... 26

4 Experiment 33 4.1 RHIC ...... 33 4.2 PHENIX...... 33 4.2.1 DriftChamber ...... 35 4.2.2 Pad Chamber 1 ...... 36 4.2.3 Ring Imaging Cerenkov Detector ...... 38

vi 4.2.4 Electromagnetic Calorimeter ...... 39 4.2.5 Hadron Blind Detector ...... 41 4.2.6 Beam Beam Counter ...... 43

5 Analysis 44 5.1 CentralityDetermination ...... 44 5.2 Detector QA and Run Group Assignments ...... 45 5.2.1 Drift Chamber and Pad Chamber 1 ...... 46 5.2.2 RICH, EMCal and HBD ...... 47 5.3 ElectronIdentiﬁcation ...... 49 5.3.1 HBD Min Pad Clusterizer ...... 49 5.3.2 Neural Network ...... 51 5.4 Signal Extraction ...... 52 5.4.1 Yield Extraction - Centrality Dependence ...... 54 5.4.2 Yield Extraction - pT Dependence ...... 59 5.4.3 Radiative Tails ...... 60 5.5 Acceptance and Eﬃciency Corrections ...... 61 5.5.1 Simulation Chain ...... 62 5.5.2 Simulated J/ψ Line Shape ...... 63 5.5.3 Simulation to Data Matching ...... 64 5.5.4 Acceptance Calculation ...... 67 5.5.5 EmbeddingCorrection...... 70 5.6 Invariant Yield and RAA ...... 71 5.6.1 p + p Reference...... 73 5.6.2 BinShiftCorrection ...... 74 5.6.3 RAA ...... 78 5.6.4 Au+Au RAA vs Npart ...... 79 5.6.5 RAA vs pT ...... 79 5.6.6 p2 vs N ...... 80 h T i part 5.7 SystematicUncertainties...... 81 5.7.1 BdN/dy vs Npart ...... 82 5.7.2 RAA vs Npart ...... 84 2 5.7.3 Bd N/dydpT vs pT ...... 84 5.7.4 RAA vs pT ...... 85 5.7.5 p2 vs N ...... 85 h T i part 6 Discussion and Comparison with Theory 88 6.1 RAA vs Npart ...... 88 2 6.2 B d N vs p ...... 91 dydpT T 6.3 RAA vs pT ...... 92 6.4 p2 vs N ...... 92 h T i part 7 Summary 98

vii Appendix A DC α vs φ Plots 100

B DC φ - Simulation/Data Comparison 104

C Acceptance Figures 107

Bibliography ...... 114 BiographicalSketch ...... 120

viii LIST OF TABLES

5.1 Npart and Ncoll values for their corresponding centrality classes...... 45

5.2 Run groups and their respective number of runs and number of events...... 48

5.3 Electron identiﬁcation variables used in neural network...... 53

5.4 Neural net cut values for each centrality bin...... 53

5.5 Best ﬁt parameters from Crystal Ball function...... 57

5.6 Fit results and yields as a function of centrality...... 60

5.7 Results of histogramming the yields from parameter sets resulting in a χ2 within 4.72 2 of χmin...... 63 5.8 Results of increasing and decreasing the mixed-event (ME) background by 2%. . . . . 64

5.9 Fit results and yields as a function of centrality and pT . A ’*’ indicates that the yield and yield error were obtained by scaling the direct sum yield and error by the ratio oftheﬁtyieldtothedirectsumyield...... 69

5.10 Average diﬀerence in φ distributions between simulations and data for each run group. 74

5.11 Embedding values and their systematic uncertainties as a function of centrality. . . . 74

2 5.12 Bd N/dydpT values, uncorrected for bin shift eﬀects. Systematic uncertainties are discussedinsection5.7...... 75

2 5.13 Correction factor r and corrected Bd N/dydpT values. Systematic uncertainties are discussedinsection5.7...... 77

5.14 p + p invariant yield as a function of pT , taken from reference [1]...... 80

5.15 p2 as a function of N . Systematic errors are described in section 5.7 ...... 81 h T i part 5.16 Summary of systematic uncertainties...... 83

ix LIST OF FIGURES

2.1 Strong coupling constant α as a function of energy scale, Q [2]...... 3

2.2 QCD phase diagram...... 4

2.3 v2 measured for hadrons as a function of pT (a) and transverse kinetic energy (b) as measuredbyPHENIX[3]...... 6

2.4 v2/number of constituent quarks (nq) as a function of pT (a) and transverse kinetic energy (b) as measured by PHENIX [3]...... 7

2.5 Two-particle angular correlations for p + p, d+Au and Au+Au collisions at √sNN = 200 GeV/c2 measuredbySTAR[4]...... 8

2.6 pT dependence of v2-v5 from [5]. The curves are theoretical predictions from [6], with the left plot using ideal hydrodynamics and the two right plots using viscous hydrodynamics with diﬀerent values of η/s...... 8

2 2.7 Particle ratios from central Au+Au collisions at √sNN = 200 GeV/c for BRAHMS (pluses) [7], PHENIX (triangles) [8], PHOBOS (circles) [9] and STAR (stars) [10–13]. The horizontal lines are theoretical predictions and their uncertainties from [14]. . . . 10

2.8 Schematic showing charmonia bound states which are stable under strong decays. Highlighted in red are the charmonia vector mesons...... 12

3.1 J/ψ RdAu as a function of pT from 2008 PHENIX data. The vertical bars are statistical uncertainties and the boxes represent correlated systematic uncertainties...... 18

′ 3.2 RdAu vs centrality for J/ψ and ψ data [15]...... 19

3.3 J/ψ RdAu for backward, mid and forward rapidities, integrated over all Ncoll and pT . The green dashed line represents a CGC calculation...... 20

3.4 J/ψ RpPb vs pT for midrapidity at ALICE. Also shown are the results from models with a pure shadowing calculation [16], a CGC calculation [17] and an energy loss calculation [18] with and without a shadowing correction...... 21

2 3.5 Ratio of J/ψ cross section to that from Drell-Yan measured at √sNN = 17 GeV/c by the NA50 collaboration [19]...... 22

3.6 Ratio of measured J/ψ yield to the expected J/ψ yield, resulting in a suppression pattern for In+In (circles) and Pb+Pb (triangles) after CNM extraction...... 23

3.7 J/ψ RAA vs Npart at 200 GeV for both the PHENIX central (blue) and forward arms (red)...... 24

x 3.8 J/ψ RAA vs Npart at 39 (blue), 62 (red) and 200 (black) GeV for forward rapidity. . . 25

3.9 Cu+Au J/ψ RAA at 200 GeV for the PHENIX forward arms...... 25

3.10 U+U J/ψ RAA at 193 GeV for the PHENIX forward arms...... 26

3.11 J/ψ RPbPb at 2.76 TeV for ALICE forward (red) and mid (blue) rapidities...... 27

3.12 CNM-removed J/ψ RAA for both RHIC (red, √sNN = 200 GeV) and SPS (green and blue, √sNN = 17.3 GeV)...... 28

3.13 Theory curves applied to PHENIX 200 GeV midrapidity data, with strong-binding (left)andweak-binding(right)...... 29

3.14 Theory curves applied to ALICE 2.76 TeV forward rapidity Pb+Pb data. The blue curve is for a charm cross section of 0.5 mb per unit rapidity, while the red curve is for a charm cross section of 0.33 mb per unit rapidity...... 29

3.15 RAA estimated for CNM eﬀects using an EKS98 shadowing parametrization. The red points are midrapidity and the blue points are forward rapidity...... 30

3.16 Survival probability vs Npart for Run-10 midrapidity data (red) and predictions. The black curve is the total prediction, the blue dashed curve is the primordial J/ψ component and the pink dotted curve is the component from feed-down...... 30

3.17 Total survival probability vs Npart for diﬀerent melting temperatures plotted with the survival probability calculated for the 2004 midrapidity data...... 31

3.18 Total survival probability vs Npart. Top left to bottom right show the survival probabilities for varying α, a parameter which indicates the thermal width of the J/ψ. . . 32

4.1 PHENIX Central Arm detector conﬁguration in 2010...... 34

4.2 AsingleDCframe...... 35

4.3 A schematic showing how α and φ are obtained...... 37

4.4 PixellayoutinPC1...... 38

4.5 Schematic of a single RICH arm ...... 39

4.6 Schematic showing a single PbSc calorimeter ...... 40

4.7 Left panel: The entire HBD. Right panel: An exploded view of one HBD arm. . . . . 42

5.1 Cross section of the DC to show what is meant by φ and α...... 47

5.2 DC α vs φ for all runs together...... 48

5.3 Pc1y vs pc1z for all runs together...... 49

xi 5.4 RICH cross φ and cross z for all runs together...... 50

5.5 RICH cross φ and cross z for a bad run...... 51

5.6 EMCal y and z hit positions for all runs...... 52

5.7 Hit distribution in the φ z plane for all runs in the HBD...... 54 − 5.8 Comparison of the normalized background (red) with the foreground (blue) shown on alogscale...... 55

5.9 J/ψ invariant mass spectrum integrated over all centrality and pT ...... 56

5.10 Best ﬁt of foreground for centrality dependence for the ﬁve most central bins...... 58

5.11 Best ﬁt of foreground for centrality dependence for the four most peripheral bins, plus theminimumbiascase...... 59

5.12 Best ﬁt plotted on the mixed-event subtracted spectra for centrality dependence for theﬁvemostcentralbins...... 61

5.13 Best ﬁt plotted on the mixed-event subtracted spectra for centrality dependence for the four most peripheral bins, plus the minimum bias case...... 62

5.14 Best ﬁt plotted on the mixed-event subtracted spectra for the pT -dependence for the 0-20% centrality bin. The pT binning from top left to bottom right goes 0-1, 1-2, 2-3, 3-4, 4-5 and 5-7 GeV/c. The blue curve is the CB + exponential ﬁt and the green curveistheexponentialalone...... 65

5.15 Best ﬁt plotted on the mixed-event subtracted spectra for the pT -dependence for the 20-40% centrality bin.The pT binning from top left to bottom right goes 0-1, 1-2, 2-3, 3-4, 4-5 and 5-7 GeV/c. The blue curve is the CB + exponential ﬁt and the green curveistheexponentialalone...... 66

5.16 Best ﬁt plotted on the mixed-event subtracted spectra for the pT -dependence for the 40-60% centrality bin. The pT binning from top left to bottom right goes 0-1, 1-2, 2-3, 3-4, 4-5 and 5-7 GeV/c. The blue curve is the CB + exponential ﬁt and the green curveistheexponentialalone...... 67

5.17 Best ﬁt plotted on the mixed-event subtracted spectra for the pT -dependence for the 60-92% centrality bin. The pT binning from top left to bottom right goes 0-1, 1-2, 2-3, 3-4 and 4-5 GeV/c. The blue curve is the CB + exponential ﬁt and the green curveistheexponentialalone...... 68

5.18 J/ψ internal radiative tail line shape from [20]...... 70

5.19 Reconstructed J/ψ spectrum (top) as compared with the simulated J/ψ spectrum (bottom)...... 71

xii 5.20 Comparison of α vs φ for data (left) and simulations (right) for the ﬁrst and largest rungroup...... 72

5.21 Comparison of pc1 y vs pc1 z for data (left) and simulations (right) for the ﬁrst and largest run group...... 73

5.22 DC phi distributions for simulations (red) and data (blue) in each DC sector (top to bottom) for each α (left to right) for run group 0...... 76

5.23 J/ψ acceptance as a function of pT for each centrality bin for run group 0...... 78

5.24 J/ψ acceptance as a function of pT for each of the six run groups all for the 0-5% centralitybin...... 79

5.25 BdN/dy as a function of N integrated over p . The boxes are systematic uncer- h parti T tainties,describedinsection5.7...... 80

5.26 BdN/dy/ N as a function of N integrated over p . The boxes are systematic h colli h parti T uncertainties,describedinsection5.7...... 81

5.27 Uncorrected 1 Bd2N/dydp as a function of p in four centrality bins. The global 2πpT T T uncertainty in each centrality is listed as a percentage in the legend. The boxes are systematic uncertainties, described in section 5.7...... 82

2 5.28 Corrected B d N vs p for Run-10 and Run-4 data. The Run-4 data are shifted to dydpT T the right by 0.2 GeV/c for ease of comparison. The boxes are systematic uncertainties, describedinsection5.7...... 84

2 5.29 Corrected B d N vs p for Run-10 and Run-4 data. The Run-4 data are shifted to dydpT T the right by 0.2 GeV/c for ease of comparison. The boxes are systematic uncertainties, describedinsection5.7...... 85

5.30 Comparison of Run-10 (blue) and Run-4 (red) pT -integrated RAA as a function of Npart. The boxes are systematic uncertainties, described in section 5.7...... 86

5.31 Comparison of Run-10 (blue) and Run-4 (red) RAA as a function of pT in four centrality bins. The boxes are systematic uncertainties, described in section 5.7...... 87

5.32 p2 as a function of N ...... 87 h T i part

6.1 Comparison of PHENIX midrapidity RAA vs Npart (blue) with PHENIX forward data(red)...... 88

6.2 Comparison of PHENIX Au+Au RAA vs Npart (red) with PHENIX Cu+Cu data(blue). 89

6.3 Comparison of PHENIX (red) Au+Au data and STAR (blue), both at 200 GeV. . . . 90

6.4 Comparison of PHENIX (red) 200 GeV Au+Au data and ALICE (blue) 2.76 TeV Pb+Pbdata...... 91

xiii 6.5 Comparison of PHENIX (blue) 200 GeV Au+Au data with theory curves from [21], where the diﬀerence between each theory curve is the value of α used represents the strength of the thermal decay width of the J/ψ...... 92

6.6 R vs N for Rapp’s strong binding scenario...... 93 AA h parti 6.7 R vs N for Rapp’s weak binding scenario...... 94 AA h parti 6.8 R vs N for a calculation done by Capella, et al...... 94 AA h parti 2 6.9 B d N vs p with calculation by Xu, et al. from [22]...... 95 dydpT T

6.10 RAA vs pT for calculation done by Xu, et al...... 95

6.11 RAA vs pT for Rapp’s strong binding scenario...... 96

6.12 RAA vs pT for Rapp’s weak binding scenario...... 96

6.13 p2 vs N for Rapp’s strong binding scenario...... 97 h T i part 6.14 p2 vs N for Rapp’s weak binding scenario...... 97 h T i part A.1 DC α vs φ for all runs in run group 0...... 100

A.2 DC α vs φ for all runs in run group 1...... 101

A.3 DC α vs φ for all runs in run group 2...... 101

A.4 DC α vs φ for all runs in run group 3...... 102

A.5 DC α vs φ for all runs in run group 4...... 102

A.6 DC α vs φ for all runs in run group 5...... 103

B.1 DC φ comparison of data (blue) and simulations (red) for run group 1...... 104

B.2 DC φ comparison of data (blue) and simulations (red) for run group 2...... 105

B.3 DC φ comparison of data (blue) and simulations (red) for run group 3...... 105

B.4 DC φ comparison of data (blue) and simulations (red) for run group 4...... 106

B.5 DC φ comparison of data (blue) and simulations (red) for run group 5...... 106

C.1 Acceptance for all centralities for run group 1...... 107

C.2 Acceptance for all centralities for run group 2...... 108

C.3 Acceptance for all centralities for run group 3...... 108

C.4 Acceptance for all centralities for run group 4...... 109

xiv C.5 Acceptance for all centralities for run group 5...... 109

C.6 Acceptance for 5-10% centrality class for all run groups...... 110

C.7 Acceptance for 10-15% centrality class for all run groups...... 110

C.8 Acceptance for 15-20% centrality class for all run groups...... 111

C.9 Acceptance for 20-30% centrality class for all run groups...... 111

C.10 Acceptance for 30-40% centrality class for all run groups...... 112

C.11 Acceptance for 40-50% centrality class for all run groups...... 112

C.12 Acceptance for 50-60% centrality class for all run groups...... 113

C.13 Acceptance for 60-92% centrality class for all run groups...... 113

xv LIST OF ABBREVIATIONS

RHIC - Relativistic Heavy Ion Collider PHENIX - Pioneering High Energy Nuclear Interactions eXperiment BNL - Brookhaven National Laboratory QGP - Quark Gluon Plasma HNM - Hot Nuclear Matter CNM - Cold Nuclear Matter SPS - Superconducting Proton Synchrotron CERN - European Organization for Nuclear Research LHC - Large Hadron Collider ALICE - A Large Ion Collider Experiment DC - Drift Chamber PC - Pad Chamber EMCal - Electromagnetic Calorimeter RICH - Ring Imaging CHerenkov Detector HBD - Hadron Blind Detector QCD - Quantum Chromodynamics QED - Quantum Electrodynamics CA - Central Arms PMT - Photomultiplier Tube ME - Mixed Event

xvi ABSTRACT

It has been believed for over 30 years that matter will become a deconfined state of quarks and gluons at sufficiently high energy densities. As the energy density increases, deconfinement occurs due to Debye screening of the color charges, which disrupts the binding of mesons and baryons. The expected deconfinement transition to the quark-gluon plasma (QGP) has been observed using collisions of heavy ions to create high energy densities, first at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory, and more recently at the Large Hadron Collider (LHC) at the European Organization for Nuclear Research (CERN). The degree to which the binding of a hadron in the plasma is disrupted depends on the hadron’s radius. Because deconfinement is caused by Debye screening, and the screening length is determined by energy density, small tightly bound heavy quark mesons (referred to as quarkonia) may become deconfined at a higher energy density than the light quark hadrons. Thus, measuring quarkonia production may provide a way to determine the screening length in the QGP, and a program of measurements of modification of charmonium and bottomonium states in heavy ion collisions has been carried out at several accelerators over the last two decades. As part of this effort, measurements of J/ψ production in Au+Au collisions have been made by the PHENIX experiment at RHIC, the subject of this thesis. Specifically, J/ψ e+e− data → from center of mass energy per nucleon (√sNN ) = 200 GeV Au+Au collisions were recorded in 2004, providing the first major quarkonia result from PHENIX. A higher statistics measurement was performed in 2007, but a non-functioning detector subsystem in the PHENIX central arms rendered the data unusable. A still larger data set was recorded in 2010, this time with the previously non-functioning detector system working. It is these 2010 data that are the focus of the present analysis. The 2010 dataset contains about five times as many measured J/ψ as the 2004 dataset. However the increase in signal is accompanied by a large increase in background electrons, which introduces difficulties not present in the 2004 analysis. The goal of this analysis was to improve on the result from the 2004 measurement.

xvii CHAPTER 1

OVERVIEW

The goal of this analysis is to improve upon an existing Au+Au J/ψ e+e− result produced from → data recorded in 2004. This analysis uses a data set recorded in 2010. The analysis described here is substantially different from the earlier one because of the presence of a new detector system, the Hadron Blind Detector (HBD), which was introduced into PHENIX to facilitate another measurement. The HBD adds a large background of electrons due to conversions of π0 decay photons within it, as well as adding a large radiative tail to the J/ψ invariant mass peak. Use of the HBD detector in the analysis eliminates some, but not all, of the large background. However, the 2010 experiment provided five times as much J/ψ signal as the 2004 experiment, and it was hoped that this would be enough to more than offset the negative effects due to the presence of the HBD. This dissertation is organized as follows. Chapter 2 provides the motivation for the analysis, focusing on the quark-gluon plasma and its relationship with charmonium production. Chapter 3 discusses cold and hot nuclear matter effects on J/ψ production and highlights some of the previous measurements of these effects. Chapter 4 details the PHENIX experiment and describes the relevant detector subsystems. Chapter 5 discusses the analysis of the data from start to finish. Chapter 6 shows a comparison of the data from this analysis with those from other analyses, as well as with theoretical predictions. Chapter 7 presents final conclusions and outlook based on the final results.

1 CHAPTER 2

MOTIVATION

2.1 Relevant Aspects of QCD

Quantum chromodynamics (QCD) is the theory of the strong interaction. Like any other Standard Model interaction, it has a force-mediating particle, which is the massless gluon. The fundamental particles which interact via gluon exchange are fermions called quarks, of which there are six ﬂavors: down, up, strange, charm, bottom and top. Like leptons, quarks have electric charge, and thus they can interact electromagnetically, described by quantum electrodynamics (QED). However, they also carry color charge, a property unique to quarks and gluons. Possible color options are red, blue and green. Each color has its own corresponding anti-color, e.g. blue and anti-blue. Quarks can arrange themselves in bound states consisting of either two (mesons) or three (baryons) quarks. The Standard Model also predicts bound states which consist of more than three quarks, namely tetraquarks and pentaquarks. These bound states must have no net color charge, i.e. they must be color neutral, carrying both color and anti-color.

2.1.1 Conﬁnement

Absent from the list of possible quark combinations is not a combination at all: it is a single quark. This is because under normal circumstances (to be defined shortly) a quark cannot exist on its own. Likewise, a gluon cannot exist on its own. Unlike the case of electromagnetism, where the force-carrying particle, the photon, does not carry electromagnetic charge, the gluon carries color charge. It carries both color and anti-color, and the possible gluon states are referred to as a color- octet state, since there are eight possible states. The gluon can interact with itself (a phenomenon completely absent from electromagnetism), from which there are two crucial consequences: asymptotic freedom and confinement. In short, confinement means that as quarks in a bound state are pulled farther apart from each other, the force between them gets stronger. Asymptotic freedom means that as two quarks in a bound state get closer to each other, the force between them weakens.

2 This is quite the opposite from electromagnetism, where the closer two charged particles are, the stronger the force between them. Although both of these effects can be summarized in a single statement, the origin of each effect is unique. If two quarks are pulled apart so the force between them increases, it eventually becomes more energetically favorable to pop two more quarks out of the vacuum, making two color neutral mesons. This is confinement. Asymptotic freedom has a different origin. The bare quark color charge is screened by qq¯ pairs in the vacuum, similar to electric charge screening in QED. If one probes closer to a quark, the vacuum charge screening effect decreases, as in QED. However, since the gluon interacts with itself, it creates an anti-screening effect that is much stronger than the screening effect from vacuum quark pairs. It is this anti-screening that results in asymptotic freedom. This effect is shown in figure 2.1 which shows the running of the strong coupling constant,

αS, as a function of the energy scale, Q. It takes more energy to probe closer to the quark, and

Figure 2.1: Strong coupling constant α as a function of energy scale, Q [2]. thus larger Q values are necessary to do this. Additionally, perturbative calculations can be done if one makes the approximation that the quarks move freely, which is the case for low αs, and thus applies when the energy transfer between quarks is large.

3 2.1.2 Quark Gluon Plasma

It is predicted that in normal nuclear matter at high energy densities the constituent quarks and gluons will not exist as mesons and baryons, but as a free-ﬂowing soup of quarks and gluons. This state of matter was termed “quark-gluon-plasma” (QGP) in 1980 [23], since it was thought of as a gas of charged particles. Although an interesting target of study in its own right, it should also be noted that the universe was believed to have been in this state a microsecond after the Big Bang. Study of this phase of matter could tell us more about the development of the early universe. Our current understanding of the QGP and its place on the QCD phase diagram is shown in ﬁgure 2.2.

Temperature, T , is on the vertical axis and baryon chemical potential, µB, a measure of the net

Figure 2.2: QCD phase diagram. baryon density, is on the horizontal axis. This diagram is still largely theoretical, although it is believed that the transition from normal nuclear matter to a QGP is a ﬁrst-order transition at higher baryon chemical potential. At low baryon chemical potential, it is predicted that there is a crossover to a QGP, but the nature of this transition is not well known. However, lattice gauge calculations have been done for µB = 0, where a transition from normal nuclear matter to a QGP is predicted to occur around T 170 MeV [24]. ≈

4 2.2 Relativistic Heavy Ion Collisions

Relativistic heavy ion collisions are those in which a heavy element (e.g. Au, Cu, Pb) is stripped of its electrons and smashed into another heavy ion at high speed. The hallmark of heavy- ion collisions (HIC) is the large amount of energy deposited in a small space, corresponding to an energy density much greater than the approximately 1 GeV/fm3 that lattice QCD calculations predict is the minimum needed to form the QGP [24]. HIC allow us to explore the QCD phase diagram. As illustrated in ﬁgure 2.2, as collisions reach higher and higher energy, points on the diagram which are higher in temperature and lower in net baryon density are reached. There are diﬀerent ways to study the hot, dense matter created at RHIC [25, 26]. Although the focus of this work is the study of charmonium production in HIC, a short summary of results suggesting the existence of a QGP from the RHIC will be presented.

2.2.1 Elliptic Flow and Quark Scaling

When two Au nuclei collide, the overlap region has the highest probability of being almond- shaped. Due to the asymmetric pressure gradient resulting from this shape, the particle production relative to the reaction plane of the two colliding Au nuclei shows anisotropy: diﬀerent values depending on the direction of motion. This eﬀect is parametrized via the number of particles at a given transverse momentum pT and azimuthal angle φ as

2 d N N0 = (1 + 2v (p ) cos[n(φ Φ )]), (2.1) dφdp 2π n T − n T n X where Φn is the event plane angle and vn are the Fourier coefficients. The second Fourier coefficient, v2 measures the elliptic flow.

PHENIX measured v2 as a function of pT and transverse kinetic energy, KET , for hadrons [3], and this is shown in figure 2.3. The left plot of figure 2.3 shows v2 as a function of pT . The right plot of the figure shows v2 as a function of KET , which includes the effects of relativity. In this plot, the baryons all fall on a single curve and the mesons all fall on a different common curve.

Figure 2.4 shows in the left hand panel a plot of v2 divided by the number of constituent quarks, nq, (2 for mesons, 3 for baryons), plotted as a function of pT divided by nq. This removes the distinct diﬀerence between mesons and baryons, but there remains a mass ordering of the curves.

The right hand panel of ﬁgure 2.4 shows v2 divided by the number of constituent quarks versus

5 Figure 2.3: v2 measured for hadrons as a function of pT (a) and transverse kinetic energy (b) as measured by PHENIX [3].

KET divided by nq. There is now scaling for all particles over the entire KET range, suggesting that the particle ﬂow is not hadronic, but partonic, as would be expected for a QGP.

2.2.2 Jet Suppression in Au+Au Collisions

Jets are the result of a partonic interaction that produces two high-pT particles which subsequently fragment into a hadronic shower. The existence of jets has been shown by looking at angular correlations between the trigger particle (pTtrig > 4.0 GeV/c) and all associated particles in the same event with 2.0 GeV/c

6 Figure 2.4: v2/number of constituent quarks (nq) as a function of pT (a) and transverse kinetic energy (b) as measured by PHENIX [3]. in the QGP, losing so much energy that the hadrons produced by its fragmentation fall below the momentum threshold for the associated particle. The strength of the coupling of these high momentum jet partons to the QGP was unexpected, and is presently the subject of a large experimental and theoretical eﬀort using RHIC and LHC data.

2.2.3 Small η/s and Near-Perfect Fluidity

It had been thought that since αs is small at RHIC energies, the medium would be weakly coupled. But the large values of v2 discussed in section 2.2.1 indicated a strongly coupled medium. This has been quantified using hydrodynamical models, which require very small values of the shear viscosity to entropy ratio, η/s, to describe the collective flow at RHIC and the LHC. A small value of η/s is indicative of a medium exhibiting near-perfect fluidity.

In addition to the elliptic ﬂow parameter, v2, one can also extract asymmetry parameters from data due to ﬂuctuations in the initial energy distribution due to the ”lumpiness” of the nucleon distributions in the colliding nuclei. These lead to terms in equation 2.1 with values of n = 3, 4,

5, etc. The simultaneous description of v2, v3, v4 and v5 has been used to constrain the value of η/s used in hydrodynamical models. One study which includes models and experimental data [30]

7 Figure 2.5: Two-particle angular correlations for p + p, d+Au and Au+Au collisions at 2 √sNN = 200 GeV/c measured by STAR [4]. predicts a value η = 0.1 0.1(theory) 0.08(experiment). (2.2) s ± ±

Figure 2.6 shows the pT dependence of v2, v3, v4 and v5 from [5]. All three plots show the same data, but each has a diﬀerent theoretical prediction from [6] based on a diﬀerent value of η/s. They use ideal hydrodynamics (η/s = 0, left), and viscous hydrodynamics (η/s = 0.08, middle, η/s = 0.16, right. The best description of the data is provided by η/s = 0.08.

Figure 2.6: pT dependence of v2-v5 from [5]. The curves are theoretical predictions from [6], with the left plot using ideal hydrodynamics and the two right plots using viscous hydrodynamics with diﬀerent values of η/s.

8 2.2.4 Chemical Equilibrium

If a QGP is created in collisions at RHIC, then the hot matter will cool below the deconﬁnement temperature, Tc. As it cools further, it will eventually reach a temperature after which no more particles will be created. The temperature at which this happens is the chemical freeze-out temperature, Tch. An extraction of that temperature can give a lower bound to Tc, which necessarily must be higher than Tch. Statistical model approaches are used to predict particle ratios. The inputs to the model are

Tch, the chemical potential, µ, and the strangeness saturation, γs, where γs = 1 corresponds to strangeness being in equilibrium. Figure 2.7 shows particle ratios for diﬀerent species, with results from PHENIX (triangles) [8], STAR (stars) [10–13], BRAHMS (pluses) [7] and PHOBOS (circles) [9]. A prediction from a thermal model in [14] is shown by the horizontal bars with the uncertainties represented by yellow bands. The data are well described by the thermal model with parameters of T = 157 3 MeV, µ = ch ± 23 3 MeV and γ = 1.03 0.04. The 157 MeV value for T is consistent with the result from ± s ± ch LQCD that the deconﬁnement temperature, Tc, is predicted to be roughly 170 MeV.

2.2.5 Hard Probes

The success of hydrodynamical models in their description of the bulk properties of the QGP, and thermal models in their description of the particle ratios formed at chemical freezeout, is striking. However while studies of the matter formed after hadronization of the QGP have shown that the QGP is very strongly coupled, they do not provide information about the mechanism of that strong coupling. For that, we turn to interactions of hard probes with the medium. Hard probes are created in hard QCD processes during the crossing of the colliding nuclei, and include jets and heavy quarks (charm and bottom). The study of jet energy loss (including that of heavy quark jets) can be used to try to understand the details of the interaction between an energetic probe that carries color charge and the medium. As mentioned earlier, there is currently a large theoretical and experimental eﬀort encompassing both the RHIC and LHC programs to understand jet modiﬁcation in nuclear collisions.

9 2 Figure 2.7: Particle ratios from central Au+Au collisions at √sNN = 200 GeV/c for BRAHMS (pluses) [7], PHENIX (triangles) [8], PHOBOS (circles) [9] and STAR (stars) [10–13]. The horizontal lines are theoretical predictions and their uncertainties from [14].

The modiﬁcation of the production of heavy quark mesons (charmonium and bottomonium) provides a diﬀerent, but also direct, means to study the medium, since it is sensitive to the strength of the color Debye screening in the QGP. In this thesis, the focus is on the use of charmonium production as a probe of the strength of the color Debye screening in the QGP.

2.3 Charmonium in Nuclear Collisions

Charmonium refers to the family of mesons consisting of charm and anti-charm quarks. The J/ψ meson is the lowest energy vector meson1 in the charmonium family and was discovered independently in 1974 by two groups, one at BNL [31] headed by Samuel Ting and one at SLAC [32] headed by Burton Richter. Its discovery was part of a series of exciting high energy physics events occurring during a timeframe known as the November Revolution. Up to that point, only the up, down, and strange quarks had been observed experimentally. The J/ψ discovery proved the

1 PC −+ The ηc(1S) has a lower mass than the J/ψ, but its quantum numbers J = 0 prohibit it from decaying to dielectrons.

10 existence of the fourth quark ﬂavor, the charm quark. However, this was only the initial step in discoveries involving charm–anti-charm pairs, as many diﬀerent states were subsequently discovered. Unlike the proton, whose mass is largely made up from the binding energy of its three constituent quarks, the J/ψ mass largely comes from the rest mass of the two charm quarks. This allows a non-relativistic potential model to be employed for predicting states in the charmonia family. The potential, called the Cornell potential [33, 34], contains two terms and can be written as

α V (r)= σr , (2.3) − r where r is the separation of the quark anti-quark pair, α = π/12, and √σ = 0.445 GeV. The ﬁrst term is a linear term, which models the conﬁnement of the two quarks. The second term is a Coulomb-like term, which describes the interaction between two charged particles. This model has been successful in predicting the masses of charmonia states to within 1% [35] of the experimentally observed masses. The J/ψ has a binding radius of 0.50 fm, compared with the 0.58 and 0.80 fm binding radii of the kaon [36] and pion [37], respectively.

Charmonia states can be characterized by a series of quantum numbers, namely nr, the radial quantum number, and L, S, and J, the orbital, spin, and total angular momenta, respectively. 2S+1 These quantum numbers are grouped to have the form (nr + 1) LJ . A diagram of charmonia states which are stable under strong decays, i.e. those which have a mass below the DD¯ threshold, is shown in figure 2.3. A D-meson is the lightest meson containing a single charm quark, and if the cc¯ pair has a mass of twice the D-meson mass, it will decay via the weak interaction into a DD¯ pair. In addition to those quantum numbers, the J/ψ also has negative parity and negative charge conjugation, for a J PC of 1−−. This is significant for two reasons. The first is that these quantum numbers allow for dilepton decay, as they are the same quantum numbers as a photon has. Thus, the J/ψ can decay to a virtual photon, which then turns into a dilepton pair. Secondly, the OZI rule [38], which is a consequence of QCD explaining why certain decay modes appear more or less frequently than others, suppresses the hadronic decay channels of the J/ψ, which gives rise to an increased branching ratio to dileptons ( 6% for both dielectrons and dimuons) [38]. The OZI rule ∼ also gives the J/ψ its characteristically narrow width of 92.9 2.8 keV [38]. ±

11 Figure 2.8: Schematic showing charmonia bound states which are stable under strong decays. Highlighted in red are the charmonia vector mesons.

2.3.1 Time Scales

In addition to having a large branching ratio for dilepton decays, because of its large mass, charm is not produced by thermal processes in the QGP. Therefore it is produced only in the initial collision, before any hot, dense matter is created. This allows us to start with a ﬁxed population of charm quarks. The unit used for discussing time scales is fm/c, where 1 fm/c = 3.33 10−24 × s. A cc¯ pair forms in around 0.07 fm/c, shorter than the time for the two nuclei to pass through each other, around 0.13 fm/c. For the cc¯ to expand into a fully formed J/ψ takes on the order of 0.25 fm/c. The QGP formation time (thermalization time) is about 0.7 fm/c [25], and lasts about 7 fm/c [25]. The lifetime of the J/ψ is on the order of 2000 fm/c, which means there is no chance that it can decay before the QGP hadronizes and the hadrons stop interacting, and it is formed well before the QGP is thermalized. Therefore charmonia formed in heavy ion collisions experience the entire evolution of the QGP.

2.4 What Can We Learn from Charmonium?

To summarize, the J/ψ is a promising probe of the QGP because a) it has a large branching ratio to easily detectable dilepton decays, b) the initial population of charm quarks is ﬁxed since heavy quarks cannot be produced thermally after the initial collision, and c) it lives much longer than the

12 QGP. Because the J/ψ is tightly bound, it has a small radius. Therefore the J/ψ is not expected to become unbound due to color charge screening until the temperature significantly exceeds the temperature at which light quark hadrons become deconfined. Observation of the modification of J/ψ production in HIC relative to proton-proton collisions therefore should be sensitive to the temperature evolution of the QGP as it expands and cools.

2.5 Motivation for this Analysis

There have been results from data taken at the Super Proton Synchrotron (SPS) (17.3 GeV), RHIC (200 GeV max) and the Large Hadron Collider (2.7 and 5.1 TeV/nucleon). All of these energies are per nucleon in the center of mass of the nuclear collision. For Au+Au collisions, dimuon measurements at PHENIX were made in 2004 and 2007. For the 2007 measurement, the luminosity was high enough that the result was limited by the systematic uncertainties. Therefore a dimuon analysis of the 2010 data was not done. A dielectron measurement was made by PHENIX in 2004, but no measurement was possible in 2007 due to the introduction of the HBD detector, which did not function during the run due to high voltage problems. The HBD was fully functional in 2010, but there was a huge background due to the mass of the HBD. This makes the analysis challenging, but it is needed due to the 2004 dielectron measurement being limited by statistical precision. Before discussing the details of the analysis of the 2010 data, previous measurements will be presented in the following chapter.

13 CHAPTER 3

CHARMONIUM IN NUCLEAR COLLISIONS

3.1 Observables

The physics quantities to be extracted from this analysis are the invariant yield, the nuclear modiﬁcation factor, R , and p2 . The R is measured as a function of transverse momentum AA h T i AA (p ), rapidity, and the number of nucleon participants (N ). The p2 is measured as a function T part h T i of Npart.

The mean value of Npart corresponds to a centrality class, where centrality is a percentage range of collisions with similar impact parameter. More head-on collisions are said to be “central”, while off-center collisions are said to be “peripheral”. The percentage range for central collisions is lower than for peripheral collisions, i.e. the 0-5% centrality class is more central and corresponds to a higher value of Npart, while the 50-60% centrality class is more peripheral and corresponds to a smaller value of Npart. The centrality determination is discussed in more detail in section 5.1. Rapidity, y, is defined as 1 E + p c y = ln z , (3.1) 2 E p c − z where pz is the momentum in the z-direction, E is the total energy and c is the speed of light in vacuum. Rapidity is the relativistic velocity in the beam direction, and is related to the polar angle, θ, with the beam-going axis defining the line connecting θ = 0◦ and θ = 180◦. Rapidity = 0 corresponds to θ = 90◦. Because some details of the physics are different depending on the rapidity, it has been common for experiments to consider separately the results obtained at midrapidity and those at forward/backward rapidity. The actual rapidity ranges vary depending on the detector. At PHENIX, midrapidity corresponds to y < 0.35 and forward rapidity corresponds to 1.2 < y < | | | | 2.2. For practical reasons, charmonium measurements made at midrapidity typically use dielectron decays, while those made at forward rapidity measure dimuon decays. Related to rapidity is the pseudorapidity, η, defined as θ η = ln tan , (3.2) − 2

14 which is directly related to the polar angle, θ. η = 0 corresponds to θ = 90◦ and as θ approaches 0, η approaches inﬁnity. In the massless limit, where particles are traveling at the speed of light, rapidity reduces to pseudorapidity.

The pT -integrated invariant yield in a given centrality class is given as a function of rapidity by eq. 3.3 dN NJ/ψ B = , (3.3) dy ∆y∆c∆pT Nevtǫtot where B is the branching ratio to dielectrons, NJ/ψ is the number of measured J/ψ’s in that centrality bin, ∆c is the width of the centrality bin, ∆y is the width of the rapidity bin, ǫtot is the total eﬃciency and Nevt is the number of events. In a given pT and centrality bin, the invariant yield can be calculated as

2 1 d N 1 NJ/ψ B = , (3.4) 2πpT dydpT 2πpT ∆y∆c∆pT Nevtǫtot where the quantities repeated from eq 3.3 still represent the same thing except for NJ/ψ, which now represents the number of measured J/ψ’s in that centrality and pT bin, ∆pT is the width of the pT bin and pT is the transverse momentum. RAA in a given centrality and pT bin, shown in eq 3.5, d2N Au+Au(i)/dydp 1 NJ/ψ T RAA(i)= 2 p+p (3.5) Ncoll (i) d N /dydpT h i NJ/ψ is the ratio of the invariant J/ψ yield in Au+Au collisions to that in p + p collisions, scaled by the average number of binary nucleon-nucleon collisions, Ncoll, which is obtained from a Glauber

Monte Carlo simulation of colliding nuclei [39]. This tells us that for an RAA = 1, charmonium production in a Au + Au collision is identical to that from a series of independent p + p collisions. The p2 is calculated as h T i N p2 dNi p ∆p 2 i=0 Ti dpT Ti Ti max pT pT p = . (3.6) h i| ≤ T N dNi p ∆p P i=0 dpT Ti Ti

This quantiﬁes the eﬀect of the broadening of thePpT spectrum.

3.2 Brief Overview of J/ψ Measurements

Charmonium measurements have been made at the SPS, RHIC and LHC, and span a large range of collision energies. Collision species are divided into three types:

15 Two small targets — Usually proton+proton (p + p) collisions used to separate the eﬀects • of a hot, dense medium and the eﬀects of a nuclear target. These experiments are used as a baseline in charmonium studies.

Small and large target — A small target (e.g. proton, deuteron) and a large target (e.g. • Au, Cu, Pb) used to study the eﬀects of a nuclear target, where the eﬀects of a hot, dense medium are assumed to be negligible.

Two large targets — Two large nuclei, not necessarily identical, used to study the eﬀects • of a hot dense medium. The eﬀects of a nuclear target are still present in these collisions.

Experiments at the SPS, RHIC and LHC have made J/ψ measurements in all of these collision- types for diﬀerent energies are listed here. All energies listed are √sNN energies.

SPS — 20 GeV S+U [40], 17.3 GeV Pb+Pb [19], 17 GeV In+In [41] • RHIC — 200 GeV p + p [1], 200 GeV d+Au [42], 39 GeV Au+Au [43], 62 GeV Au+Au [43], • 200 GeV Au+Au [44], 200 GeV Cu+Cu [45], 200 GeV Cu+Au [46], 200 GeV U+U [47]

LHC — 7 TeV p + p [48], 5.02 TeV p+Pb [49], 2.76 TeV Pb+Pb [50] •

3.3 Cold Nuclear Matter Eﬀects

Matsui and Satz predicted in 1986 that J/ψ suppression after a heavy ion collision would be evidence for the formation of a QGP [51]. This idea is based on the prediction that the J/ψ would become unbound when subjected to intense color (Debye) screening coming from the free quarks and gluons which exist in a QGP. Once the J/ψ binding radius exceeded the screening radius of the color field, the J/ψ would no longer be bound. Although this has been shown to be an oversimplified picture which does not include many of the other effects on J/ψ production, it motivated many heavy ion experiments where quarkonia suppression was observed. Effects on charmonium production are typically divided into two categories: cold nuclear matter (CNM) effects and hot nuclear matter (HNM) effects. CNM effects are those which occur due to the presence of a nuclear target in a heavy ion collision (HIC) and are independent of the presence of any hot, dense medium produced in such a collision. These effects are studied using a collision system consisting of a large nucleus (Au, Cu, Pb) and a small nucleus (p, d). It has long been assumed that these collisions do not create an energy density high enough for a transition to a QGP, so CNM effects can be isolated from HNM effects in this

16 way. CNM effects will be discussed only briefly here, as they are not the focus of my research. It should be noted that while CNM effects are still present in HIC, their extraction is not the goal of my analysis.

Nuclear shadowing — Nuclear shadowing describes the modiﬁcation of parton distribution • functions (PDFs) in a nucleus [52, 53]. The most commonly used parametrization of these eﬀects is EPS09 [54].

Gluon saturation — At high energies, gluon densities become so high that they overlap • and cannot be resolved individually [55]. Color-glass condensate (CGC) is an eﬀective theory used to describe the gluon behavior in this energy regime [56, 57].

Cronin Eﬀect — Elastic scattering of an incoming parton before a hard process causes the • pT distribution to be modiﬁed relative to p + p collisions [58].

Radiative Energy Loss — Gluons are exchanged with the medium in both the initial and • the ﬁnal state, modifying the rapidity distribution in the ﬁnal state [18, 59].

Nuclear breakup — The J/ψ is broken up in collisions with nucleons during the nuclear • crossing [52].

Extensive studies have been done to isolate and parametrize these effects. The NA60 collaboration studied these effects via p+Pb collisions at 17.3 GeV [60]. The PHENIX 2008 200 GeV d+Au experiment provided a high statistics data set that could be used to investigate CNM effects at RHIC. The physical observable, RdAu, is just RAA for a d+Au collision. The measurement was made at 12 rapidities, with three of those being at midrapidity and the other nine at forward and backward rapidity. The midrapidity result is shown as a function of pT in figure 3.1. In addition to making this measurement for the J/ψ, the measurement was also made for the charmonium 2S ′ state, the ψ [15]. The results for the J/ψ and ψ(2S) are shown as a function of Ncoll in figure 3.2.

The results were also compared with theory. Figure 3.3 shows the J/ψ RdAu versus rapidity, integrated over all Ncoll and pT . The theory curves [54] used an EPS09 parametrization of the nuclear shadowing combined with an eﬀective breakup cross section of 4 mb. The solid red line represents the theory prediction and the dotted red curves are the uncertainty from the EPS09 parametrization of the nPDF. The green dashed line represents a CGC calculation. Studies of CNM eﬀects via 5 TeV p+Pb collisions have been done at the LHC. Figure 3.4 shows

RpPb versus pT , a preliminary result from the ALICE collaboration [61] in 2014 for –1.37 < y

17 Figure 3.1: J/ψ RdAu as a function of pT from 2008 PHENIX data. The vertical bars are statistical uncertainties and the boxes represent correlated systematic uncertainties.

< 0.43. The data are compared with results from models, such as a shadowing calculation [16] based on EPS09, a CGC model [17] and a coherent energy loss model with and without an EPS09 shadowing correction [18]. The breakup cross section is expected to be negligible at LHC energies due to the very short nuclear crossing time (compared with the J/ψ formation time). Since ALICE does not have a p + p reference at 5.0 TeV, they had to make some interpolations of existing data.

3.4 Hot Nuclear Matter Eﬀects 3.4.1 SPS Results

Measurements were performed at the CERN Superconducting Proton Synchrotron (SPS) using

ﬁxed target experiments (S+U, Pb+Pb, In+In at √sNN = 20 [40], 17.3 [19], and 17 GeV [41], respectively), which showed a reduction in the J/ψ production cross section (σJ/ψ) relative to the Drell-Yan production cross section, σDY . A Drell-Yan process is one in which a quark from one nucleus and an anti–quark from the other nucleus annihilate each other and result in the production of a dilepton pair. The line represents the pattern of normal nuclear absorption, which is parametrized by a J/ψ absorption cross section σabs of 4.18 mb (measured at a diﬀerent collision energy) and a shadowing contribution calculated from the GRV 94 LO set of PDFs [62]. The

18 ′ Figure 3.2: RdAu vs centrality for J/ψ and ψ data [15].

Drell-Yan cross section is not expected to be modified by the presence of a QGP, so this was the first evidence that a QGP could possibly be created in the lab. The results from the Pb+Pb study by the NA50 experiment [19] are shown in figure 3.5. A study was done by NA60 to extract the CNM effect baseline [41] via p+Pb collisions at the same center of mass collision energy as the Pb+Pb. The CNM effects were parametrized by an effective breakup cross section using an EKS98 [63] shadowing correction. Figure 3.6 shows that after correction for CNM effects, suppression due to hot matter effects in Pb+Pb collisions is around 70% of unity for the most central collisions.

3.4.2 RHIC Results

J/ψ results from RHIC have been published at √sNN = 39 [43], 62 [43], and 200 [64], [44]

GeV for Au+Au collisions, √sNN = 200 GeV for Cu+Cu [45] and Cu+Au collisions [46], and

√sNN = 193 GeV for U+U [47] collisions. A paper discussing J/ψ production as a function of collision species size has recently been published [47], which compares data for 200 GeV Cu+Cu and

Au+Au with √sNN = 193 GeV U+U collisions. Figure 3.7 shows a comparison of the 200 GeV J/ψ R results for Au+Au at y < 0.35 and 1.2 < y < 2.2. The blue points are at y < 0.35 and AA | | | | | | were obtained using data from the 2004 RHIC run. The red points are forward rapidity and were obtained from higher statistics data from the 2007 RHIC run. The bottom panel shows the ratio

19 Figure 3.3: J/ψ RdAu for backward, mid and forward rapidities, integrated over all Ncoll and pT . The green dashed line represents a CGC calculation.

of the forward RAA to the midrapidity RAA. The data show that for all values of Npart besides the smallest value, there is greater suppression at forward rapidity. This is counter to what one might expect, since general energy density arguments would suggest there should be greater suppression at midrapidity. This became known as the “RHIC J/ψ puzzle,” and was important because it demonstrated the role that CNM eﬀects played in HIC. It is clear from ﬁgure 3.7 that the forward rapidity data have very good statistical precision and are limited by systematic uncertainties. The goal of this analysis is to obtain results at midrapidity with better statistical precision than the 2004 data set could provide. Figure 3.8 shows the results of a beam energy scan for Au+Au. The blue points are 39 GeV, the red points are 62 GeV, and the black points are 200 GeV. All data are for forward rapidity.

It appears that the RAA is larger at 39 and 62 GeV than at 200 GeV, especially for more central collisions. PHENIX studied an asymmetric system via 200 GeV Cu+Au collisions [46]. The results of this study are shown in ﬁgure 3.9. The ﬁlled black circles are the forward rapidity data, the Cu-going direction, and the open circles are the backward rapidity data, the Au-going direction. The gold points represent the 2007 forward rapidity Au+Au result for comparison. There is a 20%-30%

20 Figure 3.4: J/ψ RpPb vs pT for midrapidity at ALICE. Also shown are the results from models with a pure shadowing calculation [16], a CGC calculation [17] and an energy loss calculation [18] with and without a shadowing correction. difference in suppression between the backward and forward direction. This has been attributed to CNM effects [46]. PHENIX studied its largest collision system via 193 GeV U+U collisions [47]. The results of this study are shown in figure 3.10. The black points are the 193 GeV U+U data, and the orange points are the 200 GeV Au+Au data, both at forward rapidity. It should be noted that to compare the U+U data with the Au+Au data, the 200 GeV p + p reference data had to be scaled by 0.964, since there is no p + p reference data at 193 GeV. The 0.964 represents the difference in the J/ψ cross section between 200 and 193 GeV as estimated using PYTHIA [65]. The 193 GeV U+U data have an energy density 20% higher than that in 200 GeV Au+Au collisions [66], so this study was ≈ done to test the effect of the higher energy density on the J/ψ modification. There is slightly less suppression in the U+U data than the Au+Au for central collisions, contrary to what one would expect using energy density arguments to predict the degree of suppression. It was concluded in [47] that this is because the increased contribution from coalescence of cc¯ pairs is more prominent than the reduction due to the dissociation when the energy density increases. Coalescence effects will be discussed in section 3.4.5.

21 Figure 3.5: Ratio of J/ψ cross section to that from Drell-Yan measured at √sNN = 17 GeV/c2 by the NA50 collaboration [19].

3.4.3 ALICE Results

The LHC collaboration ALICE1 has also published heavy ion J/ψ data, as shown in ﬁgure 3.11. These data are for 2.76 TeV Pb+Pb collisions. The ﬁgure shows ALICE data [50] for both midrapidity ( y < 0.9) (blue) and forward rapidity (2.5

3.4.4 Comparison of Heavy Ion Data at Diﬀerent Energies

Figure 3.12 shows a comparison of midrapidity data from the NA50/NA60 experiments at the SPS with midrapidity data from RHIC [67]. This was an attempt to isolate the eﬀects of hot

1 J/ψ data from the LHC experiment CMS will not be discussed here as they cannot measure J/ψ down to pT = 0, as is critical for J/ψ suppression studies.

22 Figure 3.6: Ratio of measured J/ψ yield to the expected J/ψ yield, resulting in a suppression pattern for In+In (circles) and Pb+Pb (triangles) after CNM extraction.

nuclear matter on J/ψ production by removing the CNM eﬀects from RAA, using parametrizations of p+Pb and d+Au data, respectively. The “corrected” RAA is plotted vs dN/dη, where dN/dη is the number of charged particles per unit rapidity, and is a measure of energy production in the collision, and is used here as a proxy for energy density. The prominent feature of this plot is that the suppression from HNM eﬀects at 17.3 GeV and 200 GeV appears to be independent of collision species and energy when plotted against dN/dη.

J/ψ RAA data down to pT = 0 have been published from 17.3 GeV to 2.76 TeV. With CNM eﬀects accounted for, as the collision energy increases from 17.3 GeV (SPS) up to 200 GeV (RHIC), the RAA for central collisions decreases at midrapidity from 17.3 Pb+Pb to 200 GeV Au+Au. At around 200 GeV, the eﬀects of coalescence begin to dominate, as evidenced by the U+U RAA being less strongly suppressed than that for Au+Au. When the collision energy is increased to 2.76 TeV (ALICE), there is far less suppression than at 200 GeV. It is understood that color-screening dominates J/ψ production from 17.3 to 200 GeV and that coalescence begins to dominate as the collision energy increases from 200 GeV to 2.76 TeV.

23 Figure 3.7: J/ψ RAA vs Npart at 200 GeV for both the PHENIX central (blue) and forward arms (red).

3.4.5 Models for Hot Nuclear Matter Eﬀects

Models have been developed for predicting charmonium suppression in heavy ion collisions [68, 69]. One such model for describing hot nuclear matter effects is a two-component model designed by Rapp et al., [69]. The first component models the destruction of the J/ψ through Debye screening as predicted by Matsui and Satz. The second component models the coalescence (sometimes referred to as regeneration) of cc¯ pairs. Coalescence comes in the form of diagonal or off-diagonal coalescence. Diagonal coalescence is when a cc¯ pair that is initially bound becomes unbound due to its interaction with the hot, dense matter, and then becomes re-bound later on. In essence, the charm pair remain correlated after they become unbound, and it is possible for interactions with the medium to cause them to become bound again. Off-diagonal coalescence occurs when a c and ac ¯ from completely different hard processes thermalize in the QGP, find each other by chance, and then form a J/ψ. The probability for this to occur scales with the number of cc¯ pairs created in the initial collision. The number of cc¯ pairs formed scales with the energy of the collision, so off-diagonal coalescence plays a larger role at the LHC experiments than it does at RHIC. Rapp’s model includes both strong-binding and weak-binding scenarios, which reference whether the free energy (weak-binding) or internal energy (strong-binding) should be used in the potential

24 Figure 3.8: J/ψ RAA vs Npart at 39 (blue), 62 (red) and 200 (black) GeV for forward rapidity.

Figure 3.9: Cu+Au J/ψ RAA at 200 GeV for the PHENIX forward arms. model, although Rapp believes based on comparison with data (e.g. figure 3.13) that the strong binding scenario is favored. In the model, the potential tells us something about the charmonium equilibrium properties. Figure 3.13 shows PHENIX 200 GeV midrapidity data compared with theory curves. The left plot shows a strong-binding scenario and the right plot shows a weak- binding scenario. The theory curve (solid black line) is a combination of the coalescence (dotted blue, called “regeneration” in his plot), dissociation (dashed green, called “primordial” in his plot) and CNM effects (small dotted black). In both strong and weak binding scenarios, the CNM effects are parametrized with an effective breakup cross section of σabs = 3.5 mb, and those curves are the same in each panel. The dissociation and coalescence curves are different in each case, with both

25 Figure 3.10: U+U J/ψ RAA at 193 GeV for the PHENIX forward arms. curves being stronger in the weak binding case. In addition to characterizing PHENIX data, Rapp has also done a calculation for results from

ALICE. Figure 3.14 shows RAA for 2.5

3.5 Motivation for this Analysis

Figure 3.15 shows an estimate of the RAA from CNM eﬀects, derived from d+Au data, at both forward and midrapidity from 200 GeV Au+Au collisions [67]. CNM suppression is estimated to be smaller at midrapidity by 10%-40%, depending on the value of Npart. This suggests that isolating hot nuclear matter eﬀects should be easier at midrapidity than at forward rapidity making it important that we have midrapidity RAA data for Au+Au collisions that are of the best quality possible.

26 Figure 3.11: J/ψ RPbPb at 2.76 TeV for ALICE forward (red) and mid (blue) rapidities.

After the publication of the midrapidity Au+Au data from 2004 by PHENIX [64], a calculation was published [21] in which a full (3+1)-dimensional relativistic hydrodynamics calculation was used to describe the expanding QGP, and the J/ψ was treated as an impurity passing through the QGP. The calculation was used to investigate the scenario of sequential J/ψ suppression due ′ 2 to dissociation of the ψ , χC (1P charmonium state with mass 3.4 GeV/c ) and J/ψ at different tot temperatures in a dynamically evolving system. The survival probability, SJ/ψ, quantifies the probability that the charmonia states will survive the QGP after CNM effects have been accounted for. The CNM effects are parametrized by an absorption cross section of σabs = 1 mb and gluon ′ shadowing effects. An assumption in their model is that the ψ and χC have the same dissociation temperature and their plots denote both states together as χ.

Figure 3.16 shows the description of the PHENIX midrapidity RAA data (after a correction for CNM effects) obtained with the best fit values of the dissociation temperatures for the three charmonium states. The brackets represent the correlated uncertainty and the bars represent the uncorrelated uncertainty. The boxes represent the uncertainty associated with varying the absorption cross section, σabs, from 0-2 mb. Figure 3.17 shows the sensitivity of the fit to the dissociation temperature of the J/ψ, where Tc is the deconfinement temperature and TJ/ψ is the dissociation temperature of the J/ψ. The results reproduced in figures 3.16 and 3.17 were obtained assuming that the thermal width of the charmonia states changes suddenly from zero to infinity at the melting temperature. To investigate the effect of thermal broadening of the charmonia states

27 Figure 3.12: CNM-removed J/ψ RAA for both RHIC (red, √sNN = 200 GeV) and SPS (green and blue, √sNN = 17.3 GeV). by collisions with thermal quarks and gluons in the QGP, the calculation was repeated assuming several diﬀerent values of the decay width of the J/ψ at one half of the critical temperature. The results are shown in ﬁgure 3.18. It was concluded that a small decay width is required to reproduce the midrapidity PHENIX data. It will be seen later that these conclusions change in the light of the new results from this analysis of the PHENIX 2010 data.

28 Figure 3.13: Theory curves applied to PHENIX 200 GeV midrapidity data, with strong- binding (left) and weak-binding (right).

Figure 3.14: Theory curves applied to ALICE 2.76 TeV forward rapidity Pb+Pb data. The blue curve is for a charm cross section of 0.5 mb per unit rapidity, while the red curve is for a charm cross section of 0.33 mb per unit rapidity.

29 Figure 3.15: RAA estimated for CNM eﬀects using an EKS98 shadowing parametrization. The red points are midrapidity and the blue points are forward rapidity.

Figure 3.16: Survival probability vs Npart for Run-10 midrapidity data (red) and predictions. The black curve is the total prediction, the blue dashed curve is the primordial J/ψ component and the pink dotted curve is the component from feed-down.

30 Figure 3.17: Total survival probability vs Npart for diﬀerent melting temperatures plotted with the survival probability calculated for the 2004 midrapidity data.

31 Figure 3.18: Total survival probability vs Npart. Top left to bottom right show the survival probabilities for varying α, a parameter which indicates the thermal width of the J/ψ.

32 CHAPTER 4

EXPERIMENT

4.1 RHIC

The relativistic heavy-ion collider (RHIC) is located at Brookhaven National Laboratory (BNL) in Upton, NY. It consists of two concentric rings which accelerate beams of ions in opposite di- rections, with collision points at the two currently active experiments, PHENIX and STAR. The RHIC can accelerate beams of polarized and unpolarized protons up to 500 GeV, as well as heavy ions (Al, Cu, Au, U) from 7.7 to 200 GeV. RHIC began operations in 2000 with the trend of running 5-6 months of the year from January to June. The 6 months of downtime per year is needed primarily to prepare the accelerator and experiments for the next run, as well as keeping the cost of RHIC operations, which is dominated by electric power cost, manageable. RHIC labels its runs using the terminology Run-X, where X corresponds to the Xth run since operation began. The X happens to match up with the ones and tens digit of the year, e.g. Run-10 was data taken during 2010. The data in this analysis were taken during the 200 GeV Au+Au running in 2010. The life of a Au ion can be broken down into five steps. It begins in the Electron Beam Ion Source (EBIS) accelerator, where the ions are accelerated up to 2 MeV/u and stripped of 32 electrons. The ions are then transferred to the Booster, where the ions are accelerated in a circular path to an energy of 100 MeV/u and another 45 electrons are stripped off in the process. From the Booster, the ions are transferred to the Alternating Gradient Synchrotron (AGS), where they are accelerated up to 8.86 GeV/u and have their last two electrons stripped. The final step is to transfer the ions to RHIC, where they are accelerated to their desired energy.

4.2 PHENIX

The Pioneering High Energy Nuclear Interactions eXperiment (PHENIX) is an experiment that rose from the ashes, metaphorically speaking, from four proposals in the early 1990’s which never came to fruition. PHENIX comprises many subdetectors which are grouped into one of four

33 spectrometers. The two Central Arm (CA) spectrometers are located at midrapidity ( η < 0.35) | | and are optimized for detecting electrons, photons, and hadrons. The CA subsystems relevant to this analysis are the drift chamber (DC), pad chamber one (PC1), ring imaging Cerenkov detector (RICH), electromagnetic calorimeter (EMCal), and hadron blind detector (HBD). A schematic showing a cross section of the PHENIX detector when looking along the beampipe is shown in ﬁgure 4.1. The relevant event characterization subsystem is the Beam Beam Counter (BBC). The following sections brieﬂy describe the DC and PC [71], the RICH [72], the EMCal [73], the HBD [74] and the BBC [75]. The two Muon Arm (MA) spectrometers are located at forward and backward

Figure 4.1: PHENIX Central Arm detector configuration in 2010. rapidity and are optimized for detecting muons [76]. PHENIX has a central magnet that creates a field at the interaction vertex via two pairs of concentric coils. The field integral from this magnet ranges from 0.43 to 1.15 T-m [77].

34 4.2.1 Drift Chamber

The PHENIX inner tracking system is composed of the drift chamber (DC) and pad chamber 1 (PC1). The primary purpose of the DC is to measure the component of the momentum of charged particles in the r φ direction, p , as well as providing initial information for the global tracking − T in PHENIX. The DC is composed of two arms each with an acceptance of 90◦ azimuthally and ± 90 cm in the z-direction, which corresponds to an acceptance in η of 0.35. The construction of ± a single DC frame is shown in ﬁgure 4.2. The front plane of each drift chamber arm is located a

Figure 4.2: A single DC frame. distance of 2.02 m radially from the beam line, while the back end is located 2.48 m, resulting in a thickness of 46 cm. This places them in a residual magnetic ﬁeld of 600 G. The east and west arms of the DC are mirror images of each other.

35 Each arm has 20 C-shell openings, or keystones, on the north and south sides of the chamber, which individually cover 4.5 deg in φ. Each keystone has six sets of wires, termed X1, U1, V1, X2, V2, and U2. The X wires run parallel to the beamline and measure the r φ coordinate of the − track. The U and V wires run mostly parallel to the beamline, except they are tilted slightly at about 6 deg from the X wires, which allows for a measurement of the z coordinate of the track. Each X set contains 12 wires, while each U and V set contain 4 wires. Since each set has two wires, that results in a total of 40 wires for each cell. In total, there are 12800 wires in the entire DC. The single wire resolution is 165 microns in r φ and a spatial resolution of 2 mm in the z-direction. × The gas mixture in the DC volume is 48.5% Ar and 51.5% C2H6. This was chosen due to having a uniform drift velocity with an electric field 1 kV/cm, as well as having high gas gain and a low ∼ diffusion coefficient. The DC works by measuring the drift time of ionization clusters created by a charged particle passing through the DC volume. Under the assumption that the drift velocity of these clusters is constant, a linear relation between the position (x) of each cluster with respect to time (t) can be obtained, of the form x(t) = vdriftt. Track momentum must be determined from the bend of the charged particle trajectory in the magnetic field. Because the DC measures space points outside the magnetic field region, the radius of curvature of the track is not observed directly. Instead, the track momentum is derived from the angle, called α, between the line defined by the DC hits and a line drawn from the collision vertex to intersect the line of the DC hits at a radius of 2.02 m. The relationship between φ and α is shown pictorially in figure 4.3. Tracks are identified using a Hough transform technique, in which each of the DC hit positions is translated to a parameter space consisting of φ and α coordinates. Searching for local maxima in this Hough array identifies track candidates. The track candidates are then fitted using a Kalman filter. After several stages of hit association and track purging, only the tracks with an acceptable χ2 remain.

4.2.2 Pad Chamber 1

The pad chambers (PCs) are a set of three pixel detectors designed for the main purpose of providing 3D space resolution for straight line tracking. The PC consists of three layers (PC1, PC2, PC3) in the west arm and two layers (PC1, PC3) in the east arm. PC1 is the relevant layer for this analysis and is located directly behind the DC and in front of the RICH in both the east and west arms, in an area outside any residual magnetic ﬁeld. PC1 has an acceptance of 0.35 in η and φ | |

36 Figure 4.3: A schematic showing how α and φ are obtained. coverage of 2 90◦, and extends a total of 2 m in the z-direction, and has a thickness of 1.2% of a × radiation length. Each PC1 arm consists of 8 sectors of 0.5 m x 2 m, with 14400 channels on each sector. PC1 is an integral part of the tracking system, since that is where tracks are anchored, and then projected to all other subsystems. It also provides the z-coordinate for tracks. The PC is also one of the most stable PHENIX subsystems, boasting an efficiency of 99%. Each PC consists of a set of cathode planes containing a gas volume of 50% Argon and 50% ethane. In that gas volume, there is single plane of anode and field wires. One cathode plane is copper and the other plane is segmented into pixels. When a charged particle passes through the volume, it starts an avalanche on the anode wires. That charge in the avalanche is induced on pixels. A pixel is a small copper rectangle and is connected to eight other small copper rectangles. Each set of nine rectangles is called a pad. A schematic of the pad layout is shown in figure 4.4. The PC is unique in its use of pixels. Amongst other benefits, this makes the cost per channel a factor of 25 cheaper. The resolution in the z-direction is 1.7 mm and 2.5 mm in the radial direction. This is achieved using cells that are about the same size as the position resolution. The information is read out with a simple digitization and comparing the signal with a discriminator. Using a discriminator

37 Figure 4.4: Pixel layout in PC1. lends itself to registering false hits due to electronic noise. This potential problem is handled by requiring that all three pixels in a cell must register the avalanche, a so-called triple coincidence requirement. Each pixel in a cell has its own readout channel, and is designed in such a way that all three channels are adjacent. This allows the information to be reduced to the cell level, as opposed to reading out for every pixel, which saves a factor of nine in readout channels.

4.2.3 Ring Imaging Cerenkov Detector

The Ring Imaging Cerenkov Counter (RICH) is the primary electron identification subsystem of PHENIX. It consists of an east and a west arm, with each arm located directly behind PC1. Each arm is made up of a gas volume, a plane of photomultiplier tubes (PMTs), electronics and a spherical mirror. The volume of gas is 40 m3, while the mirror surface area is 20 m2, with 2560 PMTs per arm. The RICH has a total thickness of 2% of a radiation length. A diagram illustrating the construction of a RICH arm is shown in figure 4.5. The RICH works using the principle of Cerenkov radiation. When a particle travels faster than the speed of light in a medium it emits Cerenkov light. This depends on the index of refraction of the material. The RICH uses CO2, which has an index of refraction n = 1.000410. Cerenkov photons emitted by electrons are reflected off the spherical mirror and onto a plane of PMTs which detect the photons. The photons from an electron will form a ring of hits on the PMTs. Using the DC and the PC, tracks are projected to the RICH and then PMT hits are counted up between 3.4 and 8.4 cm from the track projection reflected to the PMT plane, where

38 Figure 4.5: Schematic of a single RICH arm those distances are determined by position resolution of the PMTs. The RICH is the primary electron identiﬁed in PHENIX. Because pions of less than 4.9 GeV/c momentum do not register a signal in the RICH, requiring that tracks are associated with a RICH ring suppresses charged pions relative to electrons by a factor of about 100.

4.2.4 Electromagnetic Calorimeter

The PHENIX electromagnetic calorimeter (EMCal) is used to measure the energy and position of electrons and photons. Additionally, it also plays a major role in particle identiﬁcation and can trigger on rare events, such as high pT photons and electrons. The EMCal is comprised of eight individual sectors. Six are composed of lead scintillators (PbSc) blocks, with four of them in the west arm and two in the east arm. A schematic showing a single PbSc calorimeter is shown in ﬁgure 4.6. The last two are lead glass (PbGl) calorimeters located on the lower side of the east arm. Each arm covers 90◦ in φ and has η < 0.375. The total number of channels over all sectors | | is 24768.

39 Figure 4.6: Schematic showing a single PbSc calorimeter

Both types of calorimeters use PMTs to read out the signal and they also have good energy resolution and timing characteristics. However, their design is different and they excel at different things. Using the two in conjunction with one another has the added benefit of adding independent cross checks of results, thus reducing the systematic uncertainties on those measurements. Although the design of each calorimeter is different, they both work under the principle of generating and detecting an electromagnetic shower via bremsstrahlung and pair production. The PbSc calorimeter consists of alternating layers of lead and scintillating material and covers a total area of 48 m2. The basic building block of the PbSc is a module which consists of four optically isolated towers. Each tower contains 66 sampling cells of lead and scintillator. Modules are grouped together such that it creates a plane of 12x12 towers. This set of modules is called a supermodule (SM). Each PbSc sector consists of 18 SMs, in a 6x3 plane. The main strengths of the PbSc are that it excels in timing and has better linearity in response. It has an energy resolution of σ/E = 8.1%/∆E 2.1% and a timing resolution of 200 ps for electromagnetic showers. L

40 The PbGl calorimeter is a Cherenkov detector which had been previously used in the CERN experiment WA98. One of the strengths of this calorimeter is the fact that it had been previously tested and used in WA98, in addition to having better granularity and energy resolution than the PbSc. The two PbGl calorimeters are located on the lower east arm. Each sector consists of 16x12 SMs, where each SM is an array of 6x4 towers. This results in a total of 9216 towers between the two sectors. Each PbGl module has a square cross sectional area of 40 mm, and extends 400 mm in length. The PbGl has an energy resolution of σ/E = 5.9%/∆E 0.8%. The primary function of the EMCal in this analysis is to provideL additional electron identiﬁca- tion. The EMCal, on average, contains most of the energy of an electromagnetic shower, but only a small fraction of a hadronic shower. As a result, a cut can be applied to the ratio of the EMCal energy to the track momentum that will retain essentially all electrons, but reject 90% of charged pions.

4.2.5 Hadron Blind Detector

The Hadron Blind Detector (HBD) is a Cherenkov detector initially commissioned to reduce the large combinatorial background in the low mass region to aid the study of low-mass dileptons (300- 500 MeV), while also being blind to hadrons. The source of this background is mainly γ-conversions in the beam pipe and π0 Dalitz decays. One of the ways the HBD reduces this source of background is by exploiting the fact that conversions and Dalitz decays have small opening angles. When a track observed by the central arm detectors is projected back to the HBD, a double hit will be observed, due to the fact that a small opening angle resulted in both electrons hitting the HBD in the same vicinity. The HBD has ∆φ = 135◦ and extends in η < 0.45, and has a thickness of 2.4% of a radiation | | length. Its large azimuthal acceptance relative to the rest of the central arms allows it to provide a strong veto area for pairs where only one electron fell within the central arm acceptance. The HBD is a windowless detector ﬁlled with CF4 (n=1.000620) coupled directly to a gas electron multiplier (GEM) with a CsI photocathode. A schematic of the HBD is shown in ﬁgure 4.7, where the left panel shows the entire HBD and the right panel shows an exploded view of a single arm. With this gas, hadrons with pT < 4 GeV/c will not radiate. The radiator is 50 cm long, which ensures good distinction between single and double hits, since the electrons have a long time to emit Cherenkov photons. Cherenkov photons are incident on the CsI photocathode, forming blob-like shapes. The

41 Figure 4.7: Left panel: The entire HBD. Right panel: An exploded view of one HBD arm. photo-electrons emitted from the CsI are multiplied in Gaseous Electron Multipliers (GEMs) to form the signal that is read out. The GEMs consist of layered copper plates with holes in them, which contain strong electric fields to pull photoelectrons through the holes. When hadrons travel through the electric field, the ionization electrons also go through the GEMs. The way to reject these undesired electrons is by introducing a mesh on top of the GEM with a lower negative voltage with respect to the GEM. With the electric field oriented this way, the ionization electron will be pulled up towards the mesh, and not down towards the CsI and GEM for detection. A Cherenkov photon will not ionize the gas in between the mesh and the CsI, and so when the photoelectron is created, it gets pulled immediately through the holes in the GEM. The readout plane behind the GEMs consists of hexagonal pads of area 6.2 cm2. The blobs of light created by electrons in the HBD have a maximum size of 9.9 cm2. Therefore, it is unlikely that an electron will be entirely constrained to a single pad. This improves the position resolution by allowing the position to be interpolated between pads. Each set of mesh, CsI photocathode, GEM and readout plane comprises a single sector of the HBD, and there are 12 in each arm, each with an area of 23x27 cm2.

42 4.2.6 Beam Beam Counter

The PHENIX Beam Beam Counter (BBC) is responsible for determining the timing, vertex position, and centrality of the projectile collisions, as well as providing the minimum bias trigger for the experiment, BBCLLVL1. The BBC is comprised of two identical counters surrounding the beam pipe, one north of the collision point and one south of it. Each is situated 144 cm from the center of the interaction diamond. A pseudorapidity range of 3.0 < η < 3.9 is achieved, as well | | as full azimuthal coverage, ∆φ = 2π. Each BBC is made up of 64 elements, where each element consists of a Cherenkov radiator attached to a PMT. The BBCLLVL1 trigger in the 2010 Au+Au run required that at least two PMTs in each BBC ﬁre. The eﬃciency of the trigger in Au+Au events was 92 2%. ±

43 CHAPTER 5

ANALYSIS

The RHIC Run-10 200 GeV Au+Au run lasted ten weeks from January 10th, 2010 to March 18th, 2010, during which 8.2 billion minimum bias (MB) events within the 30 cm z-vertex limits were ± recorded, corresponding to an integrated luminosity of 1.3 nb−1. The MB trigger requires that each of the BBCs had at least two hits, and this is the lowest level trigger requirement for any event in PHENIX. The 30 cm vertex cut ensures that all the events see the entire PHENIX geometric acceptance.

5.1 Centrality Determination

In addition to categorizing events via z-vertex, PHENIX also uses centrality. Centrality is loosely related to the impact parameter, b. A collision with a smaller b is said to be more central, and for a larger b, the collision is said to be more peripheral. The centrality in PHENIX is listed as a range of percentages, e.g. 0-10%, 60-92%. The percentage is categorized by looking at the total charge deposited in the BBCs. For example, all collisions that deposited the 10% most charge in the BBC are said to be in the 0-10% centrality range. All collisions that rank in the next 10% in terms of charge deposited in the BBC are said to be in the 10-20% centrality class, and so on and so forth. When all centralities classes are combined into one, the class is called minimum bias (MB).

The physical characteristics which are important are the number of participants (Npart) and the number of binary collisions (Ncoll). Npart is deﬁned as the number of nucleons which take part in the collision, and Ncoll is deﬁned as the total number of binary collisions that those Npart nucleons take part in. Ncoll is naturally greater than Npart, as a nucleon can experience more than one interaction in a given Au+Au collision. An average value of Npart and Ncoll for each centrality class is obtained by combining a Glauber model of the nuclear collision [39] with a simulation of the BBC response. Inputs to the model include the density distribution of the nucleus, typically taking the form of a Woods-Saxon potential, and also the energy dependence of the inelastic nucleon-nucleon cross

44 section. The BBC response is assumed to follow a negative binomial distribution (NBD). Table 5.1 shows N and N in each centrality class. PHENIX has an oﬃcial set of N and N h parti h colli coll part values for each data set. The uncertainties are systematic, reﬂecting the uncertainties in the input parameters to the Glauber model [39]. The values in table 5.1 were published in [78].

Table 5.1: Npart and Ncoll values for their corresponding centrality classes.

Centrality Class N N h parti h colli 0-5% 350.9 4.7 1064.1 110.0 ± ± 5-10% 297.0 6.6 838.0 87.2 ± ± 10-15% 251.0 7.3 661.1 68.5 ± ± 15-20% 211.0 7.3 519.1 53.7 ± ± 20-30% 161.6 10.0 357.3 50.7 ± ± 30-40% 109.6 9.8 207.6 30.3 ± ± 40-50% 70.3 8.0 111.2 15.5 ± ± 50-60% 41.6 7.1 54.1 11.1 ± ± 60-92% 12.5 1.2 12.1 1.5 ± ± 0-20% 277.5 13.1 770.6 165.2 ± ± 20-40% 135.6 14.0 282.4 59.1 ± ± 40-60% 56.0 10.7 82.6 19.1 ± ±

5.2 Detector QA and Run Group Assignments

There were 878 physics runs as part of the 200 GeV Au+Au data set. The term physics is used to mean that that run will be used for analysis, as opposed to a calibration run or a junk run, which are sometimes necessary during data taking. As detector performance varies over the course of the entire data taking period, it is necessary to divide the 878 runs into subsets for which a unique acceptance calculation will be done. To determine run groups, the performance of each subsystem was looked at individually on a run-by-run basis. To quantify the performance, a 2D geometric picture of each subsystem is created so that it will be easy to tell where there are dead or ineﬃcient areas. If a large fraction of a subsystem’s acceptance is dead or ineﬃcient for a substantial number of runs, then that would constitute a need to put those runs into their own run group. Additionally, it is necessary to keep track of all dead areas in each subsystem because knowledge of those areas is needed to make an accurate acceptance calculation, which will be detailed later. The run group

45 study is detailed for each subsystem below. Some plots and discussion details will be repeated from chapter 4, but are repeated for clarity here.

5.2.1 Drift Chamber and Pad Chamber 1

Drift chamber and pad chamber quality assurance was performed separately from the EMCal, RICH and HBD subsystems. This is because testing of the PC1 and DC can be done by using all charged tracks, as opposed to selecting only electrons. By looking at all charged tracks, any inefficiencies or dead areas in the EMCal, RICH or HBD will not show up in the PC1 and DC plots. This allows us to determine whether the problem is with tracking in the DC or PC1 or with one of the electron identifiers. To make this study, a set of loose cuts was used to select all charged particles, namely a DC track quality cut, a low pT cut (pT >0.2 GeV/c) and a z-vertex cut of 30 cm. Drift chamber performance was quantified by looking at 2D maps of φ vs α in each DC sector. The quantity φ is the azimuthal angle at which a track crosses the DC reference radius of 220cm. The quantity α is the azimuthal inclination of a track with respect to an infinite momentum track originating at the same vertex and crossing at the same point of DC reference radius. The value of

α goes inversely with pT . Figure 5.1 shows a cross section of the DC and how φ and α are obtained.

The DC showed large fluctuations in performance throughout the Run-10 data taking period. Figure 5.2 shows the overall performance of the DC. Dead or largely inefficient regions which were dead for the entirety of Run-10 show up as purple or white. For the purposes of assigning run groups, this same plot is looked at on a run-by-run basis, where the location of new dead areas is recorded. When a large section of the DC was dead or inefficient for a substantial number of runs (>20), those runs were grouped into their own run group. This resulted in the need to create five different run groups. Distributions of DC α vs φ for each run group are shown in appendix A. Hits in the pad chamber are described in a right handed (x,y,z) coordinate system, where z is along the beam line and y is vertical. The PC1 coordinates are represented in the QA plots as (pc1x, pc1y, pc1z). Pad chamber 1 performance was quantified by looking at 2D maps of pc1y vs pc1z in each PC1 sector, where pc1y and pc1z are the y and z coordinates of the track hit position in the PC1, respectively. Shown in figure 5.3 is pc1y vs pc1z for all runs together. A run-by-run

46 Figure 5.1: Cross section of the DC to show what is meant by φ and α. analysis of this plot showed no need to generate new run groups, as the PC1 was relatively stable throughout Run-10.

5.2.2 RICH, EMCal and HBD

The RICH, EMCal and HBD did not experience strong run-by-run fluctuations in performance. However, the RICH did lose half of an entire sector for around 50 runs. To study RICH performance, 2D plots were made of the variables cross φ and cross z, namely the φ and z coordinates where the track projection crosses the RICH plane. Figure 5.4 shows the RICH performance over all runs. For comparison, RICH performance for a bad run is shown in figure 5.5. The southwest sector for φ < -0.2 is dead. All runs which showed this behavior were grouped together into one run group. A plot of the hit distribution of the y and z hit positions is shown in figure 5.6. The dead areas are the white spots, which indicates that that area is completely dead for the entirety of the run. No additional run groups were needed to account for variations in EMCal performance. A plot of φ vs z projections to the HBD is shown in figure 5.7. The HBD was responsive for the entire run except for the black shaded region from 0-30 cm in z and just above 3 rad in φ. That

47 Figure 5.2: DC α vs φ for all runs together. region represents the EN2 module, which was not operational during Run-10. No additional run groups are needed to accommodate the performance of the HBD. The ﬁve run groups from the DC and the one group from the RICH make a total of six run groups. The number of events in each run group is shown in table 5.2.

Table 5.2: Run groups and their respective number of runs and number of events.

Run Group Number of Runs Number of MB Events ( 108) × 0 599 46.8 1 68 5.72 2 104 9.48 3 29 2.08 4 21 2.24 5 57 5.43 All 878 71.8

48 Figure 5.3: Pc1y vs pc1z for all runs together.

5.3 Electron Identiﬁcation

In addition to global event characterization, individual particles must be identiﬁed and tracked through the detector subsystems. This is a dielectron analysis, so our goal is to identify electron tracks to the best of our ability. In a Au+Au event, most of the particle production consists of hadrons, with pions being the predominantly produced particle. While tracking with the PC1 and DC and electron identiﬁcation with the EMCal and RICH subsystems is an almost standardized process, the use of the HBD in an electron analysis is unique to analysis of Run-10 data. Thus, the process used to identify electron tracks with the HBD will be detailed in the following sections.

5.3.1 HBD Min Pad Clusterizer

Several algorithms have been utilized to determine the HBD charge associated with a given central arm track projection. Only the one utilized in this analysis will be described here. It is the same method as was developed in [79]. The reason this particular algorithm was chosen is as follows. A major source of background in this experiment is the contribution of conversion electrons in the backplane of the HBD. One might assume that since such tracks would not have a match in the HBD, a CA projection should ﬁnd no HBD charge, and thus this track can be eliminated.

49 Figure 5.4: RICH cross φ and cross z for all runs together.

This works well enough for p+p and peripheral Au+Au collisions, but in central Au+Au collisions, the high multiplicity of charged particles creates a large background charge due to scintillation light in the CF4 radiator. This background charge can be mistakenly associated with a track. To handle this problem, the HBD Min Pad clusterizer pre-determines the HBD pads which can possibly be included in an electron cluster, and this optimization is done using the charge distribution of simulated single electrons. The three-step process starts with projecting a CA track to the HBD. Then, a cluster is determined by looking for the pre-selected clusters near the projection point. Once a cluster is determined, a threshold is applied to the total charge on the cluster. This threshold is set to reject a given fraction of conversion electrons, and is necessarily dependent on centrality since more central collisions generate a greater amount of scintillation light. The parameter, called hbdid, is calibrated so that selecting, for example, hbdid 5 reduces the number of backplane electrons ≥ accepted to 1/5 of the total.

50 Figure 5.5: RICH cross φ and cross z for a bad run.

5.3.2 Neural Network

The goal of this analysis is to properly identify signal electrons in a large background of misiden- tified hadrons and conversion electrons from the backplane of the HBD. The standard approach to identifying signal electrons in high multiplicity events is to make a series of one dimensional cuts on all tracks. One can select electron candidates by applying a RICH matching cut, an EM- Cal energy/momentum cut, a HBD threshold cut, etc. The problem with this approach is that it can result in a large efficiency loss. To solve this problem, a neural network approach is used to maximize the electron identification efficiency. In general, a neural network is a model which estimates some unknown function using some number of input parameters. The inputs are connected by a hidden layer of ’neurons’. The neurons can be weighted numerically, and that weighting is tuned so as to recognize what the user wants to get out of the neural network. In this case, the neural network is tuned to distinguish foreground electrons from background electrons, and was developed by the group that performed the analysis in [79]. All the detector variables one would make a set of one-dimensional cuts on are passed to the neural network, and then it is determined on a track-by-track basis if it is deemed an electron

51 Figure 5.6: EMCal y and z hit positions for all runs. track. A list of the variables used in the neural net is shown in table 5.3. The output is a number between 0 and 1, where an output close to 1 has a high chance of being a foreground electron. Electrons are selected by making a single cut on that probability. Because the background sources (misidentiﬁed hadrons and backplane/conversion electrons) vary with event multiplicity, a diﬀerent neural network is used in each centrality bin. A list of the neural network probability thresholds used for each centrality is shown in table 5.4.

5.4 Signal Extraction

The J/ψ signal is obtained in a three step process. First, a “foreground” spectrum is created by calculating the invariant mass of all unlike sign dielectron pairs within a single Au+Au event. Second, a background spectrum is obtained using an event-mixing technique, where a sample of dielectron pairs is created by forming the invariant mass spectrum of electron and positron pairs using tracks from diﬀerent events. The number of events used for this mixing was 100, and all possible combinations of electrons and positrons from diﬀerent events were used. The invariant mass of all unlike-sign pairs is calculated for all pairs of electrons in that sample as long as each

52 Table 5.3: Electron identiﬁcation variables used in neural network. Variable Detector Short Description dep EMCal Sigmalized energy/momentum emcsdr EMCal Sigmalized distance from cluster to nearest track projection prob RICH χ2-like shape variable n0 RICH Number of hit PMTs npe0 RICH Number of photoelectrons in the RICH ring χ2/npe0 RICH χ2-like shape variable normalized to number of photoelectrons disp RICH Distance between a track projection and its associated ring center hbdsize HBD Cluster size from MinPadClusterizer hbdcharge HBD Cluster charge from MinPadClusterizer hbdid HBD Reduced cluster charge threshold from MinPadClusterizer

Table 5.4: Neural net cut values for each centrality bin.

Centrality Neural Net Cut 0-10% 0.30 10-20% 0.40 20-40% 0.55 40-60% 0.70 60-92% 0.75

53 Figure 5.7: Hit distribution in the φ z plane for all runs in the HBD. − electron came from a different event. This creates a spectrum which is statistically independent from the foreground. Because the background contains pairs from many different events, it is much bigger than the foreground and so it must be normalized to match the foreground. Once normalized, the background can be subtracted from the foreground to result in a “signal” histogram. Figure 5.8 shows a plot of the normalized background (red) with the foreground (blue) plotted on top of it, where both are centrality and pT integrated. A log scale on the y-axis here is used to more clearly demonstrate the relative size of the foreground and the background in the J/ψ mass region. The raw number of measured J/ψ’s can be estimated by adding up all the counts in a fixed mass window 2 of [2.8,3.4] GeV/c . A centrality and pT integrated signal spectrum obtained by subtracting the red curve from the blue curve in figure 5.8 is shown in figure 5.9.

5.4.1 Yield Extraction - Centrality Dependence

The reason that simply adding up counts within a ﬁxed mass window is not the best way to obtain the J/ψ yield is three-fold. Firstly, when the background is very large, the shape of the foreground – background spectrum is very sensitive to the normalization of the mixed-event background estimate of the combinatorial background, which can result in some under or over subtraction, especially in the lower mass region. Secondly, even after mixed-event background

54 Figure 5.8: Comparison of the normalized background (red) with the foreground (blue) shown on a log scale. subtraction, there still remains a correlated background underneath the J/ψ peak which consists mostly of open heavy-flavor decays and Drell-Yan pairs. Third, when the background is large, better accuracy is always obtained by fitting a line shape to the signal peak. The reason for this is that the signal line shape is mostly determined by data in a subset of the mass range, and thus the fit is less subject to uncertainty caused by background statistical fluctuations in those parts of the fit range that do not affect the yield much. If the yield is determined by subtracting the background from the foreground and summing the difference, it is equivalent to assuming that the signal line shape is flat within the sum range, and that no data point is more important than any other. To account for these effects and to correctly determine the yield, a fitting technique is used. The method is to make a log-likelihood fit to the foreground spectrum which takes into account three terms. The first is a term which accounts for the shape of the J/ψ peak which consists of a Gaussian plus a tail, called the Crystal Ball (CB) [80] function, and is shown in eq. 5.1.

− 2 (m m¯ ) ¯ 2σ2 m−m e if σ > α f(m)= n 2 −n − (5.1) n − α n m−m¯ N e 2.0 α otherwise  |α| |α| −| | − α h i The CB function contains ﬁve parameters: (α, n, m, σ and N). The α and n parameters model the tail while the m and σ parameters model the mean and width of the Gaussian. The parameter

55 Figure 5.9: J/ψ invariant mass spectrum integrated over all centrality and pT .

N determines the yield. The second term in the fit introduces an exponential background that accounts for anything not properly described by the mixed event background, including physics sources such as open heavy-flavor and Drell-Yan. The parameters are the normalization, Nexp, and the slope, s. The third term in the fit is the actual mixed-event background mass spectrum. It is assumed in the fitting that the CB shape parameters do not vary with centrality. Thus the values of α, n, m, and σ should be determined simultaneously from the data at all centralities. The strategy that was adopted was the following.

Step through a range of values of α, n, m and σ in a four dimensional grid. • At each grid point, ﬁt N, N and s to the mass spectrum individually at each centrality, • exp and record the optimum χ2.

At each grid point, sum the χ2 values for all nine centralities. • Search the χ2 space for the grid point with the minimum χ2 value. That grid point is • associated with the optimum values of α, n, m and σ.

The ﬁts to the individual centralities at the optimum grid point yield the best estimates of • the CB and exponential parameters at that centrality.

In effect, we have determined the best values of our CB shape parameters and our model of the line shape is then fixed for all fits. The uncertainty in the CB yields is then provided by the fitter,

56 assuming that the model of the line shape that we determined is correct. However there must be a systematic uncertainty in the yields that is associated with our model line shape. To determine that systematic uncertainty, we do the following.

Search the χ2 space for all grid points where the χ2 is within 4.72 of the minimum χ2 value. • For each of those grid points, histogram the yield at each centrality. • Extract the RMS deviation from the histogram at each centrality. This is the systematic • uncertainty in the yield due to α, n, m and σ.

An increase in χ2 of 4.72 is the standard test for one standard deviation in a result due to four free parameters [81]. The CB best fit values are determined by stepping through a set range for each parameter. For (α, n, m and σ), there are (20, 80, 20, 30) points to step through, resulting in a total of 960,000 grid points at each centrality and a total of 9.6 million fits altogether. For every grid point in the range of the four CB parameters, a unique set of fits is done to the foreground at each centrality, during 2 which N, Nexp and s can vary. For every grid point, the total χ is obtained over all centrality bins, giving a total of 960,000 points in χ2 space. The set of four CB parameters which resulted in 2 2 the lowest total χ (χmin) are taken as the CB parameters to use to determine the yield at each centrality. The best fit CB parameters parameters are shown in table 5.5. Plots of the fit results

Table 5.5: Best ﬁt parameters from Crystal Ball function.

Parameter Value χ2 524.047 α 0.4475 n 3.9 m 3.1045 σ 0.0612

for the best fit are shown in figures 5.10 and 5.11. The red points are the mixed event background, shown just as a comparison to the black points, which are the foreground. The blue curve is a fit to the foreground. The fit results and their corresponding yields and uncertainties as a function of centrality are shown in table 5.6. To show a more descriptive picture, the fit is plotted on the mixed-event subtracted spectrum in figures 5.12 and 5.13. The black points are the mixed-event

57 104 4 Yield 10 0 - 5 Yield 5 - 10 Yield 10 - 15

103 103 103

102 102 102

10 2 2.5 3 3.5 2 2.5 3 3.5 2 2.5 3 3.5 2 2 2 Me+e- Gev/c Me+e- Gev/c Me+e- Gev/c

Yield 15 - 20 Yield 20 - 30 Foreground data 103 103 Mixed events

102 102 Total fit

10 10 2 2.5 3 3.5 2 2.5 3 3.5 2 2 Me+e- Gev/c Me+e- Gev/c

Figure 5.10: Best fit of foreground for centrality dependence for the five most central bins. subtracted points, with the green dashed curve being the exponential component and the blue curve being the CB fit plus the exponential. As outlined earlier, to determine the RMS systematic uncertainty in the yield due to the four CB shape parameters, we take the range of yields at each centrality obtained from fits with a χ2 that is within 4.72 of the minimum [81]. Out of the 960,000 fits, 14330 fall within this range. The yield and uncertainty for all fits in the prescribed χ2 range are histogrammed for each centrality. The maximum extent of that distribution divided by the yield obtained from the fit is taken as the fractional systematic uncertainty in that centrality bin due to the four CB parameters. The results of this study are shown in table 5.7. The column titled “Yield” is the yield from the fit. The column titled “Yield Variation” is the maximum deviation of the yield observed up or down for all fits that resulted in a χ2 within 4.72 of the minimum. The systematic uncertainties are taken as the average of the deviations up and down from the fit result. This gives +6% and 2.9%. − The systematic uncertainty associated with the mixed-event background normalization is determined by moving it up and down by 2% and looking at the resulting effect on the yield. The yield quoted for the J/ψ from the fits is in all cases the integral of the CB function between 2.8 and

58 2 Yield 103 30 - 40 Yield 40 - 50 Yield 10 50 - 60

102

102 10 10

10 1 1

2 2.5 3 3.5 2 2.5 3 3.5 2 2.5 3 3.5 2 2 2 Me+e- Gev/c Me+e- Gev/c Me+e- Gev/c

Yield 60 - 92 Yield 0 - 92 Foreground data

104 10 Mixed events

103 Total fit 1

102 2 2.5 3 3.5 2 2.5 3 3.5 2 2 Me+e- Gev/c Me+e- Gev/c

Figure 5.11: Best ﬁt of foreground for centrality dependence for the four most peripheral bins, plus the minimum bias case.

3.4 GeV/c2. This is done to match the mass range used in simulations to extract the yield. The systematic is taken as the full extent of the up/down variation divided by √12, which corresponds to the equivalent RMS for a ﬂat distribution. The results of that study are shown in table 5.8.

5.4.2 Yield Extraction - pT Dependence

The pT dependence of the Jψ yields was extracted in four centrality bins (0-20, 20-40, 40-60,

60-92%). For the extraction of the pT dependent yields, the optimum values of the CB shape parameters determined in the last section were used, and the fractional systematic uncertainty in the yields is taken to be the same as that determined in the last section. In some cases, a poorly-deﬁned exponential resulted in an uncertainty that was too large. To get a better estimate of the uncertainty on those points, the following was done. The yield and uncertainty were taken by doing a direct sum of the foreground – mixed-event background spectrum with all statistical errors propagated correctly. Then, the direct sum yield and uncertainty were reduced by the ratio of the ﬁt yield to the direct sum. A type B (see section 5.7) systematic uncertainty of one third of the reduction were applied to those points.

59 Table 5.6: Fit results and yields as a function of centrality.

2 Centrality χ N Nexp s Yield Yield Error 0-5% 45.5 61.7 -1.16e+08 -6.26 339 53.4 5-10% 49.1 72.7 2.65e+03 -2.07 400 42.0 10-15% 38.6 59.5 299 -1.35 328 36.9 15-20% 76.4 50.6 392 -1.34 279 35.0 20-30% 68.2 99.4 3.27e+03 -1.88 547 50.4 30-40% 48.1 73.9 2.57e+03 -2.07 406 37.8 40-50% 72.4 42.4 2.83e+03 -2.21 234 21.8 50-60% 33.4 20.9 411 -1.59 115 14.5 60-92% 29.7 22.6 9.52e+04 -4.26 124 11.6 0-92% 62.7 513 1.10e+03 -1.15 2825 106

The fit results are shown in figures 5.14, 5.15, 5.16 and 5.17, where the foreground – mixed-event spectrum is plotted with the CB + exponential fit (blue) and the exponential fit alone (green). The yields are summarized in table 5.9.

5.4.3 Radiative Tails

By counting over a fixed mass window, there are some J/ψ’s which go uncounted, due to the fact that the reconstructed mass falls outside the mass window. This effect, called internal radiation, arises from decays according to J/ψ e+e−γ, and this results in a tail on the lower mass side of → the fixed mass window. The line shape for internal radiation is given by [20]

α 2m m4 1+ r P (m)= 1+ ln r , (5.2) π M 2 m2 M 4 1 r − J/ψ − J/ψ ! − where 2 4me r = 1 2 , (5.3) r − m

α = 1/137 is the fine structure constant, me is the electron mass and MJ/ψ is mass of the J/ψ listed in the PDG [82]. The line shape is shown in figure 5.18. This line shape is then convoluted with the detector mass resolution for the J/ψ to get the net effect of the internal radiation on the J/ψ signal. The fraction of J/ψ’s which come from internal radiation is given by [20], and shown in equation 5.4. The quantity Emin is the minimal energy of the photon in the rest frame of the

60 0 - 5 5 - 10 100 10 - 15 100 Net yield Net yield 200 Net yield 50

100 0 0

0 -50 -100 -100 -100 2 2.5 3 3.5 2 2.5 3 3.5 2 2.5 3 3.5 2 2 2 Me+e- Gev/c Me+e- Gev/c Me+e- Gev/c

300 100 15 - 20 20 - 30 Mixed events subtracted Net yield Net yield 200 50 Crystal Ball + exponential 100 0 Exponential only 0 -50

-100 -100 2 2.5 3 3.5 2 2.5 3 3.5 2 2 Me+e- Gev/c Me+e- Gev/c

Figure 5.12: Best fit plotted on the mixed-event subtracted spectra for centrality dependence for the five most central bins. decaying state. 2 2 2 α MJ/ψ MJ/ψ MJ/ψ 2 2 11 Chard = 4ln ln 2 1 3ln 2 π + (5.4) 2π " 2Emin me − ! − me − 3 2 # In addition to the internal radiation effects, and larger than it, there is also a contribution to the mass spectrum from external radiation, in the form of bremsstrahlung radiation resulting from the interaction of the electrons with the detector material. Similar to internal radiation, this effect manifests itself in the form of a tail on the lower mass side of the J/ψ peak. The effects of internal and external radiation are accounted for in the calculation in the acceptance, to be discussed in the following section.

5.5 Acceptance and Eﬃciency Corrections

With an ideal detector, we could measure every single J/ψ that is produced. However, the PHENIX central arm azimuthal acceptance is roughly half of the ideal 2π azimuthal coverage, and reconstruction of a J/ψ requires that both electrons in the dielectron pair be within the PHENIX acceptance. Additionally, the subsystems which detect dielectrons do not function with 100%

61 150 30 - 40 40 - 50 50 - 60 30 Net yield Net yield Net yield 50 100 20

50 10 0 0 0

2 2.5 3 3.5 2 2.5 3 3.5 2 2.5 3 3.5 2 2 2 Me+e- Gev/c Me+e- Gev/c Me+e- Gev/c

30 60 - 92 0 - 92 Mixed events subtracted

Net yield Net yield 500

20 Crystal Ball + exponential

10 Exponential only 0 0

-10 2 2.5 3 3.5 2 2.5 3 3.5 2 2 Me+e- Gev/c Me+e- Gev/c

Figure 5.13: Best fit plotted on the mixed-event subtracted spectra for centrality dependence for the four most peripheral bins, plus the minimum bias case. efficiency. There are areas in each subsystem that were dead for some or all of Run-10, and those inefficiencies must be accounted for. This section deals with the parametrization of those effects. The calculation of the J/ψ acceptance is a two-step process, both of which involve performing simulations. First, we must find the inefficient and dead areas of each subsystem relevant to this analysis. This effectively creates a “map” of live areas of the detector, done through an iterative process of simulation to data matching. The second step is the actual calculation of the J/ψ acceptance, during which single J/ψ are thrown into one unit of rapidity centered on zero, the dead areas of the detector are masked off, and it is determined how many of the J/ψ are reconstructed after running through the full simulation chain. The full GEANT simulation of the detector should properly account for the effects of the detector mass that produce the radiative tail on the J/ψ peak.

5.5.1 Simulation Chain

Simulations in PHENIX are a three step process. The ﬁrst step is event generation. The event generator chosen was PHParticleGen, a PHENIX-specialized version of the PYTHIA [65] frame-

62 Table 5.7: Results of histogramming the yields from parameter sets resulting in a χ2 2 within 4.72 of χmin. Centrality Yield Yield Variation Up/Down % of Yield 0-5% 339.4 +17.6/ 10.4 +5.2%/ 3.1% − − 5-10% 400.3 +33.7/ 12.5 +8.4%/ 3.2% − − 10-15% 327.7 +33.5/ 10.7 +10.2%/ 3.2% − − 15-20% 278.7 +23.3/ 6.7 +8.4%/ 2.4% − − 20-30% 547.3 +32.7/ 12.3 +5.9%/ 2.2% − − 30-40% 406.5 +18.5/ 8.5 +4.6%/ 2.1% − − 40-50% 233.6 +12.4/ 3.6 +5.3%/ 0.9% − − 50-60% 114.9 +5.1/ 1.4 +4.4%/ 1.2% − − 60-92% 124.5 +1.5/ 9.5 +1.2%/ 7.6% − − 0-92% 2824.7 +205/ 84.7 +7.3%/ 3.0% − −

work. Single particles may be generated with user-specified pT , rapidity, and z-vertex distributions, and the kinematics of each particle are saved to a file. The second step takes the output from PH- ParticleGen and runs it through the PHENIX Integrated Simulation Application (PISA), which is a simulation software package based on the GEANT3 [83] libraries. This is the stage where the generated particles interact with the PHENIX detector, and the hits in each detector subsystem are saved to a file. The third step in the simulation chain is where the hits files are processed by the track reconstruction software so that we can extract the geometric (e.g. subsystem hit location) and kinematic quantities (e.g. energy, momentum) associated with that particular particle. This last stage mirrors the track reconstruction technique that is done for real data, including counting reconstructed pairs only inside a mass window of [2.8,3.4] GeV/c2.

5.5.2 Simulated J/ψ Line Shape

Figure 5.19 shows the eﬀects of reconstruction. The top panel shows the reconstructed mass spectrum. The bottom panel shows the input J/ψ spectrum from the particle generator. There is a broadening around 3.1 GeV/c2 due to the detector mass resolution, and a tail on the left hand side of the peak is noticeable, illustrating the eﬀect of radiative energy loss of the electrons in the mass of the detector. Because the acceptance is obtained by comparing the number of simulated J/ψ’s with the number reconstructed within the mass window [2.8,3.4] GeV/c2, this acceptance will be the correct one to use with the data, which also uses the number of pairs reconstructed in

63 Table 5.8: Results of increasing and decreasing the mixed-event (ME) background by 2%.

Centrality Yield from ﬁt Yield from Yield from Diﬀerence Max ME +2% ME -2% in Yield extent/√12 +65 0-5% 337.5 307.7 402.4 −30 8.1% +17 5-10% 392.2 409.9 386.9 −5 1.6% +13 10-15% 335.0 348.2 323.5 −12 2.2% +15 15-20% 279.9 294.9 272.7 −8 2.4% +15 20-30% 547.6 562.0 544.4 −4 1.0% +6 30-40% 407.7 406.6 413.7 −1 0.5% +0.5 40-50% 246.5 245.9 246.8 −0.5 0.1% +0.3 50-60% 115.2 115.5 114.9 −0.3 0.2% +0.03 60-92% 117.917 117.929 117.894 −0.03 0.02% +122 0-92% 2822.4 2945.0 2729.2 −93 2.2%

that mass window. This relies on the simulated line shape correctly describing the CB line shape ﬁt to the data.

5.5.3 Simulation to Data Matching

Distributions from simulated single electron tracks are compared to real data distributions. In the data, for each subsystem, we look at a 2D distribution of parameters which give us a picture of which regions are functional, inefficient, or completely dead, and we look at this on a run-by- run basis. This is similar to the process by which run groups were assigned, except now all the distributions that were examined for detector QA will now be compared between simulations and data. For comparison with the distributions from single electrons in the data, five million electrons and five million positrons are generated using PYTHIA. They are generated with flat pT [0.5, 10] GeV/c, y [-0.5, 0.5] and φ [0, 2π] distributions. While it is realistic to use flat distributions in η and

φ, the real pT distribution is not ﬂat. However, if the particles were generated with a realistic pT distribution, then we would have to generate a much larger number of particles in order to get an appreciable number of particles in the higher pT range. To correct for generating the electrons from a ﬂat pT distribution, the histograms created from the simulations are weighted by a pT distribution taken from p + p data.

64 0 - 20% centrality 100 100 Net yield Net yield Net yield 50 0 0

-100 0 -100 ME subtracted CB + exp. -200 -200 Exp. only -50

2 2.5 3 3.5 2 2.5 3 3.5 2 2.5 3 3.5 2 2 2 Me+e- Gev/c Me+e- Gev/c Me+e- Gev/c

30 40 10 Net yield Net yield Net yield 20 20

10 0 0

0 -20

-10 -10

-40 2 2.5 3 3.5 2 2.5 3 3.5 2 2.5 3 3.5 2 2 2 Me+e- Gev/c Me+e- Gev/c Me+e- Gev/c

Figure 5.14: Best ﬁt plotted on the mixed-event subtracted spectra for the pT -dependence for the 0-20% centrality bin. The pT binning from top left to bottom right goes 0-1, 1-2, 2-3, 3-4, 4-5 and 5-7 GeV/c. The blue curve is the CB + exponential ﬁt and the green curve is the exponential alone.

The simulated electrons are then propagated through the PHENIX detector via GEANT3. The simulated tracks are reconstructed using the same software with which the data tracks are reconstructed. QA plots are then generated for the simulations to compare with those generated for the data. In an iterative process, dead or inefficient areas observed in the data are masked off in both the simulations and data in an attempt to make the distributions simulated and measured distributions identical. The dead area masks are referred to as fiducial cuts. For example, in figure 5.20, a comparison of α vs φ in each DC sector for data and simulations after fiducial cuts have been applied is shown for the largest run group. The left side of each panel is the data distribution, and the right side is the simulations distribution. A comparison of data and simulations for the PC1 is shown in figure 5.21.

65 20 - 40% centrality ME subtracted 100 200 CB + exp. Net yield Net yield Net yield 40 Exp. only 50 20 100

0 0

0 -20 -50

2 2.5 3 3.5 2 2.5 3 3.5 2 2.5 3 3.5 2 2 2 Me+e- Gev/c Me+e- Gev/c Me+e- Gev/c

10 20 Net yield Net yield Net yield 5 5 10

0 0 0

-10 -5

-5 2 2.5 3 3.5 2 2.5 3 3.5 2 2.5 3 3.5 2 2 2 Me+e- Gev/c Me+e- Gev/c Me+e- Gev/c

Figure 5.15: Best ﬁt plotted on the mixed-event subtracted spectra for the pT -dependence for the 20-40% centrality bin.The pT binning from top left to bottom right goes 0-1, 1-2, 2-3, 3-4, 4-5 and 5-7 GeV/c. The blue curve is the CB + exponential ﬁt and the green curve is the exponential alone.

The quality of the simulation-to-data matching is judged from a comparison of the DC φ distributions. These distributions for run group 0 are shown in figure 5.22, where the red distribution represents the simulations and the blue represents the data. These distributions for the other run groups are shown in Appendix B. Table 5.10 shows the average difference between the data and the simulations in the φ distributions. The systematic uncertainty associated with the simulation to data matching is evaluated as follows: The simulated and data DC phi distributions are normalized to each other within each run group using the sum of yields over all φ for all DC sectors and all charge signs combined. Then the simulated and real DC φ distributions are summed across all run groups and separated into different DC sectors and charge signs. The RMS systematic uncertainty on the simulation to data matching is then calculated from the distribution of ratios of simulations to data yield for

66 20 ME subtracted 40 - 60% centrality CB + exp. Net yield Net yield 40 Net yield 40 Exp. only 10

20 20

0 0

2 2.5 3 3.5 2 2.5 3 3.5 2 2.5 3 3.5 2 2 2 Me+e- Gev/c Me+e- Gev/c Me+e- Gev/c

Net yield Net yield 4 Net yield 5 4

2 2 0 0 0

-5 -2 2 2.5 3 3.5 2 2.5 3 3.5 2 2.5 3 3.5 2 2 2 Me+e- Gev/c Me+e- Gev/c Me+e- Gev/c

Figure 5.16: Best ﬁt plotted on the mixed-event subtracted spectra for the pT -dependence for the 40-60% centrality bin. The pT binning from top left to bottom right goes 0-1, 1-2, 2-3, 3-4, 4-5 and 5-7 GeV/c. The blue curve is the CB + exponential ﬁt and the green curve is the exponential alone. all sectors and charge signs. The resulting uncertainty is 3.7%. The uncertainty for electron pairs can be estimated by doubling that for single electrons, where the assumption is that there is a correlation between the uncertainties of the two electrons. Therefore the systematic uncertainty associated with the simulation to data matching is 7.4%.

5.5.4 Acceptance Calculation

After determining the fiducial cuts using single electrons and implementing them, the acceptance is calculated using J/ψ simulations. J/ψ are simulated via PYTHIA with flat distributions in rapidity, z-vertex and pT and run through the GEANT-3 model of the PHENIX detector. The ratio of the number of J/ψ’s after reconstruction to the number of initially simulated J/ψ’s in a given pT bin, centrality bin and run group is the acceptance. The differences in acceptance with centrality are due to the fact that the HBD electron identification cuts are centrality dependent.

67 ME subtracted 60 - 92% centrality 10 CB + exp. 6 Net yield 15 Net yield Net yield Exp. only 4 10 5

2 5 0 0

0 -2 2 2.5 3 3.5 2 2.5 3 3.5 2 2.5 3 3.5 2 2 2 Me+e- Gev/c Me+e- Gev/c Me+e- Gev/c

4 3 Net yield Net yield

2 2

0 0

2 2.5 3 3.5 2 2.5 3 3.5 2 2 Me+e- Gev/c Me+e- Gev/c

Figure 5.17: Best ﬁt plotted on the mixed-event subtracted spectra for the pT -dependence for the 60-92% centrality bin. The pT binning from top left to bottom right goes 0-1, 1-2, 2-3, 3-4 and 4-5 GeV/c. The blue curve is the CB + exponential ﬁt and the green curve is the exponential alone.

The calculated acceptance includes both the geometric acceptance of the PHENIX detector and the electron identification efficiency. Figure 5.23 shows the J/ψ acceptance as a function of pT for different centrality sets for run group 0. Figure 5.24 shows the acceptance in the 0-5% centrality bin for all six run groups. The acceptance plots for the remaining run groups (all centralities) and for the remaining centralities (all run groups) are shown in Appendix C. The pT dependence of the acceptance is due to the decay kinematics of the J/ψ. At low pT , the electrons are emitted back to back, and so are detected in opposite arms. As pT increases, the angle between them decreases. Around 3.0 GeV/c, the acceptance is the smallest. This is roughly where the angle between the electrons is 90 degrees, and due to the PHENIX geometry, there is the smallest chance of detecting both electrons. The increase after that occurs because the electrons get close to being emitted in the same direction, which maximizes the probability that both will be detected. The exception

68 Table 5.9: Fit results and yields as a function of centrality and pT . A ’*’ indicates that the yield and yield error were obtained by scaling the direct sum yield and error by the ratio of the ﬁt yield to the direct sum yield.

2 Centrality pT χ N Nexp s Yield Yield Error 0-20% 0.5 33.8 103 -4.90e+07 -6.37 570 40.3 0-20% 1.5 53.8 96.0 -4.45e+07 -6.37 528 43.9 0-20% 2.5 39.0 42.1 45.1 -0.849 232 41.8 0-20% 3.5 70.0 10.2 1.58e+07 -7.37 56.2 15.7 0-20% 4.5 60.8 5.60 -1.27e+05 -5.00 30.8 13.4 0-20% 6.0 40.4 3.19 1.97e+20 -22.4 17.5 10.2 20-40% 0.5 51.0 55.9 2.30e+04 -2.67 307 30.0* 20-40% 1.5 34.1 72.1 53.0 -0.922 397 31.6 20-40% 2.5 33.1 32.7 242 -1.65 180 27.4 20-40% 3.5 44.9 9.92 1.60 -0.108 54.6 15.4 20-40% 4.5 29.1 5.33 2.48e+16 -17.8 29.3 7.76 20-40% 6.0 44.3 0.357 13.6 -0.991 9.0 7.0* 40-60% 0.5 38.4 20.7 1.45e+03 -2.10 114 12.0* 40-60% 1.5 43.3 28.0 2.84e+03 -2.38 154 14.4* 40-60% 2.5 42.7 11.4 115 -1.50 62.9 11.6 40-60% 3.5 50.1 1.95 7.97e-16 9.11 10.7 4.26 40-60% 4.5 32.0 1.58 19.9 -1.80 8.68 4.21 40-60% 6.0 20.0 1.36 -3.50e+06 -7.42 7.46 3.69 60-92% 0.5 27.2 9.03 2.24e+04 -3.76 49.7 7.1* 60-92% 1.5 51.5 8.09 2.39e+03 -3.34 44.5 7.0* 60-92% 2.5 22.7 3.07 10.0 -1.28 16.9 4.61 60-92% 3.5 8.67 1.10 2.86e+10 -11.8 6.05 2.46 60-92% 4.5 6.35 0.156 0.154 -0.0991 0.860 1.64

to this is for run group 5, whose shape changes at lower pT because an eighth of the RICH is completely dead. The effect becomes less pronounced at higher pT . The uncertainty in the electron identification efficiency is taken from [84], where the ratio of the number of electron pairs where both electrons passed the electron identification cuts to the number of electron pairs where only one of the two electrons passed those cuts was measured. This ratio was compared with that for simulated π0 Dalitz decays, and the difference found to be 1.1%.

The momentum resolution of the detector smears the reconstructed pT of electrons. This eﬀect was tested in [84], where a systematic uncertainty of 0.2% was assigned to the diﬀerence between the reconstructed and true pT distributions.

69 Figure 5.18: J/ψ internal radiative tail line shape from [20].

Other uncertainties relevant to the acceptance are associated with the shape of the simulated pT and rapidity distributions. We assign a systematic uncertainty of 2% each for those. Also, the shape of the J/ψ peak in simulations must match that in the data, or the mass cut of 2.8-3.4 GeV/c2 will yield different fractions of the total yield in both cases. This was tested by calculating the ratio of the yield inside the mass window 2.8-3.4 GeV/c2 to the total yield for simulations, and comparing it to the same quantity calculated from the CB fit function. The difference was found to be 0.3%, and that is taken as the systematic uncertainty on that assumption.

5.5.5 Embedding Correction

As the detector occupancy increases with increasingly central collisions, the efficiency for recon- structing tracks goes down. This efficiency is quantified by embedding simulated tracks into real events at the hits level, and then checking to see if that track survived the reconstruction process. The ratio of the number of tracks in a given centrality bin that survived reconstruction to the number of total embedded tracks in that centrality bin is the single track embedding correction for that centrality bin. This number is squared to get the pair embedding efficiency, ǫemb. The embedding study for Run-10 Au+Au electrons was performed by [79]. The results of this study are shown in table 5.11.

70 90000

Counts 80000 70000 60000 50000 Reconstructed 40000 30000 20000 10000 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Mass [GeV/c2]

×103

3000 Counts 2500

2000 Simulated 1500

1000

500

0 0 1 2 3 4 5 Mass [GeV/c2]

Figure 5.19: Reconstructed J/ψ spectrum (top) as compared with the simulated J/ψ spectrum (bottom).

5.6 Invariant Yield and RAA

The main physics targets to extract from this analysis are the J/ψ invariant yield, RAA and p2 . The invariant yield represents the number of J/ψ’s produced on a per-event basis with all h T i detector and eﬃciency eﬀects taken into account.

The J/ψ invariant yield integrated over pT as a function of rapidity in a given centrality bin is given by dN 1 NJ/ψ B + = , (5.5) e e− dy ∆c∆y N ǫ evts ∗ tot where NJ/ψ is the raw J/ψ yield in a given centrality bin integrated over all pT , Nevts is the number + − of sampled minimum bias events, B + − is the J/ψ e e branching ratio, ∆y is the width of e e → the rapidity bin, ∆c is the width of the centrality bin, and ǫtot is the correction factor representing the combined eﬀect of all eﬃciencies given by

ǫ = A ǫJ/ψ ǫ , (5.6) tot × eID emb

71 Figure 5.20: Comparison of α vs φ for data (left) and simulations (right) for the ﬁrst and largest run group.

. where A ǫJ/ψ is the acceptance electron reconstruction efficiency and ǫ is the embedding × eID × emb efficiency. The p -integrated invariant yield is plotted against N in figure 5.25. The shape of T h parti this plot indicates that more J/ψ’s are produced with increasing collision centrality. The number of J/ψ’s produced per binary collision can be found by dividing the invariant yield by N in h colli the corresponding centrality bin. This is shown in figure 5.26. The J/ψ invariant yield in a given rapidity, centrality and pT bin is given by eq 5.7. 2 1 d N 1 1 NJ/ψ B + = , (5.7) 2πp e e− dydp 2πp ∆y∆p ∆c N ǫ T T T T evts ∗ tot where NJ/ψ is the raw J/ψ yield in a given centrality and pT bin, Nevts is the number of sampled + − minimum bias events, B + − is the J/ψ e e branching ratio, ∆y is the width of the rapidity e e → bin, ∆c is the width of the centrality bin, ∆pT is the width of the pT bin, and ǫtot is the correction factor representing the combined effect of all efficiencies given by

ǫ = A ǫJ/ψ ǫ , (5.8) tot × eID emb

72 Figure 5.21: Comparison of pc1 y vs pc1 z for data (left) and simulations (right) for the ﬁrst and largest run group.

. where A ǫJ/ψ is the acceptance electron reconstruction efficiency and ǫ is the embedding × eID × emb efficiency. For the pT study, the data are divided into four centrality bins: 0-20%, 20-40%, 40-60% and 60-92%. Figure 5.27 shows the the invariant yield as a function of pT in those four centrality bins, uncorrected for bin shift effects, discussed in section 5.6.2. It is important to note that with the exception of the 60-92% centrality bin, the invariant yield is calculated out to 7.0 GeV/c. The results are shown in table 5.12.

5.6.1 p + p Reference

The p + p reference data come from the 2006 PHENIX Run-06 200 GeV p + p run [1], during which the integrated luminosity was 6.2 0.2 nb−1. Figure 5.28 (to be discussed in the next ± section) shows the p + p invariant yield as a function of pT . Table 5.14 shows the p + p invariant yield and its uncertainties. These results were taken from [1] as cross sections and then converted

73 Table 5.10: Average diﬀerence in φ distributions between simulations and data for each run group.

Run Group Number of MB Events Average Diﬀerence 0 4.68e+09 2.7% 1 5.72e+08 2.1% 2 9.48e+08 10% 3 2.08e+08 5.8% 4 2.24e+08 5.2% 5 5.43e+08 10% 0-5 7.15e+09 3.7%

Table 5.11: Embedding values and their systematic uncertainties as a function of centrality.

Centrality ǫemb syst 0-5% 0.68 0.0028 5-10% 0.71 0.0025 10-15% 0.73 0.0024 15-20% 0.75 0.0023 20-30% 0.78 0.0017 30-40% 0.81 0.0015 40-50% 0.85 0.0017 50-6% 0.88 0.0015 60-92% 0.93 0.00059

to invariant yields using the p + p inelastic cross section of 42 mb. The pT integrated result is 1.10 10−6 2.38 10−8 1.43 10−7. × ± × ± × 5.6.2 Bin Shift Correction

2 Because Bd N/dydpT is calculated at the center of each pT bin, a correction needs to be made for bin effects, since the centroid of the yield is not at the bin center. This is corrected for by moving the point up or down such that it is at the correct value when plotted at the center of each pT bin. The technique for determining those corrected values is taken from [64]. First, the uncorrected values are fit with a modified Kaplan function of the form

2 p2 pT f(pT )= p0 1+ . (5.9) p1 !

74 2 Table 5.12: Bd N/dydpT values, uncorrected for bin shift eﬀects. Systematic uncertainties are discussed in section 5.7.

1 d2N −6 −6 −6 Centrality pT 2 B 10 stat 10 syst 10 πpT dydpT × × × 0-20% 0.5 25.2 1.78 1.95 0-20% 1.5 9.47 0.786 0.735 0-20% 2.5 3.45 0.622 0.268 0-20% 3.5 0.826 0.231 0.0641 0-20% 4.5 0.334 0.148 0.0259 0-20% 6 0.0541 0.0315 0.00420 20-40% 0.5 13.1 1.28 1.28 20-40% 1.5 6.84 0.545 0.531 20-40% 2.5 2.55 0.388 0.198 20-40% 3.5 0.768 0.217 0.0596 20-40% 4.5 0.303 0.0801 0.0235 20-40% 6 0.0266 0.0207 0.00261 40-60% 0.5 6.64 0.675 0.709 40-60% 1.5 3.35 0.313 0.316 40-60% 2.5 0.936 0.173 0.0727 40-60% 3.5 0.162 0.0644 0.0126 40-60% 4.5 0.0932 0.0451 0.00723 40-60% 6 0.0233 0.0115 0.00181 60-92% 0.5 1.38 0.196 0.113 60-92% 1.5 0.483 0.0756 0.0380 60-92% 2.5 0.145 0.0396 0.0113 60-92% 3.5 0.0528 0.0215 0.00410 60-92% 4.5 0.00532 0.0101 0.000413

75 3 3 ×10 Run Group 0 α < 0 Blue - Data Red - Sims ×10 Run Group 0 α > 0 Blue - Data Red - Sims 600 600 500 500 400 400 300 300 East South 200 200 100 100 0 0 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6φ [rad] 3.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6φ [rad] 3.8

×103 Run Group 0 α < 0 Blue - Data Red - Sims ×103 Run Group 0 α > 0 Blue - Data Red - Sims 600 600 500 500 400 400 300 300 East North 200 200 100 100 02 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 02 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 φ [rad] φ [rad]

3 3 ×10 Run Group 0 α < 0 Blue - Data Red - Sims ×10 Run Group 0 α > 0 Blue - Data Red - Sims 600 600 500 500 400 400 300 300 WestSouth 200 200 100 100 0 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8φ 1 [rad] -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8φ 1 [rad]

×103 Run Group 0 α < 0 Blue - Data Red - Sims ×103 Run Group 0 α > 0 Blue - Data Red - Sims 700 600 600 500 500 400 400 300 300 WestNorth 200 200 100 100 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 φ [rad] φ [rad]

Figure 5.22: DC phi distributions for simulations (red) and data (blue) in each DC sector (top to bottom) for each α (left to right) for run group 0.

Second, a correction factor r is obtained using eq 5.9 according to

c +∆ 2 pT / c ∆ 2 f(pT )dpT pT − / r = c , (5.10) R ∆f(pT )

c where ∆ is the width of the bin and pT is the pT at the center of the bin. The corrected value of 2 Bd N/dydpT is then obtained by dividing the uncorrected value by the correction factor r. The newly corrected values are ﬁtted again and the correction factor r is obtained. This is iterated until 2 r converges. The results showing the ﬁnal values of r and the corrected values of Bd N/dydpT are shown in table 5.13. Figure 5.28 shows the bin-shift corrected results for each centrality, as well

2 as that for the p + p reference used in this analysis. A comparison of B d N vs p for Run-10 dydpT T and Run-4 is shown in ﬁgure 5.29. The data agree with each other within statistical uncertainties everywhere. Note that there is no 6 GeV/c data point for the Run-4 data set.

76 2 Table 5.13: Correction factor r and corrected Bd N/dydpT values. Systematic uncertainties are discussed in section 5.7.

1 d2N −6 −6 −6 Centrality pT r Corrected 2 B 10 stat 10 syst 10 πpT dydpT × × × 0-20% 0.5 0.991 25.4 1.80 2.25 0-20% 1.5 0.995 9.52 0.790 0.844 0-20% 2.5 1.00 3.44 0.620 0.305 0-20% 3.5 1.02 0.814 0.228 0.0722 0-20% 4.5 1.03 0.324 0.144 0.0287 0-20% 6 1.26 0.0428 0.0249 0.00380 20-40% 0.5 0.992 13.2 1.29 1.66 20-40% 1.5 0.995 6.87 0.548 0.610 20-40% 2.5 1.00 2.55 0.388 0.226 20-40% 3.5 1.01 0.760 0.215 0.0674 20-40% 4.5 1.02 0.296 0.0782 0.0262 20-40% 6 1.19 0.0223 0.0174 0.00282 40-60% 0.5 0.991 6.70 0.682 0.947 40-60% 1.5 0.996 3.37 0.314 0.402 40-60% 2.5 1.00 0.932 0.172 0.0826 40-60% 3.5 1.02 0.160 0.0633 0.0142 40-60% 4.5 1.03 0.0902 0.0437 0.00800 40-60% 6 1.25 0.0187 0.00926 0.00166 60-92% 0.5 0.990 1.40 0.198 0.136 60-92% 1.5 0.996 0.485 0.0759 0.0441 60-92% 2.5 1.01 0.144 0.0394 0.0128 60-92% 3.5 1.02 0.0516 0.0210 0.00458 60-92% 4.5 1.05 0.00509 0.00970 0.000451

77 0.014 Run Group 0 0-10% 40-50% 0.012 10-20% 50-60% 0.01 20-30% 60-92% Acceptance 0.008 30-40% 0.006

0.004

0.002

0 0 1 2 3 4 5 6 7p 8 [GeV/c] T

0.014 Run Group 0 0-20% 0.012 20-40% 0.01 40-60% Acceptance 0.008 60-92% 0.006

0.004

0.002

0 0 1 2 3 4 5 6 7p 8 [GeV/c] T

Figure 5.23: J/ψ acceptance as a function of pT for each centrality bin for run group 0.

5.6.3 RAA

RAA is deﬁned as the J/ψ invariant yield for Au+Au divided by the J/ψ invariant yield for th p + p, and then divided by the average number of binary collisions. Integrated over pT for the i centrality bin, it is given as a function of rapidity by

dN Au+Au(i)/dy 1 NJ/ψ RAA(i)= p+p , (5.11) Ncoll (i) dN /dy h i NJ/ψ

th and for the i centrality bin as a function of rapidity and pT by

d2N Au+Au(i)/dydp 1 NJ/ψ T RAA(i)= 2 p+p , (5.12) Ncoll (i) d N /dydpT h i NJ/ψ

2 Au+Au th where d N /dydpT (i) represents the Au+Au invariant yield in the i centrality bin for a given p , d2N p+p/dydp (i) represents the p + p invariant yield in the same p bin, and N is T T T h colli the average number of binary collisions for that centrality bin.

78 0-5% Centrality

0.014 Run Group 0 Run Group 1 0.012 Run Group 2

Acceptance Run Group 3 0.01 Run Group 4 Run Group 5 0.008

0.006

0.004

0.002

0 0 1 2 3 4 5 6 7 8 p [GeV/c] T

Figure 5.24: J/ψ acceptance as a function of pT for each of the six run groups all for the 0-5% centrality bin.

5.6.4 Au+Au RAA vs Npart

With the p + p reference values in hand, RAA can now be calculated. A comparison of Run-10 and Run-4 Au+Au RAA vs Npart is shown in ﬁgure 5.30. In the Run-10 measurement the 40-60% centrality class is broken into two centrality classes: 40-50% and 50-60%. The Run-10 statistical uncertainties are signiﬁcantly smaller than those on the Run-4 data.

5.6.5 RAA vs pT

RAA is also calculated in four centrality bins against pT . That result is shown in ﬁgure 5.31. The Run-10 data agree with the Run-4 data well within statistical uncertainty for the 0-20% and 20-40% centrality classes. For the 40-60% and 60-92% centrality classes, the Run-10 data tend to show weaker suppression than the Run-4 data. The Run-10 data extend to 6.0 GeV/c for three out of the four centrality classes, where the Run-4 data does not go past 5.0 GeV/c in any centrality class.

79 ×10-3 0.35 dy dN

B Syst = +6.0%, -2.9% glob 0.3

0.25

0.2

0.15

0.1

0.05

0 0 50 100 150 200 250 300 350 Npart

Figure 5.25: BdN/dy as a function of N integrated over p . The boxes are systematic h parti T uncertainties, described in section 5.7.

5.6.6 p2 vs N h T i part Finally, the p2 is calculated. The results of this are shown in table 5.15 and are plotted h T i graphically in ﬁgure 5.32, with the Run-10 data being the blue points and the Run-4 data being the red points. The Run-4 data are shifted to the right by 10 in Npart to make the plot easier to read. The Run-10 and Run-4 data agree well within their statistical uncertainties. It should be

2 noted that for this calculation of p2 , only B d N values out to 5.0 GeV/c were included so as to h T i dydpT match the Run-4 calculation.

Table 5.14: p + p invariant yield as a function of pT , taken from reference [1].

1 d2N −8 −2 −8 −8 pT 2 Bee 10 (GeV/c) stat 10 syst 10 πpT dydpT × × × 0.5 9.02 0.298 0.608 1.5 4.78 0.152 0.288 2.5 1.42 0.076 0.0939 3.5 0.422 0.0377 0.0287 4.5 0.112 0.0200 0.00690 6 0.0100 0.00189 0.00106

80 ×10-6 coll 1 /N Syst = +6.0%, -2.9% glob dy dN B 0.8

0.6

0.4

0.2

0 0 50 100 150 200 250 300 350 Npart

Figure 5.26: BdN/dy/ N as a function of N integrated over p . The boxes are h colli h parti T systematic uncertainties, described in section 5.7.

Table 5.15: p2 as a function of N . Systematic errors are described in section 5.7 h T i part N p2 (GeV/c)2 stat syst part h T i 277.5 4.1 0.55 0.13 135.6 4.7 0.58 0.18 56 3.9 0.57 0.18 12.5 3.4 0.79 0.10

5.7 Systematic Uncertainties

Systematic uncertainties in PHENIX are grouped into one of three categories called Type A, B and C. Type A systematic uncertainties are uncorrelated point-to-point, and are folded in with statistical errors and displayed as a vertical error bar on the plots. Type B systematic uncertainties are correlated point-to-point uncertainties, shown on plots as boxes. Type C systematic uncertainties are global uncertainties, usually represented as a percentage in the legend on the plot. A summary of the systematic uncertainties is presented in table 5.16. Systematic uncertainties calculated explicitly for this analysis are the systematic uncertainty associated with the determi-

81 -3 T 10 0-20%, syst = +6.0%,-2.9% glob -4 20-40%, syst = +6.0%,-2.9% N/dydp 10 2 glob d 40-60% syst = +6.0%,-2.9% ee glob -5

)*B 10 60-92%, syst = +6.0%,-2.9%

T glob *p π 10-6 1/(2

10-7

10-8

10-9

10-10

10-11 0 1 2 3 4 5 6 p [GeV/c] T

Figure 5.27: Uncorrected 1 Bd2N/dydp as a function of p in four centrality bins. 2πpT T T The global uncertainty in each centrality is listed as a percentage in the legend. The boxes are systematic uncertainties, described in section 5.7. nation of the global values of the (α, n, m, σ) parameters used in the CB model, the systematic uncertainty on the acceptance associated with the fiducial cuts, and the systematic uncertainty associated with the shape difference between the J/ψ lineshape used in the CB fit and the J/ψ line shape produced by the single J/ψ simulations. The rest were calculated in other analyses, for which a reference is given in each of those cases.

5.7.1 BdN/dy vs Npart

Type B systematics were calculated on BdN/dy by adding the fiducial, eID, momentum smearing, embedding and mixed-event normalization uncertainties in quadrature. Only the embedding and mixed-event normalization certainty vary with Npart. Type C global systematics were calculated by adding in quadrature the systematics on the BBC trigger efficiency, the assumption that the input y and pT distributions are flat, the shape of the pT and y distributions used in the acceptance calculations, the agreement between the fitted CB shape and the peak line shape in simulations, and the fitted CB shape parameters. The asymmetry in the Type C error comes from

82 Table 5.16: Summary of systematic uncertainties.

Source Value Npart pT +6.0% Fit systematic from use of −2.9% C C fixed α, n, m, σ Uncertainty due to mixed 0.2-8.1% B B event background normalization Difference in CB shape be- 0.3% C C tween simulations and data Embedding [79] 0.06-0.4% B C N [78] 9.7-19.3% B C h colli Acceptance-Fiducial cuts 7.4% B B Acceptance-y-dep [64] 2% B B Acceptance-pT -dep [64] 2% B B Momentum smearing [84] 0.2% B B BBC MB trigger effi- 3.0% B B ciency [78] eID cuts [84] 1.1% B B p + p total cross section [1] 7% C C p + p type-B [1] 12%-16% — B

83 -4 ] 10 -2 0-20%, syst = +6.0%,-2.9% glob 20-40%, syst = +6.0%,-2.9% glob -5 40-60% syst = +6.0%,-2.9% 10 glob 60-92%, syst = +6.0%,-2.9% glob p+p, syst = ±10.0% [(GeV/c) -6 glob T 10

10-7 N/dydp 2 d

ee 10-8 )*B T -9 *p 10 π

1/(2 10-10

10-11 0 1 2 3 4 5 6 p [GeV/c] T

2 Figure 5.28: Corrected B d N vs p for Run-10 and Run-4 data. The Run-4 data are dydpT T shifted to the right by 0.2 GeV/c for ease of comparison. The boxes are systematic uncertainties, described in section 5.7.

the asymmetry in the uncertainty on the ﬁtted CB parameters. When calculating BdN/dy/Ncoll vs Npart, the Type B systematic on Ncoll is added in quadrature to the Type B errors on BdN/dy.

5.7.2 RAA vs Npart

Type B systematics on RAA were calculated by adding the Type B systematics on BdN/dy/Ncoll and the p + p reference in quadrature. Type C systematics on RAA were calculated by adding the

Type C systematics on BdN/dy/Ncoll in quadrature with those in the p + p reference.

2 5.7.3 Bd N/dydpT vs pT

2 Type B systematics on Bd N/dydpT were calculated by adding the systematic uncertainties on the simulation/data matching, eID efficiency, momentum smearing, the pT shape used in the simulations and the uncertainty on scaling the fit yield by the ratio of the fit yield to the direct sum in quadrature. Type C systematics were calculated by adding in quadrature the systematic uncertainties on the BBC trigger effciency, the assumption that the input y distribution is flat, the

84 0-20% 20-40% -4 -4 ] 10 ] 10 -2 Run 10, syst = +6.0%,-2.9% -2 Run 10, syst = +6.0%,-2.9% glob glob -5 -5 10 Run 4 10 Run 4

[(GeV/c) -6 [(GeV/c) -6 T 10 T 10

10-7 10-7 N/dydp N/dydp 2 2 d -8 d -8 ee 10 ee 10 )*B )*B T -9 T -9

*p 10 *p 10 π π

-10 -10 1/(2 10 1/(2 10

-11 -11 10 0 1 2 3 4 5 6 10 0 1 2 3 4 5 6 p [GeV/c] p [GeV/c] T T

40-60% 60-92% -4 -4 ] 10 ] 10 -2 Run 10, syst = +6.0%,-2.9% -2 Run 10, syst = +6.0%,-2.9% glob glob -5 -5 10 Run 4 10 Run 4

[(GeV/c) -6 [(GeV/c) -6 T 10 T 10

10-7 10-7 N/dydp N/dydp 2 2 d -8 d -8 ee 10 ee 10 )*B )*B T -9 T -9

*p 10 *p 10 π π

-10 -10 1/(2 10 1/(2 10

-11 -11 10 0 1 2 3 4 5 6 10 0 1 2 3 4 5 6 p [GeV/c] p [GeV/c] T T

2 Figure 5.29: Corrected B d N vs p for Run-10 and Run-4 data. The Run-4 data are dydpT T shifted to the right by 0.2 GeV/c for ease of comparison. The boxes are systematic uncertainties, described in section 5.7. embedding, the ﬁtted CB parameters, the assumption that the CB line shape is the same for data and simulations and the mixed-event normalization.

5.7.4 RAA vs pT

2 Type B systematics on RAA were calculated by adding the Type B errors on Bd N/dydpT and the Type B errors on the p + p reference in quadrature. Type C systematics were calculated 2 by adding the Type C errors on Bd N/dydpT , the Type C errors in the p + p reference and the uncertainty in Ncoll in each centrality bin in quadrature.

5.7.5 p2 vs N h T i part Propagating the Type B systematic uncertainties in the calculation of p2 requires assuming h T i that the uncertainties take on a Gaussian distribution. The uncertainty distribution for the ﬁrst and last points in the pT distribution is randomly sampled. The uncertainties on the points in between 2 the ﬁrst and last points are assumed to be correlated linearly. Then all Bd N/dydpT points are

85 AA

R 1 Run 10, syst = +9.2,-7.6% glob Run 4, syst = ±12% 0.8 glob

0.6

0.4

0.2

0 0 50 100 150 200 250 300 350 Npart

Figure 5.30: Comparison of Run-10 (blue) and Run-4 (red) pT -integrated RAA as a function of Npart. The boxes are systematic uncertainties, described in section 5.7. shifted according to that correlation, and a new value of p2 is calculated. This procedure is h T i repeated many times, and the width of the resulting distribution is taken as the Type B systematic on p2 . There are no Type C systematic uncertainties on p2 since they cancel in the calculation. h T i h T i

86 0-20% 20-40%

AA 1 AA R R 1.4 Run 10, syst = +13.5%,-12.4% Run 10, syst = +13.5%,-12.5% glob glob Run 4, syst = ±10% Run 4, syst = ±10% 1.2 glob 0.8 glob 1 0.6 0.8

0.4 0.6 0.4 0.2 0.2

0 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 p [GeV/c] p [GeV/c] T T

40-60% 60-92%

AA 1.8 AA 1.8 Run 10, syst = +21.4%,-20.7% R Run 10, syst = +15.7%,-14.8% R glob glob Run 4, syst = ±28% 1.6 Run 4, syst = ±13% 1.6 glob glob 1.4 1.4 1.2 1.2 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 p [GeV/c] p [GeV/c] T T

Figure 5.31: Comparison of Run-10 (blue) and Run-4 (red) RAA as a function of pT in four centrality bins. The boxes are systematic uncertainties, described in section 5.7.

> 7 2 T

0 0 50 100 150 200 250 300

Figure 5.32: p2 as a function of N . h T i part

87 CHAPTER 6

DISCUSSION AND COMPARISON WITH THEORY

This chapter discusses the results presented in the previous chapter and compares them with existing measurements and theoretical predictions.

6.1 RAA vs Npart

The ﬁrst comparison is shown in ﬁgure 6.1, where RAA is plotted versus Npart for the Run- 10 midrapidity dielectron data (blue) and the Run-7 forward rapidity dimuon data (red). The AA

R 1.4 PHENIX Run-10, Central Arms, syst = +9.2%,-7.6% glob PHENIX Run-7 Muon Arms, syst = ±9.2% 1.2 glob

0.8

0.6

0.4

0.2

0 0 50 100 150 200 250 300 350 Npart

Figure 6.1: Comparison of PHENIX midrapidity RAA vs Npart (blue) with PHENIX forward data(red).

midrapidity data show a suppression pattern similar to that in the forward data for Npart < 100, after which the suppression is stronger in the forward data.

The second comparison is illustrated in ﬁgure 6.2, which shows RAA for the Run-10 Au+Au data and RAA for the Run-5 Cu+Cu data. The two datasets show a similar suppression pattern

88 AA 1 R Run-10, Au+Au, syst = +9.2%,-7.6% glob Run-5, Cu+Cu, syst = ± 12% 0.8 glob

0.6

0.4

0.2

0 50 100 150 200 250 300 350 Npart

Figure 6.2: Comparison of PHENIX Au+Au RAA vs Npart (red) with PHENIX Cu+Cu data(blue). out to N 100. The fact that Cu is a much smaller nucleus than Au allows the region where 50 part ≈

Shown in ﬁgure 6.4 is a comparison of the PHENIX Run-10 200 GeV Au+Au RAA with the

ALICE 2.76 TeV Pb+Pb RAA. The ALICE data provide the best comparison of LHC data with PHENIX data because ALICE is the only LHC experiment which measures quarkonia down to zero pT . The most striking feature of the comparison is that for central collisions, the RAA for the PHENIX data is a factor of three smaller than it is for the ALICE data. As mentioned in chapter 3, this can be explained as a consequence of charm coalescence due to much larger charm production at the LHC energy, and was in fact predicted [69] before the data were published.

89 AA 1 R PHENIX Run-10, syst = +9.2%,-7.6% glob STAR, |y|<1.0, syst = ±12% 0.8 glob

0.6

0.4

0.2

0 50 100 150 200 250 300 350 Npart

Figure 6.3: Comparison of PHENIX (red) Au+Au data and STAR (blue), both at 200 GeV.

Comparisons of RAA vs Npart with theory begin with the model by Gunji, et al. [21] which was discussed in section 3.5. The model uses fixed melting temperatures of the J/ψ and χ and a feed down fraction of 30% to predict the survival probability after CNM effects have been factored out, and the results compared with the Run-4 data are shown in figure 3.18. The parameter α quantifies the thermal decay width of the J/ψ when the temperature in the QGP is half the dissociation temperature of the J/ψ. It was found in [21] that the best description of the Run-4 data was obtained with α = 0.

In [21], the RAA data were modiﬁed by dividing them by the predicted CNM modiﬁcation.

For comparison with the the RAA values from this analysis, the theory curves from [21] were multiplied by the CNM correction used there to make them comparable with RAA. The results of this comparison are shown in ﬁgure 6.5. Each theory curve represents a diﬀerent value of α used in the calculation. Where the Run-4 data were best described by the curve for α = 0, the Run-10 results are best described by the curves for α = 0.1 or 0.2. Continuing with theory comparisons, Rapp and Zhao [69] developed a model in which the J/ψ is strongly bound in medium or weakly bound in medium. Although Rapp believes the strong binding

90 1.2

AA PHENIX Run-10, Au+Au, 200 GeV, |y| < 0.35, syst = +9.2%,-7.6% glob R ALICE, Pb+Pb, 2.76 TeV, |y|<0.8, syst = 13% 1 glob

0.8

0.6

0.4

0.2

0 0 50 100 150 200 250 300 350 Npart

Figure 6.4: Comparison of PHENIX (red) 200 GeV Au+Au data and ALICE (blue) 2.76 TeV Pb+Pb data. case to be more likely, both cases will be presented here. Comparisons of the model with Run-10 data for RAA vs Npart are shown in figure 6.6 (strong binding) and figure 6.7 (weak binding). The strength of the coalescence component differs between the two binding scenarios, but the difference in suppression more or less compensates so that the overall suppression is similar. A model has been developed by Capella, et al. [86] that is similar to Rapp’s in that it is a two-component model, with one component modeling the dissociation due to hot nuclear matter and the other component modeling the off-diagonal recombination of cc¯ pairs. A comparison to the data is shown in figure 6.8. The dotted red curve represents initial-state effects, the dashed-dotted yellow curve shows the effects of adding dissociation, and the solid blue curve shows the effect of adding recombination. The calculation does a good job of describing the data.

d2N 6.2 B dydpT vs pT

2 A comparison of bin-shift corrected data of B d N vs p is compared with a model by Xu, et dydpT T al. [22] in ﬁgure 6.9. The model overpredicts the data at lower pT .

91 AA 1

R Run 10, syst = +9.2%,-7.6% glob α = 0.0 0.8 α = 0.1 α = 0.2 α = 0.3 0.6 α = 0.4

0.4

0.2

0 0 50 100 150 200 250 300 350 Npart

Figure 6.5: Comparison of PHENIX (blue) 200 GeV Au+Au data with theory curves from [21], where the diﬀerence between each theory curve is the value of α used represents the strength of the thermal decay width of the J/ψ.

6.3 RAA vs pT

All comparisons with theory for pT -dependence will be only for the 0-20% centrality class. A comparison for these data with theory begins with a model from Xu, et al. [22]. The calculation is shown in figure 6.10. This is a two-component model which contains a term for the suppression of the primordial J/ψ production and a term for the regenerated J/ψ production. The primordial J/ψ yield is less suppressed as pT increases, while the regeneration component decreases with increasing pT . The model overpredicts the RAA, particularly at higher pT and the shape is completely different. A more promising model is Rapp’s model for strong and weak binding, shown in figures 6.11 (strong binding) and 6.12 (weak binding). Both calculations do a reasonably good job of repro- ducing the essentially flat distribution of the data, but both overpredict the RAA somewhat.

6.4 p2 vs N h T i part The same calculations from Rapp, et al. can also be compared with the Run-10 p2 data, again h T i via a strong-binding and weak-binding scenario, as shown in ﬁgures 6.13 (strong-binding) and 6.14

92 AA

R 1 Run 10, syst = +9.2%,-7.6% glob Strong Binding total 0.8 primordial regeneration nuc. abs. 0.6

0.4

0.2

0 0 50 100 150 200 250 300 350 Npart

Figure 6.6: R vs N for Rapp’s strong binding scenario. AA h parti

(weak-binding). The strong binding scenario provides a better description of the data.

93 AA

R 1 Run 10, syst = +9.2%,-7.6% glob Weak Binding total 0.8 primordial regeneration nuc. abs. 0.6

0.4

0.2

0 0 50 100 150 200 250 300 350 Npart

Figure 6.7: R vs N for Rapp’s weak binding scenario. AA h parti

AA 1 Run 10, syst = +9.2%,-7.6% R glob Shadowing + Dissociation 0.8 + Recombination

0.6

0.4

0.2

0 0 50 100 150 200 250 300 350 Npart

Figure 6.8: R vs N for a calculation done by Capella, et al. AA h parti

94 -4 ] 10 -2 Run 10, 0-20%, syst = +6.0%,-2.9% glob Xu et al, 0-20% 10-5 [(GeV/c) T

-6 N/dydp

2 10 d ee )*B T -7

*p 10 π 1/(2 10-8

10-9

10-10 0 1 2 3 4 5 6 7 8 9 10 p [GeV/c] T

2 Figure 6.9: B d N vs p with calculation by Xu, et al. from [22]. dydpT T AA 1 R Run 10, 0-20%, syst = +13.5%,-12.5% glob Initial 0.8 Regeneration Xu et al, 0-20% Total

0.6

0.4

0.2

0 0 1 2 3 4 5 6 7 8 9 10 p [GeV/c] T

Figure 6.10: RAA vs pT for calculation done by Xu, et al..

95 1.6

AA Run 10, 0-20%, syst = +13.5%-12.5% glob R 1.4 Total 0-20%, Strong Binding Nuc Abs w/ fte. Primordial w/ fte. + Bfd. 1.2 Regeneration

0.8

0.6

0.4

0.2

0 0 1 2 3 4 5 6 7 8 9 10 p T

Figure 6.11: RAA vs pT for Rapp’s strong binding scenario.

1.6

AA Run 10, 0-20%, syst = +13.5%-12.5% glob R 1.4 Total 0-20%, Weak Binding Nuc Abs w/ fte. Primordial w/ fte. + Bfd. 1.2 Regeneration

0.8

0.6

0.4

0.2

0 0 1 2 3 4 5 6 7 8 9 10 p T

Figure 6.12: RAA vs pT for Rapp’s weak binding scenario.

96 > 7 2 T Run 10

0 0 50 100 150 200 250 300

Figure 6.13: p2 vs N for Rapp’s strong binding scenario. h T i part

> 7 2 T Run 10

0 0 50 100 150 200 250 300

Figure 6.14: p2 vs N for Rapp’s weak binding scenario. h T i part

97 CHAPTER 7

SUMMARY

Results from a J/ψ e+e− analysis of √s = 200 GeV Au+Au data taken at the PHENIX → NN experiment in 2010 have been presented, the goal of which was to improve on the statistical precision of the 2004 measurement. The observables presented were the invariant yield and RAA as a function of N and p , and p2 as a function of N . part T h T i part For the centrality dependence of the nuclear modiﬁcation, the new analysis was successful in improving the statistical precision to the point where it is now limited by systematic uncertainties, and the systematic uncertainties are also somewhat improved over the Run-4 analysis. The centrality dependence is found to be generally in agreement with the earlier result within uncertainties, although with two notable diﬀerences. First, even though the uncertainties mostly overlap, the new

RAA result displays a tendency toward stronger suppression as the collision centrality increases. For the most central collisions the new result shows approximately 20% lower RAA than the previous result. Second, the previous result showed what has been interpreted by a number of people as a change in slope at around Npart = 160. There was speculation when the previous result was ′ published about whether this was evidence of the onset of “melting” of the χC and ψ as the energy density increases with collision centrality. However the precise forward rapidity J/ψ data from the 2007 run did not show such a feature, and the present analysis shows clearly that no such feature exists at mid rapidity either — this was evidently a statistical ﬂuctuation upward of the RAA values at Ncoll = 165 and 220 in the previous measurement. The present results at midrapidity were compared with those obtained at forward rapidity from the 2007 run and the centrality dependence was found to be more similar than that for the Run-4 data. This only slightly modiﬁes the conclusion made from the previous result, where the midrapidity suppression was found to be weaker than at forward rapidity by approximately 40%. The somewhat stronger suppression for most central collisions seen in the present result will require some reassessment of theoretical calculations of the centrality dependence of the RAA.

98 Comparison of the previous result with STAR J/ψ data from Au+Au collisions revealed a discrepancy for the most central (large Npart) collisions. The present result supports the earlier PHENIX result, but somewhat increases the discrepancy with the STAR data for the most central collisions.

For the pT dependence of the nuclear modification, the new result is statistically more precise for the most central collisions — where it is of most interest theoretically. There was little or no improvement in statistical precision for the peripheral collision data. This was due to the poorer definition of the exponential background in the mass spectra for the peripheral data, leading to increased uncertainty in the yield of the Crystal Ball function. The pT dependence for the most central collisions (0-20%) extends to higher pT than the Run-4 result. It is found to be flat within uncertainties, with an RAA of approximately 0.35. The available theoretical calculations tend to under-predict this suppression.

99 APPENDIX A

DC α VS φ PLOTS

Figure A.1: DC α vs φ for all runs in run group 0.

100 Figure A.2: DC α vs φ for all runs in run group 1.

Figure A.3: DC α vs φ for all runs in run group 2.

101 Figure A.4: DC α vs φ for all runs in run group 3.

Figure A.5: DC α vs φ for all runs in run group 4.

102 Figure A.6: DC α vs φ for all runs in run group 5.

103 APPENDIX B

DC φ - SIMULATION/DATA COMPARISON

Run Group 1 α < 0 Blue - Data Red - Sims Run Group 1 α > 0 Blue - Data Red - Sims 80000 70000 70000 60000 60000 50000 50000 40000 40000 30000 East South 30000 20000 20000 10000 10000 0 0 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6φ [rad] 3.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6φ [rad] 3.8

Run Group 1 α < 0 Blue - Data Red - Sims Run Group 1 α > 0 Blue - Data Red - Sims 80000 70000 70000 60000 60000 50000 50000 40000 40000 30000 East North 30000 20000 20000 10000 10000 02 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 02 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 φ [rad] φ [rad]

Run Group 1 α < 0 Blue - Data Red - Sims Run Group 1 α > 0 Blue - Data Red - Sims 80000 80000 70000 70000 60000 60000 50000 50000 40000 40000

WestSouth 30000 30000 20000 20000 10000 10000 0 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8φ 1 [rad] -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8φ 1 [rad]

Run Group 1 α < 0 Blue - Data Red - Sims Run Group 1 α > 0 Blue - Data Red - Sims 80000 70000 70000 60000 60000 50000 50000 40000 40000 30000 WestNorth 30000 20000 20000 10000 10000 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 φ [rad] φ [rad]

Figure B.1: DC φ comparison of data (blue) and simulations (red) for run group 1.

104 3 3 ×10 Run Group 2 α < 0 Blue - Data Red - Sims ×10 Run Group 2 α > 0 Blue - Data Red - Sims 140 120 120 100 100 80 80 60 60 East South 40 40 20 20 0 0 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6φ [rad] 3.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6φ [rad] 3.8

3 3 140 ×10 Run Group 2 α < 0 Blue - Data Red - Sims ×10 Run Group 2 α > 0 Blue - Data Red - Sims 120 120 100 100 80 80 60 60 East North 40 40 20 20 02 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 02 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 φ [rad] φ [rad]

×103 α < 0 Blue - Data Red - Sims ×103 α > 0 Blue - Data Red - Sims 140 Run Group 2 140 Run Group 2 120 120 100 100 80 80 60 60 WestSouth 40 40 20 20 0 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8φ 1 [rad] -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8φ 1 [rad]

×103 Run Group 2 α < 0 Blue - Data Red - Sims ×103 Run Group 2 α > 0 Blue - Data Red - Sims 140 120 120 100 100 80 80 60 60 WestNorth 40 40 20 20 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 φ [rad] φ [rad]

Figure B.2: DC φ comparison of data (blue) and simulations (red) for run group 2.

α < 0 Blue - Data Red - Sims α > 0 Blue - Data Red - Sims 30000 Run Group 3 Run Group 3 25000 25000 20000 20000 15000 15000

East South 10000 10000 5000 5000 0 0 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6φ [rad] 3.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6φ [rad] 3.8

Run Group 3 α < 0 Blue - Data Red - Sims Run Group 3 α > 0 Blue - Data Red - Sims 25000 25000 20000 20000 15000 15000

East North 10000 10000 5000 5000

02 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 02 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 φ [rad] φ [rad]

Run Group 3 α < 0 Blue - Data Red - Sims Run Group 3 α > 0 Blue - Data Red - Sims 25000 25000 20000 20000 15000 15000

WestSouth 10000 10000 5000 5000 0 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8φ 1 [rad] -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8φ 1 [rad]

Run Group 3 α < 0 Blue - Data Red - Sims Run Group 3 α > 0 Blue - Data Red - Sims 30000 25000 25000 20000 20000 15000 15000

WestNorth 10000 10000 5000 5000

0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 φ [rad] φ [rad]

Figure B.3: DC φ comparison of data (blue) and simulations (red) for run group 3.

105 Run Group 4 α < 0 Blue - Data Red - Sims Run Group 4 α > 0 Blue - Data Red - Sims 30000 25000 25000 20000 20000 15000 15000 East South 10000 10000 5000 5000 0 0 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6φ [rad] 3.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6φ [rad] 3.8

Run Group 4 α < 0 Blue - Data Red - Sims Run Group 4 α > 0 Blue - Data Red - Sims 30000 25000 25000 20000 20000 15000 15000

East North 10000 10000 5000 5000

02 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 02 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 φ [rad] φ [rad]

Run Group 4 α < 0 Blue - Data Red - Sims Run Group 4 α > 0 Blue - Data Red - Sims 30000 30000 25000 25000 20000 20000 15000 15000

WestSouth 10000 10000 5000 5000 0 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8φ 1 [rad] -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8φ 1 [rad]

Run Group 4 α < 0 Blue - Data Red - Sims Run Group 4 α > 0 Blue - Data Red - Sims 30000 25000 25000 20000 20000 15000 15000 WestNorth 10000 10000 5000 5000 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 φ [rad] φ [rad]

Figure B.4: DC φ comparison of data (blue) and simulations (red) for run group 4.

Run Group 5 α < 0 Blue - Data Red - Sims Run Group 5 α > 0 Blue - Data Red - Sims 80000 70000 70000 60000 60000 50000 50000 40000 40000 30000 East South 30000 20000 20000 10000 10000 0 0 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6φ [rad] 3.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6φ [rad] 3.8

Run Group 5 α < 0 Blue - Data Red - Sims Run Group 5 α > 0 Blue - Data Red - Sims 80000 70000 70000 60000 60000 50000 50000 40000 40000 30000

East North 30000 20000 20000 10000 10000 02 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 02 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 φ [rad] φ [rad]

Run Group 5 α < 0 Blue - Data Red - Sims Run Group 5 α > 0 Blue - Data Red - Sims 80000 80000 70000 70000 60000 60000 50000 50000 40000 40000

WestSouth 30000 30000 20000 20000 10000 10000 0 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8φ 1 [rad] -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8φ 1 [rad]

Run Group 5 α < 0 Blue - Data Red - Sims Run Group 5 α > 0 Blue - Data Red - Sims 80000 70000 70000 60000 60000 50000 50000 40000 40000 30000 WestNorth 30000 20000 20000 10000 10000 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 φ [rad] φ [rad]

Figure B.5: DC φ comparison of data (blue) and simulations (red) for run group 5.

106 APPENDIX C

ACCEPTANCE FIGURES

0.014 Run Group 1 0-10% 40-50% 0.012 10-20% 50-60% 0.01 20-30% 60-92% Acceptance 0.008 30-40% 0.006

0.004

0.002

0 0 1 2 3 4 5 6 7p 8 [GeV/c] T

0.014 Run Group 1 0-20% 0.012 20-40% 0.01 40-60% Acceptance 0.008 60-92% 0.006

0.004

0.002

0 0 1 2 3 4 5 6 7p 8 [GeV/c] T

Figure C.1: Acceptance for all centralities for run group 1.

107 0.014 Run Group 2 0-10% 40-50% 0.012 10-20% 50-60% 0.01 20-30% 60-92% Acceptance 0.008 30-40% 0.006

0.004

0.002

0 0 1 2 3 4 5 6 7p 8 [GeV/c] T

0.014 Run Group 2 0-20% 0.012 20-40% 0.01 40-60% Acceptance 0.008 60-92% 0.006

0.004

0.002

0 0 1 2 3 4 5 6 7p 8 [GeV/c] T

Figure C.2: Acceptance for all centralities for run group 2.

0.014 Run Group 3 0-10% 40-50% 0.012 10-20% 50-60% 0.01 20-30% 60-92% Acceptance 0.008 30-40% 0.006

0.004

0.002

0 0 1 2 3 4 5 6 7p 8 [GeV/c] T

0.014 Run Group 3 0-20% 0.012 20-40% 0.01 40-60% Acceptance 0.008 60-92% 0.006

0.004

0.002

0 0 1 2 3 4 5 6 7p 8 [GeV/c] T

Figure C.3: Acceptance for all centralities for run group 3.

108 0.014 Run Group 4 0-10% 40-50% 0.012 10-20% 50-60% 0.01 20-30% 60-92% Acceptance 0.008 30-40% 0.006

0.004

0.002

0 0 1 2 3 4 5 6 7p 8 [GeV/c] T

0.014 Run Group 4 0-20% 0.012 20-40% 0.01 40-60% Acceptance 0.008 60-92% 0.006

0.004

0.002

0 0 1 2 3 4 5 6 7p 8 [GeV/c] T

Figure C.4: Acceptance for all centralities for run group 4.

0.014 Run Group 5 0-10% 40-50% 0.012 10-20% 50-60% 0.01 20-30% 60-92% Acceptance 0.008 30-40% 0.006

0.004

0.002

0 0 1 2 3 4 5 6 7p 8 [GeV/c] T

0.014 Run Group 5 0-20% 0.012 20-40% 0.01 40-60% Acceptance 0.008 60-92% 0.006

0.004

0.002

0 0 1 2 3 4 5 6 7p 8 [GeV/c] T

Figure C.5: Acceptance for all centralities for run group 5.

109 5-10% Centrality

0.014 Run Group 0 Run Group 1 0.012 Run Group 2

Acceptance Run Group 3 0.01 Run Group 4 Run Group 5 0.008

0.006

0.004

0.002

0 0 1 2 3 4 5 6 7 8 p [GeV/c] T

Figure C.6: Acceptance for 5-10% centrality class for all run groups.

10-15% Centrality

0.014 Run Group 0 Run Group 1 0.012 Run Group 2

Acceptance Run Group 3 0.01 Run Group 4 Run Group 5 0.008

0.006

0.004

0.002

0 0 1 2 3 4 5 6 7 8 p [GeV/c] T

Figure C.7: Acceptance for 10-15% centrality class for all run groups.

110 15-20% Centrality

0.014 Run Group 0 Run Group 1 0.012 Run Group 2

Acceptance Run Group 3 0.01 Run Group 4 Run Group 5 0.008

0.006

0.004

0.002

0 0 1 2 3 4 5 6 7 8 p [GeV/c] T

Figure C.8: Acceptance for 15-20% centrality class for all run groups.

20-30% Centrality

0.014 Run Group 0 Run Group 1 0.012 Run Group 2

Acceptance Run Group 3 0.01 Run Group 4 Run Group 5 0.008

0.006

0.004

0.002

0 0 1 2 3 4 5 6 7 8 p [GeV/c] T

Figure C.9: Acceptance for 20-30% centrality class for all run groups.

111 30-40% Centrality

0.014 Run Group 0 Run Group 1 0.012 Run Group 2

Acceptance Run Group 3 0.01 Run Group 4 Run Group 5 0.008

0.006

0.004

0.002

0 0 1 2 3 4 5 6 7 8 p [GeV/c] T

Figure C.10: Acceptance for 30-40% centrality class for all run groups.

40-50% Centrality

0.014 Run Group 0 Run Group 1 0.012 Run Group 2

Acceptance Run Group 3 0.01 Run Group 4 Run Group 5 0.008

0.006

0.004

0.002

0 0 1 2 3 4 5 6 7 8 p [GeV/c] T

Figure C.11: Acceptance for 40-50% centrality class for all run groups.

112 50-60% Centrality

0.014 Run Group 0 Run Group 1 0.012 Run Group 2

Acceptance Run Group 3 0.01 Run Group 4 Run Group 5 0.008

0.006

0.004

0.002

0 0 1 2 3 4 5 6 7 8 p [GeV/c] T

Figure C.12: Acceptance for 50-60% centrality class for all run groups.

60-92% Centrality

0.014 Run Group 0 Run Group 1 0.012 Run Group 2

Acceptance Run Group 3 0.01 Run Group 4 Run Group 5 0.008

0.006

0.004

0.002

0 0 1 2 3 4 5 6 7 8 p [GeV/c] T

Figure C.13: Acceptance for 60-92% centrality class for all run groups.

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119 BIOGRAPHICAL SKETCH

Born the first son of Bob and Joan Klatsky, Jeffrey “Jack” Curry Klatsky spent his youth on the harsh streets of New York City suburb Nutley, NJ. Growing up with no discernible skills or coordination and often the brunt of “You throw like a girl” jokes, Jeff found success in the simplest of activities: running. Success in competitive running from ages 8 to 18 drew the attention of college track coaches towards the end of his tenure at Nutley High School. After heavy recruiting by assistant track coach John Mortimer, he chose the Jesuit Boston College (BC) for his undergraduate education. Jeff knew well before day one at BC that he wanted to major in physics — being interested in science and decently good at math naturally lend themselves to physics. However, first semester physics and Jeff did not get along — F’s on all three midterm exams did not bode well. The professor, Dr. Michael J Graf, strongly recommended that Jeff reconsider his choice to major in physics, but was otherwise supportive during Jeff’s many trips to office hours. Studying harder than he ever had in his life, Jeff aced the final exam, pulling off a B– in the course. Jeff decided to do undergraduate thesis work under Dr. Graf as a member of his muon spin resonance (µSR) group. Jeff submitted a senior thesis aptly titled “µSR”, for which no awards were won. As the odds of going into the realm of professional running dwindled, the decision was made to pursue higher education. Applying to graduate school in the spring of 2008 led to an almost definite choice to attend the University of Houston, but a late acceptance from Florida State University (FSU) threw a wrench into the plan. In the end, the choice was made to attend FSU due to both Dr. Graf’s insistence that FSU had a great physics program and FSU’s involvement as a member of the Atlantic Coast Conference, of which BC was also a member. Initially, Jeff went to FSU with the intent to study astrophysics, with Drs. Howard Baer and Christopher Gerardy among top candidates for a major professor. A talk was given by Dr. Anthony Frawley during the Friday Seminar Series, during which Dr. Frawley discussed his work in relativistic heavy-ion physics. Hearing about this physics for the first time, Jeff felt that it walked the fine line between science and magic, and he had to see which side of the line this work really fell on. Seven years later, the jury is still out on that one.

120