Study of Identified Hadron Spectra and Yields√
at Mid-rapidity in sNN = 200 GeV
Au+Au Collisions

Akio KIYOMICHIJanuary 2005

Study of Identified Hadron Spectra and Yields√
at Mid-rapidity in sNN = 200 GeV
Au+Au Collisions

Akio KIYOMICHI

Submitted to the Graduate School ofPure and Applied Sciencesin Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy in
Scienceat theUniversity of Tsukuba

Abstract
Heavy ion collisions at relativistic energy offer the possibility of producing highly compressed strongly interacting matter, which may form the quark-gluon plasma (QGP). We
present the results of identified hadron spectra and yields in Au+Au collisions at the energy√of sNN = 200 GeV by the PHENIX experiment using the Relativistic Heavy Ion Collider(RHIC) at Brookhaven National Laboratory (BNL).
The PHENIX is one of the major experiments at RHIC to detect a variety of signals fromquark-gluon plasma. It is designed to perform a broad study of A + A, p + A, and p + p
collisions to investigate nuclear matter under extreme condition. The detector consists ofa large number of subsystems. It comprises two central arms, two forward muon arms,
and three global detectors. For the systematic studies of identified hadron productions
in relativistic heavy-ion collisions, we have constructed a high resolution time-of-flightdetector and installed in PHENIX central arm. It is designed for good hadron identification
capability in a broad momentum range. Pions and kaons are identified up to 3 GeV/c and
2 GeV/c in pT , respectively, and protons and anti-protons can be identified up to 4.5 GeV/c.
For single particle analysis, we have measured the transverse momentum spectra and√yields for π ± , K ± , p and p at mid-rapidity in sNN = 200 GeV Au+Au collisions over abroad momentum range with various centrality selections. We have observed a clear particle mass dependence of the shapes of transverse momentum spectra in Au+Au central collisions below ∼ 2 GeV/c in pT . We also measured particle ratios of π − /π + , K − /K + , p/p,
K/π , p/π and p/π as a function of pT and collision centrality. The ratios of equal mass
particle yields are independent of pT and centrality within the experimental uncertainties.
The ratios in central Au+Au collisions are well reproduced by the statistical thermal modelwith a baryon chemical potential of µB = 29 MeV and a chemical freeze-out temperatureof Tch = 177 MeV.
Motivated by this observation that the single particle spectra are well fitted with ahydrodynamic-inspired parameterization, termed the “blast-wave” model, to extract freezeout temperature and radial flow velocity of the particle source. Since the experimental data include the decay of resonance, we have taken into account decays of mesonic(ρ , η , ω , K ∗ , , ,) and baryonic (∆, Λ, Σ, , ,) resonances whose abundances are determined by
the chemical parameters. From this analysis, we have obtained freeze-out temperature
Tfo = 108 MeV and average flow velocity hβT i = 0.57 in Au + Au central collisions at

II√

sNN = 200 GeV. It is found that Tfo decreases and βT increases from the most peripheral

to mid-central collisions, and appears to saturate in the central collisions.
Another motivation is that the suppression of high-pT hadron as a probe of QGP formation. The binary collision scaling behavior of identified charged hadrons has been measured
and compared with that of neutral pions. The central-to-peripheral ratio, RCP , approaches
unity for (p + p)/2 from pT = 1.5 up to 4.5 GeV/c. Meanwhile, charged and neutral pions are suppressed. The p/π and p/π ratios in central events both increase with pT up to
3 GeV/c and approach unity at pT ≈ 2 GeV/c. However, in peripheral collisions these ratios
saturate at the value of 0.3 – 0.4 around pT = 1.5 GeV/c. The observed RCP and p/π ratios
in intermediate pT region are not explained by the hydrodynamic model alone, but someof theoretical model qualitatively agree with data. These observations can be explained by
the hydrodynamical model with jet fragmentation (hydro + jet model) and the parton recombination at intermediate pT (recombination model). Both theoretical models reproduce
the binary collision scaling observed in the data. We have extended our identified hadronstudies to include the φ vector meson. The observed RCP for φ is similar to other mesons
despite the fact that they are more massive than protons. This scaling with quark content
favors recombination models.

Contents
1

Introduction1

1.1

Relativistic Heavy-Ion Collisions . . . . . . . . . . . . . . . . . . . . . . .

1

1.1.1

Physics of High Energy Heavy-Ion Collisions . . . . . . . . . . . .

1

1.1.2

Signatures of the Quark-Gluon Plasma . . . . . . . . . . . . . . . .

4

1.1.3

Collision Geometry of Heavy-Ion Collisions . . . . . . . . . . . .

6Particle Production in Heavy-Ion Collisions . . . . . . . . . . . . . . . . .

7

1.2.1

Single Particle Spectra . . . . . . . . . . . . . . . . . . . . . . . .

8

1.2.2

Collective Expansion . . . . . . . . . . . . . . . . . . . . . . . . .

9

1.2.3

Particle Ratios and Chemical Equilibrium . . . . . . . . . . . . . . 11

1.2

1.3

2

Hard Scattering as a Probe of QGP . . . . . . . . . . . . . . . . . . . . . . 13
1.3.1

Hard Scattering in N − N Collisions . . . . . . . . . . . . . . . . . 13

1.3.2

Hard Scattering in Heavy-Ion Collisions . . . . . . . . . . . . . . . 15

1.3.3

Reference Experiment: d+Au Collisions . . . . . . . . . . . . . . . 17

1.4

Thesis Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.5

Contributions of the Author . . . . . . . . . . . . . . . . . . . . . . . . . . 19

The PHENIX Experiment

20

2.1

RHIC : Collider Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2

PHENIX Detector Overview . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3

PHENIX Magnet System . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.4

PHENIX Global Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.5

2.4.1

Zero Degree Calorimeter . . . . . . . . . . . . . . . . . . . . . . . 26

2.4.2

Beam-Beam Counter . . . . . . . . . . . . . . . . . . . . . . . . . 28

Central Arm Spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.5.1

Drift Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.5.2

Pad Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.5.3

Time-of-Flight Counter . . . . . . . . . . . . . . . . . . . . . . . . 35

III

CONTENTS

IV
2.6

3

3.2

Time Expansion Chamber . . . . . . . . . . . . . . . . . . . . . . 38

2.6.2

Ring-Imaging Cherenkov Detector . . . . . . . . . . . . . . . . . . 39

2.6.3

Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . . . 40

2.6.4

Muon Arm Spectrometer . . . . . . . . . . . . . . . . . . . . . . . 42
46

Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.1.1

Minimum Bias Trigger . . . . . . . . . . . . . . . . . . . . . . . . 46

3.1.2

Centrality Determination . . . . . . . . . . . . . . . . . . . . . . . 48

3.1.3

Glauber Model Calculation . . . . . . . . . . . . . . . . . . . . . . 50

Track Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2.1

Track Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.2.2

Momentum Determination . . . . . . . . . . . . . . . . . . . . . . 54

3.2.3

Track Association . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.3

Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.4

Cut Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.5

3.6

5

2.6.1

Data Analysis
3.1

4

Other Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.4.1

Fiducial Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.4.2

Energy Loss Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.5.1

Comparison of Data with Simulation . . . . . . . . . . . . . . . . 61

3.5.2

Corrections of Acceptance, Decay and Multiple Scattering . . . . . 65

3.5.3

Correction of Multiplicity Dependence . . . . . . . . . . . . . . . 66

3.5.4

Weak Decay Correction . . . . . . . . . . . . . . . . . . . . . . . 67

3.5.5

Invariant Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Experimental Results

71

4.1

Transverse Momentum Distributions . . . . . . . . . . . . . . . . . . . . . 71

4.2

Mean Transverse Momentum and Particle Yields . . . . . . . . . . . . . . 74

4.3

Particle Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Discussions
5.1

81

Particle Productions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.1.1

Particle Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.1.2

Features of Chemical Equilibrium . . . . . . . . . . . . . . . . . . 82

CONTENTS

V

5.1.3

Comparison with Theoretical Phase Boundary . . . . . . . . . . . . 83

5.2

5.3

5.4

6

Transverse Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.2.1

pT Spectra of π , K, p . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.2.2

p/π ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.2.3

Feature of Thermal Equilibrium: mT Spectra . . . . . . . . . . . . 87

Collective Expansion Model . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.3.1

Blast-wave Parametrization . . . . . . . . . . . . . . . . . . . . . 90

5.3.2

Previous Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.3.3

Proposed Analysis and Results . . . . . . . . . . . . . . . . . . . . 91

Beyond the Thermal Behavior: Hard Component . . . . . . . . . . . . . . 99
5.4.1

Suppression of High pT Hadrons . . . . . . . . . . . . . . . . . . . 99

5.4.2

Comparison with Theoretical Models: hydro+jet and recombination 101

Conclusions

A Numerical Supplement

107
109

A.1 Relativistic Kinematics and Variables . . . . . . . . . . . . . . . . . . . . 109
A.2 Transverse Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
B Time-of-flight Detector

113

B.1 Detector Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
B.2 The TOF Scintillator and Photomultiplier Tubes . . . . . . . . . . . . . . . 117
B.3 Front End Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
B.4 TOF Detector Performance . . . . . . . . . . . . . . . . . . . . . . . . . . 120
C Data Tables

126

C.1 pT Spectra Data Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
C.2 Particle Ratio Data Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
D PHENIX Collaboration List

147

Acknowledgments
I would like to express my great appreciation to Prof. Y. Miake for providing me the exciting field of physics. His appropriate and valuable advice show me the way to promote thepresent work, and I could learn a lot from him as an experimental physicist. I express mythanks to Prof. K. Yagi for introducing me to this fascinating field of nuclear physics. Theirdraft of book, Quark-Gluon Plasma (K. Yagi, T. Hatsuda and Y. Miake, will be pressedfrom Cambridge University Press), is helpful to learn this field.
I wish to express my thanks to Dr. H. Sako for leading me to the PHENIX experiment. His appropriate and kind advice have helped me a lot to work at BNL. I appreciate
Dr. S. Sato for his advice and discussions on the detector construction and operation. I
could learn from him as a way of experimentalist. I express my thanks to Dr. T. Chujo for
his useful advice and discussions in the data analysis. I am much obliged to Dr. S. Esumi
for his advice and discussions in the data analysis and manuscript of this thesis.
I wish to acknowledge all the collaborators of the PHENIX experiment. I am grateful to the spokesperson Prof. W. A. Zajc for his various arrangements for my activity at
BNL, and hurtful encouragement. I would also like to thank the previous spokesperson
Prof. S. Nagamiya for his guidance, precious advice and encouragement since I joined thePHENIX experiment. I would like to express my appreciation to Dr. H. En’yo for his continuous encouragement to complete this work. I express my thanks to Prof. H. Hamagaki,
Prof. T. Sugitate and Prof. J. Chiba for their stimulate advice, supports and encouragement. I appreciate Dr. Y. Akiba and Prof. K. Kurita for their useful advice and discussions
in the data analysis. I express my special thanks to Prof. K. Shigaki, Dr. H. Ohnishi,
Dr. M. Kaneta and Dr. T. Sakaguchi for their helpful advice on this work and their friendship at BNL. I would like to appreciate Dr. S. Sawada, Dr. K. Homma, and Dr. K. Ozawa
for their advice and discussion. I appreciate Prof. N. Saito, Dr. Y. Goto, Dr. Y. Watanabe, Dr. T. Ichihara, Dr. A. Taketani, Dr. S. Yokkaichi, Dr. J. Murata, Dr. K. Okada andDr. O. Jinnouchi for their encouragement and useful discussion. I’d like to thanks to
Dr. K. Oyama, Dr. H. Torii, Dr. H. D. Sato, Dr. T. Kohama, Dr. J. Tojo, Dr. A. EnokiVI

CONTENTS

VII

zono, Mr. T. Matsumoto, Mr. T. Hachiya, Mr. T. Nakamura and Mr. S. Kametani for fruitful
discussions and friendship on BNL life.
I acknowledge the colleagues at BNL for detector construction, data taking and analysis. I would like to appreciate to Dr. C.Y. Chi and Dr. M. Chiu for TOF front-end electronics
and to Prof. J. H. Kang, Dr. Y. H. Shin and Mr. D. J. Lim for developing the TOF online
systems together. I appreciate all of the technical staff on BNL, especially M. Van Lith,W. E. Lenz, J. Labounty and K. Johnes for their helps in detector construction. I would
like to express my appreciation to Prof. B. V. Jacak, Prof. C. Ogilvie, Prof. J. Velkovska,
Dr. A. Franz, Dr. J.M. Burward-Hoy, Dr. J. Jia, Dr. F. Matathias for their useful advice
and discussions in the data analysis. I appreciate Prof. C. Maguire, Dr. J. T. Mitchell, andDr. D. P. Morrison for their computing supports and discussions in the analysis. I express
my thanks to Dr. Y. Nara, Dr. T. Hirano and Dr. C. Nonaka for their theoretical advice anddiscussions.
Here I acknowledge all the members of the high energy nuclear experiment group at
University of Tsukuba. I express my thanks Dr. S. Nishimura, Dr. M. Kurata-Nishimura,
Mr. S. Kato, Dr. K. Enosawa, Mr. K. Kanoh, Mr. Y. Yokota, Mr. Y. Ohkuma, Ms. R. Higuchi
and Ms. Y. Miyamoto for their friendship and discussions. I appreciate Ms. S. Urasawa,
Mr. D. Miura and Mr. T. Ishibashi for their encouragement and continuous friendship fromundergraduate. I appreciate Dr. M. Inaba, Mr. T. Hirano, Mr. T. Shimada, Mr. H. Hayashi,
Ms. M. Suzuki-Nara, Mr. K. Koseki, Ms. M. Aizawa, Mr. M. Ono, Mr. H. Tsuruoka,
Mr. H. Masui, Mr. S. Sakai, Mr. Y. Kuroki, Mr. S. Takagi, Mr. M. Konno and Ms. M. Shimomura for their friendship and kindness.
I acknowledge the member of the RIKEN Radiation Laboratory. I express my thanks
Ms. N. Kiyama, Ms. M. Muroi and Ms. K. Sakuma for their heartful support by the secretaries. I appreciate Dr. R. Vladimir, Dr. M. Okamura and Dr. Y. Ohtake for their encouragement. I’d like to thanks to Dr. K. Sudo, Dr. M. Hirai, Dr. M. Ohtani, Mr. T. Tabaru,
Dr. N. Fukuda, Dr. K. Tanida, Dr. T. Ohnishi, Dr. H. Takeda, Dr. H. Kano, Ms. M. Naruki,
Mr. R. Muto, Mr. F. Sakuma and Mr. N. Kamihara for their encouragement and friendship.
I am grateful to all my colleagues and friends.
Finally, I would like to express my great appreciation to my parents, Yoshiharu Kiyomichi and Fumiko Kiyomichi, for their support and encouragement to accomplish thiswork. I would like to express my sincere gratitude to late grandfather Mamoru Kitamura
for his comprehension and encouragement to my ambitious. I really wish my grandfather
find pleasure in my success from the heaven.

Chapter 1
Introduction
In this chapter, the relativistic heavy-ion collisions are introduced. We describe interpretations of particle production in heavy-ion collisions and review
the experimental probes. Finally, we present the thesis motivation.

1.1

Relativistic Heavy-Ion Collisions

1.1.1

Physics of High Energy Heavy-Ion Collisions

Heavy-ion collisions at high energies (E/m À 1) offer a unique opportunity to probe highly
excited dense nuclear matter in the laboratory. The driving force for such studies both on
experimental and theoretical side, is the expectation that a entirely new form of nuclear
matter may be created from relativistic heavy-ion reactions. That form of matter is called
the quark-gluon plasma (QGP), which is quantum chromodynamics (QCD) analogue of theplasma phase of ordinary atomic matter.
According to the lattice QCD calculations [1], it is predicted that the phase transition
from a hadronic phase to QGP phase takes place at a temperature of approximately T ≈170 MeV (≈ 1012 K) as shown in Figure 1.1. This transition temperature corresponds toan energy density ε ≈ 1 GeV/fm3 , nearly an order of magnitude larger than that of normal
nuclear matter. This value is plausible based on dimensional grounds, since such densities
correspond to the total overlap of several (light) hadrons within a typical hadron volume of
1–3 fm3 . Lattice calculations also indicate that this significant change in the behavior of thesystem occurs over a small range in temperature (∼20 MeV) indicating that it is the phasetransition, and suggest that the change of phase includes the restoration of approximatechiral symmetry resulting from greatly reduced or vanishing quark constituent masses.
1

CHAPTER 1. INTRODUCTION

2

16.0
14.0

εSB/T4ε/T4Figure 1.1: Lattice QCD results [1] for the

12.0

energy density / T 4 as a function of the tem-

10.0

perature scaled by the critical temperature

8.0

Tc . Note the arrows on the right side indi-

6.0

3 flavour
2+1 flavour
2 flavour4.0

cating the values for the Stefan-Boltzmann
limit. [1]

2.0

T/Tc

0.0
1.0

1.5

2.0

2.5

3.0

3.5

4.0

A schematic version of the phase diagram for an idealized form of nuclear matter withvanishing light quark (up and down) masses and infinite strange quark mass is presented
in Figure 1.2. For sufficiently large values of the baryon chemical potential µ this system
is considered to exhibit a first order phase transition between hadronic matter and QGP,
along with a tricritical point below which the transition becomes second order. However,
non-zero values of the light quark masses dramatically alter this simple picture: The second
order phase transition denoted by the dashed line in Figure 1.2 becomes a smooth crossover,and the tricritical point correspondingly becomes a critical point designating the end of thefirst order transition found at higher values of µ .

Figure 1.2: Theoretical phase diagram of nuclear matter for two massless quarks as a function oftemperature T and baryon chemical potential µ .

In order to understand the properties of the nuclear matter under the extreme conditions
and hopefully to capture the signal of QGP formation, various experiments have been taken1.1. RELATIVISTIC HEAVY-ION COLLISIONS
Accelerator Location

Ion beam

Momentum3√sCommissioning date

[A · GeV/c] [GeV]
AGS
SPS
RHIC

LHC

BNL
CERN
BNL

CERN

16 O, 28 Si

14.6

5.4

Oct.1986

197 Au11.4

4.8

Apr.1992

16 O, 32 S

200

19.4

Sep.1986

208 Pb

158

17.4

Nov.1994

197 Au + 197 Au

65

130

2000

197 Au + 197 Au

100

200

2001

d + 197 Au

100

200

2003

197 Au + 197 Au

31.2

62.4

2004

63 Cu + 63 Cu

100

200

2005

208 Pb + 208 Pb

2800

5600

2007 (project)

Table 1.1: List of heavy-ion accelerator facilities with the ion beams, the corresponding beam
momentum and the center of mass energy.

place both at the Alternating Gradient Synchrotron (AGS) at Brookhaven National Laboratory (BNL), and the Super Proton Synchrotron (SPS) at CERN. The Relativistic Heavy Ion
Collider (RHIC) at BNL has been operated from June 2000. This new machine provides√
collisions of Au nucleus at the center of mass energy per nucleon ( sNN ) up to 200 GeV.
The hot and dense matter produced in relativistic heavy-ion collisions may evolve
through the following scenario: pre-equilibrium, thermal (or chemical) equilibrium of partons, possible formation of QGP or a QGP-hadron gas mixed state, a gas of hot interacting
hadrons, and finally, a freeze-out state when the produced hadrons no longer strongly interact with each other. Figure 1.3 shows the space-time evolution of the medium createdin heavy-ion collisions. Since produced hadrons carry information about the collision dynamics and the entire space-time evolution of the system from the initial to the final stageof collisions, a precise measure of the transverse momentum (pT ) distributions and yields
of identified hadrons as a function of collision geometry is essential for the understandingof the collision dynamics and properties of the created matter.

CHAPTER 1. INTRODUCTION

4
timefree streaming
freeze-outt ≈ 16 fm/c, T ≈ 100 MeV

hadron gas
t ≈ 8 fm/c, T ≈ 160 MeV

mixed phasehydrodynamical expansiont ≈ 4 fm/c, T ≈ 160 MeV

equilibrated QGP
pre-equilibrium parton cascadet ≈ 0.6 fm/c, T ≈ 350 MeV

deconfined quarks and gluons
coordinate space

beam

beam

Figure 1.3: Space-time picture of a nucleus-nucleus collision.

1.1.2 Signatures of the Quark-Gluon Plasma
It is generally recognized that there is no clear signals of the quark-gluon plasma phase.
In order to catch the signals of QGP formation, a variety of probes are proposed. As thedistinct signature of the existence of QGP is still under the study, the best way to prove thepresence of a QGP phase is to measure several signatures simultaneously.
Deconfinement
Suppression of heavy quarkonia has been proposed as a signature of deconfinement. The
suppression mechanism follows directly from the Debye screening expected in the medium,
which reduces the range of the potential between charm quark and anti-quark pairs [2, 3]
If radius of a meson is larger than the Debye radius, which is determined by the plasma
temperature and density, the meson cannot survive in the plasma. It is proposed that J/Ψ
meson made of cc quarks is suitable for the detection of Debye screening effect because of
the following reasons; 1) as J/Ψ measured in leptonic decay, decay products do not interact
strongly with other hadrons, thus it is expected a penetrative probe for the early stage ofthe collisions, 2) J/Ψ’s are produced in the very early stage of the collision, 3) hadronicinteraction of J/Ψ is expected to be not too high (σΨN ∼ 6 mb), thus it has the informationof initial state condition of the collisions.

1.1. RELATIVISTIC HEAVY-ION COLLISIONS

5

Strangeness enhancement
The most often proposed signature for the possible observation of QGP are enhancements
in strangeness and anti-baryon production. In the qq̄ pair production at high energy nucleonnucleon collisions, heavy flavors are suppressed due to their masses. The ss̄ yields is about
0.1 ∼ 0.2 compared to uū or d d¯ yields. This situation may change in heavy-ion collisions.
If the hadronic matter is deconfined during the heavy-ion collision, the production of u andd quarks will be suppressed by Pauli blocking. Therefore, the enhancements of strangenessmight be one of signals of QGP. [5]Collision dynamics and equation of state
Study of collective motion of produced hadrons in final state is expected to provide information on the dynamics of heavy ion collisions. With a hydrodynamical view of collisions,collective motion is governed by a pressure gradient of compressed nuclear matter at theearly stage of collision. In the case of a phase transition from the ordinal nuclear to thequark-gluon plasma, it is expected that the equation of state should exhibit a corresponding
softening due to the increased number of degrees of freedom [4]. Thus, the observationof collective motion is crucially important to validate the hydrodynamical description of
dynamics.
If the phase transition is the first order, the equation of state will be “softest” at thecritical temperature Tc . Such softening is expected to affect the dynamic evolution of thesystem because the internal pressure drops at Tc . Thus an observation of excitation function of the transverse collective flow can be a probe for the QGP formation; drop in the
excitation function of collective flow indicates threshold energy of the QGP formation.
Parton energy loss
Another possible way of probing the quark-gluon plasma is by the energy loss of a fast
parton (quark or gluon). The mechanisms are similar to those responsible for the electromagnetic energy loss of a fast charged particle in matter, i.e. energy may be lost either by
excitation of the penetrated medium or by radiation.
The fast parton may produce the high-pT hadron, the measurement of high-pT hadronproduction is a good probe for studying the parton energy loss. The more details are described in Section 1.3

CHAPTER 1. INTRODUCTION

6

1.1.3 Collision Geometry of Heavy-Ion Collisions
Participant-Spectator Picture
Nuclei are extended objects, and therefore their geometry aspects in heavy-ion collisions
plays an important role in collision dynamics. There are two groups of nucleons; the participants which are in the overlapped region and the spectators which proceed with little
perturbation along the original direction. Figure 1.4 shows a schematic view of reaction ata high energy between symmetric Lorentz contracted nuclei in the center of mass frame.
As is shown in figure, the size of the participant/spectator is determined by the impact parameter b and there is anti-correlation between the size of the participant and that of spectator. The number of participants can be calculated by simple geometrical considerations,Glauber model.
Based on participant-spectator picture, the centralities of the Au+Au collision are defined by combined information on the energy deposition of spectator neutrons by thecalorimeter located at zero-degree and charge sum information measured by beam-line
detector (see Section 3.1).

Figure 1.4: Participant-Spectator picture of a high energy heavy-ion collision with impact parameter b. On the left (a), the two incoming nuclei in the center of mass frame are shown. On the right(b), after the collision, the nucleons are separated to participants, projectile spectators and target
spectators.

1.2. PARTICLE PRODUCTION IN HEAVY-ION COLLISIONS

7

Glauber Model
The Glauber model [6] is based on a simple geometrical picture of a nucleus-nucleus
collision. It is a semi-classical model treating the nucleus-nucleus collisions as multiple
nucleon-nucleon interactions: a nucleon of incident nucleus interacts with target nucleons
with a given density distribution. Nucleons are assumed to travel on straight line trajectories
and are not deflected even after the collisions, which should hold as a good approximation
at very high energies. Another assumption is that nucleon-nucleon inelastic cross section
in to be the same as that in the vacuum.
σNN

The nucleons are randomly distributed according to Woods-Saxon distribution, the density profile ρ (r) is defined as

ρ (r) = ρ0 ·1
1 + exp( r−R
a )

(1.1)

where R is radius of nucleus and a is surface diffuseness parameter. The density profile for
Au is shown in Figure 1.5. For the Au ion, the parameters are R = 6.38 fm, a = 0.54 fm-3

ρ(r) (fm )and ρ0 = 0.169 fm−3 . The inelastic nucleon-nucleon cross section σNN = 42mb is used on√
Au+Au collisions at sNN = 200GeV.
0.25

a = 0.54 (fm)

0.2

0.15

Figure 1.5:

0.1

nuclear density profile for Au.

Woods-Saxon

0.05

0

0

2

4

6

R = 6.38 (fm)

1.2

8

10

12

r (fm)

Particle Production in Heavy-Ion Collisions

To understand the high energy hadron-hadron collisions, Fermi proposed a statistical method [7]as follows. Because of saturation of the phase space, the multi particle production resulting
from the high energy elementary collisions is consistent with a thermal description [7, 8, 9].
In heavy-ion collisions, hydrodynamical behavior, that is, local thermal equilibrium andcollective motion, may be expected because of the large number of secondary scatterings.
The final state hadrons are the most abundant and dominant source of information of theearly stage of the collisions. Hadron momentum spectra and rapidity densities are affectedCHAPTER 1. INTRODUCTION

8
10

6

1/mTdN/dmT (a.u.)(a) Pb + Pb
104(b) Pb + Pb

Figure 1.6: Transverse mass distributions for pions, kaons, and protonsppfrom 158 A GeV Pb + Pb central colli10

K2

sions. The dashed lines represent theK+

exponential fits. This figure is takenfrom [11].
π

+

π

1

10

-2

0

0.5

1

0

0.5

1
2

mT - mass (GeV/c )by thermal freeze-out and collective flow. The particle ratios are sensitive to the chemical
properties of the system and particle production mechanism. The recent review of theexisting data obtained mainly from CERN-SPS can be found in the literature [10].

1.2.1 Single Particle Spectra
Single particle spectra, i.e., transverse momentum (pT ) distributions with single particle
inclusive measurements are one of the most common tools used in studying high energy
collisions. This is because the transverse motion is totally generated during the collisionand hence is sensitive to the collision dynamics.
Transverse momentum spectra are presented in terms of the invariant differential crosssection,
d3 σ
d3 σ
=
pT d pT dy d φ
mT dmT dy d φ
2
1
1
d σ
d2 σ
=
,
(1.2)
=
2π pT d pT dy 2π mT dmT dyqwhere pT is the transverse momentum, y is the rapidity, mT = p2T + m20 is the transverse
E

d3 σ
d p3

=

mass and m0 is the rest mass of the particle. Figure 1.6 shows inclusive mT distribution√
in 158 A GeV ( sNN = 17.2 GeV) Pb + Pb collisions measured by SPS-NA44 experiment [11]. Invariant cross sections are shown to be exponential in mT . The dashed lines inSlope T (GeV)

1.2. PARTICLE PRODUCTION IN HEAVY-ION COLLISIONS

9

Pb + Pb
S+S
p+p

0.3

0.2

+

0.1

π

0

+

p

0.5

1

K

π

0

K

p

0.5

1
2

Particle Mass (GeV/c )Figure 1.7: Inverse slope parameter T as a function of particle mass. They are compared at midrapidity in p + p, S+S and Pb+Pb collisions. This figure is taken from [11].

Figure 1.6 are fit to the function
1 dN
mT= A exp (− ),mT dmTT(1.3)

where A is a constant and T is the inverse slope parameter of the distribution. Becauseof decay products from the resonances, steeper component are exist for low-mT region ofpions. One may notice that proton and anti-proton distributions look flatter than those forpions and kaons.
The slope parameters for pions, kaons and protons are obtained and plotted as a function√of particle mass in Figure 1.7, where they are compared in p + p ( sNN = 23 GeV),√√
S+S ( sNN = 19.4 GeV) and Pb+Pb ( sNN = 17.2 GeV) collisions at mid-rapidity.
While for p + p collision the slope parameters are independent of particle species, theseparameters increase with increasing mass for heavy-ion collisions. This effect becomeslarger in Pb+Pb than that in S+S; larger the collision system, the effect becomes larger.
While the parameters of pions are similar to those in p + p, slopes of heavier particles
become flatter in A + A.

1.2.2

Collective Expansion

Most successful description of the different slope parameters and the change of shape observed in mT spectra in A + A collisions is given by the model including the common transverse expanding velocity field together with a moderate temperature of a thermalized sys-

CHAPTER 1. INTRODUCTION

10

tem. With the presence of the transverse velocity field, the mass dependence of inverse
slope parameters can be understood qualitatively as follows [12].
In case of a purely thermal motion, all particles (irrespective of their mass) would movewith the same average kinetic energy determined by the temperature, i.e.,< Ekine >∼ Tthermal .

(1.4)

On the other hand, in case of a purely collective motion, all particles would move with thesame velocity βT and consequently, the average kinetic energy would increase proportional
to their mass m0 , since

m0 βT2.
(1.5)
2Under the assumption of complete decoupling between the thermal and collective motion< Ecollective >∼of the particle, superposition of both types of motion will give the mass dependence of;< Ekine > = < Ethermal > + < Ecollective >m0 < βT >2= Tthermal +
,
2

(1.6)

where < βT > is the averaged collective velocity for all particle species. The inverse slope
parameter T0 is proportional to the average transverse kinetic energy and is given as,
T0 ∝ Tthermal + m0 · < βT >2 .

(1.7)

Furthermore, because of this velocity dependence, for heavier collision system, which
presumably stronger collective transverse flow, the value of T0 is expected to be larger. The
above observations are thus qualitatively consistent with the hypothesis of transverse hydrodynamic flow produced in the heavy-ion collisions. Quantitatively, the phenomenologicalhydrodynamical model proposed by Schnedermann et. al. [13] can be applied to the single
particle spectra for the extraction of transverse velocity and temperature at freeze-out. In
this model, termed the “blast-wave” model, collective expansion effects are incorporated
into transverse mass spectra as following:dσ∝mT dmTZ R
0r dr mT I0³ p sinh ρ ´
T

Tfo

K1

³ m cosh ρ ´
T

Tfo

,

(1.8)

where I0 and K1 represent modified Bessel functions with ρ being the transverse boost
which depends on the radial position according to ρ = tanh−1 βr (r). The detail of thisexpression is described in Appendix A.2. Here Tfo is the freeze-out temperature and R is

1.2. PARTICLE PRODUCTION IN HEAVY-ION COLLISIONS
610(a) Pb + Pb

1/mTdN/dmT (a.u.)

11

4

10

(b) S + Sp

Figure 1.8: Transverse mass distributions for pions, kaons, and protons

pcompared with results of a hydro10

dynamical model calculation. Res-

K+

2

+

K

onance decays are included in thepion spectra, and resonance effects+

on kaon and proton spectra are ne-π1+glected.

πThis figure is taken from

[11].
10

NA44 data
Thermal model

-2

0

0.5

1

0

0.5
2

1

mT - mass (GeV/c )the maximum radius of the expanding source at freeze-out. The transverse velocity profileβr (r) is parameterized as βr (r) = βT (r/R)n , with the surface velocity βT . We can vary theform of velocity profile with index n, for example, n = 0.5, 1, 2. The average of transverse
velocity is defined as
hβT i =

RR

0 βr (r)r dr
=
RR
r
dr
0

³ 2 ´
βT .
2+n

(1.9)

From the fitting results, the average of transverse velocity is independent of velocity profile [14].
Figure 1.8 shows the fitting results by the hydrodynamical flow model in central Pb +Pb and S+S collisions at mid-rapidity region [11]. Solid lines are the spectra of a source at
Tfo = 140 MeV and βT = 0.6 (hβT i = 0.4) for Pb+Pb, and a source at Tfo = 140 MeV and βT= 0.41 (hβT i = 0.27) for S+S. As show in Figure 1.8, all the particle spectra from pions toprotons are shown to be reproduced very well with two parameters, Tfo and βT .

1.2.3

Particle Ratios and Chemical Equilibrium

Hadron multiplicities and their correlations are observables in heavy-ion collisions. We canevaluate particle abundances by integrating particle yields over the complete phase space,
Unlike the momentum distributions, particle ratios are expected to be non-sensitive to theunderlying processes. It is found that the ratios of produced hadrons are well described by
the simple statistical model [15].

CHAPTER 1. INTRODUCTION

12

Figure 1.9: Hadron abundance ratios. Comparison between statistical model (horizontal bars) andexperimental ratios (filled circles) [15].

The statistical model is based on the use of a grand canonical ensemble to describe
the partition function and hence the density of the particles of species i in an equilibrated
fireball:Z∞gi
p2 d p(1.10)
2π 2 0 exp[(Ei − µi )/Tch ] ± 1
with particle density ni , spin degeneracy gi , momentum p, total energy E and chemicalni =potential µi = µB Bi − µS Si − µI3 Ii3 . The quantities Bi , Si and Ii3 are the baryon, strangenessand three-component of the isospin quantum numbers of the particle of species i. With thismodel, only two parameters, the temperature Tch and a baryon chemical potential µB are
independent and it has been shown that ratios of particle production can be well fitted.
Figure 1.9 show the comparison of the measured particle ratios and the model calculation. The model calculation include the effect of resonance decay and excluded volume
corrections. As seen in the figure, this simple model can fit the the experimental ratios
reasonably well and the temperature of Tch ∼ 170 MeV at baryon chemical potential ofµB ∼ 270 MeV are obtained. Thus, chemical equilibrium seems to hold. It is very intriguing that abundances of the multi-strange particles also show the chemical equilibrium.
Because they are supposed to decouple early from the fireball, they do not have enoughtime to reach the chemical equilibrium if they are produced in hadronic interactions.

1.3. HARD SCATTERING AS A PROBE OF QGP

1.3

13

Hard Scattering as a Probe of QGP

The spectra of high transverse momentum (pT ) hadrons resulting from the fragmentation ofhard-scattered partons potentially provide a direct probe of the properties of the initial state.
In a high-energy nuclear collision, hard scattering will occur at the earliest time during thecollision, well before the QGP is expected to form, and thus the scattered partons willsubsequently experience the strongly interacting medium created in the collision. These
partons are expected to lose energy [16] in hot and dense nuclear matter through gluon
bremsstrahlung, effectively quenching jet production. This would have many observableconsequences, of which the most directly measurable would be a depletion in the yield ofhigh-pT hadrons [17]. It has been suggested that the energy loss is larger in a mediumof deconfined color charges than in hadronic matter [18, 19], making “jet quenching” apotential signature for QGP formation. Therefore, a detailed analysis of high-pT hadronproduction may reveal information on the properties of the dense medium created early inthe collisions [19, 20, 21].

1.3.1

Hard Scattering in N − N Collisions

At the energies reached at the Relativistic Heavy Ion Collider (RHIC), high-pT hadrons
are abundantly produced. In nucleon-nucleon collisions, it has been well established that
hadrons with pT ≥ 2 GeV/c result primarily from the fragmentation of hard-scattered partons, and that the pT spectra of these hadrons can be calculated using perturbative QCD(pQCD) [22, 23]. For high-pT particles, hard scattering is described by the lowest-ordersubprocesses which corresponds to a convolution of two-body scattering. Figure 1.10
shows a schematic view of the factorization in 1 + 2 → 3 + X reaction. The corresponding
expression for the inclusive particle production cross section in nucleon-nucleon collisions
can be written as,
3
σ1,2
=

∑

Z

dxi dx j dzk · f1i (xi , µF ) · f2 (x j , µF )j(1.11)

i, j,k×σi,k j (pi , p j , pk , αs (µR ), Q2 /µR , Q2 /µF ) × D3k (zk , µF ) ,where f1i (xi , µF ) and f2 (x j , µF ) are parton distribution function (PDF), D3k (zk , µF ) is fragj

mentation function (FF), and σi,k j (· · ·) represents the cross section from two partons (i andj) into a parton (k).
The pQCD calculations are rather successful in describing high-pT particle production in high-energy N + N collisions. As an example, Figure 1.11 shows the invariant

CHAPTER 1. INTRODUCTION

14

1

f1
pi

σ
pj

2

pk

f2

D

3

Figure 1.10: Schematic diagram for a hadron reaction (1 + 2 → 3 + X) factorized into parton distribution functions ( f ), parton fragmentation functions (D), and cross section (σ ) from two partons

1

3

3

-2

E*d σ/dp (mb⋅GeV ⋅c3)

to parton.

10
10
10
10
10
10
10

(Data-QCD)/QCD∆σ/ σ (%)

10

a)

-1

Figure 1.11: a) The invariant differential-2-3

PHENIX Data

-4

KKP FF-5

Kretzer FF

cross section for inclusive π 0 production(points) at mid-rapidity in p + p collisions at√
sNN = 200 GeV, and the results from NLO
pQCD calculations with equal renormaliza--6

tion and factorization scales of pT using-7

the “Kniehl-Kramer-Pötter” [24](solid line)-8and “Kretzer” [25](dashed line) sets of frag-

40
20
0
-20
-40

b) mentation functions. b) The relative statis-

4c) between the data and the theory using KKP2(c) and Kretzer (d) fragmentation functions

0

with scales of pT /2 (lower curve), pT , and4d) 2pT (upper curve). This figure is taken fromtical (points) and point-to-point systematic(band) errors. c,d) The relative difference

2

[23].

0
0

5

10

15

pT (GeV/c)

1.3. HARD SCATTERING AS A PROBE OF QGP
cross section for the π 0 production measured by PHENIX in p + p collisions at

15√

s = 200

GeV/c [23]. The results are compared with a next-to-leading order (NLO) pQCD calculation [24, 25] based on the factorization theorem. These calculations are consistent withthe data down to pT ∼ 2 GeV/c, indicating that the particle production is dominated by thefragmentation of hard-scatted partons and the production rate is well calibrated.

1.3.2

Hard Scattering in Heavy-Ion Collisions

In heavy-ion collision, the inclusive cross section for high-pT particle production is given
by single hard parton-parton two-body scattering. The factorization theorem can be directly extrapolated to heavy-ion collisions. Naively, the hard-scattering cross section is
proportional to the number of binary scaled N + N collisions, Ncoll ,
dN AA
dN NN
=
hN
i
coll
dyd 2 pT
dyd 2 pT(1.12)

Thus, the total hard-scattering cross-section for minimum bias A-A collisions is related tothat for N + N collisions (Eq. 1.12) by,
d σ AA
hNcoll i d σ NN
= NN.
AA dyd 2 p
σinel dyd 2 pT
σinel
T
1

(1.13)At the energy reached at RHIC, a bulk medium spanning a few hundred of fm3 withenergy density exceeding several GeV/fm3 can be created 0.3-1 fm/c after the colliding
nuclei pass through each other. This matter will leave its footprint on the properties ofthe experimentally observed particles. To quantify such modifications we need a baseline
expectation for spectra from nuclear (A + A) collisions in the absence of nuclear medium
effects. Given that hard parton scatterings have small cross sections, one can regard thenuclei as an incoherent superposition of partons (“point-like scaling”). We approximate
this by modeling the A + A collision as a sum of independent nucleon-nucleon (N + N)
collisions (“binary scaling”). For a given class of A + A collisions, we can determine hNcoll ithe average number of inelastic N + N collisions per event and then define the nuclear
modification factor as the ratio,
RAA (pT ) =(1/Nevt ) d 2 N AA /d pT d η.
NN ) d 2 σ NN /d p d η(hNcoll i/σinelT(1.14)In the absence of nuclear modifications to hard scattering, the ratio RAA will be unity;
thus departures from RAA = 1 indicate nuclear medium effects. For pT above 2 GeV/c,particle production in p + A collisions is enhanced compared to binary scaling, commonlyCHAPTER 1. INTRODUCTION

RAA

16

Au+Au √sNN= 130 GeV
central 0-10%(h++h-)/2π0

2Pb+Pb(Au) CERN-SPS
α+α CERN-ISR
π0binary scaling

1

0

0

2

4

pT (GeV/c)

Figure 1.12: The ratio RAA for charged hadrons and neutral pions (weighted average of PbSc
and PbGl results) in central Au+Au collisions. The error bars indicate the statistical errors on themeasurement. The surrounding bands [shaded for π 0 ’s, brackets for (h+ +h− )/2] are the quadraturesums of (i) the systematic errors on the measurement, (ii) the uncertainty in the N + N reference,and (iii) the uncertainty in hNcoll i. Also shown are the ratio of inclusive cross sections in α + α√
compared to p + p at sNN =31 GeV [34], and spectra from central Pb + Pb, Pb + Au compared to√p + p collisions at sNN =17 GeV [35] shown as a band indicating the range of uncertainty. This
figure is taken from [30].

referred to as the “Cronin effect” [27, 28]. It is observed and studied in p + A collisions
up to 400GeV. This effect is consistent with the power law form of the jet production crosssection and with the picture of multiple parton scattering in p + A collisions, a random
walk of partons in transverse momentum enhances the production of high-pT hadrons.
This Cronin effect is observed at lower beam energy A + A collisions as below; namely√
at CERN-ISR α + α collisions at sNN =31 GeV [34] and CERN-SPS Pb + Pb, Pb + Au√
collisions at sNN =17 GeV [35].
At RHIC-PHENIX experiment, we have studied and reported the high-pT π 0 and charged√
hadron production from Au+Au collisions at sNN = 130GeV [30, 31] and 200GeV [32,33]. Figure 1.12 show the ratio RAA for central collisions. For the charged spectrum RAA

1.3. HARD SCATTERING AS A PROBE OF QGP

17rises up to 2 GeV/c, as expected; but above 2 GeV/c, RAA remains significantly below unity
for both spectra. The suppression in central collisions is in qualitative agreement with thepredictions of energy loss by scattered partons traversing a dense medium.

1.3.3

Reference Experiment: d+Au Collisions

Theoretical studies of parton propagation in high density matter suggest that partons lose asignificant fraction of their energy through gluon bremsstrahlung[16], reducing the parton
momentum and depleting the yield of high pT hadrons [17, 21]. This is a final-state effectin the spatially extended medium created in A + A collisions. Initial-state effects include
nuclear modifications to the parton momentum distributions (structure functions), and soft
scatterings of the incoming parton prior to its hard scattering. These should be present in
p + A, d + A and A + A.
Interpretations of Au+Au collisions based on initial-state parton saturation effects [36]or final-state hadronic interactions [37] also predict a considerable suppression of the hadronproduction at high-pT . It is therefore of paramount interest to determine experimentally themodification, if any, of high-pT hadron yields due to initial state nuclear effects for a system
in which a hot, dense medium is not produced in the final state. To consider the initial-state
effect or final-state effect, we have measured charged hadron and π 0 production at mid√
rapidity in d+Au collisions at sNN = 200 GeV [38].
The nuclear modification factor for d+Au collisions is defined as the ratio of invariant
yield in d+Au to that of p + p, scaled by the number of binary collisions,
RdA (pT ) =(1/Nevt ) d 2 N dA /d pT d η.
NN ) d 2 σ NN /d p d η(hNcoll i/σinel
T(1.15)The top panel of Figure 1.13 shows RdA for inclusive charged particles (h+ + h− )/2,
again compared with RAA observed in central Au+Au collisions, while the lower panel
compares (h+ + h− )/2 with π 0 .
The data clearly indicate that there is no suppression of high-pT particles in d+Au collisions. We do, however, observe an enhancement in inclusive charged particle production at
pT > 2 GeV/c. A similar enhancement was observed in p+A fixed-target experiments [28]and is generally referred to as the “Cronin effect”. The π 0 data suggest a smaller enhancement for pions than for inclusive charged particles at pT = 2-4 GeV/c. We note that the
charged spectrum includes baryons and anti-baryons, which may have a different nuclear
enhancement than the mesons [28].

CHAPTER 1. INTRODUCTION

18
R

2
1.8

sNN = 200 GeV

1.6

Figure 1.13: Top: Nuclear modifi-

1.4

cation factor RdA for (h+ + h− )/2 in

1.2

minimum bias d+Au compared to RAA

1charged hadrons
R dA d-Au min. bias
R AA Au-Au 0-10% central

0.8
0.6

in the 10% most central Au+Au collisions. Inner bands show systematic er-

0.4

rors which can vary with pT , and outer

0.2

bands include also the normalization

RdA

uncertainty. Bottom: Comparison of

1.8
1.6

RdA for (h+ + h− )/2 and the average

1.4
1.2
1

bar at the left indicates the systematicof the π 0 measurements in d+Au. The
uncertainty in common for the charged

0.8
0.6

charged hadrons

and π 0 measurements. This figure is

0.4
0.2

neutral pions

taken from [38].

0
0

1

2

3

4

5

6

7

8
9 10
pT (GeV/c)

The observation of an enhancement of high-pT hadron production in both the minimum
bias d+Au and the neutron tagged sample of p+Au collisions indicates that the suppressionin central Au+Au collisions is not an initial state effect. Nor does it arise from modificationof parton structure functions in nuclei. The data suggest, instead, that the suppression ofhigh-pT hadrons in Au+Au is more likely a final state effect of the produced dense medium.

1.4

Thesis Motivation

In this thesis, we present the results of identified hadron spectra and yields in Au+Au colli√
sions at the energy of sNN = 200 GeV by the PHENIX experiment using the Relativistic
Heavy Ion Collider (RHIC).
As reviewed in this chapter, hydrodynamic models that include radial flow successfully
describe the measured pT distributions in heavy-ion collisions at AGS and SPS. Particle
ratios have been shown to be well reproduced by two parameters: a baryon chemical potential µB and a chemical freeze-out temperature Tch . We study the hydrodynamic behavior
at RHIC energy. Especially, we like to study the pT range where the hydrodynamical anal-1.5. CONTRIBUTIONS OF THE AUTHOR

19

ysis can be applicable by taking into account the decay effects.
On the other hand, one of the most interesting observations at RHIC is that the yield ofhigh-pT neutral pions and non-identified charged hadrons in central Au+Au collisions at
RHIC are below the expectation of the scaling with the number of nucleon-nucleon binary
collisions, Ncoll . It has also been observed that the yield of neutral pions is more strongly
suppressed than that for non-identified charged hadrons in central Au+Au collisions at
RHIC. These observations suggest that a detailed study of particle composition at high-pT
is very important to understand hadron production and collision dynamics at RHIC.

1.5

Contributions of the Author

The author participated RHIC-PHENIX experiment and contributed as following,• Construction of the Time-of-Fight counter.
• Installation of the Time-of-Fight counter in PHENIX detector system.
• Operation of the Time-of-Fight counter during run period.
• Development of the detector simulation for the Time-of-Fight counter.
• Programming of the reconstruction software for the Time-of-Fight counter.
• Timing calibration for the Time-of-Fight counter.
• Analysis of the identified hadron spectra and yields in Au+Au collisions atand publish the results to Phys. Rev. C 69 034909 (2004) [40].

√sNN = 200 GeV

Chapter 2
The PHENIX Experiment
In this chapter, the RHIC collider complex and the PHENIX detector system overview are described. The detail description of PHENIX detector system
are described in section 2.2 to 2.6.

2.1

RHIC : Collider Facility

The Relativistic Heavy Ion Collider (RHIC) [41] at Brookhaven National Laboratory iscapable of accelerating a wide variety of nuclei and ions from protons to Au ions. The
top energy for heavy ion beams (e.g., for Au ions) is 100 GeV per nucleon and that for
protons is 250GeV. The design luminosity are 2 × 1026 cm−2 sec−1 for Au beams and 1.4 ×1031 cm−2 sec−1 for proton beams.
The schematic diagram of the RHIC collider facility is shown in Figure 2.1. The RHIC
complex consists of Tandem Van de Graff, Alternating Gradient Synchrotron (AGS) and
RHIC main rings. The collider consists of two quasi-circular concentric accelerator/storagerings on a common horizontal plane, one (”Blue Ring”) for clockwise and the other (”Yellow Ring”) for counter-clockwise beams. Rings are oriented to intersect with one anotherat six locations along their 3.8 km circumference. [42]Procedure of the RHIC acceleration for Au ion beams is as follow. Negatively charged
Au ions generated by pulsed sputter ion source are injected to the Tandem Van de Graaffs.
The ions are partially stripped off their electrons with a foil at the Tandem’s high voltage
terminal, and then accelerated to the energy of 1 MeV per nucleon by the second stageof the Tandem. After further stripping at the exit of the Tandem and a charge selection
by bending magnets, beams of Au ions with the charge state of +32 are delivered to the20

2.1. RHIC : COLLIDER FACILITY

21

NEW SUPPORTBUILDING
EQUIP. AREA/W
EXIT

EQUIP.
AREA
NEW
MAGNET P.S.
BUILDING

PHOBOS

BRAHMSRHIC
SUPPORT
BUILDING
OPEN
AREA

MAJOR
FACILITY
HALL

RING
ROAD

PHENIX

WIDE ANGLE
HALL

RF.
EQUIP.

COLLIDER
CENTER

N

STAR

BEAM
INJECTION

LINAC
AGS
BOOSTER

AGS

NPBF
REF

HEAVY ION
BYPASS LINE (HITB)HEAVY ION
TRANSFER LINE (HITL)TANDEM VAN DE GRAAFFHEAVY ION SOURCE

Figure 2.1: Layout of the AGS–RHIC complex

CHAPTER 2. THE PHENIX EXPERIMENT

22

Booster Synchrotron and accelerated to 95 MeV per nucleon. Then the ions are strippedagain at the exit from the Booster to reach the charge state of +77, a helium-like ion, andinjected to the AGS. The AGS accelerates the Au beams to the RHIC injection energy of
10.8 GeV per nucleon. The Au ions, injected into the AGS in 24 bunches, are de-bunched
and then re-bunched to four bunches at the injection from porch prior to the acceleration.
These four bunches are ejected at the top energy, one bunch at a time, and transferred to
RHIC through the AGS-to-RHIC Beam Transfer Line. The Au ions are fully stripped tothe charge state of +79 at the exit from the AGS. The stacking in the RHIC rings is done ina boxcar fashion.
Acceleration and storage of beam bunches at RHIC uses two RF systems; i.e., one
operating at 28 MHz to capture the AGS bunches and accelerates to the top energy, andthe other operating at 197 MHz to provide short-collision diamond (σL ∼ 25 cm) for amore reasonable detector design. The synchrotron phase transition of the RHIC lattice is at

γT = 24.7; thus all ions, except protons, must go through this transition. The RHIC collider,indeed, is the first super-conducting accelerator (hence slow ramp rate) that passes throughthe synchrotron phase transition and associated beam instability. It is important to crossthis transition rapidly in order to minimize the beam loss and the emittance growth. Thiscan be accomplished either by rapid acceleration through it with resultant orbit jump to alarger radius or by a ”γT -jump”, where sets of quadrupole are pulsed to change the tune of
the machine and thus move the transition energy momentarily. For the year 2000 operation,
the former method was used due to the lack of pulsed power supplies, while for the year
2001 run, the latter method has been implemented.

2.2. PHENIX DETECTOR OVERVIEW

2.2

23

PHENIX Detector Overview

The PHENIX [43, 44] is one of the major experiments at RHIC to detect a variety ofsignals from quark-gluon plasma. It is designed to perform a broad study of A-A, p-A, andp-p collisions to investigate nuclear matter under extreme condition. PHENIX measureselectrons, muons, photons and hadrons with excellent energy and momentum resolution.
The detector consists of a large number of subsystems. It comprises two central arms,
two forward muon arms, and three global detectors. The east and west central arms areplaced at zero rapidity and instrumented to detect electrons, photons and charged hadrons.
The north and south forward arms have full azimuthal coverage and are instrumented todetect muons. The global detectors measure the start time, vertex and multiplicity of theinteractions. The rapidity and φ coverage and other features of these subsystems is given
in Table 2.1 and a perspective drawing of the PHENIX detector with the major subsystems
labeled is shown in Figure 2.2. The details of each subsystems are described as following
section.

Figure 2.2: A cutaway drawing of the PHENIX detector. Labeled arrows point to the major detector
subsystems.

CHAPTER 2. THE PHENIX EXPERIMENT

24

Element∆η∆φ

Purpose and Special Features

Magnet: Central (CM)

±0.35

360◦

Up to 1.15 T·m.

−1.1 to −2.2360◦0.72 T·m for η = 2

1.1 to 2.4

360◦0.72 T·m for η = 2

±2.6

360◦

d 2 N/d η d φ , precise vertex,

muon (MMS)
muon (MMN)
Silicon (MVD)reaction plane determination±(3.1 to 3.9)

360◦

Start timing, fast vertex.

NTC±(1 to 2)320◦

Extend coverage of BBC for p-p and p-A.

ZDC

±2 mrad360◦

Minimum bias trigger.

±0.35

90◦ ×2

Good momentum and mass resolution,

Beam-beam (BBC)Drift chambers (DC)∆m/m = 0.4% at m = 1GeV.
Pad chambers (PC)±0.35

90◦ ×2

Pattern recognition, tracking
for nonbend direction.

±0.35

90◦

Pattern recognition, dE/dx.

RICH

±0.35

90◦ ×2

Electron identification.

TOF

±0.35

45◦

Good hadron identification, σ <100 ps.

TEC

K ± /π ± separation up to 2 GeV/c
T0

±0.35

45◦

PbSc EMCal±0.35

90◦ + 45◦

Improve TOF timing for p-p and p-A.
For both calorimeters, photon and electron
detection.

±0.35

PbGl EMCal

45◦

Good e± /π ± separation at p > 1 GeV/c by
EM shower and p < 0.35 GeV/c by TOF.
K ± /π ± separation up to 1 GeV/c by TOF.

µ tracker: (µ TS)(µ TN)µ identifier: (µ IDS)(µ IDN)−1.15 to −2.25

360◦

Tracking for muons.

1.15 to 2.44

360◦

Muon tracker north installed for year-3−1.15 to −2.25

360◦

Steel absorbers and Iarocci tubes for1.15 to 2.44360◦muon/hadron separation.

Table 2.1: Summary of the PHENIX Detector Subsystems.

2.3. PHENIX MAGNET SYSTEM

2.3

25

PHENIX Magnet System

The PHENIX magnet system [45] is composed of three spectrometer magnets with ironyokes and water-cooled copper coils. The Central Magnet (CM) is energized by two pairsof concentric coils and provides a field around the interaction vertex that is parallel to thebeam. This allows momentum analysis of charged particles in the polar angle range from70◦ to 110◦ . The north and south Muon Magnets (MMN and MMS) use solenoid coils to
produce a radial magnetic field for muon analysis. Each covers a pseudo-rapidity intervalof 1.1 to 2.3 and full azimuth. The Main Magnet coils are wound on cylindrical surfaces atthe end of large tapered pistons. Each of the three magnets provides a field integral of about
0.8 Tesla-meters. The physical and operating parameters of the magnets and their coils are
given along with a description of the magnetic fields generated. The magnetic volumes of
the PHENIX magnets are very large and complex, so a new technique was developed tomap the fields based on surface measurements of a single field component using single axis
Hall probes mounted on a rotating frame.

al
ntr

Ma

t

gne

am
Be

Ce

Nor th M

uon Ma

gnet

am

Be

Sou

th M

uon

Ma

gne
t

Figure 2.3: Line drawings of the PHENIX magnets, shown in perspective and cut away to show
the interior structures. Arrows indicate the beam line of the colliding beams in RHIC.

CHAPTER 2. THE PHENIX EXPERIMENT

26

PH ENIX

-4.0

-2.0

0.0

2.0

4.0

Z (m)

Magnetic field lines with the outer Central Magnet coil energized

Figure 2.4: CM and MM field lines shown on a cutaway drawing of the PHENIX magnets. The
beams travel along the z axis in this figure and collide at z = 0.

2.4

PHENIX Global Detectors

The timing, location and particle multiplicity of collision are determined by the BeamBeam Counters (BBC), the Multiplicity/Vertex Detector (MVD) and the Zero-Degree Calorimeters (ZDC) [46, 47]. The BBC’s provide both the time of interaction and position of a collision along z axis from the flight time of prompt particles. The MVD provides a measureof event particle multiplicity, collision vertex position and fluctuations in charged particle
distributions. The ZDC’s provide information on the collisions.

2.4.1 Zero Degree CalorimeterThe zero-degree calorimeters provide common event characterization in the four experiments at RHIC. The ZDC is a small hadronic calorimeter which measures the kinetic
energy carried by spectator neutrons.
A single ZDC consists of three modules. Figure 2.5 shows the mechanical design of a
ZDC module. Each ZDC module consists of Tungsten alloy plates and ribbons of opticalfibers in the sampling layer. The depth is 2 hadronic interaction lengths. The lights are2.4. PHENIX GLOBAL DETECTORS

Figure 2.5: Mechanical design of a ZDC module

27

CHAPTER 2. THE PHENIX EXPERIMENT

28

Figure 2.6: Plain view of the collision region and (section A-A) “beam’s eye” view of the ZDC
locationcollected into a photo-multiplier tube (PMT) via optical fibers and readout. Both time andamplitude are digitized for each PMT – as is an analog sum of the three PMT signals foreach ZDC.
Figure 2.6 shows the layout of the ZDC location. They are placed 18 m up- and downstream of the interaction point along the beam line. Each ZDC covers 2 mrad of forward
angular cone which corresponds to pseudo-rapidity region |η | > 6.0. At 11 m from theinteraction point, there are the dipole magnets to align two circulating beams to match atintersection point. The Au ions beam is bended by one dipole magnet and bended again
by another dipole magnet in the opposite side, then it is returned to the collider beam line.
For the collision, fragment protons are swept out and only fragment neutrons emitted in thevery narrow angular cone hit the ZDC.

2.4.2 Beam-Beam Counter
The beam-beam counters (BBC) measure the start time and the collision vertex point along
the beam axis (z-axis). Since the longitudinal size of the beam bunch at RHIC for Au+Au

2.4. PHENIX GLOBAL DETECTORS

29

Figure 2.7: (a) A BBC element consists of one-inch mesh dynode photomultiplier tubes mounted
on a 3 cm quartz radiator. (b) A BBC array comprises 64 BBC elements. (c) The BBC is mounted
on the PHENIX detector. The beam pipe is seen in the middle of the picture. The BBC is installedon the mounting structure just behind the central spectrometer magnet.

collisions is designed to be 25 cm RMS, the time spread of nuclear collisions could be as
much as 2 ns.
The BBC consists of two identical sets of counters, which are placed 1.44 m from theinteraction point along the beam line (one on the North side and the other on the South side)surrounding the beam pipe. This corresponds to a pseudo-rapidity range from 3.0 to 3.9
over the full azimuth. Each counter consists of 64 Čerenkov telescopes, arranged radiallyaround the beam pipe. A BBC telescope consists of one-inch mesh dynode photomultipliertubes (HAMAMATSU R6178) mounted on a 3 cm quartz radiator. Figure 2.7 shows (a) a
BBC element, (b) a BBC array and (c) the BBC mounted on the PHENIX detector.
Each BBC measures arrival times of leading charged particles from the collision. The
arrival time for each BBC is defined as the average of the hit time in each BBC. The
collision time is defined as the average arrival time of North and South BBCs. The timeof-flight measurement uses this information for start time.
The time difference between North and South side of BBCs provides the vertex position along the beam axis. Figure 2.8(a) shows a correlation of z-vertex calculated by BBC
and ZDC, and Figure 2.8(b) shows the projection of Figure 2.8(a) on to the axis of BBC

CHAPTER 2. THE PHENIX EXPERIMENTZ Vertex from ZDC [cm]

30

300

200

(a)

100

0

-100

-200

Events

-300

250

(b)

200

150

100

50

0

-150

-100

-50

0

50

100

150

Z Vertex from BBC [cm]Figure 2.8: (a) Correlation of determined z vertex between BBC and ZDC. (b) Z vertex distribution
from BBC. Hatched area corresponds to the events satisfying the PHENIX Local LVL1 trigger
condition.

z-vertex. The peak at ± 144 cm in Figure 2.8(b) corresponds to beam collisions outside of
the BBC. The z-vertex position and number of PMT’s hits in each BBC are also calculated
online and sent to the LVL1 trigger. |z-vertex| <20 cm and two or more PMT’s fired ineach BBC are required as the LVL1 trigger condition. The hatched area in Figure 2.8(b)corresponds to the events selected by the LVL1 trigger. The trigger efficiency with respect
to inelastic Au+Au collisions is evaluated by a PHENIX detector simulation with the HIJING event generator to produce Au+Au collisions as input, and was found to be 92 ±2%. The correlation between BBC charge sum and ZDC total energy is used for centrality
determination. The detail explanation of the trigger efficiency and the centrality selection
is given in section 3.1.

2.5. CENTRAL ARM SPECTROMETERS

2.5

31

Central Arm Spectrometers

PHENIX have two central arms at zero rapidity to detect electrons, photons and charged
hadrons. The central arm detectors consist of tracking system for charged particles andelectromagnetic calorimetry. The tracking system consists of drift chamber (DC), padchamber (PC) and time expansion chamber (TEC) [48]. The ring imaging cherenkov(RICH) and time-of-flight (TOF) systems provide identification of charged particle [49].
The electromagnetic calorimeter (EMCal) provides measurements of both photons and energetic electrons [50]. The following sections describe the parts of the detector that areused for charged hadron measurements.

PHENIX Detector - Second Year Physics Run
PbSc

PC3
PC2

PC3
TEC

CentralMagnet

PbSc

PbSc

PbSc
DC

DC
RICH

RICH
BB

PbSc

PbGl
MVD

PbSc

PC1

PC1

PbGl

TOF

West

Beam View

East

Figure 2.9: The two central spectrometer arms, viewed in a cut through the collision vertex.

CHAPTER 2. THE PHENIX EXPERIMENT

32

2.5.1 Drift Chamber
The drift chambers (DC) measures charged particle trajectories in the r–φ direction todetermine the transverse momentum of charged particle. By combining the polar angle
information from the first layer of the PC with the transverse momentum, the total momentum p is determined. The DC also participates in the pattern recognition at high particle
track densities by providing position information that is used to link tracks through thevarious PHENIX detector subsystems. To measure the φ → e+ e− mass with a resolution
better than its natural width of 4.4 MeV and have good tracking efficiency for the highest
multiplicities at RHIC, the DC was designed to have (i) single wire resolution better than
150 µ m in r–φ , (ii) single wire two track separation better than 1.5 mm, (iii) single wire
efficiency better than 99%, and (vi) spatial resolution in the z direction better than 2 mm.
The DC system consists of two independent gas volumes located in the west and east
arms, respectively. The chambers in the east arm and the west arm are symmetric withrespect to x = 0 plane, as seen in Figure 2.9. They are located in the region from 2 to 2.4
m from the beam axis and 2 m along the beam direction. It is in a residual magnetic fieldwith a maximum of 0.6 kG.

R
=
2m
2.0
o
90

2.5 m

m
2.46
=
R

Ti
mylar

frame

window

Figure 2.10: Construction of DC frame.

2.5. CENTRAL ARM SPECTROMETERS

33

4.5 degr.

Wire orientations, top view
V2 − planes

U2 − planes

Termination wires

Back wire

V1 − planes~ 1800 mm

X2 − planes

Gate wires
U1 − planes
Potential wire

sense (anode)
X1 − planes

wire

anode planecathode plane

U

X

V

Sector, side view

Figure 2.11: The layout of wire position within one sector and inside the anode plane (left). A
schematic diagram, top view, of the stereo wire orientation (right).

Each DC volume is defined by a cylindrical titanium frame defining the azimuthal andbeam-axis limits of the detector volume (Figure 2.10). 0.125 mm Al-mylar windows define
the limits of the gas volume radially. Each frame is filled with drift chamber modules and isdivided in 20 equal sectors covering 4.5◦ in φ . There are six types of wire modules stacked
radially in each sector: X1, U1, V1, X2, U2 and V2. Each module contains 4 sense (anode)planes and 4 cathode planes forming cells with a 2–2.5 cm drift space in the φ direction.
The X1 and X2 wire cells run in parallel to the beam to perform precise track measurements in r–φ . These wire cells are followed by two sets of small angle U,V wire planes
used in the pattern recognition. U1, V1, U2, and V2 wires have stereo angles of about 6◦
relative to the X wires and measure the z coordinate of the track. The stereo angle wasselected to minimize track ambiguities by matching the z resolution of the pad chambers.
Each of the X- and U,V-stereo cells contain 12 and 4 anode (sense) wires, respectively.
As a result, there are 40 drift cells in the DC located at different radii. The layout of wires
within one DC sector is shown in Figure 2.11. The stereo wires start in a sector on one side
and end in a neighboring sector on the other side of the DC.

CHAPTER 2. THE PHENIX EXPERIMENT

34

2.5.2 Pad Chamber
The pad chambers (PC) are multi-wire proportional chambers that form three separate layers of the PHENIX central tracking system. Each chamber contains a single plane of wires
inside a gas volume bounded by two cathode planes. One cathode is finely segmented into
an array of pixels. The charge induced on a number of pixels when a charged particle starts
an avalanche on an anode wire, is read out through specially designed readout electronics.
The PC system determines space points along the straight line particle trajectories outside the magnetic field. Figure 2.9 shows the radial location of the PC’s in the central
tracking arms. The first pad chamber layer (PC1) is located at the radial outer edge of eachdrift chamber at a distance of 2.49 m, while the third layer (PC3) is 4.98 m from the interaction point. The second layer (PC2) is located at a radial distance of 4.19 m in the west
arm only.
Anode wire
Field wire

8.4mm
Center pixel

1.5mm
2.7mm

Side pixel

8.2mm

Figure 2.12: The pad and pixel geometry (left). A cell defined by three pixels is at the center ofthe right picture

Figure 2.12 shows the pad pattern of the PC. Each cell contains three pixels and anavalanche must be sensed by all three pixels to form a valid hit in the cell. The interleaved
pixels were ganged together, nine by nine and connected to a common readout channel,
such that the three pixels in a cell are always connected to different but neighboring channels and each cell is defined by its unique channel triplet. So, the information can be broken
down to the cell level, by identifying the triplets.
This solution saves a factor of nine in readout channels compared to readout of every
pixel and a factor of three compared to a readout pad geometry where a cell is the actual
electrode connected to an electronics channel. The design goals for the position resolution
were ±4 mm. This motivated an anode wire spacing of about 8 mm. For geometrical2.5. CENTRAL ARM SPECTROMETERS

35

reasons, a spacing of 8.4 mm was chosen. Desiring a square cell geometry, a cell areaof 8.4 × 8.4 mm2 was adopted. In the z direction, this resulted in a position resolution of±1.7 mm which was substantially better than the design goals. At the positions of PC2 andPC3 it is sufficient to maintain the same angular resolution as of PC1. Thus the cells on
PC3 have 4 times the area of PC1 cells since PC3 is at twice the distance from the vertex
as compared to PC1.

2.5.3

Time-of-Flight Counter

The time-of-flight counter (TOF) serves as the primary particle identification device forcharged hadrons in PHENIX. It is designed to have about 100 ps timing resolution in orderto achieve clear particle separation in the high momentum region, i.e. π /K separation up
to 2.4 GeV/c and K/proton separation up to 4.0 GeV/c.
The TOF wall is located at a radial distance of 5.06 m from the interaction point, between the pad chamber (PC3) and the electromagnetic calorimeter (EMCal) in the east
central arm. It is designed to cover |η | < 0.35 and ∆φ = 45◦ in azimuthal angle. The
TOF system consists of 10 panels of TOF walls. One TOF wall consists of 96 segments,
each equipped with a plastic scintillator slat and photomultiplier tubes which are read out
at both ends. A total 10 TOF panels, 960 slats of scintillators and 1920 channels of PMTs
were installed and operated at the first year of operation. The slat is oriented along the r–φ
direction and provides time and longitudinal position information of particles that hit theslat.
Figure 2.13 shows a schematic view of one panel of the TOF detector. It consists of 96
plastic scintillation counters with photomultiplier tubes (PMT’s) at both ends, light guides
and mechanical supports. Scintillator rod and light guides were wrapped with thin aluminum foil and were glued on the honeycomb board. The honeycomb boards are made of
paper of a honeycomb structure sandwiched between carbon fiber sheets, which provide a“massless” rigid structure. Scintillators with two different lengths (637.7 and 433.9 mm)
are assembled in an alternating fashion in order to avoid geometrical conflicts between the
PMTs of neighboring slats. Appendix B discusses in detail the specifications and performance of the TOF counter.

PMT
200 cmBleeder
Scintillator

50 cm

Carbon fiber sheetµ-metal

Aluminium frame

Light guide

Honeycomb structured paper

CHAPTER 2. THE PHENIX EXPERIMENT

36

Figure 2.13: Schematic diagram of the components of a single TOF panel which consists of 96
plastic scintillation counters with photomultiplier tubes at both ends, light guides and supports.

2.5. CENTRAL ARM SPECTROMETERS

37

Particle identification for charged hadrons is performed by combining the informationfrom the DC, PC1, BBC and the TOF. Figure2.14 shows a contour plot of time-of-flight
as a function of the reciprocal momentum in minimum-bias Au+Au collisions after a momentum dependent track and TOF hits association residual cut between the track projection
point and TOF hits has been taken. The flight path is also corrected for each particle species
in this figure.

-1

charge/Momentum [(GeV/c) ]PHENIX High Resolution TOF

π+

6

Au+Au s = 200 A GeV

K+

4

3

10

p
2

10

2

d
0

d

10

-2
−

p

K

-4

1

π−

-6
10

15

20

25

30

35

40 45 50 55 60
Time of Flight [ns]Figure 2.14: Contour plot of the time-of-flight versus reciprocal momentum in minimum bias
Au+Au collisions at the energy of√sNN = 200 GeV. The figure clearly demonstrates the particle

identification capability using the TOF detector in the year 2001 data taking period. The flight pathis corrected for each track.

CHAPTER 2. THE PHENIX EXPERIMENT

38

2.6

Other Detectors

These detectors are mainly used for lepton and photon measurement.

2.6.1 Time Expansion Chamber
The time expansion chamber (TEC) is composed of a set of 24 large multi-wire tracking
chambers arranged in four, six-chamber sectors which reside in east central arm. It measures all charged particles passing through its active area, providing direction vectors thatare matched to additional track information from the DC’s and PC’s also located in thecentral arm. The tracking information is used to solve the complex pattern recognition
problems associated with the high particle density in relativistic heavy ion physics. It aides
in background rejection for particles passing into the EMCal and TOF wall. The detector
system allows for systematic studies of tracking efficiency and background rejection versus
multiplicity in coordination with the DC. The TEC also enhances the momentum resolutionof the central arm at pT ≥ 4GeV /c by combining with the DC to provide a long lever arm
for improved track-angle resolution. In addition the TEC measures ionization energy losses(dE/dx) of charged tracks which enables particle identification, particularly electron/pion
separation, over a momentum range important to the physics goals of the experiment.

Figure 2.15: Mechanical structure of single TEC chamber. The frame skeleton, anode-cathodeinterface board and central wire divider are shown.

2.6. OTHER DETECTORS

39

The TEC is composed of individual chambers, with six chambers stacked together toform a wedge-shaped sector. Each chamber is independent and self-supporting, made froma combination of machined graphite-composite, S2-glass and FR-4 components all epoxied
together. Individual chambers have active areas varying from 3.1m x 1.7m for the smallest
to 3.5m x 1.9 m for the largest TEC plane. The material in the detector’s active area wasminimized by using a box beam wire divider located at z=0 and widely spaced I-beamwindow supports all made of thin FR-4. The open design results in 98% of the TEC’s
fiducial area being active.
Each chamber is built in two layers: a lower layer containing structural elements forwindow support and space for inclusion of TRD radiator foils, and an upper layer containing the active elements of the wire chamber. The upper layer is filled with P-10 gas and iscomposed of a Cu-mylar cathode window, 3 cm drift space, three wire planes (field, anode,
field) oriented parallel to the z axis of the detector, and a final Cu-mylar cathode window(Figure 2.15). The anode wires are spaced on average 4 mm from each other (specifically
4.05 mm and 4.15 mm depending on the sector plane) and 3.0 mm from both cathode wire
planes. The Cu-coated mylar windows have multiple functions. They are biased to establish the proper field shaping inside the detector, serve as the gas barrier and provide an
RF shield. The wire planes are divided in half at z=0 both for ease of construction and to
decrease the average multiplicity per wire by a factor of two.

2.6.2

Ring-Imaging Cherenkov Detector

The ring imaging cherenkov (RICH) detector is designed for electron identification, andprovides e/π discrimination below the π Cherenkov threshold, which is set at about 4
GeV /c. In combination with the EMCal in each arm and the TEC in one arm, the goal is
to limit the false identification of hadrons as e+ and e− to less than 10−4 .
Figure 2.16 contains a cutaway drawing of one of the RICH detectors revealing the internal components. Each RICH detector has a volume of 40 m3 , with an entrance window
area of 8.9 m2 and an exit window area of 21.6 m2 . Each detector contains 48 composite
mirror panels, forming two intersecting spherical surfaces, with a total reflecting area of 20
m2 . The spherical mirrors focus Cherenkov light onto two arrays of 1280 UV photomultiplier tubes (HAMAMATSU H3171S), each located on either side of the RICH entrance
window. The phototubes are fitted with 2” diameter Winston cones and have magnetic
shields that allow them to operate at up to 100 Gauss. The phototube UV glass windows
absorb photons of wavelengths below 200 nm. The minimum thickness of radiator gas seen

CHAPTER 2. THE PHENIX EXPERIMENT

40

Figure 2.16: A cutaway view of one arm of the PHENIX RICH detector.
by any particle is 87 cm, the maximum is about 150 cm. The radiator gas is maintained at
a pressure of 0.5” of water above ambient. The large aluminized Kapton entrance and exit
windows are 125 µ m thick, and are supported against the internal pressure by graphiteepoxy beams. All gas seals are made using Goretex gaskets. There are black vinyl coatedpolyester light shields covering the outside of the Kapton windows. The preamplifiers forthe signals from the photon detectors are mounted directly on the RICH detector.

2.6.3 Electromagnetic Calorimeter
The primary role of the electromagnetic calorimeter (EMCal) is to provide a measurementof the energies and spatial positions of photons and electrons produced in heavy ion collisions. It also plays a major role in particle identification and is an important part of the
PHENIX trigger system. The EMCal system can trigger on rare events with high transverse
momentum (pT ) photons and electrons. Its signals are incorporated in Level-1 triggers forhigh multiplicity or large total transverse energy (ET ) events. In addition the EMCal provides a good measurement of the hadronic energy produced at mid-rapidity and thus of the
ET produced in the reaction.
The EMCal system consists of a total of 24768 individual detector modules divided
between the Pb-Scintillator calorimeter (PbSc), which provides six sectors of azimuthal
coverage and the Pb-glass calorimeter (PbGl) comprised of two sectors. Both sub-detectors

2.6. OTHER DETECTORS

41

are read out with photomultipliers and have good energy resolution and intrinsic timing
characteristics but their design is quite different and they will be described separately.

Figure 2.17: Interior view of a Pb-scintillator calorimeter module showing a stack of scintillator
and lead plates, wavelength shifting fiber readout and leaky fiber inserted in the central hole.

The Pb-scintillator electromagnetic calorimeter is a shashlik type sampling calorimeter
made of alternating tiles of Pb and scintillator consisting of 15552 individual towers andcovering an area of approximately 48 m2 . The basic building block is a module consisting of four (optically isolated) towers which are read out individually. Each Pb-scintillator
tower contains 66 sampling cells consisting of alternating tiles of Pb and scintillator. The
edges of the tiles are plated with Al. These cells are optically connected by 36 longitudinally penetrating wavelength shifting fibers for light collection. Light is read out by 30 mm
FEU115M phototubes at the back of the towers. Four towers are mechanically grouped
together into a single structural entity called a module as shown in Fig. 2.17. The PbSc√
calorimeter has a nominal energy resolution of 8.1%/ E(GeV ) ⊕ 2.1% and an intrinsic
timing resolution better than 200 ps for electromagnetic showers. A high precision calibration and monitoring system has been developed to achieve an absolute energy calibration
better than 5% for day one operation at RHIC, and to maintain an overall long term gainstability of the order of 1%.
The Pb-glass calorimeter array comprises 9216 elements of a system previously used√in CERN experiment WA98. It has a nominal energy resolution of 6%/ E (GeV) andCHAPTER 2. THE PHENIX EXPERIMENT

42

photomultiplierwith housing

steel plates

mirror foil

lead glass matrix withcarbon fibre/epoxy

LED boardreflective coverphotodiode withpreamplifier

Figure 2.18: Exploded view of a lead-glass detector supermodule.
an intrinsic timing resolution of better than 300 ps for electromagnetic showers above theminimum ionizing peak energy.
The Pb-glass calorimeter occupies the two lower sectors of the East Central arm of
PHENIX. The PHENIX Time-of-Flight system is located on the Pb-glass sectors. EachPb-glass sector comprises 192 supermodules. The Pb-glass supermodule comprises 24 Pbglass modules in an array of 6 Pb-glass modules wide by 4 modules high as shown in
Figure 2.18. The size of one Pb-glass module is 40 mm × 40 mm × 400 mm. The Pbglass modules within a supermodule are individually wrapped with aluminized mylar andshrink tube and 24 modules are glued together with carbon fiber and epoxy resin to form aself-supporting supermodule with a shared calibration system (see Figure 2.18).

2.6.4 Muon Arm Spectrometer
PHENIX have two forward muon arms at rapidity of 1.2 < |y| < 2.4 with full azimuthal
acceptance to detect muon [51]. Each muon arm must track and identify muons and provide
good rejection of pions and kaons (∼ 10−3 ). In order to accomplish this we employ a radial
field magnetic spectrometer with precision tracking (Muon Tracker: MuTr) followed by astack of absorber/low resolution tracking layers (Muon Identifer: MuID).

2.6. OTHER DETECTORS43

PHENIX Detector - Second Year Physics Run
So
uth

t
ne

M

uo
n

Central Magnet
M

ag
ne
t

No

rth

M

uo

nM

ag

BB
ZDC SouthZDC North

MuID

MuID
MVD
MuTr

South

Side View

Installed

North

ActiveFigure 2.19:

Muon Tracker
The muon tracker (MuTr) design specifications were driven by the requirements that it beable to (i) allow a clean separation of J/ψ from ψ 0, ϒ(1S) from ϒ(2S,3S) and ρ /ω fromφ , (ii) provide a large enough signal-to-background and acceptance for vector mesons tobe able to do statistically significant physics measurements in less than 1 year of RHIC
running, (iii) have low enough occupancy to be able to reconstruct tracks efficiently incentral Au+Au events and (iv) still perform well in the lower occupancy but higher event
rate p-p and p-A physics programs.

√
The relative mass resolution is approximately given by σ (M)/M = 6%/ M, where M

is in GeV. This mass resolution enables a clear separation of the ρ /ω peak from the φ ,J/ψ and ψ 0, with an acceptable separation of ϒ and ϒ0. This is consistent with a spacial
resolution of 100 microns.
The above design requirements led to a Muon Tracker design which is comprised ofthree stations of cathode-strip readout tracking chambers mounted inside conical-shaped
muon magnets (see Figure 2.20), with multiple cathode strip orientations and readout
planes in each station. The electronics design specifications were driven by the requirement that the non-stereo cathode planes provide 100 µ m resolution measurements of the44

CHAPTER 2. THE PHENIX EXPERIMENT

particle trajectories and that the readout of the system be able to meet the global PHENIX
readout requirements. Test-bench measurements from production chambers and electronics combined with simulations of the full muon tracker design show that the tracker shouldmeet the design requirements outlined above.

Figure 2.20: The South Muon ARM tracking spectrometer. Muons from the intersection region,
to the right, intercept the station 1, 2 and 3 detectors and proceed to the muon identifier detectors to
the left (not shown).

Muon Identifier
The muon identifier (MuID) consists of five layers of chambers interleaved with steel absorbers. The MuID is used for separating muons from charged hadrons and other background as well as providing trigger for single muons and dimuons.

2.6. OTHER DETECTORS

Figure 2.21: Muon identifier panel being flipped over during construction.

Figure 2.22: The south PHENIX Muon Identifier before installation of the shield wall.

45

Chapter 3
Data Analysis
This analysis is based on the experimental data of Au+Au collisions at√
sNN = 200 GeV in the second year of running at RHIC. The Au-Au run was
operated from August 2001 to November 2001.
In this chapter, we describe the event selection, track reconstruction, momentum determination, particle identification and various corrections, including geometrical acceptance, particle decay, multiple scattering and absorption
effects, detector occupancy corrections and weak decay contributions from Λand Λ to proton and anti-proton spectra. The estimations of systematic uncertainties on the measurements are addressed at the end of this chapter.

3.1

Event Selection

Figure 3.1 shows the integrated luminosity which has been delivered by RHIC in the 2001
Au-Au run period. RHIC has delivered 85 µ b−1 of integrated machine luminosity for allz at PHENIX collision point. About 42 µ b−1 was within |z| < 45 cm vertex cut. The
PHENIX experiment recorded about 24 µ b−1 of integrated luminosity.

3.1.1 Minimum Bias Trigger
For this analysis, we use the PHENIX minimum bias trigger events which are determinedby following conditions on BBC and ZDC.
• A coincidence between the north and south BBC with at least two PMTs fired in each
BBC is required. The collision vertex has to satisfy |zvtx | < 75 cm. These cuts are
performed by the BBC Level-1 (BBLL1) trigger online. [BBLL1>= 2]
46

3.1. EVENT SELECTION

47

Figure 3.1: Integrated luminosity which was delivered by RHIC in first and second Au-Au run
period as a function of day. The blue line is for PHENIX.

• At least one forward neutron has to be registered in each of the two ZDCs. [ZDCNS]• An offline collision vertex cut of |zvtx | < 30 cm is required.
The trigger efficiency for minimum bias Au nuclear interactions related to these cuts isstudied by a detailed simulation of the BBC and the ZDC. First, response for all 124 PMT
tubes and the BBLL1 board logic are tuned in the simulation to match the real data. Then
HIJING [55] simulated events are used to determine the BBC trigger efficiency. Figure 3.2
shows the extracted the BBC trigger efficiency as a function of zvtx . The systematic errors
are studied by varying the TDC (Time Digital Converter) threshold for each PMT (used by
the BBLL1 trigger) and the input dN/dy and collision vertex distribution from HIJING.
The extracted BBC trigger efficiency is
triggerεbbc= 93.1% ± 0.4%(stat.) ± 1.6%(sys.).

(3.1)

To reject the small percentage of BBC triggers that are “background” events, a ZDC coincidence with at least one neutron on both sides is required. The fraction of BBC triggers
that also satisfy the ZDC condition, (BBLL1 >= 2&&ZDCNS)/(BBLL1 >= 2), is shownin Figure 3.3 as a function of run number.
The ratio has a maximum value around 97.5% (indicated by the horizontal line). The
fact that the ratio drops to lower values in some later runs is in agreement with observations during these runs that the luminosity was high, and the BBC trigger had a higher
background rate. It is also possible that the BBC had a “hot” tube in some of these runs. A

CHAPTER 3. DATA ANALYSIS

Trig. Eff. by BBLL1

1.2

Ratio

48

BBLL1 >=2hit && |Zll1|<= ± 75cm && |Zoff|<=± 30cm )

1

0.98

1

0.96
0.94

0.8

0.92
0.6

0.9
0.88

0.4

0.86
0.2
0
-200

0.84
0.82
-150

-100

-50

0

50

100

150

zvtx (cm)

200

30500

31000

31500

32000

32500

33000

33500

Run Number

Figure 3.2: The BBC trigger efficiency as a

Figure 3.3:

function of zvtx

2&&ZDCNS)/(BBLL1 >= 2) is plotted as a

The ratio R = (BBLL1 >=function of run number.

conservative estimate for the 2.5% exclusive BBC triggers is that 40% of these events are
due to ZDC inefficiencies and 60% are “background” events. The ZDC trigger efficiency
for events that also satisfy the BBC trigger istrigger+1.0
εzdc|bbc= 99−1.5%.

(3.2)

The minimum bias trigger efficiency with the BBC and ZDC coincidence can be calculatedas,
triggertriggertrigger
εminbias= εbbc× εzdc|bbc= 92.2+2.5−3.0 %.

(3.3)

3.1.2 Centrality Determination
The events are classified by centrality, which is related to the measured fraction of the total
geometrical cross-section between two ions. The ZDC measure spectator neutrons that are
not bound in deuterons or heavier fragments. The BBC measures the number of charged
particles at forward rapidity. The centrality is determined by the combined information on
spectator neutrons measured by the ZDC and the charged sum information measured by
the BBC. A schematic figure is shown in Figure 3.4.
Figure 3.5 shows the correlation between the BBC charge sum and ZDC total energy√
for Au+Au at sNN = 200 GeV. The lines on the plot indicate the centrality definition in theanalysis. For the centrality determination, these events are subdivided into 11 bins using
the BBC and ZDC correlation: 0–5%, 5–10%, 10–15%, 15–20%, 20–30%, ..., 70–80% and3.1. EVENT SELECTION

p p
p
n
n
n
n

49

!"#$%&%'()
ImpactParameter

Participants!"#$%&%'()

BBC

n
nn
n
p
p p

ZDC

Figure 3.4: A schematic figure showing nucleus-nucleus collisions. Nucleons which have interacted with other nucleons are called “participants”. Nucleons which have not interacted go straightwith initial momenta. They are called “spectators”. Protons in the spectators are swept out by
accelerator dipole magnet and only nutrons are emitted in ZDC.

Figure 3.5: Correlation between the BBC charge sum and ZDC total energy. The lines represent
the centrality cut boundaries.

CHAPTER 3. DATA ANALYSIS

50

80–92%. Due to the statistical limitations in the peripheral events, we also use the 60–92%
centrality bin as the most peripheral bin.

3.1.3 Glauber Model Calculation
To estimate the number of nucleon-nucleon binary collisions Ncoll and participating nucleons Npart for each centrality class, a Glauber model [6] Monte-Carlo simulation that
includes the responses of the BBC and ZDC is used. A participant is defined as a nucleon
which has suffered at least one inelastic nucleon-nucleon collision. The average numberof binary collisions hNcoll i and the geometrical nuclear overlap function TAB are related
quantities:
TAB = hNcoll i/σNN(3.4)

where σNN is inelastic nucleon-nucleon cross section.
Based on a Glauber model calculation, the average nuclear overlap function TAuAu , theaverage number of nucleon-nucleon binary collisions hNcoll i, and the average number ofparticipants hNpart i are obtained with each centrality bin (Table 3.1). The systematic errorsof the Glauber quantities are estimated by varying the model assumptions, e.g.:
1. σNN = 39 mb and σNN = 45 mb (default σNN = 42 mb)
2. Woods-Saxon parameters, R = 6.65 fm, a = 0.55 fm and R = 6.25 fm, a = 0.53 fm.
(defaults : R = 6.38 fm, a = 0.54 fm)
3. an alternative neutron loss function in the ZDC
4. a different smearing function for the BBC response.
5. Each nucleon is assumed to have a hard core of 0.4 fm, the distance between thecenters of the two nucleons is always greater than 0.8 fm in the Au nucleus.
Figure 3.6 shows the systematic errors for hNcoll i, hNpart i, TAuAu and impact parameter hbi.
Figure 3.7 shows the systematic errors for the total geometric cross section. The total√
geometric Au + Au cross section at sNN = 200GeV is
geo
σAu+Au= 6847 ± 542mb.

(3.5)

3.1. EVENT SELECTION

51

Figure 3.6: Systematic errors on hNcoll i, hNpart i, TAuAu and impact parameter hbi.

Figure 3.7: Total geometrical cross section for Glauber calculation with different parameters.

CHAPTER 3. DATA ANALYSIS

52

Centrality
0- 5%
0-10%
5-10%
10-15%
10-20%
15-20%
20-30%
30-40%
40-50%
50-60%
60-70%
60-80%
60-92%
70-80%
70-92%
80-92%
60-92%
min. bias

hTAuAu i (mb−1 )25.37 ± 1.77
22.75 ± 1.56
20.13 ± 1.36
16.01 ± 1.15
14.35 ± 1.00
12.68 ± 0.86
8.90 ± 0.72
5.23 ± 0.44
2.86 ± 0.28
1.45 ± 0.23
0.68 ± 0.18
0.49 ± 0.14
0.35 ± 0.10
0.30 ± 0.10
0.20 ± 0.06
0.12 ± 0.03
0.35 ± 0.10
6.14 ± 0.45

hNcoll i
1065.4 ± 105.3
955.4 ± 93.6
845.4 ± 82.1
672.4 ± 66.8
602.6 ± 59.3
532.7 ± 52.1
373.8 ± 39.6
219.8 ± 22.6
120.3 ± 13.7
61.0 ± 9.9
28.5 ± 7.6
20.4 ± 5.9
14.5 ± 4.0
12.4 ± 4.2
8.3 ± 2.4
4.9 ± 1.2
14.5 ± 4.0
257.8 ± 25.4

hNpart i
351.4 ± 2.9
325.2 ± 3.3
299.0 ± 3.8
253.9 ± 4.3
234.6 ± 4.7
215.3 ± 5.3
166.6 ± 5.4
114.2 ± 4.4
74.4 ± 3.8
45.5 ± 3.3
25.7 ± 3.8
19.5 ± 3.3
14.5 ± 2.5
13.4 ± 3.0
9.5 ± 1.9
6.3 ± 1.2
14.5 ± 2.5
109.1 ± 4.1

Table 3.1: The average nuclear overlap function (hTAuAu i), the number of nucleon-nucleon
binary collisions (hNcoll i), and the number of participant nucleons (hNpart i) obtained
from a Glauber Monte Carlo correlated with the BBC and ZDC response for Au+Au at√
sNN = 200 GeV as a function of centrality. Centrality is expressed as percentiles of σAuAu= 6.9 barn with 0% representing the most central collisions. The last line refers to minimum
bias collisions.

3.2. TRACK RECONSTRUCTION

53

3.2

Track Reconstruction

3.2.1

Track Selection

Charged particle tracks are reconstructed by the DC based on a combinatorial Hough transform (CHT) [56] – which gives the angle of the track in the main bend plane. The main
bend plane is perpendicular to the beam axis (azimuthal direction). PC1 is used to measure
the position of the hit in the longitudinal direction (along the beam axis).
A typical track in the DC main bend plane is illustrated in Figure 3.8a. The coordinates
we chose to describe tracks in the drift chamber are φ , the azimuthal angle at the intersection of the track with a “reference radius” at the mid-radius of the drift chamber, and α ,the inclination of the track at that point. In principle, φ and α are equivalent to a slope andintercept; the main difference is that φ and α are limited to a given range of possible values
while slope and intercept are not. Figure 3.8b shows the track in the r-z plane, perpendicular to the bend plane. Because the magnetic field is along the beam direction, tracks
usually have a very small bend in this plane. Therefore, it is called the non-bend plane.
The coordinates used in this projection are zDCH (zed), the z coordinate of the intersection
point, and β , the inclination of the track at the reference radius.
y

X2

r

inclination angle

X1

αparticle

PC1 hitzδ

PC1 radius (245cm)

βzed
DC reference radius(R = 220 cm)

φxpolar angle
reference circle
R = 220 cm

θθ0

DC West Armz vertex

Figure 3.8: a) A schematic cutaway view of a track in the DC x-y (or r-φ ) plane. The X1 and X2
hits in the drift chamber are shown as small circles within an outline of the drift chamber. φ and α
are the feature space variables in the CHT transform (see text). b) A schematic cutaway view of a
track in the DC r-z plane. The track polar angle is β . The associated PC1 hit is indicated by the box
marker. The track bending angle is δ , which is small, such that the track can be approximated by
the straight line linking the PC1 hit and collision vertex measured by the BBC.

CHAPTER 3. DATA ANALYSIS54

The tracking is done separately in the r-φ and the r-z plane. The track reconstruction
in r-φ is realized using a CHT technique where any pair of hits can be mapped to a pointin the space defined by azimuth angle φ and track bending angle α . The basic assumption
is that tracks are straight lines within the DC. In this case, all hit pairs for a given track will
have the same φ and α , thus resulting in a local maximum in the feature space spanned bythese variables. The DC tracking efficiency in a high multiplicity environment is estimatedbased on an embedding technique, which will be discussed in Section 3.5.3.
After the reconstruction of the track in the main bend plane, the direction of the trackis specified by φ and α . Tracks are then reconstructed in the non-bend plane by combining
the information from the PC1 reconstructed hits and the collision vertex zvtx as measured
by the BBC. First, PC1 candidate hits within 2 cm distance from the track in the r-φ plane
are identified. Then a straight line connecting zvtx and PC1 z fixes the direction of the trackin z. The intersection points between the r-z plane and UV hit lines are calculated. UV1hits are associated to the track if they are within ±5 cm from the track in the r-z plane. If
there is more than one PC1 association, the one with more associated UV hits is accepted
to be the correct track.

3.2.2 Momentum Determination
The α measured in the drift chamber is closely related to the field integral along the track
trajectory. For tracks emitted perpendicular to the beam axis, this relation can be approximated by

α'

K1
,
p

(3.6)

where K1 is the field integral,Z

K1 = 0.3/RDC

l B dl = 87 mrad GeV/c.

(3.7)

However, due to the small non-uniformity of the focusing magnetic field along theflight path of charged particles, an accurate analytical expression for the momentum of theparticles can not be determined. A four-dimensional field integral grid was constructedwithin the entire radial extent of the central arm for momentum determination based on
drift chamber hits. The variables in the grid are zvtx , the polar angle θ0 of the particle atthe vertex, the total momentum p, and radius r, at which the field integral f (p, r, θ0 , z) is
calculated. The field integral grid is generated by explicitly swimming particles throughthe magnetic field map from survey measurement and numerically integrating to obtain3.2. TRACK RECONSTRUCTION

55

f (p, r, θ0 , z) for each grid point. An iterative procedure is used to determine the momentum
for reconstructed tracks, using equation 3.6 as an initial guess.

3.2.3

Track Association

In order to associate a track with a hit on the TOF, the track is projected to its expected
hit location on the TOF. The track matching residual of φ and z on TOF plane are shownin Figure 3.9. We estimated sigma value of φ and z as a function of momentum, [σ =a · e−b·p + c]. The offset value is also estimated from mean residual of φ and z. Tracks
are required to have a hit on the TOF within ±2σ of the expected hit location in boththe azimuthal and beam directions. The flight path-length is calculated from a fit to theChi2 / ndf = 1.462e+05 / 7aa== 0.02169
0.02169 ± 8.25e-06
bb== 4.873
4.873 ± 0.001428
cc== 0.003605
0.003605± 5.639e-07

0.03

0.025

sigma [cm]sigma [rad]reconstructed track trajectory.
12

10

Δφ sigma

0.02

8

0.015

6

0.01

4

0.005

2

0.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8

Chi2 / ndf = 2.768e+04 / 6
a0.04= 0.001112± 6.462e-07

Δφ mean

0.02

0
0

2

p [GeV/c]mean [cm]mean [rad]

0
0

Chi2
5.274e+05/7 /7
Chi2/ /ndf
ndf= =
5.274e+05a==8.543± 0.00131
a8.543± 0.00131
b==3.731± 0.0007267
b3.731± 0.0007267
c= 0.9103 ± 0.0001967
c= 0.9103 ± 0.0001967

Δz sigma

0.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8

2

p [GeV/c]5

Chi2 / ndf = 5.129e+04 / 6

4

a

3
2

= -0.4195 ± 0.0002053

Δz mean

1
0

0
-1

-0.02

-2
-3

-0.04
0

-4
0.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8

2

p [GeV/c]-50

0.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8

2

p [GeV/c]

Figure 3.9: Track matching residual on TOF. Upper figures are sigma residual of φ (left) and z(right) as a function of momentum. The dotted lines are fitted results using function σ = a·e−b·p +c.
Lower figures are mean residual of φ (left) and z (right) as a function of momentum. The dottedlines are offset value.

CHAPTER 3. DATA ANALYSIS

56

3.3

Particle Identification

The charged particle identification (PID) is performed by using the combination of threemeasurements: time-of-flight from the BBC and TOF, momentum from the DCH, and flight
path-length from the collision vertex point to the hit position on the TOF wall. The flight
path-length is calculated from a fit to the reconstructed track trajectory. The square of themass is derived from the following formula,ip2 h³ tTOF ´2
m = 2
−1 ,
c
L/c
2

(3.8)

where p is the momentum, tTOF is the time-of-flight, L is a flight path-length, and c isthe speed of light. The charged particle identification is performed using cuts in m2 andmomentum space.

Figure 3.10: Mass squared vs. momentum · charge distribution. The lines indicate the PID cut
boundaries for pions, kaons, and protons(anti-protons) from left to right, respectively.

In Figure 3.10, a plot of m2 versus momentum multiplied by charge is shown together
with applied PID cuts as solid curves. We use 2σ standard deviation PID cuts in m2 andmomentum space for each particle species. Figure 3.11 show the mass squared width

3.3. PARTICLE IDENTIFICATION

57
Minimum Bias (mean)
mean m 2

sigma m2

Minimum Bias (width)
0.18

RED : positive
BLACK : negative

0.16

1.2

1

0.14
0.8

0.12
0.1

p, p

0.6

0.08
0.4
0.06

K

±

0.2

0.04

π±

0.02

0

0
0

0.5

1

1.5

2

2.5
3
p [GeV/c]

0

0.5

1

1.5

2

2.5
3
p [GeV/c]

Figure 3.11: Momentum dependence of width (left) and centroid (right) of mass squared distributions for each particle species. Red symbols indicate for positively charged particle and black
symbols are for negatives. The minimum bias event samples are used.

(left) and centroid (right) as a function of momentum for positives (red filled symbols)
and negatives (black open symbols) for minimum bias events. The lines on the left are 1σ
PID cut boundary used in the analysis based on the following parameterization.
³2 h¢¤m2 ´i σT2OF c2 £ 2 ¡ 2
σα2
σms
4
2
4 2
2
σm2 = 2 (4m p ) + 2 4m 1 + 2 +
4p
m
+
p
,
p
L2
K1
K1

(3.9)

where σα is the angular resolution, σms is the multiple scattering term, σT OF is the overall
time-of-flight resolution and m is the centroid of m2 distribution for each particle species.
The parameters for PID are, σα = 0.835 mrad, σms = 0.86 mrad·GeV and σT OF = 120 ps.
Through improvements in alignment and calibrations, the momentum resolution is improved over the 130 GeV data [73]. The centrality dependence of the width and the mean
position of the m2 distribution has also been checked. There is no clear difference seen
between central and peripheral collisions. For pion identification above 2 GeV/c, we apply
an asymmetric PID cut to reduce kaon contamination of the pions. As shown by the lines
in Figure 3.10, the overlap region which is within the 2σ cuts for both pions and kaons is
excluded. For kaons, the upper momentum cut-off is 2 GeV/c since the pion contaminationlevel for kaons is ≈ 10% at that momentum. The upper momentum cut-off on the pions
is pT = 3 GeV/c – where the kaon contamination reaches ≈ 10%. The contamination of
protons by kaons reaches about 5% at 4 GeV/c. Electron (positron) and decay muon background at very low pT (< 0.3 GeV/c) are well separated from the pion mass-squared peak.
The contamination background on each particle species is not subtracted in the analysis.

CHAPTER 3. DATA ANALYSIS

58

For protons, the upper momentum cut-off is set at 4.5 GeV/c due to statistical limitations
and background at high pT . An additional cut on m2 for protons and anti-protons, m2 >
0.6 (GeV/c2 )2 , is introduced to reduce background. The lower momentum cut-offs are
0.2 GeV/c for pions, 0.4 GeV/c for kaons, and 0.6 GeV/c for p and p. This cut-off value
for p and p is larger than those for pions and kaons due to the large energy loss effect.

3.4

Cut Conditions

The cut conditions used in the analysis are summarized in Table 3.2. Most of the cuts
are commonly used in the other PHENIX analysis, e.g. minimum bias event selection,
BBC z-vertex cut and track quality bit selection, but there are some specific cuts in theidentified charged particle analysis using Drift Chamber and Time-of-Flight detectors. In
the following subsections, we explain fiducial cut and energy loss cut. The PID cut is
described in Section 3.3. And also we used the same (or equivalent) cuts over the single
particle Monte Carlo output to get the correction functions. See Section 3.5 for more detailabout single particle Monte Carlo simulation.
Cut

Value

Trigger

Minimum Bias

BBC z-vertex cut± 30 cm

Number of PC1 hit≥1Fiducial cut(see text)

DCH Zed cut± 75 cm

TOF z position cut± 135 cm

TOF slat cut

0 ≥ slat ID < 767 (select only E1 sector)

DCH track quality

31 or 63 (X1 && X2 w/ and w/o unique PC1 association)

TOF Matching cut

2 σ in φ and z

PC3 Matching cut

None

TOF energy loss cut

beta dependent energy loss cut (see text)

PID cut

2 σ in m2 vs momentum space and additional cuts (see text)

Table 3.2: Cut conditions used in the analysis.

3.4. CUT CONDITIONS

3.4.1

59

Fiducial Cut

The geometrical acceptance is determined by detector edges in both DCH and TOF. The
fiducial cut is introduced in order to avoid the distortion of the particle distribution near theedges and the dead regions thorough the runs.
We apply the fiducial cut in DCH z within ± 75 cm to avoid the edge effect. (Figure 3.12)

Figure 3.12: Drift chamber z distribution. In this analysis, |z| < 75 cm are required for the fiducial
cut. (solid line)

In order to avoid the dead region of the drift chamber, we determine the momentum
dependence cuts for φDCH in the φ vs. charge/p space. This is due to the fact that the deadregions in the drift chamber increase during the run. Figure 3.13 shows the fiducial area at
TOF after applying the fiducial cuts, which required TOF hit association.

3.4.2

Energy Loss Cut

The energy deposit in scintillator of TOF slat is useful to clean up noise hits on TOF wall.
We use β = L/(T OF · c), where L is flight path length from vertex to hit on TOF detector,
T OF is the time of flight, and c is the light velocity. The energy loss cut is defined as,
Eloss(cut) = a ∗ β b(3.10)

where a = 0.0014 and b = −1.66.
Figure 3.14 shows the distribution of β vs. energy loss, and the solid red line is the cut
boundary. The dashed lines above and below the solid line are the energy loss cuts used in
the systematic error estimation.

CHAPTER 3. DATA ANALYSIS

60

hinvmom_phi_north
Nent = 504854-1

Charge/p[(GeV/c) ]1/mom vs phi (with TOF) North
6

35

4

30

2

25

0

20
15

-2

10

-4
-6

Run 29531
2.6

2.8

3

5

3.2

3.4

3.6

0

hinvmom_phi_south
Nent = 479619-1

Charge/p[(GeV/c) ]1/mom vs phi (with TOF) South3.8
φ [rad]

6

30

4

25

2

20

0

15

-2
10
-4
-6

Run 29531
2.6

2.8

3

5

3.2

3.4

3.6

3.8
φ [rad]0

Figure 3.13: Fiducial area in TOF acceptance in all measured pT rage. DCH φ vs. charge/p
distribution for north (top) and south side (bottom) are shown. The fiducial cuts are already appliedin these plots.

Eloss [GeV]Eloss vs. beta

htofeloss_beta
Nent = 2.538852e+07
Mean x = 0.8979
Mean y = 0.003785
RMS x = 0.1066
RMS y = 0.001878

0.03
5

10
0.025

4

10
0.02

3

10
0.015

2

10
0.01
10
0.005
1
0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

β

1

Figure 3.14: β vs. energy loss distributions with energy loss cut boundary (solid red line in
the middle). The dashed lines above and below the solid line are only used for systematic error
estimation.

3.5. CORRECTION

3.5

61

Correction

In order to correct for 1) the geometrical acceptance, 2) in-flight decay for pions and kaons,
3) the effect of multiple scattering, and 4) nuclear interactions with materials in the detector (including anti-proton absorption), we use PISA (PHENIX Integrated Simulation
Application), a GEANT [54] based Monte Carlo (MC) simulation program of the PHENIX
detector. The single particle tracks are passed from GEANT through the PHENIX event
reconstruction software [56].
In this section, we describe how we obtain a correction factors for the inclusive transverse momentum distributions of identified charged particles. The same procedure can beapplied for all particles. We processed the following individual steps and estimated thecorrection factors for each particle species.

3.5.1

Comparison of Data with Simulation

In the Monte Carlo single particle simulation, we used following parameters in response
and reconstruction chain. The DCH response chain used run2 average efficiency map.
The TOF response chain used run2 typical parameter set which were used on run2 data
reconstruction. This parameter files contain TOF dead channel map. The dead area isabout 3%.
Since this is single particle simulation, there is no information in the BBC. We used thez coordinate of the origin of primary single particle smeared with a Gaussian distribution
with sigma = 0.7 cm. We also used the time zero coordinate of the origin of GEANT value(= 0.0 ns) smeared with a Gaussian distribution with sigma = 0.04 ns. We set the intrinsic
timing resolution of TOF in response chain. The value is 0.100 ns. It affects position
resolution for φ direction on TOF and time-of-flight resolution.
• Z-vertex resolution of BBC is 0.7 cm.
• Time zero resolution of BBC is 0.040 ns.
• Timing resolution of TOF is 0.100 ns.
Track Matching Residual
We check the track matching residual on TOF plane to compare Monte Carlo and real data.
The track matching residual of φ and z for Monte Carlo data are shown in Figure 3.15.

CHAPTER 3. DATA ANALYSIS

62

Comparing both Monte Carlo (Figure 3.15) and real data (Figure 3.9), we have good agreement for the sigma residual of φ and z. We applied same sigma parameters for Monte
Carlo and real data analysis. From mean residual of φ and z, we estimated offset value and

0.03

Chi2 / ndf = 21.45 / 7
a

0.025

0.02

= 0.01733 ± 0.0003692

b= 5.035 ± 0.06635

c= 0.003896 ± 1.156e-05

sigma [cm]sigma [rad]applied for Monte Carlo data.

12

10

8

∆z sigma∆φ sigma
0.015

6

0.01

4

0.005

2

0.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8

Chi2 / ndf = 66.36 / 6a= 0.0003499± 1.251e-05
0.04

0.02

0
0

2

p [GeV/c]∆φ meanmean [cm]mean [rad]00Chi2 / ndf = 131.1 / 7
a= 8.717 ± 0.1235
b= 4.177 ± 0.0347
c= 0.9956 ± 0.003313

5

0.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8

2

p [GeV/c]

Chi2 / ndf = 83.44 / 6a= -0.07581± 0.003456

4
3
2∆z mean

1
0

0
-1

-0.02

-2
-3

-0.04
0

-4
0.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8

2

p [GeV/c]-50

0.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8

2

p [GeV/c]

Figure 3.15: Track matching residual on TOF for Monte Carlo. Uppers are sigma residual of φ(left) and z (right) as a function of momentum. Lowers are mean residual of φ (left) and z (right) asa function of momentum.

3.5. CORRECTION63

PID cut parameters
The mass squared resolution for Monte Carlo is better than for real. Figure 3.16 showssigma and mean of mass squared for π , K, p as a function of momentum. We estimated
PID cut parameters from sigma of mass squared distribution for each particle species. The
parameters are, σα = 0.860 mrad, σms = 0.550 mrad·GeV and σT OF = 110 ps. We appliedthese PID cut parameters for Monte Carlo data analysis.

0.14
0.12
0.1
0.08

σ α = 0.86 [mrad] / 87
σ m.s. = 0.55 [mrad] / 87
σ TOF = 0.110 [ns]

0.06
0.04
0.02
0
0

0.5

1

1.5

2

2.5

3

0.5

1

1.5

2

2.5

3

1.2
1
0.8
0.6
0.4
0.2
0
0

Figure 3.16: Sigma(up) and mean (down) of mass squared as a function of momentum. Blue ispion, green is kaon and red is proton. Open circle is negative.

CHAPTER 3. DATA ANALYSIS

64
Fiducial Cut

The fiducial cut region is estimated by comparing Monte Carlo and real data. Section 3.4.1
describe about determination of fiducial cut region. We applied same fiducial cut for Monte
Carlo and real data analysis. Figure 3.17 shows the fiducial area in TOF acceptance forMonte Carlo after applying fiducial cut. The DCH φ vs charge/p are plotted for north(top) and south side (bottom), respectively. These fiducial area distributions show good
agreement both Monte Carlo and real data.
hinvmom_phi_north
Nent = 426008-1

Charge/p[(GeV/c) ]1/mom vs phi (with TOF) North
6

2

10
4
2
10
0
-2
1
-4
-6

MC
2.6

-1

2.8

3

3.2

3.4

3.8
φ [rad]10

hinvmom_phi_south
Nent = 405640-1

Charge/p[(GeV/c) ]1/mom vs phi (with TOF) South

3.6

6
2

10
4
2
10
0
-2
1
-4
-6

MC

-1

10
2.6

2.8

3

3.2

3.4

3.6

3.8
φ [rad]Figure 3.17: Fiducial area in TOF acceptance for Monte Carlo. The DCH φ vs. charge/p counterplots for north (top) and south side (bottom), respectively. The fiducial cuts are already applied inthese plots.

3.5. CORRECTION

3.5.2

65

Corrections of Acceptance, Decay and Multiple Scattering

In this section, we describe how we obtain a correction factors for the inclusive transverse
momentum distributions of identified charged particles. The same procedure can be applied
for all particles.
We generate 1×107 single particle events for each particle species (π ± , K ± , p and p)
with low pT enhanced (< 2 GeV/c) + flat pT distributions for high pT (2 – 4 GeV/c forpions and kaons, 2 – 8 GeV/c for p and p) 1 . The efficiencies are determined in each pT
bin by dividing the reconstructed output by the generated input as expressed as follows:# of reconstructed MC tracks,(3.11)# of generated MC tracks
where j is the particle species. The resulting correction factors (1/εacc ) are applied to theεacc ( j, pT ) =data in each pT bin and for each individual particle species.
Figure 3.18 shows the transverse momentum distribution of generated and reconstructed
MC tracks for each particle species. Figure 3.19 shows the correction factor as a functionof pT for each particle species.
p T dist. input&output

p T dist. input&output

7-1

proton
+

K
π+

6

10

pbar

Kπ−

6

10

5

5

10

10

4

4

10

10

3

3

10

0

10

dN/dpT [(GeV/c) ]10

dN/dpT [(GeV/c) ]

-1

7

10

1

2

3

4

5
6
p T [GeV/c]

0

1

2

3

4

5
6
p T [GeV/c]

Figure 3.18: pT distribution of Generated (top) and reconstructed (bottom) MC tracks for eachparticle species.
1 Due to the good momentum resolution at the high p

T region, the momentum smearing effect for a steeply

falling spectrum is <1% at pT = 5 GeV/c. The flat pT distribution up to 5 GeV/c can be used to obtain thecorrection factors.

CHAPTER 3. DATA ANALYSIS

66

Correction Factor

Correction Factor

4

4

Ratio (IN/OUT)

10

Ratio (IN/OUT)

10

proton
+

K
π+
3

Kπ−
3

10

10

2

2

10

0

pbar

10

1

2

3

4

5
6
p T [GeV/c]

0

1

2

3

4

5
6
p T [GeV/c]

Figure 3.19: Correction factor as a function of pT for pion (blue), kaon (green) and proton (red).
Left is positive and right is negative charge.

3.5.3 Correction of Multiplicity Dependence
In high multiplicity environment, it is expected that the track reconstruction efficiency incentral events is lower than that in peripheral events, which causes high occupancy andmultiple hits on a detector cell such as scintillator slats of the TOF. The typical occupancy
at TOF is less than 10% in the most central Au+Au collisions. To obtain the multiplicity
dependence correction, we estimate the effect of detector occupancy by embedding single
track Monte Carlo events into real events. The multiplicity dependence efficiency εmult (i, j)
was calculated in each centrality bin i and particle species j,εmult (i, j) =# of reconstructed embedded tracks.
# of embedded tracks(3.12)

This study has been performed for each particle species and each centrality bin. The trackreconstruction efficiencies are factorized (into independent terms depending on centrality
and pT ) for pT > 0.4 GeV/c, since there is no pT dependence in the efficiencies above thatpT . Figure 3.20 shows the dependence of track reconstruction efficiency for π ± , K ± , p andp as a function of centrality expressed as Npart . The efficiency in the most central 0–5%
events is about 80% for protons (p), 83% for kaons and 85% for pions. Slower particles
are more likely lost due to high occupancy in the TOF because the system responds to theearliest hit. For the most peripheral 80–92% events, the efficiency for detector occupancy

3.5. CORRECTION

67

effect is ≈ 99% for all particle species. The factors are applied to the spectra for each particle species and centrality bin. Systematic uncertainties on detector occupancy corrections

εmult(1/εmult ) are less than 3%.

1
0.9
0.8

Positive

0.7

π+

+

K
p

εmult

0.6

1
0.9
0.8

Negative

0.7

π-

-

K

p

0.6
0

50

100

150

200

250

300

350

Npart

Figure 3.20: Track reconstruction efficiency (detector occupancy correction) as a function of centrality. The error bars on the plot represent the systematic errors.

3.5.4

Weak Decay Correction

Protons and anti-protons from weak decays (e.g. from Λ and Λ) can be reconstructed as
tracks in the PHENIX spectrometer. The proton and anti-proton spectra are corrected toremove the feed-down contribution from weak decays using a HIJING [55] simulation.
HIJING output has been tuned to reproduce the measured particle ratios of Λ/p and Λ/p√along with their pT dependencies in sNN = 130 GeV Au+Au collisions [53] which include
contribution from Ξ and Σ0 . Corrections for feed-down from Σ± are not applied, as theseyields were not measured. About 2×106 central HIJING events (impact parameter b =CHAPTER 3. DATA ANALYSIS

68

0 − 3 fm) covering the TOF acceptance have been generated and processed through the
PHENIX reconstruction software.
To calculate the feed-down corrections, the p/p and Λ/Λ yield ratios were assumed to
be independent of pT and centrality. The systematic error due to the feed-down correction
is estimated at 6% by varying the Λ/p and Λ/p ratios within the systematic errors of the√sNN =130 GeV Au+Au measurement [53] (±24%) and assuming mT -scaling at high pT .
This uncertainty could be larger if the Λ/p and Λ/p ratios change significantly with pT andδfeed (p T)beam energy.

0.6

p
p

0.5



0.4
0.3
0.2
0.1
0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

p T [GeV/c]
Figure 3.21: The fractional contribution of protons (p) from Λ (Λ) decays in all measured protons(p), δfeed (pT ), as a function of pT . The solid (dashed) lines represent the systematic errors for
protons (p). The error bars are statistical errors.

The fractional contribution to the p (p) yield from Λ(Λ), δfeed (pT ), is shown in Figure 3.21. The solid (dashed) lines represent the systematic errors for protons (p). The
obtained factor is about 40% below 1 GeV/c and 30% at 4 GeV/c. We multiply the proton
and anti-proton spectra by the factor, Cfeed , for all centrality bins as a function of pT :Cfeed ( j, pT ) = 1 − δfeed ( j, pT ),where j is particle species (p, p).

(3.13)

3.6. SYSTEMATIC UNCERTAINTIES

3.5.5

69

Invariant Yield

Applying the data cuts and corrections discussed above, the final invariant yield for eachparticle species and centrality bin are derived using the following equation.
N j (i, pT )
1
d2N
1
1
=
·
·Ci j (pT ) ·,2π pT d pT dy 2π pT Nevt (i)∆pT ∆y(3.14)

where y is rapidity, Nevt (i) is the number of events in each centrality bin i, Ci j (pT ) is thetotal correction factor and N j (i, pT ) is the number of counts in each centrality bin i, particle
species j, and pT . The total correction factor is composed of:
Ci j (pT ) =

3.6

1
1
·
·Cfeed ( j, pT ).
εacc ( j, pT ) εmult (i, j)(3.15)

Systematic Uncertainties

To estimate systematic uncertainties on the pT distribution and particle ratios, various setsof pT spectra and particle ratios were made by changing the cut parameters including thefiducial cut, PID cut, and track association windows slightly from what was used in theanalysis. For each of these spectra and ratios using modified cuts, the same changes in thecuts were made in the Monte Carlo analysis. The absolutely normalized spectra with different cut conditions are divided by the spectra with the baseline cut conditions, resulting in
uncertainties associated with each cut condition as a function of pT . The various uncertainties are added in quadrature. Three different centrality bins (minimum bias, central 0–5%,
and peripheral 60–92%) are used to study the centrality dependence of systematic errors.
The same procedure has been applied for the following particle ratios: π − /π + , K − /K + ,p/p, K/π , p/π + , and p/π − .
Table 3.3 shows the systematic errors of the pT spectra for central collisions. The systematic uncertainty on the absolute value of momentum (momentum scale) are estimated
as 3% in the measured pT range by comparing the known proton mass to the value measured as protons in real data. It is found that the total systematic error on the pT spectra
is 8–14% in both central and peripheral collisions. For the particle ratios, the typical systematic error is about 6% for all particle species. The dominant source of uncertainties on
the central-to-peripheral ratio scaled by Ncoll (RCP ) are the systematic errors on the nuclear
overlap function, TAuAu (see Table 3.4). Table 3.5 and Table 3.6 show the systematic errors
on dN/dy and hpT i. The procedure for the determination of these quantities are discuss in
Section 4.2.

CHAPTER 3. DATA ANALYSIS

70

pT range (GeV/c)
Cuts
Momentum scale
Occupancy correction
Feed-down correction
Total

π+
0.2 - 3.0
6.2
3
2
7.2

π−
0.2 - 3.0
6.2
3
2
7.2

K+
0.4 - 2.0
11.2
3
3
12.0

K−
0.4 - 2.0
9.5
3
3
10.4

p
0.6 - 3.0
6.6
3
3
6.0
9.9

p
3.0 - 4.5
11.6
3
3
6.0
13.7

0.6 - 3.0
6.6
3
3
6.0
9.9

3.0 - 4.5
11.6
3
3
6.0
9.9

Table 3.3: Systematic errors on the pT spectra for central events. All errors are given in percent.

SourceOccupancy correction (central)
Occupancy correction (peripheral)
hTAuAu i (0–10%)
hTAuAu i (60–92%)
Total(π + + π − )/2
2
2
6.9
28.6
29.5

(K + + K − )/2
3
3
6.9
28.6
29.7

(p + p)/2
3
3
6.9
28.6
29.7

Table 3.4: Systematic errors on Central-to-Peripheral ratio (RCP ). All errors are given inpercent.

SourceCuts
Extrapolation
Contamination backgroundFeed-down
Total

π+
6.2
3.9
<1
7.3

Central 0–5%K+K−p
6.2 11.2 9.5 6.6
3.5 3.5
3.3 6.2
<1 <1
<1 <1
1.0
7.1 13.5 10.0 9.1

π−

p
6.6
5.9
<1
1.0
8.9

π+
6.2
5.4
<1
8.2

Peripheral 60–92%
K+ K−
p
6.2 7.7 6.6 7.7
5.3 4.6 4.4 8.6<1 <1 <1 <1
1.0
8.1 8.9 7.9 11.5

π−

p
7.7
8.6
<1
1.0
11.5

Table 3.5: Systematic errors on hpT i for central 0–5% (top) and peripheral 60–92% (bottom)
collisions. All errors are given in percent.

SourceCuts + occupancy
Extrapolation
Contamination backgroundFeed-down
Total

π+
6.5
5.4
<1
8.4

π−
6.5
4.8
<1
8.0

Central 0–5%K+K−p11.6 10.0 7.2
5.7
5.6
9.6
<1
<1
<1
8.0
12.9 11.4 14.4

p
7.2
9.2
<1
8.0
14.4

π+
6.5
8.4
<1
10.6

Peripheral 60–92%
K+
K−
p
π−
6.5
8.3
7.2
8.3
8.0
7.4
7.5 13.6
<1
<1
<1
<1
8.0
10.3 11.1 10.3 17.8

Table 3.6: Systematic errors on dN/dy for central 0–5% (top) and peripheral 60–92% (bottom)
collisions. All errors are given in percent.

p
8.3
13.6
<1
8.0
17.8

Chapter 4
Experimental Results
In this chapter, the transverse momentum spectra and yields of identified√
charged hadrons at mid-rapidity in sNN = 200 GeV Au+Au collisions areshown. Also the systematic study of particle ratios are presented. In this analysis, we use the eleven centrality classes (0–5%, 5–10%, 10–15%, 15–20%,
20–30%, ..., 70–80%, 80–92%) described in Section 3.1, combined peripheral
event class (60–92%) and minimum bias event class.

4.1

Transverse Momentum Distributions

Figure 4.1 shows the centrality dependence of the pT spectrum for π + (left) and π − (right).
For the comparison of the spectra shape, the data points are scaled vertically as quoted in
the figures. The error bars are statistical only. The pion spectra show a concave shape forall centrality bins. The spectra become steeper (fall faster with increasing pT ) in peripheral
collisions. The comparison between charged pions and π 0 [32] are shown in Figure 4.2.
Figure 4.3 shows the pT spectrum for kaons. The data can be well described by an
exponential in pT for all centralities. Finally, the centrality dependence of the pT spectra
for protons (left) and anti-protons (right) are shown in Figure 4.4. As in Figure 4.4, bothp and p spectra show a strong centrality dependence below 1.5 GeV/c, i.e. they develop
a shoulder at low pT and the spectra flatten (fall more slowly with increasing pT ) withincreasing Npart .
The invariant yields for π ± , K ± , p and p in Au+Au collisions at√
sNN = 200 GeV at

mid-rapidity are tabulated in Tables C.1 – C.20 (Appendix C.1). The data presented here
are for the the minimum bias events and each centrality classes.

71

CHAPTER 4. EXPERIMENTAL RESULTS

2

2

1/(2 π pT ) d N /dpT dy [(c / GeV) ]

72
10
10
10
10

5

Centrality
0- 5%(x20)
5-10%(x10)10-15%(x5)15-20%(x2.5)
20-30%(x1.5)30-40%(x1.0)
40-50%(x1.0)
50-60%(x1.0)
60-70%(x1.0)
70-80%(x1.0)
80-92%(x1.0)

4

3

2

10
1
-1

10

-2

10

-3

10

π+

-4

10

π-

-5

10

0

0.5

1

1.5

2

2.5
3 0
pT [GeV/c]

0.5

1

1.5

2

2.5
3
pT [GeV/c]

Figure 4.1: Centrality dependence of the pT distribution for π + (left) and π − (right) in Au+Au
collisions at√
sNN = 200 GeV. The different symbols correspond to different centrality bins. The

error bars are statistical only. For clarity, the data points are scaled vertically as quoted in the figure.

Peripheral 60-92% Pion Spectra2

1/(2 π p T) d N /dp T dy [(c / GeV) ]

10

2

10

10

1

10

1

10

10

10

10

10

-1

-2

10

10
10

-2

-3

-3

10

-4

-4

10
10

-1

2

2

2

1/(2 π p T) d N /dp T dy [(c / GeV) ]Central 0-10% Pion Spectra-5(π+ + π-)/2
π0

-6

10

-7

0

10
1

2

3

4

5

6

7

8

9

10

-5

-6

-7

0

1

2

3

4

pT [GeV/c]

5

6

7

pT [GeV/c]

Figure 4.2: Comparison between averaged charged pion pT spectra (π + + π − )/2 (red filled circle)
and π 0 (open circle) for central 0-10% (left) and peripheral 60-92% (right).

73

2

2

1/(2 π pT ) d N /dpT dy [(c / GeV) ]4.1. TRANSVERSE MOMENTUM DISTRIBUTIONS

10
10
10
10

Centrality
0- 5%(x20)
5-10%(x10)10-15%(x5)15-20%(x2.5)
20-30%(x1.5)30-40%(x1.0)
40-50%(x1.0)
50-60%(x1.0)
60-70%(x1.0)
70-80%(x1.0)
80-92%(x1.0)

5

4

3

2

10
1
-1

10

-2

10

K+

-3

10

K-

-4

10

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
pT [GeV/c]pT [GeV/c]

Figure 4.3: Centrality dependence of the pT distribution for K + (left) and K − (right) in Au+Au
collisions at√
sNN = 200 GeV. The different symbols correspond to different centrality bins. The

2

2

1/(2 π pT ) d N /dpT dy [(c / GeV) ]error bars are statistical only. For clarity, the data points are scaled vertically as quoted in the figure.

10
10

3

Centrality
0- 5%(x20)
5-10%(x10)10-15%(x5)15-20%(x2.5)
20-30%(x1.5)30-40%(x1.0)
40-50%(x1.0)
50-60%(x1.0)
60-70%(x1.0)
70-80%(x1.0)
80-92%(x1.0)

2

10
1
-1

10

-2

10

-3

10

-4

10

-5

10

-6

10

-7

10



p

p

-8

10

0

0.5

1

1.5 2

2.5 3

3.5 4 4.5 0 0.5
pT [GeV/c]

1

1.5 2

2.5 3

3.5 4 4.5
pT [GeV/c]

Figure 4.4: Centrality dependence of the pT distribution for protons (left) and anti-protons (right)
in Au+Au collisions at√
sNN = 200 GeV. The different symbols correspond to different centrality

bins. The error bars are statistical only. Feed-down corrections for Λ (Λ) decaying into proton (p)have been applied. For clarity, the data points are scaled vertically as quoted in the figure.

CHAPTER 4. EXPERIMENTAL RESULTS

74

4.2

Mean Transverse Momentum and Particle Yields

By integrating a measured pT spectrum over pT , one can determine the mean transverse
momentum, hpT i, and particle yield per unit rapidity, dN/dy, for each particle species.
For the extrapolation of pT spectrum, the following functional forms are used for different
particle species: a power-law function and a pT exponential for pions, a pT exponential
and an mT exponential for kaons, and a Boltzmann function, pT exponential, and mT exponential for protons and anti-protons. The effects of contamination background at high pT
region for both hpT i and dN/dy are estimated as less than 1% for all particle species. The
procedure to determine the mean pT and dN/dy is described below:
1. Determine dN/dy and hpT i by integrating over the measured pT range from the data.
2. Fit several appropriate functional forms (detailed below) to the pT spectra. Note that all of
the fits are reasonable approximations to the data. Integrate from zero to the first data pointand from the last data point to infinity.
3. Sum the data yield and the two functional yield pieces together to get dN/dy and hpT i ineach functional form.
4. Take the average between the upper and lower bounds from the different functional forms to
obtain the final dN/dy and hpT i. The statistical uncertainties are determined from the data.
The systematic errors from the extrapolation of yield are defined as half of the difference
between the upper and lower bounds.
5. Determine the final systematic errors on dN/dy and hpT i for each centrality bin by taking thequadrature sum of the extrapolation errors, errors associated with cuts, detector occupancy
corrections (for dN/dy) and feed-down corrections (for protons).

The overall systematic uncertainties on both hpT i and dN/dy are about 10–15%. See Table 3.5 for the systematic errors of hpT i and Table 3.6 for those of dN/dy.
Figure 4.5 shows the centrality dependence of hpT i for π ± , K ± , p and p. The error bars
in the figure represent the statistical errors. The systematic errors from cuts conditions areshown as shaded boxes on the right for each particle species. The systematic errors fromextrapolations, which are scaled by a factor of 2 for clarity, are shown in the bottom foreach particle species. The data are also summarized in Table 4.1. It is found that hpT i forall particle species increases from the most peripheral to mid-central collisions, and appears
to saturate from the mid-central to central collisions (although the hpT i values for p and p
may continue to rise). It should be noted that while the total systematic errors on hpT i listed
in Table 3.5 is large, the trend shown in the figure is significant. One of the main sourcesof the uncertainty is the yield extrapolation in unmeasured pT range (e.g. pT < 0.6 GeV/c

4.2. MEAN TRANSVERSE MOMENTUM AND PARTICLE YIELDS

75

for protons and anti-protons). These systematic errors are correlated, and therefore movethe curve up and down simultaneously.
Figure 4.6 shows the centrality dependence of dN/dy per participant pair (0.5 Npart ).
The data are summarized in Table 4.2. The error bars on each point represent the quadratic
sum of the statistical errors and systematic errors from cut conditions. The statistical errors
are negligible. The lines represent the effect of the systematic error on Npart which affects
all curves in the same way. The data indicate that dN/dy per participant pair increases
for all particle species with Npart up to ≈ 100, and saturates from the mid-central to themost central collisions. From dN/dy for protons and anti-protons, we obtain the net proton number at mid-rapidity for the most central 0–5% collisions, dN/dy| p − dN/dy| p =18.47 − 13.52 = 4.95 ± 2.74.
Npart
351.4
299.0
253.9
215.3
166.6
114.2
74.4
45.5
25.7
13.4
6.3

π+
451 ± 33450 ± 33448 ± 33447 ± 34444 ± 35436 ± 35426 ± 35412 ± 35398 ± 34381 ± 32367 ± 30π−455 ± 32454 ± 33453 ± 33449 ± 33447 ± 34440 ± 35429 ± 35416 ± 34403 ± 33385 ± 32371 ± 30K+
670 ± 78672 ± 78668 ± 78667 ± 78661 ± 77655 ± 77636 ± 54617 ± 53600 ± 52581 ± 51568 ± 51K−
677 ± 68679 ± 68676 ± 68670 ± 67668 ± 67654 ± 66644 ± 48621 ± 47606 ± 46579 ± 46565 ± 45p
949 ± 85948 ± 84942 ± 84937 ± 84923 ± 85901 ± 83868 ± 88833 ± 86788 ± 84755 ± 82685 ± 78p
959 ± 84951 ± 83
950 ± 83940 ± 83920 ± 83892 ± 82864 ± 88824 ± 86
777 ± 83
747 ± 80708 ± 81

Table 4.1: Centrality dependence of hpT i for π ± , K ± , p and p in MeV/c. The errors are systematic
only. The statistical errors are negligible.
Npart
351.4
299.0
253.9
215.3
166.6
114.2
74.4
45.5
25.7
13.4
6.3

π+
286.4 ± 24.2
239.6 ± 20.5
204.6 ± 18.0
173.8 ± 15.6
130.3 ± 12.4
87.0 ± 8.6
54.9 ± 5.6
32.4 ± 3.4
17.0 ± 1.8
7.9 ± 0.8
4.0 ± 0.4π−281.8 ± 22.8
238.9 ± 19.8
198.2 ± 16.7
167.4 ± 14.4
127.3 ± 11.6
84.4 ± 8.0
52.9 ± 5.2
31.3 ± 3.1
16.3 ± 1.6
7.7 ± 0.7
3.9 ± 0.3

K+
48.9 ± 6.3
40.1 ± 5.1
33.7 ± 4.3
27.9 ± 3.6
20.6 ± 2.6
13.2 ± 1.7
8.0 ± 0.8
4.5 ± 0.4
2.2 ± 0.2
0.89 ± 0.09
0.44 ± 0.04

K−
45.7 ± 5.2
37.8 ± 4.3
31.1 ± 3.5
25.8 ± 2.9
19.1 ± 2.2
12.3 ± 1.4
7.4 ± 0.6
4.1 ± 0.4
2.0 ± 0.1
0.88 ± 0.09
0.42 ± 0.04

p
18.4 ± 2.6
15.3 ± 2.1
12.8 ± 1.8
10.6 ± 1.5
8.1 ± 1.1
5.3 ± 0.7
3.2 ± 0.5
1.8 ± 0.3
0.93 ± 0.15
0.40 ± 0.07
0.21 ± 0.04

p13.5 ± 1.8
11.4 ± 1.5
9.5 ± 1.3
7.9 ± 1.1
5.9 ± 0.8
3.9 ± 0.5
2.4 ± 0.3
1.4 ± 0.2
0.71 ± 0.12
0.29 ± 0.05
0.15 ± 0.02

Table 4.2: Centrality dependence of dN/dy for π ± , K ± , p and p. The errors are systematic only.
The statistical errors are negligible.

CHAPTER 4. EXPERIMENTAL RESULTS

76<pT > [GeV/c]

1.2


p

p

1

0.8

+

K

π+

π-

K

-

0.6
0.4
0.2
0
0

50 100 150 200 250 300 350

050 100 150 200 250 300 350

N partNpart

Figure 4.5: Mean transverse momentum as a function of Npart for pions, kaons, protons and antiprotons in Au+Au collisions at√
sNN = 200 GeV. The left (right) panel shows the hpT i for positive(negative) particles. The error bars are statistical errors. The systematic errors from cuts conditions
are shown as shaded boxes on the right for each particle species. The systematic errors from extrapolations, which are scaled by a factor of 2 for clarity, are shown in the bottom for protons anddN/dy /(0.5N part )anti-protons (dashed-dot lines), kaons (dotted lines), and pions (dashed lines).

1

10

-1

π+
+
K
p

10

πK

p

-2

0

50 100 150 200 250 300 350 0

50 100 150 200 250 300 350

N partNpart

Figure 4.6: Particle yield per unit rapidity (dN/dy) per participant pair (0.5 Npart ) as a functionof Npart for pions, kaons, protons and anti-protons in Au+Au collisions at√
sNN = 200 GeV. The

left (right) panel shows the dN/dy for positive (negative) particles. The error bars represent thequadratic sum of statistical errors and systematic errors from cut conditions. The lines represent theeffect of the systematic error on Npart which affects all curves in the same way.

4.3. PARTICLE RATIOS

4.3

77

Particle Ratios

The ratios of π − /π + , K − /K + , p/p, K/π , p/π and p/π measured as a function of pT and√centrality at sNN = 200 GeV in Au+Au collisions are presented here.
Figure 4.7 shows the particle ratios of π − /π + (top), K − /K + (middle), and p/p (bottom) as a function of pT for central (0–5%, left) and peripheral (60–92%, right). The error
bars represent statistical errors and the shaded boxes on each panel represent the systematic errors. For each of these particle species and centralities, the particle ratios are constantwithin the experimental errors over the measured pT range.
In Figure 4.8, the pT dependence of the K/π ratio is shown for the most central 0–5%
and the most peripheral 60–92% centrality bins. The K + /π + (K − /π − ) ratios are shown on
the left (right). Both ratios increase with pT and the increase is faster in central collisions
than in peripheral ones. In Figure 4.9, the p/π and p/π ratios are shown as a function ofpT for the most central 0–5% and the most peripheral 60–92% centrality bins.
Figure 4.10 shows the centrality dependence of particle ratios for π − /π + , K − /K + andp/p. The ratios presented here are derived from the integrated yields over pT (i.e. dN/dy).
The shaded boxes on each data point indicate the systematic errors. Within uncertainties,
the ratios are all independent of Npart over the measured range.
Figure 4.11 shows the centrality dependence of K/π and p/π ratios. Both K + /π + andK − /π − ratios increase rapidly for peripheral collisions (Npart < 100), and then saturate
or rise slowly from the mid-central to the most central collisions. The p/π + and p/π −ratios increase for peripheral collisions (Npart < 50) and saturate from mid-central to central
collisions – similar to the centrality dependence of K/π ratio (but possibly flatter).
The data tables describe in Appendix C.2.

CHAPTER 4. EXPERIMENTAL RESULTS

π- / π+

78
1.4
1.2
1
0.8
0.6
0.4
0.2

K - / K+00(a) π-/ π+ (central 0-5%)
0.5

1

1.5

2

2.5 3 0p T [GeV/c](b) π-/ π+ (peripheral 60-92%)
0.5

1

1.5

2

2.5 3
p T [GeV/c]

1.4
1.2
1
0.8
0.6
0.4
0.2 (c) K -/K + (central 0-5%)

p/p

0
0

0.5

1

1.5
2 0
p T [GeV/c]-+(d) K /K (peripheral 60-92%)
0.5

1

1.5
2
p T [GeV/c]

1.2
1
0.8
0.6
0.4
0.2

Central 0-5%

Peripheral 60-92%

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
pT [GeV/c]pT [GeV/c]

Figure 4.7: Particle ratios of π − /π + (top), K − /K + (middle), and p/p (bottom) as a function ofpT for central 0–5% (left) and peripheral 60–92% (right) in Au+Au collisions at√
sNN = 200 GeV.

The error bars indicate the statistical errors and shaded boxes around unity on each panel indicate
the systematic errors.

Ratio4.3. PARTICLE RATIOS

0.8
0.7

79

Central (0-5%)
Peripheral (60-92%)

0.6
0.5

K+ / π +K - / π-

0.4
0.3
0.2
0.1
0
0

0.5

1

1.5

2
0
pT [GeV/c]

0.5

1

1.5

2
pT [GeV/c]

Figure 4.8: K/π ratios as a function of pT for central 0–5% and peripheral 60–92% in Au+Au
collisions at√
sNN = 200 GeV. The left is for K + /π + and the right is for K − /π − . The error bars

Ratio

indicate the statistical errors.
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0

Central (0-5%)
Peripheral (60-92%)

p / π+

p / π-

12

3 0
pT [GeV/c]123pT [GeV/c]

Figure 4.9: p/π + (left) and p/π − (right) ratios as a function of pT for central 0–5% and peripheral
60–92% in Au+Au collisions at√
sNN = 200 GeV. The error bars indicate the statistical errors.

CHAPTER 4. EXPERIMENTAL RESULTS

Ratio

80

1.2

1

0.8

0.6

π- / π+

0.4

-

K /K


0.2

0
0

+

p/p

50

100

150

200

250

300

350

N partFigure 4.10: Centrality dependence of particle ratios for π − /π + , K − /K + , and p/p in Au+Au
collisions at√
sNN = 200 GeV. The error bars indicate the statistical errors. The shaded boxes on

Ratio

each data point are the systematic errors.
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
+
0.04
(a) K / π+0.02
00 50 100 150 200 250 300 350 0-(b) K / π50 100 150 200 250 300 350

Ratio

N partN part

0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0



(c) p / π+(d) p / π-

50 100 150 200 250 300 350 0

50 100 150 200 250 300 350

N partN partFigure 4.11: Centrality dependence of particle ratios for (a) K + /π + , (b) K − /π − , (c) p/π + , and(d) p/π − in Au+Au collisions at√
sNN = 200 GeV. The error bars indicate the statistical errors. The

shaded boxes on each data point are the systematic errors.

Chapter 5
Discussions
As shown in Chapter 4, we have measured single particle spectra and yields√
for pions, kaons and protons in Au+Au at sNN = 200 GeV. In this chapter,
we discuss the collision dynamics using the experimental results. The particle ratios are sensitive to the chemical properties of the system and particle
production mechanism, we discuss the chemical equilibrium from within statistical thermal model. The momentum spectra of pions, kaons, and protons
are sensitive to the dynamical evolution of the system, we discuss the radialflow velocity βT and the freeze-out temperature Tfo in Au + Au collisions at
RHIC energies within the framework of the expansion source model. In thehigh-pT region, hard component is dominant. We also discuss binary collisionscaling of pT spectra to study hard component.

5.1

Particle Productions

5.1.1

Particle Ratios

Hadron abundances reflect chemical composition of the system in heavy-ion collisions. It
studied in the framework of statistical thermal model.
As is shown in Figure 4.7 and Figure 4.10 (Section 4.3), the ratios of anti-particle/particle
are all independent of pT and Npart over the measured range. The statistical thermal model(discussed in more detail in next section) predicted [67] a baryon chemical potential ofµB = 29 MeV and a freeze-out temperature of Tch = 177 MeV for central Au+Au collisions at 200 GeV. From these, the expected p/p ratio is e−2µB /Tch = 0.72, which agrees
with our data (0.73).
81

CHAPTER 5. DISCUSSIONS

82

5.1.2 Features of Chemical Equilibrium
As is described in Section 1.2.3, the particle ratios have been studied in term of chemical equilibrium. Figure 5.1 shows a comparison of the PHENIX particle ratios withthose from PHOBOS [64], BRAHMS [65], and STAR [66] in Au+Au central collisions√
at sNN = 200 GeV at mid-rapidity. The PHENIX anti-particle to particle ratios are consistent with other experimental results within the systematic uncertainties.
√
The particle ratios in central collisions at sNN =200 GeV have been analyzed withstatistical thermal model [67]. The thermal parameters, chemical freeze-out temperature
Tch = 177 ± 7 MeV and baryon chemical potential µB = 29 ± 8 MeV are extracted. The
comparison between the PHENIX data at 200 GeV for 0–5% central and the thermal model
prediction is shown in this figure and Table 5.1. There is a good agreement between data
and the model. The small µB is qualitatively consistent with our measurement of the num√
ber of net protons (≈ 5, see Section 4.2) in central Au+Au collisions at sNN = 200 GeV

Ratio

at mid-rapidity.

Au+Au sNN = 200 GeV (central)
PHENIXSTAR
PHOBOS
BRAHMS
thermal model

1

10

-1

π- / π+ K- / K p / p
+

0

1

2

3

K+ / π+ K- / π- p / π+ p / π(inclusive)
4

5

6

7

8

Figure 5.1: Comparison of PHENIX particle ratios with those of PHOBOS [64], BRAHMS [65],and STAR [66] results in Au+Au central collisions at√
sNN = 200 GeV at mid-rapidity. The thermal

model prediction [67] for 200 GeV Au+Au central collisions are also shown as dotted lines. The
error bars on data indicate the systematic errors.

5.1. PARTICLE PRODUCTIONS

83Particles

Ratio ± stat. ± sys.

Thermal Model

π − /π +0.984 ± 0.004 ± 0.057

1.004

K − /K +0.933 ± 0.007 ± 0.054

0.932

p/p

0.731 ± 0.011 ± 0.062

p/p (inclusive)

0.747 ± 0.007 ± 0.046

K + /π +0.171 ± 0.001 ± 0.010

K − /π −0.162 ± 0.001 ± 0.010

p/π +0.064 ± 0.001 ± 0.003

p/π + (inclusive)

0.099 ± 0.001 ± 0.006

p/π −0.047 ± 0.001 ± 0.002

p/π − (inclusive)

0.075 ± 0.001 ± 0.004

0.752
0.147

0.089

Table 5.1: Comparison between the data for the 0–5% central collisions and the thermal√
model prediction at sNN = 200 GeV with Tch = 177 MeV and µB = 29 MeV [67].

5.1.3

Comparison with Theoretical Phase Boundary

A detailed analysis of experimental data in heavy ion collisions from SIS through AGS,SPS up to RHIC energy makes it clear that the statistical thermal model reproduces mostof the measured hadron yields [68, 69].
The chemical freeze–out temperature, found from a thermal analysis of experimental
data in Pb–Pb collisions at the SPS and in Au–Au collisions at RHIC energy is remarkably
consistent with the critical temperature Tc ' 173 ± 8 MeV obtained [1] from lattice MonteCarlo simulations of QCD at a vanishing net baryon density. Thus, the observed hadrons
seem to be originating from a deconfined medium and the chemical composition of the system is most likely to be established during hadronization of the quark-gluon plasma. The
observed coincidence of chemical and critical conditions in the QCD medium at the SPS
and RHIC energy open the question if this property is also valid in heavy ion collisions atlower collision energies where the statistical order of the secondaries is phenomenologically well established.
Figure 5.2 shows the results on the position of the phase boundary that were obtainedusing the methods indicated above together with the freeze-out curve. The chemical freezeout points at RHIC energy are indeed lying on the phase boundary.

CHAPTER 5. DISCUSSIONS

84
T [MeV]
200

RHIC

150

SPS

AGS

100

SIS

50

Tc
const. energy density
freeze--out curve
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

µB [GeV]Figure 5.2: A compilation of chemical freeze–out parameters appropriate for A–A collisions at different energies with the phase boundary line. The freeze-out curve line represents the phenomenological condition of a chemical freeze-out at the fixed energy/particle ' 1.0 GeV. The upper thinline represents the LGT results obtained in Ref. [70] and the lower thin line describes the conditionsof constant energy density that was fixed at µ = 0. The upper point with crossed error bars denotes
the end-point of the crossover transition from Ref. [71]. This figure is taken from [69].

5.2Transverse Distributions

5.2.1

pT Spectra of π , K, p

Hadron spectra reflect conditions late in the reaction, as well as the integrated effects ofexpansion from the beginning of the collision. Figure 5.3 shows the pT distributions forpions, kaons, protons, and anti-protons. The top two plots are for the most central 0–5%
collisions, and the bottom two are for the most peripheral 60–92% collisions. The spectra
for positive particles are presented on the left, and those for negative particles on the right.
For pT < 1.5 GeV/c in central events, the data show a clear mass dependence in the shapesof the spectra. The p and p spectra have a shoulder-arm shape, the pion spectra havea concave shape, and the kaons fall exponentially. On the other hand, in the peripheral
events, the mass dependences of the pT spectra are less pronounced and the pT spectra
are more nearly parallel to each other. Another notable observation is that at pT above5.2. TRANSVERSE DISTRIBUTIONS

85≈ 2.0 GeV/c in central events, the p and p yields become comparable to the pion yields,2(1/2 π pT ) d N / dpT dy [c / GeV ] (1/2 π pT ) d N / dpT dy [c / GeV ]which is also observed in 130 GeV Au+Au collisions [72, 73].

2

10
10

π+
+
K
p

3

2

10

πK

p

2

1
10
10

-2

-3

Positive(0 - 5% central)

Negative(0 - 5% central)Positive(60 - 92% peripheral)

Negative(60 - 92% peripheral)

2

10

-1

10

2

2

1
10
10
10
10
10
10

-1

-2

-3

-4

-5

-6

0

0.5

1

1.5

2

2.5

3

3.5

4 4.5 0pT [GeV/c]

0.5

1

1.5

2

2.5

3

3.5

4 4.5
pT [GeV/c]

Figure 5.3: Transverse momentum distributions for pions, kaons, protons and anti-protons in
Au+Au collisions at√
sNN = 200 GeV. The top two figures show pT spectra for the most central

0–5% collisions. The bottom two are for the most peripheral 60–92% collisions.

5.2.2

p/π ratios

One of the most unexpected observations in heavy-ion collision at RHIC is the large enhancement of baryons relative to pions at intermediate pT ≈ 2–5 GeV/c. Figure 5.4 show
the p/π and p/π ratios as a function of pT for the 0–10%, 20–30% and 60–92% centrality
bins. In this figure, the results of p/π 0 and p/π 0 [32] are presented above 1.5 GeV/c andoverlaid on the results of p/π + and p/π − , respectively. The absolutely normalized pT
spectra of charged and neutral pions agree within 5–15%. The error bars on the PHENIX
data points in the figure show the quadratic sum of the statistical errors and the point-topoint systematic errors. The ratios increase rapidly at low pT , but saturate at different

CHAPTER 5. DISCUSSIONS

86

values of pT which increase from peripheral to central collisions. In central collisions, theyields of both protons and anti-protons are comparable to that of pions for pT > 2 GeV/c.
For comparison, the corresponding ratios for pT > 2 GeV/c observed in p + p col√lisions at lower energies ( sNN = 53GeV) [74], and in gluon jets produced in e+ + e−
collisions [75], are also shown in the figure. At high-pT region, those ratios are compatible
with the peripheral Au+Au collisions in the uncertainties. In hard-scattering processes described by pQCD, the p/π and p/π ratios at high-pT are determined by the fragmentationof energetic partons, independent of the initial colliding system, which is seen as agreement
between p + p and e+ + e− collisions.
Thus, the clear increase in the p/π (p/π ) ratios at high pT from p + p and peripheral to

Ratio

the mid-central and to the central Au+Au collisions requires ingredients other than pQCD.

1.8
1.6
1.4

Figure 5.4: Proton/pion (top) andp/πanti-proton/pion (bottom) ratios for

1.2

central 0–10%, mid-central 20–30%

1

and peripheral 60–92% in Au+Au√
collisions at sNN = 200 GeV. Open

0.8
0.6

(filled) points are for charged (neu√tral) pions. The data at s = 53 GeV

0.4

Ratio

0.2

p + p collisions [74] are also shown.

1.8
0
1.6
1.4

Au+Au 0-10%
Au+Au 20-30%
Au+Au 60-92%
p+p, s = 53 GeV
e+e-, gluon jet (DELPHI)



p/π

1.2
1
0.8
0.6
0.4
0.2
0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

p T [GeV/c]

The solid line is the (p + p)/(π + +π − ) ratio measured in gluon jets [75].

5.2. TRANSVERSE DISTRIBUTIONS

5.2.3

87

Feature of Thermal Equilibrium: mT Spectra

In order to quantify the observed particle mass dependence of the pT spectra shape andtheir centrality dependence, the transverse mass spectra for identified charged hadrons arepresented here. From former studies at lower beam energies, it is known that the invariant
differential cross sections in p + p, p + A, and A + A collisions generally show a shape ofan exponential in mT − m0 (see Section 1.2.1). For an mT spectrum with an exponential
shape, one can parameterize it as follows:1d2N
1mT − m0=· A · exp (−),
2π mT dmT dy 2π T (T + m0 )
T

(5.1)

where T is referred to as the inverse slope parameter, and A is a normalization parameter
which contains information on dN/dy. In Figure 5.5, mT distributions for π ± , K ± , p and
p for central 0–5% (top panels), mid-central 40–50% (middle panels) and peripheral 60–
92% (bottom panels) collisions are shown. The spectra for positive particles are on theleft and for negative particles are on the right. The solid lines overlaid on each spectra are
the fit results using Eq. 5.1. The error bars are statistical only. As seen in Figure 5.5, all
the mT spectra display an exponential shape in the low mT region. However, at higher mT ,the spectra become less steep, which corresponds to a power-law behavior in pT . Thus,
the inverse slope parameter in Eq. 5.1 depends on the fitting range. In this analysis, thefits cover the range 0.2 – 1.0 GeV/c2 for pions and 0.1 – 1.0 GeV/c2 for kaons, protons,
and anti-protons in mT − m0 . The low mT region (mT − m0 < 0.2 GeV/c2 ) for pions is
excluded from the fit to eliminate the contributions from resonance decays. The inverse
slope parameters for each particle species in the three centrality bins are summarized in
Figure 5.6 and in Table 5.2. The inverse slope parameters increase with increasing particle
mass in all centrality bins. This increase for central collisions is more rapid for heavier
particles.
Such a behavior was derived, under certain conditions, by E. Schnedermann et al. [13]for central collisions and by T. Csörgő et al. [76] for non-central heavy-ion collisions:
T = T0 + mhut i2 ,(5.2)

where T0 is a freeze-out temperature and hut i is a measure of the strength of the (averageradial) transverse flow. The dotted lines in Figure 5.6 represent a linear fit of the resultsfrom each centrality bin as a function of mass using Eq. 5.2. The fit parameters for positive
and negative particles are shown in Table 5.2. It indicates, that the linear extrapolationof the slope parameter T (m) to zero mass has the same intercept parameters T0 in all theCHAPTER 5. DISCUSSIONS

88

centrality classes, indicating that the freeze-out temperature is approximately independentof the centrality. On the other hand, hut i, the strength of the average transverse flow isincreasing with increasing centrality, supporting the hydrodynamic picture.
π+
+
K
p

2

10
10
1
10
10
10

-1
-2
-3

Positive

Negative(0 - 5% central)(0 - 5% central)-5

Positive

Negative-6(40 - 50% mid-central)(40 - 50% mid-central)Positive

Negative(60 - 92% peripheral)(60 - 92% peripheral)

-4
2

10
10

2

4

(1/2π mT) d N / dmTdy [c / GeV2]

10

πK

p

1
10
10
10
10
10
10

-1
-2
-3
-4

10
1
10
10
10
10
10
10
10

-1
-2
-3
-4
-5
-6
-7

0

0.5

1

1.5

2

2.5 3 3.5 0
2mT - m0 [GeV/c ]

0.5

1

1.5

2

2.5 3 3.5
2mT - m0 [GeV/c ]Figure 5.5: Transverse mass distributions for π ± , K ± , protons and anti-protons for central 0–
5% (top panels), mid-central 40–50% (middle panels) and peripheral 60–92% (bottom panels) in√
Au+Au collisions at sNN = 200 GeV. The lines on each spectra are the fitted results using mT
exponential function. The fit ranges are 0.2 – 1.0 GeV/c2 for pions and 0.1 – 1.0 GeV/c2 for kaons,protons, and anti-protons in mT − m0 . The error bars are statistical errors only.

5.2. TRANSVERSE DISTRIBUTIONS

π+

89

K+

(+)

p

hut i(+)

T0

210.2 ± 0.8 290.2 ± 2.2 414.8 ± 7.5

177.0 ± 1.2 0.48 ± 0.07

40–50% 201.9 ± 0.8 260.6 ± 2.4 326.3 ± 5.9

179.5 ± 1.2 0.40 ± 0.07

60–92% 187.8 ± 0.7 233.9 ± 2.6 260.7 ± 5.4

173.1 ± 1.2 0.32 ± 0.07

0–5%

π−

K−

(−)

p

hut i(−)

T0

211.9 ± 0.7 293.8 ± 2.2 437.9 ± 8.5

177.3 ± 1.2 0.49 ± 0.07

40–50% 203.0 ± 0.7 265.1 ± 2.3 330.5 ± 6.4

179.6 ± 1.2 0.41 ± 0.07

60–92% 189.2 ± 0.7 237.4 ± 2.6 262.1 ± 5.9

173.7 ± 1.1 0.33 ± 0.07

0–5%

Table 5.2: (Top) Inverse slope parameters for π , K, p and p for the 0–5%, 40–50% and 60–
92% centrality bins, in units of MeV/c2 . The errors are statistical only. (Bottom) The extracted fit
parameters of the freeze-out temperature (T0 ) in units of MeV/c2 and the measure of the strength of
the average radial transverse flow (hut i) using Eq. 5.2. The fit results shown here are for positive

Inverse Slope T [GeV/c]and negative particles, as denoted in the superscripts, and for three different centrality bins.

0.6
0.5

Central (0-5%)
Mid-central (40-50%)
Peripheral (60-92%)

0.4
0.3
0.2
0.1
0

π+
0.2

K+
0.4

0.6

π-

p
0.8

1 0

0.2

2

Mass [GeV/c ]



K0.4

0.6

p
0.8

1
2

Mass [GeV/c ]Figure 5.6: Mass and centrality dependence of inverse slope parameters T in mT spectra for positive(left) and negative (right) particles in Au+Au collisions at√
sNN = 200 GeV. The fit ranges are 0.2– 1.0 GeV/c2 for pions and 0.1 – 1.0 GeV/c2 for kaons, protons, and anti-protons in mT − m0 . The
dotted lines represent a linear fit of the results from each centrality bin as a function of mass using
Eq. 5.2.

CHAPTER 5. DISCUSSIONS

90

5.3

Collective Expansion Model

Up to pT ∼ 1.5 − −2.0 GeV/c, it has been found that hydrodynamic models can reproduce
the data well for π ± , K ± , p and p spectra at 130 GeV [73], and also at 200 GeV in Au+Au
collisions [77, 79]. These models assume thermal equilibrium and that the created particles
are affected by a common transverse (radial) flow velocity βT and freeze-out (stop interacting) at a temperature Tfo with a fixed initial condition governed by the equation of state(EOS) of matter.

5.3.1 Blast-wave Parametrization
A sophisticated approach to understanding the particle spectra is to compare to a functional
form which describes a boosted thermal source, based on relativistic hydrodynamics [13].
This is a two–parameter model, termed the “blast-wave” model, in which the surface radialflow velocity (βT ) and freeze-out temperature (Tfo ) are extracted from the invariant crosssection data according to the equationdN∝
mT dmTZ R
0f (r) r dr mT I0³ p sinh ρ ´
T

Tfo

K1

³ m cosh ρ ´
T
,
Tfo

(5.3)

where I0 and K1 represent modified Bessel functions with ρ being the transverse boost
which depends on the radial position according toρ (r) = tanh−1 (βT ) · r/R(5.4)

Here the parameter R is the maximum radius of the expanding source at freeze-out. The
function f (r) represent the density which is taken to to be uniform in this calculation (i.e.,β(r)f (r) = 1). The radial flow velocity profile βr (r) is defined as βr (r) = tanh ρ (Figure.5.7),
1.2

1

Figure 5.7: The definition of transverse flow ve-

0.8

βT

locity profile:: β (r) = tanh(ρ ) = tanh(tanh−1 βT ·0.6r/R) : solid line (red), β (r) = βT · (r/R)n [n=1 :β(r) = tanh(ρ)ρ = tanh-1(βT ) r/R

0.4nβ(r) = βT (r/R) [n = 1]
0.2

0
0

0.2

0.4

0.6

0.8

1

r=R

1.2

1.4

1.6

1.8

r/R

dashed line (blue)]5.3. COLLECTIVE EXPANSION MODEL91

the average of the radial flow velocity is calculated as following equation,hβT i =

5.3.2

RR

RR
RR
−1
0 βr (r)r dr
0 tanh(ρ r/R)r dr
0 tanh(tanh (βT )r/R)r dr
=
=
.
RR
RR
RR
0 r dr0 r dr0 r dr(5.5)

Previous Studies

To study the parameter correlations, we make a grid of (Tfo , βT ) pairs and then we perform achi-squared minimization for each particle type. The first fit attempt is performed simultaneously for the six particle species π ± , K ± , p and p in the range (mT − m0 ) < 1.0 GeV/c2 .
In addition to this upper limit in the fit, the fit range for pion includes a lower limit of pT >0.5 GeV/c to avoid the resonance contribution to the low-pT region.
The two–parameter Tfo vs βT fit results obtained in this analysis for the most central
0–5% collisions are shown in Figure 5.8. The contour lines are one sigma steps. Shown in
the lower panels of the figure are the χ 2 contour levels obtained from fitting each particle
spectrum separately. We observed that the parameter Tfo and βT are anti-correlated, thedifferent particles have different proffered parameter space and different sensitivity to theparameters. For example, the heavier particles are more sensitive to the radial flow velocity
than to the to the kinetic freeze-out temperature. The contours for the six particle species
do overlap at a single common point at the 3σ level.
To study the resonance contribution at low-pT region, we change the lower limit ofpT for pions. Figure 5.9 shows the fit results for the peripheral collisions. Figure 5.9a is
pT > 0.5 GeV/c and Figure 5.9b is pT > 0.8 GeV/c for pion. Due to large contribution ofresonance, the best fit values are changed by fitting range.

5.3.3

Proposed Analysis and Results

Since the experimental data include the decay of resonance, we add the decay of mesonic(ρ , η , ω , K ∗ , , ,) and baryonic (∆, Λ, Σ, , ,) resonance effects as follows:
1) Generate resonances with the transverse momentum distribution determined by eachcombinations of Tfo and βT .
2) Decay them using Monte Carlo simulation, and obtain π ± , K ± , p and p distribution.
3) Merge all particles, where the particle abundance is calculated with chemical parameters (Tch = 177MeV, µB = 29MeV) [67].

CHAPTER 5. DISCUSSIONS

92[ 0-5%] BEST FIT :βT = 0.77, T fo = 0.101, χ /NDF = 127.4/50

0.22

2

0.2

Tfo (GeV)

0.18
0.16
0.14
0.12
0.1

Figure 5.8: Contour plot for the most cen-

0.08

tral 0-5% collisions. The contour lines are

0.06

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

βT

one sigma steps. The upper plot is from a simultaneous fit with the best value shown as

0.22

the point. The lower plot is from indepen-

0.2

dent fits for the six particle spectra.

Tfo (GeV)

0.18
0.16
0.14
0.12
0.1
0.08
0.06

p p
K+ K-

π+ π0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

βT[60-92%] BEST FIT :βT = 0.63, T fo = 0.120, χ /NDF = 255.9/50

0.22
0.2

0.14
0.12

0.16
0.14
0.12

0.1

0.1

0.08

0.08
0.06

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.22

0.22

0.2

0.2

0.18

0.18

0.16
0.14

0.08
0.06

p p
+

K K

0.16
0.14
0.12
0.1

-

0.08

π+ π0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

βT

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

βT

Tfo (GeV)

Tfo (GeV)

βT

0.1

2

0.18

Tfo (GeV)

Tfo (GeV)

0.18

0.12

βT = 0.50, T fo = 0.159, χ /NDF = 30.1/42

0.2

0.16

0.06

[60-92%] BEST FIT :

0.22

2

0.06

p p
K+ K-

π+ π0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

βT

Figure 5.9: Contour plot for the most peripheral collisions. The contour lines are one sigma steps.
The right plot(b) is set a lower limit of pT > 0.8 GeV/c for pion.

5.3. COLLECTIVE EXPANSION MODEL

93

Figure 5.10 shows the fro-chart of model fit with resonance feed down. As shown in Figure 5.12, we now succeed in reproducing the spectrum with the freeze-out temperature Tfo
and radial flow velocity βT . The kinematics of the resonance decays result in very steeply
dropping daughter pion spectra and raise considerably the total pion yield at low-pT region.
Pion (+)

dN/dpT (A.U.)

10

10

10

10

10

-1

π

-2

Inclusive πdistribution

-3

-4

-5

-6

0

0.5

1

1.5

2

2.5

3

3.5

chi2 test10

2: mass = 0.140 GeV/c , Tfo = 0.180, beta = 0.400

4pT [GeV/c]rho (0)dN/dpT (A.U.)

10

10

10

10

10

10

2

: mass = 0.768 GeV/c , Tfo = 0.180, beta = 0.400

-1

ρ

-2

Decay

-3

-4

Daughter πdistribution

-5

-6

0

0.5

1

1.5

2

2.5

3

3.5

4

DATA

pT [GeV/c]

Figure 5.10: Fro-chart of model fit with resonance feed down.
The two–parameter Tfo vs βT fit results obtained in this analysis for the most central
0–5% collisions are shown in Figure 5.13. The contour lines are one sigma steps. Shownin the lower panels of the figure are the χ 2 contour levels obtained from fitting each particle spectrum separately. The contours for the six particle species do overlap at a single
common point at the 3σ level. To find the values of the parameters at this overlap point,
a simultaneous fit for the six single particle spectra (π ± , K ± , and p, p) was done which+0.0055
converges to a best fit value of Tfo = 107.8+3.7−3.3 MeV and βT = 0.773−0.0065 .

CHAPTER 5. DISCUSSIONS

94
π+ [ Tfo = 0.108 GeV , βt = 0.77 ]Decay component:
Meson source10η , η*, ω , ρ0, ρ± ,K*, φ

3

Baryon source

1/pT*dN/dpT (A.U.)∆, Λ , Σ, Ξ

10

2

10
0

0.5

1

1.5

2

2.5

3

3.5

1
-1

10

Total π+Thermal π+
Decay π+

-2

10

-3

10

0

0.5

1

1.5

2

2.5

3

3.5

pT [GeV/c]

Figure 5.11: The total π + spectrum from a thermal source with the temperature Tfo = 108 MeV
and flow velocity βT = 0.77. The thermal π + (dashed, red) and the decay daughter π + (dash-dotted,blue) add up to the total spectrum. The upper right figure show the decay component of mesonicand baryonic resonance.

π+ [ Tfo = 0.180 GeV , βt = 0.40 ]Decay component:
Meson source10η , η*, ω , ρ0, ρ± ,K*, φ

3

Baryon source

1/pT*dN/dpT (A.U.)∆, Λ , Σ, Ξ

10

2

10
0

0.5

1

1.5

2

2.5

3

3.5

1
-1

10

Total π+Thermal π+
Decay π+

-2

10

-3

10

0

0.5

1

1.5

2

2.5

3

3.5

pT [GeV/c]

Figure 5.12: The total π + spectrum from a thermal source with the temperature Tfo = 180 MeV
and flow velocity βT = 0.40. The thermal π + (dashed, red) and the decay daughter π + (dash-dotted,blue) add up to the total spectrum. The upper right figure show the decay component of mesonicand baryonic resonance.

5.3. COLLECTIVE EXPANSION MODEL

0.12

95

[0 % - 5 %] BEST FIT :βT = 0.77, Tfo = 0.108, χ2/NDF = 85.9/46

Tfo [GeV]

0.115

0.11

0.105

0.1

0.095
0.72

0.74

0.76

βT

0.22

0.78

0.8

0.82

K+ K-

0.2

π+ π-

Tfo [GeV]

0.18
p p

0.16
0.14
0.12
0.1
0.08
0.06

0.1

0.2

0.3

0.4

0.5

βT

0.6

0.7

0.8

0.9

Figure 5.13: Contour plot for the most central 0-5% collisions. The contour lines are one sigma
steps. The upper plot is from a simultaneous fit with the best value shown as the point. The lower
plot is from independent fits for the six particle spectra.

CHAPTER 5. DISCUSSIONS

96

Figure 5.14 shows χ 2 contours on the parameter space of the freeze-out temperature
Tfo and radial flow velocity hβT i for each centrality. For the most central 0–5% collisions,
we obtain freeze-out temperature Tfo = 108 MeV and average flow velocity hβT i = 0.57
(Surface flow velocity is βT = 0.77). Figure 5.15 shows the centrality dependence of the
Tfo and hβT i. The value for Tfo , βT and hβT i are tabulated in Table 5.3. It is found that Tfo
decreases and βT increases from the most peripheral to mid-central collisions, and appears
to saturate in the central collisions. The behavior of βT is in accordance with a collective
expansion picture.
Centrality

Tfo [MeV]

βT

hβT i

χ 2 /NDF

0- 5%

107.8+3.7−3.3

0.773+0.0055−0.00650.574+0.0041−0.004885.9/465-10%

109.8+3.7−3.3
113.3+3.2−2.8
116.5+4.0−4.0
123.0+3.5
−3.5
+2
132−2
142+2
−4
153+5
−5
163+7
−7
168+10−10
179+13−15
108.9+2.6
−2.4
167+7
−7

0.769+0.0055−0.0065
0.763+0.006−0.0060.754+0.007−0.0070.738+0.007−0.007+0.0050.71−0.005
0.67+0.01−0.0050.614+0.016−0.0140.555+0.025−0.0250.497+0.042−0.0370.399+0.071−0.079+0.0030.771−0.004
0.525+0.025−0.0250.570+0.0041−0.00480.564+0.0044−0.00440.555+0.0051−0.0051
0.541+0.0051−0.00510.515+0.0036−0.0036
0.481+0.0072−0.00360.434+0.0113−0.0099
0.388+0.0175−0.0175
0.344+0.0295−0.0258
0.272+0.0484−0.0539+0.0026
0.572−0.0033
0.365+0.0174−0.0174

75.7/46

10-15%
15-20%
20-30%
30-40%
40-50%
50-60%
60-70%
70-80%
80-92%
0-10%
60-92%

Table 5.3: Fitting results for each centrality

84.2/46
62.6/46
69.2/46
81.7/46
70.0/46
59.9/4647.3/46
39.7/4659.0/46148.0/46
47.1/46

Temperature Tfo (GeV)

5.3. COLLECTIVE EXPANSION MODEL

97

20-30%

0.125

0.22

0.12

peripheral
80-92%

0.2

10-15%
5-10%
0-5%

0.11
0.105

60-70%

2-σ

0.16

15-20%

2- σ

0.115

70-80%

3-σ

0.18

1- σ

0.1
0.53 0.54 0.55 0.56 0.57 0.58

50-60%

1-σ

40-50%
30-40%

0.14

20-30%
15-20%
10-15%
5-10%
0-5%

0.12
0.1 Au+Au 200GeV [π, K, p]centralFit to PHENIX 200 GeV data, PRC 69, 034909 (2004)0.08∆χ for 2-dim.:: (1-σ :2.29, 2-σ :6.18, 3-σ:11.83)
2

0.06
0

include resonance, flat particle density, linear flow profiles

0.1

0.2

0.3

0.4

0.5

Average velocity < βT>

0.6

Average velocity < βT > Temperature Tfo [GeV]

Figure 5.14: Contour plot Freeze-out temperature Tfo and radial flow velocity βT

0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0

Au+Au 200GeV [ π, K, p]
Fit to PHENIX 200 GeV data, PRC 69, 034909 (2004)

include resonance, flat particle density, linear flow profiles

0.6
0.5
0.4
0.3
0.2
0.1
0

0

include resonance, flat particle density, linear flow profiles

50

100

150

200

250

300

350

400

Npart

Figure 5.15: Freeze-out temperature Tfo (top) and radial flow velocity βT (bottom) as a function of
Npart . The error is statistical only.

CHAPTER 5. DISCUSSIONS

98

The results are plotted together with the spectra in Figure 5.16. Hydrodynamical fits
in the range (mT − m0 ) < 1GeV (solid line) are extrapolated over the entire transverse
kinematic energy range (dashed line) for comparison to the data.
By this approach, we achieve following things,• Unified view of transverse distribution by thermal and chemical equilibrium.
• Realize the spectrum component of thermal source and decay resonance.

10
10

2

(1/2π pT ) d N / dpT dy [c / GeV 2] (1/2π pT) d N / dpTdy [c / GeV 2]• Observed strong adiabatic expansion in central collisions.

10

Tfo = 0.108
βT = 0.77

3

1
10
10
10

10
10
10
10

K+

K-

p

p



-2

Positive(0 - 5% central)-3

Negative(0 - 5% central)
Tfo = 0.168
βT = 0.52

1

10

π-

-1

10

10

Tfo = 0.108
βT = 0.77

π+

2

10

2
2
2

4

Tfo = 0.168
βT = 0.52

-1
-2
-3
-4

Positive(60 - 92% peripheral)-5

Negative(60 - 92% peripheral)

-6

0

0.5 1

1.5 2

2.5 3

3.5 4 4.5 0 0.5
pT [GeV/c]

1

1.5 2

2.5 3

3.5 4 4.5
pT [GeV/c]

Figure 5.16: The top two figures show pT spectra for the most central 0–5% collisions. The bottom
two are for the most peripheral 60–92% collisions. Hydrodynamical fits in the range (mT − m0 ) <1GeV (solid line) are extrapolated over the entire transverse kinematic energy range (dashed line)
for comparison to the data.

5.4. BEYOND THE THERMAL BEHAVIOR: HARD COMPONENT

5.4

Beyond the Thermal Behavior: Hard Component

5.4.1

Suppression of High pT Hadrons

99

As discussed in Section 1.3, the spectra of high-pT hadrons potentially provide a directprobe of the properties of the initial state in heavy-ion collision.
One of the most striking features in Au+Au collisions at RHIC is that π 0 and nonidentified hadron yields at pT > 2 GeV/c in central collisions are suppressed with respect
to the number of nucleon-nucleon binary collisions Ncoll scaled by p + p and peripheral
Au+Au results [30, 31, 32]. Moreover, the suppression of π 0 is stronger than than that for
non-identified charged hadrons [30], and the yields of protons and anti-protons in central
collisions are comparable to that of pions around 2 GeV/c (see Section 5.2.1). The enhancement of the p/π (p/π ) ratio in central collisions at intermediate pT region (2.0 – 4.5
GeV/c), which was presented in Section 5.2.2, is consistent with the above observations.
These results strongly suggest significant contributions of proton and anti-proton yield tothe total particle composition at this intermediate pT region.
We present here the Ncoll scaling behavior for charged pions, kaons and protons (antiprotons) in order to quantify the particle composition at intermediate pT . The medium
modifications of hadron spectra are often quantified by the nuclear modification factor RAA
which discuss in Section 1.3.2. Figure 5.17 shows the central (0–10%) to peripheral (60–92%) ratio for Ncoll scaled pT spectra of (p + p)/2, kaons, charged pions and π 0 . We define
RCP as:Yield0−10% /hNcoll 0−10% i
RCP =
.
(5.6)
Yield60−92% /hNcoll 60−92% i
The peripheral 60–92% Au+Au spectrum is used as an approximation of the yields in p + p
collisions, based on the experimental fact that the peripheral spectra scale with Ncoll by using the yields in p + p collisions measured by PHENIX [23, 32]. Thus the meaning of the

RCP is expected to be the same as RAA . The horizontal lines in Figure 5.17 indicate theexpectations of Npart (dotted) and Ncoll (dashed) scaling. The shaded bars at the end of eachline represent the systematic error associated with the determination of these quantities forcentral and peripheral events. The error bars on charged particles are statistical errors only,
and those for π 0 are the quadratic sum of the statistical errors and the point-to-point systematic errors. The data show the Npart scaling behavior at low-pT region (pT < 0.5 GeV/c),consistent with wounded nucleon scaling. The curves on data are calculated by blast–wave
fit results and extrapolated over the entire range. This hydrodynamical behavior indicatesthat the ratio would continue to increase. However, the data show that (p + p)/2 reaches

CHAPTER 5. DISCUSSIONS

RCP

100

1.8


(p + p) / 2

1.6+(K + K - ) / 2(π+ + π- ) / 2
π0

1.4
1.2
1
0.8
0.6
0.4
0.2

0

1

2

3

4

5

6
7
pT [GeV/c]

Figure 5.17: Central (0–10%) to peripheral (60–92%) ratios of binary-collision-scaled pT spectra,
RCP , as a function of pT for (p + p)/2, charged kaons, charged pions, and π 0 [32] in Au+Au√
collisions at sNN = 200 GeV. The horizontal lines indicate the expectations of Npart (dotted) andNcoll (dashed) scaling, the shaded bars represent the systematic errors on these quantities. The curves
on data are calculated by blast–wave fit results.

unity for pT > 1.5 GeV/c. It is consistent with Ncoll scaling. The data for kaons also show
the Ncoll scaling behavior around 1.5 – 2.0 GeV/c, but the behavior is weaker than for protons. As with neutral pions [32], charged pions are also suppressed at 2 – 3 GeV/c withrespect to peripheral Au+Au collisions.
Motivated by the observation that the (p + p)/2 spectra scale with Ncoll above pT =1.5 GeV/c, the ratio of the integrated yield between central and peripheral events (scaled by
the corresponding Ncoll ) for pT >1.5 GeV/c are shown in Figure 5.18 as a function of Npart .
The pT ranges for the integration are, 1.5 – 4.5 GeV/c for (p + p)/2, 1.5 – 2.0 GeV/c forkaons, and 1.5 – 3.0 GeV/c for charged pions. The data points are normalized to the mostperipheral data point. The shaded boxes in the figure indicate the systematic errors, which
include the normalization errors on the pT spectra, the errors on the detector occupancy
corrections, and the uncertainties of the hTAuAu i determination for the numerator only. Only
60−92%
at the most peripheral data point, the uncertainty on the denominator hTAuAu
i is also

RCP (pT > 1.5 GeV/c)

5.4. BEYOND THE THERMAL BEHAVIOR: HARD COMPONENT

101

1.4
1.2
1

0.8
0.6
0.4
0.2
0
0



(p + p) / 2+(K + K ) / 2( π+ + π-) / 2
50

100

150

200

250

300

350

Npart

Figure 5.18: Centrality dependence of integrated RCP above 1.5 GeV/c normalized to the mostperipheral 60–92% value. The data shows RCP for (p + p)/2, charged kaons, and charged pions√in Au+Au collisions at sNN = 200 GeV. The error bars are statistical only. The shaded boxes
represent the systematic errors (see text for details).

added. The figure shows that (p + p)/2 scales with Ncoll for all centrality bins, while thedata for charged pions show a decrease with Npart . The kaon data points are between the
charged pions and the (p + p)/2 spectra.

5.4.2

Comparison with Theoretical Models: hydro+jet and recombination

The standard picture of hadron production at high momentum is the fragmentation of energetic partons. While the observed suppression of the π 0 yield at high pT in central collisions
may be attributed to the energy loss of partons during their propagation through the hot anddense matter created in the collisions, i.e. jet quenching [17, 16], it is a theoretical challenge to explain the absence of suppression for baryons up to 4.5 GeV/c for all centralities
along with the enhancement of the p/π ratio at pT = 2 – 4 GeV/c for central collisions.

CHAPTER 5. DISCUSSIONS22(1/2πpT )dN/dpT dY (c /GeV )

102

103

Hydro+jet
Hydro only
Jet only
PHENIX πPHENIX kPHENIX p

2

10

π-

10
1
-1

10

-2

10

10-3
-4

10

Figure 5.19: Each contribution from hydrodynamics and minijets for π − , K − , and p in Au+Au√
collisions at sNN = 200 GeV at the impact parameter of b = 2.0 fm. This figure is taken from-3

K - × 10

[82].

10-5
10-6
-7

10

-6

p × 10

10-8
10-9
10-10
-11

10

th

b=2 fm, T =100 MeV

-12

10

0

1

2

3

4

5
6
pT (GeV/c)

Hydro + jet model
The large p/π ratio is the strong radial flow that boosts the momentum spectra of heavier
particles to high-pT . These observations can be explained by the hydrodynamical modelwith jet fragmentation (hydro + jet model) [82].
The main feature of the hydrodynamic part in the hydro + jet model are the following:
Assuming local thermal equilibrium of partonic/hadronic matter at an initial time τ , thehydrodynamical model describe its space-time evolution. The equation of state (EOS) has
a first order phase transition between the QGP phase and the hadron phase at Tc = 170 MeV.
The QGP phase assumed to be free gas composed quarks with N f = 3 and gluons. For the
hadron phase, a partial chemical equilibrium model with chemical freeze-out temperature
Tch = 170MeV is employed to describe the early chemical freeze-out picture of hadronicmatter. Pure hydrodynamics predicts that p/π ratio would continue to increase essentially
up to pT → ∞. However, these particles cannot have a zero mean free path in the medium.
Any finite mean free path and a finite volume will limit the number of pT “kicks” a particle
can receive. For this reason many of the hydrodynamic calculations are not extended into
the pT region 2–5 GeV/c. Above few pT , hydrodynamics should fail to describe the dataand jet fragmentation should dominate. The hard part in the hydro + jet model is calculated

1.4

1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

p/ π+
K- / π-1.2p/ π+,PHENIX,0-10%
K- / π- ,PHENIX,0-5%

1
0.8
0.6
0.4
0.2
0
0

1

2

3

4

5

6
7
pT (GeV/c)

R AA

ratio

5.4. BEYOND THE THERMAL BEHAVIOR: HARD COMPONENT

1.4
1.2
1
0.8
0.6
0.4
0.2
0

1.4
1.2
1
0.8
0.6
0.4
0.2
0
0

103

b=2fm

PHENIX, π 0

πKprotonchargedb=5.5fm

b=7.2fm

1

2

3

4

5
6
pT (GeV/c)

Figure 5.20: The “hydro + jet” model comparison for p/π ratio and RCP . Left figure is the p/π andK/π ratios as a function of pT in Au+Au collisions at impact parameter b = 2 fm. Right figure is im√
pact parameter dependence of the suppression factors RAA in Au+Au collisions at sNN = 200 GeV
as a function of pT for π − , K − , and p. This figure are taken from [82].

using perturbative QCD. (see Section 1.3)
From this model, Figure 5.19 shows the spectra into hydro parts and minijet parts. It
is seen that both soft and hard components are important for the hadron spectra in thetransverse momentum of the range around 2 ≤ pT ≤ 5 GeV/c depending on the hadronmass. Figure 5.20 shows hydro + jet model calculations compared to the p/π , K/π ratios
and RCP from PHENIX. The model successfully represents the pion suppression and proton
boost at low to intermediate pT regions.
Parton Recombination
Another possible explanation is the dominance of parton recombination at intermediate pT ,rather than by fragmentation (recombination and fragmentation model) [83, 84, 85]. In
the recombination picture, three quarks or a quark/anti-quark pair in a densely populated
phase space can form a baryon or meson, respectively. The amplitude for this process
is determined by the hadron wave function. This process becomes important particularly
at dense environment. Meson (M) is formed from recombination of a quark (a) and an

CHAPTER 5. DISCUSSIONS

104

1.2

1.6

proton/ π+
proton/ π0
Duke
OregonTAMU w/ shower
TAMU no shower

1.4
1.2
1
0.8
0.6
0.4
0.2

1

2

3

4

5

6

7

8

9
10
pT (GeV/c)0

PHENIXp+pbar PHENIX0(b=0)/(b=12) R+F
p+pbar (b=0)/(b=12) R+F

1.0
0.8
0.6
0.4
0.2
0.0

0
0

RCP (0-10%)/(60-92%)

p/ π

PHENIX proton/π ratio

2

3

4

5 6 7
PT (GeV)8910Figure 5.21: The “recombination” model comparison for p/π ratio and RCP . Left figure is thep/π ratio measured by PHENIX and several comparisons to recombination models. Right figure is
RCP for π 0 and protons given by the ratio of particle yields at impact parameters 3 and 12 fm. This
figures are taken from [83, 86].

anti-quark (b) and baryon (B) is formed of three quarks (a, b and c) as, respectivelyZ

d 3 NM∝
dxwa (xpT )w̄b ((1 − x)pT )|ψab |2 ,
E 3
d p
Z
d 3 NB∝
dxdx0 wa (xpT )wb (x0 pT )wc ((1 − x − x0 )pT )|ψabc |2 ,
E 3
d p

(5.7)
(5.8)

where wα (pT ) is the parton distribution, x (x0 ) is the fraction of the momentum and ψab (ψabc )is the meson (baryon) wave function. For an equal momentum fraction, namely x = 1/2
for mesons and x = x0 = 1/3 for baryons,dNM= CM wa (pT /2)2 ,p T d pTdNB
= CB wb (pT /3)3 ,p T d pT

(5.9)

where CM and CB correspond to the coalescence probabilities for mesons and baryons,respectively.
Three essential features are predicted by recombination models. First, baryons at moderate pT are greatly enhanced relative to mesons as their transverse momentum is the sumof three quarks rather than two. Recombination dominates over parton fragmentation in thisregion, because, for an exponential spectrum recombination is a more efficient means of
producing particles at a particular pT . This enhancement should return to its fragmentation
values at higher pT . In the intermediate range, all mesons should behave in a similar manner
regardless of mass, as should all baryons. Secondly, recombination predicts that the collective flow of the final-state hadrons should follow the collective flow of their constituent

5.4. BEYOND THE THERMAL BEHAVIOR: HARD COMPONENT

2.5
2

φ

105

0 - 10%40 - 92%

p+p
2
π0

Rcp

1.5
1
0.5
0
0

1

2

3

4
pT [GeV/c]

5

6

7

Figure 5.22: The RCP of the φ as measured in the KK channel, compared to the protons and pions
for Au+Au collisions at√
sNN = 200 GeV. This figure is taken from [87].

quarks. Finally, recombination causes thermal features to extend to higher transverse momentum, pT >> Tc than one might naively expect since the underlying thermal spectrumof the constituents gets a multiplication factor of essentially three for baryons and two formesons. A last general feature which is true for the simplest of the models, but may notnecessarily be true for more complex models, is that at intermediate pT , recombination isthe dominant mechanism for the production of hadrons—particularly of baryons.
Figure 5.21 shows several recombination model calculations compared to the p/π ratio
and RCP from PHENIX. The general features at pT > 2 GeV/c are reasonably reproduced
that is the protons show a strong enhancement at moderate pT . Since the recombination
model’s essential ingredient is the number of constituent quarks in a hadron, the similarityof RCP for the φ and pions is nicely explained.
The competition between recombination and fragmentation of partons may explain theobserved features. The model predicts that the effect is limited to pT < 5 GeV/c, beyond
which fragmentation becomes the dominant production mechanism for all particle species.
Comparison with the φ meson
In both theoretical models, the baryon enhancement as a function of centrality can be tuned
to reproduce the apparent binary collision scaling observed in the data. An important dis-

106

CHAPTER 5. DISCUSSIONS

tinction between the two models is that in one case this enhancement is mass dependentand in the other it comes from the combination of quark momenta and thus distinguishes
between baryons and mesons.
We have extended our identified hadron studies to include the φ vector meson as measured in the K + K − decay channel. The φ is a meson, and is in that sense similar to the pion
with a valence quark and antiquark, and yet its mass is comparable to that of the proton.
Figure 5.22 shows RCP , the ratio of production in central to peripheral Au+Au collisions
scaled by binary collisions, for protons, pions and φ mesons detected via its KK decay√
channel [87] in Au+Au collisions at sNN = 200 GeV. The φ follows the suppression
pattern of the pions within errors, indicating that the surprising behavior of the protons is
not followed by the φ . This scaling with quark content, as opposed to mass, favors recombination models.

Chapter 6
Conclusions
We have presented the results of identified hadron spectra and yields in Au+Au collisions√
at the energy of sNN = 200 GeV by the PHENIX experiment using the Relativistic Heavy
Ion Collider (RHIC) at Brookhaven National Laboratory (BNL).
For the systematic study of hadron productions in relativistic heavy-ion collisions near
mid-rapidity region, we have constructed Time-of-Flight counter and installed in PHENIX
detector systems. It is designed for the good particle identification capability under thecondition of high particle density and for the wide range of kinematic coverage in Au+Au
collisions at RHIC. Using the data taken by the PHENIX central arm spectrometers, single
particle spectra and yields are analyzed.
For single particle analysis, we have measured the transverse momentum spectra and√yields for π ± , K ± , p and p at mid-rapidity in Au+Au collisions at sNN = 200 GeV overa broad momentum range with various centrality selections. We have observed a clear particle mass dependence of the shapes of transverse momentum spectra in central collisions
below ∼ 2 GeV/c in pT . Both mean transverse momenta and particle yields per participant
pair increase from peripheral to mid-central and saturate at the most central collisions for√
all particle species. The net proton number in Au+Au central collisions at sNN = 200 GeV
is ∼ 5 at mid-rapidity.
We also measured the particle ratios of π − /π + , K − /K + , p/p, K/π , p/π and p/π asa function of pT and collision centrality. The ratios of equal mass particle yields are independent of pT and centrality within the experimental uncertainties. The ratios in central
Au+Au collisions are well reproduced by the statistical thermal model with a baryon chemical potential of µB = 29 MeV and a chemical freeze-out temperature of Tch = 177 MeV. On
the other hand, both K/π and p/π (p/π ) ratios increase as a function of pT . This increase

107

108

CHAPTER 6. CONCLUSIONS

with pT is stronger for central than for peripheral events.
The particle spectra can be well fit with a hydrodynamic-inspired parameterization to
extract freeze-out temperature and radial flow velocity of the particle source. The experimental data include the decay of resonance; we added the decay of mesonic (ρ , η , ω , K ∗ , , ,)and baryonic (∆, Λ, Σ, , ,) resonance effects which the abundance is determined by chemicalparameters. The simultaneous fits of π ± , K ± , p and p spectra for the most central 0–5%
collisions, we have obtained freeze-out temperature Tfo = 108 MeV and average flow velocity hβT i = 0.57. It was found that Tfo decreases and βT increases from the most peripheral
to mid-central collisions, and appears to saturate in the central collisions.
For the high-pT region, the scaling behavior of identified charged hadrons has been
compared with results for neutral pions. The central-to-peripheral ratio, RCP , approaches
unity for (p + p)/2 from pT = 1.5 up to 4.5 GeV/c. Meanwhile, charged and neutral pions
are suppressed. The ratio of integrated RCP from pT =1.5 to 4.5 GeV/c exhibits an Ncoll
scaling behavior for all centrality bins in the (p + p)/2 data, which is in contrast to thestronger pion suppression, that increases with centrality. The p/π and p/π ratios in central
events both increase with pT up to 3 GeV/c and approach unity at pT ≈ 2 GeV/c. However,in peripheral collisions these ratios saturate at the value of 0.3 – 0.4 around pT = 1.5 GeV/c.
The standard picture of hadron production at high momentum is the fragmentation ofenergetic partons. While the observed suppression of the π yield at high-pT in central
collisions might be attributed to the energy loss of partons during their propagation throughthe hot and dense matter created in the collisions. The observed RCP and p/π ratios inintermediate pT region are not explained by the hydrodynamic model alone, but some oftheoretical model qualitatively agree with data. These observations can be explained by thehydrodynamical model with jet fragmentation (hydro + jet model). Above few GeV pT ,hydrodynamics fail to describe the data and jet fragmentation should dominate. Anotherpossible explanation is the dominance of parton recombination at intermediate pT , rather
than by fragmentation (recombination and fragmentation model). In the recombination
picture, three quarks or a quark/anti-quark pair in a densely populated phase space can forma baryon or meson, respectively. Both theoretical models reproduce the binary collisionscaling observed in the data. We have extended our identified hadron studies to include theφ vector meson. The observed RCP for φ is similar to other mesons despite the fact thatthey are more massive than protons. This scaling with quark content favors recombination
models.

Appendix A
Numerical Supplement
A.1

Relativistic Kinematics and Variables

Here, we introduce kinematic variables used in the thesis. It is useful to describe themwith Lorentz invariant variables or variables which have simple Lorentz transformation
properties, because we deal with relativistic particles and system.
We take a beam line to be z-axis of a frame. For a particle which has momentum
p = (pq
x , py , pz ) and mass m, we use a longitudinal momentum pz , a transverse momentumppT ≡ p2x + p2y , and total energy E = p2 + m2 . Transverse mass mT and rapidity y aredefined asqmT ≡p2T + m2 ,y≡

1 E + pzln.
2 E − pz

(A.1)

The total energy and longitudinal momentum of a particle can be easily related to its transverse mass and rapidity as
E = mT cosh y,pz = mT sinh y.

(A.2)

On the Bjorken’s space-time picture, the proprt time τ and space-time rapidity Y aredefined asτ=pt 2 − z2 ,1 t +zln,
2 t −zz = τ sinhY.

Y=

t = τ coshY,

109

(A.3)
(A.4)

APPENDIX A. NUMERICAL SUPPLEMENT

110

A.2 Transverse Expansion
In this section, we show the actual computation of the spectra and follow the spirits ofboost-invariant scenario. We employ cylindrical coordinates (r, φ , z) where z is the cop
ordinate along the collision axis with r ≡ x2 + y2 = z = 0 being the collision point. In√
addition we define the longitudinal proper time, τ = t 2 − z2 . To obtain the boost invariantsolutions in a longitudinal direction, we define the transverse velocity to the following form
for azimuthal symmetryµ¡u = ut , ur , uφ , uz

¢

=p

³t

1

z´
, βr (τ , r), 0,,ττ

1 − βr2(A.5)

where the overall factor in the right hand side is obtained from the normalization uµ uµ = 1.
We define the transverse rapidity ρ as
1 1 + βrln,
(A.6)
2 1 − βrppwhich gives cosh ρ = 1/ 1 − βr2 and sinh ρ = βr / 1 − βr2 . Together with Eq.(A.4), weρ = tanh−1 βr =obtain the transverse velocity form as
uµ = (cosh β coshY, sinh β , 0, cosh β sinhY ) .

(A.7)

The invariant momentum spectrum of hadrons emitted at freezeout is given by a local
thermal distribution f (x, p) [88], with the freezeout temperature T , boosted by a local
velocity field uµ at the freezeout hypersurface σ :
E

d3N
=
d p3

Z
σ

f (x, p)pµ d σµg≈(2π )3Zνe−u pν /T pµ d σµ ,(A.8)

We assume that the freeze-out takes place on σ which is a three dimensional hypersurface specified by the cylindrical coordinates:

σ µ = (σt , σx , σy , σz ) = (t(r, z), r cos φ , r sin φ , z)

(A.9)

A normal vector d σ to the surface is∂σν ∂σλ ∂σρ
drd φ dz,
d σ µ = εµνλ ρ∂r ∂φ ∂z
µ
¶
∂t
∂t
∂t
rdrd φ dz.
=
1, − cos φ , − sin φ , −
∂r
∂r
∂z

(A.10)

A.2. TRANSVERSE EXPANSION111

The four-momentum of the emitted hadron may be expressed in term of the momentumspace rapidity y and the transverse mass mT
pµ = (E, px , py , pz ) = (mT cosh y, pT cos ϕ , pT sin ϕ , mT sinh y) ,we obtainµ

p d σµ·¸∂t∂t= E − pT cos(φ − ϕ ) − pz
rdrd φ dz
∂r
∂z
·
¸
∂t
∂t
= mT cosh y − mT sinh y − pT cos(φ − ϕ ) rdrd φ dz.
∂z∂r(A.11)(A.12)The transverse velocity uµ is obtained the case of φ 6= 0:¡¢
uµ = ut , ux , uy , uz = (cosh ρ coshY, sinh ρ cos φ , sinh ρ sin φ , cosh ρ sinhY ) .

(A.13)

Then we obtainuµ pµ = E cosh ρ coshY + pT sinh ρ cos φ cos ϕ + pT sinh ρ sin φ sin ϕ + pz cosh ρ sinhY= mT cosh ρ cosh(Y − y) − pT sinh ρ cos(φ − ϕ )(A.14)For a local thermal distribution, The invariant cross section is
Z

ν
d3N
g
E 3 =
e−u pν /T pµ d σµ
3
dp
(2π )
·
¸
Z
∂t
g
∂t
=
rdrd φ dz mT cosh y − mT sinh y − pT cos(φ − ϕ )(2π )3∂z∂r³ m cosh ρ´
pT sinh ρT× exp −
cosh(Y − y) +cos(φ − ϕ )
T
T
· µ
¶
Z
Z
mT cosh ρg∂ t 1 2π pT sinh ρ cos(φ −ϕ )− Tcosh(Y −y)
=
rdrdz
e
m
cosh
y
−
sinh
y
e T
dφ
T
(2π )2∂ z 2π 0¸
Z
pT sinh ρ∂ t 1 2π
φ
−
ϕ
)
cos(
−pT
cos(φ − ϕ )e T
dφ
∂ r 2π 0ZmT cosh ρg=rdrdz e− T cosh(Y −y)
2
(2π )
· µ
¸
¶ ³
∂t
pT sinh ρ ´∂ t ³ pT sinh ρ ´× mT cosh y − sinh y
I0− pT I1(A.15)∂z
T∂r
T

Here the integration over φ is carried out by making use the modified Bessel functions
In (ζ ) defined in Eq. A.20.
The transverse mass spectrum is presented in terms of the invariant cross section:
d3N
d3N
1
d2N
=
,
E 3 =
dp
mT dmT dy d ϕ
2π mT dmT dy(A.16)

APPENDIX A. NUMERICAL SUPPLEMENT112

For the transverse mass spectrum, we integrate over ϕ and y. As for the latter, we assume that the detector system has full y acceptance and shift the integration variable y to
y −Y . Then the result is expressed by another modified Bessel functions Kn (ζ ) defined in
Eq. A.21.
gdN=
mTmT dmT
2π

Z

Z +∞mT cosh ρ

rdrdz
dye− T cosh y
−∞
·µ
¶ ³
¸
∂t
pT sinh ρ ´ pT ∂ t ³ pT sinh ρ ´× cosh(y −Y ) − sinh(y −Y )
I0
−
I1
∂z
T
mT ∂ r
T
·µ
¶ ³
Z
´
³
´
2g
∂t
mT cosh ρ
pT sinh ρ=
mT rdrdz coshY − sinhY
K1
I0
π
∂z
T
T
¸
³
´
³
pT ∂ tmT cosh ρ
pT sinh ρ ´−.
(A.17)K0
I1
mT ∂ rT
T

Here the integration over y is carried out by making use the modified Bessel functions of
the second kind Kn (ζ ) defined in Eq. A.21.

p
Lets us further parametrize the freeze-out hypersurface as t(r, z) = τ 2 (r) + z2 . Then,p
we have ∂∂ zt = z/ τ 2 (r) + z2 , ∂∂ rt = (d τ /dr)/ coshY . Knowing dz = τ coshY dY , we may
integrate over z to obtain
· ³
Z R
dN
2g
mT cosh ρ ´ ³ pT sinh ρ ´I0=
mTYmaxrdrτ (r) K1
mT dmT
π
T
T
0
¸
³
³
´
pT sinh ρ ´
mT cosh ρpT d τ
I1
−
K0
.
mT dr
T
T

(A.18)

If we further assume an instant freezer independent of r at τ = const, the second term inside
the bracket of Eq. A.18 vanishes. Then, we obtain following “blast-wave” formation.
dN∝
mT dmTZ R
0r dr mT I0³ p sinh ρ ´TT³ m cosh ρ ´
T
K1
.
T

(A.19)

modified Bessel finctionZ

1 2π
cos nφ exp(ζ cos φ )d φ ,
2π 0
Z
1 +∞
Kn (ζ ) =cosh ny exp(−ζ cosh y)dy.
2 −∞In (ζ ) =(A.20)(A.21)

Appendix B
Time-of-flight Detector
PHENIX has a capability for simultaneous measurement of many different probes such as hadrons, leptons and phonons. Since hadron productionin heavy ion collisions carries the basic information of the properties of thematter, it is important to measure identified hadrons in a wide range of pT .
In addition to single particle spectrum measurements, Hanbury-Brown-Twiss(HBT) correlation measurements and measurement of φ mesons through the
K + K − channel are also important to probe the hot and dense matter created in
Au + Au collisions at RHIC. For particle identification, time-of-flight (TOF)
measurements, where one compares the particle time of flight to the measured
momentum of the particle, are one of the most powerful methods for separating particle species. The TOF contains 960 scintillator slats oriented along ther − φ direction. It’s timing resolution was about 100 ps. In this chapter we
describe the basic design of the TOF counter, the specification of each component and the front end electronics module. Finally we present the performanceof the TOF detector using data taken in the first year of RHIC operation.

B.1

Detector Design

The PHENIX TOF system serves as a primary particle identification device for charged
hadrons in PHENIX. It is designed to have about 100 ps timing resolution in order toachieve clear particle separation in the high momentum region, i.e. π /K separation up to
2.4 GeV/c and K/proton separation up to 4.0 GeV/c.
The TOF detector is placed at a distance of 5.06 m from the collision vertex, in between

113

114

APPENDIX B. TIME-OF-FLIGHT DETECTOR

Figure B.1: The TOF detector system mounted on the PHENIX East Arm showing 10 panels of
the detector.

the Pad Chamber (PC3) and the EMCal in the east arm of PHENIX. It is designed to coverthe η range (70◦ ≤ θ ≤ 110◦ ) of the central detector over 45◦ in azimuthal angle. The TOF
detector consists of 10 panels of TOF walls. Figure B.1 shows a photo of the TOF detector
system mounted on the east central arm in the PHENIX experimental hall. All 10 panels of
the detector are seen. One TOF wall consists of 96 segments, each equipped with a plastic
scintillator slat and photomultiplier tubes which are read out at both ends.
The number of segments in the TOF system is determined by minimizing the probabilityof two or more particles hitting a single segment. For the TOF system design the double
hit probability is kept as low as possible. Assuming the charged particle rapidity density to
be dNch /dy = 1500, the charged particle multiplicity on the one TOF wall is expected toB.1. DETECTOR DESIGN

PMT
200 cmBleeder
Scintillator

50 cm

Carbon fiber sheetµ-metal

Aluminium frame

Light guide

Honeycomb structured paper

115

Figure B.2: Schematic diagram of the components of a single TOF panel which consists of 96
plastic scintillation counters with photomultiplier tubes at both ends, light guides and supports.

APPENDIX B. TIME-OF-FLIGHT DETECTOR

116

Scintilator

long slat

PMT

u-metalLucite64 cm

short slat

43cm

Figure B.3: Schematic diagram of the components of a plastic scintillation counters with photomultiplier tubes at both ends, light guides and supports.

be 9. In order to keep the occupancy below 10%, the segmentation is about 1000 and therequired area of each segment at a distance of 5.06 m away from the vertex is 100 cm2 .
A total 10 TOF panels, 960 slats of scintillators and 1920 channels of PMTs were
installed and operated at the first year of operation. The slat is oriented along the r − φdirection and provides time and longitudinal position information of particles that hit theslat. Figure B.2 shows a schematic view of one panel of the TOF detector. It consistsof 96 plastic scintillation counters with photomultiplier tubes (PMT’s) at both ends, lightguides and mechanical supports. Scintillator rod and light guides were wrapped with thinaluminum foil and were glued on the honeycomb board. The honeycomb boards are madeof paper of a honeycomb structure sandwiched between carbon fiber sheets, which provide
a “massless” rigid structure. Scintillators with two different lengths (637.7 and 433.9 mm)
are assembled in an alternating fashion in order to avoid geometrical conflicts between the
PMTs of neighboring slats. Each end of the scintillator slat is attached with optical glue
to a 180◦ bent light guide. On both sides of one panel, the light guides are bent 90◦ so
as not to conflict with the neighboring PMT’s. (Figure B.3 The scintillator slats are glued
on the honeycomb board which consists of carbon fiber sheet and honeycomb paper inorder to reduce the amount of material but also provide the wall with sufficient mechanicalstrength. The signal cables are RG58C/U and the high voltage cables are GXO3173-01.
The total radiation length including PMT’s and cables is about 6%. Using different lengthsof scintillator slats and adoption of bent light guides as described above has allowed us toachieve very small dead space between the TOF slats.

B.2. THE TOF SCINTILLATOR AND PHOTOMULTIPLIER TUBES

B.2

117

The TOF Scintillator and Photomultiplier Tubes

The plastic scintillator used in the TOF is Bicron BC404, 1.5 cm in width and 1.5 cm indepth. It has good timing characteristics with a moderate attenuation length. The physicalconstants of this scintillator are given in Table B.1.
Physical constant

Value

Light output (% anthracene)

68

Wavelength of maximum emission

408 nmDecay constant

1.8 ns

Bulk attenuation length

160 cmRefractive index (n)1.58

Table B.1: Characteristics of the BC404 Scintillator
The TOF system uses HAMAMATSU R3478S PMT’s. These tubes have a 0.75 inch
(19 mm) diameter window of borosilicate glass, an 8 stage linear-focussed dynode structure
and a bialkali photocathode. The length of the tube is about 6.7 cm. The relevant physicalconstants of this tube are given in Table B.2. The PMT’s are arranged along the direction
parallel to the scintillator bar. The magnetic field expected around the TOF system is lessthan 10 Gauss and its direction is perpendicular to the PMT. The requirement for the µ metal shielding is therefore not severe. We use a 0.5-mm thick, 7.0-cm long µ -metal shieldwith an internal diameter of 23 mm. The hit position in the vertical direction (along theslats) is derived from the time difference observed in the signals, read out at the two endsof the slat.
Physical constant

Value

Wavelength of maximum response

420 nmCurrent amplification∼ 106

Anode pulse rise time

1.3 nsElectron transit time

14 ns

Transit time spread

0.36 ns

High voltage supply−1800 Vdc

Table B.2: Characteristics of the HAMAMATSU R3478S PMT and photo.

APPENDIX B. TIME-OF-FLIGHT DETECTOR

118

B.3 Front End Electronics
The front-end electronics (FEE) of the TOF are designed to sample the PMT signals at thebunch crossing frequency (9.4 MHz) of RHIC and store them during the first level trigger
latency of 4.24 µ sec corresponding to 40 RHIC bunch crossings. The signal timing fromthe PMT is determined by a leading edge discriminator followed by a Time-to-Voltage
Converter (TVC). The charge information is converted to a voltage by a Charge-to-Voltage
Converter (QVC). The analog voltages from the TVC and the QVC are stored by a switchedcapacitor Analog Memory Unit (AMU) which stores the information during the latency andbuffers up to five accepted events. The stored voltages are digitized by a 12 bit 1.25 MHz
ADC. To eliminate the cross talk between adjacent channels there are two independent
readout channels. One is a signal channel and the other is a reference channel which serves
as an antenna for cross talk elimination. By taking the difference between the two channels,
there is now no crosstalk in the output. The block diagram of TOF-FEE architecture isshown in Figure B.4.
Read address

Write address
Tclk

Ch select

Convert

QVC + AMU

12 bit ADC

TVC + AMU

12 bit ADC

Ch 15

PMT

DISC
thresholdTclk

Ch select

Write address

Read address

ConvertCalibration pulse

Write ddress
Tclk

Read ddress
Ch select

DATA

CLK
Flag Bits

Heap Manager

Trigger
Write

Tclk

AMU Read

AMU Read

SMPL #

SMPL #

Cell #

Cell #ERR Flag

ERR Flag

Tclk

T
A Address
B
L
E

F
I
F
O

D M
U E
A M
L O
R
P Y
O
R
T

Page 2 k x 1 6

1st WD PAGE
WR
CTR
RD
EOR

Read address

Write address

SMPL SEQ

SMPL #Ch select

Write address

F C
OO
RN
MT
A R
T O
L

Read address
Ch select

Convert

QVC + AMU

12 bit ADC

TVC + AMU

12 bit ADC

Ch 0

PMT

DISC
thresholdTclk

Ch select

Write address

Read address

ConvertCalibration pulse

Figure B.4: The block diagram of TOF front-end electronics module.

B.3. FRONT END ELECTRONICS

119

Figure B.5 shows the time and charge measurement principle of TOF-FEE system in
PHENIX. The value of the timing signal measured by TVC (Tmea ) is the timing difference
between the discriminator’s output and next beam clock.
Tmea = (Tclk + 106ns) − TT OF(B.1)

The TVC takes 3 clock cycle (charge up, sampling reset) per valid hits. After sampling,
the TVC is discharged immediately. The charge is measured by the difference of the QVC
value before and after integration,
Charge = Q post − Q pre .

(B.2)

The QVC takes each clock cycles. The QVC is reset regularly with external NIM pulse.

Beam Clock

0

Tclk
1

T clk + 106 ns
2

4

3

TOF PMT
thresholdTmea,TOF
TOF DISC

TTOF
holdcharging

X

reset

TOF TVC
Q-pre

Q-postTmea,TOF

AMU WriteX

TOF QVCX

Figure B.5: Time and charge measurement principle. The timing measured by the TVC is thedifference between the discriminator’s output and next beam clock. The charge is measured bydifference of QVC value before (Q-pre) and after integration (Q-post).

APPENDIX B. TIME-OF-FLIGHT DETECTOR

120

B.4 TOF Detector Performance
Particle identification for charged hadrons is performed by combining the information fromthe DC, PC1, BBC and the TOF. The designed time-of-flight resolution is about 100 psec.
This allows us to achieve a PID capability for high momentum particles, a 4σ π /K separation at momenta up to 2.4 GeV/c and a K/p separation up to 4.0 GeV/c. Figure B.6
illustrates the particle separation capabilities of the TOF system. A track is reconstructedfrom hits in the DC and PC1 that point to the TOF detector. In this reconstruction we use
a window for TOF association adjusted so that the residuals between the projection point
and the reconstructed TOF hit position is within 2.5 standard deviations. The flight-path
length of the track from the event vertex to the TOF detector as calculated by the momentum reconstruction algorithm is used to correct the time-of-flight value measured by the
TOF detector.

-1charge/Momentum [(GeV/c) ]PHENIX High Resolution TOF

π+

6

Au+Au s = 200 A GeV

K+

4

3

10

p
2

10

2

d
0

d

10

-2
−

p

K

-4

1

π−

-6
10

15

20

25

30

35

40 45 50 55 60
Time of Flight [ns]Figure B.6: Contour plot of the time-of-flight versus reciprocal momentum in minimum bias
Au+Au collisions at the energy of√sNN = 200 GeV. The figure clearly demonstrates the particle

identification capability using the TOF detector in the year 2001 data taking period.

B.4. TOF DETECTOR PERFORMANCE

121

Figure B.7 shows the time-of-flight resolution for various particles. For this example amomentum range of 1.4 < pT < 1.8 GeV/c for π + was used. The resulting time-of-flight
resolution was σ = 96 ps. Figure B.8 shows the mass-squared distribution for positive (top)and negative (bottom) charged particles integrated over all momenta. The vertical axes inthese figures are in arbitrary units. The figure demonstrates that clear particle identification
using the TOF was achieved in the first year of RHIC running. The timing resolution given
above for the complete TOF system is achieved after slewing effect corrections and runby-run timing offset calibrations are made.

π60

1.4< p <1.8GeV/c5040

σ ~ 96ps

30
20

p

K

10
0

-1

0

1

2

3
4
TOF - L/c(beta) [ns]Figure B.7: The time-of-flight resolution in the transverse momentum range 1.4 < pT <1.8 GeV/c
for positively charged pions. The overall time-of-flight resolution of 96 psec is achieved.

APPENDIX B. TIME-OF-FLIGHT DETECTOR

122

mass2_p

Squared Mass vs p

Nent = 54875
Mean = 0.1315(a.u.)

RMS = 0.27

10

10

4

Positive

π+

3

K
10

+

Proton

2

10

1
-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4
2 2

Mass squared [(GeV/c ) ]mass2_m

Squared Mass vs p

Nent = 37422(a.u.)

Mean = 0.1136

10

RMS = 0.2449

4

Negative

π−
10

10

3

K

2

-

p

10

1

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4
2 2

Mass squared [(GeV/c ) ]Figure B.8: Mass squared distribution for positive particles (top) and negative particles (bottom)
without a momentum cutoff including all momenta. Going from left to right clear peaks for pions,
kaons and protons can be seen in each panel.

B.4. TOF DETECTOR PERFORMANCETOF construction pictures

Figure B.9: Construction at Tsukuba. [1996–1997]

123

124

APPENDIX B. TIME-OF-FLIGHT DETECTOR

Figure B.10: Construction at BNL. [1998–1999]

B.4. TOF DETECTOR PERFORMANCE

Figure B.11: Installed on PHENIX east central arm. August, 1999

125

Appendix C
Data Tables
C.1

pT Spectra Data Tables

The invariant yields for π ± , K ± , p and p in Au+Au collisions at√
sNN = 200 GeV at

mid-rapidity are tabulated in Tables C.1 – C.20. The data presented here are for the theminimum bias events and each centrality bin (0–5%, 5–10%, 10–15%, 15–20%, 20–30%,..., 70–80%, 80–92%, and 60–92%). Errors are statistical only.

126C.1. PT SPECTRA DATA TABLES

127

Table C.1: Invariant yields for π + at mid-rapidity in the minimum bias, 0–5%, 5–10%, and10–15% centrality bins, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.05
2.15
2.25
2.35
2.45
2.55
2.65
2.75
2.85
2.95

Minimum bias
1.07e+02 ± 8.8e-01
6.06e+01 ± 5.0e-01
3.63e+01 ± 3.1e-01
2.18e+01 ± 2.0e-01
1.34e+01 ± 1.3e-01
8.71e+00 ± 9.5e-02
5.41e+00 ± 6.3e-02
3.59e+00 ± 4.5e-02
2.35e+00 ± 3.1e-02
1.58e+00 ± 2.2e-02
1.05e+00 ± 1.5e-02
7.59e-01 ± 1.2e-02
5.16e-01 ± 8.3e-03
3.37e-01 ± 5.6e-03
2.44e-01 ± 4.2e-03
1.77e-01 ± 3.3e-03
1.27e-01 ± 2.4e-03
9.01e-02 ± 1.9e-03
6.68e-02 ± 1.2e-03
4.71e-02 ± 8.9e-04
3.27e-02 ± 6.8e-04
2.60e-02 ± 6.2e-04
1.94e-02 ± 5.3e-04
1.49e-02 ± 4.7e-04
1.13e-02 ± 4.2e-04
9.30e-03 ± 4.0e-04
6.20e-03 ± 3.2e-04
5.17e-03 ± 3.1e-04

0–5%
3.29e+02 ± 2.7e+00
1.97e+02 ± 1.6e+00
1.20e+02 ± 1.1e+00
7.26e+01 ± 6.7e-01
4.49e+01 ± 4.5e-01
2.93e+01 ± 3.3e-01
1.82e+01 ± 2.2e-01
1.21e+01 ± 1.6e-01
7.96e+00 ± 1.1e-01
5.32e+00 ± 8.0e-02
3.55e+00 ± 5.7e-02
2.55e+00 ± 4.5e-02
1.72e+00 ± 3.3e-02
1.13e+00 ± 2.3e-02
8.05e-01 ± 1.8e-02
5.70e-01 ± 1.4e-02
4.18e-01 ± 1.2e-02
2.80e-01 ± 9.0e-03
2.09e-01 ± 6.1e-03
1.36e-01 ± 4.8e-03
9.10e-02 ± 3.8e-03
7.20e-02 ± 3.6e-03
5.40e-02 ± 3.2e-03
3.78e-02 ± 2.8e-03
2.65e-02 ± 2.5e-03
2.27e-02 ± 2.5e-03
1.28e-02 ± 1.9e-03
1.03e-02 ± 1.8e-03

5–10%
2.76e+02 ± 2.3e+00
1.64e+02 ± 1.4e+00
9.93e+01 ± 8.7e-01
6.02e+01 ± 5.6e-01
3.74e+01 ± 3.8e-01
2.43e+01 ± 2.7e-01
1.53e+01 ± 1.8e-01
1.01e+01 ± 1.3e-01
6.56e+00 ± 9.3e-02
4.47e+00 ± 6.8e-02
2.99e+00 ± 4.9e-02
2.15e+00 ± 3.9e-02
1.45e+00 ± 2.8e-02
9.36e-01 ± 2.0e-02
6.68e-01 ± 1.6e-02
4.84e-01 ± 1.3e-02
3.42e-01 ± 1.0e-02
2.50e-01 ± 8.3e-03
1.82e-01 ± 5.6e-03
1.27e-01 ± 4.6e-03
8.06e-02 ± 3.5e-03
6.28e-02 ± 3.3e-03
4.57e-02 ± 2.9e-03
3.59e-02 ± 2.7e-03
2.50e-02 ± 2.4e-03
2.19e-02 ± 2.4e-03
1.21e-02 ± 1.8e-03
1.08e-02 ± 1.8e-03

10–15%
2.39e+02 ± 2.0e+00
1.39e+02 ± 1.2e+00
8.41e+01 ± 7.4e-01
5.08e+01 ± 4.7e-01
3.16e+01 ± 3.2e-01
2.05e+01 ± 2.3e-01
1.29e+01 ± 1.6e-01
8.56e+00 ± 1.1e-01
5.56e+00 ± 8.0e-02
3.72e+00 ± 5.7e-02
2.51e+00 ± 4.2e-02
1.81e+00 ± 3.3e-02
1.23e+00 ± 2.5e-02
7.93e-01 ± 1.7e-02
5.78e-01 ± 1.4e-02
4.19e-01 ± 1.1e-02
2.99e-01 ± 9.1e-03
2.07e-01 ± 7.3e-03
1.56e-01 ± 5.0e-03
1.05e-01 ± 4.1e-03
8.05e-02 ± 3.5e-03
5.78e-02 ± 3.1e-03
4.06e-02 ± 2.7e-03
3.18e-02 ± 2.5e-03
2.44e-02 ± 2.3e-03
1.83e-02 ± 2.1e-03
1.30e-02 ± 1.8e-03
1.04e-02 ± 1.8e-03

APPENDIX C. DATA TABLES

128

Table C.2: Invariant yields for π + at mid-rapidity in 15–20%, 20–30%, 30–40%, and 4050% centrality bins, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.05
2.15
2.25
2.35
2.45
2.55
2.65
2.75
2.85
2.95

15–20%
2.04e+02 ± 1.7e+00
1.18e+02 ± 9.9e-01
7.09e+01 ± 6.2e-01
4.28e+01 ± 4.0e-01
2.65e+01 ± 2.7e-01
1.73e+01 ± 2.0e-01
1.07e+01 ± 1.3e-01
7.12e+00 ± 9.6e-02
4.77e+00 ± 6.9e-02
3.16e+00 ± 5.0e-02
2.10e+00 ± 3.6e-02
1.52e+00 ± 2.9e-02
1.05e+00 ± 2.2e-02
6.78e-01 ± 1.5e-02
4.93e-01 ± 1.2e-02
3.60e-01 ± 1.0e-02
2.56e-01 ± 8.2e-03
1.78e-01 ± 6.6e-03
1.35e-01 ± 4.6e-03
1.02e-01 ± 4.0e-03
6.65e-02 ± 3.1e-03
5.43e-02 ± 3.0e-03
3.97e-02 ± 2.6e-03
2.88e-02 ± 2.4e-03
2.21e-02 ± 2.2e-03
1.58e-02 ± 2.0e-03
1.37e-02 ± 1.9e-03
1.08e-02 ± 1.8e-03

20–30%
1.57e+02 ± 1.3e+00
8.82e+01 ± 7.4e-01
5.27e+01 ± 4.6e-01
3.17e+01 ± 2.9e-01
1.95e+01 ± 2.0e-01
1.27e+01 ± 1.4e-01
7.94e+00 ± 9.5e-02
5.31e+00 ± 7.0e-02
3.49e+00 ± 4.9e-02
2.34e+00 ± 3.5e-02
1.56e+00 ± 2.5e-02
1.12e+00 ± 2.0e-02
7.57e-01 ± 1.5e-02
5.07e-01 ± 1.0e-02
3.67e-01 ± 8.3e-03
2.67e-01 ± 6.7e-03
1.92e-01 ± 5.3e-03
1.38e-01 ± 4.3e-03
1.00e-01 ± 2.9e-03
7.41e-02 ± 2.4e-03
5.16e-02 ± 2.0e-03
4.12e-02 ± 1.9e-03
3.28e-02 ± 1.7e-03
2.41e-02 ± 1.5e-03
1.85e-02 ± 1.4e-03
1.55e-02 ± 1.4e-03
1.03e-02 ± 1.1e-03
9.32e-03 ± 1.2e-03

30–40%
1.07e+02 ± 8.9e-01
5.86e+01 ± 4.9e-01
3.46e+01 ± 3.0e-01
2.06e+01 ± 1.9e-01
1.26e+01 ± 1.3e-01
8.29e+00 ± 9.4e-02
5.10e+00 ± 6.3e-02
3.38e+00 ± 4.6e-02
2.22e+00 ± 3.2e-02
1.50e+00 ± 2.4e-02
9.99e-01 ± 1.7e-02
7.17e-01 ± 1.4e-02
4.98e-01 ± 1.0e-02
3.24e-01 ± 7.4e-03
2.31e-01 ± 5.9e-03
1.69e-01 ± 4.9e-03
1.22e-01 ± 3.9e-03
8.80e-02 ± 3.3e-03
6.67e-02 ± 2.3e-03
4.90e-02 ± 1.9e-03
3.58e-02 ± 1.6e-03
2.84e-02 ± 1.5e-03
2.27e-02 ± 1.4e-03
1.70e-02 ± 1.3e-03
1.40e-02 ± 1.2e-03
1.20e-02 ± 1.2e-03
7.69e-03 ± 9.7e-04
6.39e-03 ± 9.6e-04

40–50%
6.84e+01 ± 5.7e-01
3.67e+01 ± 3.1e-01
2.15e+01 ± 1.9e-01
1.26e+01 ± 1.2e-01
7.66e+00 ± 8.0e-02
4.99e+00 ± 5.8e-02
3.04e+00 ± 3.9e-02
2.02e+00 ± 2.9e-02
1.30e+00 ± 2.0e-02
8.78e-01 ± 1.5e-02
5.98e-01 ± 1.1e-02
4.26e-01 ± 9.0e-03
2.91e-01 ± 6.9e-03
1.97e-01 ± 5.2e-03
1.42e-01 ± 4.2e-03
1.03e-01 ± 3.5e-03
7.29e-02 ± 2.8e-03
5.80e-02 ± 2.5e-03
4.13e-02 ± 1.7e-03
2.92e-02 ± 1.4e-03
2.09e-02 ± 1.2e-03
1.87e-02 ± 1.2e-03
1.21e-02 ± 9.8e-04
1.11e-02 ± 1.0e-03
8.92e-03 ± 9.5e-04
7.80e-03 ± 9.5e-04
5.80e-03 ± 8.3e-04
4.49e-03 ± 7.9e-04

C.1. PT SPECTRA DATA TABLES

129

Table C.3: Invariant yields for π + at mid-rapidity in 50–60%, 60–70%, 70–80%, and 8092% centrality bins, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.05
2.15
2.25
2.35
2.45
2.55
2.65
2.75
2.85
2.95

50–60%
4.10e+01 ± 3.4e-01
2.17e+01 ± 1.9e-01
1.24e+01 ± 1.1e-01
7.20e+00 ± 7.0e-02
4.33e+00 ± 4.7e-02
2.78e+00 ± 3.4e-02
1.67e+00 ± 2.3e-02
1.11e+00 ± 1.7e-02
7.11e-01 ± 1.2e-02
4.71e-01 ± 9.2e-03
3.14e-01 ± 6.9e-03
2.31e-01 ± 5.8e-03
1.59e-01 ± 4.6e-03
1.02e-01 ± 3.4e-03
7.47e-02 ± 2.8e-03
5.60e-02 ± 2.4e-03
3.80e-02 ± 2.0e-03
2.86e-02 ± 1.7e-03
2.26e-02 ± 1.2e-03
1.60e-02 ± 1.0e-03
1.13e-02 ± 8.6e-04
9.73e-03 ± 8.5e-04
7.73e-03 ± 7.8e-04
5.77e-03 ± 7.2e-04
4.48e-03 ± 6.7e-04
3.84e-03 ± 6.7e-04
2.30e-03 ± 5.2e-04
2.16e-03 ± 5.5e-04

60–70%
2.19e+01 ± 1.9e-01
1.13e+01 ± 1.0e-01
6.37e+00 ± 6.0e-02
3.65e+00 ± 3.8e-02
2.18e+00 ± 2.6e-02
1.36e+00 ± 1.9e-02
8.36e-01 ± 1.3e-02
5.29e-01 ± 9.6e-03
3.51e-01 ± 7.3e-03
2.21e-01 ± 5.4e-03
1.51e-01 ± 4.3e-03
1.10e-01 ± 3.6e-03
7.17e-02 ± 2.8e-03
4.72e-02 ± 2.2e-03
3.50e-02 ± 1.8e-03
2.63e-02 ± 1.6e-03
1.92e-02 ± 1.3e-03
1.41e-02 ± 1.2e-03
1.12e-02 ± 8.4e-04
6.73e-03 ± 6.6e-04
5.46e-03 ± 5.9e-04
4.42e-03 ± 5.7e-04
3.27e-03 ± 5.0e-04
3.38e-03 ± 5.5e-04
2.82e-03 ± 5.2e-04
1.72e-03 ± 4.4e-04
1.35e-03 ± 4.0e-04
1.16e-03 ± 4.0e-04

70–80%
1.03e+01 ± 9.2e-02
5.27e+00 ± 5.0e-02
2.95e+00 ± 3.1e-02
1.62e+00 ± 1.9e-02
9.63e-01 ± 1.3e-02
5.91e-01 ± 9.9e-03
3.53e-01 ± 7.1e-03
2.22e-01 ± 5.4e-03
1.41e-01 ± 4.1e-03
1.01e-01 ± 3.4e-03
6.06e-02 ± 2.5e-03
4.25e-02 ± 2.1e-03
3.04e-02 ± 1.8e-03
1.89e-02 ± 1.3e-03
1.52e-02 ± 1.2e-03
1.03e-02 ± 1.0e-03
8.04e-03 ± 8.7e-04
6.06e-03 ± 7.6e-04
4.34e-03 ± 5.3e-04
3.09e-03 ± 4.5e-04
2.43e-03 ± 4.0e-04
1.98e-03 ± 3.9e-04
1.30e-03 ± 3.2e-04
1.17e-03 ± 3.3e-04
5.70e-04 ± 2.4e-04
8.51e-04 ± 3.2e-04
6.79e-04 ± 2.9e-04
2.88e-04 ± 2.0e-04

80–92%
5.20e+00 ± 5.0e-02
2.75e+00 ± 2.8e-02
1.49e+00 ± 1.8e-02
8.20e-01 ± 1.1e-02
4.72e-01 ± 8.1e-03
2.69e-01 ± 5.9e-03
1.63e-01 ± 4.4e-03
1.02e-01 ± 3.4e-03
6.51e-02 ± 2.6e-03
4.48e-02 ± 2.2e-03
2.63e-02 ± 1.6e-03
2.07e-02 ± 1.5e-03
1.30e-02 ± 1.1e-03
8.48e-03 ± 8.8e-04
7.00e-03 ± 8.1e-04
5.37e-03 ± 7.1e-04
3.87e-03 ± 6.0e-04
2.26e-03 ± 4.6e-04
1.56e-03 ± 3.1e-04
1.23e-03 ± 2.8e-04
8.48e-04 ± 2.3e-04
8.16e-04 ± 2.5e-04
3.19e-04 ± 1.6e-04
5.92e-04 ± 2.3e-04
3.37e-04 ± 1.8e-04
4.22e-04 ± 2.2e-04
1.65e-04 ± 1.4e-04
1.90e-04 ± 1.6e-04

APPENDIX C. DATA TABLES

130

Table C.4: Invariant yields for π − at mid-rapidity in the minimum bias, 0–5%, 5–10%, and10–15% centrality bins, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.05
2.15
2.25
2.35
2.45
2.55
2.65
2.75
2.85
2.95

Minimum bias
1.02e+02 ± 7.9e-01
5.92e+01 ± 4.6e-01
3.56e+01 ± 2.9e-01
2.18e+01 ± 1.9e-01
1.34e+01 ± 1.2e-01
8.36e+00 ± 8.2e-02
5.44e+00 ± 5.7e-02
3.58e+00 ± 4.1e-02
2.35e+00 ± 2.8e-02
1.62e+00 ± 2.1e-02
1.04e+00 ± 1.4e-02
7.54e-01 ± 1.1e-02
5.07e-01 ± 7.6e-03
3.61e-01 ± 5.7e-03
2.46e-01 ± 4.0e-03
1.73e-01 ± 3.0e-03
1.25e-01 ± 2.3e-03
8.97e-02 ± 1.8e-03
6.10e-02 ± 1.1e-03
4.43e-02 ± 8.7e-04
3.20e-02 ± 7.0e-04
2.52e-02 ± 6.3e-04
1.79e-02 ± 5.1e-04
1.41e-02 ± 4.8e-04
1.06e-02 ± 4.1e-04
8.05e-03 ± 3.7e-04
6.45e-03 ± 3.5e-04
4.95e-03 ± 3.2e-04

0–5%
3.15e+02 ± 2.4e+00
1.94e+02 ± 1.5e+00
1.19e+02 ± 9.8e-01
7.37e+01 ± 6.5e-01
4.57e+01 ± 4.3e-01
2.86e+01 ± 2.9e-01
1.86e+01 ± 2.0e-01
1.22e+01 ± 1.4e-01
8.02e+00 ± 1.0e-01
5.55e+00 ± 7.7e-02
3.53e+00 ± 5.2e-02
2.55e+00 ± 4.1e-02
1.71e+00 ± 3.0e-02
1.20e+00 ± 2.3e-02
8.02e-01 ± 1.7e-02
5.65e-01 ± 1.3e-02
4.05e-01 ± 1.1e-02
2.85e-01 ± 8.8e-03
1.89e-01 ± 5.8e-03
1.32e-01 ± 4.8e-03
9.24e-02 ± 4.0e-03
7.07e-02 ± 3.7e-03
4.71e-02 ± 3.0e-03
3.50e-02 ± 2.8e-03
2.69e-02 ± 2.5e-03
1.99e-02 ± 2.3e-03
1.45e-02 ± 2.1e-03
1.08e-02 ± 1.9e-03

5–10%
2.71e+02 ± 2.1e+00
1.64e+02 ± 1.3e+00
9.93e+01 ± 8.2e-01
6.17e+01 ± 5.4e-01
3.82e+01 ± 3.6e-01
2.40e+01 ± 2.4e-01
1.56e+01 ± 1.7e-01
1.02e+01 ± 1.2e-01
6.75e+00 ± 8.7e-02
4.64e+00 ± 6.5e-02
2.94e+00 ± 4.4e-02
2.19e+00 ± 3.6e-02
1.48e+00 ± 2.7e-02
1.02e+00 ± 2.0e-02
6.94e-01 ± 1.5e-02
4.91e-01 ± 1.2e-02
3.48e-01 ± 9.6e-03
2.53e-01 ± 8.1e-03
1.64e-01 ± 5.4e-03
1.20e-01 ± 4.5e-03
8.31e-02 ± 3.8e-03
6.29e-02 ± 3.5e-03
4.47e-02 ± 2.9e-03
3.33e-02 ± 2.7e-03
2.36e-02 ± 2.3e-03
1.67e-02 ± 2.1e-03
1.63e-02 ± 2.2e-03
1.16e-02 ± 2.0e-03

10–15%
2.27e+02 ± 1.8e+00
1.35e+02 ± 1.1e+00
8.18e+01 ± 6.8e-01
5.04e+01 ± 4.5e-01
3.15e+01 ± 3.0e-01
1.96e+01 ± 2.0e-01
1.28e+01 ± 1.4e-01
8.47e+00 ± 1.0e-01
5.57e+00 ± 7.2e-02
3.83e+00 ± 5.5e-02
2.46e+00 ± 3.8e-02
1.80e+00 ± 3.0e-02
1.22e+00 ± 2.2e-02
8.63e-01 ± 1.8e-02
5.86e-01 ± 1.3e-02
4.10e-01 ± 1.0e-02
3.00e-01 ± 8.5e-03
2.12e-01 ± 7.1e-03
1.42e-01 ± 4.8e-03
1.01e-01 ± 4.0e-03
7.21e-02 ± 3.4e-03
5.95e-02 ± 3.3e-03
3.97e-02 ± 2.7e-03
3.28e-02 ± 2.7e-03
2.22e-02 ± 2.2e-03
1.61e-02 ± 2.0e-03
1.21e-02 ± 1.9e-03
1.03e-02 ± 1.8e-03

C.1. PT SPECTRA DATA TABLES

131

Table C.5: Invariant yields for π − at mid-rapidity in 15–20%, 20–30%, 30–40%, and 4050% centrality bins, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.05
2.15
2.25
2.35
2.45
2.55
2.65
2.75
2.85
2.95

15–20%
1.95e+02 ± 1.5e+00
1.13e+02 ± 9.0e-01
6.86e+01 ± 5.7e-01
4.22e+01 ± 3.7e-01
2.61e+01 ± 2.5e-01
1.63e+01 ± 1.7e-01
1.06e+01 ± 1.2e-01
7.01e+00 ± 8.6e-02
4.68e+00 ± 6.2e-02
3.19e+00 ± 4.6e-02
2.05e+00 ± 3.2e-02
1.49e+00 ± 2.6e-02
9.90e-01 ± 1.9e-02
7.11e-01 ± 1.5e-02
4.85e-01 ± 1.2e-02
3.43e-01 ± 9.2e-03
2.38e-01 ± 7.3e-03
1.74e-01 ± 6.2e-03
1.16e-01 ± 4.2e-03
8.98e-02 ± 3.7e-03
6.55e-02 ± 3.2e-03
5.02e-02 ± 2.9e-03
3.62e-02 ± 2.5e-03
2.55e-02 ± 2.3e-03
2.01e-02 ± 2.1e-03
1.57e-02 ± 1.9e-03
1.30e-02 ± 1.9e-03
9.44e-03 ± 1.7e-03

20–30%
1.51e+02 ± 1.2e+00
8.62e+01 ± 6.8e-01
5.18e+01 ± 4.3e-01
3.17e+01 ± 2.8e-01
1.95e+01 ± 1.8e-01
1.22e+01 ± 1.2e-01
7.96e+00 ± 8.7e-02
5.31e+00 ± 6.3e-02
3.45e+00 ± 4.4e-02
2.36e+00 ± 3.3e-02
1.55e+00 ± 2.3e-02
1.10e+00 ± 1.8e-02
7.55e-01 ± 1.3e-02
5.41e-01 ± 1.1e-02
3.71e-01 ± 7.9e-03
2.56e-01 ± 6.1e-03
1.93e-01 ± 5.0e-03
1.36e-01 ± 4.1e-03
9.65e-02 ± 2.9e-03
6.97e-02 ± 2.4e-03
5.15e-02 ± 2.1e-03
3.83e-02 ± 1.9e-03
2.84e-02 ± 1.6e-03
2.37e-02 ± 1.6e-03
1.68e-02 ± 1.4e-03
1.35e-02 ± 1.3e-03
1.03e-02 ± 1.2e-03
8.45e-03 ± 1.2e-03

30–40%
1.02e+02 ± 7.9e-01
5.68e+01 ± 4.5e-01
3.36e+01 ± 2.8e-01
2.04e+01 ± 1.8e-01
1.26e+01 ± 1.2e-01
7.81e+00 ± 8.0e-02
5.06e+00 ± 5.7e-02
3.37e+00 ± 4.1e-02
2.18e+00 ± 2.9e-02
1.52e+00 ± 2.2e-02
9.75e-01 ± 1.5e-02
7.11e-01 ± 1.2e-02
4.76e-01 ± 9.2e-03
3.42e-01 ± 7.4e-03
2.37e-01 ± 5.7e-03
1.68e-01 ± 4.5e-03
1.20e-01 ± 3.7e-03
8.73e-02 ± 3.1e-03
6.46e-02 ± 2.2e-03
4.55e-02 ± 1.9e-03
3.60e-02 ± 1.7e-03
2.83e-02 ± 1.6e-03
1.94e-02 ± 1.3e-03
1.57e-02 ± 1.3e-03
1.30e-02 ± 1.2e-03
1.06e-02 ± 1.1e-03
8.61e-03 ± 1.1e-03
6.16e-03 ± 9.8e-04

40–50%
6.53e+01 ± 5.1e-01
3.56e+01 ± 2.8e-01
2.08e+01 ± 1.7e-01
1.24e+01 ± 1.1e-01
7.57e+00 ± 7.4e-02
4.67e+00 ± 4.9e-02
3.04e+00 ± 3.5e-02
1.99e+00 ± 2.6e-02
1.30e+00 ± 1.8e-02
8.96e-01 ± 1.4e-02
5.68e-01 ± 9.8e-03
4.18e-01 ± 8.2e-03
2.75e-01 ± 6.1e-03
2.01e-01 ± 5.0e-03
1.40e-01 ± 3.9e-03
9.60e-02 ± 3.1e-03
7.36e-02 ± 2.7e-03
5.34e-02 ± 2.3e-03
3.64e-02 ± 1.6e-03
2.72e-02 ± 1.4e-03
1.95e-02 ± 1.2e-03
1.76e-02 ± 1.2e-03
1.33e-02 ± 1.0e-03
1.06e-02 ± 1.0e-03
8.20e-03 ± 9.1e-04
6.35e-03 ± 8.5e-04
5.10e-03 ± 8.3e-04
3.72e-03 ± 7.5e-04

APPENDIX C. DATA TABLES

132

Table C.6: Invariant yields for π − at mid-rapidity in 50–60%, 60–70%, 70–80%, and 8092% centrality bins, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.05
2.15
2.25
2.35
2.45
2.55
2.65
2.75
2.85
2.95

50–60%
3.92e+01 ± 3.1e-01
2.10e+01 ± 1.7e-01
1.21e+01 ± 1.0e-01
7.13e+00 ± 6.6e-02
4.30e+00 ± 4.4e-02
2.61e+00 ± 2.9e-02
1.68e+00 ± 2.1e-02
1.10e+00 ± 1.5e-02
7.13e-01 ± 1.1e-02
4.88e-01 ± 8.8e-03
3.12e-01 ± 6.3e-03
2.29e-01 ± 5.3e-03
1.51e-01 ± 4.1e-03
1.10e-01 ± 3.4e-03
7.11e-02 ± 2.6e-03
5.38e-02 ± 2.2e-03
4.00e-02 ± 1.9e-03
2.88e-02 ± 1.6e-03
2.04e-02 ± 1.2e-03
1.53e-02 ± 1.0e-03
1.08e-02 ± 8.8e-04
8.95e-03 ± 8.4e-04
7.17e-03 ± 7.6e-04
5.72e-03 ± 7.5e-04
4.94e-03 ± 7.1e-04
3.43e-03 ± 6.3e-04
2.67e-03 ± 6.0e-04
1.73e-03 ± 5.1e-04

60–70%
2.07e+01 ± 1.7e-01
1.09e+01 ± 9.0e-02
6.21e+00 ± 5.5e-02
3.59e+00 ± 3.5e-02
2.16e+00 ± 2.4e-02
1.30e+00 ± 1.6e-02
8.30e-01 ± 1.2e-02
5.26e-01 ± 8.7e-03
3.45e-01 ± 6.6e-03
2.32e-01 ± 5.2e-03
1.47e-01 ± 3.8e-03
1.05e-01 ± 3.2e-03
7.32e-02 ± 2.6e-03
5.15e-02 ± 2.2e-03
3.83e-02 ± 1.8e-03
2.51e-02 ± 1.4e-03
1.87e-02 ± 1.2e-03
1.30e-02 ± 1.1e-03
8.63e-03 ± 7.4e-04
6.88e-03 ± 6.7e-04
4.71e-03 ± 5.7e-04
4.42e-03 ± 5.8e-04
3.04e-03 ± 4.9e-04
2.96e-03 ± 5.3e-04
2.21e-03 ± 4.7e-04
1.54e-03 ± 4.2e-04
1.24e-03 ± 4.1e-04
1.25e-03 ± 4.3e-04

70–80%
9.77e+00 ± 8.2e-02
5.19e+00 ± 4.6e-02
2.84e+00 ± 2.8e-02
1.62e+00 ± 1.8e-02
9.32e-01 ± 1.2e-02
5.61e-01 ± 8.6e-03
3.52e-01 ± 6.4e-03
2.27e-01 ± 5.0e-03
1.41e-01 ± 3.8e-03
9.75e-02 ± 3.1e-03
6.31e-02 ± 2.4e-03
4.17e-02 ± 1.9e-03
2.81e-02 ± 1.6e-03
2.11e-02 ± 1.4e-03
1.53e-02 ± 1.1e-03
1.08e-02 ± 9.5e-04
8.06e-03 ± 8.2e-04
6.03e-03 ± 7.3e-04
4.23e-03 ± 5.3e-04
3.17e-03 ± 4.6e-04
1.89e-03 ± 3.7e-04
1.96e-03 ± 4.0e-04
1.17e-03 ± 3.1e-04
1.16e-03 ± 3.4e-04
8.05e-04 ± 2.9e-04
3.78e-04 ± 2.1e-04
2.87e-04 ± 2.0e-04
6.75e-04 ± 3.2e-04

80–92%
5.03e+00 ± 4.5e-02
2.67e+00 ± 2.6e-02
1.45e+00 ± 1.6e-02
8.13e-01 ± 1.1e-02
4.54e-01 ± 7.3e-03
2.70e-01 ± 5.3e-03
1.59e-01 ± 3.9e-03
1.07e-01 ± 3.2e-03
6.63e-02 ± 2.4e-03
4.46e-02 ± 2.0e-03
2.65e-02 ± 1.5e-03
2.02e-02 ± 1.3e-03
1.28e-02 ± 1.0e-03
9.27e-03 ± 8.8e-04
6.56e-03 ± 7.3e-04
5.14e-03 ± 6.5e-04
3.51e-03 ± 5.3e-04
2.70e-03 ± 4.8e-04
1.40e-03 ± 3.0e-04
1.25e-03 ± 2.9e-04
8.66e-04 ± 2.5e-04
6.65e-04 ± 2.3e-04
5.61e-04 ± 2.1e-04
3.79e-04 ± 1.9e-04
4.14e-04 ± 2.0e-04
3.34e-04 ± 2.0e-04
2.85e-04 ± 2.0e-04
2.04e-04 ± 1.8e-04

C.1. PT SPECTRA DATA TABLES

133

Table C.7: Invariant yields for K + at mid-rapidity in the minimum bias, 0–5%, 5–10%, and10–15% centrality bins, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95

Minimum bias
5.46e+00 ± 1.1e-01
4.28e+00 ± 7.8e-02
3.11e+00 ± 5.4e-02
2.27e+00 ± 3.9e-02
1.69e+00 ± 3.0e-02
1.20e+00 ± 2.2e-02
9.06e-01 ± 1.7e-02
6.57e-01 ± 1.3e-02
4.55e-01 ± 8.9e-03
3.24e-01 ± 6.5e-03
2.43e-01 ± 5.1e-03
1.76e-01 ± 3.8e-03
1.27e-01 ± 2.9e-03
9.47e-02 ± 2.3e-03
7.24e-02 ± 1.8e-03
5.67e-02 ± 1.5e-03

0–5%
1.83e+01 ± 3.9e-01
1.48e+01 ± 2.9e-01
1.05e+01 ± 2.0e-01
7.97e+00 ± 1.5e-01
5.96e+00 ± 1.2e-01
4.19e+00 ± 8.5e-02
3.20e+00 ± 6.8e-02
2.31e+00 ± 5.2e-02
1.64e+00 ± 3.9e-02
1.13e+00 ± 2.9e-02
8.52e-01 ± 2.4e-02
6.03e-01 ± 1.8e-02
4.43e-01 ± 1.5e-02
3.61e-01 ± 1.3e-02
2.64e-01 ± 1.0e-02
2.12e-01 ± 9.1e-03

5–10%
1.50e+01 ± 3.3e-01
1.20e+01 ± 2.4e-01
8.75e+00 ± 1.7e-01
6.48e+00 ± 1.2e-01
4.81e+00 ± 9.5e-02
3.47e+00 ± 7.2e-02
2.61e+00 ± 5.7e-02
1.91e+00 ± 4.4e-02
1.32e+00 ± 3.3e-02
9.63e-01 ± 2.5e-02
7.33e-01 ± 2.1e-02
5.16e-01 ± 1.6e-02
3.84e-01 ± 1.3e-02
2.76e-01 ± 1.1e-02
2.17e-01 ± 9.0e-03
1.67e-01 ± 7.8e-03

10–15%
1.29e+01 ± 2.8e-01
9.88e+00 ± 2.0e-01
7.38e+00 ± 1.4e-01
5.39e+00 ± 1.0e-01
4.02e+00 ± 8.1e-02
2.91e+00 ± 6.1e-02
2.21e+00 ± 5.0e-02
1.63e+00 ± 3.9e-02
1.14e+00 ± 2.9e-02
7.88e-01 ± 2.2e-02
6.05e-01 ± 1.8e-02
4.33e-01 ± 1.4e-02
3.04e-01 ± 1.1e-02
2.28e-01 ± 9.3e-03
1.72e-01 ± 7.7e-03
1.37e-01 ± 6.9e-03

Table C.8: Invariant yields for K + at mid-rapidity in 15–20%, 20–30%, 30–40%, and 4050% centrality bins, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95

15–20%
1.04e+01 ± 2.3e-01
8.30e+00 ± 1.7e-01
6.20e+00 ± 1.2e-01
4.46e+00 ± 8.8e-02
3.36e+00 ± 7.0e-02
2.40e+00 ± 5.2e-02
1.81e+00 ± 4.2e-02
1.29e+00 ± 3.2e-02
8.82e-01 ± 2.4e-02
6.60e-01 ± 1.9e-02
4.91e-01 ± 1.5e-02
3.55e-01 ± 1.2e-02
2.62e-01 ± 1.0e-02
1.92e-01 ± 8.3e-03
1.48e-01 ± 7.0e-03
1.14e-01 ± 6.1e-03

20–30%
7.81e+00 ± 1.7e-01
6.22e+00 ± 1.2e-01
4.51e+00 ± 8.5e-02
3.31e+00 ± 6.2e-02
2.50e+00 ± 4.9e-02
1.74e+00 ± 3.6e-02
1.31e+00 ± 2.8e-02
9.60e-01 ± 2.2e-02
6.54e-01 ± 1.6e-02
4.68e-01 ± 1.2e-02
3.50e-01 ± 9.9e-03
2.59e-01 ± 7.9e-03
1.88e-01 ± 6.3e-03
1.34e-01 ± 5.1e-03
1.04e-01 ± 4.2e-03
8.21e-02 ± 3.7e-03

30–40%
5.11e+00 ± 1.1e-01
4.06e+00 ± 8.3e-02
2.89e+00 ± 5.7e-02
2.07e+00 ± 4.1e-02
1.60e+00 ± 3.3e-02
1.08e+00 ± 2.4e-02
8.42e-01 ± 2.0e-02
6.01e-01 ± 1.5e-02
4.22e-01 ± 1.1e-02
2.99e-01 ± 8.7e-03
2.22e-01 ± 7.2e-03
1.63e-01 ± 5.8e-03
1.14e-01 ± 4.6e-03
8.52e-02 ± 3.8e-03
6.58e-02 ± 3.2e-03
4.87e-02 ± 2.7e-03

40–50%
3.28e+00 ± 7.8e-02
2.43e+00 ± 5.3e-02
1.78e+00 ± 3.8e-02
1.26e+00 ± 2.7e-02
9.00e-01 ± 2.1e-02
6.46e-01 ± 1.6e-02
4.82e-01 ± 1.3e-02
3.48e-01 ± 1.0e-02
2.34e-01 ± 7.5e-03
1.70e-01 ± 5.9e-03
1.20e-01 ± 4.8e-03
9.25e-02 ± 4.0e-03
6.22e-02 ± 3.1e-03
4.81e-02 ± 2.7e-03
3.66e-02 ± 2.3e-03
2.91e-02 ± 2.0e-03

APPENDIX C. DATA TABLES

134

Table C.9: Invariant yields for K + at mid-rapidity in 50–60%, 60–70%, 70–80%, and 8092% centrality bins, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95

50–60%
1.93e+00 ± 5.0e-02
1.36e+00 ± 3.3e-02
1.01e+00 ± 2.4e-02
6.82e-01 ± 1.7e-02
4.77e-01 ± 1.3e-02
3.51e-01 ± 1.0e-02
2.54e-01 ± 8.2e-03
1.80e-01 ± 6.4e-03
1.28e-01 ± 5.1e-03
8.53e-02 ± 3.9e-03
6.40e-02 ± 3.3e-03
4.73e-02 ± 2.7e-03
3.39e-02 ± 2.2e-03
2.31e-02 ± 1.8e-03
1.72e-02 ± 1.5e-03
1.53e-02 ± 1.4e-03

60–70%
9.56e-01 ± 2.9e-02
6.72e-01 ± 2.0e-02
4.81e-01 ± 1.4e-02
3.40e-01 ± 1.1e-02
2.33e-01 ± 8.1e-03
1.69e-01 ± 6.4e-03
1.19e-01 ± 5.1e-03
7.84e-02 ± 3.9e-03
5.43e-02 ± 3.1e-03
3.85e-02 ± 2.5e-03
2.94e-02 ± 2.1e-03
2.10e-02 ± 1.8e-03
1.60e-02 ± 1.5e-03
1.04e-02 ± 1.2e-03
8.75e-03 ± 1.1e-03
6.49e-03 ± 9.2e-04

70–80%
4.06e-01 ± 1.7e-02
2.89e-01 ± 1.2e-02
1.88e-01 ± 8.0e-03
1.24e-01 ± 5.8e-03
9.39e-02 ± 4.8e-03
5.66e-02 ± 3.5e-03
4.40e-02 ± 3.0e-03
3.12e-02 ± 2.4e-03
2.07e-02 ± 1.9e-03
1.38e-02 ± 1.5e-03
1.34e-02 ± 1.4e-03
6.85e-03 ± 1.0e-03
5.62e-03 ± 8.9e-04
4.19e-03 ± 7.6e-04
3.39e-03 ± 6.7e-04
2.75e-03 ± 6.1e-04

80–92%
1.88e-01 ± 1.1e-02
1.48e-01 ± 7.8e-03
1.02e-01 ± 5.6e-03
5.88e-02 ± 3.9e-03
3.87e-02 ± 3.0e-03
2.99e-02 ± 2.5e-03
2.07e-02 ± 2.0e-03
1.64e-02 ± 1.7e-03
7.94e-03 ± 1.1e-03
6.53e-03 ± 9.9e-04
5.70e-03 ± 9.2e-04
2.84e-03 ± 6.4e-04
2.67e-03 ± 6.1e-04
1.85e-03 ± 5.0e-04
2.09e-03 ± 5.2e-04
1.16e-03 ± 3.9e-04

Table C.10: Invariant yields for K − at mid-rapidity in the minimum bias, 0–5%, 5–10%,
and 10–15% centrality bins, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95

Minimum bias
4.87e+00 ± 9.3e-02
3.88e+00 ± 6.7e-02
2.96e+00 ± 4.9e-02
2.20e+00 ± 3.6e-02
1.59e+00 ± 2.6e-02
1.14e+00 ± 1.9e-02
8.50e-01 ± 1.5e-02
5.96e-01 ± 1.0e-02
4.29e-01 ± 7.8e-03
3.23e-01 ± 6.2e-03
2.32e-01 ± 4.6e-03
1.67e-01 ± 3.4e-03
1.21e-01 ± 2.6e-03
8.78e-02 ± 2.0e-03
6.76e-02 ± 1.6e-03
5.10e-02 ± 1.3e-03

0–5%
1.64e+01 ± 3.4e-01
1.31e+01 ± 2.4e-01
1.01e+01 ± 1.8e-01
7.69e+00 ± 1.4e-01
5.61e+00 ± 1.0e-01
4.11e+00 ± 7.7e-02
3.03e+00 ± 6.0e-02
2.11e+00 ± 4.4e-02
1.53e+00 ± 3.4e-02
1.15e+00 ± 2.8e-02
8.42e-01 ± 2.2e-02
5.86e-01 ± 1.7e-02
4.42e-01 ± 1.4e-02
3.17e-01 ± 1.1e-02
2.52e-01 ± 9.4e-03
1.83e-01 ± 7.9e-03

5–10%
1.36e+01 ± 2.8e-01
1.09e+01 ± 2.0e-01
8.57e+00 ± 1.5e-01
6.27e+00 ± 1.1e-01
4.55e+00 ± 8.4e-02
3.36e+00 ± 6.5e-02
2.53e+00 ± 5.2e-02
1.79e+00 ± 3.8e-02
1.25e+00 ± 2.9e-02
9.45e-01 ± 2.4e-02
6.97e-01 ± 1.9e-02
4.97e-01 ± 1.5e-02
3.82e-01 ± 1.2e-02
2.64e-01 ± 9.6e-03
2.10e-01 ± 8.4e-03
1.53e-01 ± 7.1e-03

10–15%
1.12e+01 ± 2.4e-01
8.91e+00 ± 1.7e-01
6.94e+00 ± 1.3e-01
5.14e+00 ± 9.5e-02
3.82e+00 ± 7.2e-02
2.76e+00 ± 5.4e-02
2.05e+00 ± 4.3e-02
1.44e+00 ± 3.2e-02
1.05e+00 ± 2.5e-02
8.03e-01 ± 2.1e-02
5.62e-01 ± 1.6e-02
4.16e-01 ± 1.3e-02
2.93e-01 ± 1.0e-02
2.11e-01 ± 8.2e-03
1.61e-01 ± 7.0e-03
1.22e-01 ± 6.1e-03

C.1. PT SPECTRA DATA TABLES

135

Table C.11: Invariant yields for K − at mid-rapidity in 15–20%, 20–30%, 30–40%, and40-50% centrality bins, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95

15–20%
9.24e+00 ± 2.0e-01
7.61e+00 ± 1.5e-01
5.78e+00 ± 1.1e-01
4.33e+00 ± 8.1e-02
3.13e+00 ± 6.0e-02
2.23e+00 ± 4.5e-02
1.70e+00 ± 3.7e-02
1.17e+00 ± 2.7e-02
8.58e-01 ± 2.1e-02
6.26e-01 ± 1.7e-02
4.56e-01 ± 1.4e-02
3.25e-01 ± 1.1e-02
2.36e-01 ± 8.9e-03
1.83e-01 ± 7.4e-03
1.29e-01 ± 6.0e-03
1.05e-01 ± 5.5e-03

20–30%
7.05e+00 ± 1.5e-01
5.62e+00 ± 1.0e-01
4.29e+00 ± 7.7e-02
3.22e+00 ± 5.8e-02
2.29e+00 ± 4.2e-02
1.61e+00 ± 3.1e-02
1.21e+00 ± 2.5e-02
8.78e-01 ± 1.9e-02
6.29e-01 ± 1.4e-02
4.76e-01 ± 1.2e-02
3.41e-01 ± 9.2e-03
2.50e-01 ± 7.3e-03
1.72e-01 ± 5.7e-03
1.29e-01 ± 4.6e-03
1.01e-01 ± 4.0e-03
7.67e-02 ± 3.4e-03

30–40%
4.60e+00 ± 9.9e-02
3.68e+00 ± 7.1e-02
2.74e+00 ± 5.1e-02
2.04e+00 ± 3.8e-02
1.49e+00 ± 2.9e-02
1.04e+00 ± 2.1e-02
7.74e-01 ± 1.7e-02
5.39e-01 ± 1.3e-02
3.87e-01 ± 9.9e-03
2.97e-01 ± 8.3e-03
2.09e-01 ± 6.5e-03
1.43e-01 ± 5.0e-03
1.07e-01 ± 4.2e-03
7.79e-02 ± 3.4e-03
5.84e-02 ± 2.8e-03
4.31e-02 ± 2.4e-03

40–50%
2.79e+00 ± 6.4e-02
2.25e+00 ± 4.7e-02
1.69e+00 ± 3.4e-02
1.19e+00 ± 2.5e-02
8.47e-01 ± 1.8e-02
6.04e-01 ± 1.4e-02
4.49e-01 ± 1.1e-02
3.11e-01 ± 8.4e-03
2.25e-01 ± 6.8e-03
1.64e-01 ± 5.5e-03
1.21e-01 ± 4.5e-03
8.71e-02 ± 3.7e-03
6.17e-02 ± 3.0e-03
4.42e-02 ± 2.4e-03
3.24e-02 ± 2.0e-03
2.46e-02 ± 1.8e-03

Table C.12: Invariant yields for K − at mid-rapidity in 50–60%, 60–70%, 70–80%, and80-92% centrality bins, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95

50–60%
1.73e+00 ± 4.3e-02
1.25e+00 ± 2.9e-02
9.30e-01 ± 2.1e-02
6.59e-01 ± 1.6e-02
4.65e-01 ± 1.2e-02
3.22e-01 ± 9.0e-03
2.32e-01 ± 7.2e-03
1.60e-01 ± 5.5e-03
1.15e-01 ± 4.4e-03
8.85e-02 ± 3.8e-03
5.83e-02 ± 3.0e-03
4.60e-02 ± 2.5e-03
3.05e-02 ± 2.0e-03
2.07e-02 ± 1.6e-03
1.84e-02 ± 1.5e-03
1.46e-02 ± 1.3e-03

60–70%
8.11e-01 ± 2.5e-02
6.37e-01 ± 1.8e-02
4.43e-01 ± 1.3e-02
3.16e-01 ± 9.5e-03
2.31e-01 ± 7.4e-03
1.56e-01 ± 5.7e-03
1.09e-01 ± 4.5e-03
7.06e-02 ± 3.4e-03
5.72e-02 ± 2.9e-03
3.67e-02 ± 2.3e-03
2.38e-02 ± 1.8e-03
1.89e-02 ± 1.6e-03
1.53e-02 ± 1.4e-03
1.00e-02 ± 1.1e-03
7.82e-03 ± 9.5e-04
6.14e-03 ± 8.6e-04

70–80%
3.89e-01 ± 1.6e-02
2.80e-01 ± 1.1e-02
1.83e-01 ± 7.5e-03
1.40e-01 ± 5.9e-03
8.42e-02 ± 4.2e-03
5.67e-02 ± 3.2e-03
4.26e-02 ± 2.7e-03
2.98e-02 ± 2.1e-03
1.84e-02 ± 1.6e-03
1.59e-02 ± 1.5e-03
1.12e-02 ± 1.2e-03
7.86e-03 ± 1.0e-03
6.44e-03 ± 9.0e-04
3.65e-03 ± 6.6e-04
2.81e-03 ± 5.8e-04
2.12e-03 ± 5.1e-04

80–92%
1.82e-01 ± 9.9e-03
1.37e-01 ± 7.1e-03
1.02e-01 ± 5.4e-03
6.21e-02 ± 3.8e-03
3.81e-02 ± 2.7e-03
2.57e-02 ± 2.1e-03
1.73e-02 ± 1.7e-03
1.32e-02 ± 1.4e-03
9.79e-03 ± 1.2e-03
7.78e-03 ± 1.0e-03
4.22e-03 ± 7.5e-04
3.92e-03 ± 7.1e-04
2.92e-03 ± 6.0e-04
1.27e-03 ± 3.9e-04
1.44e-03 ± 4.1e-04
1.30e-03 ± 4.0e-04

APPENDIX C. DATA TABLES

136

Table C.13: Invariant yields for protons at mid-rapidity in the minimum bias, 0–5%, 5–
10%, and 10–15% centrality bins, normalized to one unit rapidity. Errors are statisticalonly.
pT [GeV/c]
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.10
2.30
2.50
2.70
2.90
3.25
3.75
4.25

Minimum bias
9.51e-01 ± 2.7e-02
8.47e-01 ± 2.4e-02
7.08e-01 ± 2.0e-02
6.06e-01 ± 1.8e-02
5.05e-01 ± 1.5e-02
4.23e-01 ± 1.3e-02
3.30e-01 ± 1.0e-02
2.71e-01 ± 8.8e-03
2.04e-01 ± 6.7e-03
1.68e-01 ± 5.8e-03
1.25e-01 ± 4.4e-03
9.38e-02 ± 3.4e-03
7.50e-02 ± 2.8e-03
5.37e-02 ± 2.1e-03
3.71e-02 ± 9.4e-04
2.15e-02 ± 5.9e-04
1.21e-02 ± 4.2e-04
7.26e-03 ± 2.8e-04
4.17e-03 ± 1.9e-04
1.70e-03 ± 8.3e-05
5.79e-04 ± 4.4e-05
2.21e-04 ± 2.7e-05

0–5%
2.90e+00 ± 9.3e-02
2.65e+00 ± 8.5e-02
2.28e+00 ± 7.3e-02
2.00e+00 ± 6.6e-02
1.68e+00 ± 5.7e-02
1.46e+00 ± 5.1e-02
1.16e+00 ± 4.2e-02
9.72e-01 ± 3.7e-02
7.42e-01 ± 2.9e-02
6.05e-01 ± 2.5e-02
4.55e-01 ± 2.0e-02
3.51e-01 ± 1.6e-02
2.85e-01 ± 1.4e-02
1.99e-01 ± 1.1e-02
1.35e-01 ± 5.0e-03
7.69e-02 ± 3.5e-03
4.39e-02 ± 2.5e-03
2.44e-02 ± 1.8e-03
1.54e-02 ± 1.4e-03
5.98e-03 ± 5.5e-04
2.05e-03 ± 3.1e-04
8.96e-04 ± 2.2e-04

5–10%
2.44e+00 ± 8.0e-02
2.24e+00 ± 7.3e-02
1.91e+00 ± 6.3e-02
1.66e+00 ± 5.5e-02
1.43e+00 ± 4.9e-02
1.22e+00 ± 4.3e-02
9.51e-01 ± 3.5e-02
7.96e-01 ± 3.1e-02
6.09e-01 ± 2.5e-02
5.08e-01 ± 2.2e-02
3.77e-01 ± 1.7e-02
2.76e-01 ± 1.4e-02
2.28e-01 ± 1.2e-02
1.61e-01 ± 9.3e-03
1.12e-01 ± 4.4e-03
6.73e-02 ± 3.2e-03
3.67e-02 ± 2.2e-03
2.27e-02 ± 1.7e-03
1.16e-02 ± 1.2e-03
5.17e-03 ± 5.0e-04
1.68e-03 ± 2.8e-04
7.04e-04 ± 1.9e-04

10–15%
2.09e+00 ± 6.9e-02
1.87e+00 ± 6.2e-02
1.60e+00 ± 5.3e-02
1.41e+00 ± 4.8e-02
1.16e+00 ± 4.1e-02
9.85e-01 ± 3.6e-02
7.92e-01 ± 3.0e-02
6.55e-01 ± 2.6e-02
5.07e-01 ± 2.1e-02
4.21e-01 ± 1.9e-02
3.02e-01 ± 1.4e-02
2.29e-01 ± 1.2e-02
1.79e-01 ± 1.0e-02
1.36e-01 ± 8.2e-03
9.18e-02 ± 3.8e-03
5.39e-02 ± 2.7e-03
3.05e-02 ± 2.0e-03
1.78e-02 ± 1.5e-03
1.04e-02 ± 1.1e-03
4.04e-03 ± 4.3e-04
1.45e-03 ± 2.5e-04
4.70e-04 ± 1.5e-04

Table C.14: Invariant yields for protons at mid-rapidity in 15–20%, 20–30%, 30–40%, and40-50% centrality bins, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.10
2.30
2.50
2.70
2.90
3.25
3.75
4.25

15–20%
1.76e+00 ± 6.0e-02
1.59e+00 ± 5.4e-02
1.34e+00 ± 4.6e-02
1.16e+00 ± 4.1e-02
9.75e-01 ± 3.5e-02
8.38e-01 ± 3.1e-02
6.47e-01 ± 2.5e-02
5.35e-01 ± 2.2e-02
4.04e-01 ± 1.8e-02
3.33e-01 ± 1.6e-02
2.60e-01 ± 1.3e-02
1.86e-01 ± 1.0e-02
1.51e-01 ± 8.9e-03
1.06e-01 ± 6.9e-03
7.41e-02 ± 3.3e-03
4.46e-02 ± 2.4e-03
2.52e-02 ± 1.7e-03
1.55e-02 ± 1.3e-03
8.35e-03 ± 9.5e-04
3.51e-03 ± 3.9e-04
1.18e-03 ± 2.2e-04
4.64e-04 ± 1.4e-04

20–30%
1.37e+00 ± 4.4e-02
1.24e+00 ± 4.0e-02
1.02e+00 ± 3.3e-02
8.90e-01 ± 2.9e-02
7.41e-01 ± 2.5e-02
6.27e-01 ± 2.2e-02
4.83e-01 ± 1.8e-02
3.93e-01 ± 1.5e-02
2.90e-01 ± 1.2e-02
2.42e-01 ± 1.0e-02
1.80e-01 ± 8.1e-03
1.36e-01 ± 6.6e-03
1.08e-01 ± 5.7e-03
7.98e-02 ± 4.5e-03
5.63e-02 ± 2.1e-03
3.19e-02 ± 1.5e-03
1.79e-02 ± 1.1e-03
1.08e-02 ± 8.0e-04
6.05e-03 ± 5.8e-04
2.54e-03 ± 2.4e-04
8.20e-04 ± 1.3e-04
3.07e-04 ± 8.3e-05

30–40%
9.68e-01 ± 3.2e-02
8.52e-01 ± 2.9e-02
7.06e-01 ± 2.4e-02
5.79e-01 ± 2.0e-02
4.83e-01 ± 1.7e-02
3.93e-01 ± 1.5e-02
3.09e-01 ± 1.2e-02
2.46e-01 ± 1.0e-02
1.89e-01 ± 8.3e-03
1.49e-01 ± 7.1e-03
1.10e-01 ± 5.6e-03
8.52e-02 ± 4.7e-03
6.68e-02 ± 4.0e-03
4.72e-02 ± 3.2e-03
3.32e-02 ± 1.5e-03
1.96e-02 ± 1.1e-03
1.07e-02 ± 7.8e-04
6.78e-03 ± 6.1e-04
4.10e-03 ± 4.7e-04
1.64e-03 ± 1.9e-04
5.66e-04 ± 1.1e-04
1.93e-04 ± 6.4e-05

40–50%
6.31e-01 ± 2.2e-02
5.39e-01 ± 1.9e-02
4.33e-01 ± 1.6e-02
3.60e-01 ± 1.4e-02
2.96e-01 ± 1.2e-02
2.33e-01 ± 9.7e-03
1.77e-01 ± 7.9e-03
1.40e-01 ± 6.7e-03
1.05e-01 ± 5.4e-03
8.39e-02 ± 4.7e-03
6.02e-02 ± 3.7e-03
4.64e-02 ± 3.1e-03
3.64e-02 ± 2.7e-03
2.53e-02 ± 2.1e-03
1.82e-02 ± 1.0e-03
9.61e-03 ± 7.2e-04
5.83e-03 ± 5.5e-04
3.73e-03 ± 4.4e-04
2.20e-03 ± 3.3e-04
8.36e-04 ± 1.3e-04
3.25e-04 ± 7.8e-05
1.07e-04 ± 4.7e-05

C.1. PT SPECTRA DATA TABLES

137

Table C.15: Invariant yields for protons at mid-rapidity in 50–60%, 60–70%, 70–80%, and80-92% centrality bins, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.10
2.30
2.50
2.70
2.90
3.25
3.75
4.25

50–60%
3.82e-01 ± 1.5e-02
3.25e-01 ± 1.3e-02
2.60e-01 ± 1.1e-02
2.08e-01 ± 9.1e-03
1.61e-01 ± 7.5e-03
1.24e-01 ± 6.2e-03
9.20e-02 ± 5.0e-03
7.34e-02 ± 4.4e-03
4.98e-02 ± 3.3e-03
4.43e-02 ± 3.1e-03
3.29e-02 ± 2.6e-03
2.37e-02 ± 2.1e-03
1.80e-02 ± 1.8e-03
1.24e-02 ± 1.4e-03
9.33e-03 ± 7.2e-04
4.86e-03 ± 5.0e-04
3.01e-03 ± 3.9e-04
1.66e-03 ± 2.9e-04
1.03e-03 ± 2.2e-04
4.01e-04 ± 8.7e-05
1.45e-04 ± 5.2e-05
4.94e-05 ± 3.2e-05

60–70%
2.04e-01 ± 9.7e-03
1.65e-01 ± 8.1e-03
1.27e-01 ± 6.5e-03
1.00e-01 ± 5.5e-03
7.43e-02 ± 4.5e-03
5.88e-02 ± 3.8e-03
3.98e-02 ± 3.0e-03
3.41e-02 ± 2.7e-03
2.41e-02 ± 2.2e-03
1.69e-02 ± 1.8e-03
1.30e-02 ± 1.5e-03
9.76e-03 ± 1.3e-03
7.16e-03 ± 1.1e-03
5.34e-03 ± 9.1e-04
3.47e-03 ± 4.2e-04
2.28e-03 ± 3.4e-04
9.91e-04 ± 2.2e-04
6.31e-04 ± 1.7e-04
4.62e-04 ± 1.5e-04
1.66e-04 ± 5.5e-05
5.72e-05 ± 3.2e-05
2.40e-05 ± 2.2e-05

70–80%
9.09e-02 ± 5.9e-03
7.04e-02 ± 4.9e-03
5.41e-02 ± 4.0e-03
4.11e-02 ± 3.3e-03
3.14e-02 ± 2.8e-03
2.40e-02 ± 2.3e-03
1.68e-02 ± 1.9e-03
1.21e-02 ± 1.6e-03
9.02e-03 ± 1.3e-03
6.98e-03 ± 1.1e-03
4.57e-03 ± 9.0e-04
3.81e-03 ± 8.0e-04
2.56e-03 ± 6.6e-04
2.04e-03 ± 5.7e-04
1.34e-03 ± 2.7e-04
6.06e-04 ± 1.8e-04
3.91e-04 ± 1.4e-04
2.37e-04 ± 1.1e-04
1.06e-04 ± 7.3e-05
6.73e-05 ± 3.6e-05
2.13e-05 ± 1.9e-05
1.02e-05 ± 1.5e-05

80–92%
4.96e-02 ± 4.2e-03
3.79e-02 ± 3.4e-03
2.62e-02 ± 2.7e-03
2.06e-02 ± 2.3e-03
1.54e-02 ± 1.9e-03
8.08e-03 ± 1.3e-03
6.94e-03 ± 1.2e-03
5.84e-03 ± 1.1e-03
3.61e-03 ± 8.1e-04
2.19e-03 ± 6.3e-04
1.36e-03 ± 4.8e-04
1.40e-03 ± 4.8e-04
8.09e-04 ± 3.7e-04
8.46e-04 ± 3.6e-04
4.08e-04 ± 1.5e-04
2.88e-04 ± 1.2e-04
2.19e-04 ± 1.0e-04
1.12e-04 ± 7.4e-05
3.22e-05 ± 4.0e-05
2.02e-05 ± 2.0e-05
2.89e-06 ± 7.7e-06
2.43e-06 ± 6.7e-06

Table C.16: Invariant yields for anti-protons at mid-rapidity in the minimum bias, 0–5%,
5–10%, and 10–15% centrality bins, normalized to one unit rapidity. Errors are statisticalonly.
pT [GeV/c]
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.10
2.30
2.50
2.70
2.90
3.25
3.75
4.25

Minimum bias
6.73e-01 ± 2.0e-02
6.16e-01 ± 1.8e-02
5.28e-01 ± 1.5e-02
4.52e-01 ± 1.3e-02
3.65e-01 ± 1.1e-02
3.19e-01 ± 9.7e-03
2.53e-01 ± 7.9e-03
2.01e-01 ± 6.5e-03
1.66e-01 ± 5.6e-03
1.22e-01 ± 4.1e-03
9.61e-02 ± 3.4e-03
7.19e-02 ± 2.7e-03
5.57e-02 ± 2.1e-03
4.04e-02 ± 1.7e-03
2.61e-02 ± 7.3e-04
1.54e-02 ± 4.8e-04
8.66e-03 ± 3.4e-04
4.79e-03 ± 2.2e-04
2.91e-03 ± 1.6e-04
1.16e-03 ± 6.7e-05
3.71e-04 ± 3.5e-05
1.35e-04 ± 2.1e-05

0–5%
2.00e+00 ± 6.8e-02
1.89e+00 ± 6.2e-02
1.67e+00 ± 5.4e-02
1.47e+00 ± 4.8e-02
1.21e+00 ± 4.1e-02
1.10e+00 ± 3.9e-02
8.90e-01 ± 3.3e-02
7.24e-01 ± 2.8e-02
6.12e-01 ± 2.5e-02
4.43e-01 ± 1.9e-02
3.46e-01 ± 1.6e-02
2.70e-01 ± 1.3e-02
2.07e-01 ± 1.1e-02
1.53e-01 ± 9.2e-03
9.75e-02 ± 4.2e-03
5.99e-02 ± 3.1e-03
3.16e-02 ± 2.2e-03
1.79e-02 ± 1.6e-03
1.04e-02 ± 1.2e-03
4.14e-03 ± 4.7e-04
1.29e-03 ± 2.5e-04
5.44e-04 ± 1.7e-04

5–10%
1.73e+00 ± 6.0e-02
1.61e+00 ± 5.4e-02
1.42e+00 ± 4.7e-02
1.25e+00 ± 4.2e-02
1.04e+00 ± 3.6e-02
9.28e-01 ± 3.4e-02
7.47e-01 ± 2.8e-02
6.08e-01 ± 2.4e-02
5.01e-01 ± 2.1e-02
3.69e-01 ± 1.6e-02
3.00e-01 ± 1.4e-02
2.17e-01 ± 1.1e-02
1.68e-01 ± 9.5e-03
1.19e-01 ± 7.7e-03
7.95e-02 ± 3.7e-03
4.59e-02 ± 2.7e-03
2.69e-02 ± 2.0e-03
1.46e-02 ± 1.4e-03
8.43e-03 ± 1.1e-03
3.55e-03 ± 4.3e-04
1.30e-03 ± 2.5e-04
3.98e-04 ± 1.4e-04

10–15%
1.48e+00 ± 5.2e-02
1.34e+00 ± 4.6e-02
1.19e+00 ± 4.1e-02
1.05e+00 ± 3.6e-02
8.82e-01 ± 3.1e-02
7.39e-01 ± 2.8e-02
6.15e-01 ± 2.4e-02
4.88e-01 ± 2.0e-02
4.09e-01 ± 1.8e-02
3.04e-01 ± 1.4e-02
2.43e-01 ± 1.2e-02
1.84e-01 ± 9.9e-03
1.45e-01 ± 8.4e-03
1.02e-01 ± 6.9e-03
6.64e-02 ± 3.2e-03
3.87e-02 ± 2.4e-03
2.29e-02 ± 1.8e-03
1.19e-02 ± 1.2e-03
7.25e-03 ± 9.6e-04
3.02e-03 ± 3.8e-04
1.09e-03 ± 2.2e-04
3.57e-04 ± 1.3e-04

APPENDIX C. DATA TABLES

138

Table C.17: Invariant yields for anti-protons at mid-rapidity in 15–20%, 20–30%, 30–40%,
and 40-50% centrality bins, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.10
2.30
2.50
2.70
2.90
3.25
3.75
4.25

15–20%
1.25e+00 ± 4.5e-02
1.16e+00 ± 4.1e-02
1.02e+00 ± 3.5e-02
8.85e-01 ± 3.1e-02
7.26e-01 ± 2.6e-02
6.43e-01 ± 2.5e-02
4.99e-01 ± 2.0e-02
4.11e-01 ± 1.8e-02
3.40e-01 ± 1.5e-02
2.45e-01 ± 1.2e-02
1.90e-01 ± 1.0e-02
1.45e-01 ± 8.4e-03
1.20e-01 ± 7.4e-03
8.41e-02 ± 6.0e-03
5.22e-02 ± 2.8e-03
3.19e-02 ± 2.1e-03
1.83e-02 ± 1.5e-03
9.79e-03 ± 1.1e-03
6.28e-03 ± 8.7e-04
2.55e-03 ± 3.4e-04
8.03e-04 ± 1.9e-04
2.92e-04 ± 1.2e-04

20–30%
9.68e-01 ± 3.2e-02
8.94e-01 ± 2.9e-02
7.83e-01 ± 2.5e-02
6.61e-01 ± 2.2e-02
5.25e-01 ± 1.8e-02
4.63e-01 ± 1.6e-02
3.65e-01 ± 1.4e-02
2.88e-01 ± 1.1e-02
2.41e-01 ± 1.0e-02
1.77e-01 ± 7.8e-03
1.43e-01 ± 6.7e-03
1.02e-01 ± 5.2e-03
7.97e-02 ± 4.4e-03
5.83e-02 ± 3.7e-03
3.90e-02 ± 1.7e-03
2.24e-02 ± 1.2e-03
1.22e-02 ± 9.0e-04
6.65e-03 ± 6.4e-04
4.33e-03 ± 5.1e-04
1.64e-03 ± 2.0e-04
5.39e-04 ± 1.1e-04
1.74e-04 ± 6.3e-05

30–40%
6.98e-01 ± 2.4e-02
6.35e-01 ± 2.2e-02
5.21e-01 ± 1.8e-02
4.42e-01 ± 1.5e-02
3.54e-01 ± 1.3e-02
2.99e-01 ± 1.2e-02
2.33e-01 ± 9.5e-03
1.80e-01 ± 7.8e-03
1.42e-01 ± 6.7e-03
1.06e-01 ± 5.3e-03
8.53e-02 ± 4.6e-03
6.32e-02 ± 3.8e-03
4.76e-02 ± 3.1e-03
3.56e-02 ± 2.7e-03
2.30e-02 ± 1.3e-03
1.34e-02 ± 9.2e-04
7.78e-03 ± 6.9e-04
4.66e-03 ± 5.2e-04
2.57e-03 ± 3.8e-04
1.05e-03 ± 1.5e-04
2.59e-04 ± 7.3e-05
1.12e-04 ± 4.9e-05

40–50%
4.51e-01 ± 1.7e-02
4.06e-01 ± 1.5e-02
3.37e-01 ± 1.3e-02
2.70e-01 ± 1.0e-02
2.05e-01 ± 8.4e-03
1.79e-01 ± 7.7e-03
1.37e-01 ± 6.4e-03
1.03e-01 ± 5.2e-03
8.40e-02 ± 4.6e-03
6.14e-02 ± 3.6e-03
4.50e-02 ± 3.0e-03
3.49e-02 ± 2.6e-03
2.66e-02 ± 2.2e-03
1.84e-02 ± 1.8e-03
1.27e-02 ± 8.8e-04
7.39e-03 ± 6.6e-04
4.11e-03 ± 4.8e-04
2.30e-03 ± 3.5e-04
1.67e-03 ± 3.0e-04
5.44e-04 ± 1.1e-04
1.75e-04 ± 5.9e-05
5.56e-05 ± 3.5e-05

Table C.18: Invariant yields for anti-protons at mid-rapidity in 50–60%, 60–70%, 70–80%,
and 80-92% centrality bins, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.10
2.30
2.50
2.70
2.90
3.25
3.75
4.25

50–60%
2.84e-01 ± 1.2e-02
2.50e-01 ± 1.1e-02
1.89e-01 ± 8.3e-03
1.58e-01 ± 7.1e-03
1.19e-01 ± 5.8e-03
9.60e-02 ± 5.1e-03
7.11e-02 ± 4.1e-03
5.31e-02 ± 3.4e-03
4.43e-02 ± 3.1e-03
3.13e-02 ± 2.4e-03
2.39e-02 ± 2.1e-03
1.79e-02 ± 1.7e-03
1.28e-02 ± 1.4e-03
1.00e-02 ± 1.3e-03
6.03e-03 ± 5.9e-04
3.46e-03 ± 4.4e-04
2.04e-03 ± 3.4e-04
1.20e-03 ± 2.5e-04
6.21e-04 ± 1.8e-04
2.61e-04 ± 7.3e-05
6.52e-05 ± 3.6e-05
4.82e-05 ± 3.2e-05

60–70%
1.58e-01 ± 8.1e-03
1.25e-01 ± 6.6e-03
9.50e-02 ± 5.2e-03
7.38e-02 ± 4.3e-03
5.50e-02 ± 3.5e-03
4.34e-02 ± 3.1e-03
3.19e-02 ± 2.5e-03
2.40e-02 ± 2.1e-03
1.90e-02 ± 1.9e-03
1.28e-02 ± 1.4e-03
9.29e-03 ± 1.2e-03
6.92e-03 ± 1.0e-03
5.66e-03 ± 9.3e-04
3.93e-03 ± 7.8e-04
2.58e-03 ± 3.8e-04
1.37e-03 ± 2.7e-04
7.56e-04 ± 2.0e-04
3.92e-04 ± 1.4e-04
2.92e-04 ± 1.2e-04
1.10e-04 ± 4.7e-05
2.77e-05 ± 2.3e-05
1.23e-05 ± 1.6e-05

70–80%
6.22e-02 ± 4.7e-03
5.43e-02 ± 4.0e-03
4.16e-02 ± 3.3e-03
3.13e-02 ± 2.7e-03
2.12e-02 ± 2.1e-03
1.73e-02 ± 1.9e-03
1.22e-02 ± 1.5e-03
9.65e-03 ± 1.3e-03
7.69e-03 ± 1.2e-03
4.43e-03 ± 8.5e-04
3.09e-03 ± 7.0e-04
2.79e-03 ± 6.6e-04
1.27e-03 ± 4.4e-04
1.54e-03 ± 4.9e-04
6.91e-04 ± 2.0e-04
5.66e-04 ± 1.8e-04
2.85e-04 ± 1.3e-04
2.26e-04 ± 1.1e-04
1.40e-04 ± 8.8e-05
3.63e-05 ± 2.8e-05
5.76e-06 ± 1.1e-05
2.71e-06 ± 8.1e-06

80–92%
3.55e-02 ± 3.4e-03
2.77e-02 ± 2.8e-03
2.06e-02 ± 2.2e-03
1.56e-02 ± 1.8e-03
1.01e-02 ± 1.4e-03
7.94e-03 ± 1.2e-03
6.05e-03 ± 1.1e-03
4.08e-03 ± 8.4e-04
3.31e-03 ± 7.6e-04
2.02e-03 ± 5.6e-04
1.70e-03 ± 5.2e-04
1.21e-03 ± 4.3e-04
7.33e-04 ± 3.3e-04
7.92e-04 ± 3.5e-04
3.59e-04 ± 1.4e-04
2.03e-04 ± 1.1e-04
1.35e-04 ± 8.5e-05
2.67e-05 ± 3.8e-05
8.76e-06 ± 2.2e-05
9.16e-06 ± 1.4e-05

C.1. PT SPECTRA DATA TABLES

139

Table C.19: Invariant yields for π ± and K ± at mid-rapidity in 60–92% centrality bin, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.05
2.15
2.25
2.35
2.45
2.55
2.65
2.75
2.85
2.95

π+
1.28e+01 ± 1.1e-01
6.61e+00 ± 5.7e-02
3.71e+00 ± 3.4e-02
2.09e+00 ± 2.1e-02
1.24e+00 ± 1.4e-02
7.63e-01 ± 9.6e-03
4.64e-01 ± 6.6e-03
2.93e-01 ± 4.8e-03
1.91e-01 ± 3.5e-03
1.26e-01 ± 2.6e-03
8.15e-02 ± 2.0e-03
5.96e-02 ± 1.7e-03
3.95e-02 ± 1.3e-03
2.56e-02 ± 9.7e-04
1.96e-02 ± 8.4e-04
1.44e-02 ± 7.1e-04
1.07e-02 ± 6.0e-04
7.68e-03 ± 5.1e-04
5.87e-03 ± 3.6e-04
3.78e-03 ± 2.9e-04
2.99e-03 ± 2.6e-04
2.47e-03 ± 2.5e-04
1.68e-03 ± 2.1e-04
1.77e-03 ± 2.3e-04
1.28e-03 ± 2.1e-04
1.02e-03 ± 2.0e-04
7.49e-04 ± 1.7e-04
5.61e-04 ± 1.6e-04

π−1.21e+01 ± 9.5e-02
6.42e+00 ± 5.2e-02
3.59e+00 ± 3.1e-02
2.06e+00 ± 1.9e-02
1.21e+00 ± 1.3e-02
7.31e-01 ± 8.4e-03
4.60e-01 ± 5.9e-03
2.95e-01 ± 4.3e-03
1.89e-01 ± 3.2e-03
1.28e-01 ± 2.5e-03
8.12e-02 ± 1.8e-03
5.71e-02 ± 1.5e-03
3.91e-02 ± 1.2e-03
2.81e-02 ± 9.7e-04
2.07e-02 ± 8.1e-04
1.41e-02 ± 6.5e-04
1.04e-02 ± 5.6e-04
7.42e-03 ± 4.8e-04
4.87e-03 ± 3.3e-04
3.87e-03 ± 3.0e-04
2.55e-03 ± 2.5e-04
2.41e-03 ± 2.6e-04
1.63e-03 ± 2.1e-04
1.54e-03 ± 2.3e-04
1.18e-03 ± 2.0e-04
7.74e-04 ± 1.7e-04
6.23e-04 ± 1.7e-04
7.27e-04 ± 1.9e-04

K+K−

5.35e-01 ± 1.5e-02
3.83e-01 ± 9.7e-03
2.66e-01 ± 6.8e-03
1.81e-01 ± 4.9e-03
1.26e-01 ± 3.7e-03
8.85e-02 ± 2.9e-03
6.34e-02 ± 2.3e-03
4.35e-02 ± 1.8e-03
2.87e-02 ± 1.4e-03
2.03e-02 ± 1.1e-03
1.68e-02 ± 9.7e-04
1.06e-02 ± 7.5e-04
8.39e-03 ± 6.5e-04
5.68e-03 ± 5.2e-04
4.91e-03 ± 4.7e-04
3.59e-03 ± 4.1e-04

4.74e-01 ± 1.3e-02
3.62e-01 ± 8.8e-03
2.50e-01 ± 6.2e-03
1.78e-01 ± 4.6e-03
1.21e-01 ± 3.4e-03
8.21e-02 ± 2.5e-03
5.80e-02 ± 2.0e-03
3.91e-02 ± 1.5e-03
2.94e-02 ± 1.3e-03
2.07e-02 ± 1.0e-03
1.35e-02 ± 8.2e-04
1.05e-02 ± 7.0e-04
8.47e-03 ± 6.2e-04
5.15e-03 ± 4.6e-04
4.15e-03 ± 4.1e-04
3.29e-03 ± 3.7e-04

APPENDIX C. DATA TABLES

140

Table C.20: Invariant yields for protons and anti-protons at mid-rapidity in 60–92% centrality bin, normalized to one unit rapidity. Errors are statistical only.
pT [GeV/c]
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.10
2.30
2.50
2.70
2.90
3.25
3.75
4.25

p
1.17e-01 ± 4.8e-03
9.26e-02 ± 3.9e-03
7.01e-02 ± 3.1e-03
5.48e-02 ± 2.6e-03
4.10e-02 ± 2.1e-03
3.09e-02 ± 1.7e-03
2.16e-02 ± 1.3e-03
1.77e-02 ± 1.2e-03
1.25e-02 ± 9.4e-04
8.85e-03 ± 7.8e-04
6.42e-03 ± 6.3e-04
5.08e-03 ± 5.5e-04
3.58e-03 ± 4.6e-04
2.79e-03 ± 3.9e-04
1.77e-03 ± 1.8e-04
1.08e-03 ± 1.4e-04
5.42e-04 ± 9.5e-05
3.32e-04 ± 7.4e-05
2.04e-04 ± 5.8e-05
8.58e-05 ± 2.3e-05
2.76e-05 ± 1.3e-05
1.24e-05 ± 9.1e-06

p
8.63e-02 ± 3.8e-03
7.00e-02 ± 3.1e-03
5.31e-02 ± 2.5e-03
4.07e-02 ± 2.0e-03
2.92e-02 ± 1.6e-03
2.32e-02 ± 1.4e-03
1.70e-02 ± 1.1e-03
1.27e-02 ± 9.4e-04
1.02e-02 ± 8.3e-04
6.51e-03 ± 6.2e-04
4.76e-03 ± 5.2e-04
3.69e-03 ± 4.5e-04
2.60e-03 ± 3.7e-04
2.11e-03 ± 3.4e-04
1.23e-03 ± 1.5e-04
7.22e-04 ± 1.2e-04
3.97e-04 ± 8.5e-05
2.17e-04 ± 6.2e-05
1.49e-04 ± 5.2e-05
5.24e-05 ± 1.9e-05
1.14e-05 ± 8.7e-06
5.08e-06 ± 6.1e-06

C.2. PARTICLE RATIO DATA TABLES

C.2

141

Particle Ratio Data Tables

The ratios of anti-particle/particle measured as a function of pT (Tables C.21–C.27) and√centrality (Tables C.36–C.42) at sNN = 200 GeV in Au+Au collisions are tabulated.
The ratios of K/π (Tables C.28–C.31) and p/π (Table C.32–C.35) as a function of pT are
also tabulated.
Table C.21: π − /π + vs. pT Central (0-5%)
pT [GeV/c]
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.05
2.15
2.25
2.35
2.45
2.55
2.65
2.75
2.85
2.95

π − /π +0.957466
0.985735
0.988715
1.0152
1.016140.974639
1.024191.01075
1.00777
1.044310.994569
1.00098
0.991924
1.06993
0.996205
0.990885
0.969285
1.017740.900701
0.969844
1.01490.981962
0.872258
0.926298
1.016430.876785
1.12719
1.04642

Stat. Err
0.0108386
0.0113168
0.011890.0129776
0.0140238
0.0146318
0.0165982
0.0178344
0.0190503
0.0213183
0.0216472
0.0239656
0.0256721
0.0301215
0.0309089
0.0342661
0.0371367
0.0454356
0.0383941
0.0492246
0.0616524
0.0713501
0.0761743
0.101928
0.134170.1389990.23259
0.26209

Sys. Err
0.055533
0.0571726
0.0573455
0.0588814
0.0589363
0.0565291
0.059403
0.0586234
0.0584508
0.0605703
0.057685
0.0580567
0.0575316
0.0620559
0.0577799
0.0574713
0.0562185
0.059029
0.0522406
0.056251
0.0588643
0.0569538
0.050591
0.0537253
0.0589528
0.0508535
0.0653769
0.0606926

Table C.22: π − /π + vs. pT Peripheral (60-92%)
pT [GeV/c]
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.05
2.15
2.25
2.35
2.45
2.55
2.65
2.75
2.85
2.95

π − /π +0.948930.970338
0.970189
0.986006
0.978866
0.958889
0.990725
1.008150.990833
1.020420.995222
0.957329
0.991001
1.0956
1.05152
0.975835
0.972191
0.966195
0.830706
1.02233
0.853348
0.976019
0.973440.873141
0.916944
0.757713
0.831459
1.2959Stat. Err
0.010933
0.011472
0.0121975
0.0134646
0.0148279
0.0163472
0.0190215
0.0221512
0.0246458
0.0290904
0.0325835
0.0364374
0.0437177
0.0561949
0.0609568
0.0662536
0.0757114
0.0895788
0.0763071
0.111425
0.110786
0.143371
0.176860.172251
0.216275
0.22604
0.29699
0.511151

Sys. Err
0.055038
0.0562796
0.056271
0.0571884
0.0567742
0.0556156
0.0574621
0.058473
0.0574683
0.0591843
0.0577229
0.0555251
0.057478
0.0635448
0.0609881
0.0565984
0.0563871
0.0560393
0.0481809
0.0592954
0.0494942
0.0566091
0.0564595
0.0506422
0.0531827
0.0439474
0.0482246
0.0751624

APPENDIX C. DATA TABLES

142

Table C.23: K − /K + vs. pT Central (0-5%)

Table C.24: K − /K + vs. pT Peripheral (60-92%)

pT [GeV/c]
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95

pT [GeV/c]
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95

K − /K +0.898844
0.889577
0.959843
0.965118
0.941609
0.980866
0.947405
0.916562
0.933744
1.01870.987732
0.971392
0.996458
0.876869
0.954324
0.86042

Stat. Err
0.0267777
0.0238841
0.0247583
0.0248376
0.024992
0.0270415
0.0276913
0.0280294
0.0303916
0.0356997
0.0375261
0.0404556
0.0451965
0.0430984
0.0514233
0.0524042

Sys. Err
0.052133
0.0515954
0.0556709
0.0559769
0.0546133
0.0568902
0.0549495
0.0531606
0.0541572
0.0590848
0.0572885
0.0563407
0.0577945
0.0508584
0.0553508
0.0499044

Table C.25: p/p vs. pT Central (0-5%)
pT [GeV/c]
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.1
2.3
2.5
2.7
2.9
3.25
3.75
4.25

p/p
0.68951
0.712713
0.73101
0.736244
0.719409
0.755606
0.769890.745183
0.825053
0.731295
0.761274
0.770284
0.7251940.770250.724176
0.778882
0.719541
0.736885
0.670069
0.692255
0.627522
0.607027

Stat. Err
0.0321448
0.0328213
0.0334939
0.0342573
0.0343607
0.0374725
0.0398593
0.0403655
0.0467199
0.0438201
0.048314
0.0523973
0.0531511
0.0624643
0.0413287
0.0538694
0.065372
0.0854318
0.0983822
0.101403
0.156272
0.23984

Sys. Err
0.0427496
0.0441882
0.0453226
0.0456471
0.0446034
0.0468475
0.0477332
0.0462013
0.0511533
0.0453403
0.047199
0.0477576
0.044962
0.0477555
0.0448989
0.0482907
0.0446115
0.0456869
0.0415443
0.0429198
0.0389064
0.0376357

K − /K +0.886941
0.945889
0.941417
0.985671
0.961988
0.92720.914415
0.897972
1.025891.020590.803198
0.991018
1.00874
0.906489
0.845204
0.91656

Stat. Err
0.0335849
0.0332914
0.033292
0.0366679
0.0391291
0.0416124
0.0461903
0.0510247
0.0659854
0.0750557
0.0673834
0.0957383
0.106742
0.116425
0.116963
0.14709

Sys. Err
0.0514426
0.0548616
0.0546022
0.0571689
0.0557953
0.0537776
0.0530361
0.0520824
0.0595018
0.0591942
0.0465855
0.0574791
0.0585068
0.0525763
0.0490219
0.0531605

Table C.26: p/p vs. pT Peripheral (60-92%)
pT [GeV/c]
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.1
2.3
2.5
2.7
2.9
3.25
3.75
4.25

p/p
0.739699
0.755839
0.756991
0.743343
0.710274
0.751543
0.787698
0.721420.814944
0.734908
0.741776
0.725716
0.726744
0.757069
0.693528
0.669031
0.732649
0.654012
0.726441
0.611011
0.411293
0.409961

Stat. Err
0.0444199
0.046385
0.0485329
0.0506493
0.0526111
0.061160.0715585
0.0719526
0.0906561
0.0949341
0.109148
0.117763
0.1391120.160937
0.111093
0.137209
0.202738
0.238308
0.327224
0.277024
0.369192
0.575587

Sys. Err
0.0458613
0.046862
0.0469334
0.0460872
0.044037
0.0465956
0.0488373
0.044728
0.0505265
0.0455643
0.0459901
0.0449944
0.0450581
0.0469383
0.0429987
0.0414799
0.0454242
0.0405488
0.0450394
0.0378827
0.0255001
0.0254176

C.2. PARTICLE RATIO DATA TABLES

143

Table C.27: p/p vs. pT (Minimum Bias)
pT [GeV/c]
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.1
2.3
2.5
2.7
2.9
3.25
3.75
4.25

p/p
0.707462
0.726951
0.745031
0.746203
0.723701
0.752394
0.766490.741634
0.814023
0.724222
0.771602
0.765792
0.743242
0.751736
0.702342
0.714374
0.714924
0.659917
0.696633
0.680084
0.639874
0.609606

Stat. Err
0.0288444
0.0294881
0.0299795
0.0304332
0.0301031
0.0324272
0.0340711
0.0340348
0.0382622
0.0351452
0.0382693
0.0397655
0.0400783
0.0423895
0.0265656
0.0297922
0.0377343
0.0402772
0.0504722
0.051579
0.0767322
0.120051

Sys. Err
0.0608418
0.0625178
0.0640726
0.0641734
0.0622383
0.0647059
0.0659181
0.0637805
0.070006
0.0622831
0.0663577
0.0658581
0.0639188
0.0646493
0.0604014
0.0614362
0.0614834
0.0567529
0.0599104
0.0584872
0.0550292
0.0524261

Table C.28: K + /π + vs. pT Central (0-5%)
pT [GeV/c]
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95

K + /π +0.152121
0.203336
0.2336
0.271772
0.327879
0.347032
0.401574
0.433756
0.460921
0.442816
0.494649
0.536572
0.550532
0.63390.631001
0.758117

Stat. Err
0.00354289
0.004379
0.00495461
0.00591241
0.00748147
0.00835229
0.0102534
0.0117113
0.013201
0.013679
0.0165727
0.0195863
0.0219767
0.0275176
0.030144
0.040729

Table C.29: K + /π + vs. pT Peripheral (60-92%)

Sys. ErrpT [GeV/c]
0.00943151
0.45
0.0126068
0.55
0.0144832
0.65
0.0168499
0.75
0.0203285
0.85
0.021516
0.95
0.0248976
1.05
0.0268929
1.15
0.0285771
1.25
0.0274546
1.35
0.0306683
1.45
0.0332675
1.55
0.034133
1.65
0.0393018
1.75
0.039122
1.85
0.0470033
1.95

K + /π +0.144390.1831780.21435
0.236847
0.2721190.302603
0.331629
0.346321
0.351324
0.340854
0.424388
0.415043
0.427335
0.393658
0.461005
0.467455

Stat. Err
0.00413693
0.00499529
0.00594108
0.00705893
0.00894806
0.0110048
0.0135421
0.016
0.0186808
0.0205096
0.0282166
0.0330855
0.0375954
0.0411178
0.0515587
0.0616281

Sys. Err
0.00895216
0.011357
0.0132897
0.0146845
0.0168714
0.0187614
0.020561
0.0214719
0.0217821
0.0211329
0.0263121
0.0257327
0.0264948
0.0244068
0.0285823
0.0289822

APPENDIX C. DATA TABLES

144

Table C.30: K − /π − vs. pT Central (0-5%)
pT [GeV/c]
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95

K − /π −0.138294
0.178175
0.220657
0.269118
0.301443
0.336772
0.377519
0.380694
0.432732
0.450657
0.492559
0.4871550.550671
0.560960.621261
0.640928

Stat. Err
0.00306037
0.00365361
0.00444585
0.00547838
0.00636934
0.00747096
0.00893147
0.00950161
0.0115535
0.0131162
0.0155036
0.0168376
0.0207976
0.0233132
0.0283973
0.034013

pT [GeV/c]
Sys. Err
0.00857422
0.45
0.0110469
0.55
0.0136808
0.65
0.0166853
0.75
0.0186894
0.85
0.0208799
0.95
0.0234062
1.05
0.023603
1.15
0.0268294
1.25
0.0279408
1.35
0.0305387
1.45
0.0302036
1.55
0.0341416
1.65
0.0347795
1.75
0.0385182
1.85
0.0397375
1.95

Table C.32: p/π + vs. pT Central (0-5%)
pT [GeV/c]
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.1
2.3
2.5
2.7
2.9

p/π +
0.0646409
0.0904598
0.125508
0.165361
0.211399
0.274289
0.325878
0.381552
0.430832
0.538133
0.565018
0.61537
0.683019
0.711554
0.783806
0.945540.96017
0.992269
1.3365

Stat. Err
0.00217313
0.00308416
0.00430889
0.00584442
0.00772416
0.0103891
0.0128933
0.0159602
0.0188002
0.025122
0.0279089
0.0327739
0.0392303
0.0452083
0.0340629
0.0525536
0.0713159
0.10206
0.193417

Table C.31: K − /π − vs. pT Peripheral (60-92%)
K − /π −0.132
0.175725
0.206149
0.243462
0.264226
0.278304
0.306052
0.304764
0.362152
0.363378
0.343963
0.375425
0.409949
0.365684
0.400789
0.443441

Stat. Err
0.00366525
0.00458762
0.00550014
0.00682683
0.0081088
0.00953729
0.0118645
0.013309
0.0176737
0.0206725
0.0232365
0.0281166
0.0338501
0.0369236
0.0451788
0.057764

Sys. Err
0.00818401
0.010895
0.0127813
0.0150946
0.016382
0.0172548
0.0189752
0.0188954
0.0224534
0.0225294
0.0213257
0.0232763
0.0254168
0.0226724
0.0248489
0.0274933

Table C.33: p/π + vs. pT Peripheral (60-92%)

Sys. Err pT [GeV/c]
0.00555912
0.65
0.00777954
0.75
0.0107937
0.85
0.014221
0.95
0.0181803
1.05
0.0235888
1.15
0.0280255
1.25
0.0328135
1.35
0.0370516
1.45
0.0462794
1.55
0.0485915
1.65
0.0529218
1.75
0.0587397
1.85
0.0611936
1.95
0.0674073
2.1
0.0813164
2.3
0.0825746
2.5
0.0853351
2.7
0.114939
2.9p/π +0.0940895
0.121414
0.151096
0.187395
0.214704
0.245723
0.264227
0.296344
0.315437
0.345492
0.326856
0.352425
0.335835
0.363426
0.368314
0.39638
0.314617
0.288419
0.312786

Stat. Err
0.00397164
0.00536262
0.00701646
0.00932005
0.0115865
0.0145912
0.017631
0.0216266
0.0259637
0.0330717
0.0351717
0.0418389
0.0470085
0.0564291
0.0410877
0.0566075
0.0620752
0.0740105
0.105493

Sys. Err
0.00809169
0.0104416
0.0129942
0.016116
0.0184645
0.0211322
0.0227235
0.0254856
0.0271276
0.0297123
0.0281096
0.0303086
0.0288818
0.0312547
0.031675
0.0340887
0.0270571
0.024804
0.0268996

C.2. PARTICLE RATIO DATA TABLES

Table C.34: p/π − vs. pT Central (0-5%)
pT [GeV/c]
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
1.85
1.95
2.1
2.3
2.5
2.7
2.9

p/π −

0.0438624
0.0661495
0.0895809
0.120451
0.150909
0.198459
0.25226
0.284048
0.358354
0.367812
0.431772
0.47837
0.511018
0.53852
0.611174
0.736463
0.77190.769071
0.821256

Stat. Err
0.00154061
0.00227585
0.00308156
0.00421958
0.00544851
0.00753499
0.0100549
0.0119089
0.0159144
0.0172667
0.0218059
0.0261426
0.0304075
0.0362572
0.0301507
0.0458647
0.0666452
0.0884184
0.132828

145

Table C.35: p/π − vs. pT Peripheral (60-92%)

Sys. Err pT [GeV/c]
0.00377217
0.65
0.00568886
0.75
0.00770396
0.85
0.0103588
0.95
0.0129782
1.05
0.0170675
1.15
0.0216944
1.25
0.0244282
1.35
0.0308184
1.45
0.0316319
1.55
0.0371324
1.65
0.0411398
1.75
0.0439475
1.85
0.0463127
1.95
0.0525609
2.1
0.0633359
2.3
0.0663834
2.5
0.0661401
2.7
0.070628
2.9

Table C.36: π − /π + vs. Npart
Npart
351.4
299
253.9
215.3
166.6
114.2
74.4
45.5
25.7
13.4
6.3

π − /π +0.984201
0.997229
0.968558
0.962930.977273
0.969567
0.964838
0.967325
0.958872
0.964984
0.971025

Stat. Err
0.0049369
0.00500613
0.00486565
0.00484265
0.00488647
0.00486067
0.00486577
0.00494973
0.00507733
0.00553412
0.00625725

Sys. Err
0.0570837
0.0578393
0.0561764
0.0558499
0.0566819
0.0562349
0.0559606
0.0561048
0.0556146
0.0559691
0.0563194

Table C.38: p/p vs. Npart
Npart
351.4
299
253.9
215.3
166.6
114.2
74.4
45.5
25.7
13.4
6.3

p/p
0.731953
0.742626
0.74260.749601
0.738992
0.744046
0.746218
0.756393
0.759773
0.739620.737784

Stat. Err
0.0116658
0.0121516
0.012443
0.0129325
0.0116483
0.0125436
0.0138783
0.0163038
0.0203813
0.0284461
0.0363725

Sys. Err
0.062948
0.0638659
0.0638636
0.0644657
0.0635533
0.063988
0.0641747
0.0650498
0.0653405
0.0636073
0.0634495

p/π −0.0711005
0.0957039
0.115449
0.1381720.153909
0.180976
0.209130.223318
0.259398
0.231749
0.230575
0.262094
0.251047
0.284765
0.281321
0.291385
0.250272
0.223266
0.219691

Stat. Err
0.00322222
0.00439192
0.00556397
0.00711537
0.00869701
0.0113154
0.0145976
0.0173994
0.0225333
0.0233536
0.0267238
0.0340199
0.0381667
0.0490566
0.0378904
0.0514544
0.0590408
0.0710798
0.0875284

Sys. Err
0.00611465
0.00823054
0.0099286
0.0118828
0.0132362
0.0155639
0.0179852
0.0192053
0.0223082
0.0199304
0.0198294
0.0225401
0.0215901
0.0244898
0.0241936
0.0250591
0.0215234
0.0192009
0.0188935

Table C.37: K − /K + vs. Npart

Npart
351.4
299
253.9
215.3
166.6
114.2
74.4
45.5
25.7
13.4
6.3

K − /K +0.933841
0.94272
0.920505
0.925989
0.927478
0.932175
0.917311
0.923619
0.916084
0.981581
0.968334

Stat. Err
0.00796795
0.00820853
0.00815443
0.00838429
0.00799809
0.00848459
0.00908818
0.010479
0.0128362
0.0195033
0.025965

Sys. Err
0.0541627
0.0546778
0.0533893
0.0537074
0.0537937
0.0540662
0.0532041
0.0535699
0.0531329
0.0569317
0.0561634

APPENDIX C. DATA TABLES

146

Table C.39: K + /π + vs. Npart

Npart
351.4
299
253.9
215.3
166.6
114.2
74.4
45.5
25.7
13.4
6.3

K + /π +0.171047
0.167582
0.165128
0.160557
0.158613
0.152447
0.146874
0.139298
0.129979
0.112338
0.108754

Stat. Err
0.00123418
0.00122603
0.0012238
0.00121019
0.00114938
0.00115294
0.00118405
0.00125364
0.00140097
0.00168682
0.00216993

Sys. Err
0.0106049
0.0103901
0.0102379
0.00995452
0.00983403
0.00945169
0.00910616
0.00863646
0.00805872
0.00696493
0.00674277

Table C.40: K − /π − vs. Npart

Npart
351.4
299
253.9
215.3
166.6
114.2
74.4
45.5
25.7
13.4
6.3

Table C.41: p/π + vs. Npart
Npart
351.4
299
253.9
215.3
166.6
114.2
74.4
45.5
25.7
13.4
6.3

p/π +

0.064502
0.0642273
0.0626094
0.061324
0.0621517
0.0616229
0.0599168
0.0583358
0.0550752
0.0505031
0.0519336

Stat. Err
0.000751529
0.00076539
0.000760693
0.000764915
0.000720009
0.00075611
0.000798928
0.000890211
0.00102933
0.00132667
0.00170869

Sys. Err
0.00399912
0.00398209
0.00388179
0.00380209
0.00385341
0.00382062
0.00371484
0.00361682
0.00341466
0.00313119
0.00321988

K − /π −0.162295
0.158422
0.156935
0.154397
0.150532
0.146568
0.139639
0.133004
0.124179
0.11427
0.108453

Stat. Err
0.00109956
0.00109179
0.00109615
0.00109677
0.00103039
0.00104445
0.00106893
0.00114346
0.0012917
0.00162492
0.00206464

Sys. Err
0.0100623
0.00982218
0.00972998
0.00957263
0.00933295
0.00908719
0.0086576
0.00824624
0.00769911
0.00708472
0.00672408

Table C.42: p/π − vs. Npart

Npart
351.4
299
253.9
215.3
166.6
114.2
74.4
45.5
25.7
13.4
6.3

p/π −
0.0479703
0.0478294
0.0480031
0.0477381
0.0469977
0.0472895
0.0463404
0.0456153
0.0436395
0.0387085
0.0394592

Stat. Err
0.0005745
0.000587613
0.000604115
0.000617567
0.000554593
0.000595914
0.000644667
0.000732573
0.000870989
0.00110982
0.00147087

Sys. Err
0.00297416
0.00296542
0.00297619
0.00295976
0.00291386
0.00293195
0.0028731
0.00282815
0.00270565
0.00239993
0.00244647

Appendix D
PHENIX Collaboration List
S.S. Adler,5 S. Afanasiev,17 C. Aidala,5 N.N. Ajitanand,43 Y. Akiba,20,38 J. Alexander,43
R. Amirikas,12 L. Aphecetche,45 S.H. Aronson,5 R. Averbeck,44 T.C. Awes,35 R. Azmoun,44
V. Babintsev,15 A. Baldisseri,10 K.N. Barish,6 P.D. Barnes,27 B. Bassalleck,33 S. Bathe,30
S. Batsouli,9 V. Baublis,37 A. Bazilevsky,39,15 S. Belikov,16,15 Y. Berdnikov,40 S. Bhagavatula,16
J.G. Boissevain,27 H. Borel,10 S. Borenstein,25 M.L. Brooks,27 D.S. Brown,34 N. Bruner,33
D. Bucher,30 H. Buesching,30 V. Bumazhnov,15 G. Bunce,5,39 J.M. Burward-Hoy,26,44 S. Butsyk,44
X. Camard,45 J.-S. Chai,18 P. Chand,4 W.C. Chang,2 S. Chernichenko,15 C.Y. Chi,9 J. Chiba,20
M. Chiu,9 I.J. Choi,52 J. Choi,19 R.K. Choudhury,4 T. Chujo,5 V. Cianciolo,35 Y. Cobigo,10
B.A. Cole,9 P. Constantin,16 D.G. d’Enterria,45 G. David,5 H. Delagrange,45 A. Denisov,15
A. Deshpande,39 E.J. Desmond,5 O. Dietzsch,41 O. Drapier,25 A. Drees,44 K.A. Drees,5R. du Rietz,29 A. Durum,15 D. Dutta,4 Y.V. Efremenko,35 K. El Chenawi,49 A. Enokizono,14
H. En’yo,38,39 S. Esumi,48 L. Ewell,5 D.E. Fields,33,39 F. Fleuret,25 S.L. Fokin,23 B.D. Fox,39
Z. Fraenkel,51 J.E. Frantz,9 A. Franz,5 A.D. Frawley,12 S.-Y. Fung,6 S. Garpman,29,∗ T.K. Ghosh,49
A. Glenn,46 G. Gogiberidze,46 M. Gonin,25 J. Gosset,10 Y. Goto,39 R. Granier de Cassagnac,25
N. Grau,16 S.V. Greene,49 M. Grosse Perdekamp,39 W. Guryn,5 H.-Å. Gustafsson,29 T. Hachiya,14J.S. Haggerty,5 H. Hamagaki,8 A.G. Hansen,27 E.P. Hartouni,26 M. Harvey,5 R. Hayano,8 X. He,13
M. Heffner,26 T.K. Hemmick,44 J.M. Heuser,44 M. Hibino,50 J.C. Hill,16 W. Holzmann,43
K. Homma,14 B. Hong,22 A. Hoover,34 T. Ichihara,38,39 V.V. Ikonnikov,23 K. Imai,24,38
L.D. Isenhower,1 M. Ishihara,38 M. Issah,43 A. Isupov,17 B.V. Jacak,44 W.Y. Jang,22 Y. Jeong,19J. Jia,44 O. Jinnouchi,38 B.M. Johnson,5 S.C. Johnson,26 K.S. Joo,31 D. Jouan,36 S. Kametani,8,50
N. Kamihara,47,38 J.H. Kang,52 S.S. Kapoor,4 K. Katou,50 S. Kelly,9 B. Khachaturov,51
A. Khanzadeev,37 J. Kikuchi,50 D.H. Kim,31 D.J. Kim,52 D.W. Kim,19 E. Kim,42 G.-B. Kim,25
H.J. Kim,52 E. Kistenev,5 A. Kiyomichi,48 K. Kiyoyama,32 C. Klein-Boesing,30 H. Kobayashi,38,39
L. Kochenda,37 V. Kochetkov,15 D. Koehler,33 T. Kohama,14 M. Kopytine,44 D. Kotchetkov,6
A. Kozlov,51 P.J. Kroon,5 C.H. Kuberg,1,27 K. Kurita,39 Y. Kuroki,48 M.J. Kweon,22 Y. Kwon,52
G.S. Kyle,34 R. Lacey,43 V. Ladygin,17 J.G. Lajoie,16 A. Lebedev,16,23 S. Leckey,44 D.M. Lee,27
S. Lee,19 M.J. Leitch,27 X.H. Li,6 H. Lim,42 A. Litvinenko,17 M.X. Liu,27 Y. Liu,36
C.F. Maguire,49 Y.I. Makdisi,5 A. Malakhov,17 V.I. Manko,23 Y. Mao,7,38 G. Martinez,45
M.D. Marx,44 H. Masui,48 F. Matathias,44 T. Matsumoto,8,50 P.L. McGaughey,27 E. Melnikov,15
F. Messer,44 Y. Miake,48 J. Milan,43 T.E. Miller,49 A. Milov,44,51 S. Mioduszewski,5
R.E. Mischke,27 G.C. Mishra,13 J.T. Mitchell,5 A.K. Mohanty,4 D.P. Morrison,5 J.M. Moss,27
F. Mühlbacher,44 D. Mukhopadhyay,51 M. Muniruzzaman,6 J. Murata,38,39 S. Nagamiya,20
J.L. Nagle,9 T. Nakamura,14 B.K. Nandi,6 M. Nara,48 J. Newby,46 P. Nilsson,29 A.S. Nyanin,23

147

148

APPENDIX D. PHENIX COLLABORATION LIST

J. Nystrand,29 E. O’Brien,5 C.A. Ogilvie,16 H. Ohnishi,5,38 I.D. Ojha,49,3 K. Okada,38 M. Ono,48
V. Onuchin,15 A. Oskarsson,29 I. Otterlund,29 K. Oyama,8 K. Ozawa,8 D. Pal,51 A.P.T. Palounek,27
V.S. Pantuev,44 V. Papavassiliou,34 J. Park,42 A. Parmar,33 S.F. Pate,34 T. Peitzmann,30
J.-C. Peng,27 V. Peresedov,17 C. Pinkenburg,5 R.P. Pisani,5 F. Plasil,35 M.L. Purschke,5A. Purwar,44 J. Rak,16 I. Ravinovich,51 K.F. Read,35,46 M. Reuter,44 K. Reygers,30 V. Riabov,37,40
Y. Riabov,37 G. Roche,28 A. Romana,25 M. Rosati,16 P. Rosnet,28 S.S. Ryu,52 M.E. Sadler,1
N. Saito,38,39 T. Sakaguchi,8,50 M. Sakai,32 S. Sakai,48 V. Samsonov,37 L. Sanfratello,33 R. Santo,30
H.D. Sato,24,38 S. Sato,5,48 S. Sawada,20 Y. Schutz,45 V. Semenov,15 R. Seto,6 M.R. Shaw,1,27
T.K. Shea,5 T.-A. Shibata,47,38 K. Shigaki,14,20 T. Shiina,27 C.L. Silva,41 D. Silvermyr,27,29
K.S. Sim,22 C.P. Singh,3 V. Singh,3 M. Sivertz,5 A. Soldatov,15 R.A. Soltz,26 W.E. Sondheim,27
S.P. Sorensen,46 I.V. Sourikova,5 F. Staley,10 P.W. Stankus,35 E. Stenlund,29 M. Stepanov,34
A. Ster,21 S.P. Stoll,5 T. Sugitate,14 J.P. Sullivan,27 E.M. Takagui,41 A. Taketani,38,39 M. Tamai,50
K.H. Tanaka,20 Y. Tanaka,32 K. Tanida,38 M.J. Tannenbaum,5 P. Tarján,11 J.D. Tepe,1,27
T.L. Thomas,33 J. Tojo,24,38 H. Torii,24,38 R.S. Towell,1 I. Tserruya,51 H. Tsuruoka,48 S.K. Tuli,3
H. Tydesjö,29 N. Tyurin,15 H.W. van Hecke,27 J. Velkovska,5,44 M. Velkovsky,44 L. Villatte,46
A.A. Vinogradov,23 M.A. Volkov,23 E. Vznuzdaev,37 X.R. Wang,13 Y. Watanabe,38,39 S.N. White,5F.K. Wohn,16 C.L. Woody,5 W. Xie,6 Y. Yang,7 A. Yanovich,15 S. Yokkaichi,38,39 G.R. Young,35
I.E. Yushmanov,23 W.A. Zajc,9,† C. Zhang,9 S. Zhou,7,51 L. Zolin,17(PHENIX Collaboration)
1 Abilene Christian University, Abilene, TX 79699, USA
2 Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
3 Department of Physics, Banaras Hindu University, Varanasi 221005, India
4 Bhabha Atomic Research Centre, Bombay 400 085, India
5 Brookhaven National Laboratory, Upton, NY 11973-5000, USA
6 University of California - Riverside, Riverside, CA 92521, USA
7 China Institute of Atomic Energy (CIAE), Beijing, People’s Republic of China
8 Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo

113-0033, Japan
9 Columbia University, New York, NY 10027 and Nevis Laboratories, Irvington, NY 10533, USA
10 Dapnia, CEA Saclay, Bat. 703, F-91191, Gif-sur-Yvette, France
11 Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary
12 Florida State University, Tallahassee, FL 32306, USA
13 Georgia State University, Atlanta, GA 30303, USA
14 Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan
15 Institute for High Energy Physics (IHEP), Protvino, Russia
16 Iowa State University, Ames, IA 50011, USA
17 Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia
18 KAERI, Cyclotron Application Laboratory, Seoul, South Korea
19 Kangnung National University, Kangnung 210-702, South Korea
20 KEK, High Energy Accelerator Research Organization, Tsukuba-shi, Ibaraki-ken 305-0801, Japan
21 KFKI Research Institute for Particle and Nuclear Physics (RMKI), H-1525 Budapest 114, POBox 49,

Hungary
22 Korea University, Seoul, 136-701, Korea
23 Russian Research Center “Kurchatov Institute”, Moscow, Russia
24 Kyoto University, Kyoto 606, Japan
25 Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay, F-91128, Palaiseau,

France26 Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
27 Los Alamos National Laboratory, Los Alamos, NM 87545, USA
28 LPC, Université Blaise Pascal, CNRS-IN2P3, Clermont-Fd, 63177 Aubiere Cedex, France
29 Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden

149
30 Institut fuer Kernphysik, University of Muenster, D-48149 Muenster, Germany
31 Myongji University, Yongin, Kyonggido 449-728, Korea
32 Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, Japan
33 University of New Mexico, Albuquerque, NM, USA
34 New Mexico State University, Las Cruces, NM 88003, USA
35 Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
36 IPN-Orsay, Universite Paris Sud, CNRS-IN2P3, BP1, F-91406, Orsay, France
37 PNPI, Petersburg Nuclear Physics Institute, Gatchina, Russia
38 RIKEN (The Institute of Physical and Chemical Research), Wako, Saitama 351-0198, JAPAN
39 RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973-5000, USA
40 St. Petersburg State Technical University, St. Petersburg, Russia
41 Universidade de São Paulo, Instituto de Fı́sica, Caixa Postal 66318, São Paulo CEP05315-970, Brazil
42 System Electronics Laboratory, Seoul National University, Seoul, South Korea
43 Chemistry Department, Stony Brook University, SUNY, Stony Brook, NY 11794-3400, USA
44 Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, NY 11794, USA
45 SUBATECH (Ecole des Mines de Nantes, CNRS-IN2P3, Université de Nantes) BP 20722 - 44307,

Nantes, France
46 University of Tennessee, Knoxville, TN 37996, USA
47 Department of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan
48 Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan
49 Vanderbilt University, Nashville, TN 37235, USA
50 Waseda University, Advanced Research Institute for Science and Engineering, 17 Kikui-cho, Shinjuku-ku,

Tokyo 162-0044, Japan
51 Weizmann Institute, Rehovot 76100, Israel
52 Yonsei University, IPAP, Seoul 120-749, Korea

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