Proton and Antiproton Productionin High Energy Heavy Ion Collisions at RHIC

Masahiro KONNO(Doctoral Program in Physics)

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
Relativistic heavy ion collisions is a means to approach Quark-Gluon Plasma (QGP) state
which is composed of deconfined and freely moving quarks and gluons. Currently, generating andexploring the QGP state is underway at Relativistic Heavy Ion Collider (RHIC) at Brookhaven
National Laboratory. The PHENIX experiment is one of the experiments at RHIC.
Particle production in relativistic heavy ion collisions is a basic and important topic for bothunderstanding the collision dynamics and search for the QGP state. It is usually divided into twoparts in transverse momentum - soft and hard particle productions. Soft part (pT . 2 GeV/c)means particle emission from a thermal source with collective flow, hard part (pT & 2 GeV/c)means hard scattering followed by jet fragmentation.
One of the remarkable findings at RHIC is particle-type dependences of hadron yields andemission patterns, especially its difference between baryons and mesons, at intermediate pT (2-5√
GeV/c). In central sN N = 200 GeV Au+Au collisions, there is a significant suppression in meson yields compared to expectations from peripheral Au+Au and scaled p+p results. In contrast,a large enhancement of baryons relative to mesons was observed at intermediate p T . Moreover, in
elliptic flow measurements, a baryon-meson difference was also found in its magnitude. This difference between baryons and mesons are explained by hydrodynamic flow, quark recombination
models, and so on. Multiple mechanisms are thought to be involved for intermediate-pT hadronproduction. However we do not know the exact relative contributions of those mechanisms at
the moment.
The purpose of this thesis is to study hadron production mechanisms at intermediate pT
and final-state interactions between hadrons produced in relativistic heavy ion collisions. We
have performed a systematic study of proton and antiproton spectra in Au+Au/Cu+Cu/p+p√
collisions at sN N = 200/62.4 GeV. The data set taken in the PHENIX experiment allows
us to study the energy dependence and system size dependence of the baryon enhancement.
The spectra have been measured at mid-rapidity (|η| < 0.35) over the range of 0.5 < p T < 6
GeV/c with particle identification by time-of-flight and threshold-type Cherenkov light emission
methods. The pT range of charged hadron identification has been extended by the high statistics
data. Also the particle identification capability at high pT has been enhanced by introducing
an Aerogel Cherenkov counter in PHENIX. The identified hadron production can be studied
up to 5 GeV/c for charged pions, and 7 GeV/c for (anti)protons. In this thesis, we present
identified charged hadron pT spectra (π/K/p and their antiparticles), particle ratios, nuclear
modification factors, chemical/kinetic freeze-out properties and their scaling properties between
different collision systems.

2
In all collision systems (Au+Au, Cu+Cu), we confirm the baryon enhancement at intermediate pT . We find that the baryon enhancement and freeze-out properties (kinetic freeze-out
temperature, transverse flow velocity) can be scaled with the number of participant nucleons,
which is corresponding to the system volume, between Au+Au and Cu+Cu collisions at the same√
collision energy sN N = 200/62.4 GeV even though the overlap region has a different shape. At
lower energy 62.4 GeV, proton production seems to be more affected by baryon number transport
process. Therefore antiproton would be a good indicator of the baryon enhancement.
Using a simple two-component model including soft (thermal emission with collective radialflow) and hard (jet fragmentation with quenching effect) hadron components, we can reproduce
the measured pT spectra, and identify crossover region from soft to hard hadron productions atintermediate pT . We estimate the relative fraction of soft and hard components - soft and hardcomponents become of equal size in this pT region (2-4 GeV/c). The crossing point depends on
collision centrality. It is shifted to higher pT in more central collisions due to radial flow effect.
Radial flow effect is significant in central Au+Au collisions compared to smaller systems. Thiseffect pushes heavier particles like protons to higher pT . We think that the baryon enhancement
at intermediate pT can be attributed to radial flow effect. We also discuss the relation between
this radial flow picture and quark recombination picture. In a simple recombination picture, they
are not inconsistent. The difference of chemical and kinetic freeze-out temperatures provides ahint for the duration time of hadronic stage.
At high pT & 5 GeV/c, p/π (p̄/π) ratios in central Au+Au collisions approach the values
in p+p collisions. And RCP shows similar suppression for pions and (anti)protons, though they
have different sensitivities to quark and gluon jets. The results indicate that hard-scatteredpartons (quarks and guluons) have similar energy loss when traversing the nuclear medium, andparton fragmentation function does not change.

Acknowledgments
I first would like to express my great gratitude to Prof. Y. Miake for his appropriate advices
and continuous encouragement. I learned a lot of things from him in many aspects. I would
like to thank Prof. S. Esumi for valuable advices and discussions. I am always taught from his
many-sided ways of thinking, and of course his toughness. I would like to thank Prof. T. Chujo
for many advices especially on data analysis. His elaborateness and constant work to anythingis example for me.
I would like to express my warm appreciation to all the present and past members of the highenergy nuclear physics group at University of Tsukuba. I would like to thank Prof. M. Inaba,
Mr. S. Kato for their helps. I wish to express my thanks to Dr. S. Sato, Dr. A. Kiyomichi
for many useful advices in life at Tsukuba and BNL. I would like to thank Dr. H. Masui, Dr.
S. Sakai, Ms. M. Shimomura, Mr. S. Takagi, Mr. S. Kaminaga for their help, friendship anddiscussions. I also acknowledge Mr. Y. Nagata, Mr. M. Oka, Mr. K. Miki, Mr. Y. Ikeda, Mr.
R. Tanabe and many other colleagues for their friendship.
I would like to express my thanks to all the members of the PHENIX collaboration for many
useful advices and helps in detector work and data analysis. I wish to express my thanks to
Dr. A. Enokizono, Prof. V. Greene, Dr. K. Homma, Dr. A. Taranenko (the Global-Hadron
physics group convenors), Dr. E. Kistenev, Prof. R. Lacey, and many other people for their kindencouragement and many useful advices.
I acknowledge for all the members of the PHENIX-J for their friendship and valuable discussions during my stay at BNL. I would like to thank Prof. H. Hamagaki and Prof. K. Ozawa for
their arrangement and support during stays at BNL.
Finally, I would like to express my great appreciation to my parents and brothers Masanori,
Mikie, Hideki, and Tatsuya for their support and encouragement. I could never finish my thesis
without their great help and understanding.

Contents
1 Introduction

1

1.1

Quantum Chromodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.2

Quark Gluon Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.3

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

3

1.3.1

p+p, p(d)+A, A+A Collisions . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.3.2

Collision Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.3.3

RHIC Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

1.3.4

Hadron Production at Intermediate pT . . . . . . . . . . . . . . . . . . . . 11

1.4

Thesis Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Experimental Setup

14

2.1

Relativistic Heavy-Ion Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2

PHENIX Detector Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3

Global Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4

2.3.1

Beam Beam Counters (BBC) . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.2

Zero Degree Calorimeters (ZDC) . . . . . . . . . . . . . . . . . . . . . . . 20

Central Arm Spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.1

Central Arm Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.4.2

Drift Chambers (DC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.4.3

Pad Chambers (PC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.4.4

Electromagnetic Calorimeters (EMCal) . . . . . . . . . . . . . . . . . . . . 25

2.4.5

Time of Flight Detector (TOF) . . . . . . . . . . . . . . . . . . . . . . . . 26

2.4.6

Aerogel Cherenkov Counter (ACC) . . . . . . . . . . . . . . . . . . . . . . 27

3 Data Analysis
3.1

29

Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.1

Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.1.2

Minimum Bias Trigger and Efficiency . . . . . . . . . . . . . . . . . . . . . 29

3.1.3

Centrality Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.1.4

Participant-Spectator Model and Glauber Model . . . . . . . . . . . . . . . 31

iii
3.2

Charged Particle Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2.1

Track Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2.2

Track Association and Selection . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3

Event and Track Selection Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.4

Quarlity Assurance - run-by-run stability check . . . . . . . . . . . . . . . . . . . 39

3.5

Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5.1

Time of Flight Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.5.2

Aerogel Cherenkov Counter . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.5.3

Particle Contamination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.6

Background Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.7

Fiducial Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.8

Monte Carlo Correciton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.9

3.8.1

Spectra Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.8.2

Multiplicity-dependent Efficiency Correction . . . . . . . . . . . . . . . . . 54

Invariant Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.10 Weak Decay Feed-down . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.11 Systemtaitc Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4 Results
4.1

61

Transverse Momentum Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.1.1

pT spectra (ACC) – Au+Au 200 GeV . . . . . . . . . . . . . . . . . . . . . 62

4.1.2

pT spectra (TOF) – Au+Au 200 GeV . . . . . . . . . . . . . . . . . . . . . 63

4.1.3

pT spectra (ACC) – Cu+Cu 200 GeV . . . . . . . . . . . . . . . . . . . . . 64

4.1.4

pT spectra (TOF) – Cu+Cu 200 GeV . . . . . . . . . . . . . . . . . . . . . 65

4.1.5

pT spectra (TOF) – p+p 200/62.4 GeV . . . . . . . . . . . . . . . . . . . . 67

4.2

Mean Transverse Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.3

Particle Yield at Mid Rapidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.4

Particle Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.5

4.4.1

p/π ratios vs. pT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.4.2

p/π ratios vs. Npart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.4.3

p/p ratio vs. pT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Nuclear Modification Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.5.1

RAA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.5.2

RCP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5 Discussions
5.1

84

Freeze-out Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.1.1

Chemical Freeze-out – Statistical Model Fit . . . . . . . . . . . . . . . . . 85

iv
5.1.2
5.2

Kinetic Freeze-out – Blast-wave Model Fit . . . . . . . . . . . . . . . . . . 88

Hadron Production at Intermediate pT . . . . . . . . . . . . . . . . . . . . . . . . 97
5.2.1

Proton and Antiproton Enhancement . . . . . . . . . . . . . . . . . . . . . 97

5.2.2

Two-component Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Decomposition of pT Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Fraction of Soft/Hard Components . . . . . . . . . . . . . . . . . . . . . . 106
Soft/Hard Separation in Particle Ratios. . . . . . . . . . . . . . . . . . . 109

Soft/Hard Separation in Particle Yield . . . . . . . . . . . . . . . . . . . . 111
Soft/Hard Separation in Elliptic Flow . . . . . . . . . . . . . . . . . . . . . 112
Summary of Two-component Model . . . . . . . . . . . . . . . . . . . . . . 114
5.2.3

Quark Recombination Picture . . . . . . . . . . . . . . . . . . . . . . . . . 114

5.2.4

Jet Fragmentation and Jet Quenching . . . . . . . . . . . . . . . . . . . . . 116

6 Conclusions

120

A Kinematic Variables

122

Chapter 1
Introduction
In this chapter, the current relativistic heavy-ion physics is reviewed with major
findings at RHIC. The motivation of this thesis is given.

1.1

Quantum Chromodynamics

In our current understanding, the fundamental elements of hadrons are quarks and gluons. Theyinteract with each other via strong force which is described in Quantum Chromodynamics (QCD).
And we know that quarks are confined inside a hadron. The question is: “Quarks can exist as anapparent degree of freedom?” Lattice QCD calculations predict a phase transition from hadronicmatter to a deconfined state at high temperature and high energy density, in which quarks andgluons are freely moving over a large volume. This state is called Quark-Gluon Plasma (QGP).
Many static properties of the high-temperature phase of QCD matter have been studied in detailby means of lattice calculations [1]. Among these are the equation of state (i.e. energy density
(T) and pressure p(T)), quantities related to color confinement such as the potential Vqq̄ (r)between a pair of heavy quarks, and quantities related to chiral symmetry breaking. The resultsof QCD calculations confirm that a dramatic rearrangement of the internal structure of hadronicmatter occurs near critical temperature Tc , which is consistent with the idea that open-color
states are free above Tc and chiral symmetry is restored, except for the small current massesof light quarks, which are not of QCD origin. Figure 1.1 shows a QCD-phase boundary thatwas obtained by Lattice QCD Monte Carlo calculations [2, 3]. The dashed line represents thelattice gauge theory results to larger values of chemical potential. Within uncertainties, theenergy density along this line is constant and corresponds to c ∼0.6 GeV fm−3 , i.e. to thesame value as that found from lattice calculations at µB = 0. It is said that the QCD phasetransition indeed sets in when the energy density reaches a certain critical value. Figure 1.1
also shows a compilation of chemical freeze-out parameters, extracted from experimental datathat were obtained in a very broad energy range from GSI/SIS through BNL/AGS, CERN/SPS

1. Introduction

2and BNL/RHIC [4, 5]. At SPS and RHIC the chemical freeze-out parameters seem to reachthe critical conditions obtained from lattice calculations. Figure 1.2 shows results from a lattice

Figure 1.1: Lattice QCD Monte Carlo results on QCD-phase boundary [2, 3]. The filled point
represents the endpoint of crossover transition. Open symbols: chemical freeze-out conditions
obtained from a statistical analysis of experimental data [4, 5].

QCD calculation of the energy density (/T 4 ) as a function of temperature [6]. The sharp rise of
the energy density at Tc ∼175 MeV for two light quark flavors signals an increase of the effective

number of degrees of freedom. The transition becomes the first order for three light flavors, but
the order of the phase transition is still not clear for a realistic value of the strange quark mass.
However, a sharp crossover is clearly present.

Figure 1.2: Energy density (/T 4 ) for 2- and 3-flavor QCD with light quarks [6].

1. Introduction

1.2

3

Quark Gluon Plasma

The principle of asymptotic freedom states that the effective coupling constant αs of QCD falls
with increasing momentum transfer Q2 , or equivalently with decreasing distance between particles. In a thermal medium, the characteristic momentum transfer between massless particles is oforder the temperature T, and thus the effective coupling between quarks and gluons must become
weak when T goes up. So we expected to form a plasma composed of weakly interacting quarks
and gluons (QGP). Now the question is: “How the QGP can be detected?” The experimental
search of QGP state has been based on various possible signals which can provide evidence ofits formation. Through those signals, we try to determine if the created system is thermallyequilibrated, and if it is not just hadron gas. It was expected that the search for the QGP would
proceed by looking for its predicted properties, or by the discovery of anomalies or discontinu√
ities as a function of some experimental observable, for example, collision energy sN N in A+A
collisions. Various experimental signatures/probes have been proposed with their sensitivity to
expected properties of the QGP. For example, degrees of freedom, strangeness enhancement,
J/ψ suppression (Debye screening), jet quenching can be listed as signatures. However, it wasalso realized that systematic studies and comparison of p+p, p(d)+A and A+A data are equallyimportant to understand basic processes behind the phenomena observed in A+A collisions [7].
The importance is to distinguish the ordinary physics of relativistic heavy ion collisions from thesignatures of production of a new phenomenon like QGP. The characterization of QGP properties is also based on those signals. Here the properties include: equation of state, order of thephase transition, transport properties, hadronization mechanisms, and so on. And it is of course
important how to relate the QGP properties to observations in the laboratory.

1.3

Relativistic Heavy-Ion Collisions

Relativistic heavy ion collisions is the means to approach the QGP state. Currently, generatingand exploring the QGP state is underway at RHIC (the Relativistic Heavy Ion Collider at BNL),and soon at LHC (the Large Hadron Collider at CERN). RHIC was constructed to investigate
the properties of nuclear matter at high energy densities. The motivation for this research arosein the 1970’s from speculations about possible states of nuclear matter at high nuclear densities.
Since 1980’s many experimental relativistic heavy-ion programs have been performed at AGS,
SPS, and now being at RHIC.

1.3.1

p+p, p(d)+A, A+A Collisions

As said before, systematic studies of p+p, p(d)+A data are important both as a benchmark
for the understanding of A+A collisions and as a means to explore physics in itself. Most of

1. Introduction

4

the heavy-ion observables require p+p measurements of the same observables for comparison.
Because it is necessary to identify the specific collective effects in A+A collisions and to separate
them from phenomena present already in p+p collisions. For example, the following items canbe listed as a part: (i) Slopes of transverse-mass distributions: comparison of slopes in A+A
collisions with those in p+p allows one to determine the collective effects such as transverse
flow present in A+A and absent in p+p. (ii) Particle yields and ratios: particle ratios areindicative of chemical equilibration achieved in A+A collisions and should be compared to thosein p+p collisions. (iii) Ratios of momentum spectra: ratios of transverse momentum spectra
at sufficiently high momenta allow one to discriminate between different partonic-energy losses
of quarks and gluons. (iv) Jet fragmentation functions: model calculations of medium-induced
parton-energy loss predict a modification of jet fragmentation functions.
In p(d)+A and A+A collisions, multiple scattering occurs at both hadronic and partonic
levels. Multiple scattering influences many aspects of the dynamics of high energy nuclear collisions, in particular the initial parton scattering responsible for bulk particle production and rare
hard processes. It depends on the geometry of A+A collision. Determination of the collisiongeometry is a key element in the study of heavy ion collisions. Experimentally, the number offorward neutrons and the total multiplicity in A+A collisions are used for determining an impact parameter. The impact parameter dependence of Ncoll (number of binary nucleon-nucleon
collisions) and Npart (number of participating nucleons) can be evaluated with a Glauber model(see Section 3.1 for centrality tagging and Glauber calculation).

1.3.2

Collision Dynamics

Static properties of QGP are evaluated and predicted by lattice QCD calculations, however the
dynamical properties are still less known because the lattice gauge theory does not permit a
direct calculation of quantities related to real-time evolution.
A phenomenological picture of collision is the following. Figure 1.3 shows a picture of spacetime evolution of heavy-ion collisions. After an impact of the incoming nuclei, the kinetic energyof both nuclei would be partially dissipated in the overlapped region of colliding nuclei. The
system is heated so that it undergoes a phase transition from normal nuclear matter to QGP
state. The QGP is a deconfined state with chemical and thermal equilibration, which lasts overa short formation time (τ ∼10 fm/c). Then the system expands longitudinally and transversely,

and cools, and hadronization occurs. Eventually it freezes out to a system of hadrons which
are observable. Thus, hadrons produced in the collision are the most abundant and dominantsource of information about the collisions. However they suffer from final-state interactions,which partially mask the early information.
When colliding two nuclei, a part of the initial kinetic energy (39 TeV in Au+Au at√
sN N =

200 GeV) is redistributed after the collision in terms of particle production and collective mo-1. Introduction

5

Figure 1.3: Schematic view of space-time evolution of heavy-ion collisions.

tion. The BRAHMS experiment measures the rapidity distribution of net-protons as shown in
Figure 1.4, and determines how much kinetic energy appears to be retained [8]. The data indicates that in central Au+Au collisions, over 28 ± 3 TeV of energy is deposited in heating the

newly created medium and collective motion. The PHOBOS experiment observes the creationof approximately ∼5000 charged particles and thus ∼7500 total particles including neutral par-ticles [9]. The mean transverse momentum for pions is of order 400 MeV. If we translate this

into three dimensions and multiply by the particle number, we obtain transverse energy of only
about 4 TeV which is available for particle production (excitation) in heavy ion collisions. Thus,a large fraction of the incident energy translates into the longitudinal expansion. Indeed we cansee a flat rapidity distribution of charged particles around midrapidity. So longitudinal boost
invariance partly holds at midrapidity. Figure 1.5 shows the Bjorken energy density estimate

Figure 1.4: Rapidity distributions of net protons at AGS, SPS, RHIC [8].

Bj τ , which is the transverse energy density divided by the transverse overlap area, multipliedby τ (formation time) [10]. If we take τ = 0.35 fm/c as a reasonable time scale [11], then  Bj τ is

1. Introduction

6∼15 GeV/fm3 in central 200 GeV Au+Au collisions. The values is much larger than the energy

2∈Bjτ [GeV/fm /c]density (∼0.6 GeV/fm3 ) of the phase transition predicted by lattice QCD calculations.

4

2
200 GeV
130 GeV19.6 GeV
0

100

200

300

Np

Figure 1.5: Bj τ at RHIC three energies (PHENIX) [12].

Various modeling tools have been developed to describe the collision dynamics including
space-time evolution. Relativistic hydrodynamic calculation is one of them. The following items
are frequently explained/discussed in those models.
• Initial conditions• Thermalization• Hydrodynamical expansion• Propagation of hard probes through the matter (parton energy loss)
They try to extract basic thermodynamic and transport properties from the data, such as equation of state, viscosity, stopping power, heavy quark diffusion constant, and color screening lengthand so on.

1. Introduction

1.3.3

7

RHIC Findings

The RHIC data taken so far are already providing various findings about the properties of medium
created at RHIC. Major findings are shown below.
• High-pT suppression

One of the discoveries at RHIC is that both neutral pion and charged hadron spectra at highpT >2 GeV/c in central Au+Au collisions are suppressed relative to the p+p or peripheral
spectra normalized by the number of binary nucleon collisions (Ncoll ). Figure 1.6 shows
RAA (ratio of spectra in A+A to in p+p normalized by Ncoll ) as a function of pT for π 0 ,η, direct γ [13]. This suppression is described in terms of “jet quenching” effect (parton

Figure 1.6: RAA as a function of pT for π 0 , η, direct γ in central Au+Au collisions at√

sN N =

200 GeV [13].

energy loss via gluon radiation) which is considered as an important probe for the earlystage of heavy ion collisions where very hot, dense partonic matter (QGP) could exist. On
the other hand, direct γ is not suppressed as expected because it should not loss the energy
in the medium. At RHIC, the collision energy is high enough to occur hard scattering ofpartons (quarks and gluons) leading to jets of hadrons. Over the past years, a lot of work
has been devoted to study the propagation of jets through QCD matter experimentallyand theoretically. For example, angular multi-particle correlation studies in experiments,
pQCD calculations including nuclear effects such as parton energy loss are going on intheory side. Also, clear back-to-back angular correlations between high-pT particles seenin p+p and d+Au are absent in Au+Au data. This is another support for jet quenching[14]. In order to confirm that the observation of suppression is specific in Au+Au, a control
experiment d+Au was carried out. The d+Au collisions are expected not to produce thehot-dense state. Hence the observed absence of high-pT suppression in d+Au tells us that
initial-state effects are small, so that the suppression observed in Au+Au collisions is most
likely due to parton energy loss in the hot medium [15].

1. Introduction

8• Baryon enhancement

However the amount of the suppression depends on hadron species in the pT range of 2-4

GeV/c. Protons were found not to be suppressed in this pT range as shown in Figure 1.7.
Proton to pion ratio is clearly higher around pT = 2-3 GeV/c in central Au+Au collisions,which has never seen in elementary collisions. The STAR experiment also shows that
Λ/K 0 > 1 at pT = 2-3 GeV/c [16]. Baryons are enhanced compared to mesons. Clearly,

Figure 1.7: p(p̄)/π ratio vs. pT in Au+Au, d+Au, p+p collisions.

something is going on in this pT region which has come to be called intermediate pT .
Quark recombination model has been proposed to explain this baryon enhancement. If
light quarks have a thermal distribution like an exponential function, then the productionof protons via recombination at intermediate pT is favored over fragmentation from a powerlaw distribution. The p/π ratio is also enlarged because a proton of given pT is produced byrecombination of 3 constituent quarks of pT /3, so there is no penalty compared to forming apion from 2 quarks of pT /2. This model requires the assumption of a thermalized partonic
phase, which could be called QGP. Unfortunately, this model cannot explain all facets ofthe data at intermediate pT . For example, from angular two-particle correlation study,
baryons and mesons seem to form jet-like structure even at this pT range [17].
• Thermalization

Relative particle abundances are compared to expectations from statistical models, as stud-

ied at SPS energies. Figure 1.8 shows various particle ratios of hadronic yields measured√
at midrapidity in central Au+Au collisions at sN N = 200 GeV. They are compared toresults of a statistical model fit, which is based on a grand canonical ensemble with parameters such as temperature, chemical potential [18]. The agreement between data andthe model looks good. We now consider that final state hadrons are emitted from a locallythermal source following a statistical distribution. The fitted baryon chemical potentialµB = 28 ± 3 MeV is small compared to those at lower energies, indicating low net baryon

1. Introduction

Figure 1.8: Comparison of fit results to the data in central Au+Au collisions at

9√sN N = 200

GeV [18].

density in the medium. The chemical freeze-out temperature Tch = 157 ± 3 MeV appears
to be close to the QCD phase transition temperature from lattice calculations.

• Hydrodynamic behavior

Figure 1.9 shows transverse momentum spectra for π/K/p in Au+Au collisions at√
sN N =

200 GeV. At low pT , the spectra for protons has a convex shape compared to other particle
species. This observation indicates that the system is expanding with radial collective flow.
The strength of radial flow in central collisions is larger than that in peripheral collisions.
These features were already observed at SPS.
Large azimuthal anisotropy v2 observed in heavy-ion collisions is another discovery
at RHIC. v2 is the strength of elliptic component of collective flow which is defined as
the second moment of the fourier expansion of particle emission in azimuthal angle. The
v2 reflects the shape of initial overlap region of two nuclei, and the subsequent collective
expansion process. Compared with collisions at lower energies, the values of v2 are found to
be larger, which suggest that thermalization is taking place much faster than expected fromnormal hadronic rescattering. Thus the large v2 implies other ingredients (i.e. quarks andgluons) for thermalization than hadrons. Not only light hadrons but also decay electrons
from D, B mesons show finite v2 as large as 10% [20]. As shown in Figure 1.10, pT
dependence of v2 provides important clues to understand the particle production. At pT
region below 1.5 GeV/c, the curves of π/K/p particles are consistent with hydrodynamic
calculation. A clear departure from the hydrodynamic behavior is observed at higher p T . It

10

2

2

2

2

2

2

(1/2 π pT ) d N / dpT dy [c / GeV ] (1/2 π pT ) d N / dpT dy [c / GeV ]1. Introduction

10

3

10

2

π+
+
K
p

10

πK

p

1
10

-1

10

-2

10

-3

Positive(0 - 5% central)

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

Negative(60 - 92% peripheral)

10
1
10

-1

10

-2

10

-3

10

-4

10

-5

10

-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 1.9: Transverse momentum spectra for π/K/p in Au+Au collisions at√

sN N = 200 GeV(PHENIX) [19].

is believed that the v2 values above 2 GeV/c depend on an interplay between hydrodynamic
process and hard process.

Figure 1.10: Elliptic flow strength v2 vs. pT in 200 GeV Au+Au collisions with hydro model
lines [21].

Differential elliptic flow and radial flow patterns in Au+Au collisions at√

sN N = 200 GeV

are remarkably well described at low pT by ideal relativistic hydrodynamics calculations.
This is one of the evidences suggesting that the matter produced at RHIC exhibits verysmall viscosity (i.e. very short mean free path), thus nearly perfect fluid properties, insteadof behaving like a gas of free quarks and gluons. Moreover, v2 values of mesons and baryons

1. Introduction

11

are scaled with the number of constituent quarks (2 for mesons, 3 for baryons). The scaledv2 shows a universal curve for mesons and baryons as in Figure 1.11. This curve indicates aquark-level elliptic flow, and the hadronization is happened through quark recombination
process.
(a)

v2/nq

0.1

π++π- (PHENIX)
K++K - (PHENIX)
K0S (STAR)(b)p+p (PHENIX)Λ +Λ (STAR)+Ξ- +Ξ (STAR)

0.05

0

0

0.5
1
1.5
pT /nq (GeV/c)

2

0

0.5

1

KET/nq (GeV)

1.5

2

Figure 1.11: v2 /n vs pT /n (KET /n) for identified particle species in minimum bias 200 GeV
Au+Au collisions. n denotes the number of constituent quarks (2 for mesons, 3 for baryons) [22].

1.3.4

Hadron Production at Intermediate pT

As mentioned in Section 1.3.3, one of the most remarkable observations in heavy ion collisions
at RHIC is a large enhancement of baryons and antibaryons at intermediate pT (2-5 GeV/c). In√
central Au+Au collisions at sN N = 200 GeV, there is a significant suppression in meson yields(π, K, etc.) compared to peripheral Au+Au or p+p results. In contrast, a large enhancementof baryons (p, p, Λ, etc.) relative to mesons is observed at intermediate pT [23, 24]. The(anti)proton to pion ratio is enhanced by almost a factor of 3 when one compares most central
Au+Au events to peripheral or p+p events. On the other hand, in elliptic flow measurements,
a baryon-meson difference is also found in its magnitude (v2 as a function of pT ). We now
recognize that these observations as a baryon-meson difference at intermediate p T . In this pT
region, jet fragmentation process dominates the hadron production in p+p collisions. And we
expect that the fragmentation is independent of collision system. Therefore the large baryon
fraction observed at RHIC is one of the surprising findings. By performing a control experiment- d+Au collisions, in which only cold nuclear matter is produced, we found that the suppressionof hadron yields is not caused by initial state interactions, but by final state interactions (i.e. jet
quenching) [25]. We also found that the Cronin effect (enhancement from multiple scattering)has a particle-type dependence. The Cronin effect is larger for protons than those for pions,
kaons. However this difference between baryons and meson is not enough to account for thebaryon enhancement seen in Au+Au collisions [26].
The observed baryon enhancement is explained in some different ways:

1. Introduction

12• Strong radial flow which pushes heavier particles to larger pT [27]• Recombination of hard-scattered quarks with quarks from thermalized medium [28]• Baryon junction mechanism [29]• Medium modification of jet fragmentation [30]
The intermediate pT region is considered a transition region from soft to hard hadron production
mechanism. Here, soft part includes hydrodynamic flow [27], quark recombination [28], etc. Hard
part includes jet fragmentation and its quenching. Multiple hadronization mechanisms and finalstate interaction are involved at intermediate pT . However the relative contributions of soft/hardparts are not yet fully understood. So the next step is answering the following questions of thebaryon-meson difference at intermediate pT : “What is the origin?”, “If multiple mechanisms are
involved, what are their relative contributions?” In other words, we should know (i) what p Thydrodynamic contribution exist up to, (ii) if quark recombination process is really necessary,(iii) if we can separate radial flow between hadronic and partonic phases.

1.4

Thesis Motivation

The purpose of this thesis is to study hadron production mechanisms at intermediate pT (2-5
GeV/c) and final-state interactions between hadrons produced in relativistic heavy ion collisions.
The main target is to find the origin of the baryon enhancement at intermediate pT by focusingon (anti-)proton production. Since (anti-)proton is sensitive to collective flow due to its relatively
large mass and indicative for baryon number transport especially at lower energies.
In the PHENIX experiment, the particle identification capability has been enhanced by the
introduction of a new aerogel Cherenkov counter. (I have contributed to the R&D, construction,
installation processes of the counter.) We can now study the identified charged hadron production at higher pT than past (up to 5 GeV/c for charged pions, and 7 GeV/c for (anti)protons). We
measure identified inclusive single particle spectra using the data taken at the PHENIX experiment. The spectra are measured at mid-rapidity (|η| < 0.35) over the range of 0.5 < p T < 6 GeV/cwith particle identification by time-of-flight and threshold-type Cherenkov light emission methods. We perform a systematic study of proton and antiproton spectra in Au+Au/Cu+Cu/p+p√
collisions at sN N = 200/62.4 GeV. The data set allow us to study the energy dependence andsystem size dependence of the baryon enhancement. In addition to heavy ion data, we haveobtained high statistics 200 GeV and 62 GeV p+p data. The p+p data provides baseline spectra
to heavy ion data. It is important to quantify in-medium nuclear effects to hadron productionin heavy ion collisions.
In the thesis, we present identified charged hadron pT spectra, particle ratios, nuclear modification factors, freeze-out properties and their scaling properties between different collision

1. Introduction

13

systems. From the results, we try to estimate the relative contributions of soft/hard components
in the hadron production. And we try to answer the questions listed at the end of Section 1.3.4.
The measurement could provide valuable inputs for understanding the hadronization and nuclear
medium effects in the matter created in relativistic heavy ion collisions.

Chapter 2
Experimental Setup
In this chapter, the experimental setup is described. The RHIC facility and
PHENIX detector are explained.

2.1

Relativistic Heavy-Ion Collider

The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory is a 3.8-km circumference accelerator composed of two identical, quasi-circular rings of superconducting magnets (∼400 dipoles and ∼500 quadrupoles) with six crossing points. RHIC can accelerate nuclei(protons) up to a maximum of 100 (250) GeV/c per nucleon. The center-of-mass energies in√√
A+A and p(d)+A collisions, sN N = 200 GeV ( s = 500 GeV for p+p), are over an order of√magnitude higher than those at CERN-SPS ( sN N = 17.3 GeV). The achieved average A+A
luminosity is ∼4×1026 cm−2 s−1 . There are four dedicated experiments at RHIC: PHENIX,

STAR, BRAHMS and PHOBOS. The layout of RHIC accelerator complex is shown in Figure 2.1[31].

Figure 2.1: Layout of RHIC accelerator complex.

2. Experimental Setup

15

Table 2.1: Physics run summary table in PHENIX.
R
√
Ldt
Run
Year
SpeciessN N [GeV]Nevent
01
02
03
04

05

06

2000

Au+Au

2001/2002 Au+Au
2002/2003

2006

1µb−1

10 M

200

−1

170 M

−1

3.7 G

24 µb

p+p

200

0.15 pbd+Au

200

2.74 nb−1

5.5 G

p+p

200

0.35 pb−1

6.6 G

200

241 µb

−1

1.5 G

Au+Au

62.4

9 µb

−1

p+p

200

0.35 pb−1

6.6 G

Cu+Cu

200

3 nb−1

8.6 G

2003/2004 Au+Au

2004/2005

130

−1

58 M

Cu+Cu

62.4

0.19 nb

Cu+Cu

22.5

2.7 µb−1

9M

p+p

200

3.8 pb−1

85 G

p+p

200

10.7 pb−1

230 G

62.4

−1

28 G

p+p

0.1 pb

400 M

Heavy ion beams originate in a pulsed sputter source and are accelerated successively by
Tandem van der Graaf accelerator, Booster Synchrotron, and Alternating Gradient Synchrotron(AGS), where they are accelerated to 10.8 GeV/nucleon, fully stripped of their electrons, andinjected into RHIC. Acceleration and storage in RHIC utilize two Radio-Frequency (RF) systems,
one at 28 MHz to capture AGS bunches and accelerate to top energy, the other at 197 MHz toprovide a short collision diamond (25 cm) for efficient utilization of luminosity by the experiments.
The synchrotron phase transition of RHIC lattice is at T = 24.7, meaning that all ions except
protons pass through the beam instability at the transition. For light ions (A < 100), theluminosity is limited by beam-beam hadronic interactions, whereas for heavier ions the luminosity
lifetime is limited by intra-beam (intra-bunch) scattering. The RHIC beams are brought into
head-on collision at intersection regions. The final dipoles of the lattice are approximately 10 mfrom a collision diamond. Table 5.1.2 lists the beam species, energies, and integrated luminosity
for the RHIC runs to date. Figure 2.2 shows the nucleon-pair luminosity LN N in the past RHIC
runs [32]. In the future, RHIC is planned to be upgraded to increase its luminosity to study hard
and rare probes with low cross section or small branching ratio.

2. Experimental Setup

16

Figure 2.2: Nucleon-pair luminosity LN N in the past RHIC runs. Note: LN N is defined as LN N
= A1 A2 L.

2.2

PHENIX Detector Overview

The PHENIX (Pioneering High Energy Nuclear Interaction eXperiment) is one of the experiments
at RHIC. The PHENIX detector is designed to measure hadrons, leptons and photons with good
momentum and energy resolution. Another advantage is the ability to detect rare signals withpotential physics interest (direct photons, lepton pairs, jet fragments, etc.) by using Level-1 andLevel-2 triggers. The detector consists of a large number of detector subsystems. It is divided
into:• 2 central arm spectrometers for electron, photon and hadron measurements at mid-rapidity(|η| <0.35, ∆φ=π).

• 2 forward spectrometers for muon detection (|η|=1.15-2.44, ∆φ=2π).
• Global detectors for trigger and centrality selection.
The cut view and top view of the PHENIX detector are shown in Figure 2.3 and 2.4. The
midrapidity spectrometers have an axial magnetic field (strength 1.15 T·m), with tracking andmomentum measurements supplied by a drift chamber (DC) and 3 layers of MWPC’s with
pad readout (PC). Charged hadron identification over a broad momentum range is provided byTime of Flight (TOF), Ring Imaging Cerenkov (RICH), and Aerogel Cherenkov Counter (ACC).
Electrons and photons are measured in highly granular lead scintillator and lead glass calorimeters(EMCal). The combination of EMCal, RICH provides a hadron background rejection factor forelectron measurements of ∼ 103 over a wide momentum range. The forward muon arms havea radial magnetic field, with tracking based on drift chambers followed by a muon identifierconsisting of alternating layers of steel absorber and streamer tubes. The PHENIX detector

2. Experimental Setup

17

subsystems are summarized in Table 2.2. In the following data analysis, the global detectors anda subsets of the central arm detectors are used. They are explained in the following sections.

Figure 2.3: Cut view of PHENIX detector in 2005 (top: beam view, bottom: side view).

Figure 2.4: Top view of PHENIX detector.

2. Experimental Setup

18

Table 2.2: Summary of PHENIX detector subsystems.
Subsystem∆η∆φ

Purpose and Special Features360

muon (MMS)|η| <0.35◦-1.1 to -2.2

360◦0.72 T·m for η = 2

muon (MMN)

1.1 to 2.4

360◦0.72 T·m for η = 2

Magnet: central (CM)Beam-beam (BBC)ZDC
Drift chambers (DC)
Pad chambers (PC)
RICH
TOF

3.0< |η| <3.9

360

◦

360

◦

|η| <0.35

90◦ ×2|η| <0.35

◦

90 ×2

|η| <0.35

◦

90 ×2

|η| <0.35

20◦±2 mrad|η| <0.35

ACC

45

Trigger, start timing, z vertex, reaction plane
Minimum bias trigger.
Good momentum and mass resolution,∆m/m = 0.4% at m = 1GeV.
Pattern recognition, tracking
for nonbend direction.
Electron identification.

◦◦

PbSc EMCal|η| <0.35

90 +45

PbGl EMCal|η| <0.35

45◦

Up to 1.15 T·m.

Good hadron identification, σ ∼120 ps.

High-pT hadron identification, n = 1.011◦

For both calorimeters, photon and electron
detection.
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: (µTS)(µTN)-1.15 to -2.25
1.15 to 2.44

360◦

Tracking for muons.

360◦

Muon tracker north installed for year-3◦

Steel absorbers and Iarocci tubes forµ identifier: (µIDS)-1.15 to -2.25

360(µIDN)

1.15 to 2.44360◦muon/hadron separation.

2. Experimental Setup

2.3

19

Global Detectors

Event triggering is based on Beam-Beam Counters (BBC) and Zero Degree Calorimeters (ZDC).
The minimum bias trigger efficiency is ∼93 % for 200 GeV Au+Au case.

The PHENIX data acquisition system is able to record ∼500 MB/s to disk with event sizeof ∼100 KB (i.e. event rate of ∼5 kHz). The PHENIX on-line system takes signals from

Front End Modules (FEM) on each detector subsystem. Processing of event data begins when
Data Collection Modules (DCM) receive data via fiberoptic links from the FEM’s. The DCM’sformat/zero-suppress the data and generate data packets. These packets go to Event Builders

that assemble the events in final form. All of this is controlled by Master Timing System that
distributes the RHIC clocks. A two-level trigger system has been implemented in the PHENIX
experiment. Level 1 trigger system (LVL1) processes the reduced data from a part of detector
subsystems in parallel and makes a decision on each beam crossing. For each accepted event the
information from LVL1 is added to the detector data stream. The Level 2 trigger system (LVL2)
makes a fast analysis of each accepted event and decides if its data have to be stored or to bediscarded.
Event characterization (collision vertex, start timing, collision centrality) is also performed
with these global detectors. The BBC timing resolution of 40 ps results in a vertex position
resolution of 0.6 cm. Since the multiplicity of both forward neutrons in ZDC and charged
particles in BBC are correlated with the collision geometry, they can also be used to measure
the collision centrality (see Section 3.1.3).

2.3.1

Beam Beam Counters (BBC)Beam-Beam Counters (BBC) measure the timing and energy deposit of leading charged particles
from collisions. Two BBCs are placed 144 cm from the center of the intersection region on
North and South sides, and surround the beam pipe. This corresponds to a pseudo rapidity
range from 3.0 to 3.9 over the full azimuth. Each BBC is composed of 64 BBC elements (seeFigure 2.5). A BBC element consists of an one-inch mesh dynode photomultiplier tube mounted
on a 3 cm quartz Cherenkov radiator. The main roles of BBCs are: (i) to produce a signal for
the PHENIX Level-1 trigger, (ii) to provide a start time of Time-of-Flight measurement, (iii) tomeasure a collision vertex point along the beam axis, (iv) to determine a collision centrality and(v) to determine an angle of the reaction plane on an event-by-event basis. The BBC is designed
to operate under various collision species (dynamic range 1-30 MIPs), high radiation and large
magnetic field (0.3 T).

2. Experimental Setup

20

Figure 2.5: (a) Single Beam Beam counter. (b) A BBC array comprising 64 BBC elements. (c)BBC counter mounted on the PHENIX detector. The beam pipe is seen in the middle of thepicture.

2.3.2

Zero Degree Calorimeters (ZDC)

Zero-Degree Calorimeters (ZDC) are compact tungsten/fiber hadronic calorimeters, and detect
neutral beam fragments from collisions. Two ZDCs are used for triggering, luminosity monitoring, and centrality determination. The ZDCs are located 18 m downstream and upstream
from the interaction point along the beam axis, with acceptance 2.5 mrad centered on the beam
direction (see Figures 2.6 and 2.7). In front of the ZDCs, DX dipole magnets are installed. Theenergy flux into this acceptance in heavy ion collisions is dominated by non-interacting spectator
neutrons. Charged particles emitted from collisions are deflected out of the ZDC acceptance by
the magnets. The ZDC energy resolution is sufficient to discriminate individual beam velocity
neutrons. The luminosity for Au + Au collisions has been measured with 10% precision using aVernier scan of ZDC coincidence rates [33].

2. Experimental Setup

21

Figure 2.6: Location of ZDCs along the beam line.

Figure 2.7: Cut view at A-A position of the above picture.

2.4

Central Arm Spectrometers

Each of west and east central arm spectrometers covers a pseudo-rapidity range of |η| < 0.35

and an azimuthal angle φ of 90 degrees. As shown in the upper panel of Figure 2.3, each of
the spectrometers consists of layers of tracking and particle identification detectors. Particle
identification (PID) is a vital part of the PHENIX detector. There are multiple subsystems
dedicated for the PID. One is the Time-of-flight (TOF) subsystem using scintillation light emitted
from plastic scintillator. And the other is the RICH subsystem using Cherenkov light emitted

from radiator gas. Currently the RICH is using carbon dioxide gas (CO2 ). As well as the
TOF, Electromagnetic calorimeter (EMCal) provides flight time with larger acceptance coveragein azimuthal angle. EMCal is used also for measurement of neutral pion through two-gamma
decay.
In the past, hadron identification capability of the PHENIX has holes in the momentum
range: 2.5-5 GeV/c for π/K separation, >4 GeV/c for K/p separation. For further physics
research, extension of the momentum range was desired. So an aerogel threshold Cherenkov

2. Experimental Setup

22

counter (ACC) was proposed to extend the momentum range. By the addition of ACC withthe refractive index of 1.011, those gaps would be bridged, and hadron particle identification
can be achieved seamlessly up to pT of 7 GeV/c. The construction and installation of ACC wascompleted in 2003/2004. The ACC has started taking data from Run-4 period in PHENIX.

2.4.1

Central Arm Magnet

The PHENIX magnet system is composed of three spectrometer magnets, Central Magnet (CM)and Muon Magnets (MMN and MMS), with warm iron yokes and water-cooled copper coils.
Figure 2.8 shows the cutaway drawing of the PHENIX magnet showing CM and MM field lines.
The CM is energized by two pairs of concentric coils and provides axially symmetric magnetic
field parallel to the beam axis. The magnetic field for the central arms is axially symmetricaround the beam axis. Its component parallel to the beam axis has an approximately Gaussian
dependence on the radial distance from the beam axis, dropping from 0.48 T at the center to
0.096 T (0.048 T) at the inner (outer) radius of DC. The total field integral is about 1.15 Teslameters and that is minimized for the radius of R> 2 m (the radius of the DC). Charged particles
bend in a plane perpendicular to the beam axis. The bending angles are accurately measured
by DCs, from which the charged particle momenta can be determined.

PH

-4.0

-2.0

ENIX

0.0

2.0

4.0

Z (m)

Magnetic field lines for the two Central Magnet coils in combined (++) mode

Figure 2.8: Central magnet both colis in (++) configuration with magnetic lines.

2. Experimental Setup

2.4.2

23

Drift Chambers (DC)

Drift chambers (DC) are used to measure charged particle trajectories in r-φ plane and to determine their transverse momentum. The obtained tracking information is used to link tracks
through outer subsystems. The following performances are obtained:• Single wire efficiency: 95-96 %• Track-finding efficiency: > 99 %• Two track resolution: < 2 mm
• Single wire resolution: ∼165 µm
The DCs are located from 2 to 2.4 m in radial direction, and have 1.8 m long along the beam
direction. Each DC consists of two independent gas volumes as show in Figure 2.9. A gas mixtureof 50%Ar and 50%Ethan is chosen for the operation. Each DC covers 90◦ in azimuthal angle
φ and consists of 40 planes of sensing wires subdivided into 80 drift cells, each cell spanning
1.125◦ in azimuth. The wire planes are arranged in six types of wire modules stacked radiallyin the following order, X1, U1, V1, X2, U2, V2. Each of the X, U, and V modules contains 12
and 4 sense wires, respectively. The X, U, V wire orientations are shown in Figure 2.10. The
X1 and X2 wire modules run in parallel to the beam to perform precise track measurements
in r-φ. U1,V1 and U2,V2 wire modules are placed after X1 and X2, respectively. They havestereo angles about ±5◦ relative to the X wires and measure the z coordinate of the track. The
stereo angle is selected to match with the z resolution of pad chambers and minimize tracking

ambiguities.

Figure 2.9: Schematic view of drift chamber frame.

2. Experimental Setup

24

Figure 2.10: Left: Layout of wire position within one sector. Right: A schematic diagram ofstereo wire orientation.

2.4.3

Pad Chambers (PC)

Pad chambers (PC) are multiwire proportional chambers that form three separate layers (PC1,
PC2, and PC3) of the PHENIX tracking system. Each layer contains a single plane of wires
inside a gas volume bounded by two cathode planes. One cathode is finely segmented into anarray of pixels. Nine pixels are connected together electronically to form a pad (see Figure 2.11).
The pad size of PC1 is 0.84 cm × 0.845 cm which gives a position resolution of 1.7 mm alongz and 2.5 mm in r-φ. The pad size for PC2 and PC3 is chosen such that they have similar

angular resolution compared to PC1. PC1 determines a three-dimensional momentum vector
for each track by providing the z coordinate at the exit of DC. The information from DC andPC1 provides direction vectors through outer subsystems. PC2 and PC3 are used to reject (i)particles produced from secondary interactions or particle decays, (ii) low-momentum primary
tracks that curve around PC1 in the magnetic field and hit PC2 and PC3.

2. Experimental Setup

25

Figure 2.11: Left: Pad and pixel geometry. Right: A cell defined by three pixels.

2.4.4

Electromagnetic Calorimeters (EMCal)

Electromagnetic calorimeters (EMCal) is used to measure the spatial position and energy ofelectrons and photons. It covers the full central arm acceptance of 70◦ ≤ θ ≤ 110◦ and 2 ×
90◦ in azimuth. There are two types of calorimeters: Lead Glass (PbGl) Cerenkov calorimetersin E0/E1 sectors, Lead Scintillator (PbSc) sampling calorimeters in the other sectors. The Pbscintillator electromagnetic calorimeter is a sampling calorimeter made of alternating tiles of
Pb and scintillator consisting of 15,552 individual towers. Figure 2.12 shows a Pb-scintillator
electromagnetic calorimeter module consisting of four towers. The Pb-scintillator electromagneticp
calorimeter has a nominal energy resolution of 8.1 %/ E(GeV ) ⊕ 2.1 %. Low-pT charged

hadron identification is also possible from time-of-flight measurement (σT OF : 400-500 ps). Since
the calorimeter has 0.85 units of hadronic interaction length, high-pT charged hadrons also havea large probability of depositing a large fraction of their energy. So, it can be used to select aclean sample of high-pT charged hadrons.

2. Experimental Setup

26

Figure 2.12: Interior view of a single Pb-scintillator calorimeter module.

2.4.5

Time of Flight Detector (TOF)

Time-of-Flight detector (TOF) provides the flight time measurement for charged hadrons. The
TOF is located at a radial distance of 5.06 m from the interaction point, covering π/4 in azimuthal
direction in the lower part of the east arm as shown in Figure 2.13. TOF contains 960 scintillator
slats oriented along the r-φ direction. One TOF element consists of a plastic scintillator slat and
PMTs equipped at the both ends of the scintillator. The Schematic diagram of the components
of a single TOF panel are shown in Figure 2.14. TOF is designed to have a intrinsic timing
resolution of ∼ 100 ps in order to separate charged hadron in high momentum range: 3σ π/K

separation up to 2.4 GeV/c, 3σ K/p separation up to 4.0 GeV/c. Using the following equation,
particles are identified by their mass square value.

Tf light c 222) −1
m =p (
L(2.1)

where L is the flight path length which is the distance between TOF and the vertex position in
the magnetic field and Tf light is the flight time.

2. Experimental Setup

27

Figure 2.13: TOF detector mounted on the PHENIX East Arm.

Figure 2.14: Schematic diagram of the components of a single TOF panel.

2.4.6

Aerogel Cherenkov Counter (ACC)

Aerogel Cherenkov Counter (ACC) is a particle identification detector for high-p T charged
hadrons. It was installed in 2003/2004 and started taking collision data from Run-4 period(see Figure 2.15). ACC uses Silica aerogel (refractive index of n∼1.011) as its Cherenkov radiator. The pT reach of particle identification has been extended (up to 5 GeV/c for charged
pions, and 6 GeV/c for (anti)protons) by the introduction of ACC in PHENIX. The acceptance of the aerogel counter is about 4 m2 at a radius of ∼ 4.5 m from the beam line between
PC2 and PC3 at mid-rapidity (west arm W1 sector). The geometrical size of the detector is∼ 390(z) × 120(φ)× ∼ 30(r) cm3 (∆η = 0.70 and ∆φ = 14 deg) (see Figure 2.16). The aerogel2. Experimental Setup

28

counter is composed of 160 individual cells. The cells are stacked into an array (10 cells high (φ)
by 16 cells wide (z)). To eliminate dead space, every other cells along z-direction are flipped in
the radial direction. With this configuration, all the sensitive aerogel volumes are kept in one
plane, which contributes to the uniform detector response. The occupancy of the cells is kept
<10 % even in central Au+Au collisions. Each cell has aerogel volume (22(z) × 11(φ) × 12(r)cm3 ), followed by an integration air cube viewed by two 3-inch PMTs. The beam test done at
KEK-PS shows that the positional uniformity of light yield with this configuration is the bestof all studied configurations. The prototype has achieved 97.2 % pion detection efficiency and
2.8 % proton fake rate (3.8 σ separation) at 2 GeV/c, and provides enough photoelectron yield(∼15 pe (n=1.011) per cell per charged particle with β = 1) to separate different particles. The
readout electronics of ACC was developed based on that of PHENIX-RICH. It is designed todetect small signal like Cherenkov light.

Figure 2.15: Installation of Aerogel Cherenkov Counter.

Figure 2.16: Schematic view of ACC cell array (half sector).

Chapter 3
Data Analysis
In this chapter, we describe the analysis details such as track selection, particle
identification, Monte Carlo correction. The analysis is based on the experimental
data taken in Run-4/Run-5 (2003∼2005). The collision species and energies are:√Au+Au/Cu+Cu/p+p at s =200 GeV. (Lower energy 62.4 GeV data were analyzed
separately by other people.) Particle identification for charged hadrons is performed
with ACC (Aerogel Cherenkov counter) and TOF (Time-of-Flight counter). The main
observable is pT spectra for charged pions and (anti-)protons at mid-rapidity. Particle
ratios (p/p, p/π) are also calculated. Using the p+p spectra, nuclear modification√
factor RAA is calculated for Au+Au/Cu+Cu at sN N = 200 GeV.

3.1

Event Selection

3.1.1

Data Sets

Data sets used here are Minimum-bias triggered Au+Au/Cu+Cu/p+p collisions at√

sN N =

200 GeV. Those were taken in Run-4/Run-5 (2003∼2005) by the PHENIX experiment. The
magnetic field configuration are normal (++) and reverse (– –) fields for inner and outer coils.
The numbers of events are summarized in Table 3.1. We use the CNT nanoDST files whichcontains central arm detector information and event reconstruction information. For scanning
the real data, we prepared several analysis offline codes. The codes are run under the PHENIX
computing environment. The same code is used for single-particle Monte Carlo study to obtaincorrection factors of pT spectra.

3.1.2

Minimum Bias Trigger and Efficiency

Event triggering is based on Beam-Beam Counters (BBC) located at |η| = 3.0-3.9. A coincidence

between the north and south BBCs with minimum fired PMTs in each side is required. For 200

3. Data Analysis

30

Run

Year

Table 3.1: Summary of data sets.
√
SpeciessN N [GeV] B field setting

4

2003/2004 Au+Au

200++/– –

5

2004/2005

Cu+Cu

200

++/– –

5

2005

p+p

200

––

Nevent∼440 M∼620 M∼360 MGeV Au+Au case, the minimum number is 2. In other cases, the minimum number is 1. Thisis called BBC Local Level-1 Minimum bias trigger at Level-1 stage. Various Level-2 triggers arealso used for event monitoring and filtering. In offline analysis, a collision vertex position along
the beam axis is required within |z| < 30 cm. The vertex position is determined by the timedifference of the two BBCs. The resolution is ∼0.6 cm. Based on a detailed simulation including

BBC response and input dN/dy distributions, Minimum bias trigger efficiencies are estimated asin Table 3.2 [34]. For 200 GeV p+p case, the BBC trigger cross section is 23.0 ± 2.2 mb. If thetotal inelastic cross section is assumed at 42.0 mb, we obtain a fraction of 55 ± 5 %.
Table 3.2: Summary of Minimum bias trigger efficiencies.
√
Run Species
sN N [GeV] MB Trigger Efficiency [%]

3.1.3

4

Au+Au

200

5

Cu+Cu

200

5

p+p

200

92 ± 394 ± 455 ± 5Centrality Determination

The minimum bias data sample is subdivided into different centrality bins. The centrality isdefined as a fraction of the total geometrical cross section. A collision centrality is determinedfrom BBC (and ZDC) information. BBC measures charged particle multiplicity at forward
rapidity. ZDC measures spectator neutrons. Since the multiplicities in BBC and ZDC are
correlated with the collision geometry, they can be used to measure the collision centrality (impact
parameter |~b|). Figure 3.1 (Left) shows the correlation between the energy sum of spectator
neutrons (ZDC) and the charge sum of charged particles (BBC) in Run4 Au+Au collisions at√
sN N = 200 GeV. A centrality value are determined by calculating φ angle relative to the centeron X-axis for given BBC and ZDC values. The figure illustrates the sorting way corresponding
to percentile intervals of the cross section, with 0-5% indicating the most central collisions. For
peripheral collisions, the spectator neutrons measured by ZDC are decreased. It is consideredthat intrinsic pT from Fermi motion inside nuclei changes the direction, or they may be boundin deuterons or heavier fragments and thus swept away by the magnet. NA49 experiment also

3. Data Analysis

31

60-94 %
30-60 %
104

Run5 200 GeV Cu+Cu
10-30 %

0-10 %

3

10

102

0

100

200

300

400

500

600

700

800

BBC charge sum [MIP]

Figure 3.1: Left: ZDC energy sum vs. BBC charge sum in Run4 Au+Au collisions at√
200 GeV, Right: BBC charge sum in Run5 Cu+Cu collisions at sN N = 200 GeV.

√sN N =

reported similar spectator neutron missing [35]. Figure 3.1 (Right) shows the charge sum of√
charged particles (BBC) in Run5 Cu+Cu collisions at sN N = 200 GeV. In this case, only BBC
information is used for centrality determination. Before we start spectra measurements, we have√finished centrality calibrations (Au+Au/Cu+Cu at sN N = 200/62.4 GeV) for common use in
PHENIX.

3.1.4

Participant-Spectator Model and Glauber Model

Nucleons in heavy ion collisions can be separated into two groups : participant (the overlapped
region) and spectators (the other part and keeps its longitudinal velocity). To evaluate thenumber of nucleon-nucleon binary collisions Ncoll , the number of participating nucleons Npart ,and the impact parameter b for each centrality class, we use a Glauber model Monte-Carlosimulation that includes the responses of BBC and ZDC. A participant is defined as a nucleon
which has suffered at least one inelastic nucleon-nucleon collision. Systematic errors of the
Glauber results are estimated by comparing results for different model assumptions. For example,
in 200 GeV Au+Au case, (1) inelastic nucleon-nucleon cross section σN N = 39 mb ∼ 45 mb,(2) Woods-Saxon parameters (radius: 6.38 fm ∼ 6.65 fm, diffuseness: 0.53 fm ± 0.55 fm), etc.

The evaluated numbers are summarized in Tables 3.3 and 3.4 [36]. Figure 3.2 shows Ncoll and√Npart as a function of impact parameter for Au+Au and Cu+Cu collisions at sN N = 200 GeV.
Binary-collision scaling has a strong bias towards central collisions. It is just due to nuclear
overlap geometry. If we plot Ncoll divided by 0.5Npart as a function of Npart (right figure), theAu+Au and Cu+Cu points are on the same line. Figures 3.3 and 3.4 show Npart and Ncoll√
distributions for each centrality class in Au+Au/Cu+Cu collisions at sN N = 200 GeV. Evenin the same centrality class, the distributions have a wide spread than expected. Because weNbinary or Npart

3. Data Analysis

32

1400

Au+Au Nbinary

1200

Au+Au Npart

1000

Cu+Cu Nbinary

800

Cu+Cu Npart

600
400
200
0
0

2

4

6

8

10

12

14

b [fm]

Figure 3.2: Left: Ncoll and Npart as a function of impact parameter for Au+Au and Cu+Cu√
collisions at sN N = 200 GeV. Right: Ncoll divided by 0.5Npart as a function of Npart .

select a centrality class by looking at particle multiplicities, and any multiplicity distributions
have their statistical fluctuations. So we do not avoid mixing different centrality classes in N partand Ncoll under finite multiplicity condition.
Run4 200 GeV Au+Au

Run4 200 GeV Au+Au

104

3

10

3

10

102

102

10

10

1
0

50

100

150

200

250

300

350

400
450
Npart

1
0

200

400

600

800

1000

1200

1400
Ncoll

Figure 3.3: Npart (Left) and Ncoll (Right) distributions for each centrality class in Au+Au colli√
sions at sN N = 200 GeV.

3. Data Analysis

33

Run5 200 GeV Cu+Cu

Run5 200 GeV Cu+Cu

104

104

10

3

10

102

102

10

10

1

3

0

20

40

60

80

100

120

140
Npart

1

0

50

100

150

200

250

300

350
Ncoll

Figure 3.4: Npart (Left) and Ncoll (Right) distributions for each centrality class in Cu+Cu colli√
sions at sN N = 200 GeV.

Table 3.3: Average Npart , Ncoll , b for each centrality in 200 GeV Au+Au collisions.
class [%]
0- 10
10- 20
20- 3030- 4040- 5050- 6060- 7070- 92

hNpart i

hNcoll i

325.2 ± 3.3 955.4 ± 93.6b [fm]
3.2 ± 0.2

234.6 ± 4.7 602.6 ± 59.3

5.7 ± 0.3

114.2 ± 4.4 219.8 ± 22.6

8.7 ± 0.4

166.6 ± 5.4 373.8 ± 39.6
74.4 ± 3.8

120.3 ± 13.7

25.7 ± 3.8

28.5 ± 7.6

45.5 ± 3.3
9.5 ± 1.9

7.4 ± 0.3
9.9 ± 0.4

61.0 ± 9.9

11.0 ± 0.4

8.3 ± 2.4

13.5 ± 0.5

11.9 ± 0.5

Table 3.4: Average Npart , Ncoll , b for each centrality in 200 GeV Cu+Cu collisions.
class [%]
0- 10
10- 20
20- 3030- 4040- 5050- 6060- 7070- 8080- 94hNpart i

98.2 ± 2.4

hNcoll i

182.7 ± 20.7

b [fm]
2.4 ± 0.1

73.6 ± 2.5

121.1 ± 13.6

4.0 ± 0.2

37.3 ± 1.6

47.1 ± 5.3

6.2 ± 0.3

53.0 ± 1.9
25.4 ± 1.3
16.7 ± 0.9
10.4 ± 0.6
6.4 ± 0.5
3.6 ± 0.3

76.1 ± 8.5
28.1 ± 3.4
16.2 ± 1.9
9.0 ± 1.0

4.9 ± 0.6
2.4 ± 0.3

5.2 ± 0.3
7.1 ± 0.4
7.8 ± 0.4

8.6 ± 0.4

9.3 ± 0.5

10.0 ± 0.5

3. Data Analysis

34

Even though the Npart -Ncoll relation is the same between Au+Au and Cu+Cu on the averagevalues, the shape of overlapped colliding nuclei is different at same Npart as shown in Figure 3.5.
Figure 3.6 (left) shows Npart distributions for Au+Au and Cu+Cu with same average Npart ∼117.
Cu+Cu system has a better accuracy in small Npart region due to small fluctuation of Npart itself.
The right figure shows the number of binary collisions per nucleon. This reflects the nuclear
thickness for each nucleon. In peripheral Au+Au collisions, the distribution is wider than in
Cu+Cu collisions. A single binary collision is clearly seen for Au+Au.

Figure 3.5: Schematic drawing of overlapped colliding nuclei for Au+Au and Cu+Cu at same
Npart ∼100.

Figure 3.6: Left: Npart distributions for Au+Au and Cu+Cu with same average Npart ∼117.
Right: Number of binary collisions per nucleon for Au+Au and Cu+Cu with same average
Npart ∼117.

3. Data Analysis

35

3.2

Charged Particle Measurement

3.2.1

Track Reconstruction

Charged particle tracks are reconstructed by using the hit information at DC and PC1. In theprocess of the reconstruction, tracks that traverse both X1 and X2 wires in DC are looked, thenthe remaining tracks that traverse X1 or X2 regions are looked (see Section 2.4.2). Based on
a combinatorial Hough transform technique, tracks are found from the hit information of X1
and X2 wires. PC1 provides three-dimensional hit position to help pattern recognition. The
reconstructed tracks are labeled by quality bits which are defined by the hit information at X1,
X2, UV and PC1. This method gives the polar angle θ, azimuthal angle φ and bendig angle α ofthe intersection at the DC reference radius (R=220 cm). Figure 3.7 shows a schematic illustrationof these variables. Transverse momentum is proportional to the inverse of the bending angle α

Figure 3.7: Illustration of the Hough transform variables for drift chamber track reconstruction.

for tracks emitted perpendicular to the beam axis.
pT =

K
α

(3.1)

where K=101 mrad GeV/c is the field integral along the track trajectory. The flight path
length is calculated from the reconstructed track trajectory. The DC tracking efficiency in ahigh multiplicity environment is estimated based on an embedding technique as explained in
Section 3.8.2.

3.2.2

Track Association and Selection

Tracks reconstructed by DC-PC1 are associated with outer detectors. We find intersection points
between the trajectory and outer detectors. Projected points are then matched to measured hit
points. We subtract the projected position of each track from the track hit position. Then we3. Data Analysis

36

apply cuts on these residual distributions in both φ and z directions, in order to reduce thebackground of random track associations.
In order to do the same cut in both real and Monte Carlo (MC) data, we convert theseresidual distributions to normalized Gaussians and cut the same number of standard deviations
in real and MC data. We obtain the mean and width of these distributions as a function ofpT for particle charge signs and north/south sides. We present a typical fitting procedure for∆φ distributions in Figures 3.8, 3.9, and 3.10. Double gaussian fitting is applied to decompose
signal and random background parts. For ∆z variable, there is a centrality (hit multiplicity in
BBC region) dependence in mean and width (see Figure 3.11). The ∆z resolution is worse inperipheral than in central because of lower multiplicity. We take this dependence by doing thecorrection for each centrality bin. We have the same corrections for the matching distributions(both ∆φ and ∆z) for TOF/PC2/PC3/EMC, and in MC similarly. After the determination ofmean and width as a function of pT , we convert these distributions to normalized Gaussians with
mean=0 and sigma=1 and then reject all tracks falling outside 2 standard deviations from themean (σposition ∼8 mm at r = 5 m).

Figure 3.8: ∆φ distributions (TOF) for each pT range (0-4 GeV/c, 0.2 GeV/c step). Red line issignal, blue one is background.

3. Data Analysis

37

Figure 3.9: Mean (left) / Sigma (right) of TOF ∆φ as a function of pT . Black marker is signal,
blue one is background. Red line is a parameterization.

Figure 3.10: Normalized mean (left) / sigma (right) of TOF ∆φ as a function of pT . Black
marker is signal, blue one is background. Red line is a constant-value fit.

Figure 3.11: Mean (left) / Sigma (right) of PC3 ∆z as a function of pT for different centralitybins.

3. Data Analysis

3.3

38

Event and Track Selection Cuts

The event and track cut conditions used in the analysis are summarized below. Most of thecuts are commonly used in the past identified charged hadron analyses in PHENIX. And we
also used the same (or equivalent) cuts over the single-particle Monte Carlo simulation to obtaincorrection factors. The PHENIX common recalibrator called MasterRecalibrator is used to apply(re)calibrations for TOF (Time-of-Flight counter), ACC (Aerogel Cherenkov counter), and otherdetectors including track matching and centrality.
Common cuts for TOF and ACC analyses:• Trigger : Minimum bias trigger (Non-physics bunch crossing events removed)• BBC Z vertex cut : < 30 cm• DC Z position cut : < 75 cm
ACC specific cuts:• DC track quality : 31 or 61 or 62 or 63• PC2/PC3/EMC Matching cut : 2σ in φ and z directions (with correction)• PID cut : Requiring ACC information (Fire or Veto) with fixed Npe threshold.

(6 pe (sum) unless otherwise specified. Overflow tracks are excluded (see Section 3.8.2).)• Fiducial cut : (see text)
TOF specific cuts:• DC track quality : 31 or 63• TOF Matching cut : 2σ in φ and z directions (with correction)• PC3 Matching cut : None
• PID cut : Use isPi, isK, isP variables (after PidrecalReco),(2σ selection and 2σ veto of other particle types,
and requiring m2 > 0.6 for (anti)proton.)• TOF slat cut : None
• Eloss cut : β-dependent energy loss cut• Fiducial cut : (see text)

3. Data Analysis

3.4

39

Quarlity Assurance - run-by-run stability check

We have checked the run-by-run detector stability by looking at m2 distributions, raw pT spectraand fiducial area in DC φ vs. charge/momentum space. Figure 3.12 shows a typical example
of run-by-run quality check display. Figures 3.13 and 3.14 show the run-number dependences

Figure 3.12: Run-by-run quality check (ACC) for Run 154854 (top left: m2 vs. charge×p, top
middle: raw pT distribution, top right: Npe distribution, bottom left: charge/p vs. φ (north),bottom middle: charge/p vs. φ (south), bottom right: centrality distribution).

of mean and sigma of ACC-Npe and the raw number of tracks per event (pions) for ACC and
TOF. A switch in yield around Run 155800 corresponds to the change of magnetic field direction.
We select run numbers to obtain uniform detector response. Run numbers which have a small
statistics, or bad centrality distribution are also excluded in the analysis. With the run-by-run
check, we made the good run number lists. Note that ACC in Run5 Cu+Cu (++) phase looks
unstable. This is due to instability of drift chamber (W1 sector) in front of ACC. We appliedvery tight fiducial cut to remove this unstable region.

3.5

Particle Identification

3.5.1

Time of Flight Counter

The Time-of-Flight counter has a timing resolution of 120 ps. The overall timing resolution
including BBC timing resolution is ∼130 ps for Au+Au/Cu+Cu, and ∼140 ps for p+p. Particle

identification (PID) is based on particle mass calculated from measured momentum, time of flightand path length along the trajectory. It can be used for (anti)proton identification up to pT = 4
GeV/c. The PID cut is 2σ selection and 2σ veto of other particle types. For the upper momentum
cut off, we use 3 GeV/c, 2 GeV/c, and 4 GeV/c for pions, kaons, and protons, respectively. The

40

1.6

No. of tracks per event

Single photoelectron peak

3. Data Analysis

Mean
Sigma

1.4

0.012

1.2
1

0.01

0.008

0.8

0.006

0.6

0.004

0.4

0.002

0.2
0
108

Charge sign :Positive
Negative

0.014

3

110

112

114

116

118

120
122
Run Number

×10

0
108

3

110

112

114

116

118

120
122
Run Number

×10

Figure 3.13: Left: Mean/Sigma of photoelecron peak (ACC) vs. Run Number, Right: Numberof tracks per event (positive/negative, ACC) vs. Run Number.

Figure 3.14: Left: Number of tracks per event (ACC) vs. Run Number (including Run5 Cu+Cu
62 GeV and 22 GeV phases), Right: Number of tracks per event (TOF) vs. Run Number.

main reason is to reduce other-particle contamination. For the lower momentum cut off, we use
0.5 GeV/c. Figure 3.15 shows mass squared vs. charge × momentum distribution for TOF (realdata, Minimum bias). Mean m2 are fitted with a constant value for each particle species. Sigma
m2 values are parameterized with the following function:
2
σm
2 =


2 h

σα2
σms
m2 i σT2 OF c2  2 2
4 2
4
2
(4m
p
)
+
4m
1
+
+
4p
m
+
p
2
2
K1
K1
p2
L2

(3.2)

where p is momentum, m is particle mass, σα is angular resolution in [mrad], σms is multiple
scattering term, σT OF is overall TOF resolution and K1 is the field integral value. This parameterization is done for π/K/p simulataneously (see Figures 3.16 and 3.17). In peripheral events,a deviation of m2 mean is seen due to slightly wrong calibrations since TOF timing calibration
was done for Minimum bias events. Taking care of this centrality dependence, we apply different
PID boundaries for each centrality bin.

3. Data Analysis

41

Figure 3.15: m2 vs. charge×p distribution (TOF, Real data) with PID boundaries.

0.2
0.18

SimProject57&60 (TOF)

0.16
0.14

1.2

mean m2

σ m2

Figure 3.16: m2 sigma (left) and mean (right) vs. momentum for real data (TOF).

1

p, p

0.8

0.12

0.6

0.1
0.08

0.4

K±

0.06
0.2

0.04
0.02
0
0

π±

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 3.17: m2 sigma (left) and mean (right) vs. momentum for MC data (TOF).

3. Data Analysis

3.5.2

42

Aerogel Cherenkov Counter

The Aerogel Cherenkov counter has a refractive index of n = 1.011. This corresponds to 0.9
GeV/c, 3.3 GeV/c, 6.3 GeV/c threshold values in momentum for pions, kaons, and protons,
respectively. The aerogel counter has 320 readout channels (from Run5, just half in Run4) intotal. Calibration constants are single photoelectron peak and pedestal values for each channel.
Both collision data and LED-calibration data are available for the calibration. The calibration
constants can be touched through the recalibration module. On the other hand, the response inMonte Carlo (MC) is tuned to ajust mean and sigma values of the number of photoelectrons tothat in real data (see Figures 3.18 and 3.19). Aerogel signal is required for either case, fire (for
3

×10

4000

0.6 - 0.7 GeV/c

120

1.2 - 1.3 GeV/c

3500

100

1.8 - 1.9 GeV/c

3000

8000

2500

80
6000

60

2000
1500

4000

40

1000
2000

20
0

5

10

15

20

25

30

35

40

0

45 50
Npe

500

2.4 - 2.5 GeV/c

1000

500
5

10

15

20

25

30

35

40

0

45 50
Npe

5

10

15

20

25

30

35

40

45 50
Npe

40

45 50
Npe

120

3.0 - 3.1 GeV/c

100

3.6 - 3.7 GeV/c

400

800

80
300

600

60

400

200

200

100

0

5

10

15

20

25

30

35

40

0

45 50
Npe

40

20

5

10

15

20

25

30

35

40

0

45 50
Npe

5

10

15

20

25

30

35

30

Npe Sigma

Npe MeanFigure 3.18: Momentum-sliced Npe distributions (ACC). Red histograms are from MC pions.
25

9
8
7

20

6
5

15

4

10

Real
5
0
0

10

MC
0.5

1

1.5

2

2.5

3

3.5

4
4.5
5
Momentum [GeV/c]

3

Real

2

MC

1
0
0

0.5

1

1.5

2

2.5

3

3.5

4
4.5
5
Momentum [GeV/c]

Figure 3.19: Left: Mean of Npe vs. momentum (Npe ∝ (1 − 1/(nβ)2 )), Right: Sigma of Npe vs.

mean
momentum. Open symbols are square root of Npe.

pions) or veto (not fired, for protons) with the fixed number of photoelectrons (Npe ) threshold.
The Npe threshold is tested with changing the values. The purpose is to check the contamination
like kaons to protons. The contamination is subtracted by looking at m2 distribution from
EMCal. Figures 3.20 and 3.21 show Npe as a function of momentum in Real and MC. Figure 3.22
shows time of flight (EMCal) vs. 1/p under ACC veto condition. A clear proton peak is seen up
to high pT .

3. Data Analysis

43

Figure 3.20: Number of photoelectrons as a function of momentum (ACC, Real data). The lines
show expected response from fitting for pions and kaons.

Figure 3.21: Number of photoelectrons as a function of momentum (ACC, MC). The lines arefrom fitting.

Figure 3.22: Time of flight (EMCal) vs. 1/p under ACC veto condition.

3. Data Analysis

3.5.3

44

Particle Contamination

Particle contamination in TOF PID
To estimate the fraction of pion/kaon contamination in proton, mass squared distributions are
fitted with triple gaussian function (π/K/p) for each pT range (see Figure 3.23). Mean and sigma
m2 values of those gaussian functions are fixed at the extrapolated ones from low-pT measurement
and its expectations (see Section 3.5.1). Another fitting method is tried to reproduce actual
distributions. When looking at m2 distribution at high pT , the distribution has a long tail on theright side of proton peak. This tail is a feed-down effect (like Λ → p+π) [37]. The BG function(actually not BG, this is proton from weak decay with slightly different m2 ) is introduced totake account of the tail (see Figure 3.24). The contamination ratio of pion+kaon to proton isestimated within 2 σ of proton m2 and m2 > 0.6 GeV2 /c4 for combinations of fitting methods,
charge signs, centrality classes.
pion|σ|<2 + kaon|σ|<2
pion|σ|<2 + kaon|σ|<2 + proton|σ|<2(3.3)

pion|σ|<2 + kaon|σ|<2
pion|σ|<2 + kaon|σ|<2 + proton|σ|<2 + BG|σ|<2(3.4)

contamination ratio =or,contamination ratio =The ratios are plotted as a function of pT in Figures 3.26 ∼ 3.27. These values are used ascorrection factors to calculate final spectra.
3

3

3

×10
5000

×10

×10

1.0 ~ 1.5 GeV/c

600

4000

1.5 ~ 2.0 GeV/c

100

500
400

3000

60

300

2000

40

200
1000

0
-1.5

20

100
-1

-0.5

0

0.5

1

1.5
2
2
m 2 [(GeV/c) ]

0
-1.5

6000

2.5 ~ 3.0 GeV/c

-1

-0.5

0

0.5

1

1.5
2
2
m 2 [(GeV/c) ]3.0 ~ 3.5 GeV/c

-0.5

0

0.5

1

1.5
2
2
m 2 [(GeV/c) ]

1

1.5
2
2
m 2 [(GeV/c) ]

1

1.5
2
2
m 2 [(GeV/c) ]3.5 ~ 4.0 GeV/c

1400
1200
1000

3000

800

8000

2000

6000
4000

600
400

1000

200

2000
-1

-0.5

0

0.5

1

1.5
2
2
m 2 [(GeV/c) ]4.0 ~ 4.5 GeV/c

0
-1.5

300

600

-1

-0.5

0

0.5

1

1.5
2
2
m 2 [(GeV/c) ]4.5 ~ 5.0 GeV/c

-1

-0.5

0

0.5

1

1.5
2
2
m 2 [(GeV/c) ]

0
-1.5

0.5

5.0 ~ 5.5 GeV/c

100
80
60
40

50

100

0

120

100

200

-0.5

140

150

300

-1

160

200

400

0
-1.5

180

250

500

0
-1.5

-1

1600

4000

700

0
-1.5

1800

5000

0
-1.5

2.0 ~ 2.5 GeV/c

80

20
-1

-0.5

0

0.5

1

1.5
2
2
m 2 [(GeV/c) ]

0
-1.5

-1

-0.5

0

0.5

Figure 3.23: m2 distributions with triple gaussian fitting (positive π/K/p) in Run4 200 GeV
Au+Au MB. Blue: pions, yellow: kaons, magenta: protons, red: total.

3. Data Analysis

45

3

3

3

×10

×10
5000

1.0 ~ 1.5 GeV/c

4000

×10

1.5 ~ 2.0 GeV/c

600
500

80

400

3000

60

300

2000

40

200
1000

0
-1.5

20

100
-1

-0.5

0

0.5

1

0
-1.5

1.5
2
2
m 2 [(GeV/c) ]6000

2.5 ~ 3.0 GeV/c

-1

-0.5

0

0.5

1

0
-1.5

1.5
2
2
m 2 [(GeV/c) ]3.0 ~ 3.5 GeV/c

0

0.5

1

1.5
2
2
m 2 [(GeV/c) ]

1

1.5
2
2
m 2 [(GeV/c) ]

1

1.5
2
2
m 2 [(GeV/c) ]

1400
1200
1000

3000

800

8000

2000

6000
4000

600
400

1000

200

2000
-1

-0.5

0

0.5

1

0
-1.5

1.5
2
2
m 2 [(GeV/c) ]4.0 ~ 4.5 GeV/c

-1

-0.5

0

0.5

1

0
-1.5

1.5
2
2
m 2 [(GeV/c) ]4.5 ~ 5.0 GeV/c

300

600

100
80
60
40

50

100
-1

-0.5

0

0.5

1

20

0
-1.5

1.5
2
2
m 2 [(GeV/c) ]

0.5

120

100

200

0

140

150

300

-0.5

160

200

400

-1

5.0 ~ 5.5 GeV/c

180

250

500

0
-1.5

-0.5

1600

4000

700

-1

3.5 ~ 4.0 GeV/c

1800

5000

0
-1.5

2.0 ~ 2.5 GeV/c

100

-1

-0.5

0

0.5

1

0
-1.5

1.5
2
2
m 2 [(GeV/c) ]

-1

-0.5

0

0.5

Figure 3.24: m2 distributions with triple gaussian fitting (positive π/K/p) in Run4 200 GeV
Au+Au MB. Gaussian BG tail is included. Blue: pions, yellow: kaons, magenta: protons, sky
blue: BG (feed-down), red: total.

Figure 3.25: m2 distributions for positive particles (2.5< pT <3.0 GeV/c) [37]. The contributionof protons from feed-down decays is shown.
0.5

0.45

K/ π Contamination in Proton (TOF)

Positive

w/o BG component

0.4

w. BG component

0.35

Ratio

Ratio

K/ π Contamination in Proton (TOF)

0.5

0.45

0.3

0.3
0.25

0.2

0.2

0.15

0.15

0.1

0.1

0.05

0.05
0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
pT [GeV/c]

w/o BG component

w. BG component

0.35

0.25

0
0

Negative

0.4

0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
pT [GeV/c]

Figure 3.26: Pion/Kaon contamination ratio in proton as a function of pT for each fitting method(left: positive, right: negative) (Run4 200 GeV Au+Au).

3. Data Analysis

46

0.5

0.45

K/ π Contamination in Proton (TOF)

Positive

Ratio

Ratio

K/ π Contamination in Proton (TOF)
MB
Cent:0-10%

0.4

Cent:30-60%

0.35

0.5

0.45

0.3

0.25

0.25

0.2

0.2

0.15

0.15

0.1

0.1

0.05

0.05
0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
pT [GeV/c]

MB
Cent:0-10%
Cent:30-60%

0.35

0.3

0
0

Negative

0.4

0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
pT [GeV/c]

Figure 3.27: Pion/Kaon contamination ratio in proton as a function of pT for each centrality
class (left: positive, right: negative) (Run4 200 GeV Au+Au).

Particle contamination in ACC PID
To estimate the fraction of kaon contamination in proton, mass squared distributions (EMCal
behind ACC) are fitted with double gaussian function (kaon and proton) for each pT range (seeFigure 3.28). Mean and sigma m2 values of those gaussian functions are fixed at the extrapolated
ones from low-pT measurement and its expectations. All the fittings are done in the condition of
ACC-Veto. So, pion component is suppressed and mostly invisible for all pT range. Only in topleft figure (1.0-1.5 GeV/c), pion peak can be seen. Two fitting methods are tried to reproduce
actual distributions. One method is with background (BG) component. As in TOF, the BG(feed-down) function is introduced to take account of the tail (see Figure 3.29). Since significant
bend as a function of momentum for antiproton m2 mean is seen, peak position of antiproton
m2 at high pT has some uncertainties. We try fitting with introducing mean of antiproton m2
as an additional free parameter. This is the other fitting method. The contamination ratio ofkaon to proton is estimated within 2 σ of proton m2 for combinations of fitting methods, charge
signs, centrality classes.
kaon|σ|<2
kaon|σ|<2 + proton|σ|<2(3.5)

kaon|σ|<2
kaon|σ|<2 + proton|σ|<2 + BG|σ|<2(3.6)

contamination ratio =or,contamination ratio =The ratios are plotted as a function of pT in Figures 3.30 ∼ 3.31. These values are used ascorrection factors to calculate final spectra.

3. Data Analysis

47

3

×10
120
100

1.0 ~ 1.5 GeV/c
Positive

1.5 ~ 2.0 GeV/c
Positive

2.0 ~ 2.5 GeV/c
Positive

80
60
8000

40

6000

20
0

5000

4000

4000

5000
-2

-1

0

1

2
3
m2 [(GeV/c2)2]

2.5 ~ 3.0 GeV/c
Positive

0

3500
3000

2000
-2

-1

0

1

2
3
m2 [(GeV/c2)2]

3.0 ~ 3.5 GeV/c
Positive

800
700

0

0

1

2
3
m2 [(GeV/c2)2]02
3m2 [(GeV/c2)2]12
3m2 [(GeV/c2)2]

3.5 ~ 4.0 GeV/c
Positive

200

500
-1

1

300

1000

-2

0

400

1500

1000

-1

500

2000

2000

-2

600

2500
3000

0

100
-2

-1

0

1

2

3
m2 [(GeV/c2)2]

0

-2

-1

0

Figure 3.28: Mass squared distributions (positive) under ACC-Veto condition with double gaussian fitting (Run4 200 GeV Au+Au). Green: kaons, blue: protons, red: total.

3

×10
120
100

1.0 ~ 1.5 GeV/c
Positive

1.5 ~ 2.0 GeV/c
Positive

2.0 ~ 2.5 GeV/c
Positive

80
60
8000

40

6000

20
0

5000

4000

4000

5000
-2

-1

0

1

2
3
m2 [(GeV/c2)2]

2.5 ~ 3.0 GeV/c
Positive

0

3500
3000

2000
-2

-1

0

1

2
3
m2 [(GeV/c2)2]800

3.0 ~ 3.5 GeV/c
Positive

700

0

0

1

2
3
m2 [(GeV/c2)2]02
3m2 [(GeV/c2)2]12
3m2 [(GeV/c2)2]

3.5 ~ 4.0 GeV/c
Positive

200

500
-1

1

300

1000

-2

0

400

1500

1000

-1

500

2000

2000

-2

600

2500
3000

0

100
-2

-1

0

1

2

3
m2 [(GeV/c2)2]

0

-2

-1

0

Figure 3.29: Mass squared distributions under (positive) ACC-Veto condition with double gaussian fitting (Run4 200 GeV Au+Au). Gaussian BG tail is included. Green: kaons, blue: protons,
sky blue: BG (feed-down), red: total.

3. Data Analysis

48

Ratio

1
0.9
0.8

m2 mean fixed

Positive

Ratio

Kaon Contamination in Proton (ACC)

Kaon Contamination in Proton (ACC)

m2 mean free

0.8

w. BG

0.7

1
0.9

m2 mean free
w. BG

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1
0
0

m2 mean fixed

Negative

0.1
0.5

1

1.5

2

2.5

3

3.5

4

0
0

4.5
5
pT [GeV/c]

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
pT [GeV/c]

Figure 3.30: Kaon contamination ratio in proton (ACC-Veto) as a function of pT for each fitting
method (left: positive, right: negative) (Run4 200 GeV Au+Au).
Kaon Contamination in Proton (ACC)

1
0.9
0.8

Ratio

Ratio

Kaon Contamination in Proton (ACC)MB

Positive

Cent:0-10%
Cent:30-60%

0.7

1
0.9
0.8

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0
0

Cent:0-10%
Cent:30-60%

0.7

0.6

0.1

MB

Negative

0.1
0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
pT [GeV/c]

0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
pT [GeV/c]

Figure 3.31: Kaon contamination ratio in proton (ACC-Veto) as a function of pT for each centrality class (left: positive, right: negative) (Run4 200 GeV Au+Au).

3. Data Analysis

3.6

49

Background Subtraction

At high pT , S/N ratio of charged track association is decreased due to several backgrounds. Background (BG) components are, for example, decayed hadrons, electrons/positrons from photon
conversion, or random track association. A sketch of tracks is shown in Figure 3.32 (left). Those
are mis-reconstructed as higher-pT track than actual one [38]. The point to be kept in mind isthat pT spectra is steep in any case, so BG produced at low-pT can affect high-pT part more
sigficantly. To subtract such BG components, residual bending in φ direction can be used [38].
Due to fringe magnetic field, decayed products or electrons/positrons are bended in φ direction.
Actual track at high pT has a straight line to outer detectors. Its matching residual is sitting
around zero with tracking resolution. Positive and negative BG has opposite bending direction.
Monte Carlo study was also done to confirm the shape of residual distribution (see Figure 3.32
(right)).

Figure 3.32: Left: Sketch of tracks with photon conversion, particle decay. Right: ∆φ distribution
with background electrons from MC simulation.

Background Subtraction in TOF
S/N ratio at high pT is estimated by using TOF residual matching distributions. The residual
distributions are fitted with double gaussian function to separate signal and background parts
after applying all other cuts (see Figure 3.33). Then, S/N ratio is estimated within 2 sigma
range with the fitted results. S/N ratios are plotted as a function of pT in Figure 3.34. In caseof Proton-ID, the S/N ratio is better compared to No-PID case. The S/N ratios are used ascorrection factors to calculate final spectra.

3. Data Analysis

7000
6000

50

3.0 ~ 3.5 GeV/c

2500

600

1400

400

1200
1000

300

800

1000

2000

200

600
400

500

1000

100

200
-8

-6

-4

-2

0

2

4

6

8
10
tofsdphi

0
-10

700

4.0 ~ 4.5 GeV/c

600

1000

-8

-6

-4

-2

0

2

4

6

0
-10

8
10
tofsdphi400

4.5 ~ 5.0 GeV/c

350

800

-6

-4

-2

0

2

4

6

8
10
tofsdphi

0
-10

0

2

4

6

0
-10

8
10
tofsdphi

220

4.0 ~ 4.5 GeV/c

200
180

-6

-4

-2

0

2

4

6

0
-10

8
10
tofsdphi

-6

-4

-2

0

2

4

6

8
10
tofsdphi

0

2

4

6

8
tofsdphi

4.5 ~ 5.0 GeV/c

140
120
100
80
60
40

50
-8

-8

160

100

100
-8

-2

150

200

200

-4

200

300

400

-6

250

400

600

-8

300

500

3.5 ~ 4.0 GeV/c

500

1600

1500

3000

0
-10

3.0 ~ 3.5 GeV/c

1800

4000

1200

2000

2000

5000

0
-10

2200

3.5 ~ 4.0 GeV/c

20
-8

-6

-4

-2

0

2

4

6

0
-10

8
10
tofsdphi

-8

-6

-4

-2

Figure 3.33: Track matching residual distributions (normalized TOF ∆φ, positive) for each p T

S/N vs. pT

S/N vs. pT

S/N vs. pT

S/N

S/N

S/N

range (Run4 200 GeV Au+Au) (left: No-PID, right: Proton-ID).

10

TOF

10
10

Conditions :No PID (Positive)
No PID (Negative)
Proton (Positive)
Proton (Negative)

1

-1

10

3

3.2

3.4

3.6

3.8

Conditions :1

Conditions :MB (Positive)
MB (Negative)
0-10% (Positive)
0-10% (Negative)
30-60% (Positive)
30-60% (Negative)

1

Gaus BG (Positive)
Guas BG (Negative)
Line BG (Positive)
Line BG (Negative)

4

4.2

4.4

4.6

4.8 5
pT [GeV/c]

-1

10

3

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8 5
pT [GeV/c]

-1

10

3

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8 5
pT [GeV/c]

Figure 3.34: S/N ratio as a function of pT (Run4 200 GeV Au+Au) (left: PID condition, middle:
BG fitting function, right: centrality class).

Background Subtraction in ACC
PC2/PC3 matching residual distributions are fitted with double gaussian function or “gaussian+ straight line” function to separate signal and background parts after applying all other cuts.
Then, S/N ratio is estimated within 2 sigma range with the fitted results for combinations of cut
conditions (No-ACC-Cut/ACC-Fired/ACC-Not-Fired), charge signs, and centrality classes (seeFigures 3.35 ∼ 3.36). In case of ACC-Not-Fired, the S/N ratio is worse compared to the othertwo cases because of not confirming signal by itself. S/N ratios are plotted as a function of p T

in Figure 3.37. The S/N ratios are used as correction factors to calculate final spectra.

3. Data Analysis

2500

51

500

3.0 ~ 4.0 GeV/c

2000

2500

4.0 ~ 5.0 GeV/c

400

2000

1500

300

1500

1000

200

1000

500

100

500

0
-10

400
350

-8

-6

-4

-2

0

2

4

6

8

140

5.0 ~ 6.0 GeV/c

120

300

-8

-6

-4

-2

0

2

4

6

8

0
-10

10

160

6.0 ~ 7.0 GeV/c

140

100

250

80

200

-8

-6

-4

-2

0

2

4

6

0
-10

8

300
200
100
-8

-6

-4

-2

0

2

4

6

8

0
-10

10

5.0 ~ 6.0 GeV/c

60

120

50

100

40

-6

-4

-2

0

2

4

6

0
-10

8

-6

-4

-2

0

2

4

6

8

10

0

2

4

6

8

10

6.0 ~ 7.0 GeV/c

20
10

20
-8

-8

30

40

20

50

4.0 ~ 5.0 GeV/c

400

60

40

100

500

80

60

150

0
-10

0
-10

10

3.0 ~ 4.0 GeV/c

-8

-6

-4

-2

0

2

4

6

0
-10

8

-8

-6

-4

-2

Figure 3.35: Track matching residual distributions ((PC2 ∆φ + PC3 ∆φ)/2, positive, doublegaus) for each pT range (Run4 200 GeV Au+Au) (left: ACC-Fired, right: ACC-Not-Fired).
350
2500

3.0 ~ 4.0 GeV/c

500
400

1500

200
150

600

100
-8

-6

-4

-2

0

2

4

6

8

0
-10

10

100

5.0 ~ 6.0 GeV/c

60
50

100

40

80

50

200
-8

-6

-4

-2

0

2

4

6

8

0
-10

10

6.0 ~ 7.0 GeV/c

100

4.0 ~ 5.0 GeV/c

250

400

120

-8

-6

-4

-2

0

2

4

6

8

0
-10

10

5.0 ~ 6.0 GeV/c

50

80

40

60

30

40

20

10

20

10

0
-10

0
-10

-8

-6

-4

-2

0

2

4

6

8

10

0

2

4

6

8

10

6.0 ~ 7.0 GeV/c

30

60

20

40
20
0
-10

300

800

200

500

140

3.0 ~ 4.0 GeV/c

1000

300

1000

160

1400
1200

2000

0
-10

4.0 ~ 5.0 GeV/c

-8

-6

-4

-2

0

2

4

6

8

-8

-6

-4

-2

0

2

4

6

8

10

-8

-6

-4

-2

0

2

4

6

0
-10

8

-8

-6

-4

-2

Figure 3.36: Track matching residual distributions ((PC2 ∆φ + PC3 ∆φ)/2) under ACC-NotFired condition for each pT range (Run4 200 GeV Au+Au) (left: positive/gaus+line, right:
negative/gaus+gaus).
S/N vs. pT

Min Bias
10

S/N

S/N

S/N vs. pT

Min Bias
ACC Veto
10

Conditions :No Cut (Positive)
No Cut (Negative)
ACC Fire (Positive)
ACC Fire (Negative)
ACC Veto (Positive)
ACC Veto (Negative)

1

3

3.5

4

4.5

S/N

S/N vs. pT

ACC Veto
10

Conditions :Gaus BG (Positive)
Guas BG (Negative)
Line BG (Positive)

1

Conditions :MB (Positive)

1

0-10% (Positive)
60-80% (Positive)

Line BG (Negative)
5

5.5

6

6.5
7
pT [GeV/c]

3

3.5

4

4.5

5

5.5

6

6.5
7
pT [GeV/c]

3

3.5

4

4.5

5

5.5

6

6.5
7
pT [GeV/c]

Figure 3.37: S/N ratio as a function of pT (Run4 200 GeV Au+Au) (left: PID condition, middle:
BG fitting function under ACC-Not-Fired, right: centrality class).

3. Data Analysis

3.7

52

Fiducial Cut

Fiducial cut is introduced in order to keep uniform acceptance thorough the run duration andto match the fiducial area in real data with that in Monte Carlo (MC) simulation for acceptancecorrections. The exactly same fiducial cut on DC φ and charge/p space is applied in both real
data and MC. The applied fiducial area is shown in Figures 3.38 ∼ 3.40.

Figure 3.38: Charge/p vs. φ plane (ACC North, Run4 real). Left: ++ field, Right: – – field.

Figure 3.39: Charge/p vs. φ plane (TOF North, Run4 real). Left: ++ field, Right: – – field.

Figure 3.40: Charge/p vs. φ plane (TOF South, Run4 real). Left: ++ field, Right: – – field.

3. Data Analysis

53

In Figures 3.41 ∼ 3.42, y-z (φ-z) distributions in ACC (TOF) with a track momentum larger

than 2 GeV/c are presented. Those are projected into y (φ) and z direction each, and comparedwith MC distributions. The notch in TOF E0 sector is a known lack, that is removed in MC.
The agreement is roughly good and we do not have care anymore. The remaining difference istaken into account as systematic error. For ACC, to eliminate the edge of each cell which has
a low detection efficiency, we apply very tight fiducial cut cell-by-cell, that is, a removal of theouter 2 cm area of the cell as shown in Figure 3.41.

Figure 3.41: Radio graph and its projected distributions (Black: Run4 real, Red: MC) for ACC(++ field).

Figure 3.42: Radio graph and its projected distributions (Black: Run4 real, Red: MC) for TOF(++ field).

3. Data Analysis

54

3.8

Monte Carlo Correciton

3.8.1

Spectra Correction

To evaluate correction factors, we use a single-particle GEANT Monte Carlo simulation including PHENIX event reconstruction process called PISA (PHENIX Integrated Simulation Application). Single-particle Monte Carlo files are prepared for π/K/p species under each magnetic
field configuration. The correction includes: geometrical acceptance, decay in flight, multiple
scattering, tracking efficiency and momentum resolution. A correction factor can be calculatedusing INPUT pT distribution and OUTPUT pT distribution. The correction factor is estimatedby dividing OUTPUT with INPUT for each pT bin. Figures 3.43 and 3.44 show the evaluated104

Correction Factor

Correction Factor

correction factors as a function of pT for ACC and TOF.
Au+Au 200 GeV (ACC)

103

π+
p

102
0

1

2

3

4

5

104

Au+Au 200 GeV (ACC)

103

πp

102

6
7
pT [GeV/c]

0

1

2

3

4

5

6
7
pT [GeV/c]

104

Au+Au 200 GeV (TOF)

103

π+
+
K
p

102
0

Correction Factor

Correction Factor

Figure 3.43: Correction factors as a function of pT (ACC, Run4 200 GeV Au+Au).
104

Au+Au 200 GeV (TOF)

103

πK
p

102
1

2

3

4

5

6
7
pT [GeV/c]

0

1

2

3

4

5

6
7
pT [GeV/c]

Figure 3.44: Correction factors as a function of pT (TOF, Run4 200 GeV Au+Au).

3.8.2

Multiplicity-dependent Efficiency Correction

In high multiplicity environment like heavy ion collisions, tracking efficiency is reduced due todetector occupancy effect. To obtain multiplicity-dependent detector efficiency, we estimate theeffect of detector occupancy by embedding single Monte Carlo (MC) track into real event. The
multiplicity-dependent efficiency is calculated as embed = Nembed /Nsingle where Nembed is the3. Data Analysis

55

number of single MC tracks which passed cuts (including PID and others) in embedding real
event, and Nsingle is the number of single Monte-Carlo tracks which passed the cuts in single
MC event. Multiplicity-dependent efficiencies as a function of centrality are calculated as shownin Figure 3.45. The pT dependence on efficiencies are found to be small. For TOF, we use thenumbers in Run2 200 GeV Au+Au analysis [37]. For Cu+Cu at 200 GeV, number-of-participantsscaling is applied to adjust different centrality selection. Since ACC is a new detector from Run4,
we estimate the efficiencies by the embedding method. Figure 3.46 (left) shows overflow rate as afunction of centrality. Figure 3.46 (right) is 2D radiograph after excluding overflow tracks. Dark

1.2

1.2

Efficiency

Tracking Efficiency

spots of this figure shows that overflow is coming from direct track passing in PMT.

1.1
1

0.8

0.9
0.8

0.6

0.7

π++

0.6

50

100

150

200

Pion (-)

K
pbar
250

Pion (+)

0.4

π--

K
proton

0.5
0.4
0

1

300

Proton

0.2

350

400

N part00Antiproton
10

20

30

40

50

60

70 80 90 100
Centrality [%]Figure 3.45: Multiplicity-dependent efficiency (left: TOF, right: ACC).

OverFlow Rate [%]OverFlow Rate
10
9
8
7
6
5
4
3
2
1
0
0

10

20

30

40

50

60

70

80
90 100Centrality [%]Figure 3.46: Left: Overflow rate as a function of centrality (Run4 200 GeV Au+Au). Right: 2Dradiograph after excluding overflow tracks (Run4 200 GeV Au+Au).

3. Data Analysis

3.9

56

Invariant Cross Section

Once all correction factors are determined as a function of pT and centrality, they are applied to
raw spectra to obtain final invariant yield and spectra.
In Run5 200 GeV p+p data, the BBC effective cross section is estimated at σBBC =23.0 ±2.2 mb, and the trigger bias is estimated at 0.79 ± 0.02 [39]. We use these values in the p+p
analysis to obtain invariant cross section.

3.10

Weak Decay Feed-down

Weak decays take place very close to a collision vertex. Since heavier particles take most of
the decay momentum, these tracks are inseparable from tracks coming from the vertex of acollision. Indeed protons and anti-protons from weak decays (mainly from Λ and Λ) can bereconstructed as tracks. Feed-down contribution from weak decays are estimated from lambda
input pT distribution and GEANT Monte Carlo simulation including PHENIX reconstruction
process. The lambda input distribution is an effective distribution including higher resonanceeffect (Σ, Ξ). The data is taken from the STAR published paper [40]. Figure 3.47 shows thefraction of weak decay feed-down (anti)proton to measured (anti)proton as a function of p T in
200 GeV p+p. In the thesis, no weak decay feed-down correction is applied to the results unlessotherwise mentioned.

Figure 3.47: Fraction of weak decay feed-down (anti)proton to measured (anti)proton as a function of pT in 200 GeV p+p.

3. Data Analysis

3.11

57

Systemtaitc Uncertainties

Evaluation of Systematic Uncertainties
Systematic uncertainties are evaluated by varying cut conditions in the data analysis. The samechanges are applied in Monte Carlo to obtain the corresponding spectra. Some parts can becanceled when taking particle ratios. In the following, systematic uncertainties on TOF and
ACC analyses are explained.
Systematic Uncertainties on TOF
Systematic uncertainties on pT spectra, particle ratios are evaluated for TOF. The following cuts
are changed for the systematic uncertainty study:• PID Cut (σ in m2 ) : 2σ/3σ• Fiducial Cut (narrow/wide) : w/wo additional cut of |zed|<50 cm• Track Matching Cut : 3σ/2σ• Magnetic field direction : ++/– –• PID Contamination (from fitting methods in m2 )• BG Subtraction at high pT
In Tables 3.5 and 3.6, the evaluated systematic errors on pT spectra (particle ratio) obtainedby the cut variation method are summarized as well as the occupancy correction errors. The
total systematic errors are obtained by adding in quadrature each systematic uncertainty because
they are independent. Figure 3.48 (left) shows the systematic error (from fitting methods) ofpion/kaon contamination ratio in proton as a function of pT . Figure 3.48 (right) shows thesystematic error (from fitting methods) of S/N ratio in proton as a function of pT .

3. Data Analysis

58

Table 3.5: Systematic errors on pT spectra (TOF, Run4 200 GeV Au+Au).
p
π+
π−
p

ErrorsPID Cut

3%

3%

3%

3%

Fiducial Cut

2%

2%

2%

2%

Track Matching

5%

5%

5%

5%

Magnetic field direction (++,– –)

2%

2%

3%

3%

Occupancy correction

2%

2%

3%

3%

Pion/Kaon subtraction (>3 GeV/c, pT dependent)

-

-

<1%

<1%

BG subtraction (>3 GeV/c, pT dependent)

-

-

<2%

<2%

Total

<7%

<7% <8%<8%

Table 3.6: Systematic errors on particle ratio (TOF, Run4 200 GeV Au+Au).
Errorsp/π + p/π − p/p
PID Cut

5%

5%

2%

Fiducial Cut

3%

3%

2%

Track Matching

8%

8%

2%

Magnetic field direction (++,– –)

2%

2%

3%

Occupancy correction

4%

4%

2%

Pion/Kaon subtraction (>3 GeV/c, pT dependent)

<1%

<1%

<1%

BG subtraction (>3 GeV/c, pT dependent)

<2%

<2%

<2%

Total

<11% <11%

<5%

0.1

Systematic error of S/N estimate

Positive

0.09
0.08

Negative

0.07
0.06

systematic error

systematic error

Systematic error of K/π contami. estimate (TOF)

0.1

0.09
0.08

Positive
Negative

0.07
0.06

0.05

0.05

0.04

0.04

0.03

0.03

0.02

0.02

0.01

0.01

0
0

Min Bias
Proton

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
pT [GeV/c]

0
3

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8
5
pT [GeV/c]

Figure 3.48: Systematic errors of kaon contamination ratio in proton (left) and S/N ratio (right)
as a function of pT (Run4 200 GeV Au+Au).

3. Data Analysis

59

Systematic Uncertainties on ACC
Systematic uncertainties on pT spectra, particle ratios are evaluated for ACC. The following cuts
are changed for the systematic uncertainty study:• PID Cut (Npe threshold) : 10pe/6pe for pions, 4pe/3pe for protons• Fiducial Cut (narrow/wide) : w/wo additional cut of |zed|<50 cm• Track Matching Cut : 3σ/2σ• Magnetic field direction : ++/– –• PID Contamination (from fitting methods in m2 )• BG Subtraction at high pT (from fitting methods in track matching residual)
In Tables 3.7 and 3.8, the evaluated systematic errors on pT spectra (particle ratio) obtained by
the cut variation method are summarized as well as the occupancy correction errors. The total
systematic errors are obtained by adding in quadrature each systematic uncertainty because they
are independent. Figure 3.49 (left) shows the systematic error (from fitting methods) of kaon
contamination ratio in proton (ACC-Not-Fired) as a function of pT . Figure 3.49 (right) shows
the systematic error (from fitting methods) of S/N ratio in proton (ACC-Not-Fired) as a functionof pT . Below pT = 5 GeV/c, 1 % level is used for the errors.

ErrorsTable 3.7: Systematic errors on pT spectra (ACC, Run4 200 GeV Au+Au).
π+
π−
p
p

PID Cut

4%

4%

4%

4%

Fiducial Cut

5%

5%

9%

9%

Track Matching

3%

3%

3%

3%

Magnetic field direction (++,– –)

4%

4%

5%

2%

Occupancy correction

3%

3%

5%

5%

Kaon subtraction (2-5 GeV/c, pT dependent)

-

-

<5%

<5%

BG subtraction (>3 GeV/c, pT dependent)<3%<3% <6%

<6%

Total

<9%

<9% <15%<14%

3. Data Analysis

60

Table 3.8: Systematic errors on particle ratio (ACC, Run4 200 GeV Au+Au).
Errorsp/π + p/π − p/p
PID Cut

6%

6%

2%

Fiducial Cut

10%

10%

4%

Track Matching

1%

1%

1%

Magnetic field direction (++,– –)

3%

3%

5%

Occupancy correction

6%

6%

2%

Kaon subtraction (2-5 GeV/c, pT dependent)

<5%

<5%

<2%

BG subtraction (>3 GeV/c, pT dependent)

<5%

<5%

<3%

Total

<15%

<15% <8%systematic error

0.1

Positive

0.09
0.08

Negative

0.07
0.06

systematic error

Systematic error of S/N estimate

Systematic error of K contami. estimate (ACC)

0.1

0.09
0.08

Positive
Negative

0.07
0.06

0.05

0.05

0.04

0.04

0.03

0.03

0.02

0.02

0.01

0.01

0
0

Min Bias
ACC Veto

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
pT [GeV/c]

0
3

3.5

4

4.5

5

5.5

6

6.5
7
pT [GeV/c]

Figure 3.49: Left: Systematic error of kaon contamination ratio in proton (ACC-Not-Fired)
as a function of pT (Run4 200 GeV Au+Au). Right: Systematic error of S/N ratio in proton(ACC-Not-Fired) as a function of pT (Run4 200 GeV Au+Au).

Systematic Uncertainties on Nuclear Modification Factor
For nuclear modification factor RAA , the following errors are included:• Uncertainties of Ncoll (∼>10%) from the Glauber calculation.
• Systematic errors on pT spectra in p+p.
• Systematic errors on pT spectra in Au+Au or Cu+Cu.

Chapter 4
Results
We have measured transverse momentum spectra (π/K/p and their antiparticles), particle ratios(p/p, p/π + , p/π − ), and nuclear modificaiton factors (RAA , RCP ) with Run4 200 GeV Au+Au,
Run5 200 GeV Cu+Cu, and Run5 200 GeV p+p data sets. Mainly, we focus on p/π ratio as afunction of pT and Npart to study scaling properties of those quantities between different collision√systems (Au+Au, Cu+Cu) at different collision energies ( sN N = 200, 62.4 GeV). The following
results are shown.
• Transverse momentum (pT ) spectra• Mean transverse momentum• Particle yield (dN/dy) at mid rapidity• Particle ratio: p/π + , p/π − , p/p• Nuclear modification factor (RAA , RCP )The particle identification is performed with Aerogel Cherenkov Counter (ACC) and Time-ofFlight detector (TOF). The cross checks are done in the overlapped pT region between them. The
pT reach of particle identification is extended up to 6 GeV/c for (anti)protons by the introductionof ACC. But the statistics is still limited especially for calculating p/p ratio and (anti)proton
RCP at high pT . In the data analysis, we take into account background subtraction and particle
contamination correction. These are done by using track matching residual distributions andmass squared distributions respectively. The spectra is fully corrected for 1) geometrical acceptance, 2) particle decay, 3) multiple scattering effects based on a single particle Monte Carlosimulation. The multiplicity dependence of tracking efficiency is also taken into account for eachparticle species by using the embedding method. Feed-down corrections from weak decays are
not applied in all cases. We have done several detector calibrations, QA checks, and systematic
error studies. Also, we compared the results with independent (or previous) measured results for
PHENIX internal consistency check. The consistency is within about 10-20 %.

4. Results

62

More than 60 % in centrality, some discrepancies between Run4 and previous Run2 results
were seen. This is due to worse tracking resolution in z direction because of worse z-vertex
resolution in most peripheral. Since the track matching tuning is done in Minimum Bias data,some difference could be seen in most peripheral. Now this part is fixed in the calibration stage.

4.1

Transverse Momentum Spectra

4.1.1

pT spectra (ACC) – Au+Au 200 GeV

pT spectra of charged pions and (anti)protons for different centralities in Au+Au collisions at√
sN N = 200 GeV are shown in Figures 4.1, 4.2. For comparison of the spectral shape, thedata points are scaled vertically as quoted in the figures. The spectral shapes look similar whencomparing them between different centrality bins, i.e., those are almost parallel to each other.
In pion case, the spectra shows a concave shape than (anti)proton spectra.

0

Au+Au 200 GeV

105
104
103
102
10
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10
10-11
10-12

(1/2π p ) d2N / dp dy [c2/ GeV 2]π+

Au+Au 200 GeVπ-

0 - 5 (x1)
5 - 10 (x3e-1)
10 - 15 (x1e-1)
15 - 20 (x3e-2)
20 - 30 (x1e-2)
30 - 40 (x3e-3)
40 - 50 (x1e-3)
50 - 60 (x3e-4)
60 - 70 (x1e-4)
70 - 80 (x3e-5)T

0 - 5 (x1)
5 - 10 (x3e-1)
10 - 15 (x1e-1)
15 - 20 (x3e-2)
20 - 30 (x1e-2)
30 - 40 (x3e-3)
40 - 50 (x1e-3)
50 - 60 (x3e-4)
60 - 70 (x1e-4)
70 - 80 (x3e-5)T(1/2π pT) d2N / dpTdy [c2/ GeV 2]

105
104
103
102
10
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10
10-11
10-12

PHENIX Preliminary
1

2

3

4

5
p

6
T

7

[GeV/c]0

PHENIX Preliminary
1

2

3

4

5
p

6
T

7

[GeV/c]Figure 4.1: pT spectra identified with ACC for charged pions for different centralities in Au+Au√
collisions at sN N = 200 GeV (left:positive, right:negative).

4. Results

63

0

Au+Au 200 GeV

105
104
103
102
10
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10
10-11
10-12

(1/2π p ) d2N / dp dy [c2/ GeV 2]pp

Au+Au 200 GeV

0 - 5 (x1)
5 - 10 (x3e-1)
10 - 15 (x1e-1)
15 - 20 (x3e-2)
20 - 30 (x1e-2)
30 - 40 (x3e-3)
40 - 50 (x1e-3)
50 - 60 (x3e-4)
60 - 70 (x1e-4)
70 - 80 (x3e-5)T

0 - 5 (x1)
5 - 10 (x3e-1)
10 - 15 (x1e-1)
15 - 20 (x3e-2)
20 - 30 (x1e-2)
30 - 40 (x3e-3)
40 - 50 (x1e-3)
50 - 60 (x3e-4)
60 - 70 (x1e-4)
70 - 80 (x3e-5)T(1/2π pT) d2N / dpTdy [c2/ GeV 2]

105
104
103
102
10
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10
10-11
10-12

PHENIX Preliminary
1

2

3

4

5
p

6
T

7

0

PHENIX Preliminary
1

2

3

4

5

[GeV/c]p

6
T

7[GeV/c]Figure 4.2: pT spectra identified with ACC for protons and antiprotons for different centralities√
in Au+Au collisions at sN N = 200 GeV (left:positive, right:negative).

4.1.2

pT spectra (TOF) – Au+Au 200 GeV

pT spectra of π/K/p for different centralities in Au+Au collisions at√
sN N = 200 GeV areshown in Figures 4.3∼4.5. At low pT < 1 GeV/c, pion shows a concave shape, kaon shows an
exponential decreasing feature. A convex shape is clearly seen in (anti)proton spectra.

0

Au+Au 200 GeV

105
104
103
102
10
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10
10-11
10-12

(1/2π p ) d2N / dp dy [c2/ GeV 2]π+

Au+Au 200 GeVπ-

0 - 5 (x1)
5 - 10 (x3e-1)
10 - 15 (x1e-1)
15 - 20 (x3e-2)
20 - 30 (x1e-2)
30 - 40 (x3e-3)
40 - 50 (x1e-3)
50 - 60 (x3e-4)
60 - 70 (x1e-4)
70 - 80 (x3e-5)T

0 - 5 (x1)
5 - 10 (x3e-1)
10 - 15 (x1e-1)
15 - 20 (x3e-2)
20 - 30 (x1e-2)
30 - 40 (x3e-3)
40 - 50 (x1e-3)
50 - 60 (x3e-4)
60 - 70 (x1e-4)
70 - 80 (x3e-5)T(1/2π pT) d2N / dpTdy [c2/ GeV 2]

105
104
103
102
10
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10
10-11
10-12

PHENIX Preliminary
1

2

3

4

5
p

6
T

7

[GeV/c]0

PHENIX Preliminary
1

2

3

4

5
p

6
T

7

[GeV/c]Figure 4.3: pT spectra identified with TOF for charged pions for different centralities in Au+Au√
collisions at sN N = 200 GeV (left:positive, right:negative).

4. Results

64

0

Au+Au 200 GeV

105
104
103
102
10
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10
10-11
10-12

(1/2π p ) d2N / dp dy [c2/ GeV 2]

K+

Au+Au 200 GeVK-

0 - 5 (x1)
5 - 10 (x3e-1)
10 - 15 (x1e-1)
15 - 20 (x3e-2)
20 - 30 (x1e-2)
30 - 40 (x3e-3)
40 - 50 (x1e-3)
50 - 60 (x3e-4)
60 - 70 (x1e-4)
70 - 80 (x3e-5)T

0 - 5 (x1)
5 - 10 (x3e-1)
10 - 15 (x1e-1)
15 - 20 (x3e-2)
20 - 30 (x1e-2)
30 - 40 (x3e-3)
40 - 50 (x1e-3)
50 - 60 (x3e-4)
60 - 70 (x1e-4)
70 - 80 (x3e-5)T(1/2π pT) d2N / dpTdy [c2/ GeV 2]

105
104
103
102
10
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10
10-11
10-12

PHENIX Preliminary
1

2

3

4

5
p

6
T

7

0

PHENIX Preliminary
1

2

3

4

[GeV/c]

5
p

6
T

7

[GeV/c]Figure 4.4: pT spectra identified with TOF for charged kaons for different centralities in Au+Au√
collisions at sN N = 200 GeV (left:positive, right:negative).

0

Au+Au 200 GeV

105
104
103
102
10
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10
10-11
10-12

(1/2π p ) d2N / dp dy [c2/ GeV 2]

p

Au+Au 200 GeVp

0 - 5 (x1)
5 - 10 (x3e-1)
10 - 15 (x1e-1)
15 - 20 (x3e-2)
20 - 30 (x1e-2)
30 - 40 (x3e-3)
40 - 50 (x1e-3)
50 - 60 (x3e-4)
60 - 70 (x1e-4)
70 - 80 (x3e-5)T

0 - 5 (x1)
5 - 10 (x3e-1)
10 - 15 (x1e-1)
15 - 20 (x3e-2)
20 - 30 (x1e-2)
30 - 40 (x3e-3)
40 - 50 (x1e-3)
50 - 60 (x3e-4)
60 - 70 (x1e-4)
70 - 80 (x3e-5)T(1/2π pT) d2N / dpTdy [c2/ GeV 2]

105
104
103
102
10
1
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10
10-11
10-12

PHENIX Preliminary
1

2

3

4

5
p

6
T

7

0

PHENIX Preliminary
1[GeV/c]

2

3

4

5
p

6
T

7

[GeV/c]Figure 4.5: pT spectra identified with TOF for protons and antiprotons for different centralities√
in Au+Au collisions at sN N = 200 GeV (left:positive, right:negative).

4.1.3

pT spectra (ACC) – Cu+Cu 200 GeV

pT spectra of charged pions and (anti)protons for different centralities in Cu+Cu collisions at√
sN N = 200 GeV are shown in Figures 4.6, 4.7. The particle identification is performed with
ACC. The spectral shape in both pion and (anti)proton seem to be similar to those in Au+Au
collisions. Comparisons between Au+Au and Cu+Cu systems are shown in the following sectionsin terms of mean transverse momentum and particle yields (see Sections 4.2, 4.3).

Cu+Cu410

sNN = 200 GeV

102

T

π+

0 - 5 % (x1)
5 - 10 % (x10-1)
10 - 15 % (x10-2)-315 - 20 % (x10 )20 - 30 % (x10-4)-5
30 - 40 % (x10-6)
40 - 50 % (x10 )50 - 60 % (x10-7)-8
60 - 70 % (x10 )-970 - 80 % (x10 )-1080 - 94 % (x10 )

1

10-2

106
10

π-

2

5

0 - 5 % (x1)
5 - 10 % (x10-1)
10 - 15 % (x10 -2)-3
15 - 20 % (x10 )20 - 30 % (x10 -4)-530 - 40 % (x10 -6)
40 - 50 % (x10 )50 - 60 % (x10 -7)-860 - 70 % (x10 )-970 - 80 % (x10 )-1080 - 94 % (x10 )

102
1

T

T

10-4

10-6

10-6

10-8

10-8

10-10

10-10

10-12

10-12

10-14

10-14

10-16

10-16

0

sNN = 200 GeV

10-2

10-4

10-18

Cu+Cu

4

T

106

(1/2π p ) d2N / dp dy [c2/ GeV 2]65(1/2π p ) d2N / dp dy [c2/ GeV 2]

4. Results

1

2

3

4

5

6

7

10-18

0

1

3

4

pT [GeV/c]

67pT [GeV/c]

sNN = 200 GeVp

0 - 5 % (x1)
5 - 10 % (x10-1)
10 - 15 % (x10-2)-315 - 20 % (x10 )20 - 30 % (x10-4)-5
30 - 40 % (x10-6)
40 - 50 % (x10 )50 - 60 % (x10-7)-8
60 - 70 % (x10 )-970 - 80 % (x10 )-1080 - 94 % (x10 )

102
1

10-2

106

p

2

5

0 - 5 % (x1)
5 - 10 % (x10-1)
10 - 15 % (x10 -2)-3
15 - 20 % (x10 )20 - 30 % (x10 -4)-530 - 40 % (x10 -6)
40 - 50 % (x10 )50 - 60 % (x10 -7)-860 - 70 % (x10 )-970 - 80 % (x10 )-1080 - 94 % (x10 )

102
1

T

T

10-4

10-6

10-6

10-8

10-8

10-10

10-10

10-12

10-12

10-14

10-14

10-16

10-16

0

sNN = 200 GeV

10-2

10-4

10-18

Cu+Cu

104

T

Cu+Cu

104

(1/2π p ) d2N / dp dy [c2/ GeV 2]

106T(1/2π p ) d2N / dp dy [c2/ GeV 2]

Figure 4.6: pT spectra identified with ACC for charged pions for different centralities in Cu+Cu√
collisions at sN N = 200 GeV (left:positive, right:negative).

1

2

3

4

5

6

7

10-18

0

1

3

4

pT [GeV/c]

67pT [GeV/c]

Figure 4.7: pT spectra identified with ACC for protons and antiprotons for different centralities√
in Cu+Cu collisions at sN N = 200 GeV (left:positive, right:negative).

4.1.4

pT spectra (TOF) – Cu+Cu 200 GeV

pT spectra of π/K/p for different centralities in Cu+Cu collisions at√

sN N = 200 GeV areshown in Figures 4.8 ∼ 4.10. The particle identification is performed with TOF. The spectral

shape in both π/K/p are similar to those in Au+Au collisions. But the degree of convex shapein (anti)proton looks weaker. Cu+Cu collisions can provide better impact parameter resolution

than peripheral Au+Au collisions. So a detailed system size dependence is shown in the following
sections (see Sections 4.2, 4.3).

Cu+Cu410

sNN = 200 GeV

102
1

T

π+

0 - 5 % (x1)
5 - 10 % (x10-1)
10 - 15 % (x10-2)-315 - 20 % (x10 )20 - 30 % (x10-4)-5
30 - 40 % (x10-6)
40 - 50 % (x10 )50 - 60 % (x10-7)-8
60 - 70 % (x10 )-970 - 80 % (x10 )-1080 - 94 % (x10 )

10-2

106
10

π-

2

5

0 - 5 % (x1)
5 - 10 % (x10-1)
10 - 15 % (x10 -2)-3
15 - 20 % (x10 )20 - 30 % (x10 -4)-530 - 40 % (x10 -6)
40 - 50 % (x10 )50 - 60 % (x10 -7)-860 - 70 % (x10 )-970 - 80 % (x10 )-1080 - 94 % (x10 )

102
1

T

T

10-4

10-6

10-6

10-8

10-8

10-10

10-10

10-12

10-12

10-14

10-14

10-16

10-16

0

sNN = 200 GeV

10-2

10-4

10-18

Cu+Cu

4

T

106

(1/2π p ) d2N / dp dy [c2/ GeV 2]66(1/2π p ) d2N / dp dy [c2/ GeV 2]

4. Results

1

2

3

4

5

6

7

10-18

0

1

3

4

pT [GeV/c]

67pT [GeV/c]

10sNN = 200 GeVK+

0 - 5 % (x1)
5 - 10 % (x10-1)
10 - 15 % (x10-2)-315 - 20 % (x10 )20 - 30 % (x10-4)-5
30 - 40 % (x10-6)
40 - 50 % (x10 )50 - 60 % (x10-7)-8
60 - 70 % (x10 )-970 - 80 % (x10 )-1080 - 94 % (x10 )

102
1
-2

10

106
10

2

5

-

102
1
-2

T

T

10-6

10

-8

10-8

10

-10

10-10

-12

10-12

-14

10-14

-16

10-16

10
10
10
10

0

K

0 - 5 % (x1)
5 - 10 % (x10-1)
10 - 15 % (x10 -2)-3
15 - 20 % (x10 )20 - 30 % (x10 -4)-530 - 40 % (x10 -6)
40 - 50 % (x10 )50 - 60 % (x10 -7)-860 - 70 % (x10 )-970 - 80 % (x10 )-1080 - 94 % (x10 )

10-4

-6

10

sNN = 200 GeV

10

10-4

-18

Cu+Cu

4

T

Cu+Cu

4

(1/2π p ) d2N / dp dy [c2/ GeV 2]

106T(1/2π p ) d2N / dp dy [c2/ GeV 2]

Figure 4.8: pT spectra identified with TOF for charged pions for different centralities in Cu+Cu√
collisions at sN N = 200 GeV (left:positive, right:negative).

1

2

3

4

5

6

7

pT [GeV/c]

10-18

0

1

3

4

6

7

pT [GeV/c]

Figure 4.9: pT spectra identified with TOF for charged kaons for different centralities in Cu+Cu√
collisions at sN N = 200 GeV (left:positive, right:negative).

Cu+Cu410

sNN = 200 GeV

102

T

p

0 - 5 % (x1)
5 - 10 % (x10-1)
10 - 15 % (x10-2)-315 - 20 % (x10 )20 - 30 % (x10-4)-5
30 - 40 % (x10-6)
40 - 50 % (x10 )50 - 60 % (x10-7)-8
60 - 70 % (x10 )-970 - 80 % (x10 )-1080 - 94 % (x10 )

1

10-2

106

p

2

5

0 - 5 % (x1)
5 - 10 % (x10-1)
10 - 15 % (x10 -2)-3
15 - 20 % (x10 )20 - 30 % (x10 -4)-530 - 40 % (x10 -6)
40 - 50 % (x10 )50 - 60 % (x10 -7)-860 - 70 % (x10 )-970 - 80 % (x10 )-1080 - 94 % (x10 )

102
1

T

T

10-4

10-6

10-6

10-8

10-8

10-10

10-10

10-12

10-12

10-14

10-14

10-16

10-16

0

sNN = 200 GeV

10-2

10-4

10-18

Cu+Cu

104

T

106

(1/2π p ) d2N / dp dy [c2/ GeV 2]67(1/2π p ) d2N / dp dy [c2/ GeV 2]

4. Results

1

2

3

4

5

6

7

10-18

0

1

3

4

pT [GeV/c]

67pT [GeV/c]

Figure 4.10: pT spectra identified with TOF for protons and antiprotons for different centralities√
in Cu+Cu collisions at sN N = 200 GeV (left:positive, right:negative).

4.1.5

pT spectra (TOF) – p+p 200/62.4 GeV

pT spectra of π/K/p in Minimum Bias p+p collisions at√

sN N = 200/62.4 GeV are shown in

Figure 4.11 ∼ 4.13. The particle identification is performed with TOF. The p+p spectra can beused as reference spectra to the measured spectra in Au+Au and Cu+Cu. Nuclear modification
factors (RAA , RCP ) are shown in the following section (see Section 4.5).

Figure 4.11: pT spectra identified with TOF for π/K/p in Minimum Bias p+p collisions at√
sN N = 200 GeV (left:positive, right:negative). The vertical axis is invariant cross section.

4. Results

Figure 4.12: pT spectra for pions in Minimum Bias p+p collisions at

68√

sN N = 200/62.4 GeV.

Figure 4.13: pT spectra for protons (left) and antiprotons (right) in Minimum Bias p+p collisions√
at sN N = 200/62.4 GeV.

4. Results

4.2

69

Mean Transverse Momentum

Mean transverse momentum hpT i is calculated for quantitative comparison of particle spectral

shape especially at low pT as shown in Figure 4.14. For extrapolation of pT spectra at unmeasured
low pT , the following functions are used for different particle species: power-law function for pions,mT exponential for kaons and (anti)protons.
p0
1 d2 N= A()n2πpT dpT dy
p0 + p T

(4.1)

1
d2 N
mT − m= A exp(−)
2πmT dmT dy
T

(4.2)

where A, p0 , n, T are fitting parameters. We can see clear hadron mass and centrality dependences of hpT i. These dependences are consistent with radial flow picture. In this sense, radialflow more affects heavier particles than lighter ones. The strength of radial flow is larger incentral collisions than in peripheral collisions. hpT i is scaled with Npart between Au+Au and√Cu+Cu collisions at both sN N = 200 GeV and 62.4 GeV. Those are smoothly connected to
p+p values.

Figure 4.14: Mean trasverse momentum as a function of Npart in Au+Au/Cu+Cu/p+p collisions√
at sN N = 200 GeV (left) and 62.4 GeV (right).

4. Results

4.3

70

Particle Yield at Mid Rapidity

Particle yield per unit rapidity dN/dy is calculated for comparison of particle abundances at midrapidity as shown in Figure 4.15. The same functions in hpT i calculation are used to evaluate

dN/dy values. dN/dy/(0.5Npart ) is plotted as the vertical quantity. dN/dy is expected to bescaled with the number of participants Npart since the low-pT component of spectra is dominant
in particle abundance and it is produced by soft coherent hadron production process. Actually√
Npart scaling is seen between Au+Au and Cu+Cu collisions at sN N = 200 GeV. But at 62.4
GeV, Au+Au values are lower than those in Cu+Cu. This may be caused by the difference ofgeometrical overlap shapes between the two systems (see Chapter 5).

Figure 4.15:

Particle yield dN/dy as a function of Npart divided by 0.5Npart in√
Au+Au/Cu+Cu/p+p collisions at sN N = 200 GeV (left) and 62.4 GeV (right).

4. Results

71

4.4

Particle Ratios

4.4.1

p/π ratios vs. pT

Particle ratios p/π + , p/π − as a function of pT for different centralities in Au+Au/Cu+Cu col√lisions at sN N = 200/62.4 GeV are shown in Figures 4.16 ∼ 4.18. Proton and antiprotonenhancement is observed in all collision systems (Au+Au, Cu+Cu) in central to mid-central. We

1.4
1.2

Au+Au 200 GeV

0 - 10 %10 - 30 %
30 - 60 %
60 - 80 %p+p

PHENIX Preliminary

1

Ratio

Ratio

find that pT dependence in Cu+Cu is similar to that in Au+Au.

0.6

0.4

0.4

0.2

0.2

0
0

1

2

3

4

5

0 - 10 %10 - 30 %
30 - 60 %
60 - 80 %p+pFilled : p/ πOpen : p/ π00.8Open : p/π0

0.6

1.2

Au+Au 200 GeV

PHENIX Preliminary

1

Filled : p/π+

0.8

1.4

0
0

6
7
8
pT [GeV/c]

1

2

3

4

5

6
7
8
pT [GeV/c]

1.4
1.2

Cu+Cu

0 - 10 %10 - 30 %
30 - 60 %
60 - 94 %sNN = 200 GeV

1Filled : p/π+Open : p/π0

0.8

Ratio

Ratio

Figure 4.16: p/π + (left) and p/π − (right) ratios as a function of pT for different centralities in√
Au+Au collisions at sN N = 200 GeV. The PID is done by ACC.

1.4
1.2

0.4

0.4

0.2

0.2
2

3

4

5

6
7
8
pT [GeV/c]

Filled : p/ πOpen : p/ π0

0.8
0.6

1

0 - 10 %10 - 30 %
30 - 60 %
60 - 94 %sNN = 200 GeV

1

0.6

00

Cu+Cu

00

1

2

3

4

5

6
7
8
pT [GeV/c]

Figure 4.17: p/π + (left) and p/π − (right) ratios as a function of pT for different centralities in√
Cu+Cu collisions at sN N = 200 GeV. The PID is done by ACC.

4. Results

72

Figure 4.18: p/π ratios as a function of pT for different centralities in Au+Au/Cu+Cu collisions√
at sN N = 62.4 GeV (upper:p/π + , lower:p/π − ). The PID is done by TOF.

4.4.2

p/π ratios vs. Npart

For detailed comparison of the magnitude of p/π ratios (p/π + and p/π − ) between different col1/3

lision systems, we plot the p/π ratios as a function of Npart , which is corresponding to systemsize (the system volume is proportional to Npart ), for each pT interval (see Figures 4.19 ∼ 4.23).

Rectangular bands put on data points show systematic errors. The magnitude of p/π ratios are√
1/3
scaled with Npart between Au+Au and Cu+Cu collisions at the same collision energy sN N =200/62.4 GeV.

4. Results

73

1.4
1.2
1

p/π+ (Au+Au)
p/π+ (Cu+Cu)p/ π- (Au+Au)
p/ π- (Cu+Cu)

Ratio

Ratio

p/π vs Npart in Au+Au and Cu+Cu at 200 GeV (TOF)
0.6 - 1.5 GeV/c(integrated)

1.4
1.2

sNN = 200 GeV

0.8

0.6

0.6

0.4

0.4

0.2

0.2
1

2

3

4

5

6

7

Ratio

Npart

1.4

p/π+ (Au+Au)
p/π+ (Cu+Cu)

1.2
1

00

8

1/3

p/ π- (Au+Au)
p/ π- (Cu+Cu)

1.0 - 2.0 GeV/c(integrated)sNN = 200 GeV

1

0.8

00

p/π+ (Au+Au)
p/π+ (Cu+Cu)p/ π- (Au+Au)
p/ π- (Cu+Cu)

1

2

3

4

5

6

7

8

Npart1/3

2.0 - 3.0 GeV/c(integrated)sNN = 200 GeV

0.8
0.6
0.4
0.2
00

1

2

3

4

5

6

7

8

Npart1/3

1/3

Figure 4.19: p/π ratios as a function of Npart for different pT regions (Au+Au and Cu+Cu at
200 GeV). The PID is done by TOF.

1.4
1.2
1

p/π+ (Au+Au)
p/π+ (Cu+Cu)p/ π- (Au+Au)
p/ π- (Cu+Cu)

Ratio

Ratio

p/π vs Npart in Au+Au and Cu+Cu at 200 GeV (ACC)
3.0 - 4.0 GeV/c(integrated)

1.4
1.2

sNN = 200 GeV

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

00

1

2

3

4

5

6

7

8

Npart

1/3

1/3

00

p/π+ (Au+Au)
p/π+ (Cu+Cu)p/ π- (Au+Au)
p/ π- (Cu+Cu)

4.0 - 5.0 GeV/c(integrated)sNN = 200 GeV

1

2

3

4

5

6

7

8

Npart

1/3

Figure 4.20: p/π ratios as a function of Npart for different pT regions (Au+Au and Cu+Cu at
200 GeV). The PID is done by ACC.

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
00

74
p/π vs Npart in Au+Au and Cu+Cu at 62.4 GeV

p/ π+ (Au+Au 62 GeV)
p/ π+ (Cu+Cu 62 GeV)

12p/ π- (Au+Au 62 GeV)
p/ π- (Cu+Cu 62 GeV)

3

4

5

Ratio

Ratio

4. Results

1.5 - 2.5 GeV/c(integrated)

6

7

8

Npart1/3

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
00

p/ π+ (Au+Au 62 GeV)
p/ π+ (Cu+Cu 62 GeV)

12p/ π- (Au+Au 62 GeV)
p/ π- (Cu+Cu 62 GeV)

3

4

5

2.0 - 3.0 GeV/c(integrated)

6

7

8

Npart1/3

1/3

Figure 4.21: p/π ratios as a function of Npart for different pT regions (Au+Au and Cu+Cu at

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
00

p/π vs Npart ((dET /dη)) in Au+Au at 200 and 62.4 GeV
p/ π+ (Au+Au 200 GeV)
p/ π+ (Au+Au 62 GeV)

12p/ π- (Au+Au 200 GeV)
p/ π- (Au+Au 62 GeV)

3

4

5

Ratio

Ratio

62.4 GeV).

2.0 - 3.0 GeV/c(integrated)

6

7

8

Npart

1/3

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
00

p/ π- (Au+Au 200 GeV) 2.0 - 3.0 GeV/c(integrated)p/ π- (Au+Au 62 GeV)

p/ π+ (Au+Au 200 GeV)
p/ π+ (Au+Au 62 GeV)

1

2

3

4

5

6

7
8
9
(dE /dη)1/3 [GeV1/3]
T

1/3

Figure 4.22: p/π ratios as a function of Npart (left) (dET /dη)1/3 (right) and for different pT

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
00

p/π vs Npart in Cu+Cu at 200 and 62.4 GeV
p/ π+ (Cu+Cu 200 GeV)
p/ π+ (Cu+Cu 62 GeV)

12p/ π- (Cu+Cu 200 GeV)
p/ π- (Cu+Cu 62 GeV)

3

4

5

Ratio

Ratio

regions (Au+Au at 200 GeV and 62.4 GeV).

1.5 - 2.5 GeV/c(integrated)

6

7

8

Npart1/3

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
00

p/ π+ (Cu+Cu 200 GeV)
p/ π+ (Cu+Cu 62 GeV)

1

1/3

2

p/ π- (Cu+Cu 200 GeV)
p/ π- (Cu+Cu 62 GeV)

3

4

5

2.0 - 3.0 GeV/c(integrated)

6

7

8

Npart1/3

Figure 4.23: Left/Middle: p/π ratios as a function of Npart for different pT regions (Cu+Cu at
200 GeV and 62.4 GeV).

4. Results

75

However the Npart scaling does not work between different collision energies 200 and 62.4
GeV in Au+Au collisions. Instead, p/π − ratio is scaled with transverse energy density dET /dη.
p/π + ratio is still not scaled even in this case. Larger yield of proton at 62.4 GeV indicates thatbaryon transport process is not small at lower energy.

4.4.3

p/p ratio vs. pT

Particle ratio p/p is shown as a function of pT for Minimum Bias, centrality-selected cases in√
Au+Au and Cu+Cu collisions at sN N = 200 GeV in Figures 4.24 ∼ 4.27. Rectangular bands
put on data points show systematic errors. The ratios are almost independent of pT and centrality

Ratio

up to 6 GeV/c in both Au+Au and Cu+Cu, and has a value of 0.7 ± 0.1 at 1 < pT < 6 GeV/c.
1.4
1.2

Au+Au 200 GeV (MB)

1
0.8
0.6

p/p (ACC)
p/p (TOF)
p/p (Run2)

0.4
0.2
0

0

PHENIX Preliminary
1

2

3

4

5

6

7
8
pT [GeV/c]

Figure 4.24: p/p ratio as a function of pT in Minimum Bias Au+Au collisions at
GeV.

√

sN N = 200

1.2 PHENIX Preliminary

1.4 Au+Au 200 GeV 10 - 30 %1.2 PHENIX PreliminaryRatio

1.4 Au+Au 200 GeV 0 - 10 %

Ratio

76

Ratio

Ratio

4. Results

1.4 Au+Au 200 GeV 30 - 60 %1.2 PHENIX Preliminary

1.4 Au+Au 200 GeV 60 - 80 %1.2 PHENIX Preliminary

1

1

1

1

0.8

0.8

0.8

0.8

0.6

0.6

0.6

0.6

0.4

p/p (ACC)

0.4

p/p (ACC)

0.4

p/p (ACC)

0.4

p/p (ACC)

0.2

p/p (TOF)
p/p (Run2)

0.2

p/p (TOF)
p/p (Run2)

0.2

p/p (TOF)
p/p (Run2)

0.2

p/p (TOF)
p/p (Run2)

6 7 8
p [GeV/c]0

6 7 8
p [GeV/c]0

6 7 8
p [GeV/c]

0

0

0

1

2

3

4

5

0

1

2

3

4

5

T

0

1

2

3

4

5

T

0

1

2

3

4

5

6 7 8
p [GeV/c]T

T

Figure 4.25: p/p ratio as a function of pT for different centralities in Au+Au collisions at√

sN N =Ratio

200 GeV.
1.4

sNN = 200 GeV (MB) -- ACC

1.2
1
0.8
0.6
0.4

p/p (Cu+Cu)
p/p (Au+Au)

0.2
00

1

2

3

4

5

6
7
p [GeV/c]T

Figure 4.26: Left: p/p ratio as a function of pT in Minimum Bias Cu+Cu collisions at√

sN N =

200 GeV. Right: p/p ratio as a function of pT in Minimum Bias collisions (Au+Au and Cu+Cu

1.2

0 - 10 %1.4 Cu+Cu s = 200 GeV
NN
1.2 10 - 30 %Ratio

1.4 Cu+Cu s = 200 GeV
NN

Ratio

Ratio

Ratio

at 200 GeV).
1.4 Cu+Cu s = 200 GeV
NN
1.2 30 - 60 %1.4 Cu+Cu s = 200 GeV
NN
1.2 60 - 94 %

1

1

1

1

0.8

0.8

0.8

0.8

0.6

0.6

0.6

0.6

0.4

p/p (ACC)

0.200p/p (TOF)
1

2

3

4

5 6 7
pT [GeV/c]

0.4

p/p (ACC)

0.200p/p (TOF)
1

2

3

4

5 6 7
pT [GeV/c]

0.4

p/p (ACC)

0.200p/p (TOF)
1

2

3

4

5 6 7
pT [GeV/c]

0.4

p/p (ACC)

0.200p/p (TOF)
1

2

3

4

5 6 7
pT [GeV/c]

Figure 4.27: p/p ratio as a function of pT for different centralities in Cu+Cu collisions at
200 GeV.

√sN N =

4. Results

4.5

77

Nuclear Modification Factors

It is useful to calculate nuclear modification factors, in order to look at the centrality dependenceof pT spectra in detail. The nuclear modification factors are defined relative to nucleon-nucleon
collisions (RAA ) or relative to peripheral collisions (RCP ).

4.5.1

RAA

Nuclear modification factor RAA is shown for Au+Au and Cu+Cu collisions at
in Figures 4.28 ∼ 4.35. RAA is defined as follows: 
1 d2 σ N +N
1 d2 N A+A/
RAA (pT , y) =N +N dp dy
hNcoll i dpT dy
σinel
T

√

sN N = 200 GeV(4.3)

where hNcoll i is the average number of binary nucleon-nucleon collisions. The denominator is

N +N
the spectra in Run5 p+p at 200 GeV. The value of σinel
is taken to be 42 mb. If any nuclear

effects are absent, RAA is expected to be unity. We find that (anti)protons are enhanced at 1.5- 4 GeV/c, while pions and kaons are suppressed, for all centralities. K ∗ , φ RAA from STAR
experiment are also shown for comparison [42].

Figure 4.28: RAA (π/K/p) as a function of pT in 0-10% Au+Au collisions at 200 GeV.

Figure 4.29: RAA (π/K/p) as a function of pT in 10-30% Au+Au collisions at 200 GeV.

4. Results

Figure 4.30: RAA (π/K/p) as a function of pT in 30-60% Au+Au collisions at 200 GeV.

Figure 4.31: RAA (π/K/p) as a function of pT in 60-80% Au+Au collisions at 200 GeV.

Figure 4.32: RAA (π/K/p) as a function of pT in 0-10% Cu+Cu collisions at 200 GeV.

78

4. Results

Figure 4.33: RAA (π/K/p) as a function of pT in 10-30% Cu+Cu collisions at 200 GeV.

Figure 4.34: RAA (π/K/p) as a function of pT in 30-60% Cu+Cu collisions at 200 GeV.

Figure 4.35: RAA (π/K/p) as a function of pT in 60-80% Cu+Cu collisions at 200 GeV.

79

4. Results

80

Figure 4.36 shows RAA at pT = 2.25 GeV/c as a function of Npart in Au+Au/Cu+Cu collisions√
at sN N = 200 GeV. While a weak suppression is seen for pions, kaons in central, (anti-)protons
are clearly enhanced for all centralities. At most peripheral, all particle species (pions, kaons, and(anti)protons) are slightly enhanced (i.e., above unity). This enhancement could be attributed
to the Cronin effect (enhancement from multiple scattering) as seen in d+Au collisions. Similar
Npart dependence of RAA is observed for Au+Au/Cu+Cu. This could be called Npart scaling of
RAA at the same collision energy as well as p/π ratio. Looking at the difference between Au+Au
and Cu+Cu more seriously, RAA of Cu+Cu is slightly larger than that of Au+Au. This relation
is similar to that seen in dN/dy comparison.

Figure 4.36: RAA for pions (left) and (anti)protons (right) at pT = 2.25 GeV/c as a function of√
Npart in Au+Au/Cu+Cu at sN N = 200 GeV. Overall systematic error (∼15%) is not included.

4.5.2

RCP

Nuclear modification factor RCP is shown for Au+Au and Cu+Cu collisions at√
sN N = 200

GeV in Figures 4.37 ∼ 4.39. RCP is defined as follows:
RCP (pT , y) =

d2 N A+A,centcenthNcoll
i dpT dy1/

d2 N A+A,peri
perihNcoll
i dpT dy
1

!

(4.4)

where hNcoll i (average number of binary nucleon-nucleon collisions) are taken from the PHENIX

Glauber model calculation. The overall systematic error (Ncoll uncertainties) on RCP is shown
as a vertical band. The statistical errors are shown as error bar on each data point. For proton
RCP , the statistical errors have been significantly reduced compared to the previous Run2 resultsby the high statistics data and the introduction of ACC. The result shows a stronger suppression
for pions than protons in the intermediate pT range (2-4 GeV/c). Over the measured pT range,

4. Results81

we do not observe a difference in RCP between particles and antiparticles. At higher pT weobserve an approaching trend of proton RCP into pion RCP . Figure 4.38 shows pion and proton
RCP including Ks0 and Λ particles. Ks0 is suppressed as pions, but Λ is less suppressed atintermediate pT . RCP results can be grouped into baryon’s and meson’s groups. The grouping of
RCP according to the number of constituent quarks could be attributed to quark recombination
picture at hadronization. Figure 4.39 shows pion and proton RCP including K ∗ and φ particles.
The centrality dependence is seen in the magnitude of RCP . In central, pions are more suppressedthan in peripheral. The magnitude relation between pions and (anti)protons does not change
in any centrality bin. K ∗ and φ RCP shows similar magnitude as pion RCP . So mesons can begrouped even though K ∗ and φ have relatively large mass (892 MeV for K ∗ , 1020 MeV for φ).

4. Results

Figure 4.37: RCP (0-10%/60-80%) for π/K/p as a function of pT in Au+Au collisions at

82

√

sN N

√

sN N

= 200 GeV. The Run2 proton RCP is also plotted.

Figure 4.38: RCP (0-10%/60-80%) for π/K/p as a function of pT in Au+Au collisions at= 200 GeV. Ks0 , Λ RCP from STAR experiment are also shown [41].

4. Results

83

Figure 4.39: RCP for pions, kaons, and (anti)protons as a function of pT in Au+Au collisions at√
sN N = 200 GeV. The centrality selection is 0-10%/60-80%, 10-30%/60-80%, 30-60%/60-80%
from top to bottom. K ∗ , φ RCP from STAR experiment are also shown for comparison [42].

Chapter 5
Discussions
In this chapter, we discuss freeze-out properties and hadron production at intermediate pT (2-5 GeV/c), especially (anti)proton production, in relativistic heavy
ion collisions at RHIC. Statistical model and blast-wave model are used to extract
chemical/kinetic freeze-out properties. Also we compare the obtained particle ratioswith quark recombination models, PYTHIA calculations.

5.1

Freeze-out Properties

Bulk properties of heavy ion collisions are originated from soft hadrons with transverse momentum pT .2 GeV/c. Soft hadrons are decoupled from the collision area at late stage ofthe space-time evolution. A concept of freeze-out is useful for characterizing bulk properties.
Freeze-out is defined by a space-time hypersurface, where the mean free path of hadrons becomes larger than the typical scale of the expanding system. So local thermal equilibrium is nolonger maintained due to the lack of interactions between hadrons.
As first observed at AGS, SPS, and confirmed at RHIC, the shapes and the normalizationsof the hadron momentum spectra reflect two different stages of the collision [43]. The freeze-out
can be separated into two stages as follows:• Chemical freeze-out: ratios of particle abundances are fixed because inelastic scatteringscease. In other words, chemical composition of emitting particles is frozen after hadronization.

• Kinetic freeze-out: kinetic equilibrium is no longer maintained. Until this freeze-out, thespectral shapes are affected by hadronic scatterings.

The freeze-out properties such as temperatures, chemical potentials, radial flow velocity can beextracted from hadron yield or spectral shape. These are parameterizations to reproduce thedata based on models.

5. Discussions

5.1.1

85

Chemical Freeze-out – Statistical Model Fit

As shown in Figure 4.15, dN/dy of π/K/p as a function of Npart in different collision systems. A
fast increase with system volume is observed reaching a saturation at about ∼100 participants.

We can see that dN/dy is roughly scaled with Npart between Au+Au and Cu+Cu at the same√sN N . Assuming a simple proportionality between the system volume and the number of participants, one can say that bulk yields are controlled by the system volume. Strictly speaking,peripheral Au+Au values are slightly lower than those in Cu+Cu. This may be caused by thedifference of geometrical overlap shapes between the two systems. The shape of the overlapped
region in peripheral Au+Au is more deformed. The number of nucleon-nucleon collisions per
nucleon is larger than in Cu+Cu than in peripheral Au+Au. This could be one of the reasons.
Ratios of dN/dy (Au+Au, Cu+Cu) are almost flat as a function of Npart within the experimental
uncertainty. This means that a factorization of energy and system volume dependences can be
done.
Figure 5.1 shows antibaryon-to-baryon ratios as a function of collision energy. In 62.4 GeV

Au+Au collisions, p/p ratio is about 0.5 and follows the smooth curve from SPS to RHIC. It is

Anti-Baryon/ Baryon Ratio (y = 0)

consistent with the preliminary Λ/Λ ratio measured by STAR.
AGS

1

SPS

RHIC

Central Au+Au, Pb+Pb
-1

10

-2

10

PHENIXSTAR (Λ/ Λ)
NA44
NA49
E802

-3

10

-4

10

1

10

10

2

sNN (GeV)

Figure 5.1: Beam energy dependence of antibaryon-to-baryon ratios from AGS to RHIC.

It is well known that total hadron yields and ratios can be described by a purely statisticalmodel. The statistical model approach is established by analyses of particle ratios in high energy
heavy ion collisions in GSI-SIS to CERN-SPS energy and elementary collisions (e+ +e− , p + p,
and p + p). The hadron yields are given by pT -integrated yield which is dominated by low-pT
particles. In statistical model, the measured hadron yields and their ratios are controlled bychemical potentials and chemical freeze-out temperature.

5. Discussions

86

We adopt a grand canonical ensemble for a chemical freeze-out model [44]. In the model, thedensity of a particle species i is given by:
ρi = γs(s+s)imi
Q i µqSi µs
g i 3 mi 2
T
(
)
K
(
)
exp(
)
exp(
)
2
ch
2π 2
Tch
Tch
Tch
Tch

(5.1)

where Tch is chemical freeze-out temperature, γs is strangeness saturation factor, µq is chemical
potentials for u/u/d/d quarks, and µs is for s/s quarks. mi is mass of particle species i , gi isnumber of spin-isospin degree of freedom. Qi and Si are net numbers of valence u/d quarks
and s quark of particle species i , respectively. K2 is the second-order modified Bessel function.
Note that we use the Boltzmann approximation for all hadrons except for pions, where the Bose
distribution is applied. The resonance decay to lower mass hadrons after chemical freeze-out isalso taken into account. Known resonances up to mass of 1.7 GeV/c2 are included. Since thedata are taken in mid-rapidity region, therefore we do not apply any conservation laws.

Figure 5.2: Chemical freeze-out temperature Tch as a function of Npart in Au+Au/Cu+Cu/p+p√
collisions at sN N = 200 GeV (left) and 62.4 GeV (right).

Figure 5.3: Chemical potential µq a function of Npart in Au+Au/Cu+Cu/p+p collisions at√
sN N = 200 GeV (left) and 62.4 GeV (right).

5. Discussions

87

Chemical freeze-out temperature Tch is found to be independent of collision centrality as√
shown in Figures 5.2 and 5.3. We obtain almost the same Tch ∼160 MeV at sN N = 62.4,
200 GeV. It is universal to both elementary (p+p) and heavy ion collisions (Au+Au, Cu+Cu).

Small but finite chemical potential µq reflects that net baryon density is small but not zeroaround mid-rapidity. The chemical potential is larger at 62.4 GeV than at 200 GeV. The centrality dependence of chemical potential µq is almost flat at 200 GeV, but at 62.4 GeV it increases
with Npart . The increase is consistent with larger baryon stopping in central collisions. Between
Au+Au and Cu+Cu collision systems, Tch , µq are scaled with Npart . As well as particle abundances dN/dy, particle ratios and chemical freeze-out properties are controlled just by the system√size at the same sN N .
As a conclusion of this section, we can say that hadrons are emitted from a thermal source.
It is locally chemically equilibrated. The degree to which chemical equilibrium among hadrons isestablished provides important constraints on microscopic chemical reaction processes and theirtimescales. Since strangeness saturation factor γs (in Equation 5.1) increases with Npart , thedegree of chemical equilibrium including strange quarks is more higher in central collision thanin peripheral collisions. In this sense, the thermalization may reach up to a certain level even ina small system p+p collisions.
The chemical freeze-out temperature is flat in centrality, and near the critical temperature T c(∼170 MeV) predicted from lattice QCD calculation. Hadronic scatterings from hadronization
to chemical freeze-out must be negligible because they would result in dropping Tch . So theobserved chemical equilibrium cannot have been generated via hadronic scatterings due to theshort time duration between chemical freeze-out and hadronization.
Nevertheless the picture of thermal hadron production does not require the existence of parton phase. It is important to understand if and how the thermal properties of the observed
hadrons relate to the thermal properties of quarks and gluons in the QGP. We will discuss this
topic in Section 5.1.2.

5. Discussions

5.1.2

88

Kinetic Freeze-out – Blast-wave Model Fit

In Section 5.1.1, we discussed chemical freeze-out properties using pT -integrated yields and theirratios. On the other hand, the spectral shape of pT spectra also contains information about
hadron production mechanisms and final-state interactions between produced hadrons. The
measured hadron spectra reflects properties at the stage when hadrons stop interactions. This
moment is called kinetic (thermal) freeze-out. In p+p collisions, pT spectra are well describedby mT -exponential function at low pT . this is called “mT scaling” between different particle
species. This means that mT -exponential slope parameters (or equivalently mean pT ) are thesame between particle species. This scaling implies that initial parton distributions dominate
the particle production process [45]. However, from previous studies at SPS, mT scaling does notwork in heavy-ion collisions. As shown in Figure 5.4, mean transverse momentum hpT i has a clear

mass dependence. hpT i linearly increases with hadron mass. If a thermal source for all hadron

species is boosted with the same velocity in radial direction, the expansion should result in sucha characteristic mass dependence as observed here. Thus, the observation is consistent with aradial collective flow picture. In central collisions, hpT i for any hadron species is larger than in

Figure 5.4: Mean transverse momentum hpT i vs. hadron mass in 0-5% (0-20% for d, d) central√
Au+Au collisions at sN N = 200 GeV.

peripheral (see Figure 4.14). Especially the increase of (anti)protons is significant. This meansthat the radial flow velocity is larger in central collisions. Moreover, Npart scaling in hpT i is also
observed between Au+Au and Cu+Cu systems as well as particle abundances dN/dy. The nextquestion is: what causes the radial flow. We think now that it is scatterings among constituents inthe collision overlap region. The constituents are quarks and gluons before hadronization, thenhadrons after hadronization. The scatterings convert density gradients into outward pressure
gradients resulting in radial collective flow.

5. Discussions

89

In theoretical model, relativistic hydrodynamic calculations reproduce the data well at low
pT [27]. A separation of thermal motion and collective flow requires a thermal model based onsuch a hydrodynamic approach. Several models have been developed to reproduce the measured
hadron momentum spectra. Such models use concepts borrowed from relativistic hydrodynamics
but they do not include the complete time evolution of the system. They contain essential
freeze-out features of the hydrodynamic calculation. For this reason, they are called hydroinspired models. Hydro-inspired models are a very effective parameterization of the final state,that use few parameters with clear physical interpretation.
A so-called blast-wave model is one of them. The blast-wave model originates from thepaper [46], where a relativistic formula for particle distribution corresponding to a thermalized
and radially expanding system was first given. Assuming (1) longitudinal boost-invariance,(2) cylindrically symmetric systems, (3) freeze-out occurs instantaneously at all radii, (4) the
Cooper-Frye formula [47] leads to the following formulation [48]:dN∝
mT dmT

Z R
0rdrmT I0 (mT coshρpT sinhρ
)K1 (
)
Tf o
Tf o

r
βT (r) = βs ( )nR
where mT =

(5.2)
(5.3)

p
p2T + m2 , ρ(r) = tanh−1 βT (r). The velocity profile in radial direction should be

fixed since the variation can affect the absolute yield at extrapolated high pT . We have tested
different velocity profiles with changing n values as follows:

Figure 5.5: Velocity profile βT (r)/βT,max in radial direction for different n.

5. Discussions

90

Table 5.1: χ2 /n.d.f. (n.d.f = 46) values for combinations of n and centrality range in 200 GeV
Au+Au collisions. βT (r) = βs ( Rr )n .
n=0.5 n=1.0 n=2.0
Central

5.3

2.8

3.7

Mid-central

3.5

1.6

1.9

Peripheral

3.4

2.8

1.8

We found that n = 1.0 is a reasonable number. Also this is consistent with results of fullhydrodynamic calculations [27]. In the following analysis, n is set to be 1.0 (linear velocity
profile). The blast-wave model does not predict the absolute normalizations of the spectra,
hence extra parameters are required to normalize each spectra. This part is now done by thestatistical model described in Section 5.1.1.

Figure 5.6: pT spectra for π/K/p in Au+Au collisions at√

sN N = 200 GeV with Blast-wave

fitting result (see text for detail).

The measured pT spectra are fitted with the above function for π/K/p simultaneously (seeFigure 5.6). The transverse flow velocity and kinetic freeze-out temperature are extracted. Fromprevious studies [49], kinematics of resonance decays results in very steeply dropping daughter
pion spectra and raise considerably the total pion yield at low-pT region (<0.5 GeV/c). To
minimize the contribution from resonance decays, we apply tight pT cuts in the fitting (π: 0.6-

5. Discussions

91

1.2 GeV/c K: 0.4-1.4 GeV/c, p,p: 0.6-1.7 GeV/c). The high-pT cut off is set to be mT − m <1.0 GeV/c2 for rejecting hard component of spectra.

To study the parameter correlations, we make a grid of (Tf o , βT ) pairs and then perform a χ2
minimization for each particle type. We observe that the parameter Tf o and βT are anti-correlated
as shown in Figure 5.7, since the spectra can be made flatter by increasing either the temperatureor the transverse flow. Different particles have different sensitivity to the parameters. For
example, heavier particles are more sensitive to the radial flow velocity than to the kinetic freezeout temperature. This ambiguity in Tf o -βT can be removed by fitting spectra simultaneously
for different mass particles and searching for overlap region in Tf o -βT plane. The contours of six
particle species overlap at a single common point within 3 σ level.

Figure 5.7: χ2 contour map as a function of Tf o and βT for π/K/p in Au+Au collisions at√
sN N = 200 GeV (top: combined, bottom: separate for π/K/p).

The extracted parameters are shown in Figures 5.8 and 5.9. The kinetic freeze-out temperature Tf o and flow velocity hβT i depend on collision centrality. In more central collisions,freeze-out occurs at lower temperature and with larger radial flow than in peripheral collisions.

In central Au+Au collisions, Tf o is about ∼120 MeV, hβT i is about ∼0.5c. As expected, thekinetic freeze-out temperature is lower than chemical freeze-out temperature. This provides anevidence for further expansion in the duration form chemical to kinetic freeze-out, driving thesystem to lower temperature.

5. Discussions

92

Figure 5.8: Transverse flow velocity as a function of Npart in Au+Au/Cu+Cu/p+p collisions at√
sN N = 200 GeV (left) and 62.4 GeV (right).

Figure 5.9: Kinetic freeze-out temperature as a function of Npart in Au+Au/Cu+Cu/p+p colli√
sions at sN N = 200 GeV (left) and 62.4 GeV (right).

We can see Npart scaling again, which is of Tf o and hβT i between Au+Au and Cu+Cu systems.
√
And we obtain almost same Tf o and hβT i at sN N = 62.4, 200 GeV. On the other hand, a finite

transverse flow is observed even in p+p. Is thermal behavior expected in a small system p+p?

There may be no established mechanism which makes local thermal equilibrium possible in p+p
collisions. This kind of discussion is similar to that in chemical freeze-out. So, the degree ofthermalization in small system is another and important topic. Here we assume local thermal
equilibrium in heavy ion collisions which is a larger system.

5. Discussions

93

To study the relation between the freeze-out time and system size, we compare the freeze-out
parameters with a simple adiabatic expansion model (ideal gas ; P = (1/3), P : pressure, :energy density). This model includes longitudinal expansion with the velocity of light and radial
expansion with the extracted flow velocity βT . With thermodynamics relations, we obtains ∝ T3(5.4)

where s is the entropy density, T is the temperature. The conservation of total entropy iss(t)V (t) = s(t0 )V (t0 )(5.5)

V (t) = tπ(R0 + βT t)2(5.6)

t0 is a given initial time. R0 is the radius of the overlap region. T0 = T (t0 ). Then, we obtain thetime dependence of temperature
T (t) = T0 (t0 (R0 + βT t0 )2 1/3)
t(R0 + βT t)2(5.7)

Since the system size increases with time, the mean free path L(t) increases with time. We
define a freeze-out time tf o when L(t) is equal to radial size R(t). In this case, tf o is 1-parameter
function, which is determined by the most central freeze-out parameters.
L(t) =tπ(R0 + βT t)2
V (t)
=
αNp σ
αNp σ

(5.8)

R(t) = R0 + βT t

(5.9)

where α is a proportionality coefficient for the total number of particles, Np is the number ofnucleon participants, and σ is the cross section. From a L(t) = R(t) relation, we obtainq
tf o = ( R02 + 4βT KNp − R0 )/2βT(5.10)

where K(= ασ/π) is a free parameter which is determined by a centrality bin. Substituting tf o

to Equation 5.7, we have the freeze-out temperature Tf o . Figure 5.10 (left) shows temperature
as a function of time with a common fixed freeze-out time (10 fm/c). Because the freeze-out
temperature is lower in central than in peripheral, the magnitude relation does not change evenreversing in time. The peripheral temperature is higher than central one at any time. We
scale temperature at τ = 1 fm/c with bjorken energy density Bj τ (see Figure 1.5) and a Bj∝ T 4 relation. The most central freeze-out time is fixed at 10 fm/c. As shown in Figure 5.10
(right), the central temperature is higher than peripheral one as expected. Then, we compare

the model prediction with other centrality bins. This simple model reproduces the result well(see Figure 5.11). In summary, the centrality dependence of freeze-out temperature is explained
only by the change of the system size (Npart ), resulting in a Npart scaling. The difference of
freeze-out temperatures between chemical and kinetic freeze-out’s shows a finite expansion timeat hadronic stage. The expansion time is more longer in central than in peripheral.

5. Discussions

94

Figure 5.10: Left: Temperature as a function of time with a common fixed freeze-out time (10fm/c). Right: Temperature as a function of time with scaled temperatures at t =1 fm/c.

Figure 5.11: Freeze-out time (left) and temperaure (right) as a function of Npart .

5. Discussions

95

We emphasized Npart scaling between Au+Au and Cu+Cu systems several times. It is observed in hadron abundances (dN/dy) and chemical/kinetic freeze-out properties. We can saythat the number of participants Npart , representing the system size, is a key parameter to explain
1/3

bulk properties of the collision system. For the positive correlation of Npart and system size, results of HBT radii measurements can be referred [50]. Geometrical shape of the overlapped region
does not affect the properties. In short, Cu+Cu looks like peripheral Au+Au. And peripheral
Au+Au/Cu+Cu approaches p+p.
In this sense, the next question is: “Is there another key parameter for bulk properties?” An
important observable is v2 (elliptic flow coefficient). We test the scaling of v2 between different
collision systems below. Figure 5.12 (left) shows v2 as a function of Npart for different pT for√
charged hadrons in Au+Au/Cu+Cu at sN N = 200 GeV. v2 does not look scaled by Npartin the region Npart ∼80. In non-central heavy-ion collisions, the initial overlap zone between

the colliding nuclei is spatially deformed. If the constituents produced in the reaction zone

rescatter efficiently, this spatial anisotropy gets transferred to momentum space. The initial
spatial eccentricity should rather be an appropriate variable. The eccentricity is calculated
within a Glauber model, assuming the minor axis of the overlap region to be along the impact
parameter vector. Actually v2 looks scaled by this eccentricity shown in Figure 5.12 (right). It
is also reported that v2 is scaled by participant eccentricity, which accounts for nucleon position

0.3

Charged hadrons v
2
Au+Au 200 GeV, p = 0.6 GeV/c
T
Au+Au 200 GeV, p = 1.4 GeV/c
T
Au+Au 200 GeV, p = 2.3 GeV/c
T
Cu+Cu 200 GeV, p = 0.6 GeV/c
T
Cu+Cu 200 GeV, p = 1.4 GeV/c
T
Cu+Cu 200 GeV, p = 2.3 GeV/c

0.25
0.2

T

v2

v2

fluctuations in the colliding nuclei [51].
0.3
0.25
0.2

0.15

0.15

0.1

0.1

0.05

0.05

0
0

50

100

150

200

250

300

350

400
Npart

0
0

Charged hadrons v2
Au+Au 200 GeV, p = 0.6 GeV/c
T
Au+Au 200 GeV, p = 1.4 GeV/c
T
Au+Au 200 GeV, p = 2.3 GeV/c
T
Cu+Cu 200 GeV, p = 0.6 GeV/c
T
Cu+Cu 200 GeV, p = 1.4 GeV/c
T
Cu+Cu 200 GeV, p = 2.3 GeV/c
T

0.05

0.1

0.15

0.2

0.25

0.3

0.35
0.4
Eccentricity

Figure 5.12: v2 as a function of Npart (left) and eccentricity (right) for different pT for charged√
hadrons in Au+Au/Cu+Cu at sN N = 200 GeV [22].

5. Discussions

96

In summary, soft components show a similarity in chemical/kinetic freeze-out properties be√
tween sN N = 200 GeV and 62.4 GeV. Only baryon chemical potential shows the difference
due to the difference of baryon number transport. This difference affects the normalization ofpT spectra. It does not affect the spectral shape anyway. Freeze-out properties are almost same
when comparing them at same Npart between Au+Au and Cu+Cu.
At significantly larger pT the thermal picture begins to give way to hard power-law component and the slopes can no longer be interpreted in a collective flow picture. Next we look at
this switching region from soft to hard hadron production using a two-component model (seeSection 5.2.2).

5. Discussions

5.2

Hadron Production at Intermediate pT

5.2.1

Proton and Antiproton Enhancement

97

The pT dependence of particle ratios provides more insights to the hadron production. Especially p/π ratio is focused on in this section in terms of the baryon enhancement. Fig. 5.13 showsp/π + (p/π − ) ratios as a function of pT for different centralities in Au+Au and Cu+Cu collisions√
at sN N = 200 GeV. The p/π ratios in the intermediate pT range (2-5 GeV/c) show a clear
centrality dependence, higher relative proton production in more central collisions. In central
collisions, the p/π ratio shows that approximately equal amounts of protons and pions are produced in the momentum range of pT = 2-4 GeV/c. This is significantly higher than the resultsin elementary collisions (p+p, e+ +e− ) or pQCD calculations, p/π ∼0.2 [52, 53]. In the most pe-ripheral collisions, the values are consistent with p+p values. A definite turnover is observed for
all centrality classes. The peak position is at 2-3 GeV/c, independent of centrality. Beyond thepeak, the ratios are falling toward the values in p+p collisions. The observed behavior indicatesa transition from soft to hard hadron production at intermediate pT . At least, the large baryon
enhancement at intermediate pT indicates that the dominant source of hadron production in thispT range is not jet fragmentation.

Figure 5.13: p/π + (top) and p/π − (bottom) ratios as a function of pT for different centralities in√
Au+Au/Cu+Cu/p+p collisions at sN N = 200 GeV.

5. Discussions

98

The baryon enhancement is also observed in nuclear modification factors (RAA , RCP ) (seeSection 4.5). If jet fragmentation dominates for the hadron production in intermediate pT region
and parton energy loss in the created matter is the same between quarks and gluons, one should
expect similar values of RCP for pions and protons. But we do not see such a behavior of RCP .
This means that soft hadron production like radial flow effect may still be significant even at thispT . However at higher pT we observe an approaching trend of proton RCP into pion RCP . The
observed behavior indicates a transition from soft to hard hadron production (jet fragmentation
with energy loss) at intermediate pT .
The lower energy data provides an important information on the baryon production andtransport at mid-rapidity. Figure 5.14 shows the p/π + (p/π − ) ratios as a function of pT in√
Au+Au and Cu+Cu collisions at sN N = 62.4 GeV. The ratios show a peak structure around√
2-3 GeV/c and a centrality dependence as seen at sN N = 200 GeV. Comparing to the 200 GeV
data, the 62.4 GeV data shows a larger proton contribution at intermediate pT , while there is aless antiproton contribution. These observations are related to the following points: (1) larger
difference between the slopes of spectra from thermal emission and jet fragmentation at 62.4
GeV than that at 200 GeV [54]. The pT spectra at 62.4 GeV is steeper than that at 200 GeV.
The steepness reflects the difference in initial jet production at the two collision energies, (2)larger baryon chemical potential at 62.4 GeV than that at 200 GeV, (3) stronger transport ofbaryon number from the incoming beams to midrapidity at lower energy. In order to separate
baryon number transport from the baryon enhancement, antiproton is a good probe to study thebaryon enhancement than proton which is more affected by baryon number transport process.
Another thing to be taken into account is p−p annihilation in hagron gas at late collision stage.
In the limiting case that thermal motion (T ∼120 MeV) is dominant without collective flow, therelative momentum between particles is ∼500 MeV (β ∼0.4). The experimental p−p annihilation

cross section is ∼100 mb at p = 500 MeV [55]. On the other hand, proton number density inhadron gas (central collision) is estimated as follows: proton yield at mid-rapidity dN p /dy is∼18, and the freeze-out volume Vf o is ∼1.1 × 103 fm3 at τ = 10 fm/c (see Section 5.1.2), so theproton number density is np = (dN p /dy)/Vf o = ∼1.7 × 10−2 fm−3 . The mean free path λ forannihilation is ∼5.9 fm. The duration time of hadron gas ∆t is estimated to be ∼4 fm/c. Fromthese numbers, the survival rate of antiprotons is exp (−β∆t/λ) ∼0.76. This rate reduces the

p/p ratio with ∼10 % for p/p = 0.7. With higher pT , the annihilation cross section is very small.
Proton and antiproton enhancement at intermediate pT is observed in all collision systems.

The pT dependence in Cu+Cu is similar to that in Au+Au. Figure 5.15 (left) shows p/π + ( p/π − )√1/3
ratio as a function of Npart at pT = 2-3 GeV/c in Au+Au/Cu+Cu collisions at sN N = 200 GeV.
Even though the overlapped region of colliding nuclei has a different geometrical shape for thesame number of participating nucleons Npart , the data shows similar system size dependences inboth systems. This could be called Npart scaling on p/π ratio at the same collision energy. The

5. Discussions
Npart scaling is also observed at lower energy

99√

sN N = 62.4 GeV between Au+Au/Cu+Cu (seeSection 4.4.2). On the other hand, the Npart scaling is not observed between different energies 62.4
GeV and 200 GeV in Au+Au. Instead, transverse energy per unit pseudo-rapidity (dET /dη) is
useful for such scaling between different collision energies as shown in Figure 5.15 (right). Indeedp/π − ratio is scaled with dET /dη ((dET /dη)1/3 used for comparison), but p/π + is not scaled.
Proton yield at 62.4 GeV is larger than that at 200 GeV. This shows that proton production at
62.4 GeV is partly from baryon number transport, not only proton-antiproton pair production.
In conclusion, Npart , representing the initial system size, is a control parameter for the baryon
enhancement. Transverse energy density dET /dη is a connection key between different collisionenergies.

5. Discussions

100

1.4
1.2
1

p/π+ (Au+Au)
p/π+ (Cu+Cu)p/ π- (Au+Au)
p/ π- (Cu+Cu)

Ratio

Ratio

Figure 5.14: p/π + (top) and p/π − (bottom) ratios as a function of pT for different centralities in√
Au+Au/Cu+Cu/p+p collisions at sN N = 62.4 GeV.

2.0 - 3.0 GeV/c(integrated)sNN = 200 GeV

0.8
0.6
0.4

Phenix preliminary

0.2
00

1

2

3

4

5

6

7

8
N1/3
part

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
00

p/ π+ (Au+Au 200 GeV)
p/ π+ (Au+Au 62 GeV)

p/ π- (Au+Au 200 GeV) 2.0 - 3.0 GeV/c(integrated)p/ π- (Au+Au 62 GeV)

Phenix preliminary
1

2

3

4

5

6

7
8
9
(dE /dη)1/3 [GeV1/3]
T√
1/3
Figure 5.15: Left; p/π ratio as a function of Npart for 2-3 GeV/c in Au+Au/Cu+Cu at sN N√
= 200 GeV. Right; p/π ratio as a function of (dET /dη)1/3 for 2-3 GeV/c in Au+Au at sN N =62.4/200 GeV.

5. Discussions

5.2.2

101

Two-component Model

As mentioned in Section 5.1.2, low-pT spectra is described well by hydrodynamical calculations.
To extract freeze-out properties, a hydro-inspired model called Blast-wave was used. It is expected that such a hydrodynamic picture will break down at high pT where partonic cross sections
are small and the mean free path is long, meaning that hard partons cannot be brought to thermal equilibrium. In this region, initial hard scattering and jet fragmentation should dominate.
Since radial collective flow pushes particles into higher pT , soft hadrons would be visible at relatively high pT . We think that a two-component model including both soft and hard hadronproduction processes is a natural way to describe the hadron production at intermediate p T . Using the following two-component model, we try to separate soft and hard components for pionsand (anti)protons, and to explain the baryon enhancement.
Decomposition of pT Spectra
The soft and hard components are defined below:
Soft: The soft component uses the result from Blast-wave fit at low pT . The blast-wave model
describes thermal distributions with radial flow. Extrapolation of the thermal distributions
to higher pT is not unrealistic.
dN=A
pT dpT sof t

Z R
0rdrmT I0 (pT sinhρmT coshρ
)K1 (
)
Tf o
Tf o

(5.11)

Hard: The hard component is the p+p spectra normalized by the number of nucleon-nucleon
collisions Ncoll with pT -independent constant suppression factor. The p+p spectra includes
jet fragmentation following initial hard scattering. NLO pQCD or PYTHIA calculations
have still ambiguity of fragmentation function especially on baryon spectra. We use our
p+p spectra measured in PHENIX as hard component. We assume that each jet event ina single heavy ion collision is independent, thus it is proportional to Ncoll . The constantsuppression factor represents jet quenching effect. At high pT (> 5 GeV/c), π 0 and charged
hadrons RAA show similar suppression and flat pT dependence. A constant fractional energy
loss and a power-law spectrum imply that RAA = constant as observed.
dN
dN= RAA × Ncoll ×
pT dpT hardpT dpT p+p(5.12)

5. Discussions

102

These two components are added as a two-component description of the spectra.
dN
dN
dN
=
+
pT dpT sum pT dpT sof t pT dpT hard

(5.13)

To avoid double counting between soft and hard components, we introduce a cut-off pT = 2
GeV/c. If we consider feedback of energy lost by jet quenching, we should add the energy loss
back to the system. It is found to be about 2% of the total energy in central Au+Au collisions[56]. Hence we safely neglect this feedback effect.

Figures 5.16, 5.17 show comparisons of the two-component description with the data forpions and (anti)protons. The two-component model can successfully describe the spectra for√both particle species in Au+Au collisions at sN N = 200 GeV for all centralities. Apparently,
there is a large difference between the slopes of the soft and hard spectra. This indicates that
there is a rather narrow pT interval (1-2 GeV/c) in which the dominant hadron production
mechanism changes from boosted thermal emission to jets fragmentation with energy loss.

5. Discussions

Figure 5.16: pT spectra for pions in Au+Au collisions at

103√

sN N = 200 GeV with lines (blue: soft,

red: hard, magenta: soft+hard).

Figure 5.17: pT spectra for (anti)protons in Au+Au collisions at(blue: soft, red: hard, magenta: soft+hard).

√sN N = 200 GeV with lines

5. Discussions

104

The extracted RAA is plotted in Figure 5.18. The charged pion RAA is consistent with π 0 ’s one
as expected. The (anti)proton RAA is slightly higher than pion RAA . This suggests the differenceof energy loss in the medium between quarks and gluons. Since pions and (anti)protons reflect
different sensitivities to quarks and gluons in jet fragmentation process. We will be back to this
discussion in Section 5.2.4.

Figure 5.18: Extacted RAA from the 2-component model as a function of Npart in 200 GeV
Au+Au collisions.

Here we introduce one more assumption. If the constant suppression factor RAA is the same forpions and protons, how well the spectra are reproduced? In this case, the factor is taken fromπ 0 ’s RAA results (pT > 5 GeV/c). The same factor is applied for both pions and (anti)protons.
The comparisons are shown in Figures 5.19 and 5.20. The pion spectra is well reproduced again
as expected. On the other hand, the (anti)proton spectra show residual component around p T= 4 GeV/c. This residual indicates another component such as soft-hard recombination process
if our assumption is correct.

5. Discussions

Figure 5.19: pT spectra for pions in Au+Au collisions at

105√

sN N = 200 GeV with lines (blue: soft,

red: hard with fixed RAA , magenta: soft+hard).

Figure 5.20: pT spectra for (anti)protons in Au+Au collisions at(blue: soft, red: hard with fixed RAA , magenta: soft+hard).

√sN N = 200 GeV with lines

5. Discussions

106

Table 5.2: χ2 /n.d.f. (n.d.f = 12) for comparisons of 2-component model and data for different
centralities in 200 GeV Au+Au collisions. Only statistical error is used.
0-10% 10-30% 30-60% 60-80%
+

1.6

2.0

2.1

2.3

π−

1.6

1.7

2.1

2.3

p

1.8

2.7

3.0

2.8

p

1.9

2.9

3.0

2.6

π

Table 5.3: χ2 /n.d.f. (n.d.f = 12) for comparisons of 2-component model (RAA fixed with π 0 ) anddata for different centralities in 200 GeV Au+Au collisions. Only statistical error is used.
0-10% 10-30% 30-60% 60-80%
π+

1.6

2.0

2.1

2.3

π−

1.6

1.7

2.1

2.3

p

2.1

3.0

3.1

2.8

p

2.1

3.3

2.8

2.4

The χ2 /n.d.f. (n.d.f. = 12) are summarized in Tables 5.2.2 and 5.2.2. The case of (anti)protonwith fixed π 0 RAA is somewhat worse than others.

Fraction of Soft/Hard Components
Using our two-component model, we can estimate the fraction of soft and hard components inthe measured pT spectra as shown in Figures 5.2.2 and 5.22. Both soft and hard components
are necessary to reproduce the hadron spectra at intermediate pT (2-5 GeV/c). We can definea crossing point pT at which soft and hard yields are equal. The crossing point depends on
hadron species as shown in Figure 5.25. It moves toward high pT with higher mass because ofradial flow push. It also depends on collision centrality. It is higher in central with the same
reason. The soft component has a significant fraction at intermediate pT . At a given pT , we haverelatively-hard pions and relatively-soft (anti)protons.

5. Discussions

107

Figure 5.21: Fraction of soft (blue) and hard (red) components for π + (top) and π − (bottom)√
as a function of pT in Au+Au collisions at sN N = 200 GeV. The residual fraction is plotted inmagenta.

Figure 5.22: Fraction of soft (blue) and hard (red) components for protons (top) and antiprotons√(bottom) as a function of pT in Au+Au collisions at sN N = 200 GeV. The residual fraction isplotted in magenta.

5. Discussions

108

Figure 5.23: Fraction (RAA fixed with π 0 ’s one) of soft (blue) and hard (red) components for√π + (top) and π − (bottom) as a function of pT in Au+Au collisions at sN N = 200 GeV. The
residual fraction is plotted in magenta.

Figure 5.24: Fraction (RAA fixed with π 0 ’s one) of soft (blue) and hard (red) components for√
protons (top) and antiprotons (bottom) as a function of pT in Au+Au collisions at sN N = 200
GeV. The residual fraction is plotted in magenta.

5. Discussions

109

Figure 5.25: Crossing point as a function of Npart in Au+Au collisions at√

sN N = 200/62.4 GeV.

Soft/Hard Separation in Particle Ratios
Particle ratios at low pT are described by a statistical model (see Section 5.1.1). On the other
hand, at high pT , we expect particle ratios are determined by jet fragmentation which would
be universal. How about at intermediate pT ? We can describe particle ratios by using our
two-component model. Figure 5.26 shows p/π + (p/π − ) ratios with several estimated curves(blast-wave fitting, p+p experimental data, PYTHIA p+p calculation) for (anti)proton soft/hardfractions. The denominator is pions from the data.
pdata
psof t + phard
=
πdata
πdata

(5.14)

We find that radial flow effect, which is represented by blast-wave, could be one of the explanations of the baryon enhancement. Since there is some difference above 2 GeV/c, so othercontributions such as jet fragmentation are needed. Hard p/π ratios (data subtracted by blastwave) are also plotted in the same figure. Figure 5.27 shows p/p ratio as a function of p T . As
in p/π ratio, hard p/p is estimated. The hard ratios (p/π, p/p) are consistent with the values in
p+p collisions and PYTHIA calculations.

5. Discussions

110

Figure 5.26: p/π + (top) and p/π − (bottom) ratios as a function of pT in Au+Au collisions√
at sN N = 200 GeV. Blue points are the data. Red points are the estimated ratio (hardcomponent). Black line: blast-wave p/π ratios, black dashed line: blast-wave p divided by πdata, magenta dashed line: the scaled p+p, cyan dashed line: PYTHIA (see text).

Figure 5.27: p̄/p ratio as a function of pT in Au+Au collisions at√

sN N = 200 GeV. Blue points

are the data. Red points are the estimated ratio (hard component) (see text).

5. Discussions

111

Soft/Hard Separation in Particle Yield
Figures 5.28 and 5.29 show particle yield dN/dy (soft/hard/sum) divided by 0.5 Npart as afunction of Npart for each lower-side pT cutoff value. Both soft and hard yields are not scaledwith Npart , i.e. not showing flat Npart dependence. Soft yields monotonically increase with Npart .
Hard yields also increase with Npart up to mid-central, but decrease in most central. This decreaseis due to jet suppression which is more significant in central collisions. The monotonic increase ofsummed dN/dy at low pT with Npart is caused just by soft component, not by inclusion of hardcomponent. In right panels (pT >4 GeV/c), the main contribution for pions is hard component
suffered by jet quenching effect, while (anti)protons still show significant soft component in its
yield. As we know, it is due to radial flow effect. The larger value of (anti)proton RAA around

00

Sum
Soft
T
0.015 (Filled: positive,
Open: negative) Hard
Au+Au at sNN = 200 GeV
Pion (p > 2 GeV/c)

0.01

100

150

200

250

300

350

00

400

Npart

Sum
Soft
T
(Filled: positive, Open: negative) Hard
Au+Au at sNN = 200 GeV
Pion (p > 4 GeV/c)

0.2

0.1

0.005
50

0.3

×10

part

part

1

0.02

dN/dy / (N

/2)

Sum
Soft
T
2 (Filled: positive, Open: negative) Hard
Au+Au at sNN = 200 GeV
Pion (p > 0 GeV/c)

/2)

-3

3

dN/dy / (NdN/dy / (N

part

/2)

pT = 4 GeV/c simply comes from radial flow, not absence of jet quenching (see Section 4.5).

50

100

150

200

250

300

350

00

400

Npart

50

100

150

200

250

300

350

400

Npart

00

/2)
part

Au+Au at sNN = 200 GeV
Proton (p > 2 GeV/c)dN/dy / (N

/2)

0.1

0.02

Sum
Soft
0.015 (Filled: positive, Open: negative) Hard

partdN/dy / (N

0.2

Sum
Soft
T
(Filled: positive, Open: negative) Hard
Au+Au at sNN = 200 GeV
Proton (p > 0 GeV/c)dN/dy / (N

0.3

part

/2)

Figure 5.28: Particle yield dN/dy divided by 0.5Npart for charged pions as a function of Npart in√
Au+Au collisions at sN N = 200 GeV (pT cut: 0, 2, 4 GeV/c from left to right).

T

0.01

100

150

200

250

300

350

400

Npart

00

-3

×10

Sum
Soft
(Filled:positive,Open:negative)
Hard
0.1
Au+Au at sNN = 200 GeV
Proton (p > 4 GeV/c)
T

0.05

0.005
50

0.15

50

100

150

200

250

300

350

400

Npart

00

50

100

150

200

250

300

350

400

Npart

Figure 5.29: Particle yield dN/dy divided by 0.5Npart for (anti)protons as a function of Npart in√
Au+Au collisions at sN N = 200 GeV (pT cut: 0, 2, 4 GeV/c from left to right).

5. Discussions

112

Soft/Hard Separation in Elliptic Flow
Figures 5.30 and 5.31 show v2 (soft/hard/sum) as a function of pT for different centralities. v2
is defined as the second Fourier coefficient of particle emission in azimuthal direction.
dN= N0 1 + 2v2 cos(2(φ − ΦRP ))dφ(5.15)

where φ is the azimuthal angle of emitted particles, ΦRP is the azimuthal angle of the reaction
plane. We think that measured v2 is the average of soft v2 and hard v2 with the corresponding
fractions to the total yield.
v2sum = f sof t v2sof t + f hard v2hard(5.16)

Soft v2 (v2sof t ) is a purely hydrodynamic contribution, which is now described by blast-wave
parameterization [57].
v2 =

R 2π
0

dφ cos(2φ)I2 ( pTTsinhρ)K1 ( mTTcoshρ
)
fo
fo
R 2π
)K1 ( mTTcoshρ)
dφI0 ( pTTsinhρ
0fofo(5.17)

Hard v2 (v2hard ) is caused by the difference of jet quenching effect between in-plane and outof-plane (azimuthal dependence of the partonic energy loss). Since we know the fractions ofsoft and hard components (f sof t , f hard ) (see Figure and 5.22), we can extract v2hard from theseinformation. The estimated v2hard shows a finite value at high pT as expected.

5. Discussions

113

Figure 5.30: v2 (blue) for π +/− (filled), π 0 (open) as a function of pT in Au+Au collisions at√
sN N = 200 GeV [58, 59]. The curves are blast-wave fitting results. The red points are estimatedhard v2 .

Figure 5.31: v2 (blue) for p, p as a function of pT in Au+Au collisions at√

sN N = 200 GeV [59].

The curves are blast-wave fitting results. The red points are estimated hard v2 .

5. Discussions

114

Summary of Two-component Model
Using a simple two-component model including soft and hard hadron components, we can reproduce the measured pT spectra for pions and protons, and identify crossover region from soft tohard hadron production at intermediate pT . We estimate the relative fraction of soft and hardcomponents. Here soft component is thermal emission with collective radial flow. Hard component is jet fragmentation with quenching effect. Soft and hard components become of equal sizein this pT region (2-4 GeV/c). The crossing point depends on collision centrality. It is shiftedto higher pT in more central collisions due to radial flow effect. In terms of soft production,
radial flow effect is significant in central Au+Au collisions compared to smaller systems (seeSection 5.1.2). This effect pushes heavier particles like protons to higher pT . The contributionof soft component is comparable to that of hard component even at high pT (. 5 GeV/c). We
think that the baryon enhancement at intermediate pT can be attributed to radial flow effect.

5.2.3

Quark Recombination Picture

Quark recombination was proposed as one of hadron production mechanisms. The baryon enhancement and the constituent quark number scaling of v2 at intermediate pT are explained byquark recombination models. Since the quark number scaling of v2 is very indicative, quark recombination process is thought to be a possible hadron production mechanism. Recombinationof thermal quarks is a usual way which explained by thermal models. In addition to this process,there is another recombination process where one of the recombining quarks originates from jet
fragmentation, and the other quark is from thermal source. Hadrons from such recombination
are not accounted for in our two-component model.
Theoretical model calculations for p/π ratios [28] are compared to the experimental data
in Figure 5.32. These models are similar in that they subscribe to a recombination processof quarks, but they have different implementations. Quark recombination models qualitatively
describe the observed ratios at intermediate pT , but in general underpredict the results at high
pT .

115
Ratio

5. Discussions
2
1.8
1.6
1.4
1.2

Au+Au atsNN = 200 GeV (0 - 10 %)proton/ π+

PHENIX Preliminary

proton/ π0
Duke
OregonTAMU w/ shower
TAMU no shower

1
0.8
0.6
0.4
0.2

00

1

2

3

4

5
6
7
p [GeV/c]T

Figure 5.32: p/π + ratio in Au+Au collisions at√

sN N = 200 GeV. Curves show some model

predictions [28].

Separation of radial flow between quark and hadronic phases is an important point. In a
simple recombination picture, hadronic and partonic radial flow effects cannot be separated.
The blast-wave parameterization of radial flow also works for partonic phase. The following
equations are a blast-wave parameterization for mesons and baryons [60].
dNM∝
mT dmTZ R

pT sinhρ)rdrmT I0 (
Tf o
0
Z
q
q
coshρ
× Dxi |φM (x1 , x2 )|2 K1 ([ m2 + x21 p2T + m2 + x22 p2T ])Tf o
Z R
pT sinhρdNB∝
rdrmT I0 ()
mT dmT
Tf o
0
Z
q
q
q
coshρ
2
2 2
2 2
2
2
× Dxi |φB (x1 , x2 , x3 )| K1 ([ m + x1 pT + m + x2 pT + m2 + x23 p2T ])Tf o(5.18)(5.19)

Indeed, if we take xi (momentum fraction of quark i ) with equal weight, these equations are
consistent with Equation 5.2.
As mentioned in Section 5.1.2, there is the difference of temperatures of chemical and kinetic
freeze-outs. This is an evidence for further expansion at hadronic phase. Even if quark phase iscreated before hadronization, final-state hadronic scattering should be taken into account.

5. Discussions

5.2.4

116

Jet Fragmentation and Jet Quenching

At high pT , even if partons propagating through the medium have a large energy loss, the leading parton is expected to punch out of the medium before fragmentation. Thus, we expect: (1)same suppression factor for different hadrons, because a parton losing energy does not know
the type of hadrons which will be eventually created, and (2) particle ratios of hadrons abovesome pT threshold to be universal. (Fragmentation functions are independent of the process. If
jet fragmentation occurs in the medium, there may be some modification of the fragmentation
functions.) When we compare hard component to expectation from p+p spectra or pQCD calculations, soft component such as hydrodynamic contribution should be subtracted as performed
in Section 5.2.2.
A fundamental question for the jet quenching mechanism is whether there is a difference
between gluon jets and quark jets. Since gluons in QCD have stronger interaction than quarks,
larger energy loss of gluon jets is expected than that of quark jets. Identified hadrons at high p Tprovide a sensitivity to the difference between quark and gluon fragmentation. Proton and pion
production at high pT is expected to have significant contributions from quark fragmentation
while antiprotons are mostly from gluon fragmentation [61]. Therefore, p̄/p and p̄/π ratios are
sensitive to the possible color charge dependence of energy loss. Figure 5.34 shows the fraction ofquark and gluon jets in p+p jet events. This is estimated by PYTHIA (LO-pQCD based event
generator, version 6) calculation [62]. We notice that quark jet is dominant at high p T thangluon jet. At 62.4 GeV, the quark-jet dominant region is lower than at 200 GeV. By changing√
collision energy sN N , we expect to see the difference of quark and gluon jet contribution at thesame pT .

Figure 5.33: Quark and gluon jet contributions for pions as a function of pT in PYTHIA p+p√
jet events at sN N = 200 GeV (left) and 62.4 GeV (right).

5. Discussions

117

Figure 5.34: Quark and gluon jet contributions for (anti)protons as a function of pT in PYTHIA√
p+p jet events at sN N = 200 GeV (left) and 62.4 GeV (right).

p/π + and p̄/π − ratios from PYTHIA are almost constant at high pT (see Figures 5.35 and√5.36). As shown in Figure 5.13, p/π (p̄/π) ratios in central Au+Au/Cu+Cu collisions at sN N =200 GeV approach the values in p+p collisions at high pT & 5 GeV/c. And RCP shows similar
suppression for pions and (anti)protons (see Section 4.5.2), though they have different sensitivities
to quark and gluon jets. The results indicate that hard-scattered partons (quarks and guluons)
have similar energy loss when traversing the nuclear medium, and parton fragmentation function
does not change.

Figure 5.35: p/π + ratio as a function of pT in PYTHIA p+p collisions at√

sN N = 200 GeV (left)

and 62.4 GeV (right).

In quark fragmentation, a leading hadron is more likely to be a particle rather than an antiparticle, and there is no such preference in gluon jet. A decrease of p/p ratio with pT would thenindicate a significant quark jet contribution to the baryon production. A pQCD-based calculationshows a significant effect from energy loss on p̄/p ratio due to the large energy loss of gluons in
the medium [61]. In contrast, the measured ratio does not show such a clear decreasing trend(see Figure 5.37 (left)). The p̄/p ratios show almost flat pT dependence and are independent of5. Discussions

118

Figure 5.36: p̄/π − ratio as a function of pT in PYTHIA p+p collisions at√

sN N = 200 GeV (left)

and 62.4 GeV (right).

centrality at√

sN N = 200 GeV (see Section 4.4.3). The soft component would lead to a lowerp̄/p ratio for peripheral Au+Au relative to central Au+Au since radial flow strength is lower in

Ratio

peripheral. However such a centrality dependence is not observed.

1.4
1.2

Au+Au 200 GeV (MB)Au+Au without energy loss
Au+Au with energy loss

1
0.8
0.6
0.4
0.2
00

p/p (ACC)
p/p (TOF)
p/p (Run2)
1

2

PHENIX Preliminary
3

4

5

6

7
8
p [GeV/c]T

Figure 5.37: Left: p/p ratio as a function of pT in minimum bias Au+Au collisions at√

sN N =

200 GeV. Curves are the predictions from a jet quenching model [61]. Right: p/p ratio as a√function of pT in Au+Au collisions at sN N = 62.4 GeV.

The decreasing trend in p/p ratio is expected to be observed at√

sN N = 62.4 GeV. It is

known from lower beam energies, where quark fragmentation is more dominant, that the p̄/π
and p̄/p ratios are very small [63]. As shown in Figure 5.38 (data) and 5.39 (PYTHIA), the flatp̄/p ratio of ∼ 0.6 in 62.4 GeV p+p collisions is likely dominated by gluon fragmentation. The

62.4 GeV Au+Au data also shows flat pT dependence in p/p (see Figure 5.37 (right)). If weobtain enough statistics, we will confirm whether particle ratios are the same between Au+Au
and p+p at high pT .

119

Ratio

5. Discussions

2
1.8
1.6

p+p at s = 62.4 GeV

1.4

p/p ratio

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
p [GeV/c]T

Figure 5.38: Left: p/p ratio as a function of pT in minimum bias p+p collisions at√

s = 200

GeV. Blue band is systematic errors. Right: p/p ratio as a function of pT in minimum bias p+p√
collisions at s = 62.4 GeV.

Figure 5.39: p̄/p ratio as a function of pT in PYTHIA p+p collisions atand 62.4 GeV (right).

√

sN N = 200 GeV (left)

Chapter 6
Conclusions
We have performed a systematic study of proton and antiproton spectra in Au+Au, Cu+Cu,√
p+p collisions at sN N = 62.4/200 GeV. The data set taken in the PHENIX experiment allows
us to study energy dependence and system size dependence of the baryon enhancement in relativistic heavy ion collisions. We present identified charged hadron pT spectra (π/K/p and theirantiparticles), particle ratios, nuclear modification factors, chemical/kinetic freeze-out properties and their scaling properties between different collision systems. The spectra are measured
at mid-rapidity (|η| < 0.35) over the range of 0.5 < pT < 6 GeV/c with particle identification by
time-of-flight and threshold-type Cherenkov light emission methods. The pT range of charged
hadron identification has been extended by the high statistics data. Also the particle identification capability at high pT has been enhanced by introducing an Aerogel Cherenkov counterin PHENIX. The identified hadron production can be studied up to 5 GeV/c for charged pions,and 7 GeV/c for (anti)protons.
In all collision systems (Au+Au, Cu+Cu), we confirm the baryon enhancement at intermediate pT (2-5 GeV/c). In terms of binary collision scaling, protons and antiprotons are enhanced,
while pions are suppressed at intermediate pT . We observe a turnover of p/π ratios at pT = 2-3
GeV/c, indicating a transition from soft to hard hadron production. We find that the baryon enhancement and freeze-out properties (freeze-out temperature, transverse flow velocity) are scaledwith the number of participant nucleons Npart , which is corresponding to the system volume, be√tween Au+Au and Cu+Cu collisions at the same collision energy sN N = 200/62.4 GeV eventhough the overlapped collision zone has a different shape. The system volume is a control parameter. Comparing to the 200 GeV data, the 62.4 GeV data shows a slightly larger proton
contribution at intermediate pT , while there is a less antiproton contribution. At lower energy
62.4 GeV, proton production seems to be more affected by baryon number transport process.
Therefore antiproton would be a good indicator of the baryon enhancement. Instead of N part
scaling, transverse energy density dET /dη scaling of p/π − is also workable between different
collision energies.

6. Conclusions

121

Using a simple two-component model including soft and hard hadron components, we canreproduce the measured pT spectra for pions and protons, and identify crossover region fromsoft to hard hadron production at intermediate pT . We estimate the relative fraction of soft andhard components. Here soft component is thermal emission with collective radial flow. Hardcomponent is jet fragmentation with quenching effect. Soft and hard components become ofequal size in this pT region (2-4 GeV/c). The crossing point depends on collision centrality. It is
shifted to higher pT in more central collisions due to radial flow effect. In terms of soft production,
radial flow effect is significant in central Au+Au collisions compared to smaller systems. Thiseffect pushes heavier particles like protons to higher pT . The contribution of soft component
is comparable to that of hard component even at high pT (. 5 GeV/c). We think that thebaryon enhancement at intermediate pT can be attributed to radial flow effect. This is thought
to be one of unique properties of hadron production in relativistic heavy ion collisions. The nextquestion is what the relation of hadronic and partonic radial flow is. The difference of freeze-out
temperatures between chemical and kinetic freeze-out’s shows a finite lifetime of hadronic stage.
We also discuss the relation between this radial flow picture and quark recombination picture. In a simple recombination picture, hadronic and partonic radial flow effects cannot be
separated. Since the constituent quark number scaling of elliptic flow v2 is very indicative, quark
recombination process is thought to be a possible hadron production mechanism.
At high pT & 5 GeV/c, p/π (p̄/π) ratios in central Au+Au collisions approach the values
in p+p collisions. And RCP shows similar suppression for pions and (anti)protons, though they
have different sensitivities to quark and gluon jets. The results indicate that hard-scatteredpartons (quarks and guluons) have similar energy loss when traversing the nuclear medium, andparton fragmentation function does not change.

Appendix A
Kinematic Variables
Here, we introduce kinematic variables used in the thesis. For a particle which has the momentum
p = (px , py , pz ) and mass m, we define the following variables. The beam line is taken as z-axis.
Transverse momentum pT and transverse mass mT and total energy E are:qqppT = p2x + p2y ,mT = p2T + m2 ,E = p2 + m2 .

Rapidity y is:y=

1 E + pzln.
2 E − pz

(A.1)

(A.2)

The rapidity y is invariant under Lorentz transformation. In the relativistic limit (p  m),pseudo-rapidity η is equivalent to y:θη = − ln(tan( )) ∼ y.
2

(A.3)

Differential particle yield is described with Lorentz invariant yield:
E

1
d2 N
1 d2 N
d3 N
=
E
=
dp3
2πpT dpT dpz
2πpT dpT dy(A.4)

where N is the number of counted particles per event. Particle yield dN/dy is the integrated one
over pT .

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