Nuclear modification of electron yields
from charm and bottom hadrons in√
Au+Au collisions at sN N = 200 GeV

Hidemitsu Asano

Depertment of Physics, Kyoto University
A dissertation submitted in partial fulfillment of therequirements for the degree of Doctor of Science

Janually, 2015

Contents
List of Figures

iv

List of Tablesix

Acronyms and Abbreviationsx

Nomenclaturesxi

Abstracti

1 Overview

1

2 Quark Gluon Plasma and Heavy Ion Collision
2.1 Quark Gluon Plasma . . . . . . . . . . . . . . . . . . . . . . .
2.2 High energy Heavy Ion Collision experiment . . . . . . . . . .
2.2.1 Nuclear stopping power . . . . . . . . . . . . . . . . . .
2.2.2 Picture of space-time evolution . . . . . . . . . . . . .
2.2.3 Collision Geometry . . . . . . . . . . . . . . . . . . . .
2.2.4 Nuclear Modification Factor: RAA . . . . . . . . . . . .
2.3 States of created matter at RHIC . . . . . . . . . . . . . . . .
2.3.1 Jet quenching and energy loss . . . . . . . . . . . . . .
2.3.2 Collectivity of the QGP . . . . . . . . . . . . . . . . .
2.3.3 Temperature of the created matter . . . . . . . . . . .

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3 Heavy quark as a probe of the QGP
3.1 Heavy flavor hadron production . . . . . . . . . . . . . . . . .
3.2 Decay of charm and bottom hadrons . . . . . . . . . . . . . .
3.3 Heavy flavor hadron measurement in RHIC and the LHC . . .
3.3.1 Overview of heavy flavor measurement . . . . . . . . .
3.3.2 Single electron measurements at PHENIX . . . . . . .
3.3.3 Electron-hadron correlation . . . . . . . . . . . . . . .
3.3.4 Direct reconstruction measurement . . . . . . . . . . .

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3.3.5 Non-prompt J/ψ measurement . . . . . . . . . . . . .
3.3.6 Separating charm and bottom . . . . . . . . . . . . . .
Energy loss of heavy quark in the QGP . . . . . . . . . . . . .
3.4.1 Dead Cone effect . . . . . . . . . . . . . . . . . . . . .
3.4.2 Recent theoritical development . . . . . . . . . . . . .
Motivation of separating charm and bottom . . . . . . . . . .

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4 Experiment
4.1 Relativistic Heavy Ion Collider (RHIC) . . . . . . . . . . . . .
4.2 PHENIX experiment . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Detector Overview . . . . . . . . . . . . . . . . . . . .
4.2.2 Beam-Beam Counter and trigger . . . . . . . . . . . .
4.2.3 Central arms . . . . . . . . . . . . . . . . . . . . . . .
4.2.4 Drift Chamber . . . . . . . . . . . . . . . . . . . . . .
4.2.5 Pad Chamber . . . . . . . . . . . . . . . . . . . . . . .
4.2.6 Ring Imaging Čherenkov Detector . . . . . . . . . . . .
4.2.7 Electromagnetic Calorimeter . . . . . . . . . . . . . . .
4.3 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Silicon Vertex Tracker Upgrade . . . . . . . . . . . . . . . . .

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5 Analysis
5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Track reconstruction in Central arms . . . . . . . . . . . . . .
5.3 Electron identification . . . . . . . . . . . . . . . . . . . . . .
5.4 Event reconstruction in VTX . . . . . . . . . . . . . . . . . .
5.4.1 VTX alignment . . . . . . . . . . . . . . . . . . . . . .
5.4.2 VTX hit reconstruction . . . . . . . . . . . . . . . . . .
5.4.3 The primary vertex reconstruction . . . . . . . . . . .
5.4.4 Association of a central arm track with VTX . . . . . .
5.5 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.1 z-vertex selection . . . . . . . . . . . . . . . . . . . . .
5.5.2 Data quality assurance . . . . . . . . . . . . . . . . . .
5.6 DCA measurement with the VTX . . . . . . . . . . . . . . . .
5.6.1 DCAT and DCAL . . . . . . . . . . . . . . . . . . . . .
5.6.2 DCA distribution of hadron tracks . . . . . . . . . . .
5.7 Electron DCA distribution and Background Components . . .
5.7.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.2 Mis-identified hadron . . . . . . . . . . . . . . . . . . .
5.7.3 High-multiplicity background . . . . . . . . . . . . . .
5.7.4 Photonic electrons and conversion veto cut . . . . . . .
5.7.5 Ke3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3.4

3.5

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5.7.6 Quarkonia . . . . . . . . . . . . . . . . . . . . . . . . . 93
Normalization of electron background components . . . . . . . 94
Unfolding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.9.1 Overwiew . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.9.2 Unfolding method . . . . . . . . . . . . . . . . . . . . . 98
5.9.3 Modeling the likelihood function . . . . . . . . . . . . . 99
5.9.4 Decay model and matrix normalization . . . . . . . . . 100
5.9.5 Regularization/prior . . . . . . . . . . . . . . . . . . . 105
5.9.6 Parent charm and bottom hadron yield and their statistical uncertainty . . . . . . . . . . . . . . . . . . . . 106
5.10 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . 108
5.8
5.9

6 Results
112
6.1 Invariant yield of charm and bottom hadron . . . . . . . . . . 112
6.2 Bottom electron fraction . . . . . . . . . . . . . . . . . . . . . 113
6.3 RAA of charm electrons and bottom electrons . . . . . . . . . 114
7 Discussion
118
7.1 Re-folded comparisons to data . . . . . . . . . . . . . . . . . . 118
7.2 Comparison with STAR D0 yield measurement . . . . . . . . . 122
7.3 Comparison with theoretical models . . . . . . . . . . . . . . . 124
8 Conclusion

128

Acknowledgements

130

Appendix A Detailed Normalization of electron background components
132
A.1 Photonic electrons simulation . . . . . . . . . . . . . . . . . . 132
A.2 Fraction of nonphotonic electrons FNP . . . . . . . . . . . . . 137
A.3 Normalization of Dalitz and conversion components . . . . . . 140
A.4 Normalization of Ke3 and quarkonia components . . . . . . . . 142
Appendix B Coordinate offset and coordinate offset calibration143
Bibliography

145

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List of Figures
Summary of measurements of αs as a function of the momentum transfer Q. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Lattice QCD results from Hot QCD collaboration [1] . . . . .
2.3 The net-proton (number of protons − number of anti-protons)
rapidity distribution at AGS, SPS and RHIC measured by
BRAHMS. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Time evolution of heavy ion collision from initial nucleusnucleus collision to hadronic freeze out . . . . . . . . . . . . .
2.5 Parton distribution function times Bjorken-x as a function of
Bjorken-x obtained in NNLO NNPDF2.3 global analysis [2, 3]
2.6 Energy density as a function of the number of participants Np
from PHENIX data [4]. . . . . . . . . . . . . . . . . . . . . . .
2.7 pT spectrum of inclusive charged hadrons and explanationfrom fragmentation and recombination process. . . . . . . . .
2.8 Geometry of a collision between nucleus A and B. . . . . . . .
2.9 An illustrated example of the relationship of the impact parameter (b), Npart , overlap area of colliding nucleus, the multiplicity distribution and centrality taken from [5]. . . . . . . .
2.10 Number of participants (Npart ) and Number of binary collisions (Ncoll ) for Au+Au and Cu+Cu collisions from GlauberMonte Carlo calculation [5]. . . . . . . . . . . . . . . . . . . .
2.11 Nuclear modification factor, RAA , for π 0 in central (0-10%)
and peripheral (80-92%) Au+Au collisions and minimum-bias
d+Au collisions at mid-rapidity. . . . . . . . . . . . . . . . . .
2.12 Illustration of the collision geometry in a non-central heavy
ion collision. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.13 Illustration of pressure gradient originated from spatial asymmetry of reaction zone. . . . . . . . . . . . . . . . . . . . . .
2.14 STAR measurement of v2 with hydrodynamical predictions for√minimum bias Au+Au at sN N = 200 GeV from [6] . . . . . .
2.1

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2.15 Invariant cross section (p+p) and invariant yield (Au+Au) of
direct photons as a function of pT . . . . . . . . . . . . . . . . 22
2.16 Electron pair mass distribution for p+p and Au+Au (Minimum Bias). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1
3.2
3.3

3.4
3.5

3.6

3.7
3.8

3.9

4.1

4.2
4.3
4.4
4.5

Schematic view of time evolution of heavy quarks. . . . . . .
Charm and bottom quark production cross section as a function of center of mass energy in p+p or p̄ + p collisions. . . . .
Electron from heavy flavor yield (0.8 < pT < 4.0 GeV/c ) mea√
sured in Au+Au collision at sN N = 200 GeV scaled by the
number of binary collisions (Ncoll ). The yield in p+p collisions
is also shown. . . . . . . . . . . . . . . . . . . . . . . . . . . .
PHENIX measurement of RAA and v2 of electron from heavy
flavor from 2004/2005 data. . . . . . . . . . . . . . . . . . . .
The nuclear modification factors for heavy flavor electron at
midrapidity in central d+Au, Cu+Cu, and Au+Au collisions√
at sN N = 200 GeV with PHENIX. . . . . . . . . . . . . . .
The azimuthal angle between heavy flavor electrons and hadrons
measured with STAR in p+p collisions and relative contributions of bottom decays to the total yield of electrons fromheavy flavor hadron decays as functions of the electron pT . . .
Centrality dependence of the D0 pT differential invariant yieldwith STAR in Au+Au collisions. . . . . . . . . . . . . . . . .
The ratio of gluon spectra off charm and light quarks for transverse quark momenta p⊥ = 10 GeV/c and p⊥ = 100 GeV/c
in QGP matter from Ref.[7]. . . . . . . . . . . . . . . . . . .
The differential cross section per nucleon pair of charm andbottom quarks calculated to NLO in QCD compared to single
electron distributions calculated with the fragmentation anddecay scheme of Ref.[8]. . . . . . . . . . . . . . . . . . . . . .
Au ion pass through three accelerators (Tandem Van de Graaff,
AGS Booster, and AGS) and four charge-stripping stations to
prepare the fully stripped Au ions for injection to the RHIC
ring [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A schematic view of the PHENIX detector configuration forthe 2011 run. . . . . . . . . . . . . . . . . . . . . . . . . . . .
PHENIX global coordinate system. . . . . . . . . . . . . . . .
A picture of Beam-Beam counters . . . . . . . . . . . . . . . .
A schematic view of Drift Chameber . . . . . . . . . . . . . .

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4.6

The layout of DCH wire position within one sector and inside the anode plane and top view of the DCH stereo wire
orientations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.7 The pad and pixel geometry in the pad chamber. . . . . . . . 54
4.8 A cutaway view of one arm of the RICH detector [10]. . . . . . 55
4.9 Top view of the RICH in the PHENIX east arm [11]. . . . . . 55
4.10 Schematic view of a Pb-scintillator (PbCc) module . . . . . . 56
4.11 Schematic view of a Pb-glass (PbGl) module . . . . . . . . . . 57
4.12 A schematic diagram of the PHENIX Data Acquisition system. 58
4.13 A picture of the VTX detector and a schematic view fo the
VTX detector . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.14 schematic view of a pixel sensor . . . . . . . . . . . . . . . . . 62
4.15 A schematic of the circuitry within one pixel cell in the ALICE1LHCb sensor-readout chip. . . . . . . . . . . . . . . . . . 63
4.16 A picture of a pixel ladder and schematic view of a pixel ladder 63
4.17 A picture of a stripixel detector and Schematic view of a stripixel 64
4.18 X strips and U strips . . . . . . . . . . . . . . . . . . . . . . . 64
4.19 Conceptual schematic of a single SVX4 channel circuit. . . . . 65
5.1

Charged particle momentum vector reconstruction using DCH
hit information [12]. . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2 Matching variable between the reconstructed track momentum(p) and the energy measured in the EMCal (E): dep = (E/p−µE/p ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.3 The distributions for the difference in the primary vertex calculated from by the East and West VTX barrels (East - West)in x, y and z-axis . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.4 An illustration of a tracking with the VTX in x-y plane. . . . 75
5.5 An illustration of a tracking with the VTX in r-z plane. . . . 75
5.6 Illustration of the definition of DCAT ≡ L - R in the transverse
plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.7 Distance of closest approach distributions for all VTX-associated√tracks in Au+Au at sN N = 200 GeV collisions . . . . . . . . 80
5.8 The DCAT resolution as a function of pT for all tracks in MB
events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.9 Simulated primary electron DCAT and DCAL distribution before and after embedding in real Au+Au data. . . . . . . . . . 85
5.10 Distribution of correlated hits near electron tracks for 1 <pT < 2 GeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.11 charge x ∆φ vs pT for B0(top-left), B1(top-right), B2(bottomleft), B3(bottom-right). . . . . . . . . . . . . . . . . . . . . . 89vi

5.12 The survival rate as a function of electron pT (peT ) for electrons
from photon conversion, Dalitz decay of π 0 , η, electron fromdirect photon and heavy flavor decay electrons. . . . . . . . . 92√
5.13 DCAT distributions for electrons in MB Au+Au at sN N = 200 GeV
that pass the reconstruction and conversion veto cut in theindicated five electron-pT selections. Also shown are the normalized contributions for the various background components
detailed in Section 5.7. . . . . . . . . . . . . . . . . . . . . . 96
5.14 The decay matrix encoding the probability for charmed hadrons
decaying to electrons within |η| < 0.35 as a function of bothelectron pT (peT ) and charm hadron pT (pcT ) and an example
decay matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.15 The probability for (a) charm and (b) bottom hadrons in agiven range of hadron pT (pcT and pbT for charm and bottom
hadrons respectively) to decay to electrons at mid-rapidity as
a function of electron pT (peT ). . . . . . . . . . . . . . . . . . 104
5.16 The joint probability distributions for the vector of hadronyields, θ, showing the 2-D correlations between parameters.
The diagonal plots show the marginalized probability distributions for each hadron pT bin. . . . . . . . . . . . . . . . . . 107
5.17 The relative contributions from the different components tothe uncertainty on the fraction of electrons from bottom hadron
decays as a function of pT . . . . . . . . . . . . . . . . . . . . 110
6.1
6.2

6.3

6.4

7.1

Charm (hc ) and bottom (hb ) hadron invariant yield as a function of pT , integrated over all rapidities. . . . . . . . . . . . . 113
The fraction of heavy flavor electrons from bottom hadron
decays as a function of pT from this work and from fonll
p+p calculations [8]. . . . . . . . . . . . . . . . . . . . . . . . 114
bottom electron fraction as a functionof pT compared to mea√
surements in p+p collisions at s = 200 GeV from PHENIX [13]and STAR [14]. Also shown are the central values for fonll√[8] for p+p collisions at sN N = 200 GeV. . . . . . . . . . . . 115(a) The RAA for c → e, b → e and combined heavy flavor [11]b→ec→eas a function of peT . (b) The ratio RAA/RAA
as a function ofepT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
The heavy flavor electron invariant yield as a function of pTfrom measured data [11] compared to electrons from the refolded charm and bottom hadron yields. . . . . . . . . . . . . 120

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7.2

7.3

7.4

The DCAT distribution for measured electrons compared tothe decomposed DCAT distributions for background components, electrons from charm decays, and electrons from bottom
decays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
The invariant yield of D0 mesons as a function of pT for |y| < 1
inferred from the unfolded yield of charm hadrons integrated
over all rapidity compared to measurements from STAR [15]. 123
Bottom electron fraction as a function of pT compared to aseries of model predictions detailed in the text. . . . . . . . . . 124

A.1 Electrons’ vertex position in radial direction in π 0 simulation
before the application of conversion veto. . . . . . . . . . . . 134
A.2 The ratio of conversion electrons to electrons from Dalitz decay
from π 0 simulation as a function of reconstructed electron pT . 135
A.3 Diagram of Dalitz decay of η meson. . . . . . . . . . . . . . . 137
A.4 The fraction of π 0 , η, and direct photon Dalitz decay electrons
in all Dalitz electrons as a function of electron pT (peT ). . . . . 139
A.5 The fraction of nonphotonic electrons to inclusive electrons as
a function of electron pT (peT ). . . . . . . . . . . . . . . . . . 140
A.6 The fraction of π 0 , η, and direct photon electrons in all photonic electrons as a function of electron pT (peT ). . . . . . . . 141
B.1 (Left) the vtx local coordinate system for the WEST VTX andthe EAST VTX. (Right) the schematic view when the VTX
is retracted. . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
B.2 Parameters of DC hit information and beam center positionin the DCH coordinate system. . . . . . . . . . . . . . . . . . 144

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List of Tables
3.1

3.2
4.1
4.3

4.4
7.1

Decay modes, Branching ratios (B.R.), decay momentum∗ (p)and life times for main charm hadrons from PDG [3]. Charge
conjugates are abbreviated. . . . . . . . . . . . . . . . . . . . 29
The same as table 3.1 but for bottom hadrons from PDG [3].
Charge conjugates are abbreviated. . . . . . . . . . . . . . . . 30
Summary of data sets with collision species, collision energy,
and integrated luminosity delivered to PHENIX. . . . . . . . 47
A summary of the VTX detector. For each layer (B0 to B3),
the detector type, read out chip, the central radius (r), ladder
length (l), sensor thickness (t), sensor active area (∆φ × ∆z),
the number of sensors per ladder (NS ), the number of ladders (NL ), pixel/strip size in φ (∆φ) and z (∆z), the numberof read-out channels (Nch ), and the average radiation length
including the support and on-board electronics (X0 ) are given. 61
Occupancy of the each VTX layer for central Au+Au collisions
at 200 GeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
The log likelihood values (LL) summed over each DCAT distribution and for the comparison to the heavy flavor electron
invariant yield. . . . . . . . . . . . . . . . . . . . . . . . . . . 119ix

Acronyms and Abbreviations
Acronyms and abbreviations used in this dissertation:
AGS Alternating Gradient Synchrotron.
ALICE A Large Ion Collider Experiment (at the LHC).
BBC Beam-Beam Counters (subsystem of PHENIX).
BNL Brookhaven National Laboratory.
BRAHMS Broad RAnge Hadron Magnetic Spectrometers (experiment at
RHIC).
CMS Compact Muon Solenoid (experiment at the LHC).
DCA Distance of Closest Approach.
DCH Drift Chamber (subsystem of PHENIX).
EMCal Electromagnetic Calorimeter (subsystem of PHENIX).
LHC Large Hadron Collider.
LHCb Large Hadron Collider beauty experiment.
MB Minimum Bias.
PC Pad Chamber (subsystem of PHENIX).
PDF Parton Distribution Function.
PHENIX Pioneering High Energy Nuclear Interaction eXperiment (at RHIC).
pQCD pertavative Quantum Chromodynamics.
QCD Quantum Chromodynamics.
QGP Quark Gluon Plasma.
RHIC Relativistic Heavy Ion Collider.
RICH Ring Image Čherenkov Detector (subsystem of PHENIX).
SPS Super Proton Synchrotron (CERN).
STAR Solenoidal Tracker at RHIC (experiment).
VTX Silicon Vertex Tracker (subsystem of PHENIX).

xNomenclatures
Nomenclatures used in this dissertation:
Ncoll Number of binary collisions.
Npart Number of participants.
N N Nucleon-Nucleon (collision).
pT transverse momentum.
√sN N Center of energy per nucleon pair.
Tc psudocritical temperature.
DCAL DCA along the beam axis.
DCAT DCA in transverse plane.

xiAbstract
This dissertation details the measurement of electrons from semileptonic√
decay of charm and bottom hadrons from Au+Au collisions at sN N = 200
GeV by using the PHENIX detector in the relativistic heavy ion collider(RHIC).
Heavy quarks (charm or bottom) are one of suitable probes of a Quark
Gluon Plasma (QGP). Due to their large masses, the production process ofheavy quarks is restricted to initial nucleon-nucleon collisions. Thus, heavy
quarks carry information about the entire time-evolution of the medium.
We previously measured the yields of electrons from semileptonic decays√of charm and bottom hadrons inclusively in Au+Au collisions at sN N = 200
GeV. It indicated substantial modification in the momentum distribution of
the parent heavy quarks due to the QGP created in these collisions. However,at that time, PHENIX was not able to distinguish electrons from charm andbottom hadrons independently. In order to understand these medium effects
in more detail, the separation of electrons from charm and bottom hadrons
are aimed to reveal the mass dependence of energy loss in the medium.
For the first time, by using the Silicon Vertex Tracker (VTX) installedin PHENIX to measure precision displaced tracking, we have succeeded inseparating the electrons from charm and bottom hadrons in Au+Au collisions√
at sN N = 200 GeV in the transverse momentum (pT ) from 1 GeV/c to 8
GeV/c at midrapidity region (|η| < 0.35). The invariant yield of charmand bottom hadrons as a function of pT were calculated. Based on thisseparation, the fraction of the electrons from bottom hadrons were obtained.
Further, by using that for p+p collision, the nuclear modification factor RAA
was extracted both for charm and bottom electrons.
We have observed that bottom electron is suppressed for higher pT region(pT > 4 GeV/c ) in Au+Au collisions compared to p+p collisions for the firsttime in RHIC energy. While the magnitude of suppression is smaller thanthat of charm in the region of 3 < pT < 4 GeV/c , it is similar for higher pT
region within systematic uncertainty.

Chapter 1
Overview
According to the lattice Quantum Chromodynamics (QCD) calculations [16,17], quarks and gluons are deconfined at the high temperature above ∼ 150
MeV. To date, it is well established that heavy Ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) create
a new state of matter -QGP- that is described as an equilibrated system withinitial temperature in excess of 340 – 420 MeV [18–22].
This QGP follows hydrodynamical flow behavior with extremely small
dissipation, characterized by the shear viscosity to entropy density ratio η/sand is thus termed a near-perfect fluid [18, 23–25].
However, these recently established knowledge of QGP still raises newquestions about the property of QGP and how QCD works in this environment.
Heavy flavor hadron (D, B) measurement has several advantages to light
hadrons (π, K...etc.) to investigate the property of the QGP because of their
specific production mechanism. The heavy quarks (Q = c, b) are mainly produced via hard scatterings at the initial nucleon-nucleon collisions, because
the large momentum transfer is needed to produce heavy quarks [26]. This
heavy quarks are clean probes which experience the entire time-evolution of
the QGP as they pass through it.
The PHENIX collaboration has measured transverse momentum distribution of electrons1 from semileptonic decay of charm and bottom hadrons
produced in Au+Au collisions and observed it is significantly modified compared with p+p collisions from the year 2004/2005 data at RHIC. This result
was unexpected, because in the perturbative QCD based calculation, parton energy loss in the QGP is believed to be dominated by gluon radiative
energy loss [27], which was predicted much smaller for heavy quarks than1

Here and throughout this dissertation, “electrons” is used to refer to both electronsand positrons.

1Section CHAPTER 1. OVERVIEW
that for light partons [7]. In the past measurements before the year 2010,
the PHENIX was not able to distinguish electrons from charm and bottom
hadrons independently in Au+Au collisions.
In order to separate the contribution from charm and bottom, the PHENIX
collaboration has developed the silicon vertex tracker (VTX) [28] and installed it covering at midrapidity region in 2010. The VTX was designed
to give precise tracking reconstructions of the distance of closest approach(DCA) to the collision vertex. This enables the separation of electrons fromsemi-leptonic decay of charm and bottom hadrons statistically in Au+Au
collisions, because the decay kinematics and life time of charm (cτD0 = 123µm, cτD± = 312 µm) and bottom (cτB 0 = 455 µm, cτB ± = 491 µm ) hadrons
are different [3].
In the result, the suppression of electrons from bottom hadrons is observedfor higher pT region (pT > 4 GeV/c ) in Au+Au collisions compared to p+p
collisions for the first time in RHIC energy. It strongly implies bottom quarks
suffer energy loss in the QGP medium. The magnitude of suppression issmaller than that of charm in the region of 3 < pT < 4 GeV/c and similar
for higher pT region within systematic uncertainty. The new analysis method
using the VTX detector was established and the same method can be appliedfor high statistics data taken in 2014/2015.
This dissertation details the first measurement of electrons from semilep√
tonic charm and bottom hadron decays from Au + Au collisions at sN N =200 GeV in year 2011 using the VTX detector. The organization of this dissertation is as follows: In Chapter 2, physics backgrounds of the QGP andheavy ion collisions are reviewed.
In Chapter 3, heavy quark as a probe of the QGP and past measurements
at RHIC and the LHC are reviewed. In the measurements at RHIC, charmand bottom contribution was not separated. The motivation of charm/bottom
separation are also explained in this chapter.
In Chapter 4, the accelerator RHIC, the relevant PHENIX apparatus inyear 2011 and the VTX detector which was installed in the end of year 2010
are introduced.
In Chapter 5, the analysis method to separate the contribution of electrons from charm and bottom using PHENIX central arms and the VTX are
explained. After that, the unfolding procedure using electron DCA distributions and pT spectra are explained.
In Chapter 6, results of invariant yield of charm and bottom hadron,bottom electron fraction, and nuclear modification factor of charm electronsand bottom electrons in Au+Au collisions are shown.
Chapter 7 is for dicussions about these results. The consistency checkwith previously published results of invariant yield of heavy flavor electrons2Section CHAPTER 1. OVERVIEW
and STAR D0 measurement shown. After that, comparison of thereticalmodels are shown.
The conclusion of this measurement are described in Chapter 8.

Major Contributions
The major part of this dissertaion is based on the published paper “Single electron yields from semileptonic charm and bottom hadron decays in√
Au+Au collisions at sN N = 200 GeV by A. Adare et al.” [29]. The major
contributions of the author as a PHENIX collaborator are listed as follows:• Construction, quality assurance and maintenance of pixel detectors (inner two layers of the VTX detector).
• Development of online monitoring system of pixel detectors.
• Commissioning and operation of the VTX detector during 2011 - 2014.
• Calibration of VTX sensors alignment.
• Establish the analysis method of electron DCA distributions using VTX
detector.
• Publication of the paper “Single electron yields from semileptonic charm√and bottom hadron decays in Au+Au collisions at sN N = 200 GeV”
[29] with paper preparation group in PHENIX.

3

Chapter 2
Quark Gluon Plasma and Heavy
Ion CollisionThis chapter is dedicated to giving a brief introduction to the Quark
Gluon Plasma (QGP) and the high enegy heavy ion collision. In section
2.1, the current understanding of QGP based on Quantum Chromodynamics(QCD) is reviewed. In section 2.2, the basic picture of space-time evolutionof the matter created in heavy ion collisions is described. After that thegeometry of collisions, which is important to understand the experimental
results are explained. In the last section 2.3, the states of created matter in
RHIC is explained from three important experimental results; jet quenching,strong collectivity, and temperature.

2.1

Quark Gluon Plasma

High energy Heavy Ion Collision experiments aim to create and investigate the property of a high temperature matter which consists of deconfined
quarks and gluons. The new state of deconfined quarks and gluons is calleda QGP. QGP is expected based on the “Asymptotic freedom” property of
QCD. Asymptotic freedom was discovered in early 1970s by Gross, Wilczek
and Politzer [30–32], and means that the QCD coupling constant αs decreases with increasing the momentum transfer Q, as shown in Figure 2.1.
The discovery of asymptotic freedom arises the expectation; asymptonic freedom makes interaction at very short distances (or high momenta) arbitrarily
weak, so that if the temperature or net baryon density is high enough, atransition should occur from normal nuclear matter, where quarks and gluons are confined in hadrons, to the new state of matter where the quarks andgluons are deconfined [33, 34].
4

Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION
Sept. 2013

τ decays (N3LO)
Lattice QCD (NNLO)DIS jets (NLO)
Heavy Quarkonia (NLO)
e+e– jets & shapes (res. NNLO)
Z pole fit (N3LO)(–)
pp–> jets (NLO)

α s(Q)
0.3

0.2

0.1

QCD αs(Mz) = 0.1185 ± 0.0006
1

10Q [GeV]

100

1000

Figure 2.1: Summary of measurements of αs as a function of the momentum
transfer Q from PDG2014 [3]. Also shown in bottom is the αs value when
Q2 = Mz (Mz is Z boson’s mass, NLO: next-to-leading order; NNLO: nextto-next-to leading order; res.NNLO: NNLO matched with resummed nextto-leading logs; N3 LO: next-to-NNLO).
Lattice QCD calculations predict that the transition from a low temperature hadronic phase to a QGP phase should occur at a temperature of ∼ 150
MeV for zero net baryon density. In early expectations, this transition could
be first−order phase transition between normal nuclear matter and QGP
phase. The QCD transition at finite-temperature and low baryon chemical
potentials (µb ) is, however, not a real phase transition, but a rapid crossover,meaning that it involves a rapid and smooth change, as opposed to a discontinuity, as the temperature is varied [35]. µb at RHIC (∼ 45 MeV [36]) is muchsmaller than typical hadron mass. Even though there is no well-defined separation of phases because of the crossover behavior of the transition, recent
lattice QCD results by Budapest-Wuppertal collaboration [37] and HotQCD
collaboration [1], for example, show that thermodynamic properties (pressure, energy density, and entropy density) really change rapidly around thecrossover region. Figure 2.2 shows the lattice QCD results on pressure, energy density, and entropy density normalized by 1/T 4 by HotQCD Collaboration [1].
Instead of genuine critical temperature at which phase transition occurs,“pseudocritical temperature” is used to depict the phase diagram of QCD.
5Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION
While there are several definitions of pseudocritical temperature Tc , an example of the pseudocritical temperature Tc = 154 ± 9 MeV is shown as avertical band in the Figure 2.2. This Tc is defined for chiral phase transition,
at which up, down and strange quarks rapidly acquire their physical masses,
taking chiral symmetry as order parameter [17]. There is another way todefine the Tc , for example, as the inflection point of /T 4 and ( − 3p)/T 4 ,where p is the pressure and  is energy density [16].

Figure 2.2: Lattice QCD results from Hot QCD collaboration [1]. The figure
shows pressure, energy density, and entropy density normalized by 1/T 4 as afunction of the temperature. The dark lines show the prediction of the hadronresonance gas (HRG) model. The horizontal line at 95π 2 /60 corresponds tothe ideal gas limit for the energy density and the vertical band marks the
crossover region, Tc = 154 ± 9 MeV (see also texts) .
While deconfinement and chiral phase transition have not been directly
observed in RHIC and the LHC experiments, there have been several experimental results which strongly indicate the creation of QGP. Three important observations which are understood as evidence of QGP found in Au+Au
collisions at RHIC, jet quenching, strong collectivity, and temperature are
discussed in section 2.3. An overview of the evidence for the creation of quarkgluon matter at RHIC can be found in those summary papers [18, 19, 38, 39]from four experiments at RHIC.

6

Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION

2.2

High energy Heavy Ion Collision experiment

2.2.1

Nuclear stopping power

In order to create a QGP state in heavy ion collisions, sufficient energy
must be released from the two colliding nuclei into the QGP. The kinetic
energy that is removed from the nuclei depends on the amount of stopping
power between the colliding nuclei.
The stopping power can be estimated from the rapidity loss experienced
by the baryons in the colliding nuclei. The rapidity, y, of a particle is definedas:
1 E + pz,
y = ln2 E − pz
where E and pz are energy and z component of momentum, respectively.
The average rapidity loss, δy, is defined as the difference,δy = yp − hyi
between the incoming beam rapidity yp and the average rapidity after thecollision which is expressed as [39].
 Z yp
Z yp
dN
dN
y
hyi =
dy
dy
dy
dy
0
0
Here dN/dy denotes the number of net-baryons (number of baryons minus
number of antibaryons) per unit rapidity.
Figure 2.3 shows the measurement of net protons (number of protons −√number of anti-protons) rapidity distribution at AGS ( sN N = 5 GeV Au+Au),√√
SPS ( sN N = 17 GeV Pb+Pb) and RHIC ( sN N = 200 GeV Au+Au)
data [40]. One can assume the rapidity distribution of net neutrons, net
Λs, net Σs are similar with net protons. Thus the net proton distributions
represents the net baryon distributions.
The distributions yield a strong beam energy dependence as shown in
Figure 2.3. At RHIC (red points), the distribution is almost flat up to y ∼ 3.
It means incident nucleons do not lose all their kinetic energy and baryon
chemical potential (µb ) at RHIC (µb ∼ 25 [39] – 45 MeV [36]) is quite smaller
than AGS and SPS at midrapidity. In analogy to optics, it is often said thata nucleus becomes transparent in high energy collisions.
The average rapidity loss measured by BRAHMS is δy = 2.0 ± 0.1. Theenergy loss per participant nucleon is estimated to be ∼ 70 GeV from therapidity loss and transverse momentum spectra of baryons [40]. Thus, thetotal kinetic energy loss of two incoming nuclei at RHIC is estimated to be∼ 28 TeV (70 GeV × 2 × 197) in most central 197 Au +197 Au collision.
7Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION

Figure 2.3: The net-proton (number of proton − number of anti-proton)√
rapidity distribution at AGS (green, Au+Au at sN N = 5 GeV), SPS (blue,√
Pb+Pb at sN N = 17 GeV), and RHIC measured by BRAHMS (red, Au+Au√
at sN N = 200 GeV) [40]. The data are most central collisions (0-5 %centrality. See subsection 2.2.3 for the definition of centrality). yp denotes
beam rapidity.

2.2.2

Picture of space-time evolution

The kinetic energy removed from two incoming nuclei is converted into
other degree of freedom. This subsection overviews the basic space-time
picture from initial collisions in partonic levels to freeze out in hadronic
phase originated from the kinetic energies released in heavy ion collisions.
Figure 2.4 is a simplified sketch of this sequence.
Au Au

collision

thermalization

mixed phase

QGP

hadronization

hadronic phasehadronization

time

Figure 2.4: Time evolution of heavy ion collision from initial nucleus-nucleus
collision to hadronic freeze out
In high energy heavy ion collisions, two incoming nuclei are Lorentzcontracted along the collision axis. Figure 2.5 shows the parton distributionfunctions (PDF), which describe the initial distribution of quarks and gluons8Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION

1

1
NNPDF2.3 (NNLO)

0.9
0.8
0.7

0.8
g/10

d

0.6

uv

0.5

0.5

0.4

c
uv

0.4
dv

0.3

s

0.2
u

0.1
0
-3
10

xf(x,µ 2=104 GeV 2)

s

0.7

0.6

0.3

g/10

0.9

xf(x,µ 2=10 GeV2)

x

b

dv

0.2

d

0.1

c
10-2

u

10-1

0
-3
10

1

10-2

x

10-1

1

Figure 2.5: Parton distribution function times Bjorken-x as a function of
Bjorken-x obtained in NNLO NNPDF2.3 global analysis [2, 3]
in colliding two protons as a function of Bjorken-x. 1 Bjorken-x is the fractionof the nucleon’s momentum carried by the struck parton:x=

Q2.
2p · qHere q is the transfer of four-momentum. p is the four-momentum of a
nucleon, and Q2 = −q 2 . As shown in Figure 2.5, there are a lot of small
Bjorken-x gluons. Most of the produced hadrons at RHIC and LHC at
midrapidity region are originated from those gluons.
At the initial nucleon-nucleon (N N ) collision, scattering of these partons
take place. After that, those partons suffer multiple elastic and inelastic
scattering generating a lot of softer partons. They are supposed to be in
the local thermal equilibrium within the time scale τ ∼ 1 fm/c = 1/ΛQCD .
This process is called thermalization of partons and the typical time scale forthe system to relax to the local equilibrium distribution is called relaxation
time. As will be discussed in 2.3.2, the assumption of rapid realization of
1

The PDF for free protons are known to be modified for protons bound in nucleus [41].
Such effects which are not due to the production of a QGP are termed initial state effects.

9Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION
local thermal equilibrium (∼0.6 – 1 fm/c) works well to describe azimuthal
anisotropy (v2 ) of produced hadrons at RHIC in hydrodynamical model.
Phenomenologically, the energy density after the initial N N collision canbe roughly estimated through Bjorken’s formula [42]Bj (τ ) =1 dET,
cτ A⊥ dy2

∈Bjτ [GeV/fm /c]√where τ = t2 − z 2 is the proper time, and A⊥ is nuclei transverse overlap
area. ET is a sum of transverse energies of all particles emitted in an event.
dET
is the transverse energy per unit rapidity.
dy
Figure 2.6 shows the PHENIX data on Bj τ as a function of number ofparticipants Np at three collision energy [4]. If τ is around 1 fm/c, energy

42
200 GeV
130 GeV19.6 GeV
0

100

200

300

Np

Figure 2.6: Energy density as a function of the number of participants Np
from PHENIX data [4].
√densities at sN N =130 and 200 GeV are above 1 GeV/c /f m3 except forvery peripheral collision. According to the lattice QCD calculation (Figure 2.2), the energy density around the pseudocritical temperature TC is∼ 0.3 GeV/fm3 . The PHENIX data indicate energy density to be realized at
RHIC is high enough to create a QGP.
As the QGP system expands, the energy density and temperature decrease. When the temperature gets smaller than Tc , quarks are confinedand color neutral hadrons are produced. The cooling down process is called“freeze out”. It is expected to happen gradually, in the later stage of collision, so that confined phase and deconfined phase are mixed (mixed phase),
as illustrated in Figure 2.4,.
The hadronization process is explained by fragmentation and recombination of partons [43]. As shown in Figure 2.7, transverse momentum pT
10Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION
spectrum above 6 GeV/c is dominated by fragmentation, which can be fit
by a power law function as it is characteristic in pQCD at large transverse
momentum. The region below 4 GeV/c is dominated by so-called recombination (coalecense) process.

Figure 2.7: pT spectrum of inclusivce charged hadrons and theoretical explanation from [43]. Top: inclusive charged hadron pT spectrum in central√
Au+Au collisions at sN N = 200 GeV from PHENIX data [44]. Bottom:
ratio of proton to π + as a function of pT .
In the recombination picture, three quarks or a quark-antiquark pairwhich are close enough in a phase space can form a baryon or meson, respectively. The pT spectrum of hadron generated from recombination falls off
faster than fragmentation with increasing pT . Eventually, the total amountof hadrons are fixed after the hadronization process. After that, produced
hadrons are allowed to free-stream and particle spectra at this moment are
seen by the detector.

2.2.3

Collision Geometry

The geometry of the collision must be taken into account in the analysis
and interpretation of the experimental data. The impact parameter (b in11Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION
Figure 2.8) can be changed from 0 to the transverse nuclear size. The spacetime evolution of collision may be different in central and peripheral collisions.
In the centre-of-mass frame, owing to Lorentz contraction in the longitudinal
direction, the two nuclei can be seen as two thin disks of transverse size
2RA ' 2A1/3 f m. Some relevant quantities which characterize the collisiongeometry are listed below:
1. Npart : The number of participant nucleons involved in a heavy ion
collision. This is the total number of protons and neutrons which takepart in the collision.
2. Ncoll : The total number of binary collisions (N N collisions).
3. centrality: The value to quantify the overlap of two colliding nuclei.
As illustrated in Figure 2.9, centrality takes a range from 0% to 100%as the impact parameter ranges b=0 to b = RA + RB . 0% centrality
means the most central collision. When collisions are not selected bycentrality, it is called minimum bias (MB) collision (or event).
The geometrical quantities listed above (Npart ,Ncoll , centrality) are usuallyestimated by a probabilistic model generally called “Glauber model” [5, 45,
46].
The Glauber Model
In Glauber model, a collision of nucleus A and nucleus B is treated as
the multiple independent nucleon-nucleon interactions. The nucleons travel
on straight-line trajectories and do not change their trajectories after thecollisions at all. This approximation works well since the crossing time of√
Au+Au is 0.12 fm/c at sN N = 200 GeV and the nucleon can move totransverse direction 0.12 fm at maximum. This is much smaller than theradius of nucleon (∼ 0.8 fm). The simplest version of the Monte Carloapproach, a nucleon-nucleon collision takes place if the nucleons’ distance, din the plane orthogonal to the beam axis satisfiesqNNd ≤ σin/π,NNwhere σinis the total inelastic nucleon-nucleon cross section in vacuum. At
NN
RHIC, it is assumed σin= 42 mb at 200 GeV which is extracted from fits
to the total and elastic cross section of other experiments [3]. Secondary
particle production and possible excitation of nucleons are not considered inthis model.

12Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION

Figure 2.8: Geometry of a collision between nucleus A and B.
The probability per unit transverse area of finding a nucleon at the transverse position s in Figure 2.8 isZ
TA (b) = dzρ(z, s),Rwhere ρ(z, s) is the nucleon number density at location (z, s) ( d3 rρ(z, s) =1).
Then, the product TA (s)TB (s − b)d2 s gives the probability per unit areaof nucleons being located in the overlapping area of nucleus A and nucleus
B. Integrating this product over all values of s defines the nuclear overlap
function, TAB (b), with impact parameter, b as follows:Z
TAB (b) = TA (s)TB (s − b)d2 s,
For a heavy and spherical nucleus such as Au or Pb, the Woods-Saxon
parametrization is a good approximation:
ρnm,
ρA (r) =1 + exp (r − RA )/awhere ρnm = 0.16 fm−3 is the normal density of nuclear matter. R is thenuclear charge radius, a is the skin depth: for 197 Au, R = 6.38 fm anda = 0.535 fm [47].
13Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION
The number of participants (Npart ), and the number of binary nucleonnucleon collisions, (Ncoll ), in the Glauber model are expressed as follows,
Npart (b)Rin= d2 s TA (s) (1 − exp (−σN
N TB (s)))
R 2in+ d s TB (s − b) (1 − exp (−σN
N TA (s))) ,Ncoll (b) =Rind2 s σNN TA (s)TB (s − b)in= σN N TAB (b).

(2.1)

(2.2)

Figure 2.10 shows the number of binary nucleon-nucleon collisions (Ncoll )and the number of participants (Npart ) in Au+Au collisions as function of
impact parameter.

2.2.4

Nuclear Modification Factor: RAA

Once the number of binary collisions (Ncoll ) is obtained from Glaubermodel, experimental observables in Au+Au can be compared with those in
p+p as baseline, by using nuclear modification factor RAA , which is definedas
RAA (pT , y; b) =d2 NAA /dydpT.
Ncoll × d2 Npp /dydpT

The numerator represents the observed hadron (or photon, lepton) spectra
for species X in nucleus-nucleus collision, and the denominator represents
the corresponding spectra produced in proton-proton collision scaled with
the number of binary collisions (Ncoll ). Since hard scattering, QCD process
which involves large momentum transfer, is point-like with distance scale
1/pT ≤ 0.1 fm, the cross section p(d)+A or A+B collisions, compared top+p, is proportional to the relative number of possible point-like encounters.
This binary-scaling property in Au+Au collisions is seen in high-pT direct
photon spectra (subsection 2.3.3) and total yield of charm (section 3.1).

2.3

States of created matter at RHIC

2.3.1

Jet quenching and energy loss

At RHIC, high pT particles (pT ≥ 5 GeV/c ) are produced from hardcollision processes. In this subsection, parton production and its energy loss
14

Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION

Figure 2.9: An illustrated example of the relationship of the impact parameter (b), Npart , overlap area of colliding nucleus, the multiplicity distribution
and centrality taken from [5].

15Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION

Figure 2.10: Number of participants (Npart ) and Number of binary collisions (Ncoll ) for Au+Au and Cu+Cu collisions from Glauber Monte Carlocalculation [5]. The lines represent the mean values.
in the medium in nucleon-nucleon collision is reviewed. After that, so-called
jet quenching discovered in Au+Au collision at RHIC is also discussed.
The definition of jet is ambiguous. Here the most commonly used definition for hadron-hadron collision is introduced [48, 49]: a jet is a concentrationof transverse energy ET in a cone of radius R, wherep
R = (∆η)2 + (∆φ)2 .
Here φ is the azimuthal angle and η is the pseudorapidity variable:
η = − ln tan(θ/2).
In the two-dimensional η, φ plane, curves of constant R are circles around theaxis of the jet. Jet production in hadronic collisions is a hard QCD process.
An elastic parton scattering (2 → 2) or inelastic parton scattering (2 → 2 +X) of two partons from each of the colliding nuclei results in the productionof two or more high-pT partons in the final state. The jet observable can
not be the residue of a single parton because of color conservation, energy
momentum conservation, and quantum-mechanical interference [50].
One of major discoveries that established the formation of dense partonic
matter at RHIC is the strong suppression of high-pT particles in central
16Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION
Au+Au collisions [44, 51]. This phenomena is called “jet quenching”, which
is originally suggested by Bjorken in 1980’s [52].
Figure 2.11 shows the nuclear modification factor (RAA ) for π 0 in central (0-10%) and peripheral (80-92%) Au+Au collisions and minimum-bias
d+Au collisions at mid-rapidity. The suppression provides direct evidence
that Au+Au collisions at RHIC have produced matter at extreme densities,
greater than ten times the energy density of normal nuclear matter [18, 53].
The RdA measurement in Figure 2.11 provides a test of the possible contribution of initial state nuclear effects to the observed suppression above
and demonstrates that there is no significant initial state effect of nuclear
parton distributions compared to the Au+Au RAA with pT > 2 GeV/c at
mid-rapidity. Thus, the suppression of high pT hadrons in Au+Au collisions
is interpreted as final state effect of the produced dense medium. The datasuggest a small enhancement in d+Au collisions, consistent with expectations
due to the Cronin effect [54]. The Cronin effect is expected to come from themultiple scattering of the incident partons while passing through the nucleus
before the collision, which smears the axis of the hard scattering relative tothe axis of the incident beam, leading to the enhancement in mid-rapidity
region [55, 56].
The suppression of the high pT hadrons (RAA < 1) from the fragmentation of a parton is due to energy loss in the created matter in the reaction. The energy loss of a particle in a medium, ∆E, provides important
information on its properties. In general, ∆E depends both on the particle
characteristics (energy E or transverse momentum pT and mass m) and on
the plasma properties (temperature T , particle-medium interaction couplingα, and path-length of the matter L). The recent theoretical developments
are reviewed in [49, 57]
The total energy loss ∆E of a particle traversing a plasma with temperature T is the sum of collisional and radiative loss : ∆E = ∆Ecoll + ∆Erad
Collisional energy loss is the energy loss process through elastic scattering inside a QGP of temperature [52, 58]. This was thought to dominate at low particle momentum. Radiative energy loss happens throughthe bremsstrahlung of gluons. This loss is believed to dominate at higher
momentum.
Compared to the radiative energy loss, collisions energy loss was usuallyconsidered to be small for light flavor (leading) partons, especially when theenergy of the jet is sufficiently high. However in recent realistic calculationof nuclear modification factor RAA at RHIC and LHC energies, collisionalenergy loss may give non-negligible contribution [59–61].

17

Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION

1.6
Au-Au, CentAu-Au, Periph

1.4

d-Au, min-bias

1.2

RAA

1
0.8
0.6
0.4
0.2
0

0

2

4

6

8

10

pT (GeV/c)
Figure 2.11: Nuclear modification factor, RAA , for π 0 in central (0-10%) andperipheral (80-92%) Au+Au collisions and minimum-bias d+Au collisions at
mid-rapidity. The shaded boxes on the left show the systematic errors for
the Au+Au RAA values resulting from overall normalization of spectra anduncertainties in the nuclear overlap function TAB . The shaded box on theright shows the same systematics error for the d+Au points. Reprinted from[18] with permission from Elsevier.

18

Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION

2.3.2

Collectivity of the QGP

In addition to the discovery of jet quenching, RHIC experiments found
one more important observable related to the collectivity of created matter.
The collectivity is described by hydrodynamics and called “flow”.
In Au+Au non-central collision, the reaction zone of nucleus-nucleus collision is elliptic around the beam axis as illustrated in Figure 2.12. If themean free path among the produced particles is much larger than the typicalsize of the system, the azimuthal distribution of particles does not depend on
azimuthal angle on average due to the symmetry of the production process.
On the other hand, if the mean free path is very small compared to the sizeof reaction zone, hydrodynamics can be applied to describe the space-time
evolution of the system. In the absence of viscosity, initial multiple scattering of partons should transform the initial state spatial asymmetry (elliptic
shape) into asymmetry in momentum space [62], because the pressure gradient in x-axis is larger than y-axis as illustrated in Figure 2.13. This is called“elliptic flow”, which is quantitatively characterized by v2 variable defined in
the following paragraph.

Figure 2.12: Illustration of the collision geometry in a non-central heavy ion
collision. Left figure illustrates reaction zone in the transverse plane. Right
figure illustrates reaction plane of the collision.
The method of analyzing flow is summarize in Ref. [63]. The azimuthal
distribution of the associate particles with respect to reaction plane can be
expanded into a Fourier series :19Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION

Figure 2.13: Illustration of pressure gradient originated from spatial asymmetry of reaction zone.

dN
N=[1 + 2v1 cos(φ) + 2v2 cos(2φ) + · · ·],dφ
2πRdφ cos(nφ) dN
dφ
R
vn =
= hcos(nφ)i,dN
dφ dφ
where φ is the azimuthal angle of momentum and vn are the Fourier coefficientof n-th harmonics. Because of the symmetry around the y-axis in Figure 2.12,
the sine terms vanish in this expansion.
At RHIC, STAR discovered large v2 of inclusive charged hadrons fromthe first RHIC run [64]. A lot of observables, particle dependence of v2 , v2
with different collision system, and v1 , v3 , · · · has been also measured after
that. At low pT , below around 2 GeV/c , the measurements of v2 is well fit
by hydrodynamical calculations which assume equilibrium established earlyin the collision (∼ 0.6 – 1 fm/c) and small viscosity over entropy density(for example, η/s ∼ 0.16 from Ref. [6]). It is often termed a near-perfect
fluid [18, 23–25].

20

Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION25
ideal
η/s=0.03
η/s=0.08
η/s=0.16
STAR

v2 (percent)

20
15
10
5
0
0

1

2
pT [GeV]3

4

Figure 2.14: STAR measurement of v2 with hydrodynamical predictions for√minimum bias Au+Au at sN N = 200 GeV from [6]2.3.3

Temperature of the created matter“Direct photons” stands for the photons which emerge directly from aparton collision. In this subsection, the direct photon measurements arereviewed.
They do not suffer medium effect and carry information about the circumstances of their production [65]. The direct photon is called electromagnetic
probe of QGP, as they interact only weakly (α = 1/137  αs ) and theirmean free path is larger than the typical system size (∼ 10 fm). Thermalradiation from the QGP phase is predicted to be the dominant source of
direct photons with 1 < pT < 3 GeV/c in Au+Au collisions at RHIC [66].
The measurement of direct photons at low pT will allow the determinationof the initial temperature of the matter.
As shown in Figure 2.15, PHENIX observed the enhancement of direct
photon yield in Au+Au collision compared with p+p collision in the low pT(< 3GeV/c ) region [20]. The results were compared with several hydrodynamical models of thermal radiation from QGP at RHIC energies. The models assuming the formation of QGP with initial temperature ranging Tinit ∼300 – 600 MeV at times τ ∼ 0.6–0.15 fm/c are in qualitative agreement withthe data [20, 67–70]. It it well above Tc predicted by lattice QCD.
The main background photon source is hadron decay, such as π 0 → γγ.
Their contribution to the photon spectrum is large and subtraction of the decay background from inclusive photon spectrum was a very challenging task.
In the data analysis of PHENIX results in Figure 2.15, “internal conversion”
method which measure the virtual photons , instead of real photon is used to21Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION

Figure 2.15: Invariant cross section (p+p) and invariant yield (Au+Au) of
direct photons as a function of pT from [20]. The filled points are from virtualphoton measurements and open points are from real photon measurements.
The three curves on the p+p data represents NLO pQCD calculations, andthe dashed curves show a modified power-law fit to the p+p data, scaled by
TAA . The dashed (black) curves are exponential plus the TAA scaled p+p
fit. The dotted (red) curve near the 0 – 20 % centrality data is a theory
calculation [66].
separate direct photons from decay background in the low pT region (filledpoints). In general, any source of high energy photons can also emit virtualphotons, which convert to low mass e+ e− pairs. For example, gluon Compton
scattering (q + g → q + γ) has an associated process that produces low masse+ e− pairs through internal conversion (q + g → q + γ ∗ → q + e+ e− ).
The mass distribution of the e+ e− from pseudo scalar meson decay (π 0 , η →γγ) follows the Knoll-Wada formula [71].
s
2α
4m2
2m2 1
M2
1 dN
2 2
=
1 − 2e (1 + 2e )(1 − ee2 )3 |F (Mee
)| ,
(2.3)
Nγ dMee
3π
Mee
Mee Mee
M
Here Mee is the mass of the electron pair; me is the mass of electron; M is22

Section CHAPTER 2. QUARK GLUON PLASMA AND HEAVY ION
COLLISION2
the mass of the parent meson; and F (Mee
) is a hadronic form factor. The
formula above is normalized as decay rate per photon, and therefore it differsfrom the total Dalitz decay rate by a factor of 2 for π 0 ,η since these mesons
decay into two photons. In the hadron decay, Mee does not exceed parent2
ee 3
hadron mass M , so the part (1 − M) in the above formula becomes 0 if
M2(Mee → M ).
On the other hand, there is no parent hadron for direct photon, there is nophase space limitation above in Mee from direct photon. Then, if e+ e− pairyield with large Mee is measured as shown in Figure 2.16, the contribution
from hadron decay is strongly suppressed. Since 80% of the hadronic photons
are from π 0 decays, the signal to background (S/B) ratio for the direct photon
signal improves by a factor of five for Mee > Mπ0 = 135 MeV/c2 in PHENIX
measurement [20].

Figure 2.16: Electron pair mass distribution for p+p and Au+Au (MinimumBias) taken from [20] The pT ranges are shown in the legend. The solid curves
represent an estimate of hadronic sources; the dashed curves represent theuncertainty in the estimate.

23

Chapter 3
Heavy quark as a probe of the
QGP

Au Au
- initial NN collisions- formation of QQ pairb~0.02 fm/cc~0.08 fm/cuc~0.3-1fm/c

c

c

c
c

s
d

c

u
b

d

d
c

c
b

pre-equilibrium

c

u

d

u

~5 fm/c

b

d

c
d
c
s

- elastic scattering

QGP phase-u-gluon radiation~ 120 μm/c

π+-decayp

Hadronic phaseπ-~ 460 μm/c
time

recombination (or resonance)fragmentation
dissociation

e

e X ν

X

ν

Figure 3.1: Schematic view of time evolution of heavy quarks.
As discussed in the previous chapter, it is well established that the QGP
is created in RHIC and the LHC above Tc . Heavy quarks (charm or bottom)
24Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP
is the suitable probe of the QGP created in high energy heavy ion collisions.
Heavy quarks (Q), including charm (c) and bottom (b) quarks, may exist
either as bare quarks inside the QGP, or as bound states of QQ̄ when themedium temperature is still above Tc but not too high [72]. The former
state is called as “open” heavy quark and the latter as heavy quarkonium(charmonium or bottomonuim). Bound states of heavy and light quarks(Qq̄, Q̄q, Qqq...) such as D, B, Λc are also named “open” heavy flavor hadrons.
In this dissertation, the dynamics of open heavy flavor in heavy-ion collisions is concentrated. While, study of heavy quarkonium is also important
to investigate property of the QGP, it is out of scope of this dissertation.
The most important property of heavy quarks is their large masses (mc ≈1.3 GeV, mb ≈ 4.7 GeV [3]) which are much larger than ΛQCD ≈ 200 MeV
and the QGP temperature T ≈ 300 – 600 MeV at RHIC. The heavy quarks(Q = c, b) are mainly produced via hard scatterings at the initial nucleonnucleon collisions, because the large momentum transfer is needed to produce
heavy quarks [26]. The production of charm (bottom) quark pairs takes placeat timescale 1/(2mQ ) ∼ 0.08 (0.02) fm/c.
After the heavy quark production, it is expected that the total number ofheavy quarks stays constant because mc , mb  Tc and they are not destroyedby the strong interaction. This is experimentally confirmed within uncertainties [11, 73, 74]. Thus, heavy quarks carry information about the entire
time-evolution and transport properties of the QGP or the pre-equilibriumphase before the formation of the QGP as illustrated in Figure 3.1.
On the other hand, light quarks can be generated during the evolution of
the medium and even from the mixed phase by low momentum gluon fusion.
Light hadron measurements are less sensitive to the energy loss mechanism
and transport properties of the early stage of the QGP phase.

3.1

Heavy flavor hadron production

Heavy flavor hadron production in nucleon-nucleon collisions is describedby pQCD calculations. For heavy flavor hadrons, pQCD approach is warranted for all momenta since their large quark mass introduces large Q2 evenat zero momentum. This is specific contrast to gluon and light quark jets
which can be treated by pQCD only at high pT .
The experimental results and theoretical calculations of their cross section
are useful as a base line of heavy quark energy loss in Heavy ion collisions(the denominator of RAA ). Heavy flavor hadron production (D, B · ··) innucleon-nucleon collisions is described by the QCD factorization approach.
This calculation is performed by a convolution of three terms: the parton
25Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP
distribution function of nucleon 1 and nucleon 2 (f1N1 , f2N2 , respectively),
the hard parton scattering cross section dσ̂ f1 f2 →f X , and the fragmentation
function (Dfh ).

dσ

N1 N2 →hX=

X Z

dx1 dx2 dzf1N1 (x1 , µ2F I )f2N2 (x2 , µ2F I ) ×(3.1)

f1 ,f2 ,fdσ̂ f1 f2 →f X (x1 p1 , x2 p2 , ph /z, µF I , µF F , µR ) × Dfh (z, µ2F F )Here,• The fragmentation function Dfh (z, µ2F F ) describes the probability thatthe outgoing parton fragments into the observed hadron h with fractional momentum z = ph /pf , µF F is the factorization scale of fragmentation function.
• dσ̂ f1 f2 →f X (x1 p1 , x2 p2 , ph /z, µF I , µF F , µR ) is perturbative partonic crosssection computable up to a given order in αs . µR is the renormalization
scale, and µF I is the factorization scales of parton distribution function.
√
The production cross section of charm hadrons at RHIC( sN N = 200√
GeV, p+p) [75, 76], at Tevatron ( sN N = 1.96 TeV, p+p̄) [77–79] and at the√
LHC ( sN N = 2.76 TeV and 7 TeV, p+p) [80–82] are found to be larger thansuch calculations (NLO MNR calculation [83] and Fixed Order plus Nextto-Leading Logarithms (fonll) calculation [8, 84]), which is still compatible
with the theoretical uncertainties as shown in Figure 3.2 [82].
√The production cross section of bottom hadrons at RHIC( sN N = 200√√
GeV, p+p) [13, 14], at Tevatron ( sN N = 1.96 TeV, p+p̄) [85–87], UA1 ( sN N√
= 630 GeV, p+p̄) [88] and at the LHC ( sN N = 2.76 TeV and 7 TeV, p+p)
[89–91] are well described by fonll [84].
Most dominant charm and bottom production process is gluon fusiong + g → Q + Q̄ (Q = c, b) and flavor excitation g + g → Q + Q̄ + g [92]. Thisis a result of the large fraction of gluons in parton distribution function asshown in Figure 2.5.
√
In RHIC, measurement in p+p collision at sN N = 200 GeV, the total
charm-anticharm quark cross section is 551 ± 57 (stat.) ± 195 (sys.) µb [11].
Almost 99% of produced charm quarks and bottoms quarks are known toform open heavy flavor hadrons. The total cross section of J/ψ is 4.0 ±0.6(stat.)±0.6(syst.)±0.4(abs.) µb [93]. The total bottom-antibottom quarkcross section is 3.2+1.2+1.4−1.1−1.3 µb [13].
In Au+Au collisions, medium effects, such as energy loss of charm or
bottom in the QGP, can only influence the momentum distribution of charm
26

Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP

Figure 3.2: Heavy quark production cross section in p+p or p̄ + p collisions
as a function of center of mass energy in p+p or p̄ + p collisions. (Top)charm production cross section from [82]. (Bottom) Inclusive bottom production cross section per rapidity unit measured at mid-rapidity along withthe comparison to FONLL calculations from [91].

27Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP
or bottom, and the number of heavy quarks produced by binary nucleonnucleon collision are conserved [11, 73, 74]. Namely,Z Z
RAA (Q)dpT dy = 1
The thermal production of heavy quarks, are believed to be very small at
RHIC energy, because their mass (mc ≈ 1.3 GeV, mb ≈ 4.7 GeV [3]) is muchlarger than ΛQCD ≈ 200 MeV and the QGP temperature T ≈ 300 – 600
MeV.
Figure 3.3 shows the centrality dependence of the yield of electron fromheavy flavor as well as the yield in p+p [74]. Those results show that thecentrality dependence of charm quark production is consistent with Ncoll
αscaling. The Ncoll dependence of the yield was fit to Ncoll
and found α =0.938±0.075(stat.)±0.018(sys.), showing that the total yield of charm-decay
electrons is consistent with binary scaling.

Figure 3.3: Electron from heavy flavor yield (0.8 < pT < 4.0 GeV/c )√measured in Au+Au collision at sN N = 200 GeV scaled by the number ofbinary collisions (Ncoll ) from [74]. The yield in p+p collisions is also shown.

3.2

Decay of charm and bottom hadrons

Open heavy flavor hadrons can be measured by the direct reconstruction(invariant mass reconstruction) or part of their decay products. Some important decay channels of the relevant hadrons for identify open heavy flavor
hadrons in measurements are summarized in Table 3.1 and 3.2.

28

Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP
As will be discussed in the section 3.3, PHENIX has been measured electrons from semi-leptonic decay of charm and bottom hadrons (heavy flavor
electron). The advantage of semi-leptonic decay is relatively large branchingratio of heavy flavor hadrons ( ∼ 10%). The contribution from electrons fromlight neutral mesons and photon conversion are not negligible, but they canbe subtracted by cocktail method and isolation cuts (they will be introducedin chapter 5.
Table 3.1: Decay modes, Branching ratios (B.R.), decay momentum∗ (p)and life times for main charm hadrons from PDG [3]. Charge conjugates areabbreviated.
Particle Decay mode
B.R. (%)
p (MeV/c)cτ (µm)++De anything 16.07 ± 0.30
311.8+
µ anything 17.6 ± 3.2
0e+ K νe8.83 ± 0.22869
+ ∗0e K νe3.68 ± 0.10722
K −π+π+9.13 ± 0.19
846
0
+
D
e anything 6.49 ± 0.11
122.9µ+ anything
6.7 ± 0.6
e + K − νe3.55 ± 0.04
867
+ ∗−e K νe2.16 ± 0.16
719
K −π+
3.88 ± 0.05
861
+
+
Ds
e anything
6.5 ± 0.4
149.9
+
e ηνe
2.67 ± 0.29
908
e+ φνe2.49 ± 0.14720+
φπ
4.5 ± 0.4
712
∗+
0 +
D
D π
67.5 ± 0.5
39(2.1 ± 0.5) ×10−6
Λ+e+ anything
4.6 ± 1.7
59.9
c
+
e Λνe
2.1 ± 0.6871
pK − π +5.0 ± 1.3
823
∗ For a 2 body decay, p is the momentum of each decay product in the rest
frame of the decaying particle. For a 3 or more body decay, p is the largest
momentum any of the products can have in this rest frame.

29Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP

Table 3.2: The same as table 3.1 but for bottom hadrons from PDG [3].
Charge conjugates are abbreviated.
Particle
Decay mode
B.R. (%)
p (MeV/c) cτ (µm)++
Be νe X
10.8 ± 0.4
492.0
+ 0
l D νl2.26 ± 0.11
2310
+ ∗0
l D νl5.70 ± 0.19
2258
+
J/ψK
0.1016 ± 0.0033
1683
0
+
B
e νe X
10.1 ± 0.4455.4
l+ D− νl2.18 ± 0.122309
l+ D∗− νl4.95 ± 0.11
2257
J/ψKs00.0437 ± 0.0016
1683
0
+
Bs
l νX
9.5 ± 2.7
449
+0.28
J/ψφ
0.109 −0.23
1588
anythinag
9.8
±
2.3
427
Λ0b
l − νl Λ +
c
+3.2
−
+
6.5 −2.5l νl Λ c
2345
−
+ + −
5.6 ± 3.12335
l νl Λ c π π∗ For a 2 body decay, p is the momentum of each decay product in the rest
frame of the decaying particle. For a 3 or more body decay, p is the largest
momentum any of the products can have in this rest frame.

30Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP

3.3

Heavy flavor hadron measurement in RHIC
and the LHC

3.3.1

Overview of heavy flavor measurement

Measurement of heavy flavor hadrons is much more difficult than light
hadrons because their production cross section is small. Various methods ofheavy flavor detections are so far applied in RHIC and the LHC as follows,• Single electron (or muon) measurement (from admixture of charm andbottom).
• electron-hadron correlation to separate charm and bottom (only available in p+p).
• Invariant mass measurements for charm hadron and bottom hadron.
(Direct reconstruction method)• Non-prompt J/ψ (B → J/ψX) measurement.
• Displaced single electron (or muon) track to separate charm and bottom
contribution.
While heavy flavor measurements in heavy ion collisions are useful to investigate the property of the QGP, reference measurements in p+p collisions
are also important from two points of view. First, these data provide an experimental reference for corresponding measurements in heavy ion collisions.
Such a reference is necessary for the denominator of RAA . Second, these data
provide an important testing ground for pQCD calculations which, due tothe large masses of the charm and bottom quarks, should be able to predict
open heavy flavor observables even at low pT [11].
In following subsections, the previous single electron measurements at
PHENIX are emphasized as it is the first observation of suppression of heavy
quarks. The other recent measurements in RHIC and the LHC are also
reviewed after that. In the end of this section, the new method to separate
charm and bottom contribution Au+Au collisions, which is the main goal ofthis dissertation, is briefly introduced.

3.3.2

Single electron measurements at PHENIX

methodBoth charm and bottom mesons (D, B) have relatively large branchingratios (∼ 10%) to single electrons or single muons. Thus the single elec31

Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP
tron measurement has an advantage to other methods in terms of statistic.
A disadvantage is that kinematics of parent heavy flavor hadron is smeared
through the decay, thus it is rather insensitive to the heavy quark momentum.
The other disadvantage is that it cannot distinguish between the contributions from the charm and bottom hadrons without additional information.
The inclusive single electron spectra consist primarily of four components:
1. electrons from open heavy flavor decays,
2. photonic background from Dalitz decays of light neutral mesons (forexample, π 0 → e+ e− γ and photon conversions in the material,
3. nonphotonic background from K → eπν (Ke3 ) and dielectron decaysof light vector mesons, and
4. heavy quarkonia (J/ψ, Υ) and Drell-Yan background processes.
The dominant source of electron is charm hadrons in total as the bottom
production cross section is small. However due to the large Q-value forbottom decays, electrons from bottom hadrons can have an excess at highpT region. According to the fonll calculation [8], at about pT = 4 GeV/c
the contributions from charm and bottom decays are in the same level, andtowards higher pT , bottom decays become the dominant source of electrons.
Of the three background sources, the “photonic” background is the largest.
To extract the heavy flavor electron signal, the various background contributions listed above have to be subtracted from the inclusive electron spectra.
So-called “cocktail subtraction” method (pT > 1.6 GeV/c ) and “converter
subtraction” method (0.3 < pT < 1.6 GeV/c ) are used for this measurement.
A cocktail of electron spectra from background sources is estimated byusing a Monte Carlo simulation of hadron decays and then subtracted fromthe inclusive electron spectra. The PHENIX measurements of the relevant
electron sources are precise enough to constrain the background within asystematic uncertainty better than 15% for all pT [11].
The yields of photonic and nonphotonic electrons are obtained by measuring the difference between inclusive electron yields with and without aphoton converter of precisely known thickness: a brass sheet of 1.680% radiation length (X0 ).
results and interpretations in Au+Au and p+p collisions
After subtraction of various background, PHENIX first observed the suppression of electrons from heavy flavor in Au+Au collision from year 200432

Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP

RAA

data (RUN4), comparing with p+p collision from year 2005 data (RUN5)[11]. Figure 3.4 shows the PHENIX measurement of RAA (and v2 ) of electrons from open heavy flavor in the 2004/2005 data in 0-10% central andminimum bias collisions, and corresponding π 0 data [11, 94].
1.8
1.6

(a)

0-10% central

Armesto et al. (I)1.4

van Hees et al. (II)

1.2

12/(2πT) Teaney (III)3/(2πT)

Moore &

1
0.8
0.6
0.4

vHF
2

0.2

Au+Au @ sNN = 200 GeV

0.2

0.15

(b)

π 0 RAA

minimum bias

π 0 v 2, p > 2 GeV/c
T

e± RAA , e± vHF
2

0.1

0.05

PH ENIX

0

0

1

2

3

4

5

6

7

8

9

p [GeV/c]T

Figure 3.4: PHENIX measurement of RAA and v2 of electron from heavy flavor from 2004/2005 data [11]. Top panel shows RAA of heavy flavor electronsin 0-10% central collisions compared with π 0 data. Bottom panel shows theelliptic flow parameter v2 of heavy flavor electrons in minimum bias collisions
compared with π 0 ’s v2 .
While at low pT the suppression is smaller than that of π 0 , RAA of electrons from open heavy flavor approaches the π 0 value for pT ≥ 4 GeV/c . In
this pT region, the contribution of electrons from bottom hadrons was naively
expected to be large due to their large Q-value. In the 2004 Au+Au collision
data, PHENIX did not have capability to separate charm and bottom.
Although the charm and bottom contributions are not separated in thismeasurement, this suppression of heavy flavor electrons was unexpected be33

Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP
cause the radiative loss of heavy quarks were thought to be small due tothe dead cone effect, (see subsection 3.4.1), and collisional energy loss was
believed to be negligible at high pT .
Those data indicate strong coupling of heavy quarks to the medium.
Figure 3.4 shows a quantitative comparison of model calculations. Curve
I [95] shows radiative energy loss calculation with the BDMPS formalism[96]. Curves II [97] and III [98] show a calculation which considers elastic
scattering mediated by the excitation of D or B meson like resonant states in
the medium. In those calculation, heavy quark is put into a thermal medium
and Langevin-based transport model are applied for the heavy quark motionin the QGP. Ref. [97] shows that the bottom contributions can dominate
above pT ∼ 3.5 GeV/c and it reduces both suppression and elliptic flow,which was not confirmed in this PHENIX measurement.
Initial state effect
The nuclear modification factor RAA is also expected to contain effects
come from normal nuclear matter. The presence of the normal nuclear mattercan change the kinematic distributions of the observables compared to p+p
without the QGP ever being formed. This effect is generally referred to as“initial state effect”.
Figure 3.5 shows the nuclear modification factors for heavy flavor electron√at midrapidity in central d+Au, Cu+Cu, and Au+Au collisions at sN N
= 200 GeV [99]. The d+Au data show the enhancement relative to p+p
collisions between 1 < pT < 5 GeV/c .
Such an enhancement is termed “Cronin effect” [54] as explained in subsection 2.3.1 and expected to moderate the large suppression of heavy flavor√
electron in Au+Au collisions at sN N = 200 GeV, but this is not fully understood.
In the d+Au collision, it is expected that there is no QGP effect and thus
it is good control experiment to evaluate cold nuclear matter effect. This
assumption is, however, challenged by phenomena recently found in p+P b(LHC) and d+Au (RHIC) collisions (for example, “ridge”), which may comefrom hydrodynamics or gluon saturation [100–105] .

34

Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP

2

d+Au 0-20%
Cu+Cu 0-10%
Au+Au 0-10%

RAA

1.5
1

0.5
Global error: ± 9.9%

0
0

2

4
6
pT[GeV/c]8

10

Figure 3.5: The nuclear modification factors for heavy flavor electron at
midrapidity (η < 0.35) in central d+Au, Cu+Cu, and Au+Au collisions√
at sN N = 200 GeV with PHENIX [99]. The boxes around 1 are global
uncertainties, which include the Ncoll scaling error. The global error given in
the legend is from the p+p yield.

3.3.3

Electron-hadron correlation

In p+p collision, there is an alternative approach to access bottom hadrons.
Both PHENIX and STAR developed bottom and charm hadron separation
techniques based on electron-hadron correlation measurement, utilizing thedifference of decay property between charm and bottom hadrons. Due tothe fact that the combinatorial background in electron-hadron correlation
measurements increases dramatically with particle multiplicity, this method
can not be used in heavy ion collisions.
In the PHENIX, the separation of the relative contributions from charmand bottom decays was carried out based on the decay channel D/D̄ →e± + K ∓ X [13]. A correlation of the invariant mass distribution is observed
for unlike charge-sign electron-hadron pairs (e± K ∓ ) below the D-meson mass,
because of the charge correlation in D-meson decays.
In the STAR, the relative contribution from B decays to heavy flavor
electron yields was measured using the azimuthal correlations between heavy
flavor electrons and charged hadrons, and between heavy flavor electrons andD0 mesons [14].
Figure 3.6 shows the distribution of the azimuthal angle between heavy
flavor electrons and hadrons for two electron pT ranges. The distribution
is normalized to the number of heavy flavor electrons. The shapes of these35Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP
distributions are different because the decay kinematics of the charm andbottom hadron decays are different (some of them are shown in table 3.1
and table 3.2). Figure 3.6 also shows the template distributions made bypythia simulation [106] reflecting the expected shapes of the electron-hadron
azimuthal distributions from charm hadrons and bottom hadrons.
The contribution of bottom decays relative to the sum of charm andbottom decays was obtained from a fit to the azimuthal angle distributions
using a linear combination of the charm and bottom templates with therelative normalization as a fit parameter. In this way, charm contribution
and bottom contribution can be separated statistically.
STAR also performed an independent measurement using electron - D0
correlation, where D0 is identified by the invariant mass reconstruction of K
and π. In this measurement, the azimuthal angle distribution in the away-side(φ ∼ π) are dominated by charm hadrons due to the back-to-back correlation of cc̄ jets. Again, template distributions obtained by pythia simulation
were used to statistically separate charm and bottom. MC@NLO [107] simulation, which is a Monte Carlo event generator with Next-to-Leading-Ordercalculations of rates for QCD processes, is used for the fitting in this analysis
the average value with the result from the pythia simulation for the final
value.
The observed away-side correlation signal in the electron-D0 azimuthal
angle distribution was attributed to prompt charm hadron pair production(∼ 75%) and bottom hadron decays (∼ 25%), while the near side correlation
signal was mainly due to bottom hadron decays (B → Deµ ).
The contributions of bottom decays to the total electron spectrum fromheavy-flavor hadron decays obtained with these two methods are comparedin the right panel of Figure 3.6 as functions of the electron pT . The STARapparatus has larger acceptance compared to PHENIX, which is a clear advantage for such multi-particle measurements.

3.3.4

Direct reconstruction measurement

This method uses hadronic decays of heavy flavor hadron by detecting all
decay products to observe invariant mass peaks. This measurement requires
wide acceptance of detectors and good capability of particle identification as
well as high statistic data. STAR has measured D0 mesons via a hadronic√
decay channel D0 → K − + π + [15] in Au+Au collisions at sN N = 200
GeV. STAR also measured D0 and D∗+ via D0 → K − + π + and D∗+ →D0 π + → K − π + π + [108] in p+p. By comparing them, they reported thenuclear modification for D0 meson (i.e. RAA < 1) in the central collisions
while no suppression was seen in peripheral collisions (Figure 3.7).
36

Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP

Figure 3.6: (Left) The azimuthal angle between heavy flavor electrons andhadrons measured with STAR in p+p collisions is compared to charm andbottom decay templates obtained with pythia simulations for two electronpT ranges. (Right) Relative contributions of bottom decays to the total yieldof electrons from heavy flavor hadron decays as functions of the electron pT
are compared to predictions from fonll pQCD calculations [8]. Both figures
are from [14].
In STAR, Time Projection Chamber (TPC) [109] is the main tracking detector, covering the full azimuthal angle at pseudorapidity η ≤ 1. It measuresthe charged-particle momenta and provides particle-identification (PID) capability via the ionization energy loss (dE/dx) in the TPC gas, allowing separation between charged kaons and pions up to momentum p ∼ 0.6 GeV/c .
In addition to that, Time Of Flight detector (TOF) [110] gives good pions
and kaons separation up to pT = 1.6 GeV/c .
√In Pb+Pb and p+p collision at the LHC at sN N = 2.76 TeV, ALICE
reports similar modification via D+ → K − π + π + , D0 → K − π + and D∗+ →D0 π + (and their anti-particle) [111, 112].
This direct reconstruction method also could be applied for B meson.
However, since the mean multiplicity of the final state in B meson decay
is larger than D meson decay, it is rather difficult compared to D meson
reconstruction. So far, Large Hadron Collider beauty experiment (LHCb)√
measured B + → J/ψK + with J/ψ → µ+ µ− in p+p at sN N = 7 TeV [113].
The CMS has the preliminary result of measurement via B + → J/ψK + ,B 0 → J/ψK ∗ (892) and Bs → J/ψφ, with J/ψ → µ+ µ− in p+p and p+P b√
collisions at sN N = 5.02 TeV. [114].

3.3.5

Non-prompt J/ψ measurement

An alternative approach for bottom hadron production is the measurement of J/ψ emitted from displaced decay of bottom hadron vertices, uti37

Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP

Figure 3.7: Centrality dependence of the D0 pT differential invariant yieldwith STAR in Au+Au collisions (solid symbols) [15]. The curves are numberof-binary-collision-scaled Levy functions from fitting to the p+p result (opencircles) [108]. The arrow denotes the upper limit with a 90% confidence levelof the last data point for 10%-40% collisions. The systematic uncertainties
are shown as square brackets.
lizing relatively large life time (see table 3.2). Those J/ψ s are called “nonprompt J/ψ ”. This measurement requires high resolution vertex detector to
precisely separate primary and secondary vertices.
The Compact Muon Solenoid (experiment at the LHC) (CMS) measured
non-prompt J/ψ via the reconstruction of secondary µ+ µ− vertices in Pb+Pb√
and in p+p collision at sN N = 2.76 TeV and observed RAA ∼ 0.4 [115].This
is the first measurement which disentangled the charm and bottom production in Pb+Pb collision at the LHC. After that, CMS further improved theiranalysis and reconstructed b-jet [116]. Experimentally, the jet associatedwith a b hadron is commonly referred to a “b jet”, although the b quark is
not guaranteed to be the leading parton of the jet. By reconstructing a jet
total energy, it is more sensitive to the parton energy loss compared withmeasurement of fragmented J/ψ. The b-jet RAA is found to be ∼ 0.4 in themost central collisions and it is qualitatively consistent with that of inclusive
jets above pT jet ∼ 100 GeV/c [117].

38

Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP

3.3.6

Separating charm and bottom

The single electron measurement reviewed in subsection 3.3.2 has an advantage in terms of statistics in the limited acceptance of detectors comparedwith direct reconstruction method, however the relative charm and bottom
contribution are unclear.
Since the large difference of lifetime of charm hadrons and bottom hadrons(see section 3.2) are useful to separate charm and bottom contribution in the
single electron measurement, the PHENIX Collaboration proposed displaced
track measurement to separate charm and bottom contribution from single
electron data and has developed Silicon Vertex Tracker (VTX).
The Silicon Vertex Tracker (VTX) was installed in the RHIC-PHENIX
detector in the end of year 2010. The VTX was designed to give precise
tracking reconstructions of the distance of closest approach (DCA) to thecollision vertex in order to distinguish prompt particles from in-flight decays.
In this way, electrons from semi-leptonic decay of heavy flavor hadrons areable to be statistically separated. The detail of this method is described inchapter 5.

3.4

Energy loss of heavy quark in the QGP

In this subsection, the energy loss mechanism and the early theoreticalprediction for charm and bottom quarks before the experimental results fromthe year 2004 PHENIX data [11] are reviewed. After that, the recent theory
development motivated by the PHENIX results are also explained.
Before the measurement of single electron from PHENIX [11] (see subsection 3.3.2), the energy loss of fast partons in-medium was expected to be
dominated by gluon bremsstrahlung (radiative energy loss) [118]. Radiativeloss of heavy quark in-medium was thought to be much smaller than lightpartons due to the “Dead cone effect” [7].

3.4.1Dead Cone effectGluon bremsstrahlung from a heavy quark is suppressed from that of lightpartons at angles smaller than the ratio of the quark mass M to its energy
E, due to kinematics constraints.
The double differential distribution of gluons of transverse momentum k⊥
dPrad,HQ
is expressed as,
and energy ω radiated by a heavy quark ω dωdk
2
⊥

ω

2
dPrad,HQ
αs CF
k⊥
=
,
2
2
dωdk⊥
π (k⊥
+ ω 2 θ02 )239

Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP
where

1
M
= ,
E
γ
αs is the strong coupling constant and CF is the Casimir factor and for the2
c −1= 4/3. In the small angle approximation (k⊥ ∼ ωθ), it
quark case here N2N
cdPrad,0
differs from the bremsstrahlung spectrum from the light partons ω dωdk
2 by⊥
the factor
dPrad,HQ
dPrad,0θ02 −2
ω
≈
ω
·
(1
+
)
2
2
dωdk⊥
dωdk⊥
θ2
This formula means that gluon radiation at small angles with respect toθ2
the quark momentum vector is reduced by (1 + θ02 )−2 . This effect, termed“dead cone effect” [7] is larger for bottom than for charm; Thus, RAA π <RAA c < RAA b was expected against the PHENIX single electron measurement
[11].
θ0 ≡

Ratio
1
0.8
0.6
0.4
0.2
x
0.2

0.4

0.6

0.8

1

Figure 3.8: The ratio of gluon spectra off charm and light quarks for transverse quark momenta p⊥ = 10 GeV (solid line) and p⊥ = 100 GeV (dashed)in QGP matter (the path length L = 5 fm), x = ω/p⊥ , from Ref. [7].

3.4.2Recent theoritical development

Along with dead cone effect, which suppress the radiative loss of heavy
quarks in the QGP medium, there are a number of theoretical developments.
In this subsection, some of them are briefly introduced. Both collisionalenergy loss and radiative energy loss have been reconsidered.
The propagation of heavy quark in the QGP has been often treated within
the framework of Fokker-Planck equation [98, 119–123]. For slowly moving
40Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP
heavy quarks in the QGP, the dominant interaction is elastic scattering andat high momentum, radiative energy loss (gluon bremsstrahlung) is believed
to eventually become the dominant energy loss mechanism. It is currently
not known at which pT this transition occurs [120].
Transport Models
Brownian motion of heavy quarks can be considered for the collisional energy loss. The typical momentum transfer from a thermal medium to a heavy
quark is small compared to the heavy quark thermal momentum pth . Nonrelativistically, the typical kinetic energy of heavy quarks with temperatureT(3.2)
p2th /2mQ ' 3kB T /2,
where kB is Boltzman constant. Then,p2th ' 3mQ kB T.

(3.3)

This is much larger than the typical momentum transfer from the mediumof light partons, Q2 ∼ (kB T )2 . This allows a Brownian Motion approach(Fokker-Plank equation) for heavy quarks as follows,∂∂fQ (t, p) = γ[pi fQ (t, p)] + D∆p fQ (t, p) .
∂t
∂pi

(3.4)

Here, fQ is the phase-space distirbution of a heavy quark and the γ is the drag(or friction) coefficient, which determines the relaxation rate of the average
momentum to its equilibrium value: < p >= p0 exp (−γt).
The spatial diffusion constant D, characterising the dynamics of heavy
non-relativistic particles (mass M and momentum p) traversing the plasma,is connected, via the Einstein relations
D = T /(M ηD ) = 2T 2 /κ

(3.5)

to the momentum diffusion coefficient κ - the average momentum gained by
the particle per unit time. The smaller values of D yield a stronger coupling.
Recent several calculations of Ref.[124–127] provide the prediction ofcharm and bottom fraction as a function of pT using the Langevin-type approach, but the treatment of coupling between heavy quark and medium are
different in their models.

41Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP
T-matrix approach
Several lattice QCD calculations have found indications that hadronicresonances (or bound state) of heavy quarks survive up to ∼ 2TC or morehigher temperature [72, 128, 129]. Refs. [124, 130] assume that heavy-lightquark (Qq̄ or Q̄q) resonance (D or B meson) persist as hadron in the QGP
and include this effect in the collisional energy loss. The formation of thoseresonance state is non-pertavative process. To solve this, a Brueckner-type
in-medium T-matrix approach for heavy-light quark scattering in the QGP
has been applied in Ref. [124].In this calculation, it is assumed that theeffective in-medium potential can be extracted from lattice QCD calculationsof the color-singlet free energy and two different calculation are used for this[131, 132]. Both of them are suppressed in high pT in T-matrix calculations
than in pQCD calculation [97].
DGLV theory
Recent calculations of radiative energy loss via gluon emission is describedin [133, 134], using the Djordjevic, Gyulassy, Vogt, and Wicks (DGLV) theory, which is extended from GLV reaction-operator method for light-parton
radiative energy loss in the QGP [135].
This model assumes an effectively static medium and the medium effectin this approach is characterized by two parameters: the gluon density ρ(τ )of the scattering centers (or the mean free path λg of the radiated gluon) andthe Debye screening mass µD which is introduced to regulate the infraredbehavior of single scattering cross section.
Figure 3.9 shows the c and b quark distributions at midrapidity before
fragmentation as well as decay electron (c → e and b → e) distribution from
Ref. [133]. Note in this calculation, only the energy loss by medium-induced
gluon radiation is taken into account.
g, which comes from theThose results depends on the gluon density dN
dyassumption: the medium is uniformly and cylindrically expanding, i.e ρ(τ ) ≈dNg
τ πR2 with R = 6 fm in central collisions.
dy
In Figure 3.9. the electron decay distributions, c → e and b → e, are seeng
to cross each other at pT ∼ 5.5 GeV/c when dN= 0 (no suppression), thedygcrossing point is reduced to pT ∼ 3GeV/c for dN= 3500.
dy42Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP
1

10

c
c
c
b
b
b

c
0

dσ/dydpT (µb/GeV)

10

−1

10

0
1000
3500
0
1000
3500

b
−2

10

−3

10

b→e
−4

c→e

10

−5

10

2

4

6

8

10

12

14

16

pT (GeV)Figure 3.9: The differential cross section (per nucleon pair) of charm (upperblue) and bottom (upper red) quarks calculated to NLO in QCD [8] comparedto single electron distributions calculated with the fragmentation and decay
scheme of Ref.[8]. The solid, dotted and long dashed curves show the effectof DGLV heavy quark quenching with initial rapidity densities of dNg /dy =0, 1000, and 3500, respectively. This figure is taken from [133].

3.5

Motivation of separating charm and bottom

As reviewed previous sections, heavy quarks (charm or bottom) are suitable probes to charactarize the property of the QGP. Although electrons fromheavy flavor from the admixture of charm and bottom and D meson havebeen measured in RHIC and those data indicate that heavy quarks stronglyinteract with the medium, the energy loss mechanism of heavy quarks is still
unclear.
The collisional and radiative energy loss can not be distiguished directlyin experiments. However, since the different models predict different energy
loss for charm and bottom quarks due to their large mass difference (mc ≈1.3 GeV, mb ≈ 4.7 GeV [3]), the charm and bottom separation in single
electron spectrum plays an important role to discriminate those models or
limit their model parameters which characterize the property of the QGP,
for example, gluon density in DGLV theory or diffusion constant of heavy
quarks in the Langevin-type approach.
43

Section CHAPTER 3. HEAVY QUARK AS A PROBE OF THE QGP
As described in section 3.3.6, the large difference of lifetime of charm
hadrons (cτD0 = 123 µm, cτD± = 312 µm) and bottom hadrons (cτB 0 = 455µm, cτB ± = 491 µm) are useful to separate charm and bottom contribution
in the single electron measurement. This feature brings us to develop the
Silicon Vertex Tracker (VTX) which enables precision displaced tracking witha resolution < 100 µm and install it in PHENIX.

44

Chapter 4
Experiment√
The data analyzed in this dissertation are Au+Au collisions at sN N =200 GeV collected at the RHIC with the PHENIX detector at Brookhaven
National Laboratory (BNL) in the year 2011. In this chapter the accelerator
complex (section 4.1) and the details of the PHENIX detector (section 4.2)
and its Data acquisition (DAQ) (section 4.3) are explained. After that, thedetail of new VTX detector are described (section 4.4).

4.1

Relativistic Heavy Ion Collider (RHIC)

The Relativistic Heavy Ion Collider (RHIC) is a superconducting hadroncollider located at Brookhaven National Lab (BNL) in Upton, New York.
In the RHIC, the Heavy Ion collision(Au+Au,d+Au,U+U,Cu+Au..etc.) as
well as polarized p+p collision experiment has been performed from the year
2000 [136]. Collisions are delivered to 6 interaction regions spread aroundthe ring, four of which are occupied by the experiments PHENIX, STAR,
PHOBOS, and BRAHMS. The PHOBOS and BRAHMS detectors completed
data taking in 2006 and PHENIX and STAR are currently taking data at
RHIC.
Table 4.1 shows the nuclear species,energies and integrated luminositythat RHIC delivered from 2000 to 2014. The analysis in this dissertation√
uses the data from Au+Au collisions at sN N = 200 GeV in data taking inyear 2011 (RUN11).
The layout of the facility is shown in Figure 4.1. The accelerator complex
consists from Tandem Van de Graaff, Booster Synchrotron (BS), Alternating
Gradient Synchrotron (AGS) and the RHIC.
The Au ions with negative charge (Au− ) originate from a pulsed sputter
ion source and are delivered to the Tandem Van de Graaff. The Au ions45Section CHAPTER 4. EXPERIMENT

Figure 4.1: Au ion pass through three accelerators (Tandem Van de Graaff,
AGS Booster, and AGS) and four charge-stripping stations to prepare thefully stripped Au ions for injection to the RHIC ring [9].
are partially stripped of their atomic electrons with a foil located inside theTandem’s high voltage terminal, and accelerated up to ∼ 1 MeV/nucleon.
After further stripping at the exit of the Tandem and charge selection bybending magnets, beams of Au ions with a charge state of Au+32 are delivered
to the Booster Synchrotron and accelerated to 95 MeV/nucleon. The ions
are stripped again at the exit from the Booster to reach a charge state of
Au+72 and injected to the AGS, where the Au ions are accelerated further
to 10.8 GeV/nucleon, which is the require injection energy for the RHIC.
Au ions, injected into the AGS in 24 bunches, are debunched and then rebunched to four bunches at the injection front porch prior to acceleration.
These four bunches are ejected at the top energy, one bunch at a time, andtransferred to RHIC through the AGS-to-RHIC Beam Transfer Line. The
final k-shell electrons are removed at the exit from the AGS and Au ions are
fully stripped to a charge state of Au+79 .
The RHIC ring consists of two quasi-circular concentric rings on a common horizontal plane, one (“Blue Ring”) for clockwise and the other (“Yellow Ring”) for counter-clockwise beams. The rings are oriented so that thecounter-rotating beams intersect with one another at six locations along their46

Section CHAPTER 4. EXPERIMENT
3.8 km circumference with equal distance from one to the next, and collide
head-on at intersections where detectors are located.
Table 4.1: Summary of data sets with collision species, collision energy, andintegrated luminosity delivered to PHENIX.
RHIC run(year)
1 (2000)
2 (2001/2)
3 (2002/3)
4 (2003/4)
5 (2005)
6 (2006)
7 (2007)
8 (2008)
9 (2009)10 (2010)
11 (2011)
12 (2012)

13 (2013)
14 (2014)
14 (2014)
15 (2015)

beamcollision energy integrated√sN N
luminosity
species
Au+Au
130 GeV
7 µb−1
Au+Au
200 GeV
93 µb−1p+p
200 GeV
0.35 pb−1
d+Au
200 GeV24.2 nb−1
p+p
200 GeV
2.0 pb−1
Au+Au
200 GeV1260 µb−1
p+p
200 GeV
3.0 pb−1
Cu+Cu
200 GeV15.2 nb−1
p+p
200 GeV12.6 pb−1
p+p
200 GeV43.6 pb−1
Au+Au
200 GeV
3270 µb−1
d+Au
200 GeV
238 nb−1
p+p
200 GeV19.2 pb−1
p+p
500 GeV57.8 pb−1
p+p
200 GeV60.7 pb−1
Au+Au
200 GeV5.01 nb−1
p+p
500 GeV89.9 pb−1
Au+Au
200 GeV
4.97 nb−1
p+p
200 GeV37.9 pb−1
p+p
510 GeV
133 pb−1
U+U
200 GeV368 µb−1
Cu+Au
200 GeV13.5 nb−1
p+p
510 GeV543 pb−1
Au+Au
200 GeV23.1 nb−1
3
He+Au
200 GeV72.3 nb−1
p+p
200 GeV196.7 pb−1
p+Au
200 GeV
0.63 pb−1
p+Al
200 GeV
2.37 pb−1∗ Low energy runs are omitted in this table.

47Section CHAPTER 4. EXPERIMENT

4.2

PHENIX experiment

The PHENIX experiment is the one of the large experiments being heldat RHIC. In this section, the overview of PHENIX and relevant detectors
used for this measurement are described.

4.2.1

Detector Overview

The PHENIX detector shown in Figure 4.2 was designed with precision
charged particle reconstruction combined with excellent lepton identification [137].
2011

PHENIX Detector
PC3
PC2

PbSc

PbSc

DC

PbSc

PbSc

DC
BBC

RICH

RICH

PbSc

PbGl

BB
MPC VTX
PC1

PbSc

PC1

7.9 m = 26 ft

TOF-W

PC3
TEC

CentralMagnetPbGl

Aerogel
TOF-E

West
RPC3

So
u

th

MuID

10.9 m = 36 ft

ZDC South

M

uo

nM

ag

ne

Beam View

East

Central Magnet

nM
uo

rth
No

t

M

t
ne
ag

RPC3

MPC
BBC
ZDC North
MuID

VTX
MuTr

South

Side View

North

18.5 m = 60 ft

Figure 4.2: A schematic view of the PHENIX detector configuration for the2011 run. Top figure is from beam stream at z = 0 and bottom figure is fromthe perpendicular to the beam stream.

48

Section CHAPTER 4. EXPERIMENT

Figure 4.3: PHENIX global coordinate system.
Figure 4.3 shows the global coordinate system used in PHENIX. The zaxis is along with the beam direction, x-axis and y-axis are pointing to thecenter of west central arm and vertical top respectively. The rapidity, y, ofa particle is defined as:
1 E + pzln,
2 E − pz
where E and pz are energy and z component of momentum, respectively.
The pseudorapidity, η, of a particle is defined as:y=η=

1 1 + cos θln,
2 1 − cos θ

where θ is the polar angle in Figure 4.3. If the mass of the particle can beignored with respective to momentum of the particle, η ≈ y. The pseudorapidity is often used instead of θ in high energy experiment.
The PHENIX detector comprises four spectrometers: two central arms
at midrapidity (−0.35 < η < 0.35) and two muon arms at forward rapidity(−2.2 < η < −1.2 and 1.2 < η < 2.4). The central arm consists of a number of subsystems and those detectors are optimized for detecting electrons,49Section CHAPTER 4. EXPERIMENT
hadrons and photons. A schematic view of the each subsystems is shown in
Figure 4.2. In December 2010, the VTX was installed near the collision point
as shown in Figure 4.2, which enables micro-vertexing capabilities.

4.2.2

Beam-Beam Counter and trigger

Figure 4.4: (Left) A picture of Beam-Beam counters module comprising 64
Čerenkov counters. (Right) A picture of quartz radiator and PMT.
The beam-beam counters (BBC) covering pseudorapidity 3.0 < |η| < 3.9
and full azimuth are located at ± 1.44 meters along the beam axis and relative
to the nominal beam-beam collision point. Each of the BBCs comprises 64Čerenkov counters as shown in Figure 4.4.
Based on the coincidence of the BBCs, Au+Au collisions are selected via
an online Minimum Bias (MB) trigger, which requires at least two counterson each side of the BBC to be fired.
The MB sample covers 96 ± 3% of the total inelastic Au+Au cross section
with a |z-vertex| < 10 cm cut as determined by comparison with Monte
Carlo Glauber models [5, 138] in 2011. The BBCs also provide a measureof the collision position along the beam axis (z-vertex) determined by thetime-of-flight difference between hits in the two sets of BBC counters. The
systematics shift of z-vertex position of BBC with respect to the central arm(∼ 5 cm) was observed during the 2011 run and it was adjust by z-vertex
provided from VTX. The z-vertex resolution of the BBC is approximatelyσz = 0.6 cm in central Au+Au collisions.
During 2011, the pre-scale factor which prevails events of |z −vertex| < 12cm was set in the trigger algorithm to increase the number of events within
the VTX acceptance. ∼ 85% of all Au+Au collisions within that selection
were recorded by the PHENIX high-bandwidth data acquisition system.
50

Section CHAPTER 4. EXPERIMENT

4.2.3

Central arms

Electrons (e+ and e− ) are reconstructed using two central spectrometerarms as shown in Fig. 4.2, each of which covers the pseudorapidity range|η| < 0.35 and with azimuthal angle ∆φ = π/2. The detector configurationof the central arms is the same as in previous PHENIX Collaboration heavy
flavor electron publications [11, 94], but there was no He bags in 2011.
The transverse momentum of each charged particle is determined by its
bending radius in the magnetic field of central magnet system [139]. The
magnet consists of an outer and inner coil inside a steel yolk, generating ansymmetric axial magnetic field parallel to the beam axis. The field strength,
B, is 0.9 Tesla around the beam
pipe and gradually decrease along the radialR
position. The field integral B · dl is 1.15 (Tesla · m) at φ = 90◦ .
The central arms are easily moveable to allow access to detector components for commissioning and maintenance.
Charged particle tracks are reconstructed outside of an axial magnetic
field using layers of drift chamber (DCH) and multi-wire proportional pad
chambers (PC). The momentum resolution is σp /p ' 0.7% ⊕ 0.9% p (GeV).
Electron identification is performed by hits in a ring imaging Čerenkov
detector (RICH) and a confirming energy deposit in an electromagnetic
calorimeter (EMCal).

4.2.4

Drift Chamber

The Drift Chambers (DCH) are main tracking detectors in central arms.
DCHs are placed at the front of both the East and the West arms with aradius of 2.0 to 2.4 m far from the beam axis in a residual magnetic fieldwith a maximum of 0.06 Tesla[10]. Each DCH has a cylindrical shape with|z| ≤ 90 cm and π/2 azimuthal angle (φ) coverage as shown in Figure 4.5.
There are 6 types of wire modules stacked radially in each sector. They arecalled X1, U1, V1, X2, U2 and V2. Each module contains 4 sense planes
and 4 cathode planes forming wire cells with a 2 - 2.5 cm drift space in theφ direction. The X1 and X2 wire cells run in parallel to the beam axis tomeasure particle trajectories in r - φ. The U and V wires are tilted with
about 6◦ rotation with respect to the X wires, and measure the z-coordinateof the track.
Each of the X- and U,V-stereo cells contain 12 and 4 anode (sense) wires,
respectively. As a result, there are 40 drift cells in the DCH located at
different radii. The layout of wires within one DCH sector is shown in Figure
4.6. The stereo wires start in a sector on one side and end in a neighboring
sector on the other side of the DCH.
51

Section CHAPTER 4. EXPERIMENT

Figure 4.5: A schematic view of Drift Chameber
To reduce the single wire occupancy, the wires are electrically isolated
into two halves at the center of the DCH (z = 0) using kapton of 100 µm
thickness. Therefore, the DCH system has 6400 sense wire (40/2 wires/cell *80 cells/side * 2 sides/arm * 2 arms = 6400 wires). The DCH operates witha mixture of 50% Ar, 50% ethane gas and small fraction of alcohol.

4.2.5

Pad Chamber

The Pad Chambers (PC) provide the hit information in z-direction andthis is used with DCH hit information to reduce track ambiguities in highmultiplicity environment. The PCs consist of three individual layers of multiwire proportional chambers [10].
As shown in Figure 4.2, the first inner layer of the PC (PC1) are placed
between the DCH and the RICH in both the East and the West arms. The
second layer (PC2) is located behind the RICH in the West arm only. The
52

Section CHAPTER 4. EXPERIMENT

Figure 4.6: (Left) The layout of DCH wire position within one sector andinside the anode plane. (Right) Top view of the DCH stereo wire orientations.
third layer (PC3) is mounted in front of the EMCal The installed radii ofthese three PC layers correspond to 248, 419 and 490 cm from the beampipe, respectively.
Each PC contains a single plane of wires inside a gas volume bounded by
two cathode planes. One cathode is finely segmented into an array of pixels.
The charge induced on a number of pixels when a charged particle starts anavalanche on an anode wire, is read out through specially designed readout
electronics.
A special pad design was invented to archive a high pixel granularity andsmall readout channels. Figure 4.7 (left) shows the pixel configuration ofa pad. The nine by nine interleaved pixels are grouped together to form
single readout channel. Each cell recognizes a valid hit and contains threepixels which are connected to different but neighboring pads shown in Figure
4.7 (right). So, the hit information can be broken down to the cell level byidentifying the triplets of the pads. The cell size is 8.4 mm for the PC1 andPC2 , and is twice for the PC3, since the PC3 is twice far from the beam
pipe compared to the PC1. The spacial resolutions of the PC1 and PC3 inz direction is ± 1.7 mm and ±3.6 mm, respectively.

53Section CHAPTER 4. EXPERIMENT

Figure 4.7: The pad and pixel geometry in the pad chamber. A cell definedby three pixels is at the center of the right picture.

4.2.6

Ring Imaging Čherenkov Detector

The Ring Imaging Čerenkov detector (RICH) [10, 140] is a gas Čerenkov
detector and is a primary device for identifying electrons among the very large
number of charged hadrons (O(1000) times larger than electrons). The RICH
is placed behind the PC1 in both the East and the West arms. Figure 4.8
shows a cutaway view of the RICH. The RICH consists of a 40 m3 gas vessel
with an entrance and exit windows of the aluminized Kapton, 48 composite
mirror panels, forming two intersecting spherical mirrors and two arrays of
80(φ) × 16(z) photo multiplier tubes (PMT). A PMT array is placed behindthe central magnet so that particles from the collision do not directly hit
the PMT array as shown in Figure 4.9. The PMTs are equipped with 2
inch diameter Winston cones and have magnetic shields that allow themto operate at up to 100 Gauss. The spherical mirror reflects the Čerenkov
photons emitted from an electron and focuses on the PMT array forming aring-shaped pattern. The diameter of the Čerenkov ring which corresponds
the emission angle of the Čerenkov photon. The vessel is filled with CO2 gas
at 1 atm as Čerenkov radiator. This corresponds to Čerenkov threshold of
4.65 GeV/c for pion and produces an average of 12 photons per ring for acompletely relativistic particle. The diameter of CO2 gas is about 11.8 cm.

54

Section CHAPTER 4. EXPERIMENT

Figure 4.8: A cutaway view of one arm of the RICH detector [10].

Figure 4.9: Top view of the RICH in the PHENIX east arm [11].

55Section CHAPTER 4. EXPERIMENT

4.2.7

Electromagnetic Calorimeter
Front
Wavelength
shifting fibers

ModuleLayers of lead andscintillator tiles(sampling cells)

TowersPhototubes
attached here

Back

Figure 4.10: Schematic view of a Pb-scintillator (PbCc) module
The electromagnetic calorimeter (EMCal) [141] is used to measure thespatial position and energy of electrons and photons produced in heavy ion
collisions. The EMCal is located at the most outside of the central arm. The
EMCal consists of two different detector systems. One is a Pb-Scintillator
calorimeter (PbSc, Figure 4.10) which provides 4 and 2 sectors for the Westand East arms, and the other is Pb-Glass calorimeter (PbGl, Figure 4.11)
which occupies 2 lower sectors of the East arm. The location of the PbSc
and the PbGl calorimeters are shown in Figure 4.2.
The PbSc is a shashlik type sampling calorimeter made of alternatingtiles of Pb and scintillator and consists 15552 individual towers. Each PbSc
tower contains 66 sampling cells (55 × 55 × 375 mm3 ) and has a thickness of
18 radiation length (X0 ) and about 30 mm of Molie’re radius. These cells are
optically connected 36 longitudinally penetrating wavelength shifting fibers
for light collection. Light is readout by 30 mm PMT (FEU115M) at the back56

Section CHAPTER 4. EXPERIMENT

Figure 4.11: Schematic view of a Pb-glass (PbGl) moduleof the towers. A single basic structure is called as a module which consistsof 4 towers. On the other hand, the PbGl is Cerenkov calorimeter which
consists of 9216 lead glass modules with PMT readout (FEU84). Each PbGl
module is 40 ×40 × 400mm3 and has 14.4 X0 and 36 mm of Molie’re radius.
The PbGl has been used previously in CERN WA98 experiment [142]. Figure
4.10 shows an unit array of the PbGl modules. The EMCal has an importantrole in particle identification using the informations of measured energy, timeand shower shape of electromagnetic cascade. The energy resolutions of the
PbSc and the PbGl are obtained using electron and positron beam at a test
experiment for the PbSc and the PbGl respectively:
8.1%
σE
=p
⊕ 2.1%
E P bscE (GeV)σE
5.9%=p⊕ 0.8%
E P bGlE (GeV)57

Section CHAPTER 4. EXPERIMENT

Data Acquisition

GL1

GTM

ut
So
C
ZD

Data packets
over fiber~350000 ch
Shield Wall

Missing:• ARCNET Serial Interface to FEMs
• High and Low Voltage Control andassociated control systems• Alarm system

MTM

RHIC clocks

DCM

Data Packets
over Parallel
FIFO InterfaceD
ov atapa er Pa
ss NE ck
in V etg
Bu I S ss To
kenPartitioner
DCB

FEM

Clock

RHIC
Computing
Facility
End
User

Busy

Clock, Trigger,
Mode bits
over fiberhA(e S u.g bs.E y
as ste
tD m
C
)

ZD

C

N

L1

or
th

TriggerCountingrooma few miles later'trigger' is a placeholder
for a much more complex'Local Level 1' trigger system

Interaction region

Busy

4.3

GL1 Global Level 1 Trigger
GTM Granual Timing Module
MTM Master Timing Module
DCB Data Collection Board
DCM Data Collection Module
FEM Front End Module
SEB Sub Event Buffer
ATP Assembly Trigger Processor

OnlineMonitoring

SEB
SEB
SEB
SEB
ATM Switch
ATP

Linux Farm
~600 CPU's

tapestorage
1.2PB

20MB/s
250TB/yr

Figure 4.12: A schematic diagram of the PHENIX Data Acquisition system.
The number of tracks passed through the detector varies from only a few
tracks in p+p to several hundred tracks in central Au+Au collisions. The
expected interaction rate also varies from a few kHz from central Au+Au
to approximately 500 kHz for p+p collisions. To handle a variety of event
size and rate seamlessly, the PHENIX Data Acquisition system (DAQ) [143]consists of the detector front ends equipped with the pipelined and deadtimeless features and higher level trigger systems. Figure 4.12 shows a general schematic diagram of the PHENIX DAQ. The RHIC delivers the 9.4
MHz fundamental clock which corresponds to 106 ns of time interval between beam crossings. All of PHENIX Front End Electronics modules aresynchronized to the RHIC clock. Signals produced in the various subsystems
are processed by Front End Modules (FEMs) that converts the detector analog signals into digital data. The FEM for each subsystem is placed in the
PHENIX Intersection Region (IR). A FEM module can buffer the data to
wait for the Level-1 trigger LVL1 decisions and to wait for digitization andreadout of triggered event. The RHIC clock is received by the Master Timing
Module (module). The MTM distributes the master clock by fanning out the
RHIC clock, where the internal phase locked loop is used to minimize theclock jitter. The master clock is transmitted to the FEM via the Granual58Section CHAPTER 4. EXPERIMENT
Timing Module (GTM). Thus, all the FEM’s are processed in a single clock.
The GTM is prepared for a unit of detector elements. In addition, the GTM
send the control commands (mode bits) and trigger decisions. The purposeof the Level-1 trigger (LVL1) is to select interesting events and provide event
rejection for the limited DAQ rate. The Global Level-1 (GL1) system generates the LVL1 decision based on logical combinations of the Local Level-1(LL1) decisions. The LL1 is generated by individual trigger detector. The
GL1 can treat totally 128 bits of the LL1 inputs to make the LVL1 decision.
Once the LVL1 decision is generated, the decision signal is sent to the FEM
via the GTM, then the data buffered in the FEM are transfered to the Data
Collection Module (DCM) located at the PHENIX Counting House. The
FEM, GTM and DCM are connected via a fiber optic cable to eliminate alarge number of noise, cross-talk and grounding problems. At the maximum
LVL1 trigger rate, the whole FEM’s send over 100 Gbytes of data per second.
The DCM is designed to receive this large amount of data. After receiving
the data, the DCM performs the zero suppression, error checking and data
formatting to generate data packets. The zero suppression is to compress thedata by comparing the preset threshold. In addition, the DCM provides abusy signal which are returned to the GL1 to hold off further triggers. Many
parallel streams of the data packets from the DCMs are sent to the event
builder (EVB). The EVB performs the final stage of event assembly.In the
EVB, the streams of the data packets from the DCMs are first received andbuffered in a set of the Sub Event Buffers (SEB). These data are transfered
on request to a set of Assembly/Trigger Processors (ATP) via AsynchronousTransfer Mode switch (ATM). The final events assembled in the ATPs aretransmitted to the PHENIX Online Control System (ONCS) for logging andmonitoring processes. The format of the final event is called “PHENIX Raw
Data Format (PRDF)”. The raw data are sent to High Performance Storage System (HPSS) at RHIC Computing Facility (RCF) and converted tophysical quantities for analysis.

59Section CHAPTER 4. EXPERIMENT

4.4

Silicon Vertex Tracker Upgrade

Silicon Vertex Tracker (Silicon Vertex Tracker (subsystem of PHENIX)(VTX)) is used for pricise collision vertex (primary vertex) in 3 dimensional
space as well as displaced track measurement. The detail of VTX detector
is described in this section.

Figure 4.13: (Left) A picture of the one side of the VTX detector. (Right)
A schematic view of the VTX detector from beam steam with the individual
ladders shown.
The (VTX) (Figure 4.13 (left) was installed near the collision point asshown in Figure 4.2 in December 2010. In addition, a new beryllium beam
pipe with 2.16 cm inner diameter and 760 µm nominal thickness (0.24 % radiation length (X0 )) was installed to reduce conversion electrons and multiplescattering before the VTX detector.
The VTX detector [28, 144, 145] consists of four cylindrical layers ofsilicon detectors as shown in Figure 4.13 (right). The detector is separated
into west and east arms, each with nominal acceptance ∆φ ≈ 0.8π centeredon the acceptance of the outer PHENIX central arm spectrometers. The
detector covers pseudorapidity |η| < 1.2 for collisions taking place at z = 0.
The VTX can precisely measure the vertex position of a collision within|z| < 10 cm range of the center of the VTX. The main characteristics of the
VTX detector are summarized in Table 4.3.
The two inner layers, referred to as B0 and B1, of the VTX detector comprise silicon pixel detectors [146]. B0 (B1) comprises 10 (20) pixel ladders(Figure 4.16) with a central radial position of 2.6 (5.1) cm. The silicon pixel
60Section CHAPTER 4. EXPERIMENT

Table 4.3: A summary of the VTX detector. For each layer (B0 to B3),
the detector type, read out chip, the central radius (r), ladder length (l),sensor thickness (t), sensor active area (∆φ × ∆z), the number of sensors
per ladder (NS ), the number of ladders (NL ), pixel/strip size in φ (∆φ) andz (∆z), the number of read-out channels (Nch ), and the average radiation
length including the support and on-board electronics (X0 ) are given.
Layer
B0
B1
B2
B3
read out chip
ALICE1LHCb ALICE1LHCb
SVX4
SVX4
type
pixel
pixel
stripixel stripixelr (cm)
2.6
5.1
11.8
16.7
sensor areal (cm)
22.8
22.8
31.8
38.2
t (µ m)
200
200
625
625
∆φ (cm)
1.28
1.28
3.07
3.07
∆z (cm)
5.56
5.56
6.00
6.00
NS
4
4
5
6
NL
10
20
16
24
pixel/strip size ∆φ (cm)
50
50
80
80
4
∆z (cm)425 (625)425 (625)
3 × 103 × 104665Nch
1.3 × 10
2.6 × 10
1.2 × 10 2.2 × 105
X0 (%)
1.3
1.3
5.2
5.2
technology is based on the ALICE1LHCb sensor-readout chip [147], which
was developed at CERN. Each ladder is electrically divided into two independent half-ladders. Each ladder comprises four sensor modules mounted
on a mechanical support made from carbon-fiber composite.
As shown in Figure 4.14, each sensor module comprises a silicon pixel
sensor with a pixel size of 50 µm(φ) × 425 µm(z). In the region between two
chips, the pixel sensor cells are elongated in z (625 µm instead of 425 µm)
to eliminate the dead area between chips. The silicon sensors are produced
as p-in-n structures on 200 µm thick silicon. One pixel readout chip reads
256 (φ)× 32 (z)= 8192 pixels and covers approximately 1.3 cm (∆φ)× 1.4
cm (∆z) of the active area of the sensor. The number of pixels in total is8192 (pixels/chip) × 4 (chips/sensor) × 4 (sensors/ladder) × 30 (ladders) =3932160. The position resolution is σφ = 14.4 µm in the azimuthal directionand σz = 123 µm in the z direction. The typical operation bias voltage is
30 V.
Each pixel is interconnected with four pixel readout chips by bumpbonding technique, which connect electrical structures with small balls ofsolder. Figure 4.15 shows the schematic of the circuitry within one pixel
61Section CHAPTER 4. EXPERIMENT

Figure 4.14: schematic view of a pixel sensor
cell in the ALICE1LHCb chip. Each readout chip has 32 × 256 amplifierdiscriminators for individual channel and the binary output of the discriminator is delayed with a programmable delay and stored for readout by thedownstream data acquisition system (DAQ). When the readout is issued,
the data is transferred to Silicon Pixel Interface Read-Out (SPIRO) module
through the readout bus mounted on the sensor module (Figure 4.16 (bottom)). The readout bus is manufactured using flexible printed circuit (FPC)
board technology [148]. The bus consists of four 3µ m copper signal layers
and two 50 µm aluminum power layers (power and ground). The structural
material for the bus is Polyimide. SPIRO module provides all service voltages, timing and control signal, reads out the data from pixel ladder andtransfer it to the front end module (FEM) via optical cable.

62Section CHAPTER 4. EXPERIMENT

Figure 4.15: A schematic of the circuitry within one pixel cell in the ALICE1LHCb sensor-readout chip. Reprinted from [147] with permission from
Elsevier.

Figure 4.16: (Top) A picture of a pixel ladder. (Bottom) Schematic view ofa pixel ladder.

63

Section CHAPTER 4. EXPERIMENTThe two outer layers of the VTX detector, referred to as B2 and B3, areconstructed using silicon stripixel sensors, as detailed in Ref. [149, 150]. The
B2 (B3) layer comprises 16 (24) silicon stripixel ladders at a central radial
distance of 11.8 (16.7) cm. The stripixel sensor is a novel silicon sensor,
and is a single-sided, N-type, DC-coupled, two-dimensional (2-D) sensitive
detector. One sensor has an active area of approximately 30 mm × 60 mm,
which is divided into two independent sectors of 30 mm × 30 mm. Eachsector is divided into 384 × 30 pixels. Each pixel has an effective size of
80 µm (φ) × 1000 µm (z), leading to a position resolution of σφ =23 µm in
azimuthal direction.

Figure 4.17: (Left) A picture of a stripixel detector. (Right) Schematic viewof a stripixel with two independent interleaved a-pixel (blue) and b-pixel (red)[151].

Figure 4.18: (Left) X strips formed by a-pixels. (Right) U strips formed byb-pixels. These figures are from [151].
As shown in Figure 4.17, a pixel comprises two spiral shape implants(a-pixel and b-pixel) interleaved such that the charge deposited by ionizing
64Section CHAPTER 4. EXPERIMENT
particles are registered by both implants. There are 30 a-pixel implants along
the beam direction, connected to form a 30 mm long X-strip, and 30 b-pixel
implants are connected with a stereo angle of 80 mrad to form a U-strip.
X-strip and U-strip are visualized in Figure 4.18. When a charged particle
hits a pixel, both the X- and the U-strip sharing the pixel register a hit.
Thus the hit pixel is determined as the intersection of the two strips. This
design allows to simplify fabrication process for both the sensor and readout
compared with that for the double-sided strip sensor.

Figure 4.19: Conceptual schematic of a single SVX4 channel circuit [152].
c 2004 IEEE.
The stripixel sensor is read out with the SVX4 chip developed by a FNALLBNL Collaboration [153]. The stripixel sensor and each SVX4 channel are
DC-coupled. It contains 128 parallel charge integration channels, a 128 ×
46-cell analog latency pipeline capable of buffering up to 4 samples, andWilkinson type 8 bit analog to digital converters (ADCs). ADCs information
are used as weighting factor of hit information for clustering (subsection 5.4.2)
as well as dE/dx measurement. Figure 4.19 shows the conceptual schematicof a single SVX4 channel circuit.
The total number of channels in stripixel layers is 128 (channels/chip) ×
12 (chips/sensor) × (5 (sensors/ladder) × 16 (ladders/B2 layer) + 6 (sensors/ladder) × 24 (ladders/B3 layer) = 344064. The typical operation bias
voltage is 200 V.

65Section CHAPTER 4. EXPERIMENT
The detector occupancy for the central Au+Au at 200 GeV is studied byusing geant3 [154] model of the VTX detector and the HIJING [155] event
generator. The result of the simulation is summarized in the Table 4.4.
Table 4.4: Occupancy of the each VTX layer for central Au+Au collisions
at 200 GeV
Layer
Occupancy
B0
0.53%
B1
0.16%
B2
4.5% (X strip) 4.7% (U strip)
B3
2.5% (X strip) 2.7% (U strip)

66

Chapter 5
Analysis
5.1

Overview

The purpose of the analysis is to separate the electrons from charm hadron
decays and those from bottom hadron decays. The life time of B mesons(cτB 0 = 455 µm, cτB ± = 491 µm [3]) is substantially longer than that of D
mesons (cτD0 = 123 µm, cτD± = 312 µm) and the decay kinematics aredifferent. This means that the distribution of values for the distance of
closest approach (DCA) of the track to the collision vertex (primary vertex)
for electrons from bottom decays will be broader than that of electrons fromcharm decays. Thus c → e, b → e can be separated via precise measurementof the DCA distribution and pT distribution. There are other sources ofelectrons, namely Dalitz decays of π 0 and η, direct virtual photon, photon
conversions in the material, Ke3 decays, and J/ψ → e+ e− decays. With the
exception of electrons from Ke3 decays, these background components have
DCA distributions narrower than those from charm decay electrons. Thesebackground components are subtracted before the charm/bottom separation.
In the first step of the analysis, good events where the collision vertex iswithin the acceptance of the VTX detector are selected, and its function isnormal (section 5.5). Then electron tracks are reconstructed in the PHENIX
central arms (section 5.4.4). They are then associated with hits in the VTX
detector and their DCA is measured (section 5.6). At this point, the DCA
distribution of inclusive electrons has contributions from heavy flavor electrons (b → e and c → e) and several background components.
The next step is to determine the DCA shape and normalization of all
background components (section 5.7). They include mis-identified hadrons,
background electrons with large DCA caused by high-multiplicity effects,
photonic electrons (Dalitz decay electrons, photon conversions), and elec-

67Section CHAPTER 5. ANALYSIS
trons from Ke3 and quarkonia decays. The shapes of the DCA distributionsof the various background electrons are determined via data driven methods
or Monte Carlo simulation (DCA cocktail method). Then the normalizationof those background electron components in the data is determined (section 5.8).
Because the amount of the VTX detector material is substantial (13% of
one radiation length) the largest source of background electrons is photon
conversion within the VTX. This background is suppressed by a conversion
veto cut (section 5.7.4)
Once the shape and the normalization of all background components are
determined and subtracted, the DCA distribution of heavy flavor decay electrons can be described as a sum of b → e and c → e DCA distributions.
The heavy flavor DCA distribution is decomposed by an unfolding method(section 5.9).

5.2

Track reconstruction in Central arms

Charged particle tracks are reconstructed using the outer central arm
detectors, DCH and PC [94]. The DCH has six types of wire modules stacked
radially, named X1, U1, V1, X2, U2, and V2 (see subsection 4.2.4). The X
wires run parallel to the beam axis in order to measure the φ-coordinateof the track and the U and V wires have stereo angles varying from 5.4 to
6.0 degrees. Tracks are required to have hits in both the X1 and X2 sections
along with uniquely associated hits in the U or V stereo wires and at least one
matching PC hit, to reduce mis-reconstructed tracks. The track momentum
vector is determined assuming the particle originated at the Au+Au collisionvertex as reconstructed by the BBC. The incident angle of the incoming trackat a reference radius within the DCH, α, is a measure of the momentum vector
and charge of the particle, as shown in Figure 5.1.

5.3

Electron identification

Electron candidates are selected by matching tracks with hits in the RICH
and energy clusters in the EMCal. The details on the electron selection cuts
are given in Ref. [11]. In this analysis we select electron candidates within
1.0 < pT < 5.0 GeV/c , and we briefly describe the cuts in the RICH and
EMCal below.
Čerenkov photons from an electron track produce a ring-shaped cluster inthe RICH. At least three associated PMT hits are required in the RICH and

68

Section CHAPTER 5. ANALYSIS

Figure 5.1: Charged particle momentum vector reconstruction using DCH
hit information [12].
a ring-shape cut is applied. The center of the ring is required to be within
5 cm of the track projection. The probability that the associated clusterin the EMCal comes from an electromagnetic shower is calculated based on
the shower shape. Based on that probability, tracks are selected in a waythat maintains high efficiency for electrons while rejecting hadrons. Further,
the energy (E) in the EMCal is required to match the track determined
momentum (p). This match is calculated as dep = (E/p − µE/p )/σE/p , whereµE/p and σE/p are the mean and standard deviation respectively of a Gaussian
fit to the E/p distribution, determined as a function of momentum as shownin Figure 5.2. A cut of dep > −2 is used to further reject hadrons that havean E/p ratio < 1, because they do not deposit their full energy in the EMCal.
In high-multiplicity Au+Au events there is a significant probability fora random association between the track and hits in the RICH and EMCal.
This mis-identified hadron probability is estimated as follows. The z < 0and z > 0 sides of the RICH have their hits swapped in software, and thetracks are re-associated with RICH hits. Because the two longitudinal sidesof the RICH are identical, this gives a good estimate of the random hadronbackground in the electron sample.
69Section CHAPTER 5. ANALYSIS

dep 1.0 < p < 1.5 GeV/c

dep 1.5 < p < 2.0 GeV/c

dep 2.0 < p < 2.5 GeV/ccountscountscountsThe distribution of electron candidates at pT = 1.0 – 5.0 GeV/c for thenormalized EMCal energy to track momentum ratio, dep defined above, isshown in Figure 5.2. There is a large peak near zero from true electrons as
expected and a clear low-side tail from mis-identified hadron. Also shownis the result of the above swap method. The difference between the data
(black) and the “swap” distribution (red) is explained as contributions from
off-vertex electrons caused by conversions from the outer layer of the VTX
and weak decay of kaon. In the final accounting for all contributions to theidentified-electron DCA distribution, we utilize this swap method to statistically estimate the contribution of mis-identified hadron in each pT selection
as detailed in Section 5.7.2.

7000

1600

T

T

T

9000

45000

2000

8000

1800

40000
35000

1400

6000

30000

1200
5000

25000

1000
20000

4000

15000

3000

10000

2000

5000

1000

800

0

-1

0

1

2

0

3
4
dep (σ )

-4

200

-3

-2

-1

0

1

2

0

3
4
dep (σ )

-4

-3

-2

-1

0

dep 2.5 < p < 3.0 GeV/c

dep 3.0 < p < 4.0 GeV/c

dep 4.0 < p < 5.0 GeV/ccounts-2

counts-3400

counts

-4

600

T

T

1

2

3
4
dep (σ )12

3
4
dep (σ )

T

300

60

500
250
50
400

200
40

300

150
30

200

100

100

0

-4

20

50

-3

-2

-1

0

1

2

3
4
dep (σ )

0

-4

10

-3

-2

-1

0

1

2

3
4
dep (σ )

0

-4

-3

-2

-1

0

Figure 5.2: Matching variable between the reconstructed track momentum(p) and the energy measured in the EMCal (E): dep = (E/p − µE/p )/σE/pin 5 pT bins. The black distribution is for identified electrons , the red
distribution is the estimated contribution from mis-identified electrons via
the RICH swap-method, and the green distribution is for electrons after thesubtraction of mis-identified electrons.

70Section CHAPTER 5. ANALYSIS

5.4

Event reconstruction in VTX

5.4.1

VTX alignment

In order to achieve good DCA resolution to separate b → e and c → e,alignment of the detector ladders to high precision is required. The detectoralignment is accomplished via an iterative procedure of matching outer central arm tracks from the DCH and PC to the VTX hits. (See appendix B
for more detail.) The procedure is convergent for the position of each ladder.
The alignment was repeated each time the detector was repositioned following a service access. The final alignment contribution to the DCA resolution
in both φ and z is a few tens of microns.

5.4.2

VTX hit reconstruction

For layers B0 and B1, clusters of hit pixels are formed by connecting
contiguous hit pixels by a recursive clustering algorithm. An average cluster
size is 2.6 (6.7) pixels for the pixel (stripixel). The center of the cluster in thelocal 2-D coordinate system of the sensor is calculated as the hit position.
For B2 and B3 layers, 2D hit points on the sensor are reconstructed fromthe X-view and the U-view. Hit lines in the X-view (U-view) are formed byclustering contiguous hit X-strips (U-strips) weighted by deposited charges,
and then 2D hit points are formed as the intersections of all hit lines in Xand U- views. When one hit line in U-view crosses more than two hit lines
in X-view, ghost hits can be formed, because which crossing point is thetrue hit is ambiguous. These ghost hits increase the number of reconstructed
2D hits approximately by 50% (30%) in B2 (B3) in central Au+Au collisions. The ghost hit rate was studied using a full geant simulation with the
HIJING [155] generator as input. However, because the occupancy of thedetector at the reconstructed 2D hit point level is low, less than 0.1%, theseghost hits do not cause any significant issue in the analysis.
The positions of all 2-D hits in the VTX are then transferred into theglobal PHENIX 3-D coordinate system. Correction of the sensor position andorientation, determined by the alignment procedure described in the previous
section, is applied in the coordinate transformation. The resulting 3-D hit
positions in the global coordinate system are then used in the subsequent
analysis.

71Section CHAPTER 5. ANALYSIS

5.4.3

The primary vertex reconstruction

With the VTX hit information alone, charged particle tracks can be reconstructed only with modest momentum resolution δp/p ≈ 10% due to thelimited magnetic field integrated over the VTX volume and the multiple
scattering within the VTX. These tracks can be utilized to determine thecollision vertex in three-dimensions (z0 along the beam axis, and x0 ,y0 in thetransverse plane) for each Au+Au event under the safe assumption that the
majority of particles originate at the collision vertex. This vertex position iscalled the primary vertex position.
The position resolution of the primary vertex for each direction depends
on the sensor pixel and strip sizes, the precision of the detector alignment,
and the number of particles used for the primary vertex calculation and their
momentum in each event. The primary vertex resolution is evaluated fromthe difference in the primary vertex calculated from by the EAST and WEST
VTX barrels. The distributions for the EAST - WEST difference in x, y andz-axis is shown in Figure 5.3. The width of the distributions of the East West difference is larger than the resolution of the primary√vertex calculatedusing the full VTX by roughly a factor of 2. A factor of 1/ 2 comes from theassumption √the multiplicity of East/West VTX is half of full VTX, anotherfactor of 1/ 2 comes from the error propagation of East-West. Namely,
1
σ(East) = σ(West) = √ σ(full VTX),2pσ(East - West) = σ(East)2 + σ(West)2 = 2 × σ(full VTX)For Minimum Bias (MB) Au+Au collisions, the resolution values are σx =96 µm, σy = 43 µm, and σz = 75 µm. The worse resolution in x compared toy is due to the orientation of the two VTX arms. For comparison, the beamprofile in the transverse plane is σxlumi ≈ σylumi ≈ 90 µm in the 2011 Au+Au
run.

5.4.4

Association of a central arm track with VTX

Each central arm track is projected from the DCH through the magnetic
field to the VTX detector. Hits in VTX are then associated with the trackusing a recursive windowing algorithm as follows.
The association starts from layer B3. VTX hits in that layer that arewithin a certain (∆φ×∆z) window around the track projection are searched.
If hits are found in this window, the track is connected to each of the foundhits, and then projected inward to the next layer. In this case the search
72Section CHAPTER 5. ANALYSIS

6000
2500

σfit = 192.5 [µm]σres = 96.2 [µm]σfit = 85.3 [µm]σres = 42.6 [µm]

5000

2000

σfit = 150.2 [µm]σres = 75.1 [µm]

3000

2500
4000
2000

1500
3000

1500
1000
2000
1000
500

1000

0
-0.3

-0.2

-0.1

0

0.1

0.2
0.3
East
West
X vertex - Xvertex

0
-0.3

500

-0.2

-0.1

0

0.1

0.2
0.3
East
West
Y vertex - Yvertex

0
-0.3

-0.2

-0.1

0

0.1

0.2
0.3
East
West
Z vertex - Zvertex

Figure 5.3: The distributions for the difference in the primary vertex calculated from by the East and West VTX barrels (East - West) in x, y andz-axiswindow in the next layer is decreased, because there is much less uncertainty
in projection to the next layer. If no hit is found, the layer is skipped, and thetrack is projected inward to the next layer, keeping the size of the projection
window. This process continues until the track reaches layer B0, and a chainof VTX hits that can be associated with the track is formed. The window
sizes are momentum dependent and determined from a full geant3 [154]simulation of the detector so that the inefficiency of track reconstruction due
to the window size is negligible.
After all possible chains of VTX hits that can be associated with a given
central arm track are found by the recursive algorithm, a track model fit(multi-helices) is performed for each of these possible chains as shown in
Figure 5.4 and Figure 5.5 and the χ2 of the fit, χ2vtx , is calculated. The effectof multiple scattering in each VTX layer is taken into account in calculationof χ2vtx This best chain and its track model are called a VTX-associated track.
Note that at most one VTX-associated track is formed from each central arm
track.
The detail of the calculation of χ2vtx is as follows:χ2vtx =
+

n−1
X
i=0
n−2
X
i=1

∆zi2
∆φ2i
+ 2
2
σφ,i
σz,i

!

2
2
∆θxy,i∆θrz,i+ 2σθ2xy ,iσθrz ,i!

22∆θxy,n−1∆θrz,n−1
+ 2
+ 2
2
2
σθxy ,n−1 + σphi0
σθrz ,n−1 + σthe0

where
73

Section CHAPTER 5. ANALYSIS• ∆φi (∆zi ): the difference of the hit position and the projected positionof hit in azimuthal (z) direction.
• ∆θxy,i (∆θrz,i ): the angle difference of the incoming and the outgoinghelices in x-y (r-z) plane.
All the indices, i, correspond to indices of the associated hits. The counting
begins from the innermost hit, i.e. 1st ((n − 1)-th) hit is the innermost(outermost) hit. σφ,i and σz,i are resolution of each pixel: σφ,0 (σφ,1 ) = 14 µm
and σz,0 (σz,1 ) = 123 µm, σφ,2 (σφ,3 ) = 23 µm and σz,2 (σz,3 ) = 289 µm. σθxy ,iand σθrz ,i is the root mean square of√ the Gaussian approximation of themultiple scattering angle divided by 2. The radiation length of each layer
is averaged and corrected by a path length in modules of each track. σphi0
and σthe0 correspond to the resolution of the azimuthal and polar angles of a
track outside of the VTX, respectively. σphi0 is calculated to be 1 mrad fromthe position resolutions of X1 and X2 of the DCH and the distance between
X1 and X2 plane. σthe0 is calculated to be 7 mrad from the resolution ofz coordinate measured by the PC1 and BBC [156]. The primary vertex
position is not used for the χ2vtx calculation to avoid any bias on the long
lived particle.
In this analysis we require that VTX-associated tracks have associatedhits in at least the first three layers, i.e. B0, B1, and B2. An additional track
requirement is χ2vtx /NDF < 2 for pT < 2 GeV/c and χ2vtx /NDF < 3 for pT> 2 GeV/c , where NDF is the number of degrees of freedom in the track fit,
namelyN DF = 2 · Nhit − 2,
where Nhit is the number of associated hits on the VTX.

74

Section CHAPTER 5. ANALYSIS

Figure 5.4: An illustration of a tracking with the VTX in x-y plane.

Figure 5.5: An illustration of a tracking with the VTX in r-z plane.

75Section CHAPTER 5. ANALYSIS

5.5

Event selection

The data set presented in this analysis is from Au+Au collisions at
sN N = 200 GeV recorded in 2011 after the commissioning of the VTX detector. As detailed earlier, the MB Au+Au data sample was recorded using
the BBC trigger sampling 96 ± 3% of the inelastic Au+Au cross section. A
number of offline cuts were applied for optimizing the detector acceptanceuniformity and data quality as described below. After all cuts, a data sample
of 2.4×109 Au+Au events was analyzed.
√

5.5.1

z-vertex selection

The acceptance of the PHENIX central arm spectrometers covers collisions with z-vertex within ± 30 cm of the nominal interaction point. The
VTX detector is more restricted in |z| acceptance, as the B0 and B1 layers
cover only |z| < 11.4 cm. Thus the BBC trigger selected only events within
the narrower vertex range of |zBBC | < 12 cm. In the offline reconstruction,
the tracks reconstructed from VTX information alone are used to reconstruct
the Au+Au collision vertex with resolution σz = 75 µm. All Au+Au eventsin the analysis are required to have a z-vertex within ±10 cm as reconstructedby the VTX.

5.5.2

Data quality assurance

Due to a number of detector commissioning issues in this first data taking
period for the VTX, the data quality varies substantially. Therefore we divide
the entire 2011 Au+Au data taking period into four periods. The acceptanceof the detector changes significantly between these periods.
In addition, several cuts are applied to ensure the quality and the stabilityof the data. Applying electron identification cuts described in section 5.3,
the electron to hadron ratios were checked for each run, a continuous datataking period typically lasting of order one hour, and three runs out of 547
with ratios outside of 5σ from the mean were discarded. The B2 and B3
stripixel layers had an issue in stability of read-out electronics where someof the sensor modules would drop out, resulting in a reduced acceptancewithin a given run. Additional instabilities also existed in the B0 and B1
pixel layers. Detailed channel by channel maps characterizing dead, hot, andunstable channels were generated for all layers within a given run. These
maps were used to mask dead, hot, and unstable channels from the analysis,
as well as to define the fiducial area of the VTX in simulations.

76

Section CHAPTER 5. ANALYSIS
During this first year of data taking, the instability of the read-out electronics discussed above caused significant run-to-run variations in the acceptance and efficiency of the detector. It is therefore not possible to reliably
calculate the absolute acceptance and efficiency correction while maintaining
a large fraction of the total data set statistics. Instead, we report on therelative yields of charm and bottom to total heavy flavor. The DCA distributions have been checked consistent between running periods and are notimpacted by the changing acceptance. Thus we can measure the shape of
the DCA distribution using the entire data set. In the following, we use theshape of the measured DCA distribution only to separate b → e and c → ecomponents.

77Section CHAPTER 5. ANALYSIS

5.6

DCA measurement with the VTX

Charged particle tracks reconstructed in the central arms must be associated with VTX hits in order to calculate their DCA. Three-dimensional (3-D)
hit positions in the 4 layers of VTX are reconstructed. For each collision,
the primary vertex is reconstructed by the VTX. Then central arm tracks
are associated with hits in the VTX, and VTX-associated tracks are formed.
Finally, the DCA between the primary vertex and the VTX-associated tracks
are measured.

5.6.1

DCAT and DCAL

Using the primary vertex position determined above, the DCA of a track
is calculated separately in the transverse plane (DCAT ) and along the beamaxis (DCAL ). Because by design the DCAT has a better resolution than
DCAL , we first find DCAT with a track model of a circle trajectory assuming
the uniform magnetic field over the VTX. We define DCAT as
DCAT ≡ L − R,

(5.1)

where L is the distance from the collision vertex to the center of the circle
defining the particle trajectory, and R is the radius of the circle as shownin Figure 5.6. DCAL is the distance between the z-coordinate of the point
DCAT found and z-coordinate of the primary vertex. As explained in thesubsection 5.4.4, we always require a hit in layer B0. The projection is always
started from the hit position in B0.
It is notable that DCAT has a sign in this definition. The distinction
between positive and negative values of DCAT —whether the trajectory is
bending towards or away from the primary vertex—is useful since certain
background contributions have asymmetric distributions in positive and negative DCAT , as discussed in section 5.7. For electrons, the positive sideof DCAT distribution has less background contribution. There is no such
positive/negative asymmetry in DCAL .

5.6.2

DCA distribution of hadron tracks

For each VTX-associated track, the DCA is calculated separately in theradial and longitudinal direction (DCAT and DCAL ) from the track modeland the primary vertex position. Shown in Figure 5.7 is the resulting DCAT
and DCAL distributions for all VTX-associated tracks with pT = 1.0 –5.0 GeV/c . Since the vast majority of charged tracks are hadrons originating
at the primary vertex, we observe a large peak around DCAT , DCAL = 078

Section CHAPTER 5. ANALYSIS

B0

magnetic fieldPrimary vertex

Figure 5.6: Illustration of the definition of DCAT ≡ L - R in the transverse
plane.
that is well fit to a Gaussian distribution where the σ represents the DCAT ,DCAL resolution. A selection of |DCAL | < 0.1 cm is applied to reduce
background. These DCA distributions are in integer-value counts and are
not corrected for acceptance and efficiency. There are broad tails for |DCAT| > 0.03 cm. Monte Carlo simulation shows that the main source of the broad
tails is the decay of long lived light hadrons such as Λ and KS0 .
The DCAT resolution as a function of the track pT is extracted using a
Gaussian fit to the peak and is shown in Figure 5.8. The DCAT resolution
is approximately 75 µm for the 1.0 – 1.5 GeV/c bin and decreases withincreasing pT as the effect of multiple scattering becomes smaller for higher
pT . The DCAT resolution becomes less than 60 µm for pT > 4 GeV/c , where
it is limited by the position resolution of the primary vertex.

79Section CHAPTER 5. ANALYSISAll Tracks MB : 1.0 < p < 1.5

All Tracks MB : 1.5 < p < 2.0

T

All Tracks MB : 2.0 < p < 2.5

T

T

10 7
10 7

10
10

10

6

10

10

10

6

6

5

5

10 4

5

10 4
10

3

10 4
10

−0.15

−0.1

−0.05

0

0.05

0.1
0.15
DCA T (cm)

All Tracks MB : 2.5 < p < 3.0

−0.05

0

0.05

0.1
0.15
DCA T (cm)

−0.1

−0.05

0

0.05

0.1
0.15
DCA T (cm)

0.05

0.1
0.15
DCA T (cm)

T

10

5

5

10 4

5

10

4

10 4

10

10
10

−0.15

All Tracks MB : 4.0 < p < 5.0

T

6

10
10

−0.1

All Tracks MB : 3.0 < p < 4.0

T

10

3

−0.15

3

3

3

10 2
10 2

10 2
10

−0.15

−0.1

−0.05

0

0.05

0.1
0.15
DCA T (cm)

All Tracks MB p : 1.0 < p < 1.5
T

−0.15

−0.1

−0.05

0

0.05

0.1
0.15
DCA T (cm)

All Tracks MB p : 1.5 < p < 2.0

T

T

−0.15

T

6

6

6

10

10

10

0

T

10

10

−0.05

All Tracks MB p : 2.0 < p < 2.5

T

10 7

10

−0.1

5

5

10 4

5

10

4

10

3

10 4

−0.15

−0.1

−0.05

0

0.05

0.1
0.15
DCA L (cm)

All Tracks MB p : 2.5 < p < 3.0
T

−0.15

−0.05

0

0.05

0.1
0.15
DCA L (cm)

All Tracks MB p : 3.0 < p < 4.0

T

T

10
10

−0.1

−0.15

−0.1

−0.05

0

0.05

0.1
0.15
DCA L (cm)

All Tracks MB p : 4.0 < p < 5.0

T

T

T

5

10 4

5

10 4
10

10 4

10
10

3

3

10 2

3

10 2
10

10 2

−0.15

−0.1

−0.05

0

0.05

0.1
0.15
DCA L (cm)

−0.15

−0.1

−0.05

0

0.05

0.1
0.15
DCA L (cm)

−0.15

−0.1

−0.05

0

0.05

0.1
0.15
DCA L (cm)Figure 5.7: (Top 6 figures) Distance of closest approach distributions fortransverse plane (DCAT ) and (Bottom 6 figures) along the beam axis (DCAL )√for all VTX-associated tracks in minimum bias Au+Au at sN N = 200 GeV
in the range 1.0 < pT < 5.0GeV/c .

80

DCAT σ [µm]Section CHAPTER 5. ANALYSIS

90

80

70

60

50

40

30

1

1.5

2

2.5

3

3.5

4

4.5

p [GeV/c]T

Figure 5.8:
eventsThe DCAT resolution as a function of pT for all tracks in MB

81Section CHAPTER 5. ANALYSIS

5.7

Electron DCA distribution and Background
Components

5.7.1

Overview

The sample of candidate electron tracks that pass all the analysis cuts
described above contains contributions from a number of sources other thanthe desired electrons from semi-leptonic decays of charm and bottom hadrons.
In order to extract the heavy flavor contributions, all background components
must be fully accounted for and their DCAT shapes as a function of pT
incorporated. These background components are listed in the order presented
below.
1. Misidentified hadrons
2. High-multiplicity background
3. Photonic electrons
4. Kaon decay electrons
5. Heavy-quarkonia decay electrons
As described in this and the following subsection, all background components are constrained by PHENIX measurements in Au+Au and are fully
simulated through a geant3 description of the detector. This method is similar to the cocktail method of background subtraction used in the previous
analysis of inclusive heavy flavor electrons [11].
Next, we describe these background sources and their DCA distributions.
The first two components are caused by detector and multiplicity effects.
DCA distributions and normalization of these two components are determined by data driven methods, as detailed in this section. The last threecomponents are background electrons that are not the result of semi-leptonic
decays of heavy flavor hadrons. Their DCA distributions are determined byMonte Carlo simulation, and their normalization is determined by a bootstrap method described in section 5.8. Of those background electrons, photonic electrons are the dominant contribution. We developed a conversion
veto cut to suppress this background (5.7.4).

5.7.2

Mis-identified hadron

As detailed in the discussion on electron identification, there is a nonzero
contribution from mis-identified electrons. This contribution is modeled via
82Section CHAPTER 5. ANALYSIS
the RICH swap-method described in Section 5.3. From this swap method, we
obtain the probability that a charged hadron is mis-identified as an electron
as a function of pT . This probability is then applied to the DCA distributionof charged hadrons to obtain the DCA distribution of mis-identified hadrons.
The resulting DCAT distribution is shown in each panel of Figure 5.13.
Note that this component is properly normalized automatically. For eachpT bin, the DCA distribution of mis-identified prompt hadrons has a narrow Gaussian peak at DCAT = 0. The broad tails for large |DCAT | aremainly caused by decays of Λ and KS0 . In all pT bins the magnitude of thisbackground is no more than 10% of the data for all DCAT

5.7.3

High-multiplicity backgroundDue to the high multiplicity in Au+Au collisions, an electron candidate
track in the central arms can be associated with random VTX hits. Suchrandom associations can cause a background that has a very broad DCAT
distribution. Although the total yield of this background is only ' 0.1% of
the data, its contribution is significant at large DCAT where we separateb → e and c → e.
To evaluate the effect of event multiplicity on the reconstruction performance, we embed simulated single electrons—i.e. the response of the
PHENIX detector to single electrons that is obtained from a geant3 simulation—
into data events containing VTX detector hits from real Au+Au collisions.
The events are then processed through the standard reconstruction softwareto evaluate the reconstruction performance in MB Au+Au collisions.
The reconstructed DCAT and DCAL for embedded primary electrons in
MB Au+Au collisions is shown in Fig. 5.9. Here the histograms, labeled as“Single Electrons", show the reconstructed DCAT and DCAL distributionsof primary electrons before embedding. The DCAT distribution comprises
a narrow Gaussian with no large DCAT tail and the DCAL distribution
comprises a similar, but slightly broader, Gaussian with no large tail. The
blue filled triangles show the DCAT and DCAL distributions after embedding. The DCAT and DCAL distributions comprise a Gaussian peaked at
DCAT (DCAL ) ∼ 0 which is consistent with the distribution before embedding. This demonstrates that the DCA resolution of the VTX is not affectedby the high multiplicity environment. However, the embedded distributions
have broad tails at large |DCAT | and |DCAL |.
As shown in Figure 5.9(b), tracks with |DCAL | > 0.13 cm are dominatedby random associations, as they are not present in the “Single Electron”
sample. We therefore use the DCAT distribution for tracks with large |DCAL |as an estimate of this random high-multiplicity background. We choose the83Section CHAPTER 5. ANALYSIS
region 0.13 < |DCAL | cm < 0.18 to represent this background, and restrict
our signal to |DCAL | < 0.1 cm. The DCAT distribution of tracks with
0.13 < |DCAL | cm < 0.18 must be normalized in order to be used as an
estimate of the high-multiplicity background for tracks within |DCAL | <0.1 cm. This normalization is determined by matching the integrated yieldof embedded primary electrons in each |DCAL | region for 0.08 < DCAT cm <0.2, as shown in the inlay of Figure 5.9(b). The region 0.08 < DCAT cm <0.2 is dominated by random associations, as shown in Fig. 5.9(a), and istherefore safe to use for determining the normalization. The normalizationof the high-multiplicity background is determined to be 2.89 ± 0.29. The
red filled circles in Fig. 5.9(a) show the embedded DCAT distribution withlarge DCAL (0.13 < |DCAL | cm < 0.18). This distribution agrees withthe embedded DCAT distribution (blue filled triangles in Fig. 5.9) for large
DCAT . This demonstrates that the tails for large DCAT are well normalized
by the distribution of electrons with large DCAL . However, there is a small
excess in the region 0.05 < |DCAT | cm < 0.10 that is not accounted for by
the distribution with large DCAL . We address this excess in the systematic
uncertainties, as described in section. 5.10, where it is found to have only asmall effect on the extraction of b → e and c → e.
In each panel of Figure 5.13 the high-multiplicity background is shown asa red line. It is determined from the DCAT distribution of the data within
0.13 < |DCAL | cm < 0.18, as described above. The number of electron tracks
in the large DCAL region is small. We therefore fit the resulting DCAT datain each pT bin with a smooth function to obtain the shape of the red curves
shown in Figure 5.13. A second order polynomial is used in the lowest pT bin,where there are enough statistics to constrain it. The higher pT bins are fit
with a constant value. All curves are multiplied by the same normalization
factor, determined from embedded simulations as described above.

84

Yield [a.u.]

Section CHAPTER 5. ANALYSISe
T

Single Electrons 2.0<p <2.5(a)Embedded: |DCA | < 0.1 cm

103

L

Embedded: 0.13 < |DCA | < 0.18 cm
L

102
10
1
10-1
10-2

Yield [a.u.]-0.15-0.1 -0.05

(b)

0

0.05

0.1 0.15
DCAT [cm]0.08 < DCAT < 0.2

104
10
3

10

102

1

0

10

0.05 0.1 0.15 0.2 0.25 0.3 0.35
|DCA | [cm]LSingle Electrons 2.0<pe <2.5
T

Embedded1

10-10 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
|DCA | [cm]L

Figure 5.9: Simulated primary electron (a) DCAT and (b) DCAL distribution before and after embedding in real Au+Au data.

85

Section CHAPTER 5. ANALYSIS

5.7.4

Photonic electrons and conversion veto cut

Photon conversions and Dalitz decays of light neutral mesons (π 0 and η)
are the largest electron background. We refer to this background as photonic
electron background as it is produced by external or internal conversion ofphotons.
The PHENIX Collaboration has previously published the yields of π 0 and√η mesons in Au+Au collisions at sN N = 200 GeV [157, 158]. In addition
to the electrons from Dalitz decays of these mesons, the decay photons may
convert to an e+ e− pair in the detector material in the beam pipe or eachlayer of the VTX. The PHENIX Collaboration has also published the yields√
of direct photons in Au+Au collisions at sN N = 200 GeV [20, 69], that canalso be a source for conversions.
In principle with these measured yields, combined with simple decay kinematics and a detailed geant3 description of the detector material and reconstruction algorithm, one could fully account for these photonic electron
contributions as a function of DCAT and pT . However, systematic uncertainties on the measured yields for the π 0 , η, and direct photons would thendominate the uncertainty of the heavy flavor electron extraction. Therefore,
we utilize the VTX detector itself to help reject these contributions in acontrolled manner.
We require that at least the first three layers of the VTX have hits associated with the electron track. Conversions in B1 and subsequent layers are
rejected by the requirement of a B0 hit, leaving only conversions in B0 andthe beam pipe. The requirement of B1 and B2 hits enables us to impose aconversion veto cut, described below, that suppresses conversions from thebeam pipe and B0.
The conversion veto cut rejects tracks with another VTX hit within acertain window in ∆φ and ∆z around hits associated with a VTX-associatedtrack. Photons that convert to an e+ e− pair in the beam pipe will leave two
nearby hits in the first layer (B0) and/or subsequent layers of the VTX, andthus be rejected by the conversion veto cut. Similarly, conversions in B0 will
result in two nearby hits in the second layer (B1) and/or subsequent outerlayers. The same is true for e+ e− from a Dalitz decay, though with a larger
separation due to a larger opening angle of the pair.
Figure 5.10 shows distribution of charge×∆φ of hits in each layer relative
to the electron track, where charge is the sign of charge of the track. The
red histogram shows the data in MB Au+Au collisions. If the track at theorigin is not an electron, we have a flat distribution due to random hits in thedetector. These random hits have been subtracted in Figure 5.10 by using
the distribution for hadron tracks. The transverse momentum of the electron
86Section CHAPTER 5. ANALYSIS
track is in the interval 1 < pT < 2 GeV/c .
As mentioned above, these correlated hits around electron tracks arecaused by the partner e+ or e− of Dalitz decays or photon conversions. The
left-right asymmetry of the distribution is caused by the fact that the partner
e± track is separated from the electron track by the magnetic field and the
direction of the separation is determined by the charge of the electron track.
In the distribution of charge × ∆φ, the partner track is bent towards the
positive direction.
The black histogram in Figure 5.10 shows the distribution from Monte
Carlo simulations. In the simulation, the response of the PHENIX detector
to single π 0 s is modeled by geant3, and the resulting hits in the VTX andthe central arms are then reconstructed by the same reconstruction code as
the data. The correlated hits in the simulation are caused by the Dalitz decayof π 0 and photon conversion in the material of the beam pipe and the VTX
itself. The simulation reproduces the data well for charge×∆φ > 0. There isa difference between the data and the simulation for charge × ∆φ < 0. Thisis caused by a subtle interplay between the conversions and high multiplicity
effects. The difference disappears for peripheral collisions. Similar correlated
hits are observed in B1 to B3 layers in the data and they are also well
explained by the simulation.
We define a “window” of the conversion veto cut around an electron trackin each layer B0 to B3 and require that there is no hit other than the hit
associated with the electron track in the window. Since a photonic electron(Dalitz and conversion) tends to have a correlated hit in the window, as one
can see in Figure 5.10, this conversion veto cut rejects photonic background.
A larger window size can reject photonic background more effectively, but
this can also reduce the efficiency for the heavy flavor electron signal due
to random hits in the window. The window for the conversion veto cut isa compromise in terms of the rejection factor on photonic backgrounds andefficiency for heavy flavor electrons. We optimized the size of the window of
the conversion veto cut based on a geant3 simulation.
The pink hatched area shown in Figure 5.11 shows the window of theconversion veto cut in each layer. The window size is asymmetric sincecorrelated hits are mainly in the positive side of charge × ∆φ. The window
size is reduced for higher electron pT since the distribution of correlated hits
becomes narrower for higher pT .

87

Section CHAPTER 5. ANALYSIS

countcharge × ∆φ at B1

count

charge × ∆φ at B0

e± (data)
Photonic e± (sim)

105

104

104

103

103

102

102

-0.06 -0.04 -0.020e± (data)
Photonic e± (sim)105

0.02 0.04 0.06
charge × ∆ φ[rad]-0.06 -0.04 -0.02

0.02 0.04 0.06
charge × ∆ φ[rad]countcharge × ∆φ at B3

countcharge × ∆φ at B20e± (data)
Photonic e± (sim)105e± (data)
Photonic e± (sim)

105

104
10

4

10

3

10

2

103

102

-0.06 -0.04 -0.02

00.02 0.04 0.06
charge × ∆ φ[rad]-0.06 -0.04 -0.02

00.02 0.04 0.06
charge × ∆ φ[rad]Figure 5.10: Distribution of correlated hits near electron tracks for 1 <pT < 2 GeV.
Distribution of correlated hits in B0 (top-left), B1 (top-right), B2 (bottomleft), B3(bottom-right) near electron tracks for 1 < pT < 2 GeV. The redpoints are from Au+Au data and the black points are from Monte Carlosimulation.

88

Veto residual B0 ( chrg × ∆φ vs pT )0.06 (b)
103

0.04
0.02

chrage × ∆φ[rad]chrg × ∆φ[rad]Section CHAPTER 5. ANALYSIS

Veto residual B1 ( charge × ∆φ vs pT )
0.1
(b)

104

0.05

103

0

102

-0.05

10

102

0
-0.02
10

-0.04
-0.06
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
p [GeV/c]-0.1
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
pT[GeV/c]

1

103

0.05

0

-0.05

-0.1
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
pT[GeV/c]chrage × ∆φ[rad]chrage × ∆φ[rad]T

Veto residual B2 ( charge × ∆φ vs pT )
0.1
(b)

102

10

Veto residual B3 ( charge × ∆φ vs pT )
0.1
(b)

103

0.05
102

0
10

-0.05

-0.1
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
pT[GeV/c]111

Figure 5.11: charge × ∆φ vs pT for B0(top-left), B1(top-right), B2(bottomleft), B3(bottom-right). The conversion veto window is the pink hatched
area.

89

Section CHAPTER 5. ANALYSIS
Figure 5.12 shows the survival fraction of the conversion veto cut forelectrons from photon conversions and Dalitz decays as a function of electron pT from a geant3 simulation of the detector with hits run throughthe reconstruction software. The survival probability for conversions is lessthan 30% at pT = 1 GeV and decreases further at higher pT . The survival
probability for Dalitz decays is higher since a Dalitz decay partner is more
likely to fall outside of the window of the conversion veto cut due to thelarger opening angle. Also shown in Figure 5.12 is the survival fraction ofelectrons from heavy flavor decays which pass the conversion veto cut (SHF ).
As expected, their efficiency for passing the conversion veto cut is quite highand pT independent.
The efficiencies shown in Figure 5.12 are calculated without the Au+Au
high-multiplicity that may randomly provide a hit satisfying the conversion
veto cut. Since these are random coincidences, they are a common reduction
for all sources including the desired signal — heavy flavor electrons. This
common reduction factor, δrandom , is measured from the reduction of thehadron track yield by the conversion veto cut to be ' 35% at pT = 1 GeV to '25% at pT = 5 GeV for MB Au+Au collisions. Note that when we determine
the DCAT distribution of the various background components using a fullgeant3 simulation we apply the same conversion veto cuts.
The DCAT distributions from photonic background processes that survive the conversion veto cut are shown in Figure 5.13. The means of the
DCAT distributions from Dalitz decays and conversions are shifted to negative DCAT values due to the mis-reconstruction of the momentum caused by
the assumption that the tracks originate at the primary vertex, as explainedin the next paragraph. The shift is largest at the lowest pT bin and decreases
with increasing pT .
For Dalitz electrons, the shift is due to the energy loss via induced radiation (bremsstrahlung). The total radiation length of the VTX is approximately 13% as shown in Table 4.3. Thus a Dalitz electron coming from theprimary vertex loses approximately 1 − e−0.13 ≈ 12% of its energy on averagewhen it passes through the VTX. The momentum measured by the DC isclose to the one after the energy loss due to the reconstruction algorithm.
Since the momentum determined by the DC is used when projecting inward
from the hit in B0 to the primary vertex and in calculation of DCAT , this results in a slight shift in the DCAT distribution. This effect is fully accounted
for in the DCAT template of Dalitz electrons since it is generated throughthe full geant3 and reconstruction simulation.
In the case of conversions, the effect is even larger, as one can clearly see
in Figure 5.13. While a photon goes straight from the primary vertex to thebeam pipe or B0 layer where it converts, DCAT is calculated assuming that90

Section CHAPTER 5. ANALYSIS
the electron track is bent by the magnetic field. Thus the DCAT distribution
is shifted by the difference of the actual straight line trajectory and thecalculated bent trajectory. Again, this is fully accounted for with the fullgeant3 simulation. The effect is verified by selecting conversion electrons
with a reversed conversion veto cut.

91

Survival rate after the conversion veto cut

Section CHAPTER 5. ANALYSIS

1
direct γ → ee
conversions

c+b
π0 → eeγ
η → eeγ

0.8
0.6
0.4
0.2
0
0

1

2

3

4

5

6

7

peT [GeV/c]
Figure 5.12: The survival rate as a function of electron pT (peT ) for electrons
from photon conversion (black), Dalitz decay of π 0 (red), η (green), electrons
from direct photon (blue) and heavy flavor decay electrons (dark orange).

92Section CHAPTER 5. ANALYSIS

5.7.5

Ke3

The background from Ke3 decays (KS0 , K ± → eνπ) contributes electrons
over a broad range of DCAT due to the long lifetime of the kaons. Bothcontributions are determined using pythia and a full geant3 simulation,
taking into account the exact track reconstruction, electron identification
cuts, and conversion veto cut. The resulting DCAT distribution for thesekaon decays is shown in Figure 5.13. As expected, though the overall yield issmall, this contributes at large DCAT in the lower pT bins and is negligible
at higher pT .

5.7.6

Quarkonia

Quarkonia (J/ψ and Υ) decay into electron pairs. Due to the short lifetime, these decays contribute to electrons emanating from the primary vertex.
√
The J/ψ yields in Au+Au collisions at sN N = 200 GeV have been measured
by the PHENIX Collaboration [159]. The detailed modeling of these contributions out to high pT is detailed in Ref. [11]. While these measurements
include a small fraction of B → J/ψ decays, all J/ψ’s are considered prompt
when modeling the DCAT distribution. The J/ψ contribution is shown in
Figure 5.13, and is quite small and peaked about DCAT = 0 as expected.
Thus, the systematic uncertainty from the quarkonium yields in Au+Au collisions is negligible in all electron DCAT pT bins.

93Section CHAPTER 5. ANALYSIS

5.8

Normalization of electron background components

If the detector performance were stable, we could convert the DCAT
distributions from counts into absolutely normalized yields. Then one could
straightforwardly subtract the similarly absolutely normalized backgroundcontributions described above—with the normalization constrained by thepreviously published PHENIX yields for π 0 [157], η [160], etc. However,
due to detector instability during the 2011 run, such absolute normalizationof background contributions can have a large systematic uncertainty. Thus
we bootstrap the relative normalization of these background contributions
utilizing our published Au+Au results [11] from data taken in 2004.
The idea of the method is the following. PHENIX measured the invariant
yield of open heavy flavor decay electrons from the 2004 dataset. In this 2004
analysis we first measured inclusive electrons (i.e. the sum of backgroundelectrons and heavy flavor electrons). We then determined and subtracted thebackground electron components from the inclusive electron yields to obtain
the heavy flavor contribution. Thus the ratio of the background components
to the heavy flavor contribution were determined and published in [11]. We
use these ratios to determine the normalization of background components inthe 2011 data, as described in the next paragraph. Some backgrounds havethe same ratio to signal regardless of the year the data was collected, whileothers will differ due to the additional detector material added by the VTX.
√The invariant yield in Au+Au collisions at sN N = 200 GeV of heavy
flavor electrons and background electrons from Dalitz decays is a physicalobservable independent of the year the data was taken. Thus we can use theratio of heavy flavor/Dalitz that is determined in the 2004 analysis in the 2011
data. On the other hand, the invariant yield of conversion electrons depends
on the detector material present and is thus different in the 2011 data taking
period with the VTX installed compared with the 2004 data. We accountfor this difference by calculating the fraction of nonphotonic electrons in the2011 data. A detailed description of the normalization procedure is given in
Appendix A.
With this bootstrapped normalization completed, the correctly normalized background components are shown for all five pT bins vs DCAT in Figure. 5.13. Note that the normalization of mis-identified hadron and random
background is determined from the data as explained in sections 5.7.2 and5.7.3, respectively. The electron yield beyond the sum of these backgroundcomponents is from the combination of charm and bottom heavy flavor electrons.
94Section CHAPTER 5. ANALYSIS
While the DCAT distributions in Figure 5.13 are plotted within |DCAT | <0.15 cm, only a |DCAT | < 0.1 cm is used in the analysis to extract thecharm and bottom yield described later. At large DCAT , the distribution
is dominated by high-multiplicity background (subsection 5.7.3) and therefore provides little constraint in the extraction of the charm and bottom
contributions.

95

count1.5 < peT < 2.0 [GeV/c]

Au+Au MB s =200 GeV
104 PHENIX 2011NN

(a)

count

Section CHAPTER 5. ANALYSIS
2.0 < peT < 2.5 [GeV/c]
3

Au+Au MB sNN=200 GeV
PHENIX 2011

(b)

10
103

102
102
10

10

1

1

-0.1 -0.05

0

0.05

0.1 0.15
DCAT [cm]count

2.5 < peT < 3.0 [GeV/c]

103 Au+Au MB sNN=200 GeV
PHENIX 2011(c)

-0.1 -0.05

0

0.05

0.1 0.15
DCAT [cm]3.0 < peT < 4.0 [GeV/c]
Au+Au MB sNN=200 GeV
PHENIX 2011

(d)

102

102

10

10

1

1

-1
10-0.15-1
10-0.15count-1
10-0.15-0.1 -0.05

0

0.05

0.1 0.15
DCAT [cm]-110-0.15-0.1 -0.05

0

0.05

0.1 0.15
DCAT [cm]count

4.0 < peT < 5.0 [GeV/c]

102 Au+Au MB sNN=200 GeV
PHENIX 2011

(e)
Data
Mis-identified hadron

10

RandomDalitzConversion

1

Ke3
J/ψ
-1
10-0.15-0.1 -0.05

0

0.05

0.1 0.15
DCAT [cm]Figure 5.13:
DCAT distributions for electrons in MB Au+Au at√
sN N = 200 GeV that pass the reconstruction and conversion veto cut inthe indicated five electron-pT selections. Also shown are the normalized contributions for the various background components detailed in Section 5.7.
96

Section CHAPTER 5. ANALYSIS

5.9

Unfolding

5.9.1

Overwiew

After we obtain the DCAT distributions as a function of electron pT andthe various background components, we proceed to extract the remaining
charm and bottom components. If one knew the shape of the parent charmand bottom hadron pT and rapidity distributions, one could calculate inadvance the DCAT shape for electrons from each heavy flavor via a model ofthe decay kinematics. Since the decay lengths of charm and bottom hadrons
are significantly different, they will yield different DCAT distributions. In
this case, one could simultaneously fit the DCAT distribution for each pT
bin with all background components fixed across pT bins, and extract the
one free parameter: the ratio of charm to bottom contributions. However,the pT distribution of charm hadrons is known to be significantly modified
in Au+Au collisions — see for example Ref. [15]. For bottom hadrons thisis also likely to be the case. Therefore one does not know a priori the heavy
flavor DCAT distribution since it depends on the parent pT distribution. For
example, a B meson with momentum = 0 has a daughter electron with DCA= 0 no matter what the electron momentum happens to be.
Since the DCAT distributions for all electron pT result from the same
parent charm and bottom hadron pT spectrum, one can perform a simultaneous fit to all the electron pT and DCAT data in order to find the most
likely heavy flavor parent hadron pT distributions. The estimation of a setof most likely model parameters using a simultaneous fit to data is often
referred to as unfolding. Statistical inference techniques are often employed
to solve such problems; see for example the extraction of reconstructed jet
cross sections [161].
The DCAT distributions are in counts and have not been corrected forthe pT -dependent reconstruction efficiency in Au+Au collisions, and therefore
hold no yield information. To further constrain the extraction of the charmand bottom components, we include the total heavy flavor electron invariant√
yield as measured by PHENIX [11] in Au+Au collisions at sN N = 200 GeV
with 2004 data set. This measurement is more accurate than currently available with the 2011 data set, where the VTX acceptance changes with time.
The unfolding procedure, using a particular sampling method (describedin Section 5.9.2), chooses a set of trial charm and bottom parent hadronyields. The trial set of yields is multiplied by a decay matrix (describedin Section 5.9.4), which encodes the probability for a hadron in a given pTinterval to decay to an electron at mid-rapidity as a function of electronpT and DCAT . The resulting distributions of electron pT and DCAT are
97

Section CHAPTER 5. ANALYSIS
compared with the measured data using a likelihood function (described in
Section 5.9.3). In order to dampen discontinuities and oscillatory behavior,a penalty upon the likelihood (described in Section 5.9.5) is added to enforce
smoothness in the resulting hadron pT distributions (regularization).

5.9.2

Unfolding method

Here we apply Bayesian inference techniques to the unfolding problem.
A detailed introduction to these techniques is given in Ref. [162]. Bayesian
unfolding techniques provides a joint probability density over the full set ofmodel parameters. In this analysis, the vector of model parameters, θ, is thevector of parent charm and bottom hadron yields binned in pT .
Given a vector of measured data, x, and our vector of model parameters,
θ, we use Bayes’ theoremp(θ|x) =P (x|θ)π(θ)
,
P (x)

(5.2)

to compute the posterior probability density p(θ|x) from the likelihood P (x|θ)
and prior information π(θ). The function P (x|θ), quantifies the likelihoodof observing the data given a vector of model parameters. In frequentist
statistics, the P (x|θ) is often used alone to determine the best set of model
parameters. Bayesian inference, on the other hand, allows for the inclusion of
the analyzer’s a priori knowledge about the model parameters, as encodedin π(θ). The implementation of π(θ) used in this analysis is discussed in
Section 5.9.5. The denominator P (x) serves as an overall normalization of
the combined likelihood P (x|θ)π(θ) such that p(θ|x) can be interpreted asa probability density. In this analysis, p(θ|x) gives the probability for a setof charm and bottom hadron yields,θ = (θ c ; θ b ),(5.3)

given the values of the measured electron data points x. Since we are onlyinterested in the parameters which maximize p(θ|x), we can dispense withthe calculation of P (x), as it serves only as an overall normalization.
Here θ comprises 17 bins of both charm and bottom hadron pT , yieldinga 34-dimensional space which must be sampled from in order to evaluatep(θ|x). To accomplish this we employ a Markov Chain Monte Carlo (MCMC)
algorithm to draw samples of θ in proportion to p(θ|x). This makes accurate
sampling of multidimensional distributions far more efficient than uniform
sampling. In implementation, it is in fact the right hand side of Eq. 5.2 thatis sampled. The MCMC variant used here is an affine-invariant ensemble98Section CHAPTER 5. ANALYSIS
sampler described in Ref. [163] and implemented as described in Ref. [164].
It is well suited to distributions that are highly anisotropic such as spectra
which often vary over many orders of magnitude.

5.9.3

Modeling the likelihood function

This analysis is based on 21 data points of total heavy flavor electron
invariant yield, Ydata , in the range 1.0 – 9.0 GeV/c from the 2004 data
set [11], and five electron DCAT distributions Ddata, where j indexes eachjelectron pT interval within the range 1.5 – 5.0 GeV/c from the 2011 data
set. Therefore,x = (Ydata , Ddata, Ddata, Ddata, Ddata, Ddata
)
0
1
2
3
4

(5.4)

in Eq. 5.2.
Our ultimate goal is to accurately approximate the posterior distribution
over the parent hadron invariant yields θ by sampling from it. For each trial
set of hadron yields, the prediction in electron pT , Y(θ), and DCAT , Dj (θ),
is calculated byY(θ) = M(Y) θ c + M(Y) θ b

(5.5)

(D)
(D)
= Mj θ c + Mj θ b ,(5.6)

Dj (θ)(D)

where M(Y) and Mj are decay matrices discussed in Section 5.9.4. We
then evaluate the likelihood between the prediction and each measurementin the data sets Ydata and {Ddata}4j=0 . As is customary, the logarithm of thejlikelihood function is used in practice. The combined log likelihood for thedata is explicitly
ln P (x|θ) = ln P (Ydata |Y(θ)) +5
X

ln P (Ddata|Dj (θ)).
j

(5.7)

j=1

The Ydata dataset is assigned statistical uncertainties that are assumed to
be normally distributed and uncorrelated. Thus, the likelihood ln P (Ydata |Y(θ))
is modeled as a multivariate Gaussian with diagonal covariance. The systematic uncertainties on the Ydata dataset and their effect on the unfolding result
are discussed in Sec. 5.10.
The DCAT data sets, in contrast, each comprise a histogrammed distribution of integer-valued entries, and the likelihood ln P (Ddata|Dj (θ)) isjthus more appropriately described by a multivariate Poisson distribution.
However, the likelihood calculation for the DCAT data sets requires three99Section CHAPTER 5. ANALYSIS
additional considerations. First, there are significant background contributions from a variety of sources, as discussed in section 5.7. Secondly, detector
acceptance and efficiency effects are not explicitly accounted for in the DCAT
distributions. This implies that the total measured yield of signal electronsin each DCAT histogram is below what was actually produced, and consedistributions do not match the predictions inquently the measured Ddatajnormalization. Lastly, because of the high number of counts in the region
near DCAT = 0, this region will dominate the likelihood and be very sensitive
to systematic uncertainties in the DCAT shape there, even though the main
source of discrimination between charm and bottom electrons is at larger
DCAT .
To deal with the first issue, the relatively normalized background described in Sec. 5.7 is added to each prediction of the DCAT distribution forsummed electrons from charm and bottom hadrons so that the shape andrelative normalization of the background component of the measurement isaccounted for.
To handle the second, each prediction plus the background is scaled to. In this way, only the shape of theexactly match the normalization of Ddatajprediction is a constraining factor.
To deal with the third, a 5% uncertainty is added in quadrature to the statistical uncertainty when the number of counts in a given DCAT bin is greaterthan a reasonable threshold (which we set at 100 counts). This accounts forthe systematic uncertainty in the detailed DCAT shape by effectively deweighting the importance of the region DCAT ≈ 0 while maintaining theoverall electron yield normalization (as opposed to removing the data entirely). This additional uncertainty also necessitates changing the modelingof ln P (Ddata|Dj (θ)) from a Poisson to a Gaussian distribution. We havejchecked that varying both the additional uncertainty and the threshold at
which it is added has little effect on the results.

5.9.4

Decay model and matrix normalization

The pythia-6 [106] generator with heavy flavor production process included, via the parameter MSEL=4(5), is used to generate parent charm(bottom) hadrons and their decays to electrons. Electrons within |η| < 0.35
decayed from the ground state charm hadrons (D± , D0 , Ds , and Λc ) or
bottom hadrons (B ± , B 0 , Bs , and Λb ) are used to create a decay matrix between hadron pT (phT , representing charm hadron pT , pcT , or bottom hadronpT , pbT ) and electron pT (peT ) and DCAT . Here we treat the feed down decay
B → D → e as a bottom hadron decay and exclude it from charm hadron
decays.
100Section CHAPTER 5. ANALYSISThe probability for a charm or bottom hadron at a given phT to decay to anelectron at a given peT and DCAT is encoded in the multidimensional matrices(D)
M(Y) and Mj . An example decay matrix for charmed hadrons is shown in
Figure 5.14. Note that the marginal probabilities do not integrate to unity inthese matrices. This is because the decay probabilities are normalized to thenumber of hadrons that are generated at all momenta, in all directions, andover all decay channels. The probability distribution for a hadron integrated
over all rapidities and decay channels within a given phT range to decay to anelectron at |y| < 0.35 with a given peT (integrated over DCAT ) is shown in
Fig. 5.15 for an example set of phT bins.
In principle, this decay matrix introduces a model dependence to theresult. In the creation of the decay matrix we are integrating over all hadron
rapidities as well as combining a number of hadron species and their decay
kinematics to electrons. This involves two assumptions. The first is thatthe rapidity distributions of the hadrons are unmodified. BRAHMS foundthat the pion and proton RAA did not depend strongly on rapidity up toy ≈ 3 [165], justifying the assumption. This assumption will further lead us
to quote charm and bottom hadron yields as a function of pT integrated over
all rapidity. The second assumption is that all ground state charm hadrons
experience the same modification as a function of pcT . While different thanthe charm suppression, all bottom hadrons are assumed to experience thesame modification.
An enhancement in the baryon to meson production ratios in both nonstrange and strange hadrons has been measured at RHIC [166], which may
carry over into the heavy quark sector, invalidating the second assumption.
While there are some models [167] that attempt to incorporate this anomalous enhancement into the charm hadrons to help explain the measured heavy
flavor electron RAA , there are few measurements to help constrain this proposed enhancement. Following Ref. [168], we have tested the effect of thisassumption by applying the observed baryon/meson enhancement to boththe Λc /D and Λb /B ratios. As in Ref. [168], we assume that the modification asymptotically approaches 1 for hadron pT > 8 GeV/c. We find that
including the enhancement gives a lower charm hadron yield at high-pT anda larger bottom hadron yield at high-pT , but the modifications are within thesystematic uncertainties discussed in Section 5.10 and shown in Figure 6.1.
We also find a larger bottom electron fraction, which is again within thesystematic uncertainties shown in Figure 6.2. While we have not used otherparticle generators to create alternate decay matrices, we find that the D0
and D± meson pT and rapidity distributions from pythia are similar to thosegiven by Fixed Order + Next-to-Leading Log (fonll) calculations [8]. We

101

Section CHAPTER 5. ANALYSIS
have not included any systematic uncertainty due to this model dependence
in the final result.

102Section CHAPTER 5. ANALYSIS

9
8

10-3

(a)

10-4

peT [GeV/c]

7
6

10-5

5

10-6

4
3

10-7

2
10
0.20
0.15

5

10
15
c
pT [GeV/c]

-8
20 10

(b) 1.5 <peT [GeV/c] <2.0
10-4

e ± DCAT [cm]

0.10
10-5

0.05
0.00

10-6

0.05
0.10

10-7

0.15
0.200

5

10
15
pcT [GeV/c]

-8
20 10

Figure 5.14: (a) The decay matrix, M(Y) , encoding the probability forcharmed hadrons decaying to electrons within |η| < 0.35 as a function ofboth electron pT (peT ) and charm hadron pT (pcT ). (b) An example decay(D)matrix, Mj , encoding the probability for charmed hadrons decaying toelectrons within |η| < 0.35 and 1.5 < peT [ GeV/c] < 2.0 as a function of bothelectron DCAT and charm hadron pT (pcT ). In both cases the color intensity
represents the probability of decay in the given bin.
103

Section CHAPTER 5. ANALYSIS(a)0.5 < pcT < 1.0
2.5 < pcT < 3.0
4.0 < pcT < 4.5
7.0 < pcT < 8.0
12.0 < pcT < 15.0(b)

0.5 < pbT < 1.0
2.5 < pbT < 3.0
4.0 < pbT < 4.5
7.0 < pbT < 8.0
12.0 < pbT < 15.0

P(c → e)

0.015
0.010

0.005
0.000

P(b → e)

0.015
0.010

0.005
0.0001 2

3

4

5

6

peT [GeV/c]

7

8

9

Figure 5.15: The probability for (a) charm and (b) bottom hadrons in a given
range of hadron pT (pcT and pbT for charm and bottom hadrons respectively)
to decay to electrons at mid-rapidity as a function of electron pT (peT ).

104

Section CHAPTER 5. ANALYSIS

5.9.5

Regularization/prior

To penalize discontinuities in the unfolded distributions of charm andbottom hadrons, we include a regularization term to the right hand side ofequation 5.7. In this analysis we included a squared-exponential function(5.8)
ln π(θ) = −α2 |LRc |2 + |LRb |2
where Rc and Rb are ratios of the charm and bottom components of theparent hadron pT vector to the corresponding 17 components of the prior,θ prior , and L is a 17-by-17 second-order finite-difference matrix of the form
−1 1
 1 −2 1
1 −2 1.. .. ..

.
.
.
17 
L=

.. .. ..
2 
.
.
.


1 −2 1
1 −2 1
1 −1









.






(5.9)

Thus the addition of this term encodes the assumption that departuresfrom θ prior should be smooth by penalizing total curvature as measured by
the second derivative.
Here, α is a regularization parameter set to α = 1.0 in this analysis.
We determine α by repeating the unfolding procedure, scanning over α andchoosing the value of α which maximizes the resulting sum of Eq. 5.7 and− (|LRc |2 + |LRb |2 ) (Eq. 5.8 dropping α2 ). In this way we can directly compare log likelihood values for unfolding results with different α values. We
include variations on α in the systematic uncertainty as described in section 5.10.
We set θ prior to pythia charm and bottom hadron pT distributions scaled
by a modified blast wave calculation [123] which asymptotically approaches
RAA values of 0.2(0.3) for D(B) mesons at high-pT . We have tested the sensitivity of the result to θ prior by alternatively using unmodified pythia charmand bottom hadron pT distributions. We find that the result is sensitive tothe choice of θ prior dominantly in the lowest charm hadron pT bins, where
there is minimal constraint from the data. We have included this sensitivity
in the systematic uncertainty as discussed in section 5.10.

105

Section CHAPTER 5. ANALYSIS

5.9.6

Parent charm and bottom hadron yield and theirstatistical uncertainty

The outcome of the sampling process is a distribution of θ vectors, whichis 34-dimensional in this case. In principle, the distribution of θ vectors contains the full probability, including correlations between the different parameters. The 2-D correlations are shown in Figure 5.16. While it is difficult todistinguish fine details in the 34×34-dimensional grid of correlation plots, we
can see a few gross features. A circular contour in the 2-D panels represents
no correlation between the corresponding hadron pT bins. An oval shapewith a positive slope indicates a positive correlation between correspondingbins, and an oval shape with a negative slope represents an anti-correlation
between corresponding bins. A large positive correlation is seen for adjacentbins for high-pT charm hadrons and low-pT bottom hadrons. This is a consequence of the regularization, which requires a smooth pT distribution, andis stronger at the higher and lower pT regions where there is less constraint
from the data. We also see that, while there is little correlation between the
majority of nonadjacent pT bins, there does seem to be a region of negative
correlation between the mid to high pT charm hadrons and the low to mid pTbottom hadrons. Charm and bottom hadrons in these regions contribute decay electrons in the same pT region, and appear to compensate for each otherto some extent. An example of this is shown between 3.5 < pcT GeV < 4.0
and 2.5 < pbT GeV < 3.0 in Figure 5.16(b)-(d).
To summarize p(θ|x), we take the mean of the marginalized posterior
distributions (the diagonal plots in Figure 5.16) for each hadron pT bin as
the most likely values, and the 16th and 84th quantiles to represent the ±1σ
uncertainty in those values due to the statistical uncertainty in the data
modified by the regularization constraint.

106Section CHAPTER 5. ANALYSIS
3.5 <pcT <4.0(b)1.8e-02pcT

3.2e-02

2.5 <pbT <3.0(d)

2.5 <pbT <3.0

7.0e-03

(c)

yield

3.0e-03
1.8e-02 c 3.2e-02 3.0e-03
7.0e-03yield
3.5 <pT <4.0

pbT

pcT

pbT

Figure 5.16: The joint probability distributions for the vector of hadronyields, θ, showing the 2-D correlations between parameters. The diagonalplots show the marginalized probability distributions for each hadron pT bin(i.e. the 1-dimensional projection over all other parameters). Along the Yaxis the plots are organized from top to bottom as the 17 charm hadron pT(pcT ) bins from low to high pcT followed by the 17 bottom hadron pT (pbT )bins from low to high pbT . The X-axis is organized similarly from left toright. The pcT and pbT binning follows that shown in Figure 6.1. The regionof green plots shows the charm hadron yields and the correlations between
charm hadron yields. The region of blue plots shows the bottom hadronyields and correlations between bottom hadron yields. The region of orange
plots shows the correlations between charm and bottom hadron yields. Subpanels (b)-(d) show a set of example distributions. (b) The 1-D probability
distribution of charm hadron yield in 3.5 < pcT GeV < 4.0. (d) The 1-D
probability distribution of bottom hadron yield in 2.5 < pbT GeV < 3.0. (c)The correlation between (b) and (d).107

Section CHAPTER 5. ANALYSIS

5.10

Systematic uncertainties

When performing the unfolding procedure, only the statistical uncertainties on the electron DCAT and pT spectra are included. In this section we
describe how we consider the systematic uncertainties on both the measured
data and the unfolding procedure. We take the following uncertainties into
account as uncorrelated uncertainties:
1. Systematic uncertainty in the heavy flavor electron pT invariant yield
2. Uncertainty in the high-multiplicity background
3. Uncertainty in the fraction of nonphotonic electrons (FNP )4. Uncertainty in Ke3 normalization
5. Regularization parameter α
6. Uncertainty in the form of θ prior
The uncertainty in FNP (See section A.2), and Ke3 are propagated to theunfolded hadron yields by varying each independently by ±1σ, and performing the unfolding procedure with the modified background template. The
difference between the resulting hadron yields and the central values is taken
as the systematic uncertainty. The same procedure is used to determine theuncertainty in the result due to the regularization parameter, which is varied by +0.60−0.25 based on where the summed likelihood from both the data andregularization drops by 1 from the maximum value.
The uncertainty in the high-multiplicity background includes two components. The first is the uncertainty on the normalization of the highmultiplicity background DCAT distribution, as determined in section 5.7.3
and shown in Figure 5.13. This is propagated to the unfolded hadron yields
by varying the normalization by ±1σ and performing the unfolding procedure
with the modified background template, as with the FNP and Ke3 uncertainties. The second component addresses the small excess in the embedded
primary electron distribution observed in Figure 5.9 and not accounted forby using the DCAT distribution for large DCAL . We parametrize the excess,which is more than two orders of magnitude below the peak, and apply it tothe background components, re-performing the unfolding procedure to findits effect on the hadron yield. Both effects combined are small relative to thedominant uncertainties.
Incorporating the pT correlated systematic uncertainty on the heavy flavor electron invariant yield is more difficult. Ideally one would include a full108

Section CHAPTER 5. ANALYSIS
covariance matrix encoding the pT correlations into the unfolding procedure.
In practice, the methodology employed in [11] does not provide a convenientdescription of the pT correlations needed to shape the covariance matrix.
Instead we take a conservative approach by considering the cases which we
believe represent the maximum pT correlations. We modify the heavy flavor
electron invariant yield by either tilting or kinking the spectrum about agiven point. Tilting simply pivots the spectra about the given point so that,for instance, the first point goes up by a fraction of the systematic uncertainty while the last point goes down by the same fraction of its systematic
uncertainty, with a linear interpolation in between. Kinking simply folds the
spectra about the given point so that that the spectrum is deformed in theform of a V. We implement the following modifications and re-perform theunfolding procedure:
1. Tilt the spectra about pT = 1.8 GeV by ±1σ of the systematic uncertainty.
2. Tilt the spectra about pT = 5 GeV by ±1σ of the systematic uncertainty.
3. Kink the spectra about pT = 1.8 GeV by ±1σ of the systematic uncertainty.
4. Kink the spectra about pT = 5 GeV by ±1σ of the systematic uncertainty.
The pT points about which the spectra were modified were motivated by
the points in pT at which analysis methods and details changed, as discussed
in [11]. We then take the RMS of the resulting deviations on the hadronyield from the central value as the propagated systematic uncertainty due tothe systematic uncertainty on the heavy flavor electron invariant yield.
The effect of our choice of θ prior on the charm and bottom hadron yields
is taken into account by varying θ prior , as discussed in Section 5.9.5. The
differences between each case and the central value are added in quadrature
to account for the bias introduced by θ prior .
The uncertainties on the unfolded hadron yields due to the six components described above and the uncertainty determined from the posterior
probability distributions are added in quadrature to give the uncertainty
shown in Figure 6.1.
Due to the correlations between charm and bottom yields, the relative
contributions from the different uncertainties depend on the variable being

109

0.8
0.6
0.4
0.2
0.0
0.2
0.4
1

8

7

6

5

4

3

2

α Uncertainty
θprior Uncertainty

2

3

4

5

6

peT [GeV/c]

7

8

(b)

(c)

9

8

7

6

5

4

3

2

1

High-mult. Bkg. Uncertainty
FNP Uncertainty
Ke3 Uncertainty

0.8
0.6
0.4
0.2
0.0
0.2
0.4

9

(a)

Unfold Uncertainty
Spectra Systematic Uncertainty

0.8
0.6
0.4
0.2
0.0
0.2
0.4

1

Fractional Uncertainty

Section CHAPTER 5. ANALYSIS

9

Figure 5.17: The relative contributions from the different components tothe uncertainty on the fraction of electrons from bottom hadron decays as afunction of pT .
The relative contributions from the different components to the uncertainty
on the fraction of electrons from bottom hadron decays as a function of pT .
The shaded red band in each panel is the total uncertainty.
plotted. To give some intuition for this, we have plotted the relative contributions from the different uncertainties to the fraction of electrons from bottom
110Section CHAPTER 5. ANALYSIS
hadron decays as a function of pT (discussed in Section 6.1) in Figure 5.17.
One can see that the dominant uncertainties come from the statistical uncertainty on the DCAT and heavy flavor electron invariant yield, the systematic
uncertainty on the heavy flavor electron invariant yield, and FNP .

111

Chapter 6
Results
6.1

Invariant yield of charm and bottom hadron

The final result of the invariant yields of charm and bottom hadrons
is obtained. The unfolded results for MB (0%–96%) Au+Au colli√
sions at sN N = 200 GeV are shown in Figure 6.1. The unfolding procedure
applied simultaneously to the heavy flavor electron invariant yield as a function of pT (shown in Figure 7.1) and the five electron DCAT distributions(shown in Figure 7.2). It is integrated over all rapidity, as a function of pT .
As a reminder, the integration over all rapidity was carried out by assuming
the rapidity distribution within pythia is accurate and that it is unmodified in Au+Au, as detailed in section 5.9.4. The central point represents
the most likely value and the shaded band represents the 1σ limits on the
combination of the uncertainty in the unfolding procedure and the systematic uncertainties on the data, as described in section 5.10. The uncertainty
band represents point-to-point correlated uncertainties.
The uncertainties on the hadron invariant yields shown in Figure 6.1 growrapidly for charm and bottom hadrons with pT > 6 GeV/c . This is dueto the lack of DCAT information for peT > 5 GeV/c . Above peT > 5
GeV/c , the unfolding is constrained by the heavy flavor electron invariant
yield only. This provides an important constraint on the shape of the hadronpT distributions, but the DCAT distributions provide the dominant source of
discriminating power between the charm and bottom. However, due to the
decay kinematics, even high pT (> 6GeV/c ) hadrons contribute electrons in
the range 1.5 < peT < 5.0 GeV/c . We find that charm(bottom) hadrons
in the range 7 < phT < 20 GeV/c contribute 18.2% (0.3%) of the total
electron yield in the region 1.5 < peT < 5.0 GeV/c . This explains the larger
uncertainties in the bottom hadron yield compared to the charm hadron yielddN
1
2π pT dpT

112

Section CHAPTER 6. RESULTS
at high phT .
p

1001/2πpT dN/dpT [(GeV/c)−2 ]10

Au+Au MB sNN =200 GeV
PHENIX Run 4 + Run 11-1

Unfolded charm
Unfolded bottom

10-2
10-3
10-4
10-5
10-6
10-7
10-8
(a)

10-9
0

(b)
5

10

pcT [GeV/c]

15

0

5

10

15

pbT [GeV/c]

Figure 6.1: Unfolded (a) charm and (b) bottom hadron invariant yield asa function of pT , integrated over all rapidities, as constrained by electron
yield vs DCAT in 5 pT bins and previously published heavy flavor electron
invariant yield vs pT [11].

6.2

Bottom electron fraction

The fraction of bottom electrons from heavy flavor hadrons decay:
FAuAu =N (b → e)
N (b → e) + N (c → e)is computed by the obtained charm and bottom hadron yields shown in Figure 6.1 to get the invariant yield of electrons from charm and bottom decays
at midrapidity (|y| < 0.35). Here the electrons from bottom hadron decays
include the cascade decay b → c → e. The resulting bottom electron fraction
is shown as a function of pT in Figure 6.2. The central values integrated overthe pT range of each DCAT distribution are also quoted in Figure 7.2. Asin the hadron yields, the band represents the 1σ limits of the point-to-point
correlated uncertainties.
113

Section CHAPTER 6. RESULTS

1.2

FONLL
Unfold Result

b→e/(b→e + c→e)

1.0

0.8
0.6
0.4
0.2
0.01

2

|y|<0.35
p
Au+Au MB sNN =200 GeV
PHENIX Run 4 + Run 11
3
4
5
6
7
8
e
pT [GeV/c]

9

Figure 6.2: The fraction of heavy flavor electrons from bottom hadron decays
as a function of pT from this work and from fonll p+p calculations [8].
Also shown in Figure 6.2 is the bottom electron fraction predictions fromfonll [8] (pQCD calculation of expected charm and bottom yields in p+p√
collisions) at sN N = 200 GeV. We find that the bottom electron fraction
is encompassed by the fonll calculation uncertainties. The shape of theresulting bottom electron fraction shows a steeper rise in the region 2.0 <pT < 4.0 GeV/c with a possible peak in the distribution compared to thecentral value of fonll calculation.

6.3

RAA of charm electrons and bottom electrons

The fraction of electrons from bottom hadron decays has been previ√
ously measured in p+p collisions at sN N = 200 GeV by both PHENIX [13]and STAR [14]. These measurements were made through electron-hadron orelectron-D meson correlation methods as reviewed in subsection 3.3.3. Theseare very different analyses than the one presented here, and have their own
model dependencies. In Figure 6.3 we compare the bottom electron frac-114

Section CHAPTER 6. RESULTS

1.2

b→e/(b→e + c→e)

1.0

FONLL
Unfold Result
STAR e-h correlation in p + pSTAR e-D0 correlation in p + p
PHENIX e-h correlation in p + p

0.8
0.6
0.4
0.2
0.01

2

|y|<0.35
p
Au+Au MB sNN =200 GeV
PHENIX Run 4 + Run 11
3
4
5
6
7
8
e
pT [GeV/c]

9

Figure 6.3: bottom electron√fraction as a function of pT compared to measurements in p+p collisions at s = 200 GeV from PHENIX [13] and STAR [14].
√Also shown are the central values for fonll [8] for p+p collisions at sN N
= 200 GeV.
tion between our Au+Au result and the electron-hadron correlation measurements in p+p. For pT > 4 GeV/c , we find agreement between Au+Au
and p+p within the large uncertainties of both measurements. This implies
that electrons from bottom hadron decays are similarly suppressed to thosefrom charm, because the total heavy flavor electron are known to be strongly
suppressed in Au+Au collisions from the previous PHENIX measurement[11]. For reference, included in Figure 6.3 is the central value of fonll calculation which, within the large uncertainties, is consistent with the p+p
measurements.
With the additional constraints on the bottom electron fraction in p+p
from the correlation measurements and the measured nuclear modification ofheavy flavor electrons, we can calculate the nuclear modification of electrons
from charm and bottom hadron decays separately. The nuclear modificac→eb→etions, RAA
and RAA, for charm and bottom hadron decays respectively arecalculated using

115Section CHAPTER 6. RESULTS

c→e
AuAu )HF
RAA
RAA= (1−F(1−Fpp )
b→e
RAA

HF
= FAuAu
RAA
,
Fpp

(6.1)
(6.2)

where FAuAu and Fpp are the fractions of heavy flavor electrons from bottom
HF
hadron decays in Au+Au and p+p respectively and RAA
is the nuclear modification of heavy flavor electrons (combined charm and bottom). Rather
than combining all measurements for the bottom electron fraction in p+p,which introduces a further extraction uncertainty, we have chosen to calcuc→eb→elate RAA
and RAAusing only the six STAR electron-hadron Fpp values.
When performing the calculation we determine the full probability distriHF
butions assuming Gaussian uncertainties on FAuAu , Fpp and RAA. As when
determining the charm and bottom hadron yields, we take the median of the
distribution as the central value, and the 16% and 84% of the distribution
as the lower and upper 1σ uncertainties. The resulting values are shown in
Figure 6.4(a). We find that the electrons from bottom hadron decays are lesssuppressed than electrons from charm hadron decays for 3 < pT < 4 GeV/c .
b→ec→e
To further clarify this statement, we calculate the ratio of RAA/RAA, shown
HF
in Figure 6.4(b). In this ratio, the uncertainty on RAA cancels. Here again
we calculate the full probability distributions and use the same procedure as
above to determine the central values and uncertainties. We find that theb→ec→eprobability distributions for RAA/RAA
are highly nonGaussian, which leads
to the large asymmetric uncertainty band shown in Figure 6.4(b). It is clear
from the ratio that b → e is less suppressed than c → e at the 1σ level up to
pT ∼ 4 GeV.

116

Section CHAPTER 6. RESULTS

1.6 (a)c →e
b →e( c + b) → e
Phys. Rev. C 84, 044905 (2011)

1.4

RAA

1.2
1.0
0.8
0.6
0.4
0.2
3.5

(b)

Au+Au from Unfold
p + p from e-h correlations
Phys.Rev.Lett. 105 (2010)b → e /Rc → e
RAA
AA

3.0
2.5
2.0
1.5
1.0

|y|<0.35

0.5 Au+Au MB p sNN =200 GeV
0.01

PHENIX Run 4 + Run 11

2

3

4

5

6

peT [GeV/c]

7

8

9

Figure 6.4: (a) The RAA for c → e, b → e and combined heavy flavor [11]as a function of peT . The c → e and b → e RAA is calculated using Eq. 6.16.2 where FAuAu uses the unfolded result determined in this work and Fppb→ec→edetermined from STAR e − h correlations [14]. (b) The ratio RAA
/RAA
as
e
a function of pT .
117

Chapter 7
Discussion
7.1

Re-folded comparisons to data

The vector of most likely hadron yields obtained the unfolding procedure
in section 5.9, with uncertainties can be multiplied by the decay matrix tocheck the consistency of the result with the measured data (here referred
to as re-folding). Figure 7.1 shows the measured heavy flavor electron invariant yield in Au+Au collisions [11] compared with the re-folded electron
spectra from charm and bottom hadrons. We find good agreement between
the measured data and the electron spectrum from the re-folded charm andbottom hadron yields. Figure 7.2 shows the comparison in electron DCAT
space for each bin in electron pT . Shown in each panel is the measured DCAT
distribution for electrons, the sum of the background contributions discussed
in section 5.7, the DCAT distribution of electrons from charm hadron decays, and the DCAT distribution of electrons from bottom hadron decays.
Note that the sum of the background contributions is fixed in the unfolding
procedure, and only the relative contribution of charm and bottom electrons
within |DCAT | < 0.1 cm, as well as their DCAT shape, vary. For convenience,
the region of the DCAT distribution considered in the unfolding procedureis also shown, as discussed in Section 5.6.2. The sum of the backgroundcontributions, charm, and bottom electrons is shown for a direct comparison
with the data.
The summed log likelihood values for each of the DCAT distributions andthe electron invariant yield are given in Table 7.1. To aid in the interpretation of the likelihood values, we use a Monte-Carlo method to calculate
the expected likelihood from statistical fluctuations around the re-folded result. We draw samples from the re-folded result based on the data statistics
and calculate the distribution of resulting likelihood values. The number

118

Section CHAPTER 7. DISCUSSION

Table 7.1: The log likelihood values (LL) summed over each DCAT distribution and for the comparison to the heavy flavor electron invariant yield.
Also quoted is the number of data points (Np ) and the deviation from the log
likelihood value expected from statistical fluctuations (∆LL), as discussed in
the text, for each comparison.
Data set
Np
LL ∆LL [σ]ee DCAT 1.5 < pT < 2.0
50 -195.5-3.8
ee DCAT 2.0 < pT < 2.5
50 -156.5-2.9
e DCAT 2.5 < peT < 3.0
50 -115.8-0.6
ee DCAT 3.0 < pT < 4.0
50 -104.1-1.8
e DCAT 4.0 < peT < 5.0
50 -53.20.0ee Inv. Yield. 1.0 < pT < 9.0 21 -45.9-3.5
Total Sum
271 -673.8
of standard deviations from the expected value is also shown in Table 7.1.
We find that the log likelihood values are large compared to expectationsin the heavy flavor electron invariant yield as well as the lowest two DCAT
pT bins. We note that the likelihood values do not incorporate the systematic uncertainties on the data, which are handled separately as described in
Section 5.10. In particular the statistical uncertainties on the heavy flavor
electron invariant yield are much smaller than the systematics at low-pT ,making the likelihood value not surprising. We find reasonable agreement
within uncertainties between the remaining DCAT pT bins.

119Section CHAPTER 7. DISCUSSION

c →e +b →e
c →e
b →e
Phys. Rev. C 84, 044905 (2011)

10-2
10-3
[(GeV/c)−2 ]

10-4
10-5

1 d2 N
2πpT dpT dy

10-6
10-7
10-8

9

7

6

5

4

3

2

Data / Re-fold1|y|<0.35p
s =200 GeV
Au+Au
MB
10-10 PHENIX RunNN4 + Run 11
2.5
2.0
1.5
1.0
0.5
0.01 2 3 4 5 6 7
peT [GeV/c]

8

10-9

8

9

Figure 7.1: The heavy flavor electron invariant yield as a function of pTfrom measured data [11] compared to electrons from the re-folded charm andbottom hadron yields. The boxes represent the point-to-point correlated uncertainties on the measured heavy flavor electron invariant yield, while theerror bars on the points represent the point-to-point uncorrelated uncertainties. The label “PHENIX Run 4 + Run 11” on this and all subsequent plots
indicates that the unfolding result uses the heavy flavor electron invariant
yield as a function of pT from data taken in 2004 (Run 4) combined with
DCAT measurements from data taken in 2011 (Run 11).

120

Section CHAPTER 7. DISCUSSION

104 (a)Au+Au MBsNN =200 GeV
PHENIXRun 4 + Run 11

102
101

2.5-3.0 GeV/cb/(b+c)=0.427
2

0.15

0.10

0.05

0.00

0.05

0.10

0.15

Data / Re-fold

0.15

0.10

101

Au+Au MBsNN =200 GeV
PHENIXRun 4 + Run 11

p

101
100

(e)
102 4.0-5.0
GeV/c

Au+Au MBsNN =200 GeV
PHENIXRun 4 + Run 11pb/(b+c)=0.488

0.15

0.10

0.05

0.00

0.05

0.10

2.5
2.0
1.5
1.0
0.5
0.15 0.10 0.05 0.00 0.05 0.10 0.15
DCAT [cm]0.15

Data / Re-fold

0.15

0.10

0.05

0.00

0.05

0.10

2.5
2.0
1.5
1.0
0.5
0.15 0.10 0.05 0.00 0.05 0.10 0.15
DCAT [cm]0.15

Data / Re-fold

2.5
2.0
1.5
1.0
0.5
0.15 0.10 0.05 0.00 0.05 0.10 0.15
DCAT [cm](d)3.0-4.0 GeV/c
102 b/(b+c)=0.520

100

counts101

103

Au+Au MBsNN =200 GeV
PHENIXRun 4 + Run 11p

countscounts

0.05

0.00

0.05

0.10

0.15

Data / Re-fold

2.5
2.0
1.5
1.0
0.5
0.15 0.10 0.05 0.00 0.05 0.10 0.15
DCAT [cm]103 (c)

Data
Total Background
Unfolded charm
Unfolded bottom
Background + charm + bottom

101
100
0.15

0.10

0.05

0.00

0.05

0.10

2.5
2.0
1.5
1.0
0.5
0.15 0.10 0.05 0.00 0.05 0.10 0.15
DCAT [cm]0.15

Data / Re-fold

102

100

100

10

Au+Au MBsNN =200 GeV
PHENIXRun 4 + Run 11

p

GeV/c
103 2.0-2.5b/(b+c)=0.264

countscounts(b)p

1.5-2.0 GeV/c
103 b/(b+c)=0.115

Figure 7.2: The DCAT distribution for measured electrons compared to thedecomposed DCAT distributions for background components, electrons fromcharm decays, and electrons from bottom decays. The sum of the backgroundcomponents, electrons from charm and bottom decays is shown as the red
curve for direct comparison to the data. The gray band indicates the regionin DCAT considered in the unfolding procedure. Also quoted in the figure is
the bottom electron fraction for |DCAT | < 0.1 cm integrated over the given
121
pT range.

Section CHAPTER 7. DISCUSSION

7.2

Comparison with STAR D0 yield measurement

The yield of D0 mesons over |y| < 1 as a function of pT has been previously√
published in Au+Au collisions at sN N =200 GeV by STAR [15]. In order
to compare our unfolded charm hadron results over all rapidity to the STARmeasurement, we used pythia to calculate the fraction of D0 mesons within|y| < 1 compared to charm hadrons over all rapidity. Since the measurement
by STAR is over a narrower centrality region (0%–80% vs 0%-96%), we scale
the STAR result by the ratio of the Ncoll values. This comparison is shownin Figure 7.3. For added clarity, we have fit the STAR measurement with a
Levy function modified by a blast wave calculation given by1/(1−p1 )(1 − p1 )pT
f (pT ) = p0 1 −
p2
 q

p
5
×
1.3 2πp24 G(pT , p3 , p4 ) +,1 + e−pT +3


(7.1)

where G(pT , p3 , p4 ) is a standard Gaussian function, and pi are the parametersof the fit. The ratio of the data to the fit is shown in the bottom panel of
Figure 7.3. We find that, within uncertainties, the D0 yield derived from ourdata agrees with that measured by STAR over the complementary pT range.
The our D0 yield hints at a different trend than the STAR data for pT > 5
GeV/c .

122

Section CHAPTER 7. DISCUSSION(a)1/2πpT × d2 N/dpT dy [(GeV/c)−2 ]10

PHENIX Run 4 + Run 11 MB
257.8
STAR 0-80% × 291.9Levy fit × modified blast wave

0

10-1
10-2
10-3
10-4
10-5

Data/fit2

3 4 5
pT [GeV/c]

6

7

6

5

4

1

0

2.5 (b)
2.0
1.5
1.0
0.5
0.00 1

3

10-6

2

D0 |y|<1p
Au+Au at sNN =200 GeV

7

Figure 7.3: The invariant yield of D0 mesons as a function of pT for |y| < 1
inferred from the unfolded yield of charm hadrons integrated over all rapidity
compared to measurements from STAR [15]. See the text for details on thecalculation of the D0 yield inferred from the unfolded result. To match thecentrality intervals, the STAR result has been scaled by the ratio of Ncoll
values. The bottom panel shows the ratio of the data to a fit of the STARD0 yield.

123Section CHAPTER 7. DISCUSSION

7.3

Comparison with theoretical models

There are a number of theoretical calculations in the literature for theinteraction of charm and bottom quarks with the QGP. Many of these models predicted the nuclear modification factor RAA for electrons from charm
decays and, RAA for electrons from bottom decays, separately, based on different energy loss models to explain the RAA . Models plotted in Figure
7.4(a) calculate radiative energy loss, while other models plotted in Figure
7.4(b),(c),(d) take into account only collisional energy loss.
For consistency, we have assumed the fonll [8] yields for electrons from√charm (bottom) decays calculated for p+p at sN N =200 GeV and thenscaled them by the heavy-ion model results for the RAA of electrons fromcharm (bottom).

b→e/(b→e + c→e)

1.0

FONLL
Djordjevic et al. dN/dy=1000 (0-10%)
Djordjevic et al. dN/dy=3500 (0-10%)
Djordjevic et al. (0-10%)
Unfold Result

(a)

1.2
1.0

b→e/(b→e + c→e)

1.2

0.8

0.6

0.4

0.4

b→e/(b→e + c→e)

1.0

2|y|<0.35
p
Au+Au MB sNN =200 GeV
PHENIX Run 4 + Run 11
3
4
5
6
7
8
peT [GeV/c]

FONLL
Alberico et al.
D(2 π T)=6, Cao et al.
D(2 π T)=1.5, Cao et al.
Unfold Result

0.2

(c)

1.2
1.0

0.8

2

|y|<0.35
p
Au+Au MB sNN =200 GeV
PHENIX Run 4 + Run 11
3
4
5
6
7
8
peT [GeV/c]

FONLL
He et al. Au+Au
He et al. p + p
Unfold Result

9
(d)

0.8

0.6

0.6

0.4

0.4

0.2
0.01

0.01

9

b→e/(b→e + c→e)

0.2

1.2

(b)

0.8

0.6

0.01

FONLL
D(2 π T)=30, van Hees et al. (0-10%)D(2 π T)=6, van Hees et al. (0-10%)D(2 π T)=4, van Hees et al. (0-10%)
Unfold Result2|y|<0.35
p
Au+Au MB sNN =200 GeV
PHENIX Run 4 + Run 11
3
4
5
6
7
8
peT [GeV/c]

0.2
9

0.01

2

|y|<0.35
p
Au+Au MB sNN =200 GeV
PHENIX Run 4 + Run 11
3
4
5
6
7
8
peT [GeV/c]

9

Figure 7.4: Bottom electron fraction as a function of pT compared to aseries of model predictions detailed in the text.
Figure 7.4(a) compares the bottom electron fraction from one class of124Section CHAPTER 7. DISCUSSION
calculations modeling only energy loss of these heavy quarks in medium. In
an early pQCD calculation by Djordjevic, Gyulassy, Vogt, and Wicks [133],
the authors assume an effectively static medium and apply the DGLV theoryof radiative energy loss. They find that even for extreme opacities withgluon rapidity densities dNg /dy up to 3500, the bottom quark decay electrons
dominate at high-pT and that limits the single electron RAA to the range 0.5 –0.6 for pT > 5 GeV/c . Although this result is known to be higher than theprevious PHENIX measured heavy flavor electron RAA [11], we show theb → e/(b → e + c → e) predictions for gluon rapidity densities of 1000 and3500 in Figure 7.4(a). We do note that the calculations are for 0%–10%
central collisions compared to the MB data, although the calculations spana factor of 3.5 range in the gluon density. We find that the calculations with
two gluon rapidity densities dNg /dy are in good agreement with our resultsfor pT < 4 GeV/c , but are slightly above and outside the uncertainty bandon our result at higher pT .
More recent calculations which extend the theory in the previous paragraph [134] also shown in Figure 7.4(a) as a light blue line, gives a similarvalue to their previous result, but is only published for pT > 5 GeV/c . Thisupdated model assumes a dynamical medium with the average temperature
T = 221 MeV (as extracted by PHENIX direct photon measurement [20]), including the collisional energy loss [134, 169] and initial state effects [170, 171],
result in a heavy flavor electron high pT RAA closer to 0.3 and in reasonableagreement with the previous PHENIX published results [11].
Figure 7.4(b) compares the bottom electron fraction from a calculation
for collisional energy loss using a T-matrix approach which take into account heavy quark-light quark resonace states in the QGP by van Hees,
Mannarelli, Greco, and Rapp [124]. For 0% – 10% central Au+Au collisions, they provided us with different results by changing the coupling of
the heavy-quark to the medium. The coupling is encapsulated in the diffusion parameter D, where smaller values yield a stronger coupling. Shown in
Figure 7.4(b) are three results corresponding to three values of the parameter D(2πT ) = 4, 6, 30. The largest D(2πT ) value (30), corresponding to
the weakest coupling, agrees well with the p+p reference fonll result. The
successively stronger couplings push the bottom fraction contribution higher
and higher. We find that the calculations with D(2πT ) = 4, 6 are in good
agreement with our result for pT < 4 GeV/c , but begin to deviate largely at
5 GeV/c where the calculation stops.
Figure 7.4(c) compares the bottom electron fraction from another classof calculations which employ a combination of Langevin, or transport typemodeling of heavy-quarks, in the bulk QGP with energy loss mechanisms that
dominate at higher pT . In Ref. [126], Alberico et al. employed a Langevin125Section CHAPTER 7. DISCUSSION
calculation in the background of an expanding deconfined medium describedby ideal and viscous hydrodynamics, while the interaction of the heavy quarks
with the QGP is treated within a weakly coupled framework. It is notablethat this calculation has a very strong suppression of charm decay electrons
such that bottom contributions dominate even at modest pT ≥ 2 GeV/c . The
calculations are consistent with the data for pT < 4 GeV and over-predict
the bottom contribution for higher pT values.
Figure 7.4(c) also compares the bottom electron fraction from anothervariant of the Langevin calculation by Cao et al. [125]. For this calculation,
we show two results corresponding to two different input values D(2πT ) = 1.5
and 6. For the lower parameter, again stronger heavy-quark to medium
coupling, there is a sharp rise in the bottom contribution which then flattens
out. This feature is due to the increased collisional energy loss, which has alarger effect on the charm quarks, coupled with the strong radial flow effects
enabling the heavier bottom quarks to dominate even at pT ∼ 2GeV/c .
These calculations used an impact parameter of b = 6.5 fm, which shouldroughly correspond to MB collisions. We find that the calculation using thelarger value of D(2πT ) = 6.0 is in reasonable agreement with the data acrossthe calculated pT range.
Lastly, Figure 7.4(d) shows a more recent calculation by He et al. employing a T-matrix approach similar to that shown in Figure 7.4(b), but witha number of updates [127]. In this model, (1) nonperturbative heavy quark
scattering off light quarks is treated by the a updated T-marices [172], (2)the medium evolution model has been changed to an updated ideal hydrodynamical model calculation which used the equation of state derived fromlattice QCD and tuned initial conditions that sucssessfully reproduced allπ, K, p as well as multistrange hadrons observables [173] and, (3) in hadronic
phase, the diffusion of D and B mesons is continued with transport coefficients calculated from elastic scattering amplitudes off light hadrons [174]. In
this case the authors provided a calculation of the bottom electron fraction√
in both p+p and Au+Au at sN N =200 GeV [175], and we therefore do not
calculate the bottom fraction using fonll as a baseline. The calculation is
performed for the 20%–40% centrality bin, which the authors find well represents MB. We find that the calculation under-predicts the bottom fraction
for pT < 3 GeV/c , although it is worth noting that the calculation in p+p
is also below the fonll curve across the full pT range. Above pT ∼ 3 thecalculation is in agreement with the measurement. It is also worth noting
that, of the models presented here, this is the only one that shows in Au+Au
a slight decrease in the bottom fraction at high pT .
Since these models decribed above predict different bottom fraction at
pT > 4 GeV/c , it is important to reduce the uncertainty of the bottom frac126

Section CHAPTER 7. DISCUSSION
tion in higher pT region for future measurement. The T-matrix approach[124] and transport approaches [125, 126] also predict the elliptic flow parameter v2 of electron from charm and bottom separately, depending on the
coupling between heavy quark and QGP medium. Thus, the measurementof v2 for electron from charm and bottom will provide further constraints onthese models.
There are numerous other calculations in the literature [176–178] that
require mapping charm and bottom hadrons to electrons at midrapidity tomake direct data comparisons. We look forward to soon being able to test
these calculations with analysis of new PHENIX data sets. We also lookforward to being able to test those calculations in the form of RAA .

127

Chapter 8
Conclusion
We have succeeded in measuring the electrons from charm and bottom
hadrons decay separately as a function of pT from Au+Au data taken at√sN N = 200 GeV in 2011 with the enhanced vertexing capabilities provided
by the VTX detector. In conjunction with previous PHENIX results for theheavy flavor electron invariant yield as a function of pT [11], we performed
an unfolding procedure to infer the parent charm and bottom hadron yields
as a function of pT . We have found that this procedure yields consistentagreement between the heavy flavor electron invariant yield and the newly
measured electron DCAT distributions. It was also confirmed that the extracted D0 yield vs pT is in good agreement with that measured by STAR [15]over the complimentary pT region. Without a proper p+p baseline extracted
from a similar analysis it is difficult to make any quantitative statements
about the charm or bottom hadron modification within the uncetainties on
the current measurement.
We compared the extracted bottom electron fraction to measurementsin p+p collisions and have found agreement between Au+Au and p+p for
pT > 4 GeV/c within the large uncertainties on both measurements. Since
the total heavy flavor electron are known to be strongly suppressed in Au+Au
collisions from the previous measurement, the agreement between Au+Au
and p+p strongly implies that electrons from charm and bottom hadron
decays are suppressed.
Using the bottom fraction in Au+Au collisions obtained from present
analysis and that in p+p collisions measured by STAR [14], we calculated
the nuclear modification for electrons from charm and bottom hadron decays.
We have observed that bottom electron is suppressed for higher pT region(pT > 4 GeV/c ) in Au+Au collisions compared to p+p collisions for the firsttime in RHIC energy. It strongly implies bottom quarks suffer energy loss inthe matter created in Au+Au collisions at RHIC.
128

Section CHAPTER 8. CONCLUSION
The magnitude of suppression is smaller than that of charm in the regionof 3 < pT < 4 GeV/c and similar for higher pT region within systematic
uncertainty.
We further compared the bottom electron fraction to a variety of theoretical model calculations employing various energy loss mechanisms; radiative
energy loss, Langevin transport, and T-matrix approaches. We have foundthat the extracted bottom electron fraction agrees with a number of models
within the relatively large uncertainties, while it provides new constraints onsome model parameters.
Since these models predict different bottom fraction at pT > 4 GeV/c ,it is important to reduce the uncertainty of the bottom fraction in higher pT
region for future measurement. It is also important to measure the elliptic
flow parameter v2 of electrons from charm and bottom hadron decay, because
it would be sensitive to the coupling of the heavy quark to the QGP medium.
We note that a significantly larger statistics data set of Au+Au collisions√
at sN N = 200 GeV was collected in 2014 with an improved performance of
the VTX detector. The 2014 Au+Au data coupled with the p+p data taken
in 2015 should be important measurements of the nuclear modification of thecharm and bottom electrons in Au+Au collisions.

129

Acknowledgements
Many people provided substantial assistance and encouraged toward thecompletion of this work. First of all, I would like to thank my supervisor
Prof. T. Nagae, and my deputy supervisor Lecturer T. Murakami in Kyoto University for their careful supports and suggestions to complete thisdissertation.
I would like to acknowledge the Radiation Laboratory (Rad. Lab.) at
RIKEN and RIKEN BNL Research Center (RBRC) for the research activity
as well as financial supports. I would like to thank Dr. H. En’yo, who is thechief scientist of the Rad. Lab., for strongly encouraging me to complete thisentire work. I also would like to thank Dr. Y. Akiba, who is the group leaderof the experimental group of RBRC and the project manager of silicon vertex
tracker upgrade. His essential comments and management of the project werecrucial for this work.
I would like to acknowledge all the collaborators of the PHENIX experiment. I was really happy to work together with such an excellent collaboration.
I am deeply obliged to those who were involved in the R&D, production,
construction and operation of the VTX detector : Dr. R. Akimoto, Dr. N.
Apadula, Dr. S. Boose, Dr. K. Boyle, Dr. C.-H. Chen, Dr. L. Ding, Dr. A.
Dion, Dr. A. Enokizono, Dr. K. Fujiwara, Dr. S. Gal, Dr. T. Hachiya, Mr.
J. Kanaya, Dr. J. Koster, Dr. M. Kurosawa, Dr. B. Lewis, Dr. M. Lenz,
Dr. A. Manion, Dr. E. Mannel, Dr. M. McCumber, Prof. R. Nouicer, Prof.
C. Ogilvie, Dr. R. Pak, Prof. C. Pancake, Dr. R.P. Pisani, Dr. H. Sako,
Dr. S. Sato, Dr. M. Sekimoto, Mr. A. Shaver, Dr. M. Shimomura, Dr. M.
Stepanov, Dr. A. Taketani, and Dr. S. Taneja.
I would like to thank the PHENIX computing team: Prof. S. Bathe,
Dr. A. Datta, Dr. A. Franz, Dr. C. Pinkenburg and Dr. J. Seele, for their
management of calibrations of subsystems and the data production.
I would like to thank those involved in the development of VTX softwareand the VTX analysis: Dr. A. Adare, Dr. Y. Akiba, Dr. R. Akimoto, Prof.
S. Bathe, Mr. J. Bryslawskyj, Dr. C.-H. Chen, Dr. L. Ding, Dr. A. Dion,
130

Section CHAPTER 8. CONCLUSION
Dr. M. Kurosawa Dr. T. Hachiya, Mr. T. Koblesky, Dr. A. Lebedev, Dr.
D. McGlinchey, Dr. M. McCumber, Prof. J. Nagle, Prof. R. Nouicer, Mr.
T. Rinn, Prof. M. Rosati, Mr. A. Shaver, , Dr. M. Shimomura , and Dr.
M. Wysocki. A lot of discussions with them, their ideas and suggestions arevital for this work.
I would like to thank all of my friends met in the BNL.
Lastly, , I would like to express my gratitudes to my family for theircontinuous supports and encouragements.

131

Appendix A
Detailed Normalization ofelectron background components
This appendix details the calculation of the normalizations for the background components:• Photonic electrons• Kaon decay electrons• Heavy quarkonia decay electrons
using the bootstrap method described in Section 5.8. We first determine thefraction of nonphotonic electrons, FNP . We then calculate the normalizationof Dalitz and conversion components followed by the normalization of Ke3
and quarkonia components.

A.1

Photonic electrons simulation

π 0 simulation
The ratio of conversion electrons to electrons from Dalitz decay of π 0 in
2011
year 2011 data (RCD
(π 0 )) is determined by GEANT3 simulation. Since B0
hits are always required in tracking, conversion electrons come from beam
pipe and B0 as shown in Figure A.1. π 0 particles are simulated flat in pT at
first and weighted with a published spectra [157] to account for momentum
smearing effects from the finite momentum resolution of the drift chamberand radiative loss of electrons in the material.
2011
As shown in the Figure A.2, the RCD(π 0 ) is 1.10 and flat from 1 to 10
2011
GeV/c . In 2004 data [11], RCD(π 0 ) is 0.4 [179] and a systematic error of 10%132

Section APPENDIX A. DETAILED NORMALIZATION OF ELECTRONBACKGROUND COMPONENTS
is conservatively assigned to account for the fact that the actual thickness of
the Be beam pipe as well as the thickness of the contributing layer of air (infront of the He bag) are not precisely known.
2011
We assign a systematic error of 10% to the RCD(π 0 ) in 2011 data as well,since the actual radiation length of the new Be beam pipe and B0 layer are
not precisely known.

133Section APPENDIX A. DETAILED NORMALIZATION OF ELECTRONBACKGROUND COMPONENTS

Cover page

Figure A.1: Electrons’ vertex position in radial direction in π 0 simulation
before the application of conversion veto. All track cuts described in Chapter
5 are applied.

134

Section APPENDIX A. DETAILED NORMALIZATION OF ELECTRONBACKGROUND COMPONENTS

RCD(π0) in 2011 data
1.2

1RCD(π0)

0.8

0.6

0.4

0.2

0

0

1

2

3

4

5
pe [GeV/c]

6

7

8

9

10

T

Figure A.2: The ratio of conversion electrons to electrons from Dalitz decay
from π 0 simulation as a function of reconstructed electron’s pT . The red lineis the result of a fit to constant.

135

Section APPENDIX A. DETAILED NORMALIZATION OF ELECTRONBACKGROUND COMPONENTS
η simulation
As we observed in π 0 simulation, the ratio of conversion electrons toelectrons from Dalitz decay is pT independent and not sensitive to the slope
2011
of spectra. That ratio of η in 2011 data (RCD(η)) is obtained by just scaling
2011
0
RCD (π ), using theoretical relative branching ratios [180] rather than using
the experimental values which have large uncertainty.
BR(η → 2γ)
BR(π 0 → 2γ)
2011
2011
RCD
(η) = RCD(π 0 ) ∗BR(η → e+ , e− , γ)BR(π 0 → e+ , e− , γ)
2011
= RCD
(π 0 ) ∗0.01190.0162= 0.809(A.1)

We assigned a systematic uncertainty of 10% to the RCD (η) as well.
Direct photon simulation
There are two kind of photonic electrons contributions from direct photons.
• conversion electrons from real direct photons (external conversion)• electrons from direct virtual photon (internal conversion)
The relation between these two contributions is the same as for Dalitz decay of light neutral mesons. In both cases, we deal with a source emitting
photons that can be either real (π 0 (η) → γγ or direct photon) or virtual(π 0 (η) → γe+ e− or direct virtual photon). The contribution from real direct
photons are derived from geant3 simulation using the measured direct photon spectra published by PHENIX [20, 70]. The evaluation of contribution
from direct virtual photon are more complicated, because there is no direct
way to simulate it in geant3 simulation. For the estimation of the electron
contribution from direct virtual photon, we choose to use the Dalitz decayof η shown in Figure A.3 as a representative case, because the phase space
for the electron pair emission is similar up to 5 GeV/c [181, 182]. The pT
weight is applied to the virtual photon emitted from the parent η shown in
Figure A.3 to match the direct photon spectra [20, 70].
136

Section APPENDIX A. DETAILED NORMALIZATION OF ELECTRONBACKGROUND COMPONENTS
e−

γ∗

η

e+

γ
Figure A.3: Diagram of Dalitz decay of η meson.
The ratio of conversion electrons to Dalitz electrons for direct photon(γdir ) is
2011
2011
RCD
(γdir ) = RCD(η)/2.0= 0.404(A.2)

The factor 2 comes from the fact that π 0 and η decays into 2 photons.

A.2

Fraction of nonphotonic electrons FNP

We first determine FNP , the fraction of nonphotonic electrons to inclusiveelectrons after the application of all analysis cuts, including the conversion
veto cut. Note that nonphotonic electrons include contributions from heavy
flavor semi-leptonic decays, quarkonia decays, and kaon decays. Photonic
electrons are from π 0 and η Dalitz decays and photon conversions.
FNP in the 2011 data can be determined using the published 2004 result [11] as follows. Let YNP be the yield of nonphotonic electrons and YDalitz
the yield of electrons from Dalitz decays. Note that both YNP and YDalitz are
independent of the year of data taking. In the PHENIX 2004 Au+Au data
run, the ratio of the nonphotonic electron yield to the photonic electron yield
2004
(RNP
) was measured. The relation of YNP and YDalitz is as follows:
2004
2004
YNP = RNP
(1 + RCD) × YDalitz ,

(A.3)

2004
where RCD
represents the ratio of conversion electron yield to Dalitz electron
yield in the 2004 PHENIX detector. It is calculated as
X
2004
2004
RCD
=
RCD
(i) · rDalitz (i).
(A.4)
i=π 0 ,η,γdir137

Section APPENDIX A. DETAILED NORMALIZATION OF ELECTRONBACKGROUND COMPONENTS
2004
Here RCD(i) is the ratio of conversion electrons to electrons from Dalitz
decays in the 2004 PHENIX detector calculated by a full geant3 simulation.
The factors• rDalitz (π 0 )• rDalitz (η)• rDalitz (γdir )are the fractional contributions of π 0 , η, and direct photon contribution to
the total Dalitz decays, respectively1 . We only consider the contributions of
π 0 , η, and γdir (direct photon) since the sum of other contributions is small(5% or less). Thus they are normalized such thatX
rDalitz (i) = 1.
(A.5)
iFigure A.4 shows rDalitz for π 0 , η, and direct photon as a function oftransverse momentum of the electrons for MB Au+Au collisions at 200 GeV.
The ratios are calculated from the invariant yield of π 0 [157], η [158], anddirect photons [20, 69].
In the 2011 data set the observed electron yields from conversion and
Dalitz decays are modified by the electron survival probability after the conversion veto cut is applied. The yield of photonic electrons which pass theconversion veto (YP2011 ) is
YP2011 = RP2011
D × YDalitz ,X
2011
RP2011=SD (i) + SC · RCD(i) rDalitz (i),
D

(A.6)
(A.7)

i=π 0 ,η,γ

where SC is the survival probability of conversion electrons, SD (π 0 ), SD (η), SD (γdir )are survival probabilities of Dalitz decay electrons from π 0 , η, and direct
2011(i) (i = π 0 , η, γdir )is thephotons, respectively, as shown in Fig. 5.12. RCD
ratio of conversion electrons to Dalitz electrons for particle i in the 2011
PHENIX detector after the addition of the VTX and the replacement of the
2011
2011
beam pipe. It is determined to be RCD(π 0 ) = 1.10 , RCD(η) = 0.809 and
2011
RCD (γdir ) = 0.404 as described in the previous section.
The fraction of nonphotonic electrons to inclusive electrons can then be
calculated as
1

Here we include internal conversion of direct photon in Dalitz decays. Note that the
Dalitz decay of π 0 (η) is caused by internal conversion of one of two decay photons in
π 0 (η) → γγ.

138

rDalitz(fraction of electrons from Dalitz decay)

Section APPENDIX A. DETAILED NORMALIZATION OF ELECTRONBACKGROUND COMPONENTS
1
0.9

Au+Au MBsNN = 200 GeV

π0 → e+e-γ
η → e+e-γ
Direct γ → e+e-

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1

0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
peT [GeV/c]

Figure A.4: The fraction of π 0 , η, and direct photon Dalitz decay electrons
in all Dalitz electrons as a function of electron pT (peT ).

YNP
YNP + YP2011
2004
2004
)
(1 + RCD
RNP
=
2004
2004
RNP (1 + RCD ) + RP2011
D

FNP =

(A.8)
(A.9)

The resulting FNP as a function of peT and the calculated systematic uncertainties due to the uncertainties on the input yields is shown in Fig. A.5.
With FNP in hand, we obtain the number of photonic electrons, NPe , and theenumber of nonphotonic electrons, NNP
as
NPe = Ne (1 − FNP )e
NNP= Ne FNP ,(A.10)(A.11)

where N e is the number of electrons with conversion veto after the subtractionof the hadronic contamination and random background.

139Section APPENDIX A. DETAILED NORMALIZATION OF ELECTRONBACKGROUND COMPONENTS
1
0.9

Au+Au MB sNN = 200 GeV
PHENIX 2011

0.8
0.7
FNP

0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
peT [GeV/c]

Figure A.5: The fraction of nonphotonic electrons to inclusive electrons as
a function of electron pT (peT ).

A.3

Normalization of Dalitz and conversion components

In the previous section we obtained NPe , the number of photonic electrons
in the data after the conversion veto cut. There are two components in thephotonic electrons (NPe ).
1. Electrons from Dalitz decays (π 0 + η + γdir )2. Electrons from conversions in the beam pipe and B0
In the next step, we determine the normalization of Dalitz and conversions
separately. This is needed since the shape of DCAT distribution of Dalitz
and conversions are different.
After application of the conversion veto cut, we have2011
NCe (i) = SC RCD(i)(1 − δrandom )A YDalitz ,e
ND (i) = SD (i)(1 − δrandom )A YDalitz ,(i = π 0 , η, γdir )140(A.12)(A.13)(A.14)

Section APPENDIX A. DETAILED NORMALIZATION OF ELECTRONBACKGROUND COMPONENTS

fraction of photonic electrons

1
0.9
0.8

Au+Au MBsNN = 200 GeV
PHENIX 2011

0.7

π0
η
Direct γ

0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
peT [GeV/c]

Figure A.6: The fraction of π 0 , η, and direct photon electrons in all photonic
electrons as a function of electron pT (peT ).
where NCe (i) and NDe (i) are the number of electrons from conversions andDalitz from particle i after the conversion veto cut, respectively; δrandom isthe common reduction factor of tracks due to random hits in the windowsof the conversion veto cut; and A is the efficiency and acceptance without
the conversion veto cut. Since the number of photonic electron is NPe (i) =NDe (i) + NCe (i), the fraction of conversions and Dalitz decays in the photonic
electrons are
NCe (i)SC RCD (i)
=
,
e
2011
NP (i)SD (i) + SC RCD(i)
NDe (i)SD (i)=,e2011
NP (i)SD (i) + SC RCD(i)(A.15)(A.16)

The fraction of electrons from conversions (NCe /NPe ) and Dalitz (NDe /NPe )is the average of these fractions, thus:
NCe = NPeX

rph (i)2011
SC RCD(i)
2011
SD (i) + SC RCD(i)(A.17)rph (i)SD (i),
2011
SD (i) + SC RCD(i)(A.18)

i=π 0 ,η,γdir

NDe = NPeX
i=π 0 ,η,γdir141

Section APPENDIX A. DETAILED NORMALIZATION OF ELECTRONBACKGROUND COMPONENTS
where rph (i), (i = π 0 , η, γdir ) is the relative contribution of electrons from(conversion + Dalitz decay) for particle i after application of conversion vetocut. Figure A.6 shows rph (i) (i = π 0 , η, γdir ) as a function of peT .
The conversion contributions are nearly the same for π 0 , η and γdir , andeffectively cancel when calculating the ratio. Therefore, rph (Figure A.6) isalmost identical with rDalitz (Figure A.4).

A.4

Normalization of Ke3 and quarkonia components

The ratio of electrons from kaons to all nonphotonic electrons before theapplication of the conversion veto cut, δK , is calculated from the ratio of thenonphotonic electron yield to the electron yield from kaons [11]. Compared
to Ref. [11], we find that ∼ 50% of electrons from kaon decays are removed
by DCAT and DCAL cuts as well as the method used to subtract random
background, which contains some real electrons from kaon decays.
The ratio of electrons from J/ψ decays to all nonphotonic electrons before
the application of the conversion veto cut, δJ/ψ , is taken from Ref. [11]. The
survival rate for electrons from J/ψ decays , SJ/ψ , is taken to be unity, while
the survival rate for Ke3 decays, SK , is taken to be the same value as that forelectrons from charm and bottom decays (namely, SHF ). See Section 5.7.4
for details.
After application of conversion veto cut, the normalizations of these twononphotonic electron components are described by
e
e
NJ/ψ
= NNP
δ
e
NK

e
= NNP
δ

δJ/ψ SJ/ψ
J/ψ SJ/ψ +δK SK +(1−δJ/ψ −δK )SHF

δK S K
J/ψ SJ/ψ +δK SK +(1−δJ/ψ −δK )SHF

(A.19)(A.20)The number of each DCA component satisfies this sum rule
Ne = NNe P + NPee+ NDe + NCe= Nce + Nbe + NKe + NJ/ψ142

(A.21)(A.22)

Appendix B
Coordinate offset and coordinate
offset calibration
The VTX WEST barrel and the VTX EAST barrel are mechanicallyindependent modules and the relative position between the center of VTXWest coordinate system (O(VTX WEST)) and VTX-East coordinate system(O(VTX EAST)) can be moved on the extension rail (Figure B.1, right) in
the PHENIX experimental hall.

Figure B.1: (Left) the vtx local coordinate system for the WEST VTX andthe EAST VTX. (Right) the schematic view when the VTX is retracted.
There are 3 coordinate systems in the PHENIX central arm; VTX-East,
VTX-West and DCH coordinate system. For the association of a central
arm track with VTX described in Section 5.4.4, we need to match those 3
coordinate systems. The west and east half barrels of VTX and DCH in
143

Section APPENDIX B. COORDINATE OFFSET AND COORDINATEOFFSET CALIBRATION
the east and west arms are mechanically separated and the relative positions
are shifted in the PHENIX apparatus. Each time after we open up theapparatus to access to the detectors, we need to calibrate relative positionsof the detectors. The offset calibration is done in the zero magnetic field
run, assuming the beam center position is stable during the run. The beam
center position is used to connect those 3 different coordinate system.

Figure B.2: Parameters of DC hit information and beam center position in
the DCH coordinate system.
Figure B.2 shows a DCH geometry and beam center position. The beam
center position in the x and y direction, dx and dy, are related to dα and φas follows,−dx sin φ + dy cos φsin dα =.
R
Here dx, dy << R is assumed, where R (220 cm) is the middle radius of X1
and X2 plane in DCH.
The beam center position in the VTX-West and VTX-East coordinate
system can be also obtained by the center of primary vertex distribution
which is calculated by VTX half-barrel.

144

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