GlebPhysicsThesis

HEAVY QUARK JET REST FRAME
IDENTIFICATION TECHNIQUE AND
INCOHERENT ANALYSIS AT ALICE
By
Gleb Batalkin
A THESIS
Presented to the Faculty of the Graduate School of
Creighton University in Partial Fulfillment of the
Requirements for the Degree of Master of Science in
the Department of Physics
Omaha, 2015

c Copyright by Gleb Batalkin, 2015.
All rights reserved.

Abstract
Using the ALICE analysis framework, this thesis studies a novel rest frame jet iden-
tification technique as well as the photo-nuclear production of the meson in Ultra
Peripheral Collisions (UPCs) at ALICE. A unique jet identification technique was
developed which substantially reduces the number of non-heavy flavor jets in a jet
sample. Coherently produced mesons are not observed at ALICE while incoherently
produced mesons are observed with a cross section in the range between 1900 and
30600 µbarns in 2011 Pb-Pb collision data collected during Run 1 at the LHC.
iii

Acknowledgements
I wish to thank my advisors, Dr. Michael Cherney and Dr. Janet Seger, who
have guided my research work as a high energy nuclear physicist over the years. As a
graduate advisor, Dr. Cherney gave me the opportunity to visit and work at CERN
for which I am tremendously grateful. He has also made special e↵ort to support me
through the hardships I encountered during my graduate studies. Thank you, Dr.
Cherney.
I would also like to thank Dr. Martin Poghosyan for his willingness to answer
questions regarding the ALICE analysis framework and especially for his contribution
to the simulations that are so critical to this work.
Also, I wish to thank the many others have helped and taught me through the
years including Dr. Christine Nattaras, Dr. Bjorn Nilsen, Barak Gruberg, and Joel
Mazer.
Finally, this work would not have been possible without the funding and support
of the U.S. Department Of Energy, the ALICE collaboration, and the Creighton
University Physics Department.
iv

To my parents, whose sacriﬁces created opportunities I wouldn’t otherwise have.
v

Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
1 Introduction 1
1.1 History of Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Fermions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.2 Bosons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Large Hadron Collider 6
2.1 A Large Ion Collider Experiment . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Inner Tracking System . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 Time Projection Chamber . . . . . . . . . . . . . . . . . . . . 10
2.1.3 Transition-Radiation Detector . . . . . . . . . . . . . . . . . . 11
2.1.4 Time Of Flight . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.5 Particle Identiﬁcation . . . . . . . . . . . . . . . . . . . . . . . 14
3 Jets 17
3.1 Jet Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Jet Quenching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
vi

3.3 Heavy Flavor Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4 Heavy Flavor Jet Identiﬁcation 22
4.1 b-Carrying Meson Selection . . . . . . . . . . . . . . . . . . . . . . . 22
4.2 Charm Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.3 Rest Frame Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.4 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.4.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.4.2 Selection Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 27
4.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5 Ultra-Peripheral Collisions 34
6 Meson Analysis 38
6.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.1.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.1.2 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 40
6.1.3 Particle Identiﬁcation . . . . . . . . . . . . . . . . . . . . . . . 40
6.1.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.2 Cross Section Calculations . . . . . . . . . . . . . . . . . . . . . . . . 42
6.3 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Bibliography 54
A Analyzed Run Numbers Corresponding to a Subset of 2011 Collision
Data 56
A.1 LHC11h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
B STARLight Input Parameters 57
vii

List of Tables
3.1 Quark Mass Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.1 Target Decay Branching Ratios . . . . . . . . . . . . . . . . . . . . . 23
6.1 Meson Decay Channels . . . . . . . . . . . . . . . . . . . . . . . . . 38
6.2 Real Data Yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.3 Simulated Data Yields . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.4 Cross Sections Method 1 . . . . . . . . . . . . . . . . . . . . . . . . 48
6.7 Incoherent Meson Cross Section Comparison . . . . . . . . . . . . . . 53
viii

List of Figures
1.1 Standard Model of Particle Physics . . . . . . . . . . . . . . . . . . . 4
2.1 Aerial View of CERN . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 ALICE Sub-detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Inner Tracking System Detector . . . . . . . . . . . . . . . . . . . . . 9
2.4 Time Projection Chamber Detector . . . . . . . . . . . . . . . . . . . 11
2.5 Transition Radiation Detector . . . . . . . . . . . . . . . . . . . . . . 12
2.6 Time Of Flight Detector . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.7 Characteristic Detector PID Plots . . . . . . . . . . . . . . . . . . . . 15
3.1 Hadronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.1 B±
Decay Feynman Diagrams . . . . . . . . . . . . . . . . . . . . . . 23
4.2 pL,boosted Distributions by Lepton/Kaon Pair . . . . . . . . . . . . . . 29
4.3 cos(✓) Distributions by Jet Type . . . . . . . . . . . . . . . . . . . . . 30
4.4 cos(✓) Distributions by Jet Type (Zoom) . . . . . . . . . . . . . . . . 31
4.5 Mass Distributions by Jet Type . . . . . . . . . . . . . . . . . . . . . 32
4.6 Jet Sample Purity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.1 Collision Impact Parameter . . . . . . . . . . . . . . . . . . . . . . . 35
5.2 Ultra-Peripheral Collision Lorentz Contraction . . . . . . . . . . . . . 35
5.3 Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
ix

6.1 Monte Carlo Mass Plots . . . . . . . . . . . . . . . . . . . . . . . . 42
6.2 Reconstructed Monte Carlo Plots . . . . . . . . . . . . . . . . . . . 43
6.3 Selected Real Data PID Bin Plots . . . . . . . . . . . . . . . . . . . 45
6.4 Selected Monte Carlo PID Bin Plots . . . . . . . . . . . . . . . . . 46
x

Chapter 1
Introduction
1.1 History of Particle Physics
Philosophy and science seek to understand how the world works. One way to study
this question is by studying how fundamental building blocks interact and combine
to form the world. For most of recorded history it was believed that repeatedly
splitting matter into its constituents would eventually lead to fundamental, indivisible
constituents. Literally meaning ‘indivisible’, this particle was called the ‘atom’.
This belief persisted until the late 19th and early 20th centuries. By the beginning
of the 20th century, through the works of Crookes, Schuster, and J.J. Thomson, it
was known that there exists a negatively charged particle, given the name ‘electron’.
During the early 20th century, it was shown that atoms consist mostly of empty space
but have a concentrated massive nucleus [1]. It was theorized that the electron was
part of the nucleus of an atom and that a similar, positively charged particle must
also exist. By this time, simply knowing of the existence of these constituent particles
was not enough - scientists began studying how these constituent particles interacted.
The only two forces then known - the gravitational and electromagnetic forces - could
1

not explain why the atomic nucleus did not simply ﬂy apart due to the large repulsive
Coulomb force between nearby like charges.
By the mid 20th century, the combined works of many scientists had shown that
there exist a number of particles, then believed to be fundamental, called electrons,
neutrons, and protons. Theories about how these particles interacted were based
on the gravitational and electromagnetic forces as well as a new, theorized nuclear
force. Furthermore, the advancement of quantum mechanical theory brought on
revelations including the idea of a wave-particle duality of matter as well as light
(classically represented by a wave) [1]. From the principles of quantum mechanics, it
was theorized that there must be yet smaller, unknown, constituent particles making
up the known electron, neutron, and proton. Using the spin-statistics theorem, these
yet unknown particles were split into two groups: fermions, the particles that make
up matter, and bosons, the force carrier particles that keep fermions together and
govern their interactions.
After the mid 20th century, gathering evidence to prove theories of more complex,
elusive, and even smaller particles required advances in technology. The birth of
particle accelerators, powerful machines designed to accelerate and smash together
particles in order to observe the resulting shower of constituent particles, marked the
beginning of a new era in physics. These machines turned out to be very e↵ective.
As particle accelerator and detector technologies improved, the number of unique
particles continued to increase and eventually the entire collection was embarrassingly
named the ‘particle zoo’. It was clear that all of the then-known particles could not
be elementary particles.
In 1964, the quark model laid the foundations for a concise theory capable of
explaining the observed properties of then-known particles [2]. In the 1970s, this
model was developed further into what is known today as the theory of quantum
chromodynamics. This theory deﬁned a new constituent particle - the quark. This
2

particle was proposed to be the most elementary particle which combined with other
quarks to form hadrons. Rules governing the ways in which these quarks may combine
revolve around a property of the quark, called ‘color’. It is believed that quarks cannot
exist independently. The existence of the quark has since been proven through various
rigorous indirect experiments.
In the last several decades, significant advances in accelerator and detector tech-
nologies have pushed particle physics into the realm of high energy collisions. A
theory called the Standard Model has been developed to summarize the current un-
derstanding of elementary particles and their interactions [2]. Through the use of
powerful particle accelerators capable of achieving very high energy collisions, such
as the Large Hadron Collider (LHC), which operates on the order of Tera-electron-
Volt (TeV) energies, many aspects of the Standard Model have been experimentally
verified. The most recent advancement has been the discovery (or verification) of the
Higgs boson - a particle that is believed to be responsible for giving matter mass.
1.2 Standard Model
The Standard Model of particle physics describes how elementary particles interact
to produce all other particles. The model groups elementary particles by the value of
their spin property into two groups: 1
2
-integer spin fermions and integer spin bosons.
Combining this grouping with particle color and charge properties, it is possible to
predict how particles interact with one another[2, 3]. A summary of this model can
be found in Figure 1.1.
1.2.1 Fermions
Figure 1.1 show the arrangement (based on charge and mass) of two groups of parti-
cles: quarks and leptons. The primary di↵erence between these two groups of particles
3

Figure 1.1: A graphical summary of the Standard Model of particles physics showing
the grouping of particles by spin, charge, and mass [2].
is that the leptons are not subject to strong force interactions while the quarks are.
Both groups consist of half-integer spin particles and are collectively referred to as
fermions.
1.2.2 Bosons
There are ﬁve elementary bosons. Together, bosons are responsible for mediating
all of the interactions that occur between any particles. Photons act as force-carrier
particles for electromagnetic interactions between charged particles. Gluons act as the
strong force-carriers between particles with ‘color’ (including both quarks and other
gluons). Both gluons and photons are massless but, unlike photons, gluons carry
the color property associated with the strong force interaction, meaning that gluons
may interact with other gluons as well as quarks. The other three bosons are force
4

carriers for weak interactions. The gluon, photon and Z boson are electrically neutral
while the W+
and W bosons have a charge of +1 and 1, respectively. Finally, the
recently veriﬁed Higgs boson is a spinless, neutral particle that gives mass to other
particles.
5

Chapter 2
Large Hadron Collider
Figure 2.1: An aerial view of CERN. A circular overlay has been added to show the
underground path of the LHC beam pipe [4].
The Large Hadron Collider (LHC) is a circular particle accelerator located on the
Franco-Swiss border outside Geneva, Switzerland operated by the European Organi-
6

zation for Nuclear Research (CERN). The LHC currently operates at higher collision
energies than those achieved by previous generations of particle accelerators. Among
its intended goals, the LHC was constructed to produce evidence of the Higgs Boson
as well as to study physics beyond the Standard Model.
The underground structure of the LHC, represented by the yellow circle overlay in
Figure 2.1, includes not one, but two sets of beam pipes that intersect at designated
points. During operation, ion beams are accelerated and allowed to travel in opposite
directions along these beam pipes. When the beams cross at the designated beam
pipe intersections, collisions occur. Detectors, like ALICE, are built centered about
these collision points.
2.1 A Large Ion Collider Experiment
A Large Ion Collider Experiment (ALICE) is a general-purpose heavy-ion collision
experiment on the LHC at CERN. The primary purpose of ALICE is to study the
physics of strongly interacting matter at the extreme energy densities produced in
collisions at the LHC. A diagram including the full list of sub-detectors of the 26 m
long, 16 m high, 16 m wide ALICE detector can be found in Figure 2.2. The work in
this thesis primarily relies on four detectors - The Inner Tracking System (ITS), the
Time Projection Chamber (TPC), the Transition-Radiation Detector (TRD), and the
Time-Of-Flight (TOF).
The structure and function of these sub-detectors is discussed in detail below.
Finally, the ALICE detector is partly surrounded by a massive solenoidal magnet
capable of generating a magnetic ﬁeld of up to 0.5 T throughout the inner volume
of the detector. The presence of this ﬁeld causes any charged particles that traverse
the volume of the detector to follow a curved trajectory. Curvature combined with
7

data provided by the enclosed sub-detectors is used to identify particles produced in
collisions.
Figure 2.2: The physical structure, including sub-detectors, of the ALICE detector.
Of particular interest for the work in this thesis are the ITS (1), TPC (3), TRD (4),
and TOF (5) sub-detectors [5].
8

Figure 2.3: The physical structure of the ITS [5].
2.1.1 Inner Tracking System
The Inner Tracking System (ITS) detector consists of six cylindrical layers of sil-
icon detectors detailed in Figure 2.3. The layers have respective radii of about
r = 4, 7, 15, 24, 39, and 44 cm centered about the axis of the beam pipe. ITS
covers the region within ±45 of the vertical plane. The radius of the inner layer is
limited by the 3 cm beam pipe radius, while the radius of the outer layer is designed
to be able to match tracks with those from the TPC.
Due to the high particle densities near the collision vertex (approximately 50
particles/cm2
), Silicon Pixel Detectors (SPD) capable of distinguishing particle tracks
with a resolution of up to 80 particles/cm2
are used for the two innermost layers. The
SPD layers are responsible for precisely locating the collision vertex. The following
four layers consist of Silicon Drift Detectors (SDD) and Silicon Strip Detectors (SSD).
High particle detection resolution is unnecessary in these layers as they are located
radially further outward from beam pipe. These layers are primarily responsible for
tracking particles exiting the collision vertex and are equipped with analog readouts
for particle identiﬁcation using measurements of dE/dx, the gradient at which energy
9

is deposited by particles in the detector. The ITS detector is a stand-alone low
transverse momentum (pT ) particle spectrometer with some particle identiﬁcation
capability [6].
The ITS has several important functions, including:
• to determine the primary vertex location with a resolution better than 100 µm,
• to determine the secondary vertex locations resulting from decays and interac-
tions,
• to help track and identify particles,
• to improve the tracking resolution of high-pT particles which also traverse the
TPC, and
• to reconstruct, with limited momentum resolution, particle tracks passing
through the dead regions of or not reaching the TPC.
The ITS is crucial due to its ability to identify primary and secondary vertices as
well as its ability to distinguish particles due to its high particle resolution.
2.1.2 Time Projection Chamber
The Time Projection Chamber (TPC) is a cylindrical barrel centered about the center
of the beam pipe with an inner radius of about 80 cm, an outer radius of about 250
cm, and a length of about 500 cm. The 88 m3
volume of the TPC is ﬁlled with 90%
Ne and 10% CO2. Charged particles that pass through the volume of the TPC leave a
trail of ionized gas. The TPC gas volume is divided into two regions by a conducting
disk that is held at 100 kV and serves as an anode. The end-caps of the TPC serve as
cathodes and also contain readout electronics. Figure 2.4 provides a visualization of
this arrangement which causes the positively ionized gas to drift towards the central
anode and the ionization electrons to drift towards the outer cathodes. The readout
10

electronics record magnitude of charge and timing information which is then used to
reconstruct the path of the particle through the volume of the TPC.
The TPC, one of the main tracking detectors of ALICE, fulﬁlls the following
functions:
• to provide charged-particle momentum measurements with good two-track sep-
aration,
• to provide particle identiﬁcation information via ionization dE/dx measure-
ments, and
• to identify secondary vertices.
Figure 2.4: The physical structure of the TPC [5].
2.1.3 Transition-Radiation Detector
The Transition-Radiation Detector (TRD), shown in Figure 2.5, consists of 18 super-
modules arranged in a 6-layer cylindrical shell mounted in the region directly outside
the TPC. Physically, the TRD has an inner radius of 2.9 m and an outer radius of
11

3.7 m with 1.16 · 106
readout channels with a total active area of 736 m2
(including
the areas of each inner layer). Each module contains a radiator and a drift chamber.
Charged particles crossing the radiator emit transition radiation as they cross mate-
rials with di↵erent dielectric constants. The drift chamber, which is physically glued
to and follows the radiator, is a 30 mm deep chamber with a drift field of 700 Vcm 1
.
Electrons that drift through this chamber are collected by the read-out electronics
and amplified to form and record a signal. By using signals from adjacent read-out
pads, it is possible to infer the momentum of the particle [7, 8].
Figure 2.5: The physical structure of the TRD. Note that there are 18 total super-
modules, each of which is constructed from 6 radial layers and 5 longitudinal stacks
[8].
In the context of the work carried out in this thesis, the TRD provides the neces-
sary information to distinguish the relatively few electrons from the many pions. In
the TRD, the specific energy loss of electrons is larger than that of pions, making it
12

possible to distinguish one from the other. In general, the TRD fulfills the following
functions:
• to contribute to particle identification and
• to contribute to particle track reconstruction.
2.1.4 Time Of Flight
The Time Of Flight (TOF) detector, as shown in Figure 2.6, is also cylindrical with
an inner radius of about 3.7 m and a total outer surface area of nearly 160 m2
. Like
the TRD, the TOF also has 18 modules, which are constructed from 5 longitudinal
stacks of Multi-gap Resistive Plate Chambers (MRPCs). Each MRPC is a stack of
resistive glass plates held at a high external voltage. Charged particles traversing
the stack trigger an electron avalanche in each layer of the MRPC. An anode pickup
electrode collects and sums the signals from each layer. In total, 1638 MRPCs with
157248 readout pads are used. Based on the signals from multiple adjacent MRPCs,
it is possible to match particle tracks to those provided by the tracking detectors in
ALICE and to calculate particle time of flight as well as velocity [9, 10].
The purpose of the TOF detector is:
• to measure the time of flight of each charged particle through the TRD and
• to calculate particle velocity which is useful for particle identification.
13

Figure 2.6: The physical structure of the TOF. Note that there are 18 modules, each
of which is constructed from 5 longitudinal stacks of MRPC strips [9].
2.1.5 Particle Identification
Particle Identification (PID) at ALICE primarily employs information provided by
the detectors described previously - ITS, TPC, TRD, and TOF. These detectors
provide particle track, energy deposition (dE/dx), and velocity information which
can be combined to identify and distinguish charged particles. A set of plots showing
the characteristic PID plots of each detector are shown in Figure 2.7.
In the TPC, momentum information of a charged particle passing through its
volume can be found by applying the Lorentz Force equation:
~F = q( ~E + ~v ⇥ ~B), (2.1)
where q and ~v are the charge and velocity of the particle, while ~E and ~B are the electric
field of the TPC and the magnetic field of ALICE. The drift velocity resulting from
the presence of the TPC’s electric field is insignificant, leaving the particle’s equation
14

Figure 2.7: dE/dx spectrum for the ITS (1), TPC Signal vs. track momentum (2),
track velocity ( ) vs. momentum for the TOF (3), and signal amplitude for electrons
and pions in the TRD (4) [11, 12].
of motion to be given by:
~F = q~v ⇥ ~B. (2.2)
It can be shown that this equation leads to,
mv? = qrB, (2.3)
where m, v?, and q are the mass, tangential velocity, and charge of the particle;
r is the radius of curvature of its path; and B is the magnitude of the magnetic
ﬁeld of ALICE. Therefore, the component of a charged particle’s momentum that is
15

perpendicular to the magnetic ﬁeld is given by,
p? = qrB. (2.4)
Combining this momentum with the velocity measured by the TOF detector leads
to a calculation of the mass of the charged particle. Therefore, ALICE can identify
charged particles with good precision across a broad momentum range (0.1 to 10+
GeV/c) [9, 10, 13].
16

Chapter 3
Jets
3.1 Jet Physics
Phenomena observed in high energy nuclear physics include the production of pairs
of collimated beams of hadrons, called “jets”. Collisions at the LHC occur between
very energetic (1.38 TeV beam energies during Run 1 [14]) protons. When oppositely
moving protons collide, the quarks that they carry interact and scatter, which results
in the quarks being deflected in opposite directions in their center of mass frame. The
same behavior is observed for heavy ion collisions.
From Quantum Chromodynamics (QCD), it is known that quarks are subject
to color confinement, which means that they cannot exist as independent entities
(without being grouped with other quark(s) and/or antiquarks) [2]. It follows that
quarks deflected in collisions cannot simply move apart and exist on their own. From
QCD, it is also known that the potential energy between a pair of quarks increases
with their separation. The potential energy between two quarks as a function of
separation can be approximated by,
U(r) =
4↵s
3r
+ kr, (3.1)
17

where r is the separation and k, ↵s are constants [2]. The potential energy increases
as the quark pair separates until the energy density in the region of space between
them is su cient to create a quark-antiquark pair. Each of the original quarks pairs
up with one of the newly formed quarks or anti-quarks. This process, known as
hadronization, continuously repeats to form a collimated beam of hadrons - a jet
[15]. Figure 3.1 depicts this process. Jets form from the scattering of two quarks,
where one is in a nucleon in one beam particle and the other is in a nucleon in the
other beam particle. These quarks deflect in opposite directions, meaning that jets
are expected to always form in pairs and to also travel in opposite directions. It is
therefore expected that jets are observed in oppositely moving pairs and with similar
energies, assuming there is no significant interaction with the collision medium [15].
Experimentally, a jet can be defined in terms of the collection of particles in a
momentum cone centered about and aligned with the momentum vector of the leading
hadron. The cone is defined in terms of an angle between the momenta vectors of the
particles in the jet and the weighted average of the momenta of the leading hadron
and the particles produced in its wake.
18

Figure 3.1: Visual representation of the hadronization process in quark scattering.
Shown is a pair of quarks interacting via the strong force after scattering. Potential
energy between these quarks grows with their separation until there is enough energy
to produce a new quark/anti-quark pair. Each subsequent quark has a smaller veloc-
ity. The di↵erence in velocities between quark pairs results in increasing separation
which results in continued production of quark/anti-quark pairs over time.
3.2 Jet Quenching
Conditions immediately following central and peripheral ion collisions at the LHC are
similar to those of the early moments of the Big Bang - matter is in a high temperature
and high density state [15]. Jets formed inside the volume of this medium lose energy
and undergo a broadening of their jet cone through interactions with the matter in
19

the medium. The combination of these two phenomena is known as jet quenching.
Energy loss occurs as a result of two e↵ects, the ﬁrst of which is a Bremsstrahlung-like
gluon radiation given by,
dE
dx
⇡ C2
↵sµ2
4
(
L
)ln(
2E
µ2L
), (3.2)
where C2 is the Cassimir constant of the propagating quark, µ is the Debye screening
mass, L is the distance traveled in the medium, and is the gluon’s mean-free-path
[15]. The second e↵ect is the scattering between the quarks carried by the hadrons in
the jet with partons (quarks and gluons) in the hot, dense medium produced in the
initial collision. Loss of energy through multiple scattering is approximated in terms
of dE/dx by the Bjorken equation,
dE
dx
⇡
3
2
✏
1
2 log(
4ET
M2
), (3.3)
where ✏ and T are the energy density and temperature of the medium; E and M are
the energy and mass of the particle. Note that the energy lost through scattering is
proportional to the logarithm of the inverse square of the mass [16]. Therefore, heavy
ﬂavor jets which form from heavier particles lose less energy through scattering than
their lighter counterparts. The energy loss through scattering in general is expected
to be an order of magnitude smaller than the energy loss due to the gluon radiation
e↵ect [15, 17].
Experimentally, it is possible to observe jet quenching by identifying events with
a single detectable jet. Such events occur only if one jet was suppressed. It is also
possible to observe a pair of jets with one or both jets partially suppressed, which is
evident through broadened jet cones or reduced jet energy of one jet relative to the
other. How much energy is lost depends on the point of origin of each jet within the
hot, dense post-collision medium and on the mass of the leading hadron [15].
20

Table 3.1: Quark Masses [18].
Quark Mass (GeV/c2
)
u 0.0023 ± 0.0005
d 0.0048 ± 0.0005
c 1.275 ± 0.025
s 0.095 ± 0.005
t 173.5 ± 0.8
b 4.65 ± 0.03
3.3 Heavy Flavor Jets
A heavy ﬂavor jet is produced from the hadronization of a pair of t, b, or c quarks.
The b and c quarks are the second and third heaviest quarks, as shown in Table 3.1,
with a mass of 4.65 ± 0.03 GeV and 1.275 ± 0.025 GeV respectively [18]. Particles
containing t quarks are not produced with good statistics at the LHC. For this reason,
the work in this thesis focuses on jets produced by particles containing b and c quarks.
The motivation for studying heavy ﬂavor jets is that these jets are more massive and
therefore lose less energy due to the scattering. Such jets are ideal for studying the
gluon-radiation aspect of jet quenching which can provide insight about interactions
that occurred in the medium immediately following the Big Bang.
21

Chapter 4
Heavy Flavor Jet Identification
As mentioned in the previous chapter, there is motivation to study jets produced
by heavy quarks. The energies at the LHC and the detector capabilities of ALICE
are well suited for the study of jet quenching in heavy flavor jets. By identifying
a b-quark-carrying particle with a unique decay mode and performing a rest frame
analysis, it is possible to select a jet sample with a high fraction of bottom jets. The
following sections discuss this bottom jet identification approach.
4.1 b-Carrying Meson Selection
There are many particles that carry b quarks. It is important to identify one such
particle that decays in a su ciently unique way (compared to jets with di↵erent
leading hadrons) to be distinguishable by the ALICE detector. An excellent candidate
is the charged B meson, which is composed of a combination of up and bottom quarks
and has a mass of 5.28 ± 0.31 GeV/c2
.
One observable decay channel of the B±
meson has a final state of l±
⌫lK±
, where
the K+
is composed of u¯s and K of ¯us. This decay is unique in that the same final
state is not found in jets formed by the hadronization of lighter quarks (including
up, down, or strange) because the kaon must decay from a parent carrying a quark
22

heavier than a strange quark. These lighter jet types will be referred to from here
as, “other jets”. An example decay is given in Figure 4.1. The branching ratios of
the most probable decay channels resulting in these decay products (B±
to Dl±
⌫l to
K±
anything) are given in Table 4.1.
Table 4.1: Decay channels and their branching ratios for B± and D mesons [18].
Meson Mode Fraction( i/ )
B±
l±
⌫lanything ( 10.99 ± 0.27 ) %
B±
Dl±
⌫l ( 9.8 ± 0.7 ) %
D K±
anything ( 54.7 ± 2.8 ) %
D K±
l⌥
⌫lanything ( 8.46 ±1.3
0.5 ) %
Figure 4.1: Feynman diagrams for a possible decay of B±
meson [18].
The lepton in this unique decay state is the first generation lepton, meaning that
it is expected to be the leading (greatest momentum) lepton of its type. As a result,
the first step in identifying bottom jets is to identify jets that contain a like-signed
leading lepton and kaon pair within the jet cone. This is intended to be a first-pass
selection of bottom jets. The maximum e ciency of this selection is the product of
the branching ratio of B+
decaying into Dl+
⌫l at a rate of 9.8% and the daughter
D decaying into K±
anything at a rate of 54.7% resulting in a rate of 5.36%. This
considers the e ciency of selection of positive B mesons only. Including negative B
23

mesons, the maximum e ciency of first-pass selection is 10.72%. Events identified
by selecting such like-signed pairs are not expected to be purely composed of bottom
jet events because it is possible for stray leptons produced in the initial collision
to coincidentally contaminate the jet, leading to a false identification. Section 4.3
describes how rest frame analysis can help to purify the sample.
4.2 Charm Contribution
As shown in Table 4.1, charm mesons (Ds) have a decay channel in which the final
state contains a lepton/kaon pair with opposite signs. An event with a pair of charm
jets comes from the decay of a charm meson and its anti-particle. Because there is a
pair of charm and anti-charm mesons (whose quarks may change flavor into strange
quarks), it is possible for them to decay in such a way that the combined final states
contain K+
K l+
l , and 2⌫l. The first pass selection criteria described in the previous
section selects events with like-signed lepton/kaon pairs. Therefore, it is possible for
charm based decays to be selected in the first pass selection sample. This means that
the final sample will have contributions from charm based heavy flavors jets and not
only bottom jets.
4.3 Rest Frame Analysis
Rest frame analysis makes use of Lorentz transformations to boost each particle’s
longitudinal momentum (pL with respect to the original hadron) to the rest frame of
the original hadron (in this case, a B±
meson). The longitudinal momentum compo-
nent of each particle is obtained by taking the dot product between the momentum
vectors of the particle with that of the leading hadron in the jet,
~pL = ~p · ûhadron, (4.1)
24

where the hadron momentum unit vector, ˆuhadron is given by,
ˆuhadron =
~phadron
||~phadron||
. (4.2)
Then, the Lorentz transform for momentum is given by the following equation[2]
,
p0
L = hadron(pL
vhadronE
c2
), (4.3)
where hadron is the Lorentz factor of the leading hadron given by,
hadron =
1
q
1 2
hadron
, (4.4)
and,
hadron =
vhadron
c
, (4.5)
In practice, a more useful expression in natural units is obtained by the following
steps,
hadron =
1
r
1
v2
hadron
c2
=
1
r
1
m2v2
hadron
m2c2
=
1
r
1
p2
hadron
E2
hadron
, (4.6)
hadron =
Ehadron
q
E2
hadron p2
hadron
=
Ehadron
m0,hadron
, (4.7)
where m0,hadron is the rest mass of the original leading hadron. The rest mass is
invariant under a Lorentz transform and can therefore be obtained by summing the
momenta and energies of the decay products and by using,
m2
0 = E2
p2
. (4.8)
To boost each particle in the jet to the rest frame of the original hadron, it is
necessary to use quantities that are not known - the energy and momentum of the
25

original hadron. However, it is possible to estimate the ratio given by equation 4.7
by summing the energy and momenta of the first generation decay products of the
original hadron - the leading lepton and like-signed kaon.
Performing the Lorentz transformation reveals the decay distribution for the par-
ticles in the jet cone parametrized as cos(✓), where ✓ is the angle between the boosted
momentum vector (~pboosted) of each particle in the jet and ~phadron. cos(✓) can be found
using the dot product,
~A · ~B = || ~A|| || ~B|| cos(✓). (4.9)
So,
cos(✓) =
~pboosted · ~phadron
||~pboosted|| ||~phadron||
. (4.10)
Particles that are descendants of spin-0 B mesons have no favored decay direction
and are therefore expected to have a flat distribution in cos(✓) in the rest frame of the
B meson. Particles that are not decay products of the B meson with momenta vectors
that coincidentally travel along the jet momentum axis tend to be over boosted or
under boosted resulting in a distribution with peaks at large |cos(✓)|. By selecting
particles in the flat region of this distribution, which are likely the decay products of
the B meson, it is possible to estimate the invariant mass of the particle that produced
the jet by using equation 4.8.
4.4 Methods
4.4.1 Data
Monte Carlo (MC) Simulations were used to develop this bottom jet identification
algorithm. The simulation was generated for proton-proton collisions under a 0.5 T
magnetic field and at 2760 GeV energies using Jet-Jet Pythia6 [19]. This simulation
can be found at /alice/sim/2012/LHC12a15a/ on the CERN Grid.
26

4.4.2 Selection Algorithm
The ALICE analysis framework provides a Jet Finder algorithm which identifies col-
lections of particles moving in a cone along the same axis. Also, in MC simulations,
kinematic and identification information is available for every particle, including in-
termediate singular quarks (which is not possible in the final state in the real world
according to QCD). While working with simulations, bottom jets are defined to be
jets that contain an early stage b quark moving in the jet cone. Likewise, charm jets
are defined to be jets that contain a c quark but do NOT contain a b quark. Jets
formed from other hadrons are considered to be ‘other jets’. Given the information
available in the simulation, all jet types are known and can be compared against the
results of the rest frame analysis.
In implementing the selection algorithm, Particle Identification (PID) cuts are
applied first. These include:
• Real charged particle selection via Particle Data Group’s Monte Carlo number-
ing scheme (PDGID) such that |10 < PDGID < 20|, |100 < PDGID|,
• Primary vertex within 3 cm of beam pipe center and within 100 cm of collision
vertex , and
• Particles within the jet cone by requiring particle ~p within 50 of jet axis.
The algorithm then carries out rest frame analysis by identifying jets with a like-
signed pair of leading electron/kaon and µ/kaon pairs, estimating , velocity, and
energy of the leading hadron, and performing the Lorentz transformation on each
particle in the jet cone to obtain a boosted pL. Then, the pL,boosted is used to calculate
cos(✓) which is used to calculate the invariant mass of the leading hadron by summing
over the momenta and energies of all particles with 0.5 < cos(✓) < 0.5.
27

4.5 Results
Figure 4.2 shows the results of the application of the selection algorithm separated
by jet type (for electron/kaon and muon/kaon pairs). These plots on their own do
not show significant di↵erences between jet types. Figures 4.3 and 4.4 show the
cos(✓) distributions which by themselves do not reveal di↵erences between jet types.
However, using these distributions to calculate the mass of the parent as previously
described leads to the mass distributions shown in Figure 4.5.
The parent mass distribution for the µ/K estimate in bottom jets shows a promis-
ing peak below the mass of the B±
hadron. It is reasonable for the mass to be under-
approximated due to the nature of the method. An estimate of the number of bottom
mesons remaining after the selection can be found by counting the number of entries
where the parent mass is between 3.5 GeV/c2
and 5.5 GeV/c2
in the µ/K estimate
parent mass distribution. Based on this, the final sample contains about 22 bottom
jets. The simulation used for this work contains 8617 bottom jets, of which 98 bottom
jets contain a like-signed µ/K pair. Therefore the e ciencies of selection are 22.45%
out of the bottom jets that contain a µ/K pair and 0.2553% overall.
Similarly, the parent mass distribution for the µ/K estimate in charm jets shows
a peak below the charm meson mass of 1.86 ± 0.07 GeV/c2
. The number of entries
where the parent mass is between 3.5 GeV/c2
and 5.5 GeV/c2
is 156. The simulation
contains 79527 charm jets, of which 669 contain a like-signed µ/K pair. Therefore
the e ciencies of selection are 23.32% out of the charm jets that contain a µ/K pair
and 0.1962% overall.
Finally, Figure 4.6 shows the improvement in purity of the selected jet sample
which becomes dominated by heavy flavor jets over the unselected sample which is
dominated by lighter jets. Note that this method is useful for selecting not only
bottom jets but also charm jets, as there is a high fraction of charm jets remaining
in the final sample due to the charm contamination described in section 4.2.
28

Figure 4.2: pL,boosted distributions. Note that these distributions show no signiﬁcant
di↵erences between jet types.
29

Figure 4.3: Boosted angular distributions. Note that the entries at |cos(✓)| >> 0
values correspond to particles that are over or under boosted.
30

Figure 4.4: Boosted angular distributions with reduced range in cos(✓). Note that
the entries in this cos(✓) range in Bottom jets likely correspond to particles that are
descendants of the particle that produced the jet because the distribution in this
range is somewhat ﬂat.
31

Figure 4.5: Leading hadron estimated mass distributions (parent mass calculated us-
ing particles in the ﬂat region of the previously shown boosted angular distributions).
32

Figure 4.6: Composition of jet samples. Raw represents a sample of simulated jets
with no selection criteria. Note that such a sample is dominated by Other jets.
Selected represents the same sample of simulated jets after the application of the
ﬁrst-pass selection criteria. Note that the sample is now dominated by heavy ﬂavor
jets.
33

Chapter 5
Ultra-Peripheral Collisions
Collision types in High Energy Nuclear Physics can be defined in terms of an impact
parameter, b, the separation between the centers of oncoming nuclei as seen in Figure
5.1. Collisions are considered ‘Central’ when b ⇠ 0, ‘Peripheral’ when 0 < b < 2r,
and ‘Ultra-Peripheral’ when b > 2r. This and the following chapter focus on Ultra-
Peripheral Collisions (UPCs).
UPCs are particularly interesting because particles are still generated in this type
of collision even though no nucleon-nucleon collision occurs. The LHC accelerates
heavy ions to speeds of about 0.999999991 c, or 3 m/s slower than the speed of
light. At these speeds, relativistic e↵ects are dominant, meaning that due to Lorentz
contraction the shape of each nucleus is no longer spherical, but rather more like
that of a disk with the normal vector of the disk aligned with the velocity vector of
the nucleus. See Figure 5.2. This contraction causes the electromagnetic fields to be
concentrated in the plane perpendicular to the velocity of the nucleus rather than
uniformly distributed. This results in an increased electromagnetic flux surrounding
each nucleus in the plane perpendicular to its motion. Particles produced in UPCs
are the result of interactions of these intense electromagnetic fields [20].
34

Figure 5.1: The impact parameter, b, defined as the separation between the centers
of mass of oncoming nuclei.
Figure 5.2: Lorentz contraction causes the shape of the nucleus to contract along the
direction of motion, concentrating its electromagnetic field [20].
Weizsacker and Williams proposed that these electromagnetic fields can otherwise
be represented as a flux of virtual photons [20]. This means that UPCs can occur in
one of two ways:
35

• A photo-nuclear interaction between particles of spin 1 and spin 0 resulting in
the production of a spin 1 particle and
• A 2-photon interaction (both spin 1) resulting in the production of a spin 0, 1,
or 2 particle.
For this reason, UPCs are uniquely useful for studying electromagnetic processes
including photo-excitation and photonuclear-production of hadrons [20].
Furthermore, photo-production in UPCs can occur coherently, where the photon
couples with all nucleons, or incoherently, where the photon couples with a single
nucleon [21]. A visualization is provided in Figure 5.3. The momentum of the photon
is given by,
p =
h
, (5.1)
which implies that coherently produced particles have a smaller total momentum
than incoherently produced particles. In Pb-Pb collisions, the coherent coupling
wavelength, , is twice the radius of the Pb nucleus which leads to,
p =
h
=
h
2r0A1/3
=
h
11.30 fm
= 0.1097 GeV/c. (5.2)
Therefore, in Pb-Pb collisions, coherent photo-production is characterized by a lower
transverse momentum (pT < 0.1 GeV/c) while incoherent photo-production is char-
acterized by a higher pT (pT > 0.1 GeV/c) for vector mesons [21].
Through UPCs, it is possible to study electromagnetic interactions - the most
common type of interaction in matter. The meson is particularly interesting to
study because its mass is between the masses of the ⇢ and J/ mesons. This makes
it possible to study electromagnetic interactions as a function of mass by using the
⇢, , and J/ mesons. As explained in the following chapter, coherently produced
mesons are impossible to detect presently at ALICE. However, it is possible to study
36

Figure 5.3: Coherent photo production couples with all nucleons while incoherent
photo production couples with a single nucleon [20, 22].
the mass dependence of photo-nuclear production by studying incoherently produced
mesons and comparing their cross section to those of the ⇢ and J/ .
37

Chapter 6
Meson Analysis
The meson is composed of a strange quark-antiquark pair with a rest mass energy
of 1019.461 ± 0.019 MeV [18]. With a mass between that of the ⇢0
and the J/ , the
meson allows for the study of the mass dependence of photo-nuclear interactions.
Table 6.1 summarizes the most probable decay channels of the meson.
Table 6.1: Most probable meson branching ratios [18].
Decay Mode Fraction( i/ )
K+
K ( 48.9 ± 0.5 ) %
K0
LK0
S ( 34.2 ± 0.4 ) %
⇢⇡ + ⇡+
⇡ ⇡0
( 15.32 ± 0.32 ) %
⌘ ( 1.309 ± 0.024 ) %
In this work, the ! K+
K decay channel is studied. The decay products are
two charged particles that can be detected by ALICE, and nearly 50% of mesons
decay through this process. Kaons have a rest mass energy of 493.677 ± 0.016 MeV.
Each kaon daughter of a meson that decayed at rest has a maximum p of 127
MeV/c [18]. Recall from the previous chapter that the maximum momentum of a
coherently produced particle in Pb-Pb collisions is 110 MeV/c. Consider the best case
combination of these momenta where one daughter moves in the direction of motion
of the parent and the other moves in the opposite direction. In this case, one kaon
38

daughter would have a momentum of 237 MeV/c while the other, 17 MeV/c. Recall
that the ALICE detector is held in a 0.5 T magnetic field and that the momentum
of a charged particle in a magnetic field is,
mv? = qrB, (6.1)
where q is the constant charge of the particle, B is the magnetic field of the ALICE
detector; mv? is the particle’s pT ; and r is the radius of curvature of the particle’s path.
Note that the smaller the particle’s pT , the smaller the radius of curvature. At ALICE,
if the particle’s pT is smaller than 150 MeV/c, then the radius of curvature of its path
becomes too small to be detected. Therefore, coherently produced mesons are not
expected to be detectable at ALICE using standard analysis techniques because even
in the best case scenario, only one of the kaon daughters of a meson decay would
be detected.
6.1 Methods
6.1.1 Data
This analysis uses LHC11h data, which is a subset of the data collected in Pb-Pb
collisions during Run 1 in 2011. Full details regarding the run conditions for each
run number, including detector problems and reconstruction issues, can be found on
the MonALISA Repository tool in the ‘Run Condition Table’ view. The run numbers
used for this analysis were chosen to exclude any detector malfunctions with a specific
focus on the ITS, TPC, TRD, and TOF. These run numbers can be found in Appendix
A.
Data Analysis was carried out by using the ALICE Analysis Framework and by
running on the CERN Grid.
39

6.1.2 Event Selection
To identify mesons in UPCs, events with exactly two oppositely charged tracks,
where each track is considered a good track according to the 2010 standard track
cuts, are selected using the CCUP-4 trigger (veto in the VZERO forward detector
and tracks in the ITS as well as TOF). The following is a list of general cuts applied
as part of the selection,
• Good quality tracks using 2010 standard track cuts in ITS and TPC,
• Require two tracks per event, and
• Require sum of track charges to be zero.
6.1.3 Particle Identification
The ALICE Analysis Framework provides a method for obtaining the probability that
a track fits a given mass hypothesis. This probability is expressed as a number of
standard deviations (n- ) under the assumption that detectors have a gaussian re-
sponse function. Detectors for which the framework provides n- calculations include
ITS, TPC, TRD, TOF, HMPID, EMCAL, and PHOS [23]. The probability of being
a particular particle that has a certain momentum is folded into this quantity. In
this analysis, a systematic study is performed by varying the |n- K± | and |n- ⇡± | cut
values. It is advantageous to define these cuts as a circle such that,
• (n K± )2
= (n (Track1) K± )2
+ (n (Track2) K± )2
and
• (n ⇡± )2
= (n (Track1) ⇡± )2
+ (n (Track2) ⇡± )2
.
Using this definition, the number of standard deviations for the two particles are
added in quadrature.
40

6.1.4 Simulations
STARlight, a Monte Carlo simulator that models two-photon and photon-Pomeron
interactions in UPCs, was used as the simulation generator for this analysis. A full
listing of the input parameters used can be found in Appendix B. Most importantly,
the simulation was set to model Pb-Pb collisions with 1370 GeV ion energies where no
nuclear breakup occurs in order to model UPCs (impact parameter b > 2R, where R
is the radius of the nucleus). Data produced by STARlight contains standard Particle
Data Group particle identiﬁcation codes as well as vertex and momentum information
for each particle in the simulation. The STARlight output was then reconstructed
by using the ALICE Reconstruction Framework. Ultimately, the purpose of the
simulations is two-fold: to calculate detection e ciencies which in turn are used to
ﬁnd the cross-section of photo-nuclear production; and to be used for error analysis.
The mass and pT distributions as generated by STARlight are shown in Figure
6.1. The same distributions after being passed through the ALICE reconstruction
framework are shown in Figure 6.2. Note that many of the generated particles are
not detected due to their low pT . The excluded region is where coherent production
would have been observed.
41

Figure 6.1: STARLight Monte Carlo incoherent meson mass and pT distributions.
6.2 Cross Section Calculations
The cross section, which represents the particle production rate in collisions, can be
calculated using,
=
Y ield
✏detLintegrated
, (6.2)
where Yield is the number of particles in the mass peak, ✏ is the detection e ciency
calculated using Monte Carlo simulations, and Lintegrated is the integrated luminosity
42

Figure 6.2: Reconstructed Monte Carlo incoherent meson mass and pT distributions.
of the analyzed events calculated in the analysis note, [24]. Note that the runs
analyzed as part of this work are a subset of the runs analyzed in the luminosity
calculations in [24]. Therefore, the luminosity value used in cross section calculations
here is scaled according to the fraction of events analyzed.
In this work, cross sections are ﬁrst calculated for each of the following data ‘bins’:
• 1st
bin: 0 < (n- K± )2
< 2 & 0 < (n- ⇡± )2
< 18,
• 2nd
bin: 0 < (n- K± )2
< 2 & 18 < (n- ⇡± )2
< 32,
43

• 3rd
bin: 0 < (n- K± )2
< 2 & 32 < (n- ⇡± )2
,
• 4th
bin: 2 < (n- K± )2
< 8 & 0 < (n- ⇡± )2
< 18,
• 5th
bin: 2 < (n- K± )2
< 8 & 18 < (n- ⇡± )2
< 32,
• 6th
bin: 2 < (n- K± )2
< 8 & 32 < (n- ⇡± )2
,
• 7th
bin: 8 < (n- K± )2
< 18 & 0 < (n- ⇡± )2
< 18,
• 8th
bin: 8 < (n- K± )2
< 18 & 18 < (n- ⇡± )2
< 32, and
• 9th
bin: 8 < (n- K± )2
< 18 & 32 < (n- ⇡± )2
,
corresponding to circular kaon inclusion and pion exclusion cuts with varying radii.
Figures 6.3 and 6.4 show the parent invariant mass distributions in real and re-
constructed Monte Carlo data (respectively) for the pion exclusion bins (3, 6, 9 from
above). Note that as the kaon inclusion cuts are loosened, more background is ob-
served. The regions before and after the peak in these plots are parametrized using
a
p
x ﬁt to determine the number of entries due to background in the peak. Then,
the yield for each bin is calculated by summing the number of entries in the peaks
(deﬁned to be between 1.005 and 1.035 GeV/c) and subtracting the number of entries
due to background.
In order to calculate the e ciency for each cross section calculation, each recon-
structed distribution (shown in Figure 6.4) is divided by the generated parent mass
distribution (shown in Figure 6.1). E ciency is averaged for cross section calculations
in each PID bin.
44

Figure 6.3:
p
x ﬁtted mass distributions separated by TPC PID bins in real data.
45

Figure 6.4:
p
x ﬁtted mass distributions separated by TPC PID bins in Monte
Carlo data.
46

In this work, three methods of calculating weighted cross sections are explored.
The di↵erences between the three methods are only in the way e ciencies are used
and weights are calculated for each weighted cross section calculation. The Yields
(particles in the peak) used in each method are summarized in Tables 6.2 for real
data and 6.3 for Monte Carlo data. In the ﬁrst method, only the pion exclusion bins
(bins 3, 6, 9) of the previously listed PID bins are used. For each bin, a cross section
is calculated via equation 6.2 by using the background-subtracted Yields with the
detection e ciency averaged over these three bins. Cross sections are then weighted
by their variances,
!i =
1
SD2
, (6.3)
where SD2
is the variance associated with the cross section measured in each bin.
The Standard Deviation (SD) is calculated using Yields from the entire peak. The
cross sections, SDs, weights (expressed in percentages), and weighted cross sections
calculated using this method are shown in Table 6.4.
Table 6.2: real data Yields (Y) separated by bin. Background is calculated using
the
p
x ﬁt shown in Figure 6.3.
Bin Ypeak Ybg Ybg subtracted
1 76 27.2 48.8
2 4 5.91 1.91
3 82 28.0 54.0
4 130 75.4 54.6
5 18 7.65 10.3
6 113 49.0 64.0
7 129 99.3 29.7
8 11 7.20 3.79
9 85 47.9 37.1
47

Table 6.3: simulated data Yields (Y) separated by bin. Background is calculated
using the
p
x ﬁt shown in Figure 6.4.
Bin Ypeak Ybg Ybg subtracted
1 0 0 0
2 1 0 1
3 106 13 93
4 2 0 2
5 4 0 4
6 377 24.3 353
7 8 0 8
8 3 0 3
9 325 19 306
Table 6.4: meson cross sections, SDs, weights, and weighted cross sections separated
by bins calculated using Method 1 (detection e ciency is averaged over the three PID
bins and weighted cross sections are weighted by variance).
Bin (µbarns) SD (µbarns) ! (%) bin (µbarns)
3 3600 610 37 1350
6 4300 720 27 1160
9 2500 620 36 900
Total 3400
In the second method, the pion exclusion bins (bins 3, 6, 9) are used again.
Here, the e ciency is NOT averaged over the three PID bins. Instead, cross section
calculations use the e ciency associated with each PID bin. These cross sections are
then weighted by each bin’s fraction of total Yieldsbg, subtracted as predicted by Monte
Carlo such that,
Fractional Weight =
Y ieldi, bg subtracted, bin
Y ieldi, bg subtracted, tot
. (6.4)
The cross sections, Yield fractions (from Table 6.3), weights, and weighted cross
sections calculated using this method are shown in Table 6.5.
48

Table 6.5: meson cross sections, Monte Carlo background subtracted Yield fractions,
weights, and weighted cross sections separated by bins calculated using Method 2
(detection e ciency is unique to each bin and weighted cross sections are weighted
by Monte Carlo predicted background fractions per bin).
Bin (µbarns) Yi, bg/Yi, bg tot
Fractional
Weight
(%) bin (µbarns)
3 42700 93/752 12 5280
6 53300 353/752 47 25000
9 880 306/752 41 360
Total 30600
In the third method, all PID bins are used. Cross sections are calculated as a
function of kaon PID bins (subsequently referred to as bin groups) such that the ﬁrst
cross section, for example, is calculated for bins 1, 2, and 3 (corresponding to the
ﬁrst bin group). Here, e ciency is weighted by Yieldbg, subtracted fractions in each bin
group as predicted by Monte Carlo,
Fractional Weight =
Y ieldbin group, bg subtracted, bin
Y ieldbin group, bg subtracted, group
. (6.5)
The cross section for each group of bins is then weighted by the statistical variance
of the cross section for that group of bins. The e ciencies, Monte Carlo background
subtracted Yield fractions, fractional weights, statistical group weights (expressed as
percentages), and cross sections per group are shown in Table 6.6.
49

Table 6.6: meson e ciencies, Monte Carlo background subtracted Yield fractions,
fractional weights, statistical group weights, and cross sections per group separated
by bins calculated using Method 3 (detection e ciency is weighted by Monte Carlo
predicted background fractions per bin and group cross sections are weighted by
statistical weights).
Bin ✏ (x10 4
) YFraction
Fractional
Weight
(%) !grp (%) grp (µbarns)
1 0 0 0
2 1.19 1/94 1
3 0.90 93/94 98
Group 0.13 103
4 6.36 2/359 0.56
5 1.11 4/359 1.1
6 0.85 353/359 98.3
Group 0.07 81
7 10.0 8/317 2.5
8 34.1 3/317 .9
9 29.8 306/317 96.5
Group 99.8 1700
Total 1890
These three methods reveal a large spread in cross section values. The weighted
cross section found in Method 1 is used in the discussion of the statistical and system-
atic error due to luminosity because its value falls between those found in Methods
2 and 3. Methods 2 and 3 are used in error analysis for the systematic error due to
particle identiﬁcation.
50

6.3 Error Analysis
Error associated with the final weighted cross section includes statistical error, sys-
tematic error from luminosity calculations, and the systematic error from the large
di↵erences in particle identification between real data and Monte Carlo. The error is
dominated by the uncertainty in particle identification. The statistical error and the
error associated with uncertainty in the luminosity are calculated to show this is the
case.
Statistical error based on the analysis used in Method 1 is considered to be the
standard deviation of the mean (SDmean) of the weighted cross sections given by[25]
,
SDmean =
SD
p
# of entries
, (6.6)
where the standard deviation in a weighted calculation is given by[25]
,
SD =
1
q
⌃i(!i)
, (6.7)
where mean is the weighted average of the cross sections, and !i is the weight of the
i-th calculation. This corresponds to an ✏stat of 124 µbarns.
Systematic error associated with luminosity calculations is computed as a function
of the final weighted cross section. After scaling the luminosity reported in [24], the
associated error is L+4.15%
6.91%. Luminosity is inversely proportional to cross section.
Thus, the upper limit on the systematic error due to luminosity is the product of the
lower limit on luminosity and the final weighted cross section. Likewise, the lower
limit is the product of the upper limit on luminosity and the final weighted cross
section. With a weighted cross section of 3400 µbarns from Method 1, ✏sys, lum is
+240
140 µbarns.
51

Methods 2 and 3 were selected to demonstrate what might be considered to be
extremes in ways the data could have been analyzed. The Monte Carlo simulation
significantly overestimates the particle identification capabilities of the ALICE detec-
tor. There is a large discrepancy between n- values for data and those for Monte
Carlo. Systematic error associated with the particle identification is then found by
considering the di↵erences between the three analysis methods. Method 2 provides
the highest weighted cross section while Method 3, the lowest. The upper systematic
error limit is considered to be the di↵erence between the weighted cross sections from
Methods 2 and 1. The lower limit is considered to be the di↵erence between the
weighted cross sections from Methods 1 and 3. Thus, ✏sys, MC is +27200
1500 µbarns.
Note that the Monte Carlo simulation used in this work di↵ers so immensely in its
prediction of the particle identification in each bin from what is observed in real data
that the systematic error associated with the Monte Carlo is completely dominant
compared to all other sources of error. For this reason, it makes more sense to provide
a range in which the photo-nuclear production cross section of incoherent mesons
must fall in Pb-Pb collisions at the LHC.
6.4 Results
As expected, coherently produced mesons were not detected using ALICE TPC
tracks in the 2011 data set. The observed incoherent meson photo-nuclear pro-
duction cross section is observed to be in the range between 1900 and 30600 µbarns
in this study using 2011 Pb-Pb collision data from the LHC. This cross section can
be compared to the cross sections of the ⇢0
and J/ mesons reported in [26] and
[27] respectively. Prior to making a comparison, these cross sections must be scaled
to account for the their rapidity dependence. This is done by calculating the frac-
tion of total rapidity space represented by the reported measurement and scaling the
52

cross section accordingly. Furthermore, these sources report cross sections for coher-
ent photo-nuclear production but include Monte Carlo modeling of the fraction of
coherent vs incoherent photo-nuclear production present in the real data pT distri-
bution. To estimate the coherent:incoherent ratio, the number of coherent entries
in the Monte Carlo model is divided by the number of incoherent entries. The re-
ported cross sections are then further scaled according to this coherent:incoherent
scale factor. The scaled incoherent ⇢0
photo-nuclear production cross section is
97000 ± 2200 (stat) +9600
11000 (sys) µbarns. The scaled incoherent J/ photo-nuclear
production cross section is 91 ± 16 (stat) +22
24 (sys) µbarns. These cross sections are
converted into a range by combining the statistical and systematic errors in quadra-
ture and reported in Table 6.7. As expected, the range for the cross section of the
meson ﬁts between the ranges of the ⇢0
and J/ .
Table 6.7: Incoherent scaled ⇢0
and J/ as well as measured incoherent meson
cross section ranges in Pb-Pb collisions with Run 1 energies at the LHC.
Meson Incoherent range (µbarns)
⇢0
86000 107000
1900 30600
J/ 60 120
53

Bibliography
[1] J. Taylor, C. Zafiratos, and M. Dubson, Modern Physics for Scientists and En-
gineers (2nd Edition). Addison-Wesley, 2003.
[2] D. Gri ths, Introduction to Elementary Particles. Wiley-VCH, 2008.
[3] D. H. Perkins, Introduction to High Energy Physics. Addison-Wesley, 2000.
[4] “CERN Aerial View.” http://commons.wikimedia.org/wiki/File:CERN_
Aerial_View.jpg, 2008.
[5] ALICE Collaboration, “ALICE’s eyes.” http://aliceinfo.cern.ch/Public/
en/Chapter2/Chap2Experiment-en.html, 2008.
[6] ALICE Collaboration, “Technical Design Reports.” http://aliceinfo.cern.
ch/Documents/TDR/index.html, 2008.
[7] ALICE Collaboration, “The Transition Radiation Detector (TRD).” http://
aliceinfo.cern.ch/Public/en/Chapter2/Chap2_TRD.html, 2008.
[8] C. Lippman for the ALICE collaboration, “The ALICE Transition Radiation De-
tector.” http://www.slac.stanford.edu/econf/C0604032/papers/0043.PDF,
2006.
[9] ALICE Collaboration, “The ALICE Time of Flight Detector.” http://
aliceinfo.cern.ch/Public/en/Chapter2/Chap2_TOF.html, 2008.
[10] F. Bellini for the ALICE Collaboration, “Particle identification with the alice
time-of-flight detector and a few physics results,” JINST, vol. 9 C10019, 2014.
[11] A. Kalweit for the ALICE collaboration, “Particle Identification in the ALICE
Experiment,” J. Phys. G: Nucl. Part. Phys, vol. 38 #12, 2011.
[12] L. Bryngemark, “Charged pion identification at high pt in alice using the tpc
de/dx,” in 6th International Workshop on High-pT physics at the LHC, 2011.
[13] C. Zampolli for the ALICE Collaboration, “Particle identification with the alice
detector at the lhc,” in Physics at LHC, 2012.
[14] E. O. for Nuclear Research, “About CERN.” http://home.web.cern.ch/about.
54

[15] R. Cabrera, “Simulation of Jets in Heavy Ion Collisions for the ALICE Experi-
ment,” Master’s thesis, Creighton University, Omaha, NE, 2003.
[16] J. D. Bjorken, “Energy Loss of Energetic Partons in Quark-Gluon Plasma: Pos-
sible Extinction of High pT Jets in Hadron-Hadron Collisions.” fermilab-pub-
82/59-thy, 1982.
[17] W. Xin-Niang, “Modified Fragmentation Function and Jet Quenching at RHIC,”
Nuclear Physics A, vol. 702, 2002.
[18] LBNL, “Particle Data Group.” http://pdg.lbl.gov/.
[19] ALICE, “MonALISA Repository for ALICE.” http://alimonitor.cern.ch/
map.jsp.
[20] C. Bertulani, S. Klein, and J. Nystrand, “Physics of ultra-peripheral nuclear
collisions,” Annu. Rev. Nucl. Part. Sci., vol. 55, 2005.
[21] The ALICE Collaboration, “Coherent j/ photo production in ultra-peripheral
pb-pb collisions at
q
(sNN ) = 2.76 tev,” Physics Letters B, vol. 718, 2013.
[22] B. R. Gruberg, “⌘c Photon Production Simulations for Run2,” in ALICE Week,
2014.
[23] ALICE, “AliPIDResponse Class Documentation.” http://personalpages.
to.infn.it/~puccio/htmldoc/AliPIDResponse.html#AliPIDResponse:
fTRDResponse.
[24] C. Mayer, E. Kryshen, “Luminosity Determination for Central Barrel UPC Trig-
gers in Pb-Pb runs,” ALICE Analysis Notes, 2012.
[25] A. MacMillan, D. Preston, J. Wolfe, and S. Yu, “Basic statistics:
mean, median, average, standard deviation, z-scores, and p-value.”
https://controls.engin.umich.edu/wiki/index.php/Basic_statistics:
_mean,_median,_average,_standard_deviation,_z-scores,_and_p-value,
2007.
[26] The ALICE Collaboration, “Coherent ⇢0
photoproduction in ultra-peripheral
Pb-Pb collisions at
p
sNN = 2.76 TeV .” arXiv:1503.09177, 2015.
[27] J. Nystrand for the ALICE Collaboration, “Photonuclear vector meson produc-
tion in ultra-peripheral Pb-Pb collisions studied by the ALICE experiment at
the LHC,” in 10th Conference on Quark Confinement and the Hadron Spectrum
(Confinement X), 2012.
55

Appendix A
Analyzed Run Numbers
Corresponding to a Subset of 2011
Collision Data
Please note, further information about these run numbers may be found by using the
MonALISA Repository tool found at http://alimonitor.cern.ch/map.jsp.
A.1 LHC11h
170572 170387 170315 170312 170311 170309 170308 170270 170269
170268 170230 170228 170207 170204 170203 170193 170163 170155
170085 170083 170040 169965 169591 169590 169588 169587 169586
169557 169555 169553 169550 169515 169512 169506 169504 169498
169475 169420 169419 169418 169417 169415 169411 169238 169167
169160 169156 169144 169099 169094 169091 169035 168826 168512
168511 168464 168361 168342 168311 168115 168108 168107 168076
168069 167988 167987 167920 167915
56

Appendix B
STARLight Input Parameters
The following parameters were used as inputs to the embedded version of STARLight
within the ALICE Simulation framework in AliROOT version ‘vAN-20141128’ and
ROOT version ‘v5-34-08-6’:
BEAM 1 Z = 82 Z of projectile
BEAM 1 A = 208 A of projectile
BEAM 2 Z = 82 Z of target
BEAM 2 A = 208 A of target
BEAM 1 GAMMA = 1470 Gamma of the colliding ions
BEAM 2 GAMMA = 1470 Gamma of the colliding ions
W MAX = 4.0 Max value of w
W MIN = -1 Min value of w
W N BINS = 100 Bins i w
RAP MAX = 8. max y
RAP N BINS = 100 Bins i y
CUT PT = 0 Cut in pT? (0 = no, 1 = yes)
PT MIN = 1.0 Minimum pT in GeV
PT MAX = 3.0 Maximum pT in GeV
CUT ETA = 1 Cut in pseudorapidity? (0 = no, 1 = yes)
ETA MIN = -3 Minimum pseudorapidity
ETA MAX = 3 Maximum pseudorapidity
PROD MODE = 4 gg or gP switch (1 = 2-photon, 2 = coherent vector
meson (narrow), 3 = coherent vector meson (wide), 4 = incoherent vector
meson, 5 = A+A DPMJet single, 6 = A+A DPMJet double, 7 = p+A
DPMJet single, 8 = p+A Pythia single )
PROD PID = 333 Channel of interest (not relevant for photonuclear pro-
cesses)
57

RND SEED = RANDOM NUMBER Random number seed
BREAKUP MODE = 1 Controls the nuclear breakup
INTERFERENCE = 0 Interference (0 = o↵, 1 = on)
IF STRENGTH = 1. % of intefernce (0.0 - 0.1)
COHERENT = 0 Coherent=1,Incoherent=0
INCO FACTOR = 1. percentage of incoherence
INT PT MAX = 0.24 Maximum pt considered, when interference is
turned on
INT PT N BINS = 120 Number of pt bins when interference is turned on
SetRapidityMotherRange(-3,3)
SetEtaChildRange(-2,2)
58

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