THÈSE
Pour obtenir le grade de

DOCTEUR DE LA COMMUNAUTÉ UNIVERSITÉGRENOBLE ALPES
préparée dans le cadre d’une cotutelle entre laCommunauté Université Grenoble Alpes etl'Université de Tsukuba
Spécialité : Physique Subatomique et AstroparticulesArrêté ministériel : le 6 janvier 2005 – 25 mai 2016

Présentée par

Ritsuya Hosokawa
Thèse dirigée par Christophe Furget et Rachid Guernane
codirigée par Tatsuya Chujo et Shinichi Esumi
préparée au sein des Laboratoire de Physique Subatomique etde Cosmologie et Tomonaga Center for the History of the
Universe
dans les École Doctorale de Physique et Graduate School ofPure and Applied Sciences

Mesure des propriétés des jets dans lescollisions pp et Pb-Pb à 5.02 TeV avec
l’expérience ALICE auprès du LHC
Thèse soutenue publiquement le 29 Mars 2019,devant le jury composé de :Monsieur Tatsuya CHUJO
Maître de Conférences, Université de Tsukuba, Membre

Monsieur Shinichi ESUMIProfesseur, Université de Tsukuba, Membre

Monsieur Christophe FURGET
Professeur, Université Grenoble Alpes, Membre

Monsieur Rachid GUERNANE
Chargé de Recherche, LPSC, Membre

Monsieur Kazuhiko HARA
Professeur, Université de Tsukuba, Membre

Monsieur Yasuo MIAKE
Professeur, Université de Tsukuba, Président

Monsieur Ken OYAMA
Professeur, Nagasaki Institute of Applied Science, Rapporteur

Monsieur Yves SCHUTZ
Directeur de Recherche, IPHC, Rapporteur

Measurement of jet properties in pp and Pb-Pb√
collisions at sNN = 5.02 TeV with the ALICE
experiment at the LHC

Ritsuya Hosokawa

March 2019

Measurement of jet properties in pp and Pb-Pb√
collisions at sNN = 5.02 TeV with the ALICE
experiment at the LHC
Ritsuya Hosokawa
Doctral Program in Physics

Submitted to
the Graduate School of Pure and Applied Sciencesat the University of Tsukuba
andDoctoral School of Physics
at Université Grenoble Alpes
in Partial Fulfillment of the Requirements
forthe Degree of Doctor of Philosophy in ScienceAbstract

Jets, defined as collimated sprays of high-momentum particles, are experimental signaturesof hard-scattered quarks and gluons produced in hadronic interactions. Jet production
cross sections are calculable within perturbative Quantum ChromoDynamics (pQCD), andtherefore jet measurements provide stringent tests of pQCD predictions. In ultrarelativistic
heavy-ion collisions, jets are well calibrated probes of the Quark-Gluon Plasma (QGP).
Under extreme conditions of high temperature and/or high pressure, partons are deconfinedand form a strongly interacting QCD medium. The initial hard scattered partons lose energy
while traversing this medium due to radiative and collisional energy loss. Consequently,
jet properties get modified in comparison with the vacuum case, phenomenon named jet
quenching. QGP transport properties can be studied by measuring jet quenching.
√
The charged jet production cross sections in proton-proton collisions at s = 2.76 TeV√
and s = 7 TeV were measured by the ALICE experiment. The predictions of pQCD
calculations with Leading-Order (LO) accuracy were compared with the measurements andexhibited only poor agreement by about 20-50 %. In Pb-Pb collisions, the strength of jet√√
suppression was quantitatively assessed at sNN = 2.76 TeV and sNN = 5.02 TeV throughthe measurement of the nuclear modification factors (RAA ). The strength of charged jet
suppression was quantified as a function of in-medium parton path-length based on themeasured RAA . The jet elliptic flow v2 , defined as the jet azimuthal distribution relative tothe 2nd order event plane, which is sensitive to the diﬀerence of the in-medium parton path√
length in-plane and out-of-plane, was measured at sNN = 2.76 TeV. The measured jet v2 in
mid-central Pb-Pb collisions was consistent with model predictions. The medium response√
was studied through jet-track correlations at sNN = 2.76 TeV as a function of centrality.
The result suggested that the in-medium suppressed energy was re-distributed to large
angles with respect to the jet axis. The phenomenon was described by a phenomenologicalcalculation taking into account hydrodynamical evolution of the medium.
In this thesis, two complementary aspects of jet physics with the ALICE detector at the
LHC are studied. First, the upgrade of the ALICE electromagnetic calorimeter trigger system is presented. The Di-jet Calorimeter (DCal) was installed during LHC Long Shutdownii

1 to extend the azimuthal coverage of the existing ElectroMagnetic Calorimeter (EMCal)
and PHOton Spectrometer (PHOS). The trigger system has been upgraded to account forthis new detector configuration. We upgraded the firmware for the Summary Trigger Unit
(STU), which is the electronics of the trigger system, to implement a brand new algorithm
combining information from the three calorimeters. We also carried out the upgrades of
the new data stream format and communication error monitoring between the electronics
components of the trigger system. We performed the commissioning of the trigger systembefore the 2015 Pb-Pb data taking which ensured a stable operations of the trigger systemthroughout the LHC Run2 (2015-2018). The new physics results utilizing the triggered data
are coming out at the time of writing.
The second issue addressed in this thesis is charged jet measurements in pp and Pb√
Pb collisions at sNN = 5.02 TeV. The measurement of the production cross section of
charged jets reconstructed with cone resolution parameter R = 0.2, 0.3, 0.4, and 0.6 in√pp collisions at s = 5.02 TeV and for jet transverse momentum 5 < pch
T,jet < 100 GeV/c
is outlined. A comparison of the production cross section to LO and Next-Leading-Order(NLO) pQCD predictions is shown. Good agreement, within about 10% discrepancy, of the
production cross section with NLO pQCD calculations is found for 10 < pch
T,jet < 100 GeV/cwith large theoretical uncertainties. The NLO pQCD calculations shows large discrepancy
from the measured result at lower pT,jet (5 < pch
T,jet < 10 GeV/c) though the theoreticaluncertainties are still large. The systematic uncertainties on the pQCD calculation could
be improved with higher-order calculation, such as Next-to-Next-to-Leading Order. It may
also be important to understand non-perturbative eﬀects, such as the underlying event,for an improved understanding of the jet production cross section in this low pT,jet region.
√
The measurement of charged jet v2 in mid-central (30-50%) Pb-Pb collisions at sNN =5.02 TeV is presented. The result is compared with the charged jet v2 in Pb-Pb collisions√
at sNN = 2.76 TeV. No collision energy dependence on the charged jet v2 is found.
The result is also compared with a toy-model Glauber simulation based on the estimatedjet suppression strength from the measured charged jet RAA . It is found that both jet
RAA and jet v2 are simultaneously described by a medium-induced constant jet transverse
momentum suppression of ∆pT ∝ ρ1.1 ⟨Lσ ⟩2.6 . Here, ⟨L⟩ is the average in-medium parton

path-length estimated with a Glauber simulation and ρ is the centrality dependent initialenergy density. This result is close to the in-medium radiative energy loss scenario of√∆pT ∝ ρ3/4 L2 . However, one another scenario of ∆pT ∝ ρL is not ruled out due tocurrent large uncertainties. Finally, the measurement of charged jet-hadron correlations√
in mid-central (30-50%) Pb-Pb collisions at sNN = 5.02 TeV with respect to the 2ndiii

order event plane is also presented in order to study initial collision geometry dependenceof jet modification in Pb-Pb collisions. The near-side correlation functions for trigger jets
assoc
pT,jet > 20 GeV/c and associated tracks 0.7 < passoc
T,track < 2 GeV/c, 2 < pT,track < 4 GeV/c

are measured. Broader near-side jet peak shape out-of-plane jet in comparison with the inplane one is observed for 0.7 < passoc
T,track < 2 GeV/c associates. A near-side peak position shift
in azimuth towards in-plane direction is also observed for both pT ranges. The measured
jet-hadron correlations are compared to the JEWEL model predictions. Only the peak
position shift for low-pT associates is partially reproduced. This result suggests that thenear-side peak shape modification w.r.t 2nd -order event plane cannot be described onlyby the in-medium parton energy loss and parton shower evolution. The medium-inducednear-side jet modification may be understood as a combination of in-medium radiation,
initial geometry dependent energy suppression, and medium response with hydrodynamical
evolution.

iv

Acknowledgments

Firstly, I would like to express the deepest gratitude to Prof. R. Guernane and Prof. T.
Chujo, who supported my reserch activities and also daily life in France and Japan. Theygave me a lot of advices on my analysis and support for works overseas. I would like toexpress appreciation to Dr. H. Yokoyama who also supported reserch activities. Especially,no doubt that the trigger system upgrade for ALICE calorimeters could not be completed
without his co-working.
I would like to express deep gratitude to Prof. Y. Miake, Prof. Y. R. Schutz and Prof. C.
Furget. They gave me the opportunity to reserch the high-energy nuclear physics. I also
would like to thank for their careful reading of my thesis. I express deep gratitude to Prof.
K. Oyama for careful reading and reviewing this PhD thesis. My deep appreciation goes toProf. S. Esumi. He gave me a lot of meaningful advices for the physics analysis. I would
like to thank professional instructions about electronics from Prof. I. Motoi. I would like toexpress many thanks to Prof. O. R. Bourrion, Prof. G. C. Balbastre, Prof. J. Faivre who
gave me meaningful advices when I was working at Grenoble. I appreciate Prof. S. Sakai,
Dr. H. Masui, Dr. Y. Watanabe, Prof. N. Jaime, who gave me insightful advices and many
support for my works. I recieved technical support from Mr. S. Kato, who maintained thecomputing system at University of Tsukuba.
I would like to express deep gratitude to all the current and previous members of High energy nuclear physics group at University of Tsukuba and Universitè Grenoble Alpes (LPSC).
Especially, I would like to thank for frendship and a lot of discussions with Dr. T. Nonaka,
Mr. W. Sato, Dr. R.Aoyama, Dr. T. Sugiura, Dr. N. Tanaka, Dr. H. Nakagomi, Dr.
D. Watanabe, Dr. S. Mizuno, Dr. H. Hassan. I also express my thank to frendship with
Dr. T. Todoroki, Dr. T. Niida, Dr. J. Bhom, Mr. K. Oshima, Ms. H. Ozaki, Mr. T.
Kobayashi, Mr. K. Kihara, Mr. J. Lee, Mrs. I. Sakatani, Mr. T. Shioya, Mr. M. Hirano,
Mr. H. Yamamoto, Mr. B. Kim, Mr. K. Ito, Ms. S. Kudo, Ms. M. Chang, Mr. Y. Fukuda,
Mr. K. Sato, Mr. T. Ichisawa, Mr. H. Kato, Mr. D. Kawana, Mr. Y. Kawamura, Mr.
T. Suzuki, Mr. K. Nakagawa, Mr. T. Nishimatsu, Mr. H. Joung, Mr. M. Takamura, Mr.
K. Tadokoro, Ms. K. Nakagawa, Ms. M. Hatakeyama, Ms. Y. Hoshi, Mr. N. Ito, Mr. K.
v

Okubo, Ms. Y. Sato, Mr. Y. Sudo, Mr. K. Tsukui, Mr. R. Nakazato, Mr. K. Mitamura,
Mr. K. Yasaki.
I would like to express deep gratitude to ALICE Asian France (AAF) colloborators. Especially, Prof. O. Busch, who is now resting in peace, provided me large amount of knowledge
and insightful advices for my analysis. I’m confident that I wouldn’t achieve my studies
without him. I would like to thank Prof. Y. Mao, Prof. H. Pei for their advices for mytasks and management of the collaboration.
I would like to express ,any thanks to the colleagues, Dr. D. Sekihata, Ms. H. Murakami,
Dr. S. Yano, Dr. T. Okubo, Mr. K. Terasaki, Mr. K. Yamakawa, who spent good time
together at CERN.
Finally, I would like to thank my parents, Mr. Y. Hosokawa and Mrs. Y. Hosokawa for
their understanding and continuous support for my activities.

vi

Contents

Abstractii

Acknowledgmentsv

1 Introduction

1

1.1

Quantum Chromodynamics (QCD)
1.1.1. . . . . . . . . . . . . . . . . . . . . .

2

Asymptotic freedom and Confinement . . . . . . . . . . . . . . . . .

3

1.2

Hard scattering and Jets

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.3

Quark-Gluon Plasma (QGP) . . . . . . . . . . . . . . . . . . . . . . . . . .

7

1.4

Relativistic heavy-ion collisions . . . . . . . . . . . . . . . . . . . . . . . . .

7

1.4.1

Space-time evolution. . . . . . . . . . . . . . . . . . . . . . . . . .

10

1.4.2

Collision geometry - Participants and spectators . . . . . . . . . . .

11

1.4.3

Collision geometry - Event plane . . . . . . . . . . . . . . . . . . . .

14

1.5

Parton energy loss in the hot and dense QCD medium . . . . . . . . . . . .

14

1.6

Experimental results of jet measurements in pp collisions. . . . . . . . . .

17

1.6.1

Charged jet cross section . . . . . . . . . . . . . . . . . . . . . . . .

17

1.6.2

Charged jet cross section ratio . . . . . . . . . . . . . . . . . . . . .

18

1.7

1.8

Experimental evidence of nuclear matter eﬀects. . . . . . . . . . . . . . .

20

1.7.1

Jet quenching. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

1.7.2

Azimuthal anisotropic flow . . . . . . . . . . . . . . . . . . . . . . .

24

Thesis motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 Experimental apparatus

29
31

2.1

The Large Hadron Collider (LHC) . . . . . . . . . . . . . . . . . . . . . . .

31

2.2

The ALICE detector complex . . . . . . . . . . . . . . . . . . . . . . . . . .

32

2.2.1

VZERO (V0) detector . . . . . . . . . . . . . . . . . . . . . . . . . .

32

2.2.2

Inner Tracking System (ITS) . . . . . . . . . . . . . . . . . . . . . .

34

2.2.3

Time Projection Chamber (TPC). . . . . . . . . . . . . . . . . . .

37

2.2.4

Electromagnetic Calorimeters (EMCal, DCal, PHOS) . . . . . . . .

40

vii

2.2.5Time-Of-Flight (TOF) detector . . . . . . . . . . . . . . . . . . . . .

41

3 Development of the Level-1
trigger system for the ALICE ElectroMagnetic Calorimeters

43

3.1

Overview of the trigger system . . . . . . . . . . . . . . . . . . . . . . . . .

44

3.2

Trigger algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

3.3

List of tasks carried out . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

3.4

Trigger performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

4 Datasets and analysis methods

59

4.1

Data samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

4.2

Event selections

59

4.3

Charged particle tracking and selection. . . . . . . . . . . . . . . . . . . .

60

4.4

Jet reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

4.5

Measurement of charged jets in pp collisions

61

4.6

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . .

4.5.1

Underlying event estimation in pp collisions. . . . . . . . . . . . .

61

4.5.2

Raw jet spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

4.5.3

Detector eﬀect correction by unfolding. . . . . . . . . . . . . . . .

62

4.5.4

Validation of the unfolding . . . . . . . . . . . . . . . . . . . . . . .

65

4.5.5

Inclusive jet cross section . . . . . . . . . . . . . . . . . . . . . . . .

66

Measurement of charged jets in Pb-Pb collisions. . . . . . . . . . . . . . .

68. . . . . . . . . . . . . . . . . . . .

68

4.6.1

Measurement of the event plane

4.6.2

Underlying event estimation in Pb-Pb collisions. . . . . . . . . . .

70

4.6.3

Charged jet yield with respect to event plane . . . . . . . . . . . . .

71

4.6.4

Charged jet-hadron correlations with respect to event plane . . . . .

74

5 Systematic uncertainties

83

5.1

Systematics for charged jet production cross section in pp collisions . . . . .

83

5.2

Systematics for charged jet v2 in Pb-Pb collisions . . . . . . . . . . . . . . .

95

5.3

Systematics for charged jet-hadron correlation in Pb-Pb collisions . . . . . .

96

6 Results and Discussions
6.1

6.2

103

Charged jets in pp collisions . . . . . . . . . . . . . . . . . . . . . . . . . . .

103

6.1.1

Charged jet inclusive diﬀerential cross section . . . . . . . . . . . . .

103

6.1.2

Charged jet cross section ratio . . . . . . . . . . . . . . . . . . . . .

111

Charged jets in Pb-Pb collisions . . . . . . . . . . . . . . . . . . . . . . . . .

114

6.2.1

114

Charged jet v2 in mid-central Pb-Pb collisionsviii. . . . . . . . . . . .

6.2.2

Charged jet-hadron correlations in mid-central Pb-Pb collisions . . .

119

7 Summary

125

A A Large Ion Collider Experiment129

B Quality Assurance for pp collisions

130

ix

List of Tables

1

The four fundamental interactions in nature. The relative strength of Gravitation is taken to have a value of 1. . . . . . . . . . . . . . . . . . . . . . .

3

2

Summary of ultrarelativistic heavy-ion programs . . . . . . . . . . . . . . .

93Reconstruction conditions of jets . . . . . . . . . . . . . . . . . . . . . . . .

61

4

Summary of the systematic uncertainties in jet cross section for R=0.2-0.6
and in various of jet transverse momentum ranges.

5. . . . . . . . . . . . .

95

Systematic uncertainties of in-plane correlation function in various ∆ϕ bins.
pT,jet > 20(GeV/c), passoc=0.7-2(GeV/c).
T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6100

Systematic uncertainties of out-of-plane correlation function in various ∆ϕbins. pT,jet > 20(GeV/c), passoc=0.7-2(GeV/c).
T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

Systematic uncertainties of in-plane correlation function in various ∆ϕ bins.
pT,jet > 20(GeV/c), passoc=2-4(GeV/c). . . . . . . . . . . . . . . . . . . . .
T

8

101

Systematic uncertainties of out-of-plane correlation function in various ∆ηbins. pT,jet > 20(GeV/c), passoc=2-4(GeV/c). . . . . . . . . . . . . . . . . .
T

13

101

Systematic uncertainties of in-plane correlation function in various ∆η bins.
pT,jet > 20(GeV/c), passoc=2-4(GeV/c). . . . . . . . . . . . . . . . . . . . .
T

12

101

Systematic uncertainties of out-of-plane correlation function in various ∆ηbins. pT,jet > 20(GeV/c), passoc=0.7-2(GeV/c). . . . . . . . . . . . . . . . .
T

11

101

Systematic uncertainties of in-plane correlation function in various ∆η bins.
pT,jet > 20(GeV/c), passoc=0.7-2(GeV/c). . . . . . . . . . . . . . . . . . . .
T

10

100

Systematic uncertainties of out-of-plane correlation function in various ∆ϕbins. pT,jet > 20(GeV/c), passoc=2-4(GeV/c). . . . . . . . . . . . . . . . . .
T

9

100

101

The ratio of near-side jet peak width in azimuth (∆ϕ) out-of-plane over theone of in-plane. The results from data are compared to JEWEL predictions.
det
assoc
assoc
pch,
T,jet > 20GeV/c, 0.7 < pT,track < 2 GeV/c and 2 < pT,track < 4 GeV/c . .

x

122

14

The ratio of near-side jet peak width in eta (∆η) out-of-plane over the oneof in-plane. The results from data are compared to JEWEL predictions.
det
assoc
assoc
pch,
T,jet > 20GeV/c, 0.7 < pT,track < 2 GeV/c and 2 < pT,track < 4 GeV/c . .

15

122

The amplitudes of the sine function (Eq. 61) obtained by fitting the peak
position in azimuth as a function of the angle between the trigger jet axis andthe event plane. The results from data are compared to JEWEL predictions.
det
assoc
assoc
pch,
T,jet > 20GeV/c, 0.7 < pT,track < 2 GeV/c and 2 < pT,track < 4 GeV/c . .

xi

122

List of Figures

1

The Standard Model of elementary particles . . . . . . . . . . . . . . . . . .

2

2

Static quark potential V (r) from 2+1 flavor lattice QCD calculations [1] . .

4

3

Sketch of the hard scattering in hadronic collisions [2] . . . . . . . . . . . .

5

4

The Parton Distribution Functions from HERAPDF1.0 at Q2 = 10 GeV2 [3].

6

5

π+

The individual Fragmentation Functions for positively charged pions zDi

at Q2 = 10 GeV2 [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

6

A sketch of the QCD phase diagram [5] . . . . . . . . . . . . . . . . . . . .

7

7The energy density normalized by T 4 as a function of the temperature.

SB

is the Stefan-Boltzmann limit ϵSB = 3pSB [6] . . . . . . . . . . . . . . . . .

8

8Sketch of the space-time evolution of a nucleus-nucleus collision [2] . . . . .

10

9

Left: Two heavy-ions before the collision with impact parameter b. Right:
The spectators continue unaﬀected, while in the participant zone particle
production takes place. [7] . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

11

Mean value of n (n̄) versus b-centrality (cb ) [8]. Red circles show the result
calculated directly by binning TR ENTo results in cb and dashed blue line
shows the result reconstructed from the fit of P (n). The inset shows a zoomof the most-central collisions, where n̄(cb ) is compared to n(c) (dotted line).

11

Distribution of the sum of amplitudes in the ALICE V0 scintillators. The
distribution is fitted with the NBD-Glauber fit shown as a line [9] . . . . .

12

12
13

A sketch of a non-central Pb-Pb collision. Colored circles are nucleons. Solidcircles are participants and dashed circles are spectators. The original figure
which was made with a Glauber Monte-Carlo simulation was taken from
Ref. [10]. The reaction plane and 2nd , 3rd -order event plane (ψ2 , ψ3 ) aredisplayed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

Left: Feynman diagram of collisional parton energy loss. Right: Feynman
diagram of radiative parton energy loss. [2] . . . . . . . . . . . . . . . . . .

14

15
15

Comparison of the average energy loss of light quarks by radiative and collisional energy losses at RHIC energy [2] . . . . . . . . . . . . . . . . . . . . .
xii

18

15

The diﬀerential production cross section for charged jets reconstructed with
R = 0.2, 0.4 and 0.6 measured by ALICE. The results are compared to someLO pQCD-based predictions [11] . . . . . . . . . . . . . . . . . . . . . . . .

16

19

The ratio of charged jet cross section reconstructed with R = 0.2, 0.4 and0.6 measured by ALICE. The results are compared to some LO pQCD-based
predictions [11] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

Two-particle correlations in pp, d+Au and Au+Au collisions at

√

19

sNN =

assoc < ptrig [12].
200GeV for 4 < ptrig
T < 6 GeV and 2 < pTT(a): Comparison of eﬃciency corrected two-particle azimuthal distributions
for minimum-bias and central d+Au collisions, and for pp collisions.
(b): Comparison of two-particle azimuthal distributions for central d+Au
collisions, minimum-bias pp collisions and for central Au+Au collisions. . .
18

20Comparison of the RAA for neutral pions (π 0 ), charged hadrons (h± ), andcharged particles in central heavy-ion collisions at SPS, RHIC, and LHC [13]. 21

19

The RAA for direct photons, W ± and Z 0 bosons, charged particles and bquarks measured from secondary J/ψ particles [14].

20. . . . . . . . . . . . .

Comparison of charged jet RAA in Pb-Pb collisions at

22√

sNN = 5.02 TeV√
measured by ALICE and full jet RAA in Pb-Pb collisions at sNN = 2.76
TeV measured by ATLAS [15]Left: Centrality range is 0-10% Right: Centrality range is 10-30% . . . . . .

21

23

Left: Elliptic flow coeﬃcient v2 of charged particles (orange, green) and R= 0.2 full jets measured within |η| < 2.1 (blue) superimposed on the resultsof R = 0.2 charged jets v2 within |η| < 0.7 (black) in mid-central collisions(30-50%)

Right: v2 of R = 0.2 charged jets predicted by JEWEL (red) for mid-central
collisions (30-50%) compared to data (black). [16] . . . . . . . . . . . . . .
22

23

The radial jet momentum distribution P(∆r) of jets in pp (top left) and√
Pb-Pb (middle row) collisions at sNN = 5.02 TeV. The bottom row shows
the ratio between Pb-Pb and pp data for the several intervals of ptrack. The
Tshaded bands are systematic uncertainties [17]23. . . . . . . . . . . . . . . .

25

Jet shape function for (a) leading and (b) sub-leading jets in dijet events in√central Pb-Pb and in pp collisions at sNN = 2.76 TeV [18] . . . . . . . . .

26

xiii

24

Left: Initial overlap of two nuclei in an oﬀ-center collision in coordinate
space.
Right: Collective elliptic expansion into the direction of reaction plane in
momentum space.

25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

The experimental results of anisotropic flow coeﬃcients (vn ) [19]Left: (a) Anisotropic flow coeﬃcients vn integrated over 0.2 < pT < 5.0
GeV/c, as a function of event centrality for the two-particle and multi-particle
cumulant methods.
(b),(c) are the ratios to the various hydrodynamic calculations. ”Ref. [25]”and ”Ref. [27]” in the figure correspond to Ref. [20],[21] respectively in the
bibliography.
Right: Comparison of the integrated elliptic flow results from various experiments at various collision center-of-mass energies. . . . . . . . . . . . . . .

27

26

Sketch of the CERN accelerator complex . . . . . . . . . . . . . . . . . . . .

31

27

The ALICE detector at the LHC Run2 . . . . . . . . . . . . . . . . . . . . .

32

28

The installation of V0 detector in ALICE . . . . . . . . . . . . . . . . . . .

33

29

Sketch of V0A and V0C array segmentation. The scintillator thicknesses are
2.5 and 2 cm respectively. The two segments separated by dashed lines areconnected to the same PMT. . . . . . . . . . . . . . . . . . . . . . . . . . .

33

30

PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

31

Centrality resolution measured by the ALICE detectors in Pb-Pb collisions√
at sNN = 2.76 TeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

Event plane resolution measured by V0A and V0C in Pb-Pb collisions at√
sNN = 2.76 TeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

33

Sketch of ITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

34

Resolution of vertex determination . . . . . . . . . . . . . . . . . . . . . . .

37

35

Left: Sketch of TPC. Right: 3D view of TPC tracks reconstructed from a32

central Pb-Pb collision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36

38

Left: Tracking eﬃciency with only TPC. Right: Tracking eﬃciency withITS+TPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

37

Tracking pT resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

38

Electromagnetic calorimeters (EMCal, DCal and PHOS). . . . . . . . . . .

40

39

Components of EMCal, DCal (left) and PHOS (right). . . . . . . . . . . . .

41

40

Cross-section of the MRPC strip for the ALICE TOF. . . . . . . . . . . . .

42

41Time resolution of the ALICE MRPC-TOF. . . . . . . . . . . . . . . . . . .

42

xiv

42

Di-jet energy balance and di-jet energy resolution obtained from simulation.

43

43

Overview of ALICE trigger system layout . . . . . . . . . . . . . . . . . . .

44

44

An example of trigger sequence [22]. . . . . . . . . . . . . . . . . . . . . . .

45

45Overview of the configuration of the trigger electronics for ALICE EMCal(top), DCal (bottom left), and PHOS (bottom right) . . . . . . . . . . . . .

46

46

Flow of the signals for the trigger processing . . . . . . . . . . . . . . . . . .

47

47

Top view of the Summary Trigger Unit (STU) board . . . . . . . . . . . . .

47

48

A typical serial data frame [22]. . . . . . . . . . . . . . . . . . . . . . . . . .

48

49

Trigger patches for L0 and L1 trigger. Each small square corresponds to one
FastOR region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

50

Flowchart of the STU L1-Jet trigger processing in heavy-ion collisions . . .

50

51

Modification of readout region by one TRU. This picture shows an example
for one SM of EMCal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

52

The old (left, [23]) and new (right, [24]) CDH. . . . . . . . . . . . . . . . . .

52

53

An example of the old error counter operation. . . . . . . . . . . . . . . . .

52

54

An example of the new error counter operation. . . . . . . . . . . . . . . . .

53

55

Correlation of underlying event energy density estimated by EMCal and DCal
STUs [25]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

56

Rejection factor of L1-jet triggers given by DCal and EMCAL [25] . . . . .

55

57

Rejection factor of L1-jet triggers given by EMCal (left) and DCal (right)
as a function of underlying event energy density and threshold. x-axis is theestimated underlying event energy density and y-axis is the trigger threshold.
z-axis is the rejection factor and its variation is expressed as colors. . . . . .

56

58

L1-jet trigger turn-on curves given by DCal and EMCAL [25] . . . . . . . .

56

59

Enhancement of the EMCAL L1-jet trigger for full jets with various jet
radii [26]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

Enhancement of the EMCAL L1-gamma trigger as a function of reconstructed
EMCal cluster energy [26]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

57
57

pT spectra of reconstructed PHOS clusters in minimum-bias (black) and L1gamma triggered events (red) are shown in the top panel. The ratio of these
spectra is shown in the bottom panel [26].
Left: Central (0-5 %) Pb-Pb collisions
Right: peripheral (60-80 %) Pb-Pb collisions. . . . . . . . . . . . . . . . . .
xv

58

62

63
64
65

The azimuthal distribution of global tracks (Red: w/ SPD hits), complementary tracks (Blue: w/o SPD hits) and hybrid tracks (Black) in pp collisions√
at s = 5.02 TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

Charged jet raw pT spectra reconstructed with R =0.2,0.3,0.4, and 0.6 in pp√
collisions at s = 5.02 TeV without UE subtraction . . . . . . . . . . . . .

63

Charged jet raw pT spectra reconstructed with R =0.2,0.3,0.4, and 0.6 in pp√
collisions at s = 5.02 TeV with UE subtraction . . . . . . . . . . . . . . .

64

Left: Detector response matrix for R = 0.4 anti-kT clusters reconstructedwith charged tracks. Right: Probability distribution of the relative momentum diﬀerence of simulated ALICE detector response to charged jets in pp√
collisions at s = 5.02 TeV for four diﬀerent pT intervals. Charged jets are
simulated using PYTHIA8 Monash-2013 and reconstructed with the anti-kT
jet finding algorithm with R = 0.4. . . . . . . . . . . . . . . . . . . . . . . .

66

65

MC closure test results: the statistics in the PYTHIA8+GEANT3 production
is divided into two sub-samples. One is used to build the response matrix
and the other one is used to obtain the input spectrum. . . . . . . . . . . .

6766

MC closure test results: we performed the closure test with diﬀerent generators. In this figure, PYTHIA8+GEANT3 MC production is used to extract
the response matrix and PYTHIA6+GEANT3 MC production is used to

68
69

extract input spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

V0A and V0C event plane correlation before (Left) and after (Right) correc√
tion in Pb-Pb collisions at sNN = 5.02 TeV . . . . . . . . . . . . . . . . .

69

Left: Parameter χn in the mathematical expression of event plane resolution
for V0C. Right: Probability distribution of ψ2meas − ψ2true . The figure is takenfrom Ref. [27] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
71
72

70

V0C 2nd order event plane resolution estimated with 3-sub detector method(V0C-V0A-TPC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

A event fitting result to the track distribution with Eq. 48 in mid-central√
Pb-Pb collisions at sNN = 5.02 TeV. . . . . . . . . . . . . . . . . . . . . .

72

The raw jet pT spectra w.r.t the 2nd order V0C event plane in 30-50% cen√
trality Pb-Pb collisions at sNN = 5.02 TeV.
Left: average UE subtracted,

73

Right: local UE subtracted. . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

Definition of in-plane and out-of-plane directions in this jet v2jet measurement.

73

xvi

74

The δpT distribution estimated with the RC method in 30-50% centrality√
Pb-Pb collisions at sNN = 5.02 TeV.
Left: the 2-dimensional δpT distribution w.r.t 2nd -order V0C event plane,
Right: projections of the 2-dimensional δpT distribution w.r.t 2nd -order V0C
event plane in several intervals of the angle between event plane and RC axis. 74

75

Classification of trigger jet events w.r.t V0C event plane. ∆φ = φjet − ψ2,V0C

76

Near-side jet-hadron correlation functions w.r.t V0C event plane for ptrigger
T,jet >
20 GeV/c, 0.7 < passoc< 2 GeV/c. . . . . . . . . . . . . . . . . . . . . . . .
T

77

77

Near-side jet-hadron correlation functions w.r.t V0C event plane for ptrigger
T,jet >
20 GeV/c, 2 < passoc< 4 GeV/c. . . . . . . . . . . . . . . . . . . . . . . . .
T

78

75

78

Near-side correlation functions as a function of ∆φ. Flow background unsubtracted distribution (Red), background distribution estimated in the sideband regions (Blue) and background subtracted distribution (Green). The
unit of Y-axis is a.u.
assoc < 2 GeV/c. The characters on top of each
ptriggerT,jet > 20 GeV/c, 0.7 < pT

panel ((a)-(h)) correspond to trigger jet event classes given in Fig. 75 . . . .
79

79

Near-side correlation functions as a function of ∆η. Flow background unsubtracted distribution (Red), background distribution estimated in the sideband regions (Blue) and background corrected distribution (Green) are shown.
The fitting results with Lorentzian function to the background corrected distributions are shown as black lines. The unit of Y-axis is a.u.
assoc < 2 GeV/c. The characters on top of each
ptriggerT,jet > 20 GeV/c, 0.7 < pT

panel ((a)-(h)) correspond to trigger jet event classes given in Fig. 75 . . . .
80

80

Near-side correlation functions as a function of ∆φ. Flow background unsubtracted distribution (Red), background distribution estimated in the sideband regions (Blue) and background subtracted distribution (Green). The
fitting results with Lorentzian function to the background corrected distributions are shown as black lines. The unit of Y-axis is a.u.
assoc < 4 GeV/c. The characters on top of each
ptriggerT,jet > 20 GeV/c, 2 < pT

panel ((a)-(h)) correspond to trigger jet event classes given in Fig. 75 . . . .
xvii

81

81

Near-side correlation functions as a function of ∆η. Flow background unsubtracted distribution (Red), background distribution estimated in the sideband regions (Blue) and background corrected distribution (Green) are shown.
The unit of Y-axis is a.u.
assoc < 4 GeV/c. The characters on top of each
ptriggerT,jet > 20 GeV/c, 2 < pT

panel ((a)-(h)) correspond to trigger jet event classes given in Fig. 75 . . . .

82

82

Parameterized tracking eﬃciency from full detector simulation . . . . . . .

84

83

Comparison of tracking eﬃciencies from ALICE full simulation and fast simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

Systematic uncertainty from tracking eﬃciency uncertainty of ±3% for jet

cone R = 0.2 (left), R = 0.4 (right) . . . . . . . . . . . . . . . . . . . . . . .

85

84
85

Systematic uncertainty from tracking resolution uncertainty for jet cone R =0.2 (left), R = 0.4 (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

86

Raw jet spectra fitted with a sum of two Tsallis functions. . . . . . . . . . .

87

87

Ratio of spectra to fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

88

Shifted and unshifted fit spectrum assuming secondary contribution . . . .

88

89

Systematic uncertainty from secondary contribution to jet spectra . . . . .

89

90

The average of underlying event pT density estimated by the perpendicularcone as a function of leading jet pT . . . . . . . . . . . . . . . . . . . . . . .

90

91

Shifted and unshifted fit spectra assuming uncertainty on UE measurement

91

92

Ratio of shifted to unshifted fit spectra . . . . . . . . . . . . . . . . . . . . .

91

93

Systematic uncertainty in the jet cross section from Underlying event subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

94

92

Systematic uncertainty from the choice of unfolding method. The lines in
the figure represent fit results with linear function and the values at the bin
centers are assigned as the bin-by-bin systematic uncertainties. . . . . . . .

95

Systematic uncertainty from the choice of regularization parameter k by varying nominal ±2 in the pT range of 5-20 (GeV/c) . . . . . . . . . . . . . . .

96

93

Systematic uncertainty from the choice of regularization parameter k by varying nominal ±2 in the pT range of 20-100 (GeV/c) . . . . . . . . . . . . . .

97

92

94

Systematic uncertainty from the choice of event generator for jet cone R = 0.2(left) and R = 0.4 (right), showing the ratio to nominal PYTHIA8 Monash
2013 tune. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xviii

94

98

An example of flow shape fit in the side-band region for pT,jet > 20 GeV/c,
2 < passoc
T,track < 4GeV/c. The characters attached to top of each panels aredefined in Fig. 75. The y-axis is expressed in arbitrary unit. . . . . . . . . .

99

98

An example of flow shape MC simulation and peak fitting with Gaussian for
pT,jet > 20 GeV/c, 2 < passoc
T,track < 4GeV/c. The characters attached to topof each panels are defined in Fig. 75. The y-axis is expressed in arbitrary
arbitrary unit.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
√100 Charged jet diﬀerential cross sections in pp collisions at s = 5.02 TeV. Sta-99

tistical uncertainties are smaller than the marker size. UE is not subtracted.
The systematic uncertainties are shown as shaded bands around the data
points. Data are scaled by diﬀerent factors to enhance visibility.

. . . . . .

105

101 Charged jet diﬀerential cross sections with UE subtraction in pp collisions at√
s = 5.02 TeV. Statistical uncertainties are smaller than the marker size.
The systematic uncertainties are shown as shaded bands around the data
points. Data are scaled by diﬀerent factors to enhance visibility.

. . . . . .

106

102 Comparison of the charged jet cross section to LO pQCD MC predictions
with diﬀerent jet resolution parameters R = 0.2, 0.3, 0.4, and 0.6. UE is
not subtracted. Statistical uncertainties are displayed as vertical error bars.
The systematic uncertainty on the data is indicated by a shaded band drawn
around unity. The red lines in the ratio correspond to unity. . . . . . . . . .

107

103 Comparison of the charged jet cross section to LO pQCD MC predictions.
UE subtraction is applied. Statistical uncertainties are displayed as verticalerror bars. The systematic uncertainty on the data is indicated by a shadedband drawn around unity. The red lines in the ratio correspond to unity. . .

108

104 Comparison of the charged jet cross section to NLO pQCD MC predictions(POWHEG+PYTHIA8). UE is not subtracted. Statistical uncertainties are
displayed as vertical error bars. The systematic uncertainty on the data is
indicated by a shaded band drawn around unity. The red lines in the ratio
correspond to unity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

109

105 Comparison of the charged jet cross section to NLO pQCD MC prediction(POWHEG+PYTHIA8). UE subtraction is applied. Statistical uncertainties
are displayed as vertical error bars. The systematic uncertainty on the data
is indicated by a shaded band drawn around unity. The red lines in the ratio
correspond to unity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xix

110

106 Charged jet cross section ratios for σ(R = 0.2)/σ(R = 0.4) (Red) and σ(R =0.2)/σ(R = 0.6)(Blue) in comparison with LO (PYTHIA) and NLO event
generators with matched parton showers and modelling of hadronization andthe underlying event (POWHEG+PYTHIA8). UE is not subtracted. The
systematic uncertainty of the cross section ratio is indicated by a shadedband drawn around data points. No uncertainties are drawn for theoreticalpredictions for better visibility in upper panel. . . . . . . . . . . . . . . . .

112

107 Comparison of the charged jet cross section ratio with UE subtraction to√other results. The results in pp collisions at s = 5.02 TeV are compared√√to the results of pp collisions at s = 7 TeV and p-Pb collisions at sNN =5.02 TeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
108 Charged jet v2 in mid-central (30-50%) Pb-Pb collisions at
TeV (Red).

113√

sNN = 5.02
jet
The result is compared to the v2 in mid-central (30-50%) Pb-

Pb collisions at√

sNN = 2.76 TeV (Black) . . . . . . . . . . . . . . . . . . .

115

109 Estimated R = 0.2 charged jet pT suppression as a function of in-medium
parton path-length L. The result are fitted by a linear (left) or quadratic
function (Right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

115

110 Definitions of the eﬀective overlapping region for in-medium parton pathlength calculation with Glauber MC simulation.
Left: The overlapping region of average nucleus radii of two colliding nuclei [25].
Right: The elliptical region defined by participant distribution. The major
and minor axes are defined as 1 σ of the slice of participant distribution inplane and out-of-plane. The x′ axis is corresponding to the participant event
plane direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

117

111 The reduced chi-square for jet v2 (red) and ∆pT linear fit (blue).
Left: The reduced chi-square as a function of the ⟨LHS ⟩ exponent (α).

Right: The reduced chi-square as a function of the ⟨Lσ ⟩ exponent (α).

. .

112 The reduced chi-square as a function of the exponent of ⟨Lσ ⟩ (α) and of ρ(β) for ∆pT (derived from R=0.2 jet RAA ) fit (left) and for jet v2 (right). .

118

119

113 Near-side jet-hadron correlations for in-plane jets (|∆φ(φjet−ψ2 )| < π/4, Red)det
and out-of-plane jets (|∆φ(φjet−ψ2 )| > 3π/8, Green). pch,
> 20 GeV/c.
T,jet

0.7 < passoc
T,track < 2 GeV/c. α is selected so that the fit function height is 1. .
xx

120

114 Near-side jet-hadron correlations for in-plane jets (|∆φ(φjet−ψ2 )| < π/4, Red)det
and out-of-plane jets (|∆φ(φjet−ψ2 )| > 3π/8, Green). pch,
> 20 GeV/c,
T,jet

2 < passoc
T,track < 4 GeV/c. α is selected so that the fit function height is 1. . .

121

115 The near-side peak position w.r.t jet axis in azimuth as a function of angle
det
assoc
between jet axis and event plane. pch,T,jet > 20GeV/c. Left: 0.7 < pT,track <2 GeV/c, Right: 2 < passoc
T,track < 4 GeV/c . . . . . . . . . . . . . . . . . . . .

121

116 The world map on the earth. The countries collaboration with ALICE arecolored in red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

129

117 φ-η distributions of hybrid tracks for each run used for data analysis. . . . .

130

118 φ and η distributions of charged tracks (a) with Hybrid track cut (black),(b) with SPD hits and ITS refit (red), and (c) without SPD hit and ITS refit(blue) .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

131

119 Validation of hybrid tracks pT spectra per data collection period. . . . . . .

131

xxi

Chapter 1

Introduction

One of the ultimate questions for Physics is ’What is the origin of matter and how its constituents interact with each other?’. In our current understanding, the world is governedby four fundamental interactions - electromagnetic, weak, strong, and gravity. Today, thetheory of general relativity [28] and the Standard Model [29, 30] are the successful theories
to describe the fundamental interactions and the elementary particles. Three of the fundamental interactions - electromagnetic, weak and strong - are well modeled in the frameworkof the Standard Model while the gravity interaction is described by the theory of generalrelativity. The Standard Model is the integration of the electroweak model which describes
the electromagnetic and weak interactions, and Quantum ChromoDynamics (QCD) which
describes the strong interactions.
The elementary particles are classified into two groups in the Standard Model: fermionsand bosons. Quarks and leptons are fermions and they compose the matters while the gaugebosons (photon, gluon, Z and W ) play the role of force carriers. The Higgs boson is the
only scalar boson in the Standard Model which gives mass to fundamental particles [31].
The elementary particles in the Standard Model are listed in Fig. 1.
The physics of quarks and gluons, which are collectively called ’partons’, in other words
the physics at the scale where the QCD eﬀects are dominant, is the subject of this thesis.
Partons cannot be isolated and are confined under normal conditions into bound states,
which are called ’hadrons’. However, indirect signatures of a parton can be observed inhigh-energy particle collisions as collimated sprays of high-momentum final-state particles,
known as ’Jets’.
In this thesis, jets are measured with a twofold interest. Firstly, a measurement of jet
production cross sections provides stringent tests of theoretical predictions since the elementary process of jet production is one of the most fundamental processes in QCD. In√
this work, the charged jet production cross section in pp collisions at s = 5.02 TeV ismeasured and compared to several perturbative QCD (pQCD) based model predictions.
Secondly, the Quark-Gluon Plasma (QGP), the state of hot and dense QCD matter formed
in ultrarelativistic heavy-ion collisions, can be probed by measuring jets. As mentioned
above, partons are normally confined into hadrons but, under extreme conditions of hightemperature and/or high density, partons are deconfined to form a hot and dense QCD1

2

Chapter 1. Introduction

medium. Measurements of jets allow to probe the entire evolution of QGP in ultrarelativistic heavy-ion collisions since jets originate from hard-scatterings taking place at the earlystages of the collision. It is expected that the energy of these initial hard-scattered partons is suppressed while traversing the QGP which results in modifying the jet properties
in comparison with QCD vacuum. In Ref. [25], the charged jet production cross sections√in Pb-Pb collisions at sNN = 5.02 TeV were measured to build the charged jet nuclear
modification factors (RAA ) by using the results obtained in pp collisions. In this thesis,
more diﬀerential measurements of jet v2 and jet-hadron correlations in Pb-Pb collisions at√
sNN = 5.02 TeV are presented to study jet modifications owing to parton energy loss andre-distribution in the QGP.

Figure 1: The Standard Model of elementary particles [32]1.1

Quantum Chromodynamics (QCD)

The interaction between partons is dominantly governed by the strong interaction. On
larger scales, the strong interaction is eﬀective in binding nucleons inside nuclei.
The Quantum ChromoDynamics (QCD) is a non-Abelian quantum field theory that

Section 1.1. Quantum Chromodynamics (QCD)

Interaction
Weak
StrongElectromagnetic
Gravitation

Relative strength
1025
1038
1036
1

3

Carrier
Z and W boson
gluon
photongraviton (undiscovered)

Table 1: The four fundamental interactions in nature. The relative strength of Gravitation
is taken to have a value of 1.

describes the strong interaction [33, 2]. The gauge symmetry of QCD quantum numbers,
the ’color charges’, are described by a SU (3) group. The SU (3) group consists of a set ofunitary 3 × 3 matrices. The fundamental representation of SU (3) is a triplet. The threecolor charges of quarks (Red, Green, Blue) form a SU (3) symmetry group. The SU (3)group has 32 − 1 = 8 generators which correspond to 8 gluons. Since gluons carry color
charges, not only quarks but also gluons do interact with each other.
The gauge invariant QCD Lagrangian is expressed as:
1
L = q̄(iγ µ ∂µ − m)q − g(q̄γ µ Ta q)Gqµ − Gaµν Gµν(1)a4
where q, q̄ are the color and anti-color fields, γ µ is the Dirac γ−matrix, g is the strong
coupling constant, Gaµ is the gauge field for a given color a. Gaµν is the field strength tensor
which is expressed as:
Gaµν = ∂µ Gaν − ∂ν Gaµ − gfabc Gbµ Gcν .

(2)

The coupling constant g is given as a function of the theory’s equivalent of the fine structure
constant αs (Q2 ) as:g≡!
4παs (Q2 )(3)where Q is the energy scale of the process.
1.1.1

Asymptotic freedom and Confinement

One of the most remarkable features of QCD is that the coupling constant becomes small
at large energy scale. This behavior is known as ’asymptotic freedom’. It suggests that
perturbative calculations are applicable for large energy scale QCD processes. The αs at
leading order in perturbative expansion of the strong coupling is given as a function of theenergy scale Q by:
αs (Q2 ) = g 2 /4π =1β0 ln(Q2 /Λ2QCD )(4)

where, β0 is the 1-loop β-function coeﬃcient and ΛQCD is the QCD scale parameter. ΛQCD
is an important parameter for the predictive capability of QCD because it gives the starting

4

Chapter 1. Introductionenergy scale at which a perturbative calculation becomes applicable. The current mostprobable value of ΛQCD is 210 ± 14 MeV [29].

While asymptotic freedom allows to probe partons at large energy scale, the growthof the coupling constant at small energy scale leads to the binding of partons into colorsinglet hadrons of size of the order of 1 fm. This behavior is known as ’color confinement’or simply ’confinement’. The potential of a static quark and anti-quark pair is obtained
phenomenologically by fitting the lattice QCD calculations with the following function:

V (r) = V0 −

α
+ σr
r

(5)

where r is the distance between two quarks and V0 , α, σ are the unknown parameters.
The fit result is shown in Fig. 2.
þ
2.0

V(r)
1.5

1.0

0.5
0

10

5

15

r
Figure 2: Static quark potential V (r) from 2+1 flavor lattice QCD calculations [1]1.2

Hard scattering and Jets

Hard parton scatterings of large momentum transfer (Q2 ≫ ΛQCD ) is the dominantmechanism for high-transverse momentum (pT ) hadron production in high-energy nucleusnucleus collisions. The production cross section of high-pT hadrons is calculable from theunderlying parton-parton processes using the ’factorization theorem’ [34]. The hadronic
production cross section of a hadron h, to order O(1/Q2 ), is expressed as:

dσAB→h = fa/A (x1 , Q2 ) ⊗ fb/B (x2 , Q2 ) ⊗ dσab→c (x1 , x2 , Q2 ) ⊗ Dc→h (z, Q2 )(6)Section 1.2. Hard scattering and Jets

5

Figure 3: Sketch of the hard scattering in hadronic collisions [2]where fa/A (x, Q2 ) is the Parton Distribution Function (PDF), the probability of findinga parton of flavour a with momentum fraction x = pa /pA in a nucleus A. dσab→c is thepartonic hard-scattering cross section for partons a and b. Dc→h is the Fragmentation
Function (FF) which is the probability of the outgoing parton c to fragment into hadron
h with z = ph /pc . For example, Fig. 4 shows the PDF measured with deep inelastic e± p
scattering [3] and Fig. 5 shows the FF for positively charged pions based on single-inclusive
pion production in electron-positron annihilation, lepton-nucleon deep-inelastic scattering,and proton-proton collisions [4].
As illustrated in Fig. 3, hard scattered partons undergo a so-called parton shower before
fragmenting into final state hadrons resulting in collimated sprays of high-pT hadrons. This
collimated spray of hadrons, called ’jet’, is the typical experimentally measurable signatureof partons. Since most of jets originate from 2 → 2 parton scattering process, two jets areusually produced back-to-back in azimuth (di-jets).

6

Chapter 1. Introduction

Figure 4: The Parton Distribution Functions from HERAPDF1.0 at Q2 = 10 GeV2 [3].

Figure 5: The individual Fragmentation Functions for positively charged pions zDiπ
Q2 = 10 GeV2 [4].

+atSection 1.3. Quark-Gluon Plasma (QGP)

1.3

7

Quark-Gluon Plasma (QGP)

Because of color confinement, partons are bound into hadrons under normal conditions asmentioned in Sec. 1.1.1. However, at extremely high temperatures and/or densities, partonsare expected to deconfine and behave like free particles because of asymptotic freedom.
Deconfined partons form a strongly interacting QCD medium, called ’Quark-Gluon
Plasma’ (QGP) by analogy with classical electromagnetic ’plasma’. Historically, QGP formation was originally predicted by Collins and Perry [35], who predicted that matter composed of quarks may exist under extreme conditions such as in the core of neutron stars andin early Universe a few µs after the Big Bang. Results from recent lattice QCD calculations,predict a critical temperature Tc ∼ 150−200 MeV and energy density ϵc ∼ 0.5−1.2 GeV/fm3

for the phase transition from hadronic to QGP state. Fig. 6 illustrate our current understanding of the QCD phase diagram and Fig. 7 shows the results of lattice QCD calculations.
The experimental evidence of QGP formation is introduced in Sec. 1.7.1 and 1.7.2.

Figure 6: A sketch of the QCD phase diagram [5]1.4

Relativistic heavy-ion collisions

Relativistic heavy-ion collisions provide unique experimental conditions for QGP formation in the laboratory. Particle accelerators propel massive nuclei to almost speed of lightand cause them to collide. As of 2018, high-energy heavy-ion collision experiments are
performed at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider(LHC). These are circular particle accelerators built at Brookhaven National Laboratory

8

Chapter 1. Introduction

Figure 7: The energy density normalized by T 4 as a function of the temperature. SB is the
Stefan-Boltzmann limit ϵSB = 3pSB [6](BNL) and European Organization for Nuclear Research (CERN) respectively. An energy√
density of 5.4 ± 0.6 GeV/fm3 in central Au+Au collisions at sNN = 200 GeV was re√ported at RHIC [36] and 13 ± 2 GeV/fm3 in central Pb-Pb collisions at sNN = 2.76 TeV

at LHC [37]. RHIC and LHC have both reached energy densities in heavy-ion collisions
higher than the predicted critical energy density for QGP formation. At RHIC, various
nucleus species are accelerated to diﬀerent center-of-mass energies to study system size andenergy dependence of QGP observables and to explore the QCD phase diagram. At LHC,
proton and lead nuclei are accelerated up to the currently world’s top center-of-mass energy√of sNN = 5.02 TeV. Longer QGP life-time and larger jet production cross sections are
expected at LHC energies than at RHIC top energy. Therefore, studies of partonic energy
loss in QGP with hard probes, such as jets, are one of the main subjects of the LHC physics
program. Features of ultrarelativistic heavy-ion collision experiments performed at BNL
and CERN are summarized in Table 2. The experimental datasets of pp and Pb-Pb colli√
sions at sNN = 5.02 TeV used for the measurements presented in this thesis were recorded
in 2015 by the ALICE detector at the LHC [38].

Section 1.4. Relativistic heavy-ion collisions

9

Table 2: Summary of ultrarelativistic heavy-ion programs√Year

Accelerators

Location

Species

1986

AGS

BNL

16 O, 28 Si

5.4

197 Au4.8

16 O, 32 S

19.4

1994

208 Pb

17.4

2000

197 Au130

2001

197 Au200

2003

d-197 Au

200

2004

197 Au200, 62.4

2005

63 Cu

200, 62.4, 22.4

2007

200 Au200

2008

d-197 Au

200, 62.4

2010

197 Au200, 62.4, 39, 11.5, 7.7

2011

197 Au200, 19.6, 27

2012

238 U

193

2012

63 Cu-197 Au

200

2014

197 Au200, 14.6

2014

3 He-197 Au

200

2015

p-197 Au

200

2015

p-197 Al

200

2016

197 Au200

2016

d-197 Au

200, 62.4, 19.6, 39

2017

197 Au54

2018

96 Zr,96 Ru

200

2018

197 Au27

2010

208 Pb2760

2011

208 Pb2760

2013

p-208 Pb

5020

2015

208 Pb5020

2016

p-208 Pb

5020, 8160

2017

129 Xe5440

2018

208 Pb

5020

1992
1986

SPS
RHIC

LHC

CERN
BNL

CERN

sNN Energy(GeV)

10

1.4.1

Chapter 1. Introduction

Space-time evolution

In this section, a global picture of heavy-ion collisions is described. Fig. 8 shows the spacetime evolution of a nucleus-nucleus collision. The initial collision time is τ = 0.

Figure 8: Sketch of the space-time evolution of a nucleus-nucleus collision [2]1.) Before collision (τ < 0)
Nuclei are accelerated to the desired center-of-mass energy. Due to Lorentz contraction, the longitudinal thickness of the nuclei is contracted to 2R/γ, where R is theradius of the nuclei and γ is the Lorentz factor.
2.) Nuclear overlap and Pre-equilibrium (0 < τ < τ0 )During collision, a large amount of partons are created experiencing multiple interactions leading to the formation of partonic matter. The collision energy is deposited
into the initial overlapping region of the two colliding nuclei. During the early stagesof the collision, hard processes occur.
3.) QGP formation and hydrodynamical evolution (τ0 < τ < τc )If the system reaches the critical conditions during step 2.), a QGP state is created attime τ0 . The space-time evolution of the QGP can be described by the equations ofrelativistic hydrodynamics. Following the hydrodynamical expansion of the system,
the mean free path-length of partons increases and the system cools down.

Section 1.4. Relativistic heavy-ion collisions

114.) Chemical freezeout (τc < τ < τch )When the system conditions drop below the critical conditions at time τc (corresponding to the critical temperature Tc ) partons confine back into individual hadrons when
their mean free path-length becomes comparable to the system size. Hadron species
are fixed at time τch (Tch ), which is called ’chemical freezeout’.
5.) Kinetic freezeout (τch < τ < τf o )Hadrons continue to interact elastically after chemical freezeout. Momenta and energies of hadrons are fixed when the mean free path-length of hadrons becomes sufficiently longer than the system size. This stage called ’kinetic freezeout’ takes placeat time τf o (Tf o ). We are able to detect hadrons after freezeout steps, 4.) and 5.).
1.4.2

Collision geometry - Participants and spectators

In this section, geometrical aspects of relativistic heavy-ion collisions are explained. The
understanding of collision geometry is essential to explore QGP properties. Fig. 9 illustrates
two nuclei before and after a non-central heavy-ion collision.

Spectatorsb

Participants
before collision

after collision

Figure 9: Left: Two heavy-ions before the collision with impact parameter b. Right:
The spectators continue unaﬀected, while in the participant zone particle production takes
place. [7]The impact parameter b, which is defined as the distance between the center of two
nuclei, determines the overlap area of the two colliding nuclei. The degree of overlap, called’centrality’, is defined as a function of the impact parameter b [8] as:
" b
# $
1
cb ≡
P inel b′ 2πb′ db′(7)
σ inel 0
where σinel is the inelastic nucleus-nucleus cross section and Pinel (b) is the probability of
inelastic collision with impact parameter b. Experimentally, the impact parameter cannot be measured. Therefore, centrality is determined with a cumulative distribution of a

12

Chapter 1. Introduction

measurable observable n, such as particle multiplicity:
c≡

" ∞
n

# $
P n′ dn′(8)

where the probability distribution of c is constant by construction: P (c) = 1 for 0 < c < 1.
Fig. 10 shows the mean multiplicity value of n (n̄), which was calculated by the TR ENTO
model [39], versus centrality defined by impact parameter (cb ). In the inset of this figure,n̄(cb ) is compared to n(c), the multiplicity which gives the centrality c defined by Eq. 8.
It is found that n̄(cb ) deviates from n(c) only above n ∼ 170 which corresponds to 1.5%
centrality. Fig. 11 shows an example of the experimentally determined centrality with
ALICE V0 scintillation counters. The centrality is estimated via a Glauber fit of themultiplicity distribution measured by the V0 detector and described by a Negative Binomial
Distribution (NBD) [40].

Figure 10: Mean value of n (n̄) versus b-centrality (cb ) [8]. Red circles show the result
calculated directly by binning TR ENTo results in cb and dashed blue line shows the result
reconstructed from the fit of P (n). The inset shows a zoom of the most-central collisions,where n̄(cb ) is compared to n(c) (dotted line).
As illustrated in Fig. 9, nucleons from the two incoming nuclei can be grouped into
’participants’, the nucleons which took part in the collision and ’spectators’ which did not.
For a given impact parameter, the Glauber model [41] gives the number of participantsSection 1.4. Relativistic heavy-ion collisions

13

Figure 11: Distribution of the sum of amplitudes in the ALICE V0 scintillators. The
distribution is fitted with the NBD-Glauber fit shown as a line [9]Npart , the number of nucleon-nucleon collisions Ncoll , and the distributions of participants
and spectators.
Nucleons inside nucleus A are distributed with a density ρ by a Wood-Saxon distribution:
ρA (r) =ρ0
1 + exp ([r − RA ] /a)(9)where r is the distance of each nucleon from the center of nucleus A, RA is the radius of
nucleus A, and a is a diﬀusion parameter at the surface of nucleus A. ρ0 is a normalization%
parameter so that d3 rρA (r) = A.

The nuclear thickness function at impact parameter b, which represents the number ofnucleons of nucleus A per unit area is given" as:TA (b) =dzρA (z, b) .

(10)

Then, the number of participants Npart can be expressed as:
N part =
+

"

"

#
# NN
$$
dsTA (s) 1 − exp −σinel
TB (s)## NN$$
dsTB (s − b) 1 − exp −σinel
TA (s)(11)

NN is the inelastic nucleon-nucleon cross section.
where σinel

The number of nucleon-nucleon collisions Ncoll is:
N coll = A B TAB (b)σ NN
inel

(12)

14

Chapter 1. Introduction

where A, B are the mass number of nucleus A and B, and TAB (b) =%From geometry considerations, the number of collisions Ncoll scales as:

TA (s)TB (s − b)d2 s.

4/3

N coll ∝ N part .
1.4.3

(13)

Collision geometry - Event plane

The plane defined by the beam axis and the impact parameter vector is called the ’reaction
plane’ (RP). In non-central heavy-ion collisions, the participants form an almond-like shape(Fig. 12). As presented in Ref. [42], [43], the nth -order participant eccentricity εn is definedas:εn =where r =&< r2 cos nφpart >2 + < r2 sin nφpart >2 / < r2 >(14)!
x2 + y 2 and φpart is the azimuthal angle of a participant. The nth -orderparticipant event plane (EP) ψnpart , which directs the minor axis of the n-gon formed by theparticipants region, is defined as:
#'
( '
($
atan 2 r2 sin (nφpart ) , r2 cos (nφpart ) + π
part
ψn =
.
(15)
n
In this thesis, the direction of RP and ψn are referred to as ’in-plane’ and the direction
perpendicular to RP and ψn as ’out-of-plane’. In reality, the reaction plane reconstructedfrom the participant distribution is expressed as the superposition of the nth -order event
planes since the number of nucleons is finite. The 2nd -order event plane corresponds to theelliptic shape of the initial collision geometry which is mainly derived from the almond-likeshape of the overlap region between the two nuclei. Higher-order event planes are sensitive
to the fluctuations of the initial geometry of participants. For the measurements in Pb-Pb
collisions discussed in this thesis, jets are measured w.r.t the 2nd -order event plane to study
the initial collision geometry dependence of parton energy loss. For example, a stronger
parton energy loss is expected in the out-of-plane direction than in-plane since the mean
parton path-length is longer out-of-plane. The in-medium parton energy loss is describedin Sec. 1.5 and experimental results of the EP dependence of energy loss are shown inSec. 1.7.1.

1.5

Parton energy loss in the hot and dense QCD medium

In the QGP, the energy of hard scattered partons is suppressed due to collisional and/or
radiative in-medium energy loss. As a result, the observed jet properties are modified incomparison with QCD vacuum. For example, jet pT suppression and jet shape modifications
have been observed [25, 17]. This phenomenon is called ’jet quenching’. Measurement ofjet quenching in heavy-ion collisions allows to probe the entire evolution since jets originate

Section 1.5. Parton energy loss in the hot and dense QCD medium

15!#!"#$%&'()
*+#("

!"

Figure 3

Figure 12: A sketch of a non-central Pb-Pb collision. Colored circles are nucleons. Solidcircles are participants and dashed circles are spectators. The original figure which wasmade with a Glauber Monte-Carlo simulation was taken from Ref. [10]. The reaction planeand 2nd , 3rd -order event plane (ψ2 , ψ3 ) are displayed.
from the hard scattered partons in the early stages of the collision. Since the elementary
processes involved in jet production can be described within pQCD, jets are well calibrated
probes of the QGP properties.
In this section, an overview of the collisional and radiative energy loss mechanisms in
QGP is given.

E

E-!E

!E

E
!E

E-!E
X
(medium)

Fig. 3. Diagrams for collisional (left) and radiative (right) energy losses of a quark of energy

Figure 13: Left: Feynman diagram of collisional parton energy loss. Right: Feynman
diagram of radiative parton energy loss. [2]Collisional energy loss
The collisional energy loss induced by elastic scatterings within the medium dominates

16

Chapter 1. Introduction

at low momentum [2]. The average energy loss per parton scattering is given as:" tmax
'
(
1
dσ
1scat
∆Ecoll≈t dt(16)
σT m2Ddt
where dσ
dt is the cross section and t the momentum transfer. mD is the Debye massequal to (4παs )1/2 T ∼ 1 GeV at leading order pQCD calculation. The lower limit of
the integrated momentum transfer tmin is given by the QGP Debye mass squared as:tmin = m2D (T ) ∼ 4παs T 2 (1 + Nf /6) .

(17)

The upper limit tmax is given as:tmax = s ∼ ET .

(18)

With Eq. 16, 17, 18 and taking the dominant contribution to the t-diﬀerential partonparton elastic cross section,dσ
4παs2 (t)
12π
)
≈ Ci
, with αs (t) =dtt2(33 − 2n ) ln t/Λ2
f

QCD

*

(19)

where Ci is the colour factor for individual parton combinations (Ci = 9/4, 1, 4/9
for gg, gq, qq respectively). Thus, the collisional energy loss per unit length for lightpartons is given as:+,
dEcoll ++
1
ET
2
=
C
α
(ET
)m
ln
.
(20)
R s
D
dl +q,g
4m2DThe collisional energyas:+ loss per unit
+ length for .heavy-quarks is given,-/#$
dEcoll ++dEcoll ++
2
ET
2
2
−
=−
− CR πT αs M αs (ET ) ln
(21)
dl +Q
dl +q 9M2
where CR = 4/3, 3 for quarks and gluons respectively. The collisional energy loss is−linear with parton path-length and depends only logarithmically on the initial partonenergy.
Radiative energy loss
The radiative energy loss which dominates at high momentum is induced by inelastic
scatterings within the medium [2]. It is defined by analogy with the single or doublediﬀerential photon and gluon Bremsstrahlung spectrum and leads as follows:" E" E " kT,max
dIrad
d2 Irad
1scat
1scat
2
∆Erad
=
ω
dω, or ∆Erad=ω(22)
2 dωdk⊥dωdωdk⊥
where ω, k⊥ are the energy and transverse momentum of the radiated photon andgluon.
The total energy loss for incoherent scatterings can be expressed as ∆E tot = N ·∆E 1scat , where the opacity N = L/λ, L being the thickness of the medium and λ isSection 1.6. Experimental results of jet measurements in pp collisions

17

the mean free parton path-length. The energy loss per unit length, or stopping powerof the medium, is given as:'(∆E tot
dE
−
=
.
dl
L

(23)

In QCD, when considering partons traversing a QGP, the initial parton energy issuppressed mainly by in-medium multiple gluon emission. The radiated gluon spectrum ωdIrad /dω is calculated starting from the DGLAP splitting functions in thevacuum [44]:

0

1
0
1
1 + (1 − z)2
1 + z 4 + (1 − z)4
Pq→qg (z) = CF
, and Pg→gg (z) = CAzz(1 − z)(24)

where the color factor CA = 3, CF = 4/3 and the fraction of the energy of the parent
parton taken by the radiated gluon is given by z = ω/E. A medium-induced enhancement of radiation is taken into account by modifying Eq. 24. The resulting spectrumof radiated gluons, ωdIrad /dω ∝ Pq,g→g (ω/E), has been computed by various groups
with various approximations. In several models, all medium-induced modifications
are often represented by the ’transport coeﬃcient’ parameter q̂ ≡ m2D /λ. For a thinmedium (L ≪ λ), gluon bremsstrahlung (gluonsstrahlung) is calculated by the Bethe-

Heitler (BH) expression while for the thick medium case (L ≫ λ) the gluonsstrahlung
is aﬀected by the Landau-Pomeranchuk-Migdal (LPM) regime. In the LPM regime,

the soft or hard gluon emission cases are diﬀerentiated according to the characteristic
gluonsstrahlung energy ωc = 12 q̂L2 . The basic QCD radiative energy loss is eventually
expressed as:
Bethe-Heitler(BH) regime (L ≪ λ)
# #
$$
dIrad
BH
ω
≈ αs q̂L2 /ω =⇒ ∆Erad≈ αs q̂L2 ln E/ m2D L
dω

(25)

”Landau-Pomeranchuk-Migdal” (LPM) regime (L ≫ λ)2 !
2
3q̂L2 /ωq̂L2(ω < ωc )
dIrad
LP M
ω
≈ αs
=⇒ ∆Erad ≈ αs
. (26)# #$$dωq̂L2 /ωq̂L2 ln E/ q̂L2 (ω > ωc )1.6

Experimental results of jet measurements in pp collisions

In this section, experimental results of jet measurements in pp collisions are summarized.
1.6.1

Charged jet cross section

Production cross section of jets is dominantly determined by perturbatively calculable partonic hard scattering cross sections. As mentioned in Sec. 1.2, the jet cross section is

18

Chapter 1. Introduction

12<∆E> (GeV)

10

total
radiative
collisional

8
6
4
2
0
0

5

10

15
Ei (GeV)

20

25

30

Figure 14: Comparison of the average energy loss of light quarks by radiative and collisionalenergy losses at RHIC energy [2]expressed as the product of a perturbative part and non-perturbative part. Thus, measurements of jets in simple collision system, such as pp collisions, represent a good test of
the predictive capabilities of pQCD-based models. The charged jets diﬀerential production√
cross sections are shown in Fig. 15 for R = 0.2, 0.4 and 0.6 jets in pp collisions at s = 7
TeV measured by the ALICE Collaboration. Here, ’charged jets’ means jets reconstructedwith charged hadrons only and ’R’ is the jet resolution parameter, also called the jet radius.
The results are compared to pQCD calculations at Leading-Order (LO) accuracy. None ofthe predictions give a quantitative description of the data over entire kinematic range.
Higher-order pQCD calculations give better description of the full jet cross section measurement [45]. Here, ’full jets’ means jets reconstructed with neutral particles in addition
to charged hadrons. Therefore, charged jet cross section may also be well described byhigher-order pQCD calculations.
1.6.2

Charged jet cross section ratio

The ratio of charged jet production cross sections for R = 0.2, 0.4 and 0.6 jets in pp√
collisions at s = 7 TeV is shown in Fig. 16. These ratios are sensitive to the jet radial
shape. According to these results, high-pT jets are more collimated. These results arequantitatively well described by LO pQCD calculations except in the low pT region of theσ(R = 0.2)/σ(R = 0.6) ratio.

10-2

(a)

(b)

ALICE
PYTHIA Perugia-0

10-3

pp

(c)

s = 7 TeVPYTHIA Perugia-2011

ptrack
> 0.15 GeV/cT

PYTHIA AMBT1|ηtrack| < 0.9

HERWIG

19

UE subtracted

PHOJET

10-4

MC/dataT

d2σjet,ch /dp dη (mb c/GeV)

Section 1.6. Experimental results of jet measurements in pp collisions

10-5

10-6

|ηjet | < 0.7|ηjet | < 0.5|ηjet | < 0.3

FastJet anti-k T R = 0.2

FastJet anti-k T R = 0.4

FastJet anti-k T R = 0.6

1.5
1
0.5

20 30 40 50

60 70 80 90 100 20

30

40

50

pjet,ch (GeV/c)

60

70

80

90 100 20

30

40

50

60

70

pjet,ch (GeV/c)

T80

90 100pjet,ch (GeV/c)

T

T

Fig. 5: (Color online) Top panels: Charged jet cross sections measured in the ALICE experiment in pp

σjet,ch ( R = 0.2 )σjet,ch ( R = 0.2 )or jet,chjet,chσ( R = 0.4 )σ( R = 0.6 )Figure 15: The diﬀerential production cross section for charged jets reconstructed with R= 0.2, 0.4 and 0.6 measured by ALICE. The results are compared to some LO pQCD-based
predictions [11]pp s = 7 TeV

0.9

UE subtracted

FastJet anti-k T
jet

0.8

|η | < 0.3; |η track| < 0.9
p track> 0.15 GeV/c
T

0.7
0.6
0.5
ALICE

0.4

PYTHIA Perugia-2011

0.3

HERWIG

20

30

40

50

60

70

80

90

100

pjet,ch (GeV/c)T

6: (Color online) Ratios of jet cross sections for charged jets reconstructed using antiFigure 16: The ratio of charged jet cross section reconstructed with R = 0.2, 0.4 and 0.6
measured by ALICE. The results are compared to some LO pQCD-based predictions [11]

20

Chapter 1. Introduction

1.7

Experimental evidence of nuclear matter eﬀects

In this section, experimental evidence of nuclear matter eﬀects is summarized.
1.7.1

Jet quenching

Owing to in-medium partonic energy loss, as described in Sec. 1.5, jet quenching is observed in ultrarelativistic heavy-ion collisions. One of the most remarkable observations ofjet quenching was made in di-hadron correlation measurements performed by the STAR
Collaboration at RHIC (see Fig. 17).

0.2

h++ h-

d+Au FTPC-Au 0-20%
d+Au min. bias(a)p+p min. bias
Au+Au central(b)(1/Ntrigger) dN/d(∆φ)

0.1

0

0.2

0.1

0
0

π/2

π

∆φ (radians)√
Figure 17: Two-particle correlations in pp, d+Au and Au+Au collisions at sNN = 200GeV
assoc < ptrig [12].
for 4 < ptrig
T < 6 GeV and 2 < pTT(a): Comparison of eﬃciency corrected two-particle azimuthal distributions for minimumbias and central d+Au collisions, and for pp collisions.
(b): Comparison of two-particle azimuthal distributions for central d+Au collisions,minimum-bias pp collisions and for central Au+Au collisions.
The observed back-to-back two-peak structure can be ascribed to the di-jet topology in
QCD vacuum. Near-side (∆φ ∼ 0) and away-side (∆φ ∼ π) peaks are observed in pp andd+Au collisions as expected. However, in central Au+Au collisions, the away-side peak is

not visible anymore. This result, which is interpreted as the suppression of the away-side
jet production due to medium-induced parton energy loss, is considered to be the evidenceSection 1.7. Experimental evidence of nuclear matter eﬀects

21

of QGP formation in central ultrarelativistic heavy-ion collisions.
The nuclear modification factor (RAA ) is one of the proven observables to quantify
nuclear matter eﬀects in heavy-ion collisions. With N AA and N pp being the yields of agiven observable with certain pT in AA and pp collisions respectively, RAA is defined as theratio of the yield in AA collisions over the yield in pp collisions scaled by the number ofbinary nucleon-nucleon collisions Ncoll :dN AA /dpT
dN AA /dpT
RAA =
=
.
(27)
⟨Ncoll ⟩ dN pp /dpT
⟨TAA ⟩ dσ pp /dpT
RAA = 1 means no observation of nuclear eﬀects and departure of RAA from unity
suggests some nuclear matter eﬀects. Particularly, the suppression of hard processes, suchas high-pT hadrons or jets, suggests medium-induced partonic energy loss. Note that RAA= 1 does not always mean the absence of nuclear matter eﬀects since other eﬀects could
balance leading to RAA = 1.
Fig. 18 shows the single hadron RAA measured by several experiments at various collisionenergies. A strong collision energy dependent suppression of high-pT hadrons is observed.

27.4 pb-1 (5.02 TeV pp) + 404 µb-1 (5.02 TeV PbPb)

2
1.8

CMS

SPS 17.3 GeV (PbPb) LHC 5.02 TeV (PbPb)
CMS (0-5%)π± NA49 (0-5%)

Models 5.02 TeV (PbPb)

1.6

RHIC 200 GeV (AuAu)
π0 PHENIX (0-5%)

CUJET 3.0 (h±+π0, 0-10%)1.4

h± STAR (0-5%)

Andres et al. (0-5%)

LHC 2.76 TeV (PbPb)

CMS (0-5%)

SPS

0.6

RHIC

0.4

LHC

0.2
0

v-USPhydro+BBMG (0-5%)

ATLAS (0-5%)

1
0.8

SCETG (0-10%)

ALICE (0-5%)

1.2

RAA

π0 WA98 (0-7%)110p (GeV)

100

T

Figure 18: Comparison of the RAA for neutral pions (π 0 ), charged hadrons (h± ), andcharged particles in central heavy-ion collisions at SPS, RHIC, and LHC [13].
On the other hand, the RAA of high-pT photons and Z, W bosons is consistent withunity as shown in Fig. 19. This result supports the hypothesis that in-medium energy loss

22

Chapter 1. Introduction

2

CMS (* preliminary)∫

1.8

PbPb sNN = 2.76 TeVµ* Z (0-100%) p > 20 GeV/c

-1

T
µ

L dt = 7-150 µb

W (0-100%) p > 25 GeV/c
T

1.6

Isolated photon (0-10%)b-quarks (0-100%)1.4(via secondary J/ψ )

RAA

1.2
1

0.8
0.6
0.4
Charged particles (0-5%)

0.2
0

0

20

40

60

p (m ) (GeV)
T

80

100

T

±

Figure 19: The RAA for direct photons, W ± and Z 0 bosons, charged particles and b-quarks
measured from secondary J/ψ particles [14].
of color-charged partons is the dominant mechanism at work in high-pT hadron suppression,colorless particles not being suppressed in the medium.
Although single high-pT hadron measurements provide valuable insights into partonic
energy loss, they were shown to have severe limitations in their interpretation by imposing
a strict separation between medium eﬀects and jet fragmentation. Conversely, the measurement of fully reconstructed jets mitigates the fragmentation bias and allows to assess theparton kinematics which is required for a detailed description of jet-medium interaction.
The large production cross section of high-pT jets at LHC energies allows to measure fullyreconstructed jets in heavy-ion collisions.
The jet RAA measured at LHC are shown in Fig. 20. The jet RAA shows a strong suppression which grows with the collision centrality. This result emphasizes in-medium parton
path-length dependence of jet quenching. In order to study the path-length dependence of√jet suppression, the jet v2 in Pb-Pb collisions at sNN = 2.76 TeV was measured by the
ALICE and ATLAS Collaborations as shown in Fig. 21. These results show a positive jet v2 ,which suggests a larger jet yield in-plane than out-of-plane. This behaviour is quantitatively
consistent with the JEWEL model predictions [46].
Another interesting question related to jet quenching is the understanding of how theSection 1.7. Experimental evidence of nuclear matter eﬀects

ALI-PREL-114186

23

ALI-PREL-114190

√

0.3

ALICE

ch jetPb-Pb sNN = 2.76 TeV
R = 0.2 anti-k T, |η |<0.7
jetv2

30-50%, Stat unc.

Syst unc. (shape)
calo jet

30-50%, JEWEL

ALICEch jetv230-50%, Stat unc.

Pb-Pb sNN = 2.76 TeV

Syst unc. (shape)

R = 0.2 anti-k T, |η |<0.7

ch jetv2

0.2

Syst unc. (correlated)
ATLAS v 20.2

v 2ch jetv 2part, v 2jet√
Figure 20: Comparison of charged jet RAA in Pb-Pb collisions at sNN = 5.02 TeV measured√
by ALICE and full jet RAA in Pb-Pb collisions at sNN = 2.76 TeV measured by ATLAS [15]Left: Centrality range is 0-10% Right: Centrality range is 10-30%30-50%

jet

Syst unc. (correlated)part

CMS v 2 {|∆η|>3} 30-50%
part

ALICE v 2 {|∆η|>2} 30-50%

0.1

0.1
0

0
(b)

0
)

p

50

T, track> 0.15 GeV/c , p

T, lead> 3 GeV/ c

100
150
jet
part
p , p (GeV/c )
T

T

(b)

20

p

30

40

50

T, track60> 0.15 GeV/c , p lead > 3 GeV/ c
T70

80 90 100ch jetp(GeV/c )T

Figure 21: Left: Elliptic flow coeﬃcient v2 of charged particles (orange, green) and R = 0.2
full jets measured within |η| < 2.1 (blue) superimposed on the results of R = 0.2 charged
jets v2 within |η| < 0.7 (black) in mid-central collisions (30-50%)
Right: v2 of R = 0.2 charged jets predicted by JEWEL (red) for mid-central collisions(30-50%) compared to data (black). [16]24

Chapter 1. Introduction

suppressed parton energy is transported and re-distributed in the medium. The jet radial√
profile in pp and Pb-Pb collisions at sNN = 5.02 TeV measured by the CMS Collaboration
with jet-track(-hadron) correlations is shown in Fig. 22,P(∆r) =

1 1
Σjets Σtracks∈(∆ra ,∆rb ) ptrack, ∆r < 1Tδr Njets(28)

where r is the distance between the jet axis and the tracks. These results show the suppression of high-pT hadrons in Pb-Pb collisions in comparison with the pp case. An enhancementof low-pT hadrons can also be observed at large radial distance from jet axis, suggestingthat the parton energy deposited in the medium is re-distributed in the form of low-pT
hadrons at large radial distance. A model calculation including a hydrodynamical medium
response (see [18] and references therein) reproduced this observation as shown in Fig. 23,
where the jet shape is given by:ρ(∆r) = 4

jets

P(∆r)
4

track
tracks pT(29)

and P(∆r) is defined in Eq. 28. This result suggests that the understanding of the non-statichydrodynamical evolution of the medium will be important to reveal the mechanism of theenergy flow in the medium.
1.7.2

Azimuthal anisotropic flow

In non-central ultrarelativistic heavy-ion collisions, a QGP is formed in the almond shaped
overlap region of the two colliding nuclei as shown in Fig. 24 (Left). During the collective
expansion of the QGP, this initial spatial anisotropy of the overlap region is converted intoa momentum anisotropy of the final state hadrons as shown in Fig. 24 (Right).
The azimuthal momentum distribution of final-state particles in an event can be expanded into a Fourier series as:dN∝ 1 + 2 (v1 cos [φ − ψr,n ] + v2 cos [2 (φ − ψr,n )] + · · · )(30)
dφwhere φ is the azimuthal angles of the particles in momentum space and N is the yield ofparticles. ψr and ψn are the azimuthal angle of the reaction plane and the nth -order event
plane respectively. The Fourier coeﬃcients of nth -order harmonics are expressed as:
vn = ⟨cos [n (φ − ψr,n )]⟩ .

(31)

Non-zero vn means an anisotropic particle production with respect to ψr,n . The azimuthal anisotropic particle production in heavy-ion collisions was observed as shown in
Fig. 25.
This phenomenon is currently understood as a hydrodynamical evolution of the medium
dominantly driven by the pressure gradient in the medium. The diﬀerence of the pressureΡ(∆r)

0.8

0
0

1

2

0.2

T

∆r

0.4

0.6

ptrk > 4 GeVT

ptrk > 2 GeV

0.8

0.8

1.5

2

2.5

01

3

00

00

∆r

0

0

0.5

0.6

0.6

0.5

0.4

0.4

1

10

102

1

0.2

0.8

103

0.2

0.2

∆r

0.4

0.4

PbPb
10-30%

T

T

0.6

0.6

8 < ptrk< 12 GeVTT

2 < ptrk< 3 GeV

trkT

4 < p < 8 GeVTT

3 < ptrk< 4 GeV

1 < p < 2 GeV

trk

Radial momentum distribution

0.8

0.8

00

0

0.5

1

1.5

2

2.5

01

3

1

10

102

103

jet

anti-kT R=0.4 jets, p > 120 GeV, |η |<1.6
0.7 < p < 1 GeV

trk

PbPb
30-50%

0.2

CMS

0.4

0.6

0.8

1

!"#$%

0.2

∆r

0.4

0.6

0.8

1

Radial profile of transverse

0.2

PbPb
0-10%

T

20 < ptrk< 300 GeV

T

T

16 < ptrk< 20 GeV

12 < ptrk< 16 GeV

pp 27.4 pb-1 (5.02 TeV) PbPb 404 µb-1 (5.02 TeV)

1

1.5

2

2.5

3

01

0.6

30

0.4

1

1

T

10

ptrk > 0.7 GeV

1

103

10

PbPb

Ρ(∆r)

0.2

0.8

102

PbPb0.4 0.6
50-100%0.2

T

0.7 < ptrk< 300 GeV

pp reference

102

103

0

1

10

102

/ Ρ(∆r)pp

Ρ(∆r)

103

Section 1.7. Experimental evidence of nuclear matter eﬀects
25

Figure 22: The radial jet momentum distribution P(∆r) of jets in pp (top left) and Pb-Pb√(middle row) collisions at sNN = 5.02 TeV. The bottom row shows the ratio between
Pb-Pb and pp data for the several intervals of ptrack. The shaded bands are systematicT
uncertainties [17]

26

Chapter 1. Introduction

2.76 TeV

2.76 TeV

0-30 %

0-30 %PYTHIA(r)(r)

PYTHIAp jet
T,1 > 120 GeV/cp jet
T,2 > 50 GeV/c
1,2> 5 /6

p jet
T,1 > 120 GeV/cp jet
T,2 > 50 GeV/c
1,2> 5 /6rr

Figure 23: Jet shape function for (a) leading and (b) sub-leading jets in dijet events in√central Pb-Pb and in pp collisions at sNN = 2.76 TeV [18]

(a)

(b)

y!

py!
x!

z!

px!
pz!

Figure 24: Left: Initial overlap of two nuclei in an oﬀ-center collision in coordinate space.
Right: Collective elliptic expansion into the direction of reaction plane in momentum space.

0.15

0.1

ALICE Pb-Pb
5.02 TeVv 2 {2, |∆η|>1}
v 3 {2, |∆η|>1}
v 4 {2, |∆η|>1}
v 2 {4}v 2 {6}v 2 {8}2.76 TeVv 2 {2, |∆η|>1}
v 3 {2, |∆η|>1}
v 4 {2, |∆η|>1}
v 2 {4}27

Hydrodynamics
5.02 TeV, Ref. [27]v 2 {2, |∆η|>1}
v 3 {2, |∆η|>1}

v2

vn

Section 1.7. Experimental evidence of nuclear matter eﬀects

0.08
0.06
0.04

0.05

ALICE
STAR
PHOBOSPHENIX
NA49
CERES
E877
EOS
E895
FOPI

0.02
0

(a)
Ratio

−0.02
1.2

v 2 v 3 v 4 Hydrodynamics, Ref. [25]η/s(T), param1
η/s = 0.20

1.1

−0.04
−0.06

Ratio

1

(b)

−0.08

1.2

1

1.1

0

10

20

30

40

50

60

70

102

3

10

104

sNN (GeV)

(c)

1

10

80

Centrality percentile

Figure 25: The experimental results of anisotropic flow coeﬃcients (vn ) [19]Left: (a) Anisotropic flow coeﬃcients vn integrated over 0.2 < pT < 5.0 GeV/c, as a functionof event centrality for the two-particle and multi-particle cumulant methods.
(b),(c) are the ratios to the various hydrodynamic calculations. ”Ref. [25]” and ”Ref. [27]”in the figure correspond to Ref. [20],[21] respectively in the bibliography.
Right: Comparison of the integrated elliptic flow results from various experiments at various
collision center-of-mass energies.

28

Chapter 1. Introduction

gradient in-plane and out-of-plane leads to the azimuthal anisotropy of particle production.
This process mainly plays a role for soft (low-pT ) particle production and is the main sourceof background for jet measurements in heavy-ion collisions.

Section 1.8. Thesis motivation

1.8

29

Thesis motivation

In this thesis, measurements of charged jets in pp and Pb-Pb collisions at√

sNN = 5.02

TeV with the ALICE detector are performed for a twofold purpose.
1.) As a test of pQCD calculations
Jet production, which is one of the most fundamental QCD processes, is calculable within perturbation theory as mentioned in Sec. 1.1.1, 1.2. However, final-state
observables include non-perturbative eﬀects which can only be extracted experimentally. Some models are often combined with pQCD calculations to account for these
non-perturbative eﬀects. In the studies discussed in this thesis, the measurementsof charged jet diﬀerential production cross sections for R = 0.2, 0.3, 0.4 and 0.6 in√pp collisions at s = 5.02 TeV were compared to Leading-Order (LO) and Next-toLeading-Order (NLO) pQCD-based model predictions.
2.) Exploration of jet quenching in ultrarelativistic heavy-ion collisions
The strength of jet suppression and the modification of jet radial profile as a func√tion of centrality have been measured in Pb-Pb collisions at sNN = 5.02 TeV. Thesestudies control in-medium mean path-length of partons to a certain extent by selecting
centrality. However, the mean path-length largely fluctuates even in mid-central collisions of similar centralities due to the large eccentricities of the initial collision system
which leads to large diﬀerences of parton path-length in-plane and out-of-plane. In
this thesis, R = 0.2 charged jet production in mid-central (30-50%) Pb-Pb collisions√
at sNN = 5.02 TeV is measured w.r.t the 2nd -order event plane. A measurementof charged jet v2 is performed to study the path-length dependence of jet energy
suppression in-plane and out-of-plane. Charged jet-hadron correlations are also studied to measure the modification of jet radial profiles and jet energy suppression andre-distribution.

Chapter 2
2.1

Experimental apparatus

The Large Hadron Collider (LHC)The Large Hadron Collider (LHC) is the world’s largest particle accelerator [47]. It was
built at CERN for the purpose of high-energy particle and nuclear physics experiments. So
far, proton-proton (pp), proton-lead (pPb), lead-lead (Pb-Pb), and xenon-xenon (Xe-Xe)√
collisions were provided by the LHC. Maximum center-of-mass energies of s = 13 TeV in√
pp collisions and sNN = 5.02 TeV in Pb-Pb collisions were achieved.
The LHC is the last ring of the CERN accelerator complex as illustrated in Fig. 26.

Figure 26: Sketch of the CERN accelerator complex
To reach the LHC energies, the particle beams are pre-accelerated before injection into the
LHC ring by an accelerator chain which consists of LINAC, storage ring, and synchrotron.
The proton beams are accelerated by LINAC 2 up to an energy of 50 MeV and the lead-ion
beams are accelerated by LINAC 3 up to an energy of 4.2 MeV/n. Proton beams are then31

32

Chapter 2. Experimental apparatus

transfered to the PS Booster (synchrotron) and lead-ion beams to the LEIR (Low-Energy
Ion Ring). The beam energy is then pushed up to 25 GeV by the Proton Synchrotron (PS).
Finally, the beams are subjected to further acceleration at the Super Proton Synchrotron(SPS) up to 450 GeV and then injected into the LHC ring.

2.2

The ALICE detector complex

The ALICE detector consists of diﬀerent sub-detectors dedicated to various purposes asshown in Fig. 27.

Figure 27: The ALICE detector at the LHC Run2
The ALICE detectors are classified into three groups:• ’Central barrel detectors’ for particle tracking and electro-magnetic calorimetry (|η| <1).

• ’Muon arm’ for muon tracking (−4 < η < 2.5).
• ’Global detectors’ for event triggering, event characterization and classification.
In the following sections of this chapter, the ALICE detectors used for the jet measurements
are introduced.
2.2.1

VZERO (V0) detector

The VZERO (V0) detector is a multi-segmented scintillation counter. The V0 detector
is one of the global detectors installed in the forward and backward rapidity regions. The

Section 2.2. The ALICE detector complex

33

V0 covering the forward region is called ’V0A’ (2.8 < η < 5.1) and the one covering the
backward region is called ’V0C’ (−3.7 < η < −1.7).

Figure 28: The installation of V0 detector in ALICE. [48]Each of the V0 arrays is segmented in 4 rings and each ring is divided into 8 sections asshown in Fig. 29.

Figure 29: Sketch of V0A and V0C array segmentation. The scintillator thicknesses are 2.5
and 2 cm respectively. The two segments separated by dashed lines are connected to thesame PMT [48].
The design of the V0 elementary cells is shown in Fig. 30. Wave-Length-Shifting (WLS)
fibers are embedded on both faces of the V0A segment or glued along their radial edges for
V0C rings 0-1.

34

Chapter 2. Experimental apparatus

Figure 30: Design of the V0A and V0C rings 0-1 (bottom) elementary cell. Two scintillatingsets (scintillator and WLS fibers) are connected to a single PMT through four clear fiber
beams for V0C rings 2-3. [48]In this study, the V0 detector is used for the following purposes:• Minimum-bias trigger (coincidence between V0A and V0C).
• Multiplicity measurement for centrality determination

The resolution of the centrality determination is 0.5-2% as shown in Fig. 31.

• Measurement of event plane from the multiplicity distribution

The event plane resolution is shown in Fig. 32. For example, the resolution for ψ2 (R2in Fig. 32) is about 60-80% in mid-central Pb-Pb collisions.

• Pileup removal.

2.2.2

Inner Tracking System (ITS)The Inner Tracking System (ITS) consists of 3 diﬀerent types of silicon detectors.
The innermost two layers of the ITS are ’Silicon Pixel Detectors’ (SPD). Each SPD
module is composed of a two-dimensional sensor matrix of reverse-biased silicon diodes. The
pixel size is 50 µm (in the plane perpendicular to the beam axis, rφ)×425 µm (along the beam axis, z).
A pair of hits on each of the two SPD layers is called a ’tracklet’ and is used for primaryvertex determination and multiplicity measurements. SPD also contributes to the L0 trigger
for pileup removal.

centrality resolution (%)

Section 2.2. The ALICE detector complex

35

4.5 ALICE Pb-Pb sNN = 2.76 TeV
43.5
3

ZDC vs ZEM (4.8<η<5.7)
V0A (2.8< η<5.1)
V0C (-3.7< η<-1.7)
TPC (|η|<0.8)
SPD (|η|<1.4)
V0A+V0C

2.5
2
1.5
1
0.5
0
0

10

20

30

40

50

60

70

80

centrality (%)

Rn

Figure 31: Resolution of centrality measured by ALICE detectors in Pb-Pb collisions at√
sNN = 2.76 TeV. [49]

ALICE Pb-Pb sNN = 2.76 TeV

1

V0C [-3.7 < η < -1.7]
R2
R3
R4/Ψ

2

R4/Ψ

4

V0A [2.8 < η < 5.1]

10-1

R2
R3
R4/Ψ

2

R4/Ψ

4

Rn from 3-sub

0

10

20

30

40

50
60
centrality percentile

Figure 32: Event plane resolution measured by V0A and V0C in Pb-Pb collisions at= 2.76 TeV. [49]

√

sNN

36

Chapter 2. Experimental apparatus$%&'()*

!"#
!##
!!#
y
x
z

Figure 33: Sketch of ITS [50].
The intermediate two layers are ’Silicon Drift Detectors’ (SDD). The sensitive area ofan SDD sensor is split into two drift regions by a central cathode. Each drift region isequipped with anodes for charge collection. Two-dimensional position can be reconstructedwith the drift time of the charges and the anode segmentation.
The outer two layers are ’Silicon Strip Detectors’ (SSD). Each SSD module consists ofa 1536 strip double-sided silicon sensor connected through aluminum-kapton micro-cables
to twelve front-end chips. The pitch of the strips is 95 µm and the P-N-side stereo angle is
35 mrad. It allows a two-dimensional measurement of the track position with a good ghost
hit rejection
In this study, the ITS is used for the following purposes:• Primary vertex reconstruction

Primary vertex (the position of the initial collision) is reconstructed from SPD trackSPD . The resolulets. The primary vertex reconstructed with SPD is referred to as zvertex

tion of the primary vertex reconstruction is of the order of 150-200 µm in pp collisions
as shown in Fig. 34.
• Background event removal

An event is identified as a pileup event and rejected if multiple vertices are reconstructed within this event. Additionally, out-of-bunch pileup events are rejected basedon online-vs-oﬄine SPD Fast-OR (FO) correlations.

• Tracking

Section 2.2. The ALICE detector complex

37

Charged particle tracks are reconstructed from hits in the ITS over the pseudo-rapidity
range |η| < 0.9. The reconstructed ITS track segments are combined with TPC (seevertex sigma (µm)

Sec. 2.2.3) track segments to improve the tracking resolution and reduce fake tracks.

800

ALICE
pp s = 7 TeV

x SPD
y SPD
x TRK
y TRK

600

σ = σD ⊕ασDX = 40 ± 2 µm
α x = 297 ± 6 µm
βx = 1.37 ± 0.04400

β(dN/dη)σDY = 42 ± 2 µm
α y = 290 ± 6 µm
βy = 1.39 ± 0.04

200

0

0

5

10

15

20

25

30

35

40

45

dN/dη

Figure 34: Resolution of vertex determination [49].

2.2.3Time Projection Chamber (TPC)

The Time Projection Chamber (TPC) is the main charged particle tracking detector of the
ALICE experiment. A sketch of the TPC is shown in Fig. 35 (left). The TPC is 510 cm
along the beam axis and has a diameter of 469 cm providing a drift volume of 88 m3 . The
drift volume is filled with a light sensitive medium (gas). The gas mixture during LHC
Run1 was Ne(90%):CO2 (10%) and changed to Ar(90%):CO2 (10%) during LHC Run2 toenable a more stable detector response. The drift volume is divided into two regions by acentral electrode made of aluminized mylar foil which generates a drift field of 400 V/cm.
The maximum drift time is about ∼ 100 µs. The TPC has 557,568 readout pads andcorresponding front-end electronics (FEE) readout channels.

In this study, the TPC is used for the following purposes:• Tracking

Charged particle tracks are reconstructed from x-y hits on the readout pads and thedrift time for z position. The full tracking range of the TPC covers a pseudorapidity
range of |η| < 0.9. The reconstructed tracks are combined with ITS track segments

38

Chapter 2. Experimental apparatus

Figure 35: Left: Sketch of TPC [51]. Right: 3D view of TPC tracks reconstructed from acentral Pb-Pb collision [52]to improve tracking resolution and to reduce fake tracks. The tracking eﬃciency isshown in Fig. 36 and the tracking pT resolution is shown in Fig. 37• Primary vertex reconstruction

Primary vertex is reconstructed from ITS+TPC tracks. In this thesis, the z coordinate
track andof the primary vertex reconstructed with ITS+TPC tracks is referred to as zvertex

hereafter ’primary vertex’ refers to the track vertex otherwise not specified. The
resolution of the primary vertex position in the transverse plane is of the order of 100µm as shown in Fig. 34.
• Background event removal

Out-of-bunch pileup events are rejected if the number of TPC clusters is too large incomparison with the number of primary tracks.

Section 2.2. The ALICE detector complex

39

Tracking Efficiency

TPC efficiency

this thesis

1
0.9
0.8
0.7

1.2
ALICE Pb-Pb sNN = 5.02 TeV
1

0.8

0.6

0.6

ALICE |η|<0.8 (MC)

0.5

PYTHIA (pp)0.4
Pb-Pb sNN=2.76 TeV, centrality 0-5%

0.3

0.4

10 - 30 %Pb-Pb sNN=2.76 TeV, centrality 80-90%

0.2

30 - 50 %pp s=8 TeV

0.1
0
0

HIJING (PbPb)
0 - 10 %50 - 90 %

0.2
2

4

6

8

10
p (GeV/c)

0

T

1

10

p track (GeV/c)
T,gen

)

<*
!*%+ !!"#$%&'(('

Figure 36: Left: Tracking eﬃciency with only TPC [49], Right: Tracking eﬃciency withITS+TPC [25].

,-,*2

OPL?Q
+<=>9( ; :: (8(1-,.()#$9(6 " 67,-4,-,*0)=?(;@ABCADEB#(@FA&G;)=?(@FA&G;(&EB;@FAHB#C(@E(I#F@#J,-,*.

)=?KL)M(&EN>HB#C(@FA&G;)=?KL)M(&EB;@FAHB#C(@E(I#F@#J

,-,*
,-,,4
,-,,2
,-,,0
,-,,.
,

,

,-*

,-.

,-/

,-0

,-1

,-2

,-3

,-4

,-5

*
<*

*%+) !!"#$%&'(('

Figure 37: Tracking pT resolution [49].

40

Chapter 2. Experimental apparatus

2.2.4

Electromagnetic Calorimeters (EMCal, DCal, PHOS)

ALICE has three electromagnetic calorimeters located inside the central barrel: EMCal(ElectroMagnetic Calorimeter), DCal (Di-jet Calorimeter) and PHOS (PHOton Spectrometer).

Figure 38: Electromagnetic calorimeters (EMCal, DCal and PHOS) [25].
EMCal and DCal are sampling calorimeters. Their main purpose is to measure highenergy photons, electrons, and jets.

The size of each cell, which consists of 77 lead-

scintillator layers, is (∆x, ∆y, ∆z) = (60 mm, 60 mm, 246 mm) and (∆φ, ∆η) = (0.0143, 0.0143).
An EMCal and DCal cell is called a ’tower’. 4 towers compose 1 ’module’. 12 modules compose 1 ’strip’ and 24 strips compose 1 ’Super Module’ (SM) as shown in Fig. 39 (left).
EMCal is composed of 10 + 2 × (1/3) SMs and DCal is composed of 6 × (2/3) + 2 × (1/3)

SMs. EMCal and DCal are made of 10 + 2 × (1/3) SMs and 6 × (2/3) + 2 × (1/3) SMs
respectively, corresponding to a total of 12,288 EMCal towers and 5,376 DCal towers. The

coverage of EMCal is 80◦ < φ < 187◦ , |η| < 0.7 while DCal covers 260◦ < φ < 327◦ ,|η| < 0.7.

Section 2.2. The ALICE detector complex

41

Figure 39: Components of EMCal, DCal (left) and PHOS (right).
PHOS is an homogeneous type of electromagnetic calorimeter. The main purpose of
PHOS is to measure the photons with high energy and position resolution. Each cell ismade of lead tungstate (PbWO4 ) with the size of (∆x, ∆y, ∆z) = (22 mm, 22 mm, 180 mm)
and (∆φ, ∆η) = (0.004, 0.004). Each PHOS cell is called ’crystal’. 3584 crystals compose 1
SM. PHOS consists of 3.5 SMs and covers 250◦ < φ < 320◦ , |η| < 0.13.

Chapter 3 describes the upgrade of the calorimeter trigger system for high-pT photon,

electron, and jet identification carried out during LHC Long-Shutdown 1 (LS1, 2013-2015)
and in the early period of LHC Run2 (2015).
2.2.5

Time-Of-Flight (TOF) detector

Multigap-Resistive Plate Chambers (MRPC) are used for the ALICE Time-Of-Flight (TOF)
detector. The main purpose of the TOF detector is to provide PID information. Fig. 40
shows the layout of a MRPC module.
The whole TOF detector is segmented into 1593 strips and each strip covers 120 ×

7.4 cm2 . The strips are mounted in 87 separate modules which are grouped into 18 sectors
covering 2π in azimuth. The coverage in pseudo-rapidity is |η| < 0.9. The gas mixture is√C2 H2 F4 : SF6 = 97% : 3%. In Pb-Pb collisions at sN N = 5.02 TeV, a time resolution of
56 ps was achieved as shown in Fig. 41.
In this study, the TOF detector is used to remove background events by the correlationof ITS+TPC and ITS+TPC+TOF tracks.

42

Chapter 2. Experimental apparatus

Figure 40: Cross-section of the MRPC strip for the ALICE TOF [53].

ALI-PERF-128066

Figure 41: Time resolution of the ALICE MRPC TOF [54].

Chapter 3

Development of the Level-1
trigger system for the ALICEElectroMagnetic Calorimeters

DCal (Sec. 2.2.4) was installed during the LHC Long Shutdown 1 (LS1: 2013-2015) toenhance the jet measurement capabilities of the ALICE detector. DCal, which enlarges
the acceptance opposite in azimuth of EMCal, allows di-jet measurements with fully reconstructed jets (neutral+charged constituents). This increases the acceptance by about 44%
and the di-jet energy resolution (the definition is given in Fig. 42) by 10% as shown in
Fig. 42.

Figure 42: Di-jet energy balance and di-jet energy resolution obtained from simulation. [55]Eﬃcient event triggering is essential for the measurement of rare probes, such as highpT jets, in order to use eﬀectively the limited bandwidth of the Data Acquisition (DAQ)
system. In this chapter, the development of the trigger system for the ALICE calorimeters(EMCal, DCal and PHOS) is described. The firmware development and commissioning
have been done in cooperation with H. Yokoyama [25].
4344

Chapter 3. Development of the Level-1
trigger system for the ALICE ElectroMagnetic Calorimeters

3.1

Overview of the trigger system

The detectors can be classified into ’trigger detectors’ which generate trigger signals and’readout detectors’ which collect the data. Some detectors belong to both categories.

Figure 43: Overview of ALICE trigger system layout
Fig. 43 shows an overview of the the trigger system layout which is steered by the’Central Trigger Processor’ (CTP). Trigger signals from individual detectors are processedby the CTP. There are 3 hardware trigger levels: Level-0 (L0), Level-1 (L1), and Level-2(L2) which gradually reduce event rates. L0 triggers are issued by trigger detectors which
are fast enough. L1 triggers are primarily issued by relatively slow detectors or after somedata processing to select any specific events using a longer latency than that of L0. Thus,
some detectors can contribute to both L0 and L1 triggers. The L0 and L1 latencies are 800
ns and 6.1 µs respectively. L2 triggers are mainly used for pileup event protection, mainly
coming from the long drift time of TPC and its latency is ∼100 µs. Fig. 44 shows a typicalexample of trigger sequence.

EMCal, DCal and PHOS can contribute to both to L0 and L1 triggers. In this thesis,
we focused on the development of the L1 trigger system, which aims at enriching data setswith high-pT photons, electrons, and jets.

!"#$%&'"($%&

012+3$!$
56+7*8)29$:;$<#

012+3$=$82>25329$
:;$<#

!$%

!$&

!#

!"

012+3$#$
4+56+7*8)29$:;$<!

012+3$=$56+7*8)29$
:;$<!

45

!"

!#

!"

!"

012+3$.$
4+56+7*8)29$:;$<!

012+3$!$56+7*8)29$:;$<!

Section 3.2. Trigger algorithm'"($%&$)*+,,$%&-!.#"/$%&,,$%&-!.#"/$%&

Figure 44: An example of trigger sequence [22].
Fig. 45 shows an overview of the trigger electronics configuration for EMCal, DCal, andPHOS. Fig. 46 shows the EMCal electronics chain. Raw signals from individual towers areread out by the Front-End Electronics (FEE), where the analog sum of 2 × 2 cells, called’FastOR’, is calculated. Signals from twelve (EMCal, DCal) or fourteen (PHOS) FEE are
sent to one ’Trigger Region Unit’ (TRU) where each FastOR is shaped and digitized. TRUs
process FastOR signals to provide the L0 decision.
The L0 and FastOR time sum (simply called ’FastOR’ hereafter) signals from all TRUs
are sent to the ’Summary Trigger Unit’ (STU). The TRUs are connected to the STU by
category 7 Ethernet cables and the signals are transmitted by Low Voltage Diﬀerential
Signaling (LVDS). TRU data word length is 12 bit. When taking data, one word of header(0xAAA) is sent at first in order to recognize that a new frame is being sent. The interpacket, which is a known word like ’0xC03’, is sent for synchronization while no data arebeing transferred. The typical serial data frame is shown in Fig. 48. STU calculates thecoincidence of L0 from TRUs and processes FastORs to provide the L1 decision. Finally,
all trigger signals are sent to CTP and FastOR signals are transmitted to DAQ. Theseelectronics mentioned above are operated based on the LHC clock of 40 MHz (corresponds
to 25 ns cycle).

3.2

Trigger algorithm

The L1 trigger calculation relies on a ’sliding window’ algorithm. The whole detector
acceptance is scanned by a ’patch’. A trigger is fired if the sum of the FastOR signals within

46

Chapter 3. Development of the Level-1
trigger system for the ALICE ElectroMagnetic Calorimeters!

Figure 45: Overview of the configuration of the trigger electronics for ALICE EMCal (top),
DCal (bottom left), and PHOS (bottom right)

Section 3.2. Trigger algorithm

Figure 46: Flow of the signals for the trigger processing

Figure 47: Top view of the Summary Trigger Unit (STU) board

47

*$'+$%

Chapter 3. Development of the Level-1
trigger system for the ALICE ElectroMagnetic Calorimeters*$'+$%

48!"#$%&'()$#&'()$#!"#$%&'()$#&'()$#!"#$%&'()$#

Figure 48: A typical serial data frame [22].

Figure 49: Trigger patches for L0 and L1 trigger. Each small square corresponds to one
FastOR region

Section 3.3. List of tasks carried out

49

a patch exceeds a given programmable threshold. Fig. 49 shows the diﬀerent trigger patch
types used for L1 calculation. The patch for the L1-γ trigger, which aims at triggering on
events containing a high-pT photon or electron, consists of 2 × 2 FastORs region. 4 × 4
FastORs compose one ’Subregion’ and the patch for the L1-Jet trigger, which aims at
triggering on high-pT jet events, consists of 2 × 2 or 4 × 4 subregions.

In heavy-ion collisions, the underlying event energy density is fluctuating considerably

event-by-event due to the large soft background, therefore the trigger threshold should
also vary on an event-by-event basis. In the trigger algorithm developed in this work,
the underlying event density is estimated on the opposite-side calorimeters in azimuth andsubtracted from each patch energy to deal with this event-by-event large fluctuations asfollows:
1.) Calculate the summed energy in each subregion.
2.) Find the median value among all subregions
3.) Exchange the calculated median value between opposite-side calorimeters in azimuth.
4.) Subtract the median value (estimated underlying event energy) from each L1 patch.
5.) Compare the resulting L1 patch amplitude to threshold.
The flowchart of the trigger processing in EMCal and DCal is shown in Fig. 50.
A STU firmware version using the energy measured by the PHOS calorimeter in combination with the DCal one has been developed. However, after some data analysis, it was
discontinued due to the large energy scale diﬀerence between DCal and PHOS. Therefore,
the underlying event energy estimate in heavy-ion collisions is performed without PHOS
for LHC Run 2.

3.3

List of tasks carried outa.) STU firmware upgrade– Adaptation to the new detector configuration (Fig. 51)
The calorimeter region readout by one TRU has been changed since the size of
the DCAL SM is 2/3 of the EMCal one. Besides, the firmware has been revised
to cope with the data flow related to the new detector mapping.
– Update of trigger algorithm in heavy ion collisions
The background subtraction algorithm has been upgraded as described in Sec. 3.2.
The results of its performance will be presented in the following section.

50

Chapter 3. Development of the Level-1
trigger system for the ALICE ElectroMagnetic Calorimeters

Figure 50: Flowchart of the STU L1-Jet trigger processing in heavy-ion collisions– Update of the Common Data Header (CDH) version of the readout data stream
All data from each detector includes a Common Data Header (CDH) at the
beginning of data payload. The CDH version has been updated to the newconvention adopted for LHC Run 2 by ALICE (Fig. 52).
– Upgrade of the error monitoring counter for TRU-STU communication
The old firmware for LHC Run 1 had a 16 bit error counter to detect communication errors between TRU-STU and STU-STU (Fig. 53). The old error
counter overflows every 25(ns) × 65535 ∼ 1.6 (ms). For the LHC Run 2, thenumber of bit length assigned to the error counter has been extended to 32
bits and a 32 bit trial counter, which counts the number of test packets (interpackets), has been implemented (Fig. 54). The new error counter overflows every 25(ns) × 4294967295 ∼ 107 (s). A precise data communication error rateestimation has been enabled by this upgrade.

The firmware has been written in Hardware Description Language (VHDL) and has
been developed based on the LHC Run1 version. The firmware is implemented as
R -5 FPGA device (the product of Xilinx, inc.), whicha digital circuit in the Virtex⃝

Section 3.3. List of tasks carried out

51

R Design Suite, which is the IDE (Integrated Deequips the STU board. The ISE⃝

velopment Environment) for the products of Xilinx inc., has been utilized for thedevelopment and compilation of the firmware, and for the simulation of the logic.
b.) Tests in laboratory
The firmware has been installed on a testbench at CERN. In order to validate thetrigger algorithm and output data.
c.) Commissioning tasks at LHC Point 2
The firmware has been developed in the real environment of LHC Point 2. Commissioning tasks have been performed before the start of the 2015 Pb-Pb run. The STU
routine operation through on-line Detector Control System (DCS) has been developed
during this commissioning phase.

Figure 51: Modification of readout region by one TRU. This picture shows an example for
one SM of EMCal.

52

Chapter 3. Development of the Level-1
trigger system for the ALICE ElectroMagnetic Calorimeters!

Figure 52: The old (left, [23]) and new (right, [24]) CDH.

– No precise communication error rate estimation possible

LHC clockInter-packet (TRU/STU are sending 3 word synchronization patterns continuously bw data)
c03

d0b

c93

c03

c93

d0b

c03

!!!"

c03

c93

d0b

c93

???

!!!"

???

???

???

!!!"

0xﬀﬀ

0x0

0x1

Error packet

Received data
c03

c93

???

c03

Communication isin error

Error counter(16 bit)
0x0

0x1

0x2

(rough schematic)

Figure 53: An example of the old error counter operation.

Section 3.4. Trigger performance

LHC clock• Enough time for DCS periodic read for monitoring

Inter packet & data

c03

53

Header data

c93

d0b

aaa

Data! """!

c03

???

d0b

aaa

0x2

0x3

0x4

c03

c93

d0b

c03

???

c03

c93

???

???

0xﬀﬀﬀﬀ

0x0"""!

Received datad0b

Data!"""!

Error

Trial counter(32 bit)

0x0

0x1

0x5

Error counter (32 bit)
0x0

0x1

0x6

!

Reset

0x2 ! 0xﬀﬀﬀfa

0x0

Trial flag
Error flag(rough schematic)

Figure 54: An example of the new error counter operation.

3.4

Trigger performance

In this section, the trigger system performance evaluated with the data recorded during
LHC Run2 is shown. Fig. 55 shows the correlation of the underlying event energy density
measured by EMCal and DCal. In this figure, a clear positive correlation has been observed
and the values are reasonably consistent. This result confirmas the correction of the underlying event energy density calculation made by EMCal and DCal and that the data exchange
between EMCal and DCal STUs have been performed correctly. Fig. 56 shows the rejection factor of the L1-jet trigger, which represents the capability to control event rates, For
example, a 20 GeV trigger threshold results in a ∼100-1000 of event rejection (event rate isdecreased by a factor ∼ 1/100 - 1/1000). Fig. 57 shows the rejection factor of L1-jet trigger

as a function of estimated underlying event density and trigger threshold. In this figure, it
is found that the L1-jet trigger gives stable rejection factor over a widened underlying event
energy density range, which correlates to centrality. This results implies that, in case where
the event-by-event underlying event subtraction is enabled, the kinematic cutoﬀ for jets by
the L1 trigger will be more stable for triggers wide centrality range than in the case without
event-by-event underlying event subtraction. Fig. 58 shows the L1-jet trigger turn-on curve,
which represents how rapidly the full selection eﬃciency is reached, in Pb-Pb collisions at√
sNN = 5.02 TeV as a function of the energy of the online jet trigger patch, where ’online’means that the energy was estimated based on the raw amplitudes from each cell without
oﬄine calibration. The turn-on curve is calculated as a ratio of the trigger patch energy
in an event triggered by both the L1-jet and MB over the one in the MB triggered event.

54

Chapter 3. Development of the Level-1
trigger system for the ALICE ElectroMagnetic Calorimeters

The turn-on curve shows a sharp rising and reasonably reaches plateau. Fig. 59 shows theenhancement from the EMCal L1-jet trigger for R = 0.2, 0.3, 0.4, and 0.5 full jets in pp√
collisions at s = 13 TeV and Fig. 60 shows the one of EMCal L1-gamma trigger for the
EMCal clusters, which corresponds to the energy deposit of a particle, in pPb collisions at√
sNN = 8.16 TeV. The EMCal L1-jet trigger enhances the full jet yields per trigger by afactor 2000-8000 and the EMCal L1-gamma enhances the high-energy cluster yields by afactor 200-800 for these datasets, in comparison with the yields in minimum-bias triggered
events. Fig. 61 shows the pT spectra of reconstructed PHOS clusters in central (0-5 %,√left) and peripheral (60-80 %, right) Pb-Pb collisions at s = 5.02 TeV with minimum-bias
and L1-gamma triggers. Both results show a sharp rising around the threshold. However,
the heights of plateaus, which gives the photon enhancement factor provided by the trigger
system, are diﬀerent between these two centrality intervals. The enhancement factor is ∼100 for central events and ∼2000-3000 for peripheral events. This should come from the factthat the background subtraction is not performed for PHOS L1-gamma trigger, resulting
in larger patch energies in central collisions.
As shown in Fig. 55-Fig. 61, the L1 trigger system shows reasonable behavior and it
gives good performance on the physics analysis. The new physics results utilizing the triggerρ (DCAL) (GeV)

data, which have been collected in 2015-2018, start to come out now (e.g. Ref. [56, 57]).

300
250

ALICE Pb-Pb sNN = 5.02 TeV
L1-Jet Trigger
LHC15o run245793

104

200

3

10

150
102

100
10

50
0
0

50

100

HIROKI YOKOYAMA

150

200

250

300

1

ρ (EMCAL) (GeV)

Figure 55: Correlation of underlying event energy density estimated by EMCal and DCal
STUs [25].

L1 Trigger Rejection

Section 3.4. Trigger performance

55

10
ALICE Pb-Pb sNN = 5.02 TeV
L1-Jet Trigger, 16× 16 patch

1

LHC15o run245793

10−1

EMCAL
DCAL

10−2
10−3
10−4
10−5
−10

0
HIROKI YOKOYAMA

10

20

30

40

50

Trigger Threshold (GeV)

Figure 56: Rejection factor of L1-jet triggers given by DCal and EMCAL [25]

56

Chapter 3. Development of the Level-1
trigger system for the ALICE ElectroMagnetic Calorimeters

hDCALRej
1

35
10!
30
25

10!

20

Threshold[GeV]

Threshold[GeV]hEMCALRej
40

40

1

35
10!
30
25

10!

20
!

10

15
10

!

10

15
10

10!
5
0
0

10!
5

!

50

100

150

HIROKI YOKOYAMA

200
250
300
Rho(DCAL)[GeV]

10

0
0

!

50

100

150

HIROKI YOKOYAMA

200
250
300
Rho(EMCAL)[GeV]

10

L1 Trigger Efficiency

Figure 57: Rejection factor of L1-jet triggers given by EMCal (left) and DCal (right) as afunction of underlying event energy density and threshold. x-axis is the estimated underlying event energy density and y-axis is the trigger threshold. z-axis is the rejection factor
and its variation is expressed as colors.

1.4
1.2

ALICE Pb-Pb sNN = 5.02 TeV
L1-Jet Trigger, 16× 16 patch
LHC15o run245793

1
0.8
0.6
0.4

EMCAL L1J Low
EMCAL L1J HighDCAL L1J Low
DCAL L1J High

0.2
0
−10

0
HIROKI YOKOYAMA

10

20

30

40

50

Jet Trigger Patch Energy (GeV)

Figure 58: L1-jet trigger turn-on curves given by DCal and EMCAL [25]Section 3.4. Trigger performance57

min bias

Figure 59: Enhancement of the EMCAL L1-jet trigger for full jets with various jet radii [26].

p-Pb, sNN = 8.16 TeV
103

EMCAL L1/

1 dN
N evt dE

clust

ALICE Preliminary

1 dN
N evt dE

clust

102

EMCal L1 Gamma trigger (threshold = 8 GeV) / min bias
EMCal L1 Gamma trigger (threshold = 5.5 GeV) / min bias

10

Fermi function fit (8-30 GeV), R trig = 816.9 ± 8.1
Fermi function fit (5.5-30 GeV), R trig = 259.7 ± 1.7

1
0

5

10

15

20

25

30

E (GeV)
ALI−PREL−153509

Figure 60: Enhancement of the EMCAL L1-gamma trigger as a function of reconstructed
EMCal cluster energy [26].

58

Chapter 3. Development of the Level-1
trigger system for the ALICE ElectroMagnetic Calorimeters

Figure 61: pT spectra of reconstructed PHOS clusters in minimum-bias (black) and L1gamma triggered events (red) are shown in the top panel. The ratio of these spectra isshown in the bottom panel [26].
Left: Central (0-5 %) Pb-Pb collisions
Right: peripheral (60-80 %) Pb-Pb collisions.

Chapter 4
4.1

Datasets and analysis methods

Data samples√
For the studies presented in this thesis, the datasets of pp collisions at s = 5.02 TeV√
and Pb-Pb collisions at sNN = 5.02 TeV collected by the ALICE experiment in 2015 wereanalyzed. Monte-Carlo (MC) full detector simulation data anchored to selected LHC periods
were also analyzed to assess the corresponding detector response. pp and Pb-Pb events weregenerated by PYTHIA6,8 [58],[59] and HIJING [60] MC event generators respectively. The
detector eﬀects were described with GEANT3-based detailed simulations [61].

4.2

Event selections

The analyzed events were collected with a Minimum-Bias (MB) trigger. During 2015 datataking, the MB trigger was defined by the coincidence between V0A and V0C detectors.
After MB trigger selection, several primary vertex quality cuts were applied:• A primary vertex is reconstructed with at least 1 (pp) or 2 (Pb-Pb) contributors fromSPD tracklets.

track | < 10(pp), 8(Pb-Pb) cm.
• |zvertex
track − z SPD | < 0.5(pp), 0.2(Pb-Pb) cm (see Sec. 2.2.2, 2.2.3).
• |zvertex
vertexSPD have to be better than 0.25 cm.
Here, the resolution on zvtx

In order to remove pile-up events, multi-vertex events reconstructed by SPD were rejected in pp collisions. For the Pb-Pb collisions, optional cuts mainly related to pile-up
rejection were additionally applied as follows:• Event selection with centrality correlation– ±5.55 σ cut of V0 centrality using the correlation between V0 and SPD estimatedcentralities.

• Event selection related to track multiplicity, e.g.
– ±4σ cut on the multiplicity correlation of tracks reconstructed from the primaryvertex + ITS + TPC + TOF hits and primary vertex + ITS + TPC tracks.
59

60

Chapter 4. Datasets and analysis methods– event rejection with large number of TPC clusters
After events selection, about 108 pp and about 5.5 × 107 Pb-Pb (0-80% centrality)

events remained. In this study, 30-50% centrality events in Pb-Pb collisions were analyzed
corresponding to about 1.4×107 events. The centrality was determined with the V0 detector
as shown in Fig. 11.

4.3

Charged particle tracking and selection

For this study, primary tracks are reconstructed with ITS+TPC detectors so-called ’global
tracks’. A Kalman filter tracking method has been developed to perform the global tracking
at ALICE [62]. The ALICE standard global track selection requires at least one hit in oneof the two SPD layers. However, due to large dead areas in SPD, the azimuthal distributionof reconstructed tracks is not uniform. The tracking uniformity is one of the key factors toreconstruct jets with high spatial and momentum resolution. Therefore, a dedicated track
selection, called ’hybrid track’ selection, has been developed for jet measurements. Hybrid
tracks are made up of two track classes:• Global tracks: fully reconstructed ITS+TPC tracks with at least one SPD hit andinward track refit [62] through the ITS.

• Complementary tracks: ITS+TPC tracks with no SPD hit. Instead, the reconstructed
tracks are constrained to the primary vertex and the track parameters are recalculated to improve the track spatial and momentum resolutions. The inward track refit
through the ITS is still required.
The azimuthal distributions of global and complementary tracks are shown in Fig. 62.
The hybrid track selection recovers track uniformity reasonably well.
The acceptance of tracks is 0 < φtrack < 2π, |ηtrack | < 0.9. A kinematic cut of 0.15 <pT,track < 100 GeV/c is applied to ensure good track pT resolution.

4.4

Jet reconstruction

Signal jets were reconstructed with the anti-kT clustering algorithm [63] implemented in
the FastJet software package [64]. Jets are reconstructed with jet resolution parameters
R = 0.2, 0.3, 0.4, and 0.6 for pp collisions and R = 0.2 for Pb-Pb collisions. To evaluate
event-by-event background pT density for jets in Pb-Pb collisions, jet reconstruction withthe kT clustering algorithm is also performed with the resolution parameter of R = 0.4. The
inputs to jet finding algorithms are all tracks passing the hybrid track selection. The pseudorapidity of reconstructed jet is restricted by a fiducial cut to |ηjet | < 0.9 − R. Consequently,

Section 4.5. Measurement of charged jets in pp collisions

61

This thesis

Figure 62: The azimuthal distribution of global tracks (Red: w/ SPD hits), complementary√
tracks (Blue: w/o SPD hits) and hybrid tracks (Black) in pp collisions at s = 5.02 TeV
jets are contained within the fully eﬃcient acceptance of the TPC, thus avoiding unexpectededge eﬀects. Jet reconstruction ingredients are summarized in Table 3.
Table 3: Reconstruction conditions of jets
FastJet version
Reconstruction algorithm
InputsCone radii R
Pseudo-rapidity
pT recombination scheme
Ghost area units for jet are determination
Jet area cut

v3.1.3anti-kT (Signal), kT (Background for Pb-Pb)
charged tracks (w/ hybrid track selection)
0.2, 0.4 (for pp and for Background of Pb-Pb )0.3, 0.6 (for pp)|ηjet | < 0.9−R
pT -scheme
0.005
Areajet > 0.6πR2 (for Pb-Pb)

4.5

Measurement of charged jets in pp collisions

4.5.1

Underlying event estimation in pp collisions

Jets come from hard processes but reconstructed jets include contributions from soft processes even in pp collisions. These soft contributions are classified as Underlying Event(UE). Experimentally, it is diﬃcult to distinguish if low-pT jets come from hard or soft

62

Chapter 4. Datasets and analysis methods

processes. The same underlying event definition both for experimental data analysis andtheoretical calculations must be used to make a fair comparison. In this analysis, the perpendicular cone method is chosen as the UE estimator [11]. The sum of track pT in a cone
perpendicular to the leading jet axis is divided by jet area to obtain the jet background pT
density ρ on an event-by-event basis:
n
5
cone
2
ρ=
pperp.
Ti ,track /πR

(32)

i=0

cone
where R are the jet cone radius of signal jets and pperp.
is the transverse momenta of
Ti ,track

tracks within a cone perpendicular to the leading jet axis. The background pT is subtracted
jet-by-jet as follows
praw
T,jet − ρ · Ajet

(33)

where Ajet is the jet area. In this thesis, results obtained both with and without UE
subtraction are shown.
4.5.2

Raw jet spectra

Fig. 63 and Fig. 64 shows the inclusive raw jet spectra without and with UE subtraction
respectively. These raw spectra are distorted (folded) by detector eﬀects such as ineﬃciency
and finite resolution. They must be unfolded from these eﬀects to make comparison withthe theoretical predictions. With the data sample used in the present analysis, a statisticalreach up to pch
T,jet = 100 GeV/c is achieved. Jets are measured down to very low transverse
momenta similarly to the study presented in Ref. [65]. The pT binning is chosen so thatthe number of entries exceeds ten entries per bin for all cone radii in order to ensure stable
unfolding results.
4.5.3

Detector eﬀect correction by unfolding

In order to correct the measured jet pT spectra from detector eﬀects, an unfolding method
based on the Singular Value Decomposition (SVD) approach [66] is employed within the’RooUnfold’ software package [67],[68]. The basic concept of raw jet spectra spectra unfolding is explained hereafter.
The relation between the true spectrum Tt and the measured spectrum Mm can be expressed as:
Mm = Rdet
m,t · Tt

(34)

where the detector ’response matrix’ (RM), Rdet
m,t , represents the distortion of the observable
by a detector response. The subscripts m, t are the bin number indices. If Rdet
m,t is known,
the true spectrum can be estimated as the product of the inverse matrix of Rdet
m,t andSection 4.5. Measurement of charged jets in pp collisions

63

This thesis

dN/dp

T

109
108
pp s = 5.02 TeV

107
106

Min. bias

105

anti-k T , R = 0.3, |η | < 0.6
jet

104
103
102
10
1
−1

10

0

10

20

30

40

50

60

70

80
p

T,jet

109

T

dN/dp

dN/dp

T

109

90 100(GeV/ c )

108

108

107

pp s = 5.02 TeV

107

pp s = 5.02 TeV

106

Min. bias

106Min. bias

105

anti-k T , R = 0.4, |η | < 0.5105

anti-k T , R = 0.6, |η | < 0.3

jet

jet

104

104

103

103

102

102

10

10

1

1

−1

−1

10

0

10

20

30

40

50

60

70

80
p

T,jet

90 100(GeV/ c )

10

0

10

20

30

40

50

60

70

80
p

T,jet

90 100(GeV/ c )Figure 63: Charged jet raw pT spectra reconstructed with R =0.2,0.3,0.4, and 0.6 in pp√
collisions at s = 5.02 TeV without UE subtraction

64

Chapter 4. Datasets and analysis methods

This thesis

dN/dp

T

109
108
pp s = 5.02 TeV

107

Min. bias

106

anti-k T , R = 0.3, |η | < 0.6

105

UE subtracted

jet

104
103
102
10
1
−1

10

0

20

40

60

80
100
p corr UE (GeV/ c )
T,jet

109

T

dN/dp

dN/dp

T

109
108
pp s = 5.02 TeV

107

108
pp s = 5.02 TeV

107

Min. bias

Min. bias

106

anti-k T , R = 0.4, |η | < 0.5

106anti-k T , R = 0.6, |η | < 0.3

105

UE subtracted

105

UE subtracted

jet

jet

104

104

103

103

102

102

10

10

1

1

−1

−1

10

0

20

40

60

80
100
p corr UE (GeV/ c )
T,jet

10

0

20

40

60

80
100
p corr UE (GeV/ c )T,jetFigure 64: Charged jet raw pT spectra reconstructed with R =0.2,0.3,0.4, and 0.6 in pp√
collisions at s = 5.02 TeV with UE subtraction

Section 4.5. Measurement of charged jets in pp collisions

65

Mm . In this study, the detector responses were evaluated by GEANT3-based full detector
simulations.

This thesis

Figure 65: Left: Detector response matrix for R = 0.4 anti-kT clusters reconstructed withcharged tracks. Right: Probability distribution of the relative momentum diﬀerence of√
simulated ALICE detector response to charged jets in pp collisions at s = 5.02 TeV for
four diﬀerent pT intervals. Charged jets are simulated using PYTHIA8 Monash-2013 andreconstructed with the anti-kT jet finding algorithm with R = 0.4.

4.5.4

Validation of the unfolding

The following tests were performed to check the validity of the unfolding solution:• Split the available MC statistics into two exclusive sub-samples.

One group is used to construct the response matrix and the other group is used to
extract the jet spectrum folded by the detector eﬀects. Fig. 66 shows the ratio of
the unfolded spectrum over the true spectrum (left) and the ratio of the re-folded
spectrum over the detector level spectrum (right). Both ratios are consistent withunity within a few percent.

• Comparison of diﬀerent event generators

The dependence of the unfolded spectrum on event generators is tested. The detector
response is evaluated with PYTHIA8+GEANT3 MC dataset while the detector leveljet spectrum is extracted from PYTHIA6+GEANT3. Fig. 67 shows the ratio of theunfolded spectrum over the true spectrum (left) and the ratio of the re-folded spectrum

66

Chapter 4. Datasets and analysis methods

over the detector level spectrum (right). The ratios are consistent with unity within a
few percent except in the low pT range (pT < 20GeV/c). For the PYTHIA8+GEANT3
production, a lower limit on the hard scattering kinematic range is required to enhance
the statistics of high-pT jets (pT,hard > 5GeV/c ). This results in the bias observed inFig. 67 (left) at low-pT .
The results of these two tests validated the unfolding procedure. In this study, thedetector response extracted from a MB MC production is used to correct the jet spectra
at low pT (pT < 20 GeV/c) to avoid the above mentioned bias due to event generation. A
high-pT jet enhanced MC production is used to correct jet spectra in pT region with good
statistical precision (pT > 20 GeV/c).

Refolded / Measured

This thesis

χ2 / ndf 12.71 / 13p0
1 ± 0.0

1.3

1.2

1.1

1

0.9

0.8

0.7
0

10

20

30

40

p

50

T,jet

60

(GeV/c)Figure 66: MC closure test results: the statistics in the PYTHIA8+GEANT3 production
is divided into two sub-samples. One is used to build the response matrix and the otherone is used to obtain the input spectrum.

4.5.5

Inclusive jet cross section

The inelastic double-diﬀerential jet cross section is defined as:
d2 σjet
Njet
1
=
·
(35)
dpT dη
Lint ∆pT ∆ηwhere Njet is the number of jets in each pT bin of width ∆pT and ∆η is the pseudorapidity
evt ε
evt
interval. The integrated luminosity Lint = Ntrig
vtx /σV0 . Here, Ntrig is the number oftriggered events after vertex selection (see Sec. 4.2). σV0 is the measured visible inelastic
cross section, which is the product of the true inelastic cross section and the MB trigger
eﬃciency by the V0 detector, evaluated by Van der Meer (VdM) scan. The measured√
visible inelastic pp cross section at s = 5.02 TeV is σV0 = 51.2 mb [69]. The number ofSection 4.5. Measurement of charged jets in pp collisions

67

This thesis

Refolded / Measured

Ratio of Measured and Refoldedχ2 / ndf

1.2

p0

1.626 / 13
0.9991 ± 0.0060

1.15
1.1

1.05
1
0.95
0.9
0.85
0.8
0

5

10

15

20

25

30

35

40

45

p

50
T,jet

Figure 67: MC closure test results: we performed the closure test with diﬀerent generators.
In this figure, PYTHIA8+GEANT3 MC production is used to extract the response matrix
and PYTHIA6+GEANT3 MC production is used to extract input spectrum.
triggered event in Eq. 35 has to be corrected for the vertex selection eﬃciency εvtx which
imposes that all events including a jet in the acceptance must have a reconstructed vertex.
The eﬃciency is evaluated before the vertex position cut (|zvertex | < 10 cm) is applied,
assuming a negligible vertex position dependence. In this study, 1/εvtx ∼ 1.024 is used forthe correction.

68

Chapter 4. Datasets and analysis methods

4.6

Measurement of charged jets in Pb-Pb collisions

4.6.1

Measurement of the event plane

Experimentally, the nth -order event plane angle ψnmeas is determined event-by-event fromthe measured particle azimuthal distribution as follows:
5
Qn,x =
wi cos (nφi )

(36)

i

Qn,y =

5

wi sin (nφi )

(37)

,

(38)

i

1
ψnmeas = tan−1
n

Qn,y
Qn,x

-

where Qn,x , Qn,y are the event flow vectors, wi is a weight, and φi is the azimuthal angle ofmeasured particle i. In the V0-based EP determination used in this analysis, V0C detector
segments are used instead of measured particles. The weight wi and azimuthal angle φi in
Eq. 36, 37, 38 refer to the charge output of the V0 PMT and azimuthal angle of segment i
respectively.
Since the relative positions of the two colliding nuclei are random, the azimuthal distribution of the event plane should be flat. However, in reality, the azimuthal distribution of
the measured event planes is usually not constant related to some unphysical eﬀects due toexperimental apparatus, such as non-uniform PMT gains, oﬀset of the beam position, andnon-uniform acceptance. Calibrations were applied on the measured event plane to correct
for such unphysical eﬀects. The PMT gains were calibrated so that all PMTs have thesame ADC mean value. Qn,x , Qn,y distributions were re-centered and ψnmeas distribution
is flattened [70]. Fig. 68 shows the correlation of event plane measured by V0A and V0C
detectors before and after the correction. The distortion of the correlation observed before
correction is fixed by the correction process.
The analytical expression of the event plane resolution is formulated in Ref. [70], [27]as:.
, 2, 2 -/√# meas
$1(
π
χn
χn
true
−χ2n /4
cos kn ψn− ψn= √ χn eI(k−1)/2+ I(k+1)/2
(39)
4
4
2 2
√
where Ik is the modified Bessel function. The parameter χn is expressed as χn = vn 2N'0where N is the number of particles used to measure the event plane.
The analytical expression of the distribution of the measured event plane angle w.r.t
the true event plane is given in Ref. [71] as:7√dN
1 −χ2n /2 6
z2
=
e
1
+
z
π[1
+
erf(z)]ed [kn (ψnmeas − ψntrue )]π# meas$true
where z = χn cos kn ψn− ψn
and erf(z) is the error function.

(40)

Section 4.6. Measurement of charged jets in Pb-Pb collisions

69

2

2

event plane (V0C(ψ ))This thesis
1.5
1
0.5
0
− 0.5
−1
− 1.5
−2
−2

−1.5

−1

−0.5

0

0.5

1
1.5
2
event plane (V0A(ψ ))2Figure 68: V0A and V0C event plane correlation before (Left) and after (Right) correction√in Pb-Pb collisions at sNN = 5.02 TeVExperimentally, the correlation of event planes measured with detectors A and B iscalculated as:'# 0 meas1$( '# 0 meas1
0 meas1$(
meas
cos n ψn,A
− ψn,B= cos n ψn,A
− ψntrue − n ψn,B
− ψntrue'# 0 meas1$( '# 0 meas1$((41)= cos n ψn,A
− ψntruecos n ψn,B
− ψntrue
8 meas 9
8 meas 9= Res ψn,A · Res ψn,B:;
meas
where Res ψn,A,B
is the resolution of the nth -order event plane measured with the detector
A,B. In symmetric collision systems, Res {ψn,A } will equal Res {ψn,B } if detector A and B

cover a symmetric acceptance and have similar average multiplicity. Thus, the event plane
resolution is given by:
8 meas 9
8 meas 9
Res ψn,A= Res ψn,B
=

<=

) 6
7*>
meas − ψ meas
cos n ψn,A
.
n,B

(42)

In ALICE, most of the forward/backward detectors have asymmetric acceptance on
rapidity. In this case, the event plane resolution can be evaluated with 3 detectors whichhave exclusive rapidity coverages. This method is called ’3-sub method’. The correlationsof event plane among detectors A, B and C are expressed as:⟨cos (n [ψn,A − ψn,B ])⟩ = Res {ψn,A } · Res {ψn,B }(43)⟨cos (n [ψn,B − ψn,C ])⟩ = Res {ψn,B } · Res {ψn,C }(44)⟨cos (n [ψn,C − ψn,A ])⟩ = Res {ψn,C } · Res {ψn,A } .

(45)

Chapter 4. Datasets and analysis methods

2[1+z π{1+Erf(z)}ez ]

70

1.2

χ=1.1
χ=1.0
χ=0.9
χ=0.8
χ=0.7
χ=0.6
χ=0.5
χ=0.4
χ=0.3
χ=0.2
χ=0.1
χ=0.0

z = χ cos2(Ψobs-Ψreal)
1

0.8

1
πe

-χ 2 /2

This thesis

0.6

0.4

0.2

0
-1.5

-1

-0.5

0

0.5
1
1.5
obs
obs
real
)-(φ-Ψ )=Ψ -Ψ [rad]

real

(φ-Ψ

Figure 69: Left: Parameter χn in the mathematical expression of event plane resolution for
V0C. Right: Probability distribution of ψ2meas − ψ2true . The figure is taken from Ref. [27]Combining Eq. 43, 44, 45, the EP resolution measured with the detector A is given by:?
⟨cos (n [ψn,A − ψn,B ])⟩ ⟨cos (n [ψn,C − ψn,A ])⟩Res {ψn,A } =(46)⟨cos (n [ψn,B − ψn,C ])⟩In the measurement presented in this work, the event plane resolution of V0C is evaluated with the 3-sub method by utilizing the event plane correlations among V0A, V0C and
TPC.
Fig. 69 (Left) shows the evaluated parameter χn of Eq. 39. Fig. 70 shows the estimated
2nd -order event plane resolution for V0C. The 2nd order event plane resolution measured
by V0C is about 70% for mid-central Pb-Pb collisions (30-50%).
4.6.2

Underlying event estimation in Pb-Pb collisions

Controlling the systematic uncertainties of the large underlying event (UE) estimation is
one of the key elements of jet measurements in heavy-ion collisions. In this measurement,
the average UE pT density ρavg is estimated on an event-by-event basis as follows:
2 k @
pTT,i
ρavg = median
AkT,i

(47)

k

where pTT,i is the transverse momentum and AkT,i is the area of the cluster i reconstructedwith the kT -clustering algorithm.
In non-central heavy-ion collisions, the average UE pT density will show large modulations w.r.t event plane because of the anisotropic particle production ascribed to flow
eﬀects. Therefore, in this measurement, the local UE density w.r.t 2nd and 3rd order event

Section 4.6. Measurement of charged jets in Pb-Pb collisions

71

This thesis

Figure 70: V0C 2nd order event plane resolution estimated with 3-sub detector method(V0C-V0A-TPC)

plane is calculated on an event-by-event basis by fitting the azimuthal distribution of low
momentum tracks (pT < 5 GeV/c). The local UE estimate ρ(φ) is obtained by fitting thefirst three terms of the Fourier decomposition:):;*
ρ(φ) = ρ0 1 + 2 v2obs cos(2[φ − ψ2 ]) + v3obs cos(3[φ − ψ3 ]).

(48)

Fig. 71 shows an example of fitting result to the track distribution in an event.
Using ρ(φ), the jet-by-jet local UE density ρlocal is calculated as follows:
" φ+R
ρavg
local
ρ
=
ρ(φ)dφ(49)
2Rρo φ−R
The estimated local UE is subtracted jet-by-jet in a similar way as Eq. 33. This local

UE estimation method was firstly proposed for the measurement of azimuthal anisotropy√of charged jet production in sNN = 2.76 TeV Pb-Pb collisions [16].
4.6.3

Charged jet yield with respect to event plane

Fig. 72 shows the measured raw jet pT spectra w.r.t the 2nd -order V0C event plane withaverage UE subtraction (left) and with local UE subtraction (right).
The low-pT region dominated by UE becomes reasonably uniform w.r.t the ψ2 plane
after local UE subtraction. The detector level jet spectra are divided into two classes w.r.t
ψ2 as shown in Fig. 73.
The measured jet spectra are unfolded by the SVD approach in a similar way to the jet
spectra in pp collisions (Sec. 4.5.3). In heavy-ion collisions, the large UE fluctuations are
not negligible and have to be corrected for in the unfolding procedure. Thus, the relation
between the true spectrum Tt and the measured spectrum Mm is expressed as:
det
Mm = Rbkg+det· Tt = Rbkg
m,tm,d · Rd,t · Tt

(50)

Chapter 4. Datasets and analysis methods

ρ(φ) (GeV/c )72

50

This thesis

fHBestFit_2

Centrality: 42.5%

45

V 2 = -0.199429 ± 0.041452

V 3 = -0.111498 ± 0.043570

40
35
30
25
20
15
10

0.15 < pT,track< 5 GeV/ c , |ηtrack

| < 0.9ρ(φ)
50ρ (1+2V cos(2[ φ-Ψ
0

0
0

ρ

1

2

2

]))

ρ (1+2V cos(3[ φ-Ψ

2,V0C

0

3

3

4

]))

3,V0C

5

6

ϕ (rad)Figure 71: A event fitting result to the track distribution with Eq. 48 in mid-central Pb-Pb√
collisions at sNN = 5.02 TeV.

200

150

10

6

10

5

10

4

10

3

10

2

p

T,jet

(GeV/c )This thesis

100

50

0
10

−50

−1

0

1

2

3

1

4

∆φ(Jet-Ψ)

2,V0C

Figure 72: The raw jet pT spectra w.r.t the 2nd order V0C event plane in 30-50% centrality√
Pb-Pb collisions at sNN = 5.02 TeV.
Left: average UE subtracted,
Right: local UE subtracted.

Section 4.6. Measurement of charged jets in Pb-Pb collisions

73

Ψ2

in

out

out

in

Figure 73: Definition of in-plane and out-of-plane directions in this jet v2jet measurement.
where Rbkg
m,d is the response matrix of the UE fluctuations.
In this study, the UE fluctuations were estimated by the Random Cone (RC) method [72]
as:

δpT =

RC
5
i

where

4RC
i

local
ptrackπR2T,i − ρ(51)

ptrackT,i is the sum of track pT within a RC and R is the jet resolution parameter.

In this study, one RC is thrown per event is thrown.
The jet yield w.r.t event plane is expressed as:
∞
5
dN
∝1+
2vnjet cos [n (ϕjet − ψn )] .
d (ϕjet − ψn )

(52)

n=1

Using the in-plane and out-of-plane directions defined in the Fig. 73, the jet yields
in-plane and out-of-plane w.r.t event plane can be written as:
" π
" 5π
4
4
dN
dN
meas
Nin =
d
(ϕ
−
ψ
)
+
d (ϕjet − ψnmeas )
jet
n
meas
meas )−π d (ϕjet − ψ
3π
)
d
(ϕ
−
ψ
jet
n
n
4
4
(53)
" 3π
" 7π
4
4
dN
dN
meas
meas
Nout =d (ϕjet − ψn ) +d (ϕjet − ψn )π
5π
d (ϕjet − ψnmeas )d (ϕjet − ψnmeas )44Chapter 4. Datasets and analysis methods

This thesis

Probability

74

10− 1

3π /8 < |∆ φ(φ -Ψ 2 )| < 4 π /8, σ = 2.06
RC

2π /8 < |∆ φ(φ -Ψ 2 )| < 3π /8, σ = 2.21RC

π /8 < |∆ φ(φ -Ψ 2 )| < 2π /8, σ = 2.39

10− 2

RC

0 < |∆ φ(φ -Ψ 2 )| <RC

π /8, σ = 2.47

−3

10

10− 4

10− 5

10− 6

− 20

− 10

0

10

20

30

40

50

60

δp (GeV/c )T

Figure 74: The δpT distribution estimated with the RC method in 30-50% centrality Pb-Pb√
collisions at sNN = 5.02 TeV.
Left: the 2-dimensional δpT distribution w.r.t 2nd -order V0C event plane,
Right: projections of the 2-dimensional δpT distribution w.r.t 2nd -order V0C event planein several intervals of the angle between event plane and RC axis.
Considering only the 2nd -order Fourier coeﬃcient, the integrals can be evaluated as:)*
Nin = a π + 4v2jet, obs)*(54)
Nout = a π − 4v2jet, obs

where Nin , Nout are the jet yields in each pT bin, and a is a normalization constant.
Using Eq. 54, the jet elliptic azimuthal anisotropy, v2jet , is calculated as:1
π Nin − Noutv2jet =.
Res {ψ2meas } 4 Nin + Nout

(55)

Using Eq. 55, the v2jet in mid-central (30-50%) Pb-Pb collisions is measured as a functionof unfolded jet pT spectra.
4.6.4

Charged jet-hadron correlations with respect to event plane

The two-dimensional yield of associated tracks is measured to assess jet-like correlationsin Pb-Pb collisions, for the purpose of studying jet suppression and medium response injet-like events. The correlation function C(∆ϕ, ∆η) is given by the ratio of the jet-track
pairs distribution within the same event over the one in a mixed event:pair , 2Nmix
d Nsame d2 Nmix
C(∆ϕ, ∆η) = pair/Nsame d∆ηd∆ϕ d∆ηd∆ϕ

(56)

pair
pair
where Nsame, Nmixare the total number of pairs of trigger-jet and associated tracks in thesame and in a mixed event. Nsame , Nmix are the associated jet-track pairs per bin in theSection 4.6. Measurement of charged jets in Pb-Pb collisions

75

same and in a mixed event. ∆ϕ = ϕassoc − ϕtrig , ∆η = η assoc − η trig where ϕtrig , ϕassoc

are the azimuthal angles of the trigger jet and the associated track and η trig , η assoc are
the pseudo-rapidities of the trigger jet and the associated track respectively. In this study,
in order to construct a mixed event distribution, trigger and associates were taken from
diﬀerent events and therefore uncorrelated. Therefore, any structure to the correlationsin the mixed event is due to detector eﬀect instead of physics. The correlation functions
are normalized to have an average value of one. In reality, the same-event distribution issmeared due to the limited detector acceptance. The mixed-event distribution of associatedtracks yields should equal the product of single jet and track probabilities since pairs oftriggered-jet and track in mixed events have no physical correlation but is again aﬀectedby the limited detector acceptance. Therefore, the physical correlation can be extracted bytaking the ratio of the same- and mixed-event trigger-associate track distributions as shownin Eq. 56.

+,-./(.
01"2'.
"!345 # ##$%&'$()&*+,+-.&+*$

!*#
!)#
!(#
!'#
!&# !"!%#!$#!"#+,-./(.
01"2'.
"!345! # #Figure 75: Classification of trigger jet events w.r.t V0C event plane. ∆φ = φjet − ψ2,V0C
In this measurement, jets with pT,jet > 20 GeV/c after local UE subtraction were selected as triggers. In order to avoid the trivial autocorrelation among the jet axis and thejet constituent tracks, jet axis is recalculated by using the constituent tracks which has
pT,track > 4 GeV/c. The recalculated axis is determined as the center of transverse momenta of constituent tracks. In this study, two associated tracks pT ranges were selected:

76

Chapter 4. Datasets and analysis methods

0.7 < passoc< 2 GeV/c and 2 < passoc< 4 GeV/c.
T
T
The near-side (|∆ϕ| < 0.8, |∆η| < 0.8) jet-hadron correlations are studied by dividing

the sample into 8 classes according to the trigger jet azimuthal angle w.r.t 2nd -order event
plane (ψ2 ) as shown in Fig. 75. In this study, |φjet − ψ2 | < π4 is defined as ’in-plane’,π
3π|φjet − ψ2 | > 3π
8 is defined as ’out-of-plane’ and 4 < |φjet − ψ2 | < 8 is defined as ’mid-plane’.

Fig. 76, 77 show the measured near-side jet-hadron correlation functions for 0.7 <passoc< 2 GeV/c and 2 < passoc< 4 GeV/c respectively.
TT

In the correlation plots, thenear-side jet peak can be seen on top of the background distribution, that dominantly
comes from flow eﬀects associated with the event plane. The flow background distribution
must be subtracted from the correlation functions in Fig. 76, 77 to isolate the correlations
from hard components. In this study, the flow background distributions were determinedat 1 < |∆η| < 1.5 of the correlation functions which is called the ’side-band’ region. For
the 1-dimensional correlation function in azimuth, C(∆ϕ), projection of side-band distri-bution is scaled by the ratio of integration intervals. The scaled side-band distribution
is subtracted from the near-side distribution bin-by-bin. In this study, the scale factor is(Near-side integration interval)/(Side-band integration interval) = (0.8×2)/(0.5×2) = 1.6.
For the 1-dimensional correlation function in eta, C(∆η), flat background is assumed andonly the background level is estimated by constant fitting to the side-band region after
the scaling. Fig. 78, 79, 80, 81 shows the one-dimensional near-side peak distributions before background subtraction, the background distributions and the background subtracted
distributions.
The shape, peak position w.r.t jet axis, and width of the background subtracted nearside jet peak correlation functions are discussed in this thesis.

Section 4.6. Measurement of charged jets in Pb-Pb collisions

77

Figure 76: Near-side jet-hadron correlation functions w.r.t V0C event plane for ptrigger
T,jet >
20 GeV/c, 0.7 < passoc<
2
GeV/c.
T

78

Chapter 4. Datasets and analysis methods

Figure 77: Near-side jet-hadron correlation functions w.r.t V0C event plane for ptrigger
T,jet >
20 GeV/c, 2 < passoc<
4
GeV/c.
TSection 4.6. Measurement of charged jets in Pb-Pb collisions

79

This thesis

Figure 78: Near-side correlation functions as a function of ∆φ. Flow background unsubtracted distribution (Red), background distribution estimated in the side-band regions(Blue) and background subtracted distribution (Green). The unit of Y-axis is a.u.
assoc < 2 GeV/c. The characters on top of each panel ((a)-(h))
ptriggerT,jet > 20 GeV/c, 0.7 < pT
correspond to trigger jet event classes given in Fig. 75

80

Chapter 4. Datasets and analysis methods

This thesis

Figure 79: Near-side correlation functions as a function of ∆η. Flow background unsubtracted distribution (Red), background distribution estimated in the side-band regions(Blue) and background corrected distribution (Green) are shown. The fitting results withLorentzian function to the background corrected distributions are shown as black lines. The
unit of Y-axis is a.u.
assoc < 2 GeV/c. The characters on top of each panel ((a)-(h))
ptriggerT,jet > 20 GeV/c, 0.7 < pT
correspond to trigger jet event classes given in Fig. 75

Section 4.6. Measurement of charged jets in Pb-Pb collisions

81

This thesis

Figure 80: Near-side correlation functions as a function of ∆φ. Flow background unsubtracted distribution (Red), background distribution estimated in the side-band regions(Blue) and background subtracted distribution (Green). The fitting results with Lorentzianfunction to the background corrected distributions are shown as black lines. The unit of
Y-axis is a.u.
assoc < 4 GeV/c. The characters on top of each panel ((a)-(h))
ptriggerT,jet > 20 GeV/c, 2 < pT
correspond to trigger jet event classes given in Fig. 75

82

Chapter 4. Datasets and analysis methods

This thesis

Figure 81: Near-side correlation functions as a function of ∆η. Flow background unsubtracted distribution (Red), background distribution estimated in the side-band regions(Blue) and background corrected distribution (Green) are shown. The unit of Y-axis is a.u.
assoc < 4 GeV/c. The characters on top of each panel ((a)-(h))
ptriggerT,jet > 20 GeV/c, 2 < pT
correspond to trigger jet event classes given in Fig. 75

Chapter 5
5.1

Systematic uncertainties

Systematics for charged jet production cross section in pp collisions

The systematic uncertainties from the following sources are considered:• Tracking eﬃciency• Tracking resolution• Contribution from secondary particles• Underlying event subtraction• Unfolding– Choice of method– Choice of regularization parameter– Choice of event generator• Cross section normalization
Systematics: Tracking eﬃciency and track momentum resolution
The measured jet spectra are corrected for tracking eﬃciency and momentum resolution
by unfolding. A fast simulation is performed to propagate the uncertainty on the single
track eﬃciency to the jet spectrum measurement. ’True’ information of the charged finalstate particles is extracted from PYTHIA events, and the particles are reduced according
to a tracking eﬃciency parameterized as function of particle pT (Fig. 82) derived fromthe full MC simulation. The track pT is smeared with a parameterized pT resolution ofσ(1/pT ) = 0.002 (GeV/c)−1 . The fast simulation reproduces reasonably well the tracking
eﬃciency obtained from the full simulation as shown in Fig. 83.
The systematic uncertainty on tracking eﬃciency due to hybrid track cuts used in thisanalysis is studied through cut variations. The cut parameters are consistently varied
within the data and the full detector simulation, and the impact on the track spectra ofthese variations are monitored. The matching eﬃciency between ITS and TPC is estimatedby turning on and oﬀ the matching requirement for both the data and the full detector
simulation, and the impact on the track spectra of the requirement is monitored. The
83

84

Chapter 5. Systematic uncertainties

Figure 82: Parameterized tracking eﬃciency from full detector simulation

This thesis

Figure 83: Comparison of tracking eﬃciencies from ALICE full simulation and fast simulation

Section 5.1. Systematics for charged jet production cross section in pp collisions

85

combined uncertainty on single tracking eﬃciency due to the cut variations and the ITSTPC matching eﬃciency is estimated to be 3% as a total. The uncertainty on momentum
resolution is studied by comparing the tracking resolution obtained in MC and Data. A
10% uncertainty, the maximum deviation between MC and Data is assigned as Systematics
on the tracking resolution for the fast-simulation study.
The systematic uncertainty from the tracking eﬃciency uncertainty for diﬀerent jet radiiis shown in Fig. 84. It increases with jet pT and reaches a value of to about 10% at thehighest jet pT analyzed. The systematic uncertainty from pT resolution uncertainty is of
the order of 1-2%, as shown in Fig. 85.
This thesis

1/Nev dN /dp [GeV/c]-1

10
10

6

Matrix (PYTHIA6: Perugia2011)
Norminal Trk. Eff
Trk. Eff + 3%
Trk. Eff - 3%

5

T

104
3

jet

10

102
10
1

SVD unfolding: k = 8, R = 0.4

1.2

Ratio

1.1
1

0.9
0.8
10

20

30

40

50

60

p [GeV/c]

70

80

90

100

T

Figure 84: Systematic uncertainty from tracking eﬃciency uncertainty of ±3% for jet cone
R = 0.2 (left), R = 0.4 (right)

Systematics: Contribution from secondary particles
Secondary particles are predominantly produced by weak decays of strange particles (e.g.
Ks0 and Λ), photon conversions or hadronic interactions in the detector material, and decaysof charged pions. Conversion and hadronic interaction products are not part of the jet
fragmentation. Neutral strange particles stem from fragmentation, but are not relevant for
our analysis of charged particle fragmentation. Their decay products are considered as acontamination for our measurement.
Although in order to select primary particles preferentially the track cuts are applied on
the Distance of Closest Approach (DCA) to the primary vertex, the measurements should be

86

Chapter 5. Systematic uncertainties

This thesis

1/Nev dN /dp [GeV/c]-1

10
10

6

pp: s = 5.02 TeVMatrix (PYTHIA6: Perugia2011)
Norminal
Trk. Res. + 10%
Trk. Res. - 10%

5

T

104
3

jet

10

102
10
1

SVD unfolding: k = 8, R = 0.4

1.2

Ratio

1.1
1

0.9
0.8
20

40

60

p [GeV/c]

80

100

T

Figure 85: Systematic uncertainty from tracking resolution uncertainty for jet cone R = 0.2(left), R = 0.4 (right)
corrected for a small residual contamination from secondary particles. Secondary particles
contribute both to the measured jet energy and jet spectra. In the MC simulations, only
physical primaries are used for jet reconstruction. The jet energy scale is therefore corrected
implicitly by the unfolding procedure.
We estimated the uncertainty from the contribution from secondary particles to matcha jet transverse momentum scale uncertainty of 0.5%, using the same value as given in the
LHC Run1 pp charged jet analysis published by ALICE [73]. To propagate this uncertainty
to the measured cross section, a fit is performed with function made of double modified
Tsallis functions:f (x) = (p2 + p3 · x)(1 + x/(p0 · p1 )−p1 + (p6 + p7 · x)(1 + x/(p4 · p5 )−p5(57)

where p0 -p7 are free parameters and x correspons to jet pT . The result of this fit is shownin Fig. 86, for R=0.2 (left) and R=0.4 (right). The ratio of the data to the fit is presented
in Fig. ?? For both values of R, the fit function gives a good description of the spectra.
To evaluate the impact of the energy scale uncertainty on the jet cross section, thearguments of the fit function are shifted by ±0.5% and use the observed variation of thespectrum is used as systematic error. The original and shifted fit functions are shown in
Fig. 88. The resulting systematic uncertainty is about 2%, with a modest increase as a

Section 5.1. Systematics for charged jet production cross section in pp collisions

87

10− 1

R=0.4
Data

T

d2σ/dp dη (mb c /GeV)This thesis

10− 2

Fit

10− 3

10− 4

10− 5

10− 6

10

20

30

40

50

60

70

80
p

T,jet

(a) Raw jet spectrum and fit R=0.2

90 100(GeV/ c )(b) Raw jet spectrum and fit R=0.4

Figure 86: Raw jet spectra fitted with a sum of two Tsallis functions.

function of jet pT , as shown in Fig. 89.
Systematics: underlying event subtraction
The systematics associated with the measurement of the underlying event (UE) is estimatedto account for 5%, as quoted in Ref. [11]. To propagate this uncertainty to the measured jet
cross section, a double-Tsallis fit (see Eq. 57) is performed. The UE subtraction is modeled
as a jet pT shift of the spectrum. The estimated raw underlying event pT density as functionof leading jet pT is shown in Fig. 90.
The UE ’unsubtracted’ (raw) and ’subtracted’ (shifted) fit functions are shown alongwith the measured spectra in Fig. 91. The ratio of both functions is shown in Fig. 92,
and compared with the ratio of the measured spectra. The eﬀect of the UE subtraction
increases with decreasing jet pT . The exact magnitude of the shift is adjusted via a constant’fudge factor’ tuned to reproduce the data spectral ratio well, and indeed, this results show agood agreement between fit+shifted result and measured result. The systematic uncertainty
is evaluated by changing the spectral shift of the fitted function by the underlying event
uncertainty of ± 5%. The resulting variation of the jet cross section is 1-1.5% at low pT ,and decrease with increasing jet pT . For example, the systematic uncertainties from UE
subtraction for R=0.2 and 0.4 jets are shown in Fig. 93.

88

Chapter 5. Systematic uncertainties

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Figure 87: Ratio of spectra to fit

d σ/dp dη (mb c /GeV)This thesis

R=0.4

10− 1

2

T

Data
Fit
Shifted +0.5%
Shifted -0.5%

10− 2

10− 3

10− 4

10− 5
10

20

30

40

50
60
p (GeV/c)T,jet(a) Secondary:Shifted and unshifted fit spectrum R=0.2(b) Secondary:Shifted and unshifted fit spectrum R=0.4

Figure 88: Shifted and unshifted fit spectrum assuming secondary contribution

Section 5.1. Systematics for charged jet production cross section in pp collisions

89

shifted/nominal
shifted/nominal
1

ratio

1.1

This thesis

ratio

1.1

h1
Entries
Mean
RMS

1.08

1.08

0
0
0

R=0.4

1.06

R=0.2

1.06

0.8

Shifted +0.5%

1.02

1.02
0.4

1

1
0.2

0.98

0.98
0
0

10

20

Shifted -0.5%

1.04

Shifted -0.5%

1.04

0.6

Shifted +0.5%

30 0.96
40

50

60

70

80

90

0.96

100

0.94

0.94

0.92

0.92

0.9
0

10

20

30

40

50

60

70

80
p

T,jet

90 100(GeV/c)0.90(a) Secondary:Systematic uncertainty R=0.2

10

20

30

40

50

60

70

80
p

T,jet

90 100(GeV/c)(b) Secondary:Systematic uncertainty R=0.4

Figure 89: Systematic uncertainty from secondary contribution to jet spectra

Systematics: Unfolding
Choice of method
As a cross-check and validation of the unfolding method, we compared our results by SVD
unfolding with the results obtained with the iterative Bayes method implemented in RooUnfold. The iterative Bayes unfolding is regularized by choosing a number of iterations forunfolding procedure. The ratio of spectra unfolded with the iterative Bayes method for
diﬀerent choices of the regularization parameter to the default (SVD) is shown in Fig. 94.
Since the diﬀerent methods are applied to the same raw input spectra, and hence numerator
and denominator of the ratio are strongly correlated, we used binomial errors for statistical uncertainties. Within uncertainties, the solutions from both unfolding methods are inexcellent agreement. To smoothen the statistical fluctuations in the determination of thesystematic error, we fitted bin-by-bin the absolute deviation from 0 and used a linear fir
function, resulting in an uncertainty of a few percent.
Choice of regularization parameter
The SVD unfolding is regularized by a choice of an integer valued parameter which separates
statistically significant and non significant singular values of the orthogonalized response

90

Chapter 5. Systematic uncertainties

This thesis

Figure 90: The average of underlying event pT density estimated by the perpendicular coneas a function of leading jet pT .

Section 5.1. Systematics for charged jet production cross section in pp collisions

91

UE subtracted spectrum
d2σ/dp dη (mb c /GeV)This thesis

R=0.4

10

UE subtracted (Fit + Shifted)
UE subtracted (Fit + Shifted(+5%))T

UE subtracted (Fit + Shifted(-5%))
Fit (Raw)
UE subtracted (Data)

1

10− 1

10− 2

0

2

4

6

8

10

12

14

16
p

T,jet

(a) UE:Shifted and unshifted fit spectrum R=0.2

18
20(GeV/c)(b) UE:Shifted and unshifted fit spectrum R=0.4

Figure 91: Shifted and unshifted fit spectra assuming uncertainty on UE measurement

UE subtracted/unsubtracted (R=0.4)
ratioThis thesis

1.1
R=0.4
Fit + Shifted

1.05

Fit + Shifted(+5%)
Fit + Shifted(-5%)
Data

1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6

10

20

30

40

50

60

70

80
p

T,jet

(a) UE:Ratio of shifted to unshifted spectrum R=0.2

90 100(GeV/c)(b) UE:Ratio of shifted to unshifted spectrum R=0.4

Figure 92: Ratio of shifted to unshifted fit spectra

92

Chapter 5. Systematic uncertainties

Uncertainty from the UE subtraction (R=0.4)
This thesis

1.015

1.01

1.005

1

0.995

0.99

0.985
10

(a) UE:Systematic uncertainty R=0.2

20

30

40

50

60

70

80

90

100

(b) UE:Systematic uncertainty R=0.4

Figure 93: Systematic uncertainty in the jet cross section from Underlying event subtraction

Absolute Deviation from SVD (%)

Uncertainty: choice of unfolding method (SVD or Bayes), R = 0.4
This thesis

40
35
30
25
20
15
10
5
0

10

20

30

40

50

60

70

80

p

jet 90T,gen

100(GeV/c)(a) Unfolding: Uncertainty from choice of unfolding method(b) Unfolding: Uncertainty from choice of unfolding method
R=0.2
R=0.4

Figure 94: Systematic uncertainty from the choice of unfolding method. The lines in the
figure represent fit results with linear function and the values at the bin centers are assigned
as the bin-by-bin systematic uncertainties.

Section 5.1. Systematics for charged jet production cross section in pp collisions

93

varied/nominal - 1

This thesis
0.015
k =8
k =9
k =10 (nominal)
k =11
k =12
1σ
Fit (1σ )

0.01

0.005

0

− 0.005− 0.01− 0.015

6

8

10

12

14

16

18

p

T,jet

20

(GeV/c)(a) Unfolding: Diﬀerence from nominal regularization pa-(b) Unfolding: Diﬀerence from nominal regularization parameter (R=0.2)
rameter (R=0.4)

Figure 95: Systematic uncertainty from the choice of regularization parameter k by varying
nominal ±2 in the pT range of 5-20 (GeV/c)matrix. The choice is made by looking at the behavior of the so-called ’d-vector’ [74, 66],
which is not unambiguous. To estimate the related systematic uncertainties, we varied theregularization parameter by ± 2. The resulting variations are shown in Fig. 95 and Fig. 96
jet
for 5< pjet
> 20 GeV/c respectively. The diﬀerences are of the order
T <20 GeV/c and pTof 1-2%.
Choice of event generator
In this section we discuss the uncertainties related to the choice of the MC event generator
used for calculating the detector response matrix. Compared to a bin-by-bin correction, theunfolding should have a small generator dependence. However, diﬀerences in the simulated
jet spectra and jet fragmentation between diﬀerent event generators can induce diﬀerencesin the jet response matrix and on the prior used for the unfolding (in RooUnfold, thetraining sample is used to derive the prior).
Our method to estimate this uncertainty is based on a fast simulation, as describedin 5.1. We simulated PYTHIA events, extracted the charged final-state particles, applied particle-by-particle a parameterized tracking eﬃciency and pT resolution and used
the FastJet anti-kT algorithm to cluster both the original ’particle level’ tracks and the’reconstructed level’ tracks to obtain the detector response matrix. To estimate the uncertainty, we used diﬀerent PYTHIA tunes. We unfolded the measured spectrum with the
response matrix for each tune/generator, and used the ratio to the nominal PYTHIA tune
to estimate the uncertainty. The resulting uncertainties are the order of 5-10% at maximum,
as shown in Fig. 97.

94

Chapter 5. Systematic uncertainties

varied/nominal - 1

This thesis

0.1
R=0.4
iter=8
iter=9iter=10 (nominal)
iter=11
iter=121σFit (1σ )

0.08
0.06
0.04
0.02
0
− 0.02− 0.04− 0.06− 0.08
− 0.1
20

30

40

50

60

70

80

90

p

T,jet

100

(GeV/c)(a) Unfolding: Diﬀerence from nominal regularization pa-(b) Unfolding: Diﬀerence from nominal regularization parameter R=0.2
rameter R=0.4

Figure 96: Systematic uncertainty from the choice of regularization parameter k by varying
nominal ±2 in the pT range of 20-100 (GeV/c)

This thesis

1.4

pp: s = 5.02 TeV, R = 0.4
PYTHIA6: Perugia0

1.3

HERWIG

1.2

Ratio

1.1
1
0.9
0.8
0.7
0.6
10

20

30

40

50

60

p [GeV/c]T

Figure 97: Systematic uncertainty from the choice of event generator for jet cone R = 0.2(left) and R = 0.4 (right), showing the ratio to nominal PYTHIA8 Monash 2013 tune.

Section 5.2. Systematics for charged jet v2 in Pb-Pb collisions

95

Systematics: Cross section normalization√
The visible inelastic pp cross section at s = 5.02 TeV, measured by VdM scans at ALICE,is:σV0 = 51.2 ± 1.2 mb (syst.)
corresponding to a normalization systematic uncertainty of 2.3%.
Summary of systematics
The systematics of charged jet diﬀerential production cross section is summarized in Table 4. The quadratic sum of uncertainties from individual systematic uncertainty sources
are assigned as total systematic uncertainty.
Jet resolution
parameter
R = 0.2

R = 0.3

R = 0.4

R = 0.6

Jet pT bin(GeV/c)
5−6
20−25
40−50
85−100
5−6
20−25
40−50
85−100
5−6
20−25
40−50
85−100
5−6
20−25
40−50
85−100Track
eﬃciency
(%)
1
2.6
5.2
10
1.5
4.1
6.2
8.4
0.9
3.7
5.4
7.5
3.4
5.7
6.8
8.3

Track
pT resolution
(%)
negl.
negl.
negl.
negl.
0.1
0.1
0.1
0.1
1.9
1.9
1.9
1.9
1
1
1
1

Unfolding NormalizationSecondaries
(%)
(%)
(%)
1.4
2.3
3.8
7.8
2.9
3.4
4.3
7.0
1.9
1.8
2.5
4.5
2.1
1.7
2.2
4.0

2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3

2.4
2.2
2.5
2.6
2.2
2.3
2.6
2.7
2.1
2.4
2.5
2.8
1.9
2.6
2.6
2.7

Total
(%)
3.7
4.7
7.3
13.1
4.6
6.3
8.3
11.5
4.2
5.6
7.2
9.6
5.1
6.9
8
9.9

Table 4: Summary of the systematic uncertainties in jet cross section for R=0.2-0.6 and invarious of jet transverse momentum ranges.

5.2

Systematics for charged jet v2 in Pb-Pb collisions

In this measurement, the systematic uncertainties from the following sources are considered
as in Ref. [16]:• Shape uncertainties:– Unfolding– Jet pch
T -measured

96

Chapter 5. Systematic uncertainties– ρch (ϕ) fit• Correlated uncertainties:– Tracking– Jet pch
T -unfolded
Since the same ALICE detector and analysis method are used for the jet v2jet measure√ment in Pb-Pb collisions at sNN = 2.76 TeV [16], the relative uncertainties are taken fromthis previous study.

5.3

Systematics for charged jet-hadron correlation in Pb-Pb collisions

In this measurement, the systematic uncertainties from the following sources are considered:• Method of flow background shape estimation• Jet pT correction for UE• Event classification for event mixing.
• Peak shape estimator
Systematics: Method of flow background shape estimation
The underlying background distribution in the correlation function, which is dominated byflow eﬀect, is estimated by a side-band method for this study. As a systematic study, thefollowing methods are tested:• Narrower side-band subtraction :Basically, same as the nominal side-band subtraction method but the background
distribution is estimated in a narrower η range (1.1 < |η| < 1.3)

• Fitting at side-band region :Fitting is performed on background-dominated distributions in the nominal side-band
region (1 < |η| < 1.5). The fit range is restricted to |∆φ| < π/2 to avoid contributions
from the away-side peak. Fit results are subtracted from the raw distribution insteadof side-band distributions directly. The following function is tested for this systematic
study (see Fig. 98):Af (x) = B 1 +5n2vnt vna cos(x − a)where B, v, a are free parameters and n = 2-4.

B

(58)

Section 5.3. Systematics for charged jet-hadron correlation in Pb-Pb collisions

97• Flow MC simulation :The flow BackGround (BG) distribution is estimated with a Monte-Calro (MC) method
based on the measured v2 , v3 of inclusive hadron and jet, as well as two particle correlation studies done by the PHENIX Collaboration [75]. The background levels between
the data and MC distributions are adjusted based on the Zero-Yield-At-Minimum(ZYAM) assumption. The minimum point of the data distribution is estimated in theside-band region (1 < |η| < 1.5).

The discrepancy between these results and the nominal side-band method is calculated
and the RMS assigned as the systematic uncertainty. Fig. 99 shows an example of flow
MC simulation results compared to the nominal side-band distribution. The flow background shape estimation is the major source of systematic uncertainties of this jet-hadroncorrelation measurement.
Systematics: Jet pT correction for UE
Local underlying pT is subtracted from jet pT but the background fluctuation eﬀect inplane and out-of-plane still have to be considered. To assess the eﬀect from trigger jet
pT determination, all observables are calculated with uniform background pT subtraction
method (median of kT cluster is used as uniform background density estimator) as a test of
extreme case and the discrepancy from nominal result is assigned as systematic uncertainty.
Systematics: Event classification for event mixing
For the acceptance correction with event mixing, the events are divided into 10% centrality
intervals and 2 cm zvertex intervals as a nominal selection. As a systematic study of event
mixing, 5% centrality and 1 cm zvertex intervals are tested. The RMS of discrepancies fromnominal result is assigned as systematic uncertainty.
Systematics: Peak shape estimator
A fit is performed to extract quantities of peak shape. Fig. 99 shows an example of peakfitting with Gaussian. A Lorentzian function, which is also known as the ’Cauchy distribution’, gives a better description of the Near-side peak shape than a Gaussian function(see Fig. 80). So, the Lorentzian function is employed as nominal peak shape estimator.
The Lorentzian function has 3 parameters: the location parameter (peak position), thepeak height and the FWHM. The FWHM parameter, which express the ’width’, cannot bedirectly compared with σ of a Gaussian. However, only the ratio of width between in-planeand out-of-plane is the focus of in this study. The ratio will be comparable and, in fact, theboth results with Gaussian and Lorentzian function fits are comparable within statistical

98

Chapter 5. Systematic uncertainties

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Figure 98: An example of flow shape fit in the side-band region for pT,jet > 20 GeV/c,
2 < passoc
T,track < 4GeV/c. The characters attached to top of each panels are defined in Fig. 75.
The y-axis is expressed in arbitrary unit.

Section 5.3. Systematics for charged jet-hadron correlation in Pb-Pb collisions

99

This thesis

Figure 99: An example of flow shape MC simulation and peak fitting with Gaussian for
pT,jet > 20 GeV/c, 2 < passoc
T,track < 4GeV/c. The characters attached to top of each panels
are defined in Fig. 75. The y-axis is expressed in arbitrary arbitrary unit.

100

Chapter 5. Systematic uncertainties

errors. Here, the discrepancy between the peak shapes estimated from the two fit functions
are considered as systematics for peak shape (peak position, width ratio) extraction.
Summary of systematics
The calculated systematic uncertainties for correlation functions are summarized in Tab. 512. The quadratic sum of uncertainties from individual systematic uncertainty sources are
assigned as total systematic uncertainty.
∆ϕFlow BG (%)
Event mixing (%)
UE estimation (%)
Total uncertainty (%)(-0.7, -0.6)
72
6
18
74

(-0.3, -0.2)
13
5
10
17

(0.1, 0.2)
92
2
9(0.5, 0.6)
62
8
37
73

Table 5: Systematic uncertainties of in-plane correlation function in various ∆ϕ bins.
pT,jet > 20(GeV/c), passoc=0.7-2(GeV/c).
T∆ϕFlow BG (%)
Event mixing (%)
UE estimation (%)
Total uncertainty (%)(-0.7, -0.6)
21
10
28
36

(-0.3, -0.2)
753
9(0.1, 0.2)
2
1
3
4

(0.5, 0.6)
15
12
7
20

Table 6: Systematic uncertainties of out-of-plane correlation function in various ∆ϕ bins.
pT,jet > 20(GeV/c), passoc=0.7-2(GeV/c).
T∆ϕFlow BG (%)
Event mixing (%)
UE estimation (%)
Total uncertainty (%)(-0.7, -0.6)
78
6
6
78

(-0.3, -0.2)
22
3
4(0.1, 0.2)21
12

(0.5, 0.6)
35
55
37
75

Table 7: Systematic uncertainties of in-plane correlation function in various ∆ϕ bins.
pT,jet > 20(GeV/c), passoc=2-4(GeV/c).
TSection 5.3. Systematics for charged jet-hadron correlation in Pb-Pb collisions∆ϕ
Flow BG (%)
Event mixing (%)
UE estimation (%)
Total uncertainty (%)(-0.7, -0.6)
35
22
1
41

(-0.3, -0.2)
42
5
7(0.1, 0.2)
4
1
2
5

101

(0.5, 0.6)
22
40
25
52

Table 8: Systematic uncertainties of out-of-plane correlation function in various ∆ϕ bins.
pT,jet > 20(GeV/c), passoc=2-4(GeV/c).
T∆η
Event mixing (%)
UE estimation (%)
Total uncertainty (%)(-0.7, -0.6)
104
11(-0.3, -0.2)
46
7(0.1, 0.2)2
1
2

(0.5, 0.6)
95
10

Table 9: Systematic uncertainties of in-plane correlation function in various ∆η bins.
pT,jet > 20(GeV/c), passoc=0.7-2(GeV/c).
T∆η
Event mixing (%)
UE estimation (%)
Total uncertainty (%)(-0.7, -0.6)
17
13
21

(-0.3, -0.2)
31
3(0.1, 0.2)
11
1

(0.5, 0.6)
7
1
7

Table 10: Systematic uncertainties of out-of-plane correlation function in various ∆η bins.
pT,jet > 20(GeV/c), passoc=0.7-2(GeV/c).
T∆η
Event mixing (%)
UE estimation (%)
Total uncertainty (%)(-0.7, -0.6)
99
13(-0.3, -0.2)
14
4(0.1, 0.2)
11
1

(0.5, 0.6)
8
5
9

Table 11: Systematic uncertainties of in-plane correlation function in various ∆η bins.
pT,jet > 20(GeV/c), passoc=2-4(GeV/c).
T∆η
Event mixing (%)
UE estimation (%)
Total uncertainty (%)(-0.7, -0.6)
28
24
37

(-0.3, -0.2)
11
1(0.1, 0.2)
12
2

(0.5, 0.6)
13
3
13

Table 12: Systematic uncertainties of out-of-plane correlation function in various ∆η bins.
pT,jet > 20(GeV/c), passoc=2-4(GeV/c).
TChapter 6
6.1

Results and Discussions

Charged jets in pp collisions

In this section, the experimental results of charged jet inclusive production cross section√
measurement in pp collisions at s = 5.02 TeV are shown. The results are compared withmodel predictions based on LO and NLO pQCD calculations.
6.1.1

Charged jet inclusive diﬀerential cross section

The inclusive charged jet production cross sections in pp collisions are shown in Fig. 100
and Fig. 101. Jets are reconstructed using the anti-kT algorithm and the cross sections are
obtained for jet resolution parameters R = 0.2, 0.3, 0.4, and 0.6. The pseudorapidity range
is limited to |ηjet | < 0.9−R. The underlying event is not subtracted for the results presented
in Fig. 100 while it is in Fig. 101. The measured kinematic region is 5 < pch
T,jet < 100 GeV/cand spans from 5 × 10−7 to 2 × 10−1 mb (GeV/c)−1 following a power law.

The measured charged jet production cross sections are compared with several pQCD

predictions. PYTHIA is a Monte Carlo (MC) event generator based on the pQCD calculation of 2 → 2 Leading-Order (LO) parton-level hard scattering processes. PYTHIA

also includes parton shower and hadronization into final-state particles based on the Lund
model [76]. The results are compared with PYTHIA6 and PYTHIA8 for several tunes toaccount for non perturbative eﬀects. The PYTHIA6 Perugia 2011 tune [77] is based on the√
pp results from LHC at s = 0.9 and 7 TeV. The PYTHIA8 Monash 2013 tune [78] is based√on the pp results at s = 8 and 13 TeV. The PYTHIA8 A14 [79] and the CUETP8M1 [80]tunes are derived from the Monash 2013 tune which were extracted from the underlying
event measurements performed by ATLAS and CMS Collaborations. The PYTHIA6 tunes
used in this study employ the CTEQ5L [81] Parton Distribution Function (PDF) and the
PYTHIA8 tunes utilize the NNPDF2.3 LO PDF [82].
The POWHEG-BOX framework [83, 84, 85, 86] provides Next-to-Leading-Order (NLO)
pQCD calculations of 2 → 2 and 2 → 3 parton interactions at O(αs3 ). POWHEG provides
only a calculation of initial parton interactions. Therefore, some shower MC is added tosimulate the entire event evolution and obtain the final-state information. In this study,
the outgoing partons generated by POWHEG are used as input of PYTHIA8 with A14
tune to simulate the parton shower and the hadronization. The CT14nlo PDF set [87] isutilized for the calculation of initial parton interactions by POWHEG. The default values
103

104

Chapter 6. Results and Discussionsof the renormalization scale µR and factorization scale µF at which the born-level matrix
elements are evaluated are chosen to be µR = µF = pT .
Fig. 102, 103 show the comparison between the data and PYTHIA predictions. Fig. 104,
105 show the comparison between the data and POWHEG+PYTHIA8 predictions. The
underlying event is evaluated with the perpendicular cone method and subtracted fromboth the data and MC results are shown in Fig. 103 and Fig. 105. The ratios of the MC
predictions to the measured results are shown in bottom panels.
PYTHIA6 Perugia 2011 tune and PYTHIA8 Monash 2018 tune show the maximal(about 25%) diﬀerence between data and MC. Predictions from the UE tunes, A14 and
CUETP8M1, show better agreement. PYTHIA8 gives a better description of the overall
spectra shape than PYTHIA6. At LO accuracy, the measurements are only qualitatively
described by the theoretical predictions which failed to reproduce the jet spectrum over theentire measured transverse momentum range.
POWHEG+PYTHIA8, NLO pQCD-based predictions, give good agreement at the
10% level over a widened kinematic phase space (from pT > 10 GeV/c). However, thePOWHEG+PYTHIA8 predictions disagree with the data at low transverse momenta though
the theoretical uncertainties are large. In general, non-perturbative processes, such as MultiParton Interaction (MPI) and Fragmentation, play a role in this low transverse momentum
region (pT < 10 GeV/c). Next-to-Next-to-Leading Order (NNLO) calculations [88] are lesssensitive to scale factors (µR , µF ), which is the source of the largest systematic uncertainties for the current NLO calculation. None of current models can precisely describe theUE [89]. So that further studies of the UE are also crucial to understand the jet crosssection behavior in the low transverse momentum region.

Section 6.1. Charged jets in pp collisions

105

This thesis√
Figure 100: Charged jet diﬀerential cross sections in pp collisions at s = 5.02 TeV. Statistical uncertainties are smaller than the marker size. UE is not subtracted. The systematic
uncertainties are shown as shaded bands around the data points. Data are scaled by diﬀerent factors to enhance visibility.

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This thesis

Figure 101: Charged jet diﬀerential cross sections with UE subtraction in pp collisions at√
s = 5.02 TeV. Statistical uncertainties are smaller than the marker size. The systematic
uncertainties are shown as shaded bands around the data points. Data are scaled by diﬀerent
factors to enhance visibility.

Section 6.1. Charged jets in pp collisions

107

d2σ/dp dη (mb c /GeV)This thesis

1

1

10−1

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Anti-k T R = 0.4

2−3|ηtrack| < 0.9jet|η | < 0.3

10−4
10

−5

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p track> 0.15 GeV/ c
T

3

T

10

pp s = 5.02 TeV|ηjet | < 0.5

4

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Anti-k T R = 0.6

5

PYTHIA8 Monash 2013
PYTHIA8 A14 NNPDF2.3LO
PYTHIA8 CUETP8M1 NNPDF2.3LO

6

PYTHIA6 Perugia 2011

1.5

1.5

1

1
10

102

jet
p ch
(GeV/ c )
T

10

102

jet
p ch
(GeV/ c )T

Figure 102: Comparison of the charged jet cross section to LO pQCD MC predictions
with diﬀerent jet resolution parameters R = 0.2, 0.3, 0.4, and 0.6. UE is not subtracted.
Statistical uncertainties are displayed as vertical error bars. The systematic uncertainty
on the data is indicated by a shaded band drawn around unity. The red lines in the ratio
correspond to unity.

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Chapter 6. Results and Discussions

d2σ/dp dη (mb c /GeV)This thesis

1

1

10−1

10−2

1

Anti-k T R = 0.4

2−3|ηtrack| < 0.9jet|η | < 0.3

10−4
10

−5

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−6

MC / DATA

p track> 0.15 GeV/ c
T

3

T

10

pp s = 5.02 TeV|ηjet | < 0.5

4

ALICE

Anti-k T R = 0.6

5

PYTHIA8 Monash 2013
PYTHIA8 A14 NNPDF2.3LO
PYTHIA8 CUETP8M1 NNPDF2.3LO

6

UE subtracted

PYTHIA6 Perugia 2011

1.5

1.5

1

1
10

102

jet
p ch
(GeV/ c )
T

10

102

jet
p ch
(GeV/ c )T

Figure 103: Comparison of the charged jet cross section to LO pQCD MC predictions. UE
subtraction is applied. Statistical uncertainties are displayed as vertical error bars. The
systematic uncertainty on the data is indicated by a shaded band drawn around unity. The
red lines in the ratio correspond to unity.

Section 6.1. Charged jets in pp collisions

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d2σ/dp dη (mb c /GeV)This thesis

1

1

PYTHIA Tune: A14 NNPDF2.3LO

−3

10

−6

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3

T

10

−5

p track> 0.15 GeV/ cT2|ηjet | < 0.5

10−4 Anti-k T R = 0.4

MC / DATA

1POWHEG + PYTHIA8

10−2
10

pp s = 5.02 TeV

ALICE

10−1

jet

|η | < 0.3
4Anti-k T R = 0.6

5

POWHEG systematics
PDF uncertainty

6

Scale uncertainty

1.5

1.5

1

1
10

102

jet
p ch
(GeV/ c )
T

10

102

jet
p ch
(GeV/ c )T

Figure 104: Comparison of the charged jet cross section to NLO pQCD MC predictions(POWHEG+PYTHIA8). UE is not subtracted. Statistical uncertainties are displayed asvertical error bars. The systematic uncertainty on the data is indicated by a shaded band
drawn around unity. The red lines in the ratio correspond to unity.

110

Chapter 6. Results and Discussions

d2σ/dp dη (mb c /GeV)This thesis

1

1

PYTHIA Tune: A14 NNPDF2.3LO

−3

10

−6

|ηtrack| < 0.9

3

T

10

−5

p track> 0.15 GeV/ cT2|ηjet | < 0.5

10−4 Anti-k T R = 0.4

MC / DATA

1POWHEG + PYTHIA8

10−2
10

pp s = 5.02 TeV

ALICE

10−1

jet

|η | < 0.3
4Anti-k T R = 0.6

5

POWHEG systematics
PDF uncertainty

6

UE subtracted

Scale uncertainty

1.5

1.5

1

1
10

102

jet
p ch
(GeV/ c )
T

10

102

jet
p ch
(GeV/ c )T

Figure 105: Comparison of the charged jet cross section to NLO pQCD MC prediction(POWHEG+PYTHIA8). UE subtraction is applied. Statistical uncertainties are displayed
as vertical error bars. The systematic uncertainty on the data is indicated by a shadedband drawn around unity. The red lines in the ratio correspond to unity.

Section 6.1. Charged jets in pp collisions

6.1.2

111

Charged jet cross section ratio

The charged jet production cross section ratios R = 0.2 to R = 0.4 and 0.6 for |ηjet | < 0.3
are shown in Fig. 106. Statistical correlations are eliminated by dividing all data sample
into two exclusive sub-samples, each of the two samples used respectively for estimating
the numerator and denominator of the cross section ratio. The ratios are sensitive tothe jet radial profiles and provide insights into the interplay between perturbative andnon-perturbative eﬀects. The departure of the ratios from unity, due to QCD radiations,decreases with the increasing jet collimation in the high transverse momentum range. The
measurements are compared with PYTHIA and POWHEG+PYTHIA8 calculations. Bothmodels provide a good description of the ratio within a 10% accuracy. This result suggests
the significance of parton shower on this observable besides higher-order matrix element
calculations.
The results are compared with those obtained with diﬀerent collision energies and different collision systems. Fig. 107 (left) shows a comparison with the result in pp collisions√
at s = 7 TeV and Fig. 107 (right) shows a comparison with the result in p-Pb collisions√
at sNN = 5.02 TeV. No significant diﬀerence is observed that may suggest the absence ofcollision energy dependence or cold-nuclear matter eﬀects on jet radial profiles.

112

Chapter 6. Results and Discussions

This thesis

Figure 106: Charged jet cross section ratios for σ(R = 0.2)/σ(R = 0.4) (Red) andσ(R = 0.2)/σ(R = 0.6)(Blue) in comparison with LO (PYTHIA) and NLO event generators with matched parton showers and modelling of hadronization and the underlying
event (POWHEG+PYTHIA8). UE is not subtracted. The systematic uncertainty of thecross section ratio is indicated by a shaded band drawn around data points. No uncertainties
are drawn for theoretical predictions for better visibility in upper panel.

Section 6.1. Charged jets in pp collisions

113

Cross section ratio

This thesis

ALICE
jet
Anti-k T, |η |<0.3
p track > 0.15 GeV/ c1

σ(R = 0.2)/ σ(R = 0.6)

T

0.8

0.6

0.4

pp s = 5.02 TeV
UE subtracted

0.2

0

10

20

30

40

pp s = 7 TeV
50

60

70

80

90
100
ch jetp T (GeV/c )Figure 107: Comparison of the charged jet cross section ratio with UE subtraction to other√results. The results in pp collisions at s = 5.02 TeV are compared to the results of pp√√
collisions at s = 7 TeV and p-Pb collisions at sNN = 5.02 TeV.

114

Chapter 6. Results and Discussions

6.2

Charged jets in Pb-Pb collisions

In this section, the charged jet measurements in mid-central (30-50%) Pb-Pb collisions at√
sNN = 5.02 TeV are presented. The charged jets are measured w.r.t 2nd order event
plane. Charged jet v2 , which expresses the diﬀerence in jet yields in-plane and out-ofplane, is measured to quantitatively assess the parton path-length dependence of the jet
suppression. A jet-hadron correlation study is also performed to measure the initial collisiongeometry dependence of the modification of near-side jet peak shape. The width and mean
position of the near-side peaks are measured and compared between in-plane and out-ofplane emissions.
6.2.1

Charged jet v2 in mid-central Pb-Pb collisions

In non-central ultrarelativistic heavy-ion collisions, a QGP is formed in the almond-shaped
overlap region of the two colliding nuclei. Since the 2nd order event plane is strongly correlated with the initial elliptical shape of the overlap region, the jet v2 , quantifies the variationin parton energy loss for in-plane and out-of-plane jet emissions due to the diﬀerence of the
in-medium parton path-lengths. The 2nd order anisotropic flow coeﬃcient v2 is measured√
for charged jets as shown in Fig. 108 in mid-central (30-50%) Pb-Pb collisions at sNN =5.02 TeV. A positive v2 value is observed for charged jets, which implies a smaller jet yieldout-of-plane than in-plane. This result is consistent with a path-length dependent partonenergy loss since partons emitted out-of-plane have a longer in-medium path-length, leading
to a stronger energy suppression than in-plane. This result is compared with the charged jet√
v2 in Pb-Pb collisions of similar centrality but at sNN = 2.76 TeV. No significant collisionenergy dependence is observed as well as other measurements of jet quenching, such as thenuclear modification factor (RAA ).
A charged jet RAA in Pb-Pb collisions at√

sNN = 5.02 TeV is measured as a functionof centrality by using the measured charged jet production cross section in pp collisions
at the same collision energy. The strength of the jet pT -suppression, ∆pT , is estimated asa function of the in-medium parton path-length based on the measured RAA as shown in
Fig. 109 [25]. The estimated ∆pT is fitted by a linear or quadratic function. Both functions
gave good description within large uncertainties. Therefore, the dominant contribution
for in-medium energy loss among collisional energy loss (linear) and radiative energy loss
(quadratic) cannot be distinguished within the current uncertainties of the inclusive charged
jet RAA measurement.
To further investigate the path-length dependence of jet suppression, a toy MC simulation based on the Glauber model is performed and compared to the measured charged jetSection 6.2. Charged jets in Pb-Pb collisions

115

This thesis

v 2jeth1

10.8

Entries
Mean
RMS

0.35

ALICE Pb-Pb

0.3

Anti-k T, R = 0.2, |η | < 0.7
jet

0.25

s NN = 5.02 TeV, 30-50%

0.2

0.6

s NN = 2.76 TeV (w/ stat. + syst. unc.), 30-50%

0.15
0.4

0
0
0

Phys.Lett. B 753 (2016) 511-525

0.1
0.05

0.2

0
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Syst. unc. (Shape)
Syst. unc. (Correlated)− 0.05
10

20

30

40

50

20

60

70

30

80

40

90

50

100

60

70

80

90

p ch (GeV/c )T,jet√
Figure 108: Charged jet v2 in mid-central (30-50%) Pb-Pb collisions at sNN = 5.02 TeV√(Red). The result is compared to the v2jet in mid-central (30-50%) Pb-Pb collisions at sNN= 2.76 TeV (Black) [16]Figure 109: Estimated R = 0.2 charged jet pT suppression as a function of in-medium
parton path-length L [25]. The result are fit by a linear function (left) or by a quadratic
function (right)

116

Chapter 6. Results and Discussions

v2 . Here, in order to determine the eﬀective overlap region of the two colliding nuclei where
the medium is created, two definitions are tested:• def. 1) The overlap region of average nucleus radii of two colliding nuclei. (Fig. 110
left)

Here the average nucleus radius is 1.2A1/3 fm, where A is the mass number of thegiven nucleus.
• def. 2) The elliptical region defined by the distribution of participants which is estimated by Glauber MC simulation (Fig. 110 right). The length of major and minor
axes of the elliptical region are defined as 1 σ of the sliced participant distribution
in-plane and out-of-plane (projection to x′ or y ′ axis at y ′ = 0 or x′ = 0).
The def. 1 is the same definition as the one assumed in the study presented in Ref. [25].
The def. 2 is based on the event plane dependent inclusive hadron RAA study shown in
Ref. [90]. The parton path-length is calculated as the average length between the point
where the nucleon-nucleon collisions occurred and the edge of the eﬀective overlap region.
Hereafter, the path-length calculated based on def. 1 and def. 2 are referred to as LHS andLσ respectively. The toy model simulation inputs are:
• The measured charged jet production cross section in pp collisions

The R = 0.2 charged jet production cross section measurement in pp collisions shownin Fig. 100 serves as a reference for jet production without medium-induced jet suppression. The spectrum is fitted by a double-Tsallis function (Eq.57).

• The estimated ∆pT based on the RAA measurement in Pb-Pb collisions√
at sNN = 5.02 TeV
The estimated ∆pT for R = 0.2 charged jets as a function of ⟨L⟩α or ρβ ⟨L⟩α is fitted
by a linear function, where ⟨L⟩ is the in-medium parton path-length calculated with
the Glauber MC simulation and ρ is the initial energy density. In this study, only

∆pT in 0-50% centrality collisions (largest three ⟨L⟩ points in Fig. 109) are used since

the event selection bias leads to a non-negligible non-medium-induced high-pT hadronsuppression in peripheral collisions [91]. The initial energy density ρ is calculated in
the same way as Ref. [90]:
dN/dη
(59)
4πLin Lout
where Lin and Lout are the major and minor axis lengths of the eﬀective overlap region
ρ=Kand K is a constant assumed to only weakly depend on centrality and collision energy.

Section 6.2. Charged jets in Pb-Pb collisions

117

In this study, as well as in Ref. [90], K = 1 (GeV/fm) is chosen in such a way as tomake ρ expressed units of in GeV/fm3 .
Nucleons inside the nucleus are distributed according to the Woods-saxon potential. The
ppinelastic pp collision cross section σinel= 68 mb is utilized to compute the number ofparticipants. The fit functions to the R = 0.2 charged jet production cross section arey' [fm]30-50 %
15!"#$%&'()#$
10

5

0

−5

−10

−15
−15

−10

−5

0

5

10

15

x' [fm]Figure 110: Definitions of the eﬀective overlapping region for in-medium parton path-length
calculation with Glauber MC simulation.
Left: The overlapping region of average nucleus radii of two colliding nuclei [25].
Right: The elliptical region defined by participant distribution. The major and minor axes
are defined as 1 σ of the slice of participant distribution in-plane and out-of-plane. The x′
axis is corresponding to the participant event plane direction.
shifted by the expected ∆pT in-plane and out-of-plane expected from the linear fit of the∆pT as a function of ⟨L⟩α or ρβ ⟨L⟩α . The jet v2 as a function of pT is estimated based on
the set of shifted functions derived from the parameter space scanning of α and β. The

jet v2 χ2 is calculated with the measured charged jet v2data and the estimated v2MC by MC
simulation as:#$
5 v2data − v2MC 2
χ2 =22σstat.
+ σsyst.

(60)

where σstat. and σsyst. are the quadratic sum of the statistical and systematic uncertainties
respectively. The reduced chi-square (χ2 /ndf) is calculated by dividing the χ2 by the numberof data points. Fig. 111 shows the calculated reduced chi-square for the jet v2 (red) and fora linear fit of the ∆pT (blue) as a function of path-length exponent. The results suggest that

118

Chapter 6. Results and Discussions

the jet v2 measurement is more sensitive to the path-length than the RAA measurement as
a function of centrality, because the distribution of the jet v2 reduced chi-square is narrower
than that of the ∆pT . Although the optimal path-length exponent diﬀers from jet v2 to∆pT , it is eventually not constrained by both def. 1,2 due to large uncertainties. In theThis thesis

Figure 111: The reduced chi-square for jet v2 (red) and ∆pT linear fit (blue).
Left: The reduced chi-square as a function of the ⟨LHS ⟩ exponent (α).
Right: The reduced chi-square as a function of the ⟨Lσ ⟩ exponent (α).
Ref. [90], it was reported that the inclusive hadron RAA in-plane and out-of-plane scale when
taking into account the centrality dependent initial energy density ρ. Fig. 112 shows the
reduced chi-square for ∆pT linear fit (left) and jet v2 (right) as a function of the path-lengthand ρ exponents (α, β) within def. 2. α = 2.6 and β = 1.1 result in the best description√of both jet v2 and ∆pT simultaneously. In the Ref. [90], two scenarios of ∆pT ∝ ρLand ∆pT ∝ ρ3/4 L2 were proposed based on radiative energy loss calculations. This result√
is close to the ∆pT ∝ ρ3/4 L2 case. However, ∆pT ∝ ρL is not ruled out due to thelarge uncertainties. The in-medium energy loss scenario will be constrained by reducing theuncertainties. This scaling with ρ turns out to be not eﬀective within def. 1 case, because,
unlike the def. 2 case, ρ is almost constant over the 0-50% centrality interval class.

Section 6.2. Charged jets in Pb-Pb collisions

119

This thesis

Figure 112: The reduced chi-square as a function of the exponent of ⟨Lσ ⟩ (α) and of ρ (β)
for ∆pT (derived from R=0.2 jet RAA ) fit (left) and for jet v2 (right).
6.2.2

Charged jet-hadron correlations in mid-central Pb-Pb collisions

In order to explore the jet modification dependence on initial collision geometry, jet-hadroncorrelations are studied w.r.t the 2nd -order event plane. In this study, background subtracted near-side jet peaks are fit by a Lorentzian function. Fig. 113 and Fig. 114 show thenear-side peaks observed for in-plane (|∆φ(φjet−ψ2 )| < π/4) and out-of-plane (|∆φ(φjet−ψ2 )| >assoc3π/8) jet emission correlated with low (0.7 < passoc
T,track < 2 GeV/c) and high (2 < pT,track <4 GeV/c) pT associated tracks respectively. Left (Right) figures are projections of C(∆ϕ, ∆η)on ∆φ (∆η) axis.
∆φ distributions of low-pT associated tracks show a broadening of the near-side peakfrom in-plane to out-of-plane jet emission. The out-of-plane width increases by about 1020% in ∆φ. The ∆η distribution of the near-side peak shows a similar broadening for low-pT
associated tracks by about 1-10%. However, it is not so significant within the uncertainties.
On the other hand, no diﬀerence between in-plane and out-of-plane is observed for thehigh-pT associated tracks. As reported by the CMS Collaboration, for low-pT associates,
the jet radial profile broadens in the most central Pb-Pb collisions as illustrated in Fig. 22.
This suggests that the jet radial profile broadens as in-medium parton path lengthens. Thisfinding is consistent with the results obtained in the present study. Furthermore, the radial
profile for the high-pT associates is not modified for the most central collisions according to
the CMS results. This observation is again consistent with the results hereinbefore shown.

120

Chapter 6. Results and Discussions

Reflecting on these results, the observed phenomenon could be interpreted as due to:• In-medium parton shower evolution diﬀerent from the vacuum one.
• Energy re-distribution in a medium with hydrodynamical evolution

The modification of the jet radial profile reported by the CMS Collaboration is described by a model including hydrodynamical eﬀects as shown in Fig. 23. The results
shown in this thesis may also be described by a similar model.

This thesis

Figure 113: Near-side jet-hadron correlations for in-plane jets (|∆φ(φjet−ψ2 )| < π/4, Red)
det
assoc
and out-of-plane jets (|∆φ(φjet−ψ2 )| > 3π/8, Green). pch,T,jet > 20 GeV/c. 0.7 < pT,track <2 GeV/c. α is selected so that the fit function height is 1.
Fig. 115 shows the near-side azimuthal peak position w.r.t jet axis. The peak position isshifted towards the in-plane direction and this eﬀect is stronger for low-pT associates. The
medium thickness and pressure gradient will be asymmetric w.r.t the jet axis, especially in
mid-central collisions. These features may be able to describe this azimuthal asymmetry
w.r.t the jet axis due to the initial elliptical collision geometry. In order to quantify the
amplitude of the shift eﬀect w.r.t the event plane, Fig. 115 is fitted by a sine function:f (x) = M · Sin(2x)(61)

where M is a free parameter which expresses the amplitude of the sine curve.
A MC simulation by JEWEL [46], which incorporates in-medium parton energy loss
and parton shower evolution, is performed in order to compare our experimental results
to theoretical predictions. The lost energy re-distribution and hydrodynamical mediumSection 6.2. Charged jets in Pb-Pb collisions

121

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Figure 114: Near-side jet-hadron correlations for in-plane jets (|∆φ(φjet−ψ2 )| < π/4, Red)
det
assoc
and out-of-plane jets (|∆φ(φjet−ψ2 )| > 3π/8, Green). pch,T,jet > 20 GeV/c, 2 < pT,track <4 GeV/c. α is selected so that the fit function height is 1.

This thesis

Figure 115: The near-side peak position w.r.t jet axis in azimuth as a function of angle
det
assoc
between jet axis and event plane. pch,T,jet > 20GeV/c. Left: 0.7 < pT,track < 2 GeV/c,Right: 2 < passoc
T,track < 4 GeV/c

122

Chapter 6. Results and Discussions

response are not included in this simulation. The generated particles by JEWEL are reduced/smeared according to the tracking eﬃciency (Fig. 36) and resolution (Fig. 37) since
all the observables in this jet-hadron correlation study are not corrected for detector eﬀects.
The charged jets in the MC simulation are reconstructed by the anti-kT algorithm as wellas in the data analysis. The reconstructed charged jet pT is also smeared according to themeasured δpT (Fig. 74) in order to adjust the jet energy scale between data and MC simuladettion. After the jet pT smearing, jet-hadron correlations are measured for pch,T,jet > 20GeV/c,
assoc
0.7 < passoc
T,track < 2 GeV/c and 2 < pT,track < 4 GeV/c.

passoc(GeV/c)
T
Data
JEWEL

0.7 < passoc
T,track < 2

2 < passoc
T,track < 4

1.22 ± 0.07 (stat.) ±0.05
0.11 (syst.)
1.02 ± 0.02 (stat.)1.00 ± 0.03 (stat.) ±0.04
0.09 (syst.)
1.00 ± 0.03 (stat.)

Table 13: The ratio of near-side jet peak width in azimuth (∆ϕ) out-of-plane over the oneof in-plane. The results from data are compared to JEWEL predictions.
det
assoc
assoc
pch,
T,jet > 20GeV/c, 0.7 < pT,track < 2 GeV/c and 2 < pT,track < 4 GeV/cpassoc(GeV/c)
T
Data
JEWEL

0.7 < passoc
T,track < 2

2 < passoc
T,track < 4

1.07 ± 0.03 (stat.) ± 0.05 (syst.)
0.98 ± 0.02 (stat.)0.97 ± 0.02 (stat.) ± 0.02 (syst.)
0.97 ± 0.02 (stat.)

Table 14: The ratio of near-side jet peak width in eta (∆η) out-of-plane over the one ofin-plane. The results from data are compared to JEWEL predictions.
det
assoc
assoc
pch,
T,jet > 20GeV/c, 0.7 < pT,track < 2 GeV/c and 2 < pT,track < 4 GeV/c
Tab. 13 and 14 show the ratio of near-side peak width out-of-plane over the one of√in-plane in 30-50% Pb-Pb collisions at sNN = 5.02 TeV (Data). The former table isfor the peak in azimuth and the latter one is for the peak in eta. The peak width isestimated by fitting with a Lorentzian function. The data results are compared to the
JEWEL predictions. The broadening observed in the data for low-pT associates is notobserved in the JEWEL predictions within uncertainties.
passoc(GeV/c)
T
Data
JEWEL

0.7 < passoc
T,track < 2

2 < passoc
T,track < 4-0.02 ± 0.005 (stat.) ± 0.006 (syst.)-0.004 ± 0.002 (stat.)-0.008 ± 0.002 (stat.) ± 0.002 (syst.)
0.0006 ± 0.0007 (stat.)

Table 15: The amplitudes of the sine function (Eq. 61) obtained by fitting the peak positionin azimuth as a function of the angle between the trigger jet axis and the event plane. The
results from data are compared to JEWEL predictions.
det
assoc
assoc
pch,
T,jet > 20GeV/c, 0.7 < pT,track < 2 GeV/c and 2 < pT,track < 4 GeV/c

Section 6.2. Charged jets in Pb-Pb collisions

123

Tab. 15 shows the amplitudes of sine function (Eq. 61) obtained by fitting the near-side
peak positions in azimuth (∆ϕ). A similar behaviour is observed in JEWEL predictions
for low-pT associates though it is milder eﬀect in comparison with the one observed in thedata. No peak position shift is observed for high-pT associates in JEWEL predictions.
The results in Tab. 13, 14, and 15 suggest that the diﬀerence of near-side jet-like peakmodification in-plane, mid-plane, and out-of-plane cannot be described only by in-medium
parton energy loss and parton shower evolution.

Chapter 7

Summary

Jets are well calibrated experimental observables to study QCD. Measurements of jets allow
to access the initial partons because of the asymptotic freedom property of the QCD andthe elementary process of jet production being calculable with pQCD. Jets are also wellestablished probes of the QGP which is a hot and dense QCD medium formed in ultrarelativistic heavy-ion collisions. Measurements of jets allowed to probe the entire evolution of
the medium since jets originate from initial hard-scattered partons will lose energy while
traversing the medium. The properties of QGP, such as stopping power, can be assessed bymeasureing the medium induced energy suppression of jets.
In general, the pT spectrum of jets follows a power-law distribution. Hence, high-pT
jet events are rare. Event triggering is a powerful experimental technique to enable themeasurement of such rare probes. In this thesis, the trigger system development of the ALICE electromagnetic calorimeters (EMCal, DCal and PHOS) and its commissioning, which
was performed during LHC LS 1 and the first year of LHC Run2, have been described.
The Di-Jet calorimeter, called DCAL, has been installed during LS1 to enhance the jetmeasurement capabilities of the ALICE experiment. The firmware of the Level-1 online
trigger electronics, the Summary Trigger Unit (STU), has been upgraded to adapt it to
the new detector configurations of Run2. A new trigger algorithm for heavy-ion collisions,which calculates the background energy density on an event-by-event basis estimated by
the calorimeters opposite side in azimuth, has been implemented. We performed the commissioning tasks and the trigger system was operated stably throughout LHC Run2 (Late2015-2018). The physics results utilizing the trigger data are coming out.
√√
A data analysis with the pp collisions at s = 5.02 TeV and Pb-Pb collisions at sNN= 5.02 TeV datasets has been performed. Charged jet production cross sections in pp
collisions have been measured with jet resolution parameter R = 0.2, 0.3, 0.4 and 0.6.
The measured cross sections have been compared with LO and NLO pQCD-based model
predictions. The data results in the kinematic range 10 < pch
T,jet < 100GeV/c are welldescribed by pQCD calculations at NLO accuracy. On the other hand, predictions showa large discrepancy with data in lower pT,jet range while large theoretical uncertainties arepresent mainly coming from the scale factors of the pQCD calculations. The systematic
uncertainties could be improved with Next-to-Next-to-Leading Order (NNLO) calculations.
125

126

Chapter 7. Summary

It may also be important to understand non-perturbative eﬀects, such as the underlying
event, for an improved understanding of the jet production cross section in the low pT,jet
range.
The 2nd anisotropic flow coeﬃcient of charged jets, v2jet has been measured in mid-central(30-50%) Pb-Pb collisions for R = 0.2 jets. The results have been compared with the v2jet in√
mid-central (30-50%) Pb-Pb collisions at sNN = 2.76 TeV. No collision energy dependence
is found. A toy model MC Glauber simulation has been performed to study in-medium pathlength dependent parton energy loss in detail. The estimated strength of jet suppression,∆pT,jet , by RAA measurement [25] and measured production cross section of charged jetin pp collisions have been used as inputs of the simulation. The results of the toy modelMC, especially in the ∆pT,jet ∝ ρ1.1 ⟨Lσ ⟩2.6 case, simultaneously describes the v2jet and RAA√
in mid-central (30-50%) Pb-Pb collisions at sNN = 5.02 TeV. It basically supports thein-medium radiative energy loss scenario of ∆pT ∝ ρ3/4 L2 which was proposed in Ref. [90].
√However, the other scenario, ∆pT ∝ ρL, is not ruled out due to the large uncertainties.
√
The available datasets of Pb-Pb collisions at sNN = 5.02 TeV collected by the ALICE
experiment in 2018 and the upcoming data of LHC Run3 will help to discriminate between
the diﬀerent scenarios (see below also). The statistical uncertainties will be reduced byanalyzing these new data. One of the largest systematic uncertainties comes from underlying
event fluctuation. Recently, it was proposed that the underlying event fluctuation eﬀect may
be able to reduce by machine learning technique [92]. The in-medium energy loss scenario
will be further constrained by reducing the uncertainties on both v2jet and RAA .
nd order event
Jet-hadron correlations for pdet
T,jet > 20 GeV/c have been studied w.r.t 2
assoc
plane. The correlations has been studied in 0.7 < passoc
T,track < 2 GeV/c and 2 < pT,track <4 GeV/c. A broader distribution of the near-side jet peak in out-of-plane jet emission incomparison with in-plane jet emission is observed for low-pT associates. A near-side peak
position shift in azimuth towards in-plane direction has also been observed for both pTranges. The measured results have been compared to theoretical predictions by JEWEL.
The predictions don’t reproduce the measured results except for the peak position shifts
for low-pT associates which are only partially reproduced. It suggests that the near-side
peak shape modification w.r.t 2nd -order event plane cannot be described only by the inmedium parton energy loss and parton shower evolution. Therefore, the medium-inducednear-side jet modification may be understood as a combination of in-medium radiation,
initial geometry dependent energy suppression and medium response with hydrodynamical
evolution.

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As shown in this thesis and other studies, charged jet measurements with ALICE detector have been well established. In future, full jet (charged+neutral) measurements withcalorimeters using the triggered data will enhance the physics capabilities of the jet measurements. For example, full jet measurement with EMCal+DCal allows di-jet measurementwith high energy resolution in comparison with measurements of charged jets. Another remarkable challenge for the ALICE experiment will consist in the high-rate continuous data
readout with online track reconstruction foreseen for LHC Run3 [93, 94]. It will also allow
measurement of rare probes with high statistical precision.

Appendix A

A Large Ion Collider Experiment

A Large Ion Collider Experiment (ALICE) is one of the major experiments at LHC. The
main physics program of ALICE aims at revealing the properties of hot and dense nuclear
matter, i.e QGP. As of 2018, about 1800 members from 177 institutes in 41 countries are
participating with the ALICE collaboration [26].

Figure 116: The world map on the earth. The countries collaborating with ALICE arecolored in red [26].

129Appendix B

Quality Assurance for pp collisions

Track QA study was performed for datasets of pp collisions.

This thesis

Figure 117: φ-η distributions of hybrid tracks for each run used for data analysis.

130This thesis

1/Ntrigger,MB dN/dη

131

4.5
4
3.5
Hybrid tracks

3

w/ SPD hits, w/ ITS refit

w/o SPD hits, w/ ITS refit

2.5
2
1.5
1
0.5
0

(a) Charged tracks φ distribution

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8
η

(b) Charged tracks η distribution

This thesis

1/Nevent dN/dpT

Figure 118: φ and η distributions of charged tracks (a) with Hybrid track cut (black), (b)with SPD hits and ITS refit (red), and (c) without SPD hit and ITS refit (blue) .

10

pp s = 5.02 TeV
lowIR
highIR

1

10− 1

10− 2

−3

10

10− 4

−5

HIR / LIR

10

1.2
1.15
1.1
1.05
1
0.95
0.9
0.85

1

10

p

(a) Ratio of hybrid tracks pT spectra in LIR to the merged LIR
period.

T,track(GeV/ c )(b) Hybrid tracks pT spectra and ratio in LIR and HIR.

Figure 119: Validation of hybrid tracks pT spectra per data collection period.

Bibliography[1] S. Aoki et al., “2+1 flavor lattice QCD toward the physical point,” Phys. Rev. D 79
(2009) , arXiv:0807.1661 [hep-lat].
[2] S. Sarkar, H. Satz, B. Sinha, The Physics of the Quark-Gluon Plasma: Introductory
Lectures (Lecture Notes in Physics 785). Springer, 2010.
[3] H1 and ZEUS collaborations, F. Aaron, et al., “Combined Measurement and QCD
Analysis of the Inclusive e± p Scattering Cross Sections at HERA,” Journal of HighEnergy Physics 109 (2010) .
[4] D. de Florian et al., “Parton-to-Pion Fragmentation Reloaded,” Phys. Rev. D 91
(2015) .
[5] G. Aarts et al., “QCD at nonzero chemical potential: Recent progress on the lattice,”
AIP Conference Proceedings 1701 020001, (2016) .
[6] S. Borsányi et al., “The QCD equation of state with dynamical quarks,” J. HighEnerg. Phys. 77 (2010) .
[7] R. Snellings, “Collective expansion at the LHC: selected ALICE anisotropic flow
measurements,” J. Phys. G: Nucl. Part. Phys. 41 124007, (2014) .
[8] S. J. Das et al., “Relating centrality to impact parameter in nucleus-nucleus
collisions,” Phys. Rev. C 97 014905, (2018) .
[9] J. Adam, et al., A. Collaboration), “Centrality dependence of the charged-particle√
multiplicity density at mid-rapidity in Pb-Pb collisions at sNN = 5.02 TeV,” Phys.
Rev. Lett. 116 222302, (2016) .
[10] C. Loizides, J. Nagle, P. Steinberg, “Improved version of the PHOBOS GlauberMonte Carlo,” SoftwareX 1-2 (2015) 13–18, arXiv:1408.2549 [nucl-ex].
[11] ALICE Collaboration, “Charged jet cross sections and properties in proton-proton√
collisions at s =7 TeV,” Phys. Rev. D 91 112012, (2015) .
132

BIBLIOGRAPHY

133[12] J. Adams et al. (STAR Collaboration), “Evidence from d + Au Measurements for
Final-State Suppression of High-pT Hadrons in Au + Au Collisions at RHIC,” Phys.
Rev. Lett. 91 072304, (2003) .
[13] The CMS Collaboration, V. Khachatryan et al., “Charged-particle nuclear√
modification factors in PbPb and pPb collisions at sNN = 5.02 TeV,” J. HighEnerg. Phys. 39 (2017) .
[14] G. I. Veres (for the CMS Collaboration), “Overview of results on jets from the CMS
Collaboration,” Nucl. Phys. A 904-905 (2013) 146c–153c.
[15] H. Yokoyama (for the ALICE collaboration), “Measurement of Inclusive Charged Jet√
Production in pp and Pb–Pb collisions at sNN = 5.02 TeV with ALICE,” Nucl. andPart. Phys. Proceedings 289-290 (2017) 109–112.
[16] A. Collaboration, “Azimuthal anisotropy of charged jet production in√sNN = 2.76

TeV Pb-Pb collisions,” Phys. Lett. B 753 (2016) 511–525.
[17] The CMS Collaboration, A. M. Sirunyan et al., “Jet properties in PbPb and pp√
collisions at sNN = 5.02 TeV,” J. High Energ. Phys. 6 (2018) .
[18] Y. Tachibana, N. B. Chang, G. Y. Qin, “Full jet in quark-gluon plasma withhydrodynamic medium response,” Phys. Rev. C 95 044909, (2017) .
[19] J. Adam et al. (ALICE Collaboration), “Anisotropic Flow of Charged Particles in√
Pb-Pb Collisions at sNN = 5.02 TeV,” Phys. Rev. Lett. 116 132302, (2016) .
[20] H. Niemi et al., “Predictions for 5.023 TeV Pb + Pb collisions at the CERN Large
Hadron Collider,” Phys. Rev. C 93 014912, (2016) .
[21] J. Noronha-Hostler, M. Luzum, J.-Y. Ollitrault, “Hydrodynamic predictions for 5.02
TeV Pb-Pb collisions,” Phys. Rev. C 93 034912, (2016) .
[22] O. Bourrion, “STU manual.” Alice internal document.
[23] R. Divià, P. Jovanovic, P. Van de Vyvre, “Data Format over the ALICE DDL;
version 11,” Tech. Rep. ALICE-INT-2002-10-V11. CERN-ALICE-INT-2002-10-V11,
CERN, Geneva, Mar, 2007. https://cds.cern.ch/record/1027339.
[24] R. Divià, “ALICE Common Data Header specifications.” ALICE Internal Note.

134

BIBLIOGRAPHY[25] H. Yokoyama, Measurement of jet spectra reconstructed with charged particles in√
Pb-Pb collisions at sN N = 5.02 TeV with the ALICE detector at the LHC. PhD
thesis, University of Tsukuba and Université Grenoble Alpes, 2018.
[26] “ALICE Collaboration.” http://alice-collaboration.web.cern.ch.
[27] T. Todoroki, Measurements of Two-Particle Correlations with respect to√Higher-Order Event Planes in sN N = 200 GeV Au+Au Collisions at
RHIC-PHENIX. PhD thesis, University of Tsukuba, 2014.
[28] A. Einstein, “Über den einfluß der schwerkraft auf die ausbreitung des lichtes,”
Annalen der Physik 340 10, (1911) 898–908.
[29] C. Patrignani, Particle Data Group, “Review of Particle Physics,” Chinese Physics C
40 10, (Oct., 2016) 100001.
[30] R. Oerter, “The Theory of Almost Everything: The Standard Model, the Unsung
Triumph of Modern Physics,” Penguin Group 0-13-236678-9 (2006) .
[31] P. W. Higgs, “Broken symmetries, massless particles and gauge fields,” Physics
Letters 12 2, (1964) 132–133.
[32] A. Bednyakov, “Quantum Field Theory and the Electroweak Standard Model,”lectures given at ESHEP2018, Maratea, Italy (2018) , arXiv:1812.10675 [hep-ph].
[33] F. Halzen, A. D. Martin, QUARKS & LEPTONS: An Introductory Course inModern Particle Physics. Wiley, 1984. ISBN:0471887412, 9780471887416.
[34] J. Collins, D. Soper, G. Sterman, “Factorization for Short Distance Hadron - Hadron
Scattering,” Nucl. Phys. B261 (1985) 104–142.
[35] J. Collins, M. Perry, “Superdense Matter: Neutrons Or Asymptotically Free
Quarks?,” Phys. Rev. Lett 34 (1975) .
[36] S. Adler, et al. (PHENIX Collaboration), “Systematic studies of the centrality and√sN N dependence of the dET /dη and dNch /dη in heavy ion collisions at
midrapidity,” Phys. Rev. C 71 (2005) .
[37] CMS Collaboration, Pseudorapidity and centrality dependence of energy flow in
2.76TeV PbPb collisions. No. CMS-PAS-HIN-11-003. CERN, Geneva, 2011.
http://cds.cern.ch/record/1354215.

BIBLIOGRAPHY

135[38] R. Hosokawa et al., “Measurement of charged jet cross section in pp collisions at√s= 5.02 TeV.” ALICE Internal Analysis Note.
[39] J. S. Moreland, J. E. Bernhard, S. A. Bass, “Alternative ansatz to wounded nucleon
and binary collision scaling in high-energy nuclear collisions,” Phys. Rev. C 92 (2015)
011901, arXiv:1412.4708 [[nucl-th]].
[40] B. Abelev et al. (ALICE Collaboration), “Centrality determination of Pb-Pb√
collisions at sNN = 2.76 TeV with ALICE,” Phys. Rev. C 88 044909, (2013) .
[41] M. L. Miller et al., “Glauber Modeling in High Energy Nuclear Collisions,” Ann. Rev.
Nucl. Part. Sci. 57 (2007) 205–243.
[42] B. Alver, G. Roland, “Collision-geometry fluctuations and triangular flow inheavy-ion collisions,” Phys. Rev. C 81 054905, (2010) .
[43] J. L. Nagle, M. P. McCumber, “Heavy ion initial conditions and correlations between
higher moments in the spatial anisotropy,” Phys. Rev. C 83 044908, (2011) .
[44] D. d’Enterria, “Jet quenching,” arXiv:0902.2011 [nucl-ex].
[45] A. Collaboration, “Measurement of the inclusive jet cross section in pp collisions at√√
s = 2.76 TeV and comparison to the inclusive jet cross section at s = 7 TeV using
the ATLAS detector,” Eur. Phys. J. C 73 2509, (2013) .
[46] K. C. Zapp, “JEWEL 2.0.0 - Directions for Use,” Eur. Phys. J. C 74 (2014) .
[47] “CERN: Home.” https://home.cern.
[48] ALICE Collaboration, E. Abbas et al., “Performance of the ALICE VZERO
system,” JINST 8 (2013) P10016, arXiv:1306.3130 [nucl-ex].
[49] ALICE Collaboration, B. Abelev et al., “Performance of the ALICE Experiment at
the CERN LHC,” Int. J. Mod. Phys. A 29 (2014) 1430044, arXiv:1402.4476[nucl-ex].
[50] ALICE Collaboration, K. Aamodt et al., “Alignment of the ALICE Inner Tracking
System with cosmic-ray tracks,” JINST 5 (2010) P03003, arXiv:1001.0502[physics.ins-det].
[51] K. Røed, Single Event Upsets in SRAM FPGA based readout electronics for the Time
Projection Chamber in the ALICE experiment. PhD thesis, University of Bergen,
2009.

136

BIBLIOGRAPHY[52] C. Lippmann, “Performance of the alice time projection chamber,” Phys. Procedia 37(2012) 434–441.
[53] A. Akindinov et al., “Latest results on the performance of the multigap resistive platechamber used for the ALICE TOF,” Nucl. Instrum. Meth. A 533 (2004) 74–78.
[54] N. Jacazio (for The ALICE collaboration), “PID performance of the ALICE-TOF
detector in Run 2,” arXiv:1809.00574 [physics.ins-det].
[55] ALICE Collaboration, J. Allen et al., “ALICE DCal: An Addendum to the EMCal
Technical Design Report Di-Jet and Hadron-Jet correlation measurements in
ALICE,” Tech. Rep. CERN-LHCC-2010-011. ALICE-TDR-14-add-1, CERN, 2010.
[56] D. S. (for the ALICE Collaboration), “Energy and system dependence of nuclear
modification factors of inclusive charged particles and identified light hadrons
measured in pPb, XeXe and PbPb collisions with ALICE,” Nucl. Phys. A982 (2019)567–570, arXiv:1807.11240 [hep-ex].
[57] D. K. (for the ALICE Collaboration), “Probing beauty and charm production in
p-Pb collisions with high pT electrons measured with ALICE,” in 27th International
Conference on Ultra-relativistic Nucleus-Nucleus Collisions (Quark Matter 2018).
2018.
[58] T. Sjostrand, S. Mrenna, P. Skands, “PYTHIA 6.4 Physics and Manual,” J. HighEnerg. Phys. 05 (2006) .
[59] T. S. ostrand et al., “An Introduction to PYTHIA 8.2,” Comput. Phys. Commun.
191 (2015) 159–177.
[60] X.-N. Wang, M. Gyulassy, “HIJING: A Monte Carlo model for multiple jet
production in pp, pA and AA collisions,” Phys. Rev. D 44 (1991) 3501–3516.
[61] R. Brun et al., GEANT Detector Description and Simulation Tool.
No. CERN-W5013, CERN-W-5013, W5013, W-5013. CERN, 1994.
[62] A. Collaboration, “ALICE: Physics Performance Report, Volume II,” J. Phys. G:
Nucl. Part. Phys. 32 (2006) 1295.
[63] M. Cacciari, G. P. Salam, “The anti-kT jet clustering algorithm,” J. High Energ.
Phys. 04 (2008) .

BIBLIOGRAPHY

137[64] M. Cacciari, G. P. Salam, G. Soyez, “FastJet user manual,” Eur. Phys. J. C 72
(2012) 1896.
[65] ATLAS Collaboration, “Properties of jets measured from tracks in proton-proton√
collisions at center-of-mass energy s = 7 TeV with the ATLAS detector,” Phys.
Rev. D 84 (2011) 054001.
[66] A. Hoecker, V. Kartvelishvili, “SVD Approach to Data Unfolding,” Nucl. Instrum.
Meth. A 372 (1996) 469–481.
[67] “RooUnfold: ROOT Unfolding Framework.”
http://hepunx.rl.ac.uk/~adye/software/unfold/RooUnfold.html.
[68] T. Adye, “Unfolding algorithms and tests using RooUnfold,” Proceedings of the
PHYSTAT 2011 Workshop, CERN, Geneva, Switzerland (2011) 313–318,
arXiv:1105.1160 [physics.data-an].
[69] ALICE Collaboration, B. Abelev et al., “ALICE luminosity determination for pp√
collisions at s = 5 TeV,”. https://cds.cern.ch/record/2202638.
[70] A. M. Poskanzer, S. A. Voloshin, “Methods for analyzing anisotropic flow inrelativistic nuclear collisions,” Phys. Rev. C 58 (2011) 1671.
[71] J. Y. Ollitrault, “Determination of the reaction plane in ultrarelativistic nucler
collisions,” Phys. Rev. D 48 (1993) 1132.
[72] ALICE Collaboration, B. Abelev et al., “Measurement of charged jet suppression in√
Pb-Pb collisions at sN N =2.76TeV,” JHEP 30 CERN-PH-EP-2013-205.
CERN-PH-EP-2013-205, (Nov, 2013) 013. http://cds.cern.ch/record/1624179.
[73] ALICE Collaboration, B. B. Abelev et al., “Charged jet cross sections and√properties in proton-proton collisions at s = 7 TeV,” Phys. Rev. D 91
CERN-PH-EP-2014-254. CERN-PH-EP-2014-254, (Nov, 2014) 112012.
http://cds.cern.ch/record/1970694.
[74] ALICE Collaboration, S. Acharya et al., “Constraints on jet quenching in p-Pb√
collisions at sNN = 5.02 TeV measured by the event-activity dependence ofsemi-inclusive hadron-jet distributions,” Phys. Lett. B783 (2018) 95–113,
arXiv:1712.05603 [nucl-ex].

138

BIBLIOGRAPHY[75] PHENIX Collaboration, “Measurement of two-particle correlations with respect to√second- and third-order event planes in Au+Au collisions at sN N = 200 GeV,”
arXiv:1803.01749 [hep-ex].
[76] B. Andersson, G. Gustafson, B. Söderberg, “A general model for jet fragmentation,”
Z. Phys. C 20 (1983) 317.
[77] P. Z. Skands, “Tuning Monte Carlo Generators: The Perugia Tunes,” Phys.Rev. D82
074018, arXiv:1005.3457 [hep-ph].
[78] P. Skands, S. Carrazza, J. Rojo Eur. Phys. J. 3024, arXiv:1404.5630 [hep-ph].
[79] “ATLAS Run 1 Pythia8 tunes,” Tech. Rep. ATL-PHYS-PUB-2014-021, CERN,
Geneva, Nov, 2014. http://cds.cern.ch/record/1966419.
[80] CMS Collaboration, V. Khachatryan et al., “Event generator tunes obtained fromunderlying event and multiparton scattering measurements,” Eur. Phys. J. C76(2016) 155, arXiv:1512.00815 [hep-ex].
[81] CTEQ Collaboration, H. Lai et al., “Global QCD analysis of parton structure of thenucleon: CTEQ5 parton distributions,” Eur.Phys.J. 375, arXiv:hep-ph/9903282[hep-ph].
[82] R. D. Ball et al., “Parton distributions with LHC data,” Nucl. Phys. B 867 (2013)
244–289, arXiv:1207.1303 [hep-ph].
[83] S. Alioli et al., “Jet pair production in POWHEG,” JHEP 04 (2011) 081,
arXiv:1012.3380 [hep-ph].
[84] P. Nason, “A New method for combining NLO QCD with shower Monte Carloalgorithms,” JHEP 11 (2004) 040, arXiv:hep-ph/0409146 [hep-ph].
[85] S. Alioli et al., “A general framework for implementing NLO calculations in shower
Monte Carlo programs: the POWHEG BOX,” JHEP 06 (2010) 043,
arXiv:1002.2581 [hep-ph].
[86] S. Frixione, P. Nason, C. Oleari, “Matching NLO QCD computations with Parton
Shower simulations: the POWHEG method,” JHEP 11 (2007) 070,
arXiv:0709.2092 [hep-ph].
[87] S. Dulat et al., “New parton distribution functions from a global analysis of quantum
chromodynamics,” Phys. Rev. D93 (2016) 033006, arXiv:1506.07443 [hep-ph].

BIBLIOGRAPHY

139[88] T. Gehrmann et al., “Jet cross sections and transverse momentum distributions with
NNLOJET,” Contribution to the Proceedings of the RADCOR2017, 24-29 Sep., 2017,
St. Gilgen, Austria (2018) , arXiv:1801.06415 [hep-ph].
[89] ALICE Collaboration, B. Abele et al., “Underlying Event measurements in pp√
collisions at s = 0.9 and 7 TeV with the ALICE experiment at the LHC,” J. HighEnerg. Phys. 07 (2012) 116, arXiv:1112.2082 [hep-ex].
[90] P. Christiansen, K. Tywoniuk, V. Vislavicius, “Universal scaling dependence of QCD
energy loss from data driven studies,” Phys. Rev. C89 3, (2014) 034912,
arXiv:1311.1173 [hep-ph].
[91] ALICE Collaboration, S. Acharya et al., “Analysis of the apparent nuclear
modification in peripheral Pb-Pb collisions at 5.02 TeV,” arXiv:1805.05212[nucl-ex].
[92] R. Haake, C. Loizides, “Machine Learning based jet momentum reconstruction inheavy-ion collision,” arXiv:1810.06324 [nucl-ex].
[93] ALICE Collaboration, F. Costa, A. Kluge, P. Vande Vyvre, “The detector read-out
in ALICE during Run 3 and 4,” J. Phys. Conf. Ser. 898 3, (2017) 032011.
[94] D. Rohr et al., “Track Reconstruction in the ALICE TPC using GPUs for LHC Run
3,” arXiv:1811.11481 [physics.ins-det].