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

Hiroki Yokoyama
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 de la production inclusive de jets
chargés dans les collisions Pb-Pb à 5.02 TeV
avec l’expérience ALICE auprès du LHC
Thèse soutenue publiquement le 29 Mars 2018,
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 Yves SCHUTZ
Directeur de Recherche, IPHC, Rapporteur

Monsieur Toru SUGITATE
Professeur, Université de Hiroshima, Rapporteur

Measurement of jet spectra reconstructed with charged√
particles in Pb-Pb collisions at sNN = 5.02 TeV
with the ALICE detector at the LHC

Hiroki Yokoyama

March, 2018

Measurement of jet spectra reconstructed with charged√
particles in Pb-Pb collisions at sNN = 5.02 TeV
with the ALICE detector at the LHC

Hiroki Yokoyama(Doctoral Program in Physics)

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

High-energy nuclear physics aims at revealing the properties of Quark-Gluon Plasma (QGP),a new state of matter consisting of asymptotically free strong-interacting quarks and gluons.
According to lattice QCD calculation, a transition from normal nuclear matter to a QGP
is expected for energy densities exceeding the critical threshold of εc ∼ 0.18 - 0.5 GeV /fm3

(Tc = 154 ± 9 MeV ). Such extreme conditions of temperature and energy density are met
in laboratory by smashing heavy nuclei at ultra relativistic energies.

The QGP thus created is however so short lived that it can only be resolved by selfgenerated hard probes, namely produced together with the medium but on a much shortertime scale. By subsequently interacting with the expanding QGP, these well calibrated
probes carry valuable information about its transport properties.
The purpose of this thesis is the measurement of jets as hard probes of the QGP along
two complementary directions: by developing a new ALICE jet calorimeter trigger algorithm
for LHC Run 2 to eﬃciently select events containing high energy electromagnetic showers
and measuring charged jet production cross sections in Pb-Pb collisions at highest-evercentre of mass energy of 5.02 TeV provided by the LHC.
One of the basic challenges facing jet measurement in heavy-ion collisions consists inseparating jets from the soft underlying event. The magnitude of the underlying event
is quantified on an event-by-event basis and subtracted from the reconstructed jets. The
remaining background fluctuations and detector eﬀects are corrected at the event-ensemble
level by an unfolding method. Furthermore, in order to minimise the fake jet contamination,a leading track jet transverse momentum cut-oﬀ of 5 GeV/c is applied.
A strong suppression of jet production in the most central heavy-ion collisions is observed and quantified by the measurement of the nuclear modification factor, RAA . Such a
suppression is interpreted as the result of parton energy loss in the QGP, the so-called jet
quenching phenomenon. In this thesis, a phenomenological study with an original experimental observable of jet quenching, the parton path length dependence and centre-of-massiii

energy dependence of jet energy loss which is extracted from spectrum energy shift, arepresented utilising simplified energy loss model.

iv

Contents

Abstractiii

1 Introduction

3

1.1

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

4

1.2

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

5

1.2.1

History of Heavy-Ion Experiments . . . . . . . . . . . . . . . . . . .

5

1.2.2

Space-time Evolution in Heavy-Ion Collisions . . . . . . . . . . . . .

6

1.2.3

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

8Hard Probes of the QGP . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

1.3.1

Mechanism of Parton Energy Loss in QCD Matter . . . . . . . . . .

11

1.3.2

Experimental Results of Jet Quenching . . . . . . . . . . . . . . . .

15

Thesis Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

1.3

1.4

2 Experimental Setup

21

2.1

A Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

2.2

The ALICE Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

2.2.1

V0 detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

2.2.2

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

27

2.2.3

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

28

2.2.4

Electromagnetic Calorimeters (EMCAL, DCAL and PHOS) . . . . .

30

3 ALICE Calorimeter Trigger Development

35

3.1

Overview of Trigger Generation . . . . . . . . . . . . . . . . . . . . . . . . .

35

3.2

L1 Trigger Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

3.3

Trigger Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42v

4 Analysis

47

4.1

Data Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

4.2

Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

4.3

Track Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

4.3.1

Tracking Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

4.3.2

Tracking Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

4.4

Jet Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

4.5

Underlying Event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

4.6

Jet Finding Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

4.7

Unfolding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

4.7.1

Test of Unfolding Performance . . . . . . . . . . . . . . . . . . . . .

62

4.7.2

Unfolded Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

5 Systematic Uncertainties
5.1

65

Unfolding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

5.1.1

pT Range of the Unfolded Jet Spectrum . . . . . . . . . . . . . . . .

65

5.1.2

pT Range of the Measured Jet Spectrum. . . . . . . . . . . . . . .

65

5.1.3

Unfolding Method . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

5.1.4

Unfolding Regularisation Parameter . . . . . . . . . . . . . . . . . .

66

5.1.5

MC Generator and Prior Selection . . . . . . . . . . . . . . . . . . .

67

5.2

Background Fluctuation δpT Estimation . . . . . . . . . . . . . . . . . . . .

68

5.3

Correction for the Elliptic Flow Bias . . . . . . . . . . . . . . . . . . . . . .

68

5.4

Tracking Eﬃciency and Resolution . . . . . . . . . . . . . . . . . . . . . . .

70

5.5

Summary of Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . .

71

6 Results and Discussion

75

6.1

Jet Suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

6.2

78

6.3

Comparison to Charged Hadrons . . . . . . . . . . . . . . . . . . . . . . . .
√Comparison to the Jet RAA in Pb-Pb Collisions at sNN = 2.76 TeV . . . .

6.4

Jet Energy Loss Toy Models . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

6.4.1

Path Length Dependence . . . . . . . . . . . . . . . . . . . . . . . .

84

6.4.2

Centre-of-Mass Energy Dependence . . . . . . . . . . . . . . . . . .

85

7 Summary

79

87
vi

List of Tables

1.1

Heavy ion facilities. [12] . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1

Summary of LHC runs operated until 2017 [31]. The peak luminosities are6measured at ATLAS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

2.2

Specification of ALICE electromagnetic calorimeters . . . . . . . . . . . . .

32

4.1

Dataset used for the analysis. . . . . . . . . . . . . . . . . . . . . . . . . . .

47

4.2

The average underlying event density. . . . . . . . . . . . . . . . . . . . . .

56

5.1

Systematic uncertainties for 0 - 10%. . . . . . . . . . . . . . . . . . . . . .

73

5.2

Systematic uncertainties for 30 - 50% . . . . . . . . . . . . . . . . . . . . . .

73

6.1

Geometrical parameters obtained from Glauber model. . . . . . . . . . . . .

77

6.2

Estimated value of spectrum fitting from three jet energy loss models. . . .

82

vii

List of Figures

1.1

Elementary particles of the Standard Model. [3] . . . . . . . . . . . . . . . .

1.2

The energy density divided by the T 4 , computed on the lattice with diﬀerent
number of flavours. The arrows show the limit for a perfect Bose gas. [2] . .

1.3

QCD Phase diagram.

5

Chemical freezeout points are displayed (see sec-tion 1.2.2 for definition of chemical freezeout). [13] . . . . . . . . . . . . . .
1.4

4

7

Light-cone diagram of longitudinal evolution of the relativistic heavy-ion collisions for with(right) and without(left) QGP cases. [14] . . . . . . . . . . .

8

1.5

Schematic view of the participant-Spectator model. [15] . . . . . . . . . . .

9

1.6

Example of hard probes traversing the medium found in high-energy heavyion collisions and the corresponding typical properties they can reveal aboutit. [18] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.7

10

Jet quenching in central nucleus-nucleus collision. Partons which producedin the initial hard scattering lost energy inside the matter according to its
properties (e.g. transport coeﬃcient q̂ or gluon density dN g /dy ). [18] . . .

1.8

Diagrams for collisional (left) and radiative (right) energy loss of quark with

1.9

energy E. [18] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
√Light quark radiative and collisional energy loss for sNN = 5.5 TeV con-11
12

ditions for L=5fm. The thick curves correspond to the running αs and thincurves to αs = 0.5, utilise the T-dependent Debye mass from the latticecalculations. [26] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

1.10 Single particle nuclear modification factor RAA for diﬀerent collision energies
up to 2.76 TeV . [27] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

1.11 (left) Single particle nuclear modification factor RAA (for Pb-Pb collisions at√√
sNN = 2.76 TeV ) and RpA (for p-Pb collisions at sNN = 5.02 TeV ) ofparticles at LHC energies. (right) for four particle species. [27] . . . . . . .
ix

16

1.12 Nuclear modification factor RAA of R = 0.2 jets in 0-10%(left) and 10√
30%(right) most central Pb-Pb collisions at sNN = 2.76 TeV , comparing
to the calculations from two kind of model (YaJEM and JEWEL). [28] . . .

17

1.13 Nuclear modification factor RpA of charged jets for R = 0.2(left) and R =√0.4(right) in sNN = 5.02 TeV p-Pb collisions. [29] . . . . . . . . . . . . . .

18

2.1

Schematic of the CERN accelerator complex. [30] . . . . . . . . . . . . . . .

21

2.2

Nucleon-nucleon integrated luminosity delivered to each experiment for all
LHC heavy-ion runs to date. [32] . . . . . . . . . . . . . . . . . . . . . . . .

23

2.3

Cut-away view of the ALICE detector. [33] . . . . . . . . . . . . . . . . . .

24

2.4

Position of the two VZERO detectors in the ALICE layout. [44] . . . . . . .

26

2.5

The segmentation of V0A and V0C. The two scintillator segments divided

2.6

by dashed line are read out by the same PMT. [44] . . . . . . . . . . . . . .
26√
Centrality percentile resolution versus centrality in Pb-Pb collisions at sNN =2.76 TeV for various ALICE detectors. [44] . . . . . . . . . . . . . . . . . .

26

Distribution of the sum of amplitudes in V0A and V0C in Pb-Pb collisions√
at sNN = 2.76 TeV . The red line shows the fit with a Glauber model. [44]

27

2.8

Layout of the ITS which constituted in SPD, SDD and SPD. [45] . . . . . .

28

2.9

Charged particle 1/pT resolution (= σ( pT )/p2T ) as a function of 1/pT for TPC√
and ITS in p-Pb collisions at sNN = 5.02 TeV . [33] . . . . . . . . . . . . .

29

2.10 Schematic view of the TPC field cage. [37] . . . . . . . . . . . . . . . . . . .

29

2.7

2.11 TPC dE /dx as a function of momentum with superimposed Bethe-Bloch√lines for various particle species, measured in Pb-Pb collisions at sNN =5.02 TeV . [33] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

2.12 Three calorimeters installed in ALICE at Run2 period: EMCal (upper side),
PHOS (bottom side, drawn in orange) and DCal (placed on both side of
PHOS in z-direction). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

2.13 ALICE event display taken in 2015 Pb-Pb run. [33] . . . . . . . . . . . . . .

33

2.14 Invariant mass spectrum of photon pairs with pT = 9-10 GeV/c measured in√
EMCAL in sNN = 2.76 TeV Pb-Pb collisions at centrality 0-20%. [33] . .

33

2.15 Invariant mass spectrum of photon pairs with pT = 4.0-4.2 GeV/c measured√
in PHOS in sNN = 2.76 TeV Pb-Pb collisions at centrality 0-10%. [33] . .

33

3.1

36

Summary Trigger Unit board (STU). . . . . . . . . . . . . . . . . . . . . . .
x

3.2

Data flow of L1 trigger production in ALICE calorimeters. In total 7 L1photon triggers (3 for PHOS, 2 for DCAL and 2 for EMCAL) and 4 L1-Jet
triggers (2 for DCAL and 2 for EMCAL) are generated. . . . . . . . . . . .

3.3

EMCAL geometry in terms of trigger production. Each TRU charged area
contains 96 FastORs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.4

Example of L1-Jet patches (= 2 × 2 or 4 × 4 jet-primitives) in DCAL+PHOS

side. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.7

38

Example of L1-photon patch (= 2×2 FastORs). Amplitudes of these patches
are calculated over TRU boundaries. . . . . . . . . . . . . . . . . . . . . . .

3.6

38

DCAL+PHOS geometry in terms of trigger production. Each PHOS (DCAL)TRU contains 112 (96) FastORs respectively. . . . . . . . . . . . . . . . . .

3.5

37

39
40

Schematic of event background calculation. Underlying event density estimated by median method are swapped between EMCAL STU and DCAL
STU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.8Correlation of underlying event densities estimated by DCAL and EMCAL
STUs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.9

41
42

Rejection factor of L1-photon triggers given by DCAL and EMCAL in 2015
Pb-Pb run. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

3.10 Rejection factor of L1-jet triggers given by DCAL and EMCAL in 2015 Pb-Pb
run. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

3.11 (top) pT spectra of clusters reconstructed in PHOS with minimum bias andPHOS L1-photon triggers at 0-5% Pb-Pb collisions. (bottom) The ratio ofthem. [33] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

3.12 (top) pT spectra of clusters reconstructed in PHOS with minimum bias andPHOS L1-photon triggers at 60-80% Pb-Pb collisions. (bottom) The ratio ofthem. [33] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.13 EMCAL and DCAL L1-photon trigger eﬃciency in 2015 Pb-Pb run.
3.14 EMCAL and DCAL L1-Jet trigger eﬃciency in 2015 Pb-Pb run.
4.1
4.2

. . .

45

. . . . .

45

Primary vertex position along beam direction. The events with |vz | < 10cm
are selected.

44. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

Event centrality distribution calculated with the V0M (= V0A + V0C) estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xi

48

4.3

Correlation between vzSPD - vzPRI and track multiplicity for four centrality
classes. The events with bad vertex reconstruction resolution are rejected.

49

4.4

Track φ distributions for two components of hybrid tracks. . . . . . . . . . .

50

4.5

Track η distributions for two components of hybrid tracks. . . . . . . . . . .

50

4.6

Hybrid track pT distributions for four centrality classes. . . . . . . . . . . .

50

4.7

Hybrid track φ distributions for three transverse momentum classes. . . . .

50

4.8

Transverse momentum resolution (σ(pT )/pT ) for two components of hybrid

4.9

tracks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

Transverse momentum resolution (σ(pT )/pT ) for four centrality classes. . .

51

4.10 Tracking eﬃciency of hybrid tracks estimated by PYTHIA (pp) and HIJING(Pb-Pb) events, propagated through GEANT simulation. . . . . . . . . . .

52

4.11 Ratio of tracking eﬃciency in Pb-Pb collisions to pp collisions. . . . . . . .

52

4.12 (top) Jet pT distributions after average background subtraction for diﬀerent
plead
requirements. (bottom) The ratio to inclusive jet spectrum which showsTleading track pT bias. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

4.13 Reconstructed jet φ distribution with prec
T,ch jet > 40 GeV/c . . . . . . . . . .

54

4.14 Reconstructed jet η distribution with prec
T,ch jet > 40 GeV/c .

54. . . . . . . . .

4.15 Correlation between average background density and charged track multiplicity. 55
4.16 Correlation between average background density and event centrality. . . .

55

4.17 δpT distributions for two RC selections and RC in track randomised event.

57

4.18 The width of δpT distributions for two RC selections and RC in track ran4.19

domised event as a function of charged particle multiplicity. . . . . . . . . .

58

Jet finding eﬃciency for diﬀerent pleadT59

requirements. . . . . . . . . . . . . .

4.20 Jet finding eﬃciency for diﬀerent event samples; PYTHIA MB and PYTHIA
jet-production. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

4.21 Response Matrix on background fluctuation in 0-10% centrality class. . . .

60

4.22 Response Matrix on detector eﬀects in 0-10% centrality class. . . . . . . . .

60

4.23 Combined Response Matrix for 0-10% centrality class. . . . . . . . . . . . .

61

4.24 Kinematic eﬃciency, the jet yield fraction lays inside the selected window of
combined response matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

4.25 Jet momentum resolution for 0-10% centrality class. . . . . . . . . . . . . .

61

4.26 Jet momentum resolution for 30-50% centrality class. . . . . . . . . . . . . .

61

xii

4.27 pT distributions used for unfolding performance check; (red) PYTHIA generatorlevel jets, (blue) PYTHIA reconstruction-level jets, (green) and reconstructionlevel spectrum after δpT smearing. . . . . . . . . . . . . . . . . . . . . . . .

62

4.28 (top) Unfolded jet spectrum and generator-level jet spectrum. (bottom) The
ratio of these spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

4.29 (top) Refolded jet spectrum and reconstruction-level spectrum after δpT smearing. (bottom) The ratio of these spectra. . . . . . . . . . . . . . . . . . . . .

63

4.30 The cross section of charged jet with R = 0.2 in Pb-Pb and pp collisions at√
sNN = 5.02 TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

5.1

Unfolded spectra for diﬀerent unfolded jet pT range selections(top), and theirdeviations from nominal selection(bottom), in 0 - 10% centrality class. . . .

5.2

Unfolded spectra for diﬀerent measured jet pT range selections(top), and theirdeviations from nominal selection(bottom), in 0 - 10% centrality class. . . .

5.3

. . .

. . . .

. . .

70

Unfolded spectra for diﬀerent average background densities due to flow bias(top),
and their deviations from nominal value(bottom), in 0 - 10% centrality class.

5.9

69

The azimuthal dependence with respect to the event leading track of averagebackground density deviation from the nominal (full azimuth) value.

5.8

68

Unfolded spectra for diﬀerent δpT definitions(top), and their deviations fromnominal value(bottom), in 0 - 10% centrality class. . . . . . . . . . . . . . .

5.7

67

Unfolded spectra for diﬀerent event generator selections(top), and their deviations from nominal selection(bottom), in 0 - 10% centrality class.

5.6

67

Unfolded spectra for diﬀerent s regularisation parameter selections(top), andtheir deviations from nominal selection(bottom), in 0 - 10% centrality class.

5.5

66

Unfolded spectra for diﬀerent unfolding method selections(top), and theirdeviation from nominal selection(bottom), in 0 - 10% centrality class.

5.4

66

70

Unfolded spectra for diﬀerent tracking eﬃciency estimation(top), and theirdeviations from nominal value(bottom), in 0 - 10% centrality class. . . . . .

71

5.10 Unfolded spectra for diﬀerent track momentum resolution(top), and theirdeviations from nominal value(bottom), in 0 - 10% centrality class. . . . . .
6.1

71

Charged jet spectra in Pb-Pb collisions after the normalisation by the number√of binary collisions. As a pp reference, the spectrum measured with s =5.02 TeV pp run and corresponding simulation result are shown. . . . . . .
xiii

76

6.2
6.3
6.4
6.5
6.6

Charged jet nuclear modification factors of R = 0.2 in Pb-Pb collisions at√
sNN = 5.02 TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77√
Comparison of nuclear modification factor between charged particles at sNN =√2.76 TeV and charged jets at sNN = 5.02 TeV . . . . . . . . . . . . . . . .
78√
Comparison of charged jet nuclear modification factor between sNN =√2.76 TeV and sNN = 5.02 TeV . . . . . . . . . . . . . . . . . . . . . . . .
79
Comparison of nuclear modification factor of jets with R = 0.4 measured by√√
ATLAS between sNN = 2.76 TeV and sNN = 5.02 TeV . [58] . . . . . .
(top) PYTHIA Charged jet spectrum given by PYTHIA. The black line isTsallis fitting result. (bottom) The ratio of data to fitting function. . . . . .

6.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

Comparison of charged jet nuclear modification with constant energy loss
model (black line). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.9

81

Comparison of spectrum fitting from three energy loss models, in 0-10 %centrality class.

6.8

80

83

Comparison of charged jet nuclear modification with fractional energy loss
model (black line). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

6.10 Comparison of charged jet nuclear modification with jet disappearance model(black line).

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

84

6.11 The sketch of heavy-ion collision in transverse plane. The average parton
path length and overlapped area are estimated by toy model calculation. . .

85

6.12 The estimated average parton path length as a function of collision impact
parameter b.

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

85

6.13 Average energy loss of charged jets as a function of estimated parton path
length, with fitting result by linear function. . . . . . . . . . . . . . . . . . .

86

6.14 Average energy loss of charged jets as a function of estimated parton path
length, with fitting result by quadratic function. . . . . . . . . . . . . . . .

86

6.15 Average energy loss as a function of charged multiplicity par unit transverse
area in 0 - 10% centrality class for three centre-of-mass energies.

xiv. . . . . .

86

Acknowledgments

First of all, I would like to express deepest gratitude to Tatsuya Chujo and Rachid Guernane,
for their continuous supports not only on research but also daily life (e.g. proposing theopportunities of presentation, thinking about the funding, starting up and organising new
helpful meeting for the study and so on). Ritsuya Hosokawa also has given a lot of honest
opinions as co-worker through the whole studies. Without their help, no doubt that myresearch could not never been achieved at all.
I would like to thank Yasuo Miake, Christophe Furget, Yves Schutz, Shinichi Esumi.
They give some ideas, comments and suggestions about the research with a clear perspective.
Their comments sometimes brought out my motivation a lots.
On the calorimeter trigger development and commisioning, I’m grateful for the members of ALICE-EMCAL and ALICE-PHOS groups, in particular, Olivier Raymond Bourrion, Jiro Fujita, Yuri Kharlov, Jiri Kral, Martin Poghosyan, Daiki Sekihata, and Jussi
Viinikainen. They kindly instructed the know-how on the detector operation and assisted
my trigger commissioning work.
On the jet measurement, I express my gratitude to AAF (ALICE Asian France Collaboration) members, Oliver Busch, Tatsuya Chujo, Rachid Guernane, Yaxian Mao, Hua Pei,
Hadi Hassan, Ritsuya Hosokawa and Byungchul Kim. Thanks to their steady advises andassistances on the analysis, the research was able to proceed smoothly.
Many thanks to the colleagues who spent times together during the stay at CERN,
Hikari Murakami, Tsubasa Okubo, Yuko Sekiguchi, Daiki Sekihata, Kohei Terasaki, Satoshi
Yano and Daisuke Watanabe, for their friendship and meaningful discussions. I also thank
Shingo Sakai, Yosuke Watanabe and all members of Tsukuba and Grenoble groups for theirencouraging, discussing and advices.
I could never restarted the academic life and continued the research without the understanding and encouragement to my way of life from my parents, sister and an old friend.
Finally I wish to express sincere appreciation to them.
1Chapter 1

Introduction

Particle physics aims at understanding the fundamental constituents of nature and their interactions. At the present time, the constituents are classified into three categories: hadrons,
leptons and gauge bosons. Hadrons are objects which are subject to strong and weak interaction, while leptons interplay through weak interaction. When these particles carryelectro-magnetic charge, they are also aﬀected by the electro-magnetic interaction. The
gauge bosons behave as a mediator of these forces.
There are in total twelve types of particles in the lepton family: electron, muon, tau,
the respective neutrinos, and their anti-particles. Conversely, a large number of hadron
species have been found, which can be classified into two types: mesons which are madeup of quark and anti-quark pairs, and baryons which consist of three (anti-)quarks. There
are twelve types of particles in the quark family: up, charm, top (with electric charge 2/3),
down, strange, bottom (with electric charge −1/3) and their anti-particles.
The Standard Model (SM) describes the interaction among these elementary particles,
including strong, weak and electro-magnetic interactions [1, 2]. Each interaction has its
own mediator, gluons for strong interactions, Z 0 and W ± bosons for weak interactions
and the photon for electro-magnetic interactions. The main diﬀerence between electromagnetic and weak interaction is the range of the interaction which is related to the massof the its mediators: photon (mass-less), Z 0 and W ± bosons (91 GeV/c2 and 80 GeV/c2
respectively). Due to the large masses of Z 0 and W ± , the range of the weak interaction islimited, while long-range electro-magnetic interaction is allowed. All elementary particlesof the SM are summarised in Fig. 1.1.
Quantum Chromodynamics (QCD), the theory of strong interaction, deals with the interactions between quarks and gluons [4]. QCD has two particular features: the quark
confinement inside hadrons (∼ 1 fm) and the asymptotic freedom at large momentum transfer scale on short distance [5, 6, 7]. Due to asymptotic freedom, at high temperature,quarks and gluons become weakly coupled, freed from nucleons, forming a new state ofmatter called the Quark-Gluon Plasma (QGP) [8].
34Chapter 1. Introduction

Fig 1.1: Elementary particles of the Standard Model. [3]1.1

The Quark Gluon Plasma

High-energy heavy-ion physics intends to study the QGP phase of QCD at finite temperature. Lattice QCD calculations predict that a phase transition from normal nuclear matterto a QGP should occurs when energy density exceed the critical threshold of εc ∼ 0.18 -0.5 GeV /fm3 (Tc = 154 ± 9 MeV ) [9, 10, 11]. Experimentally, by colliding two heavy nuclei
at ultra-relativistic energies, one expects to form a hot and dense deconfined medium andstudy its collective (colour) dynamics.
According to QCD, the potential between a q q̄ pair is phenomenologically given by,
Vqq̄ = −

a(r)
r

+ Kr

(1.1)

where r is the distance between the two quarks, a(r) ∝ 1/ ln(1/r), and K is the string tensionof the quark and anti-quark pair. The first term of Eq. 1.1 is the colour Coulomb potential
and the second term is the linear confining potential which is a characteristic feature of
QCD. The equation encodes quark confinement: the inter-quark potential increases linearlywith the distance.
On the one hand, the energy needed to separate the two quarks grows with the distance
between them. At large distance, the linear term dominates and when the potential energy

Section 1.2. Relativistic Heavy Ion Collisions

5

Fig 1.2: The energy density divided by the T 4 , computed on the lattice with diﬀerent
number of flavours. The arrows show the limit for a perfect Bose gas. [2]is greater than twice the quarks, a new q q̄ pair is created. Therefore, deconfined single
quarks cannot be observed which is known as “quark confinement”. On the other hand,
Lattice QCD calculations predict that quarks and gluons are deconfined at high energy
density or temperature.
Based on Lattice QCD calculations, Fig. 1.2 shows that the energy density divided
by T 4 undergo a rapid crossover around the critical temperature, Tc , accompanied by anincrease of the eﬀective number of active degrees of freedom, i.e. deconfinement, and reaches
a plateau of only ∼ 70 % of the ideal limit of a Stefan-Boltzmann (SB) gas of light quarks
and gluons. Not reaching the SB limit indicates that the QGP is weakly coupled withpersisting non perturbative eﬀects.

1.2

Relativistic Heavy Ion Collisions

1.2.1

History of Heavy-Ion Experiments

The QCD phase diagram can be explored in the laboratory with high-energy nuclear collisions. The pioneering advances in relativistic heavy-ion physics were achieved at fixed-target
accelerators, starting in the early 1970’s at the Bevalac (Berkeley), followed by the AGS(BNL) and SPS (CERN). The highest centre-of-mass energy per nucleon achieved in these√experiments was sNN = 17 GeV .

6

Chapter 1. Introduction√

MachineLocationIon beam

MaximumsNN

Start of experimentBevalac

LBNL, Berkeley

up to U

2 GeV

1974

AGS

BNL, Brookhavenup to 197 Au

5 GeV

1986

SPS

CERN, Geneva

16 O,32 S,208 Pb

17 GeV

1986

RHIC

BNL, Brookhaven

197 Au,64 Cu

200 GeV

2000-present

LHC

CERN, Geneva

208 Pb

5.02 TeV

2009-present

Tab 1.1: Heavy ion facilities. [12]Later on, benefiting from the technological breakthrough of new colliding beam accelerators, far higher centre-of-mass energy per nucleon could be reached. At the turn ofthe century, the Relativistic Heavy Ion Collider (RHIC, BNL) starts to deliver Au+Au√
collisions up to sNN = 200 GeV , and lately the Large Hadron Collider (LHC, CERN)√
is capable to accelerate Pb beams up to sNN = 5.02 TeV . The main features of theseaccelerators are listed in Tab. 1.1. Fig. 1.3 summarises QCD phase diagram exploration at
various accelerators.
The increase in the centre-of-mass energy of the colliding system enables to significantly
enlarge the volume, lifetime and energy density of the formed medium, oﬀering unprecedented conditions for precision measurements of the QGP parameters (i.e. viscosity, transport coeﬃcients and so on).
1.2.2

Space-time Evolution in Heavy-Ion Collisions

A simplistic view of the system evolution could be described as a chronological sequenceof events starting from the overlapping nuclei initial time τ : (see light-cone diagram of
longitudinal evolution of the relativistic heavy-ion collisions in Fig. 1.4).
1. Until interaction ( τ < 0 )Before collision, the incoming nuclei are accelerated up to a velocity close to the speedof light. The Lorentz contracted nuclei thus have a pancake shape (∼ 1 fm thickness).
2. Nuclear overlap and Pre-equilibrium ( 0 < τ < τ0 )After collision, the system undergoes a pre-equilibrium phase with multiple partonic

Section 1.2. Relativistic Heavy Ion Collisions

7

Fig 1.3: QCD Phase diagram. Chemical freezeout points are displayed (see section 1.2.2
for definition of chemical freezeout). [13]scatterings driving towards the formation of a thermalised partonic medium. During
the early pre-equilibrium phase, hard partons (jets and heavy flavours) are produced
via large momentum transfer scatterings. The time until thermalisation, τ0 is lessthan 1 fm/c .
3. Hydrodynamic evolution ( τ0 < τ < τf )When thermalisation is realised, the equilibrated partonic medium reaches a hightemperature and energy density. The QGP is produced: the quarks and gluons inside
the medium show collective behaviour, freed from confinement. Subsequently, theexpanding system begins to cool down.
4. Freezeout ( τf < τ )The QGP keeps expanding and cooling down until hadronisation occurs at τf with subsequent “chemical freezeout”(particle species fixing) and “kinetic freezeout”(particle
momentum fixing).

8

Chapter 1. Introduction

Fig 1.4: Light-cone diagram of longitudinal evolution of the relativistic heavy-ion collisions
for with(right) and without(left) QGP cases. [14]Diﬀerent global observables convey information about these diﬀerent stages. Jets, whichmeasurement is the purpose of this work, are hard probes produced at very early stages of
the collision and thus potentially carry information about the whole system evolution (seesection 1.3).

1.2.3

Geometry of Heavy-Ion Collisions

In relativistic heavy-ion collisions, the collision geometry can be defined within the participantspectator model [16, 17]. Fig. 1.5 shows a schematic view of a collision between nuclei. The
impact parameter b, defined as the distance between the centre of nuclei, characterises thecentrality of collision (for an experimental determination, see section 2.2.1). The nucleons
taking part in the primary collisions are called “participants” while remainders are called“spectators”.

Section 1.3. Hard Probes of the QGP

9

Fig 1.5: Schematic view of the participant-Spectator model. [15]The spectators keep their longitudinal velocity and mostly travel along the beams direction, while the secondary particles emitted from participant interactions are mostly observed
around mid-rapidity. Once the impact parameter of the collision is determined, the Glauber
Model provides the number of participant nucleons (Npart ) and number of nucleon-nucleon
collisions (Ncoll ) for a given impact parameter. These quantities can be calculated (analytically or numerically) under the following assumptions:• Collisions of two nuclei are expressed in terms of the individual interactions of theconstituent nucleons.

• At high energies, nucleons travel on straight line trajectories and are essentially undeflected.

1.3

Hard Probes of the QGP

Anyone who intends to characterise the QCD matter in laboratory will inevitably confront
the challenge of its short lifetime ( ∼ 10 fm/c ) and tiny size ( ! 20 fm ). One must thensimply rule out the usage of external probes to fall back in “self-generated” probes. Amongwhich high-pT QCD processes, the so-called “hard probes”, have demonstrated excellent
proficiency. Such hard probes, especially partons with large transverse momentum
1. are produced by parton scatterings with large momentum transfer (Q2 ), hence, arelinked with QCD degrees of freedom,

10

Chapter 1. Introduction

Fig 1.6: Example of hard probes traversing the medium found in high-energy heavy-ion
collisions and the corresponding typical properties they can reveal about it. [18]2. are generated at very early stage of the collision, τ ≈ 1/pT ≤ 0.1fm/c, and are
therefore aﬀected by entire medium evolution,

3. and have measured production cross sections and/or precise estimation within perturbative QCD (pQCD).
Jets are a flagship hard probe in nuclear collisions (c.f. Fig. 1.6). An elastic or inelastic
scattering of two partons from incoming nucleus produces two or more partons in the final
state. The two outgoing partons carry a large virtuality Q which decreases by subsequentgluon-radiations and/or splittings into quark-antiquark pairs. The QCD radiation probabilities given by the DGLAP equations [19] conduct parton branching growth. At thisstage, the generated partons fragment into a lot of final-state hadrons non-perturbatively.
In general these hadrons are observed as a collimated spray of hadrons directed close toinitial parton, called as “jet”.
One of the most remarkable signatures of QGP formation observed both at RHIC [20]and LHC [21] is “jet quenching”: the attenuation of the jet yields in heavy-ion collisions compared to pp (corrected for geometry) or disappearance of back-to-back jets. Jet quenchingSection 1.3. Hard Probes of the QGP

11

Fig 1.7: Jet quenching in central nucleus-nucleus collision. Partons which produced in
the initial hard scattering lost energy inside the matter according to its properties (e.g.
transport coeﬃcient q̂ or gluon density dN g /dy ). [18]can be interpreted as energy loss of high-pT partons in the hot and dense matter producedin the reaction as illustrated in Fig. 1.7.
Some fundamental information about the medium properties are extracted from theenergy loss, ∆E. In general, the lost energy is aﬀected both by the particle characteristics(energy and mass) and by the properties of the matter (particle-medium coupling α, medium
temperature T , particle path length in the medium L and so on).
1.3.1

Mechanism of Parton Energy Loss in QCD Matter

Energetic partons traversing the QGP medium lose energy via QCD processes which canbe categorised as eliciting collisional or radiative energy loss [18]. Energy loss mechanism
is conjectured to be responsible of the strong jet quenching observed in central heavy-ion
collisions. The relative strengths of radiative and collisional energy loss contributions tojet quenching, and more generally the detailed mechanisms at work in the jet-medium
interaction are still a topic of intense theoretical developments and can be studied by themeasurement of the jet nuclear modification factor which is the subject of the thesis.

12

Chapter 1. Introduction

Fig 1.8: Diagrams for collisional (left) and radiative (right) energy loss of quark with energy
E. [18]Collisional Energy Loss
The collisional energy loss originates from the parton elastic scatterings with the medium
constituents (diagram in Fig. 1.8 left). The average loss of energy per scattering is given by!

1 scat∆Ecoll

"=1 # tmax

σT

mD 2

t

dσ
dt

dt

(1.2)

where dσ /dt is the cross section of the incoming parton-medium interaction, t is the cor1/2

responding momentum transfer and mD ∼ αs

T is the Debye mass which characterises

the lowest momentum exchange with the medium. The collisional energy loss due to elastic
scatterings of a parton with energy E inside QGP of temperature T was originally estimatedby Bjorken and Braaten-Thoma [22] and later on augmented (including running coupling,
finite energy kinematics, and quark mass eﬀects) by several authors [23, 24, 25]. Using
Eq. 1.2 with integral limits of the momentum-transfer as
1. the QGP Debye mass squared, tmin = mD 2 (T ) ≃ 4παs T 2 (1 + Nf /6)
where Nf is the number of flavours,

2. and tmax = s ≃ E T ,and taking the primary contribution of the t-diﬀerential parton-parton elastic cross section
to be:dσdt≈ Ci

4παs (t)t2, where αs (t) =12π(33 − 2nf ) ln(t/ΛQCD 2 )(1.3)

Section 1.3. Hard Probes of the QGP

13

where Ci = 9/4, 1, 4/9 are the colour factors for gg, gq, and qq scatterings respectively,
finally, the collisional energy loss per unit length has the following form for:
1. Light quarks and gluons$$dEcoll $$−dl $$2. Heavy quarks$$$$
dEcoll $dEcoll $
$
$
−
=−
dl $$
dl $$
Q

=

⎛

1
4

CR αs (E T ) mD 2 ln ⎝

2

⎡

q,g

−
q,g

9

ET
mD 2

⎞
⎠

(1.4)

⎛

CR π T 2 ⎣αs (M 2 ) αs (E T ) ln ⎝

ET
M2

⎞⎤

⎠⎦ .

(1.5)

with CR = 4/3 (3) being the quark (gluon) colour charge. The amount of ∆Ecoll is linearwith the medium thickness, and it depends only logarithmically on the initial parton energy(c.f. Fig. 1.9).
Radiative Energy Loss
Radiative energy loss through inelastic scatterings within the medium (diagram in Fig. 1.8
right), can be determined using the spectrum of single or double diﬀerential gluon/photon
2 ):bremsstrahlung (ω dIrad /dω or ω d 2 Irad /dω dk⊥

1 scat∆Erad

1 scat
∆Erad

=
=

# E

ω

dIrad
dω

# E # k max⊥

dω , orωd 2 Irad 2dω dk⊥ 2(1.6)
dω dk⊥ 2 .

(1.7)

where ω and k⊥ are the energy and transverse momentum of the radiated gluon/photon
respectively.
Considering incoherent scatterings, the total energy loss is simply given by ∆E tot =N · ∆E 1 scat , where N = L/λ is the opacity and λ = 1/(ρ σ) is the mean-free-path of theparton in the medium. Thus, the stopping power, the lost energy in unit length, is expressed
as:
−

dE
dl

=

!

∆E tot
L

"

,

(1.8)

14

Chapter 1. Introduction√
Fig 1.9: Light quark radiative and collisional energy loss for sNN = 5.5 TeV conditions
for L=5fm. The thick curves correspond to the running αs and thin curves to αs = 0.5,
utilise the T-dependent Debye mass from the lattice calculations. [26]!
"which reduces to −dE /dl = ∆E 1 scat /λ for incoherent scatterings.

A parton traversing a QGP loses energy by medium induced multiple gluon emission.

The radiated gluon spectrum, ωdI(ω, l) /dω , has been computed under various approximations. The starting point is the QCD radiation probabilities given by DGLAP splitting
functions (Pq→gg ): ωdI(ω) /dω ∝ Pq→gg (ω/E), modified to take into account the enhanced

medium induced radiation. All medium modifications are often encoded into the “transport coeﬃcient” parameter, q̂ ≡ mD 2 /λ, defined as the average traverse momentum squared

gained by the incoming parton per unit distance λ. For thin (thick) media, one deals with
the Bethe-Heitler (Landau-Pomeranchuk-Migdal) gluon bremsstrahlung spectrum. In the
LPM case, one further diﬀerentiates between the soft and hard gluon emission cases withrespect to the characteristic gluon radiation energy ωc = 1/2 q̂ L2 . Making use of Eq. 1.6
and Eq. 1.7, the basic QCD radiative energy loss formulas read
1. Bethe-Heitler (BH) regime

ω

dIrad
dω

≈ αs CR

q̂ L2
ω

⎛

BH ≈ α C q̂ L2 ln ⎝⇒ ∆Erads R

E
mD 2 L⎞⎠(1.9)

Section 1.3. Hard Probes of the QGP

15

Fig 1.10: Single particle nuclear modification factor RAA for diﬀerent collision energies up
to 2.76 TeV . [27]2. Landau-Pomeranchuk-Migdal (LPM) regime

ω

dIrad
dω

≈

⎧
0
⎨αs CR q̂ L2 /ω
⎩α C q̂ L2 /ω
s R

LPM ≈
⇒ ∆Erad⎧⎨αs CR q̂L2

(ω < ωc )1⎩α C q̂L2 ln E/(q̂ L2 )2s R(1.10)(ω > ωc )One can note that the main diﬀerences between the energy loss in a QCD and QED
plasma are the colour factors (CR ) and the extra logarithmic dependence of ∆Erad on theenergy E of the traversing particle.
1.3.2

Experimental Results of Jet Quenching

The eﬀect of energy loss can be quantified through the nuclear modification factor (RAA )as mentioned above, which is defined as the ratio of single (identified) particle or jet yields
per event in heavy-ion collisions (dN AA ) over those in pp (dN pp ), as follows:

RAA =dN AA /dpT
dN AA /dpT=.
⟨Ncoll ⟩ dN pp /dpT
⟨TAA ⟩ dσ pp /dpT(1.11)

16

Chapter 1. Introduction

Fig 1.11: (left) Single particle nuclear modification factor RAA (for Pb-Pb collisions at√√
sNN = 2.76 TeV ) and RpA (for p-Pb collisions at sNN = 5.02 TeV ) of particles at LHC
energies. (right) for four particle species. [27]

NN is the average number⟨ TAA ⟩ is the nuclear overlap function, and ⟨ Ncoll ⟩ = ⟨ TAA ⟩ × σinelof nucleon-nucleon collisions occurring in heavy-ion collisions. ⟨ Ncoll ⟩ is calculated with a
Glauber model consisting of a detailed description of the nuclear collision geometry (for areview see [17]).
No in-medium modification results in a RAA equal to unity. RAA less than unity could
suggest a reduction of production rate, energy loss of the particles or its mother particle.
Additionally for jets, it suggests the change of the jet structure due to jet(parton)-medium
interactions. RAA amplitude and overall trend as a function of transverse momentum, centrality, rapidity, particle specie (heavy or light quarks) and collision energy, can reveal theunderlying mechanism at work (shadowing, Cronin eﬀect, medium back-reaction or absorption, interplay of quark/gluon quenching, and parton spectra), but with the caveat thatseveral eﬀects might balance out each other resulting in a null net eﬀect. For instance, the√increase of sNN should result in both a hardening of the spectrum shape and a larger
energy loss which compensate each other, the arising RAA being unmodified.
The charged particle nuclear modification factors measured at SPS, RHIC and LHC√
are shown in Fig. 1.10. The LHC results at sNN = 2.76 TeV show a slightly stronger

Section 1.3. Hard Probes of the QGP

17

Fig 1.12: Nuclear modification factor RAA of R = 0.2 jets in 0-10%(left) and 10-30%(right)√
most central Pb-Pb collisions at sNN = 2.76 TeV , comparing to the calculations from twokind of model (YaJEM and JEWEL). [28]suppression than those from RHIC (Au-Au,√

sNN = 200 GeV ) and SPS (Pb-Pb,

√

sNN =

17.3 GeV ); the largest measured suppression, in the 6 to 9 GeV/c in pT range, is a factor of
about 7 at the LHC, while at RHIC only a factor of 5 was observed. A novelty observed at
the LHC is that with increasing pT the suppression becomes smaller: the RAA suppression
is followed by a rising trend from pT ∼ 6 GeV/c , but it is still smaller than unity at about
100 GeV/c . This demonstrates that even very energetic partons of highest pT suﬀer considerable energy loss when interacting with the medium.
The measurements of the RAA of charged hadrons and electro-weak bosons is shown in√
Fig. 1.11 on the left panel; the charged-particle RAA in central Pb-Pb collisions at sNN =2.76 TeV is compared with the RAA of W , Z (from leptonic decays) and (isolated) photons√
at the same energy, as well as the RpA from p-Pb collisions at sNN = 5.02 TeV . Althoughhadron production is strongly suppressed, isolated photons, W and Z bosons which do notcarry colour charge are not suppressed. This observation is compatible with the hypothesisthat the origin of the suppression of charged hadrons are final-state strong interactions withthe created hot and dense medium. Additionally, RpA , meant to distinguish initial fromfinal-state eﬀects support the same conclusion. The RpA ALICE measurement at high pT is

18

Chapter 1. Introduction

Fig 1.13: Nuclear modification factor RpA of charged jets for R = 0.2(left) and R =√0.4(right) in sNN = 5.02 TeV p-Pb collisions. [29]comparable with unity. It shows no indication of hadron production modification due tonuclear matter and is consistent with binary collision scaling. In conclusion, the global view
tends to confirm that the observed suppression of the high-pT hadron production in central
Pb-Pb collisions is not imputable to initial-state eﬀect, but instead to the presence of dense
quark-gluon matter.

√
The jet nuclear modification factor measured in Pb-Pb collisions at sNN = 2.76 TeV√
and p-Pb collisions at sNN = 5.02 TeV are shown in Fig. 1.12 and Fig. 1.13 respectively.
The jet production similarly shows strong suppression in central Pb-Pb collisions (a factor
of about 3). Conversely in p-Pb collisions the jet RpA is close to one. This support the
hypothesis of parton-medium interactions. The jet suppression in mid-central (10 - 30%)
collisions is slightly lower than in the most central collisions. The observed suppressions arein fair agreement with predictions from jet quenching models.

1.4

Thesis Motivation

As mentioned in previous section, the strong suppression of single particles/jets observedin the central AA collisions is interpreted as in terms of parton energy loss through partonmedium interaction. However, studying jet quenching via single particle measurements
biases the jet population towards surface emission, and furthermore limits the access to theSection 1.4. Thesis Motivation

19

full dynamics of the energy loss mechanism. Fully reconstructed jets copiously produced at
the LHC thanks to the increase of centre-of-mass energy, are instead expected to give better
access to the initial parton kinematics (direct comparison to theory made easier), mitigate
fragmentation bias by capturing the jet substructure in-medium modifications (provided
that the jet radius is taken large enough). Besides the fully reconstructed jet production
cross section measurements, this thesis presents a phenomenological study of jet quenchingin AA collisions at highest-ever centre of mass energy of 5.02 TeV .

Chapter 2
2.1

Experimental Setup

A Large Hadron Collider

The Large Hadron Collider (LHC) is a two-ring-superconducting hadron accelerator constructed at CERN. It is installed in the existing 26.7 km circular tunnel constructed between
1984 and 1989 for the CERN Large Electron-Positron Collider (LEP). Many superconducting magnets are used to bend or focus the beams around the circumference of the LHC,e.g. 1232 of 15 metre length dipole magnets and 392 of 5 - 7 metres quadrupole magnets.

Fig 2.1: Schematic of the CERN accelerator complex. [30]

21

22

Chapter 2. Experimental Setup

Year
2009

Collision system
pp

2010

pp
Pb-Pb
pp

2011

2012
2013
2015

2016
2017

Pb-Pb
pp
p-Pb
pp
p-Pb
pp
Pb-Pb
pp
p-Pb
pp
Xe-Xe

√

s or
0.9
2.36
7
2.76
2.76
7
2.76
8
5.02
2.76
5.02
5.02
13
5.02
13
8.16
5.02
13
5.44

√

sNN ( TeV )Peak Lumi. (cm−2 s−1 )−−0.21 × 1033
0.03 × 1027−
3.7 × 1033
0.51 × 1027
7.7 × 1033−
0.32 × 1033
5.0 × 1033
2.7 × 1027
13.8 × 1033−
20.6 × 1033−

Tab 2.1: Summary of LHC runs operated until 2017 [31]. The peak luminosities are measured at ATLAS.

Almost all these superconducting magnets adopt the “two-in-one” or “twin-bore” design,
one for clockwise beam (Beam 1) and the other for anti-clockwise beam (Beam 2).
The CERN accelerator complex is shown in Fig. 2.1. The particle beams are transferredfrom one machine to another with increasing energy before their injection in the LHC(Fig. 2.1). The first accelerator of the chain is the Linac 2 injector for proton beams (up to
50 MeV/c ) or the Linac 3 injector for heavy-ion beams (up to 160 MeV/c ), followed by theProton Synchrotron (PS) and the Super Proton Synchrotron (SPS) (up to 450 GeV/c ).
Subsequently, the beams are divided and supplied to two transfer lines, one for Beam1 andthe other for Beam 2, and are finally fed in the LHC rings.
√
The LHC was designed to deliver collisions with centre-of-mass energy of s = 14 TeV√
for proton-proton collisions, and sNN = 5.5 TeV for Pb-Pb ion collisions. The design
luminosity of the LHC is 1034 cm−2 s−1 for pp collisions and 1027 cm−2 s−1 for Pb-Pb collisions.

Section 2.2. The ALICE Experiment23

Fig 2.2: Nucleon-nucleon integrated luminosity delivered to each experiment for all LHC
heavy-ion runs to date. [32]

LHC reached the design luminosity for Pb-Pb collisions (in 2015) and pp collisions (in 2016);
and in 2017, it exceeded its design pp luminosity by a factor 2. The LHC energy ramp up
is still on-going although the bending magnet training was limited so far to 6.5 TeV /beamin pp.
The LHC started regular operation from 2009 and since then, various collision systems
and energies were provided (see Tab. 2.1). Detectors are installed in experimental caverns
at the 4 collision points: the ATLAS (at Point 1), CMS (at Point 5), ALICE (Point 2)
and LHCb (Point 8). Fig. 2.2 summarises the integrated luminosity delivered by the LHC
to each experiment during Pb-Pb and p-Pb Run1 and Run2 (still on-going at the time ofwriting this document).

24

Chapter 2. Experimental Setup

Fig 2.3: Cut-away view of the ALICE detector. [33]2.2

The ALICE Experiment

The ALICE experiment is the only LHC experiment dedicated to the study of QGP, andconsequently optimised for heavy-ion collisions. ALICE started to record pp collision data√
in 2009 at the LHC injection energy ( s = 900 GeV ). The first high-energy pp and Pb-Pb√√
runs at respectively s = 7 TeV and sNN = 2.76 TeV successfully took place in 2010.
At the end of 2011, a second Pb-Pb run of much higher statistics followed. In 2013, ALICE
collected data of asymmetric p-Pb collisions. After the first LHC long shutdown period(LS1), the second LHC run started in 2015 with increased beam energies.
ALICE is a 10,000-ton detector, 26 m long, 16 m high, and 16 m wide. The detector isdesigned to measure the particles produced in the collisions which take place at its centre,
so that the evolution of the system produced during these collisions can be reconstructed
and studied. To achieve this goal, many diﬀerent sub-detectors providing diﬀerent pieces
of information were installed. ALICE consists of 19 sub-detectors, which use diﬀerent
techniques to measure particles. The ALICE detector layout is given in Fig. 2.3.
To access the collision centrality Zero Degree Calorimeters (ZDC) [34] which are locatedabout 110 m away on both sides of the ALICE interaction point, measure the number ofSection 2.2. The ALICE Experiment25

spectators. FMD, V0 and T0 detectors [35] measure the signal from participants and their
spatial distribution. Furthermore, T0 supplies high precision measurement of interaction
time used for fast timing and triggering.
Charged particle reconstruction is provided by data from a set of cylindrical tracking
detectors called “central barrel detectors” (from inside to outside: ITS [36], TPC [37] andTRD [38]) which sample the particle trajectories into many hits. These tracking detectors
are immersed in a longitudinal magnetic field (Bmax = 0.5 T ), produced by the former L3experiment solenoid magnet, which bends particle trajectories to measure their momentum.
The particle identification (PID) is provided by combining momentum measurementwith dE /dx measurement given by ITS and TPC or velocity of charged particles measured
with TOF [39]. TOF measures time of flight traveling from the primary vertex with a
precision of a few tens of ps. Additionally, particle-specific features are exploited for PID;
the HMPID [40] measures the Cherenkov light patterns generated by fast particles extending
the PID toward high pT and the TRD measures transition radiation which is emitted whenfast and lightweight particle (mainly electron) crosses boundary of materials of diﬀerent
dielectric constants, enabling the discrimination between electrons and pions.
Electrons and photons are measured using the ALICE electromagnetic calorimeters:
EMCAL [41], DCAL [42], and PHOS [43] (PHOS is a homogeneous lead-tungsten crystal
calorimeter, EMCAL and DCAL are lead/scintillator sampling calorimeters). PHOS performs high energy- and position-resolution measurement in a limited area, while EMCAL
and DCAL have larger acceptance suitable for jet measurement but with worse energy
resolution.
In the following, a further description of the detectors used in the analysis presented inthis thesis will be given.
2.2.1

V0 detector

The V0 detector is a forward detector consisting of two arrays of 32 scintillating counters,
called V0A and V0C, which sits on each side of the ALICE interaction point. The V0A is
located 330 cm away from the primary vertex while the V0C is mounted at 90 cm in the
opposite direction. They cover the pseudo-rapidity regions of 2.8 < η < 5.1 (V0A) and−3.7 < η < −1.7 (V0C) as shown in Fig. 2.4.
V0 is made by plastic scintillator BC404 (2.5 and 2.0 cm thickness for V0A and V0C,

26

Chapter 2. Experimental Setup

Fig 2.4: Position of the two VZERO detectors in the ALICE layout. [44]Fig 2.5: The segmentation of V0A and
V0C. The two scintillator segments divided
by dashed line are read out by the same
PMT. [44]respectively). The scintillating light is collected by photomultipliers (PMT) through WaveLength Shifting (WLS) fibres of 1 mm in diameter.
The V0A array has 32 individual counters arranged in 4 rings and 8 sectors of 45◦ (seeFig. 2.5). The V0C array has 48 individual counters distributed following two inner ringsof 8 counters and two outer rings of 16 counters. The latter are paired to build one singlecell.

Fig 2.6: Centrality percentile resolution versus centrality in Pb-Pb collisions at
2.76 TeV for various ALICE detectors. [44]

√

sNN =

Section 2.2. The ALICE Experiment27

Fig 2.7: Distribution of the sum of amplitudes in V0A and V0C in Pb-Pb collisions at√
sNN = 2.76 TeV . The red line shows the fit with a Glauber model. [44]The V0 detector is dedicated to the:• discrimination of beam-gas interactions by correlating V0A and V0C timing,• estimation of collision centrality and event plane by V0A and V0C amplitudes,• measurement of the charged particle multiplicity density.
In particular, a high resolution collision centrality estimation is of prime importance forall heavy-ion measurements which include system size dependence. V0 detector allows forthe best centrality resolution as can be seen in Fig. 2.6. The centrality is estimated from a
Glauber based fitting of the charge sum distribution of the two V0 detectors (see Fig. 2.7).
2.2.2

Inner Tracking System (ITS)ITS consists of two layers of Silicon Pixel Detectors (SPD), two layers of Silicon Drift Detectors (SDD) and two layers of Silicon Strip Detectors (SSD) from inside out (see Fig. 2.8). It
is the most inner detector among central barrel detectors, covering central pseudo-rapidity
range of |η| < 0.9 and distance from the beam pipe from r = 4 cm up to r = 44 cm (4 cm

and 7 cm for SPD, 15 cm and 24 cm for SDD, 39 cm and 44 cm for SSD). The four inner
layers (SPD and SDD) provide a 2-dimensional tracking to separate tracks in a large track
density environment up to 90 tracks/cm2 , while 1-dimensional read-out is suﬃcient for the28

Chapter 2. Experimental Setup

87.2 cm

SPD
SDD
SSD
y
x
z

Fig 2.8: Layout of the ITS which constituted in SPD, SDD and SPD. [45]two outermost layers (SSD) due to smaller track densities. Outer four layers (SDD andSSD) provide an analog read-out to measure the energy loss (dE/dx) of particles traversingthem.
ITS is used to:• measure secondary vertices from weak decays of strange, charm and beauty particles,• improve tracking of charged particles (especially at low-pT ) in combination with otherdetectors (TPC, TRD),• reconstruct primary vertex position with high precision (< 100 µm ).
The charged particle pT resolution as function of pT (Fig. 2.9) shows that a primaryvertex constraint and/or the incorporation of ITS space point in the tracking drastically
improve tracking resolution compared to TPC only tracks, particularly at high-pT .
2.2.3

Time Projection Chamber (TPC)

TPC is the largest tracking device of the ALICE central barrel (and moreover, the world’s
largest TPC) with a cylindrical shape of 88 m3 volume covering distance from the beam
pipe from r = 85 cm to r = 250 cm and pseudo-rapidity range of |η| < 0.9 (corresponding
to 500 cm in the beam direction).

T

m1/p ((GeV/c) -1)

Section 2.2. The ALICE Experiment

0.016

29

p-Pb, sNN = 5.02 TeV, | d |<0.8
TPC standalone tracks

0.014

TPC tracks constrained to vertex
TPC+ITS combined tracks

0.012

TPC+ITS constrained to vertex

18/11/2013

0.01
0.008
0.006
0.004
0.002
0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1
-1

ALI-PERF-65250

1/pT ((GeV/c) )Fig 2.9: Charged particle 1/pT resolution (= σ( pT )/p2T ) as a function of 1/pT for TPC and√
ITS in p-Pb collisions at sNN = 5.02 TeV . [33]

The TPC geometry is shown in Fig. 2.10. It is divided into two drift regions by acentral electrode, filled with an Ar-CO2 (or N e-CO2 ) gas mixture. A uniform electric fieldof 400 V /cm is applied in each volume along beam direction to transport ionisation electrons
towards the readout pad chambers within a maximum drift time of ∼100 µs . The signals

Fig 2.10: Schematic view of the TPC field cage. [37]

30

Chapter 2. Experimental Setup

Fig 2.11: TPC dE /dx as a function of momentum with superimposed Bethe-Bloch lines√
for various particle species, measured in Pb-Pb collisions at sNN = 5.02 TeV . [33]read out by the ∼557k pads of multi-wire proportional end plate chambers allow for particle
trajectory reconstruction and measurement of their energy loss (dE /dx ) in the TPC gas
volume which is used for PID (Fig. 2.11).
2.2.4

Electromagnetic Calorimeters (EMCAL, DCAL and PHOS)

The EMCAL and DCAL are lead-scintillator sampling calorimeters with large acceptance,
comprising 12,288 and 5,376 individual towers respectively. They are located inside the
ALICE solenoid magnet, occupying a cylindrical volume of approximately 110 cm deep inthe radial direction, with front face located at 450 cm from the beam line (see Fig. 2.12).
The basic detector unit of EMCAL/DCAL is a “module” comprising 2 × 2 independent
detection channels (towers). The module is a sandwich of 77 plastic scintillator layers and
76 lead foils which corresponds to 20.1 X0 radiation lengths.
A particle passing through the module and interacting with the lead produces an electromagnetic shower, which in turn produces light in the plastic scintillators. Avalanche
Photodiodes (APD) convert the light which is collected and guided by WLS optical fibres,
into an electrical signal.
The structural units of EMCAL and DCAL are called “Super Modules” (SMs) arranged
following a continuous arch, spanning 20◦ in azimuth. The Super Modules are classified into

Section 2.2. The ALICE Experiment31

Fig 2.12: Three calorimeters installed in ALICE at Run2 period: EMCal (upper side),
PHOS (bottom side, drawn in orange) and DCal (placed on both side of PHOS in zdirection).

two types, full size and one-third size SMs. Each full size Super Module consists of 24 × 12

modules for EMCAL and 16 × 12 modules for DCAL, and one-third size SM contains 24 × 4
modules. A total of 10 full size SMs and 2 one-third SMs constitute EMCAL, while DCAL
numbers 6 full size and 2 one-third SMs.
PHOS is a high resolution electromagnetic calorimeter made of lead tungstate crystals(PbWO4 ), covering a limited acceptance at central rapidity, and located inside the solenoid
magnet at 440 cm from the beam line. The basic unit of the detector is a “crystal” which
size is 22 × 22 × 180mm3 corresponding to 20 X0 radiation lengths, and on which the readout APD is directly glued.

When high energy photons or electrons cross lead tungstate, they induce electromagnetic
cascade (pair production and bremsstrahlung) and make it scintillate. However the leadtungstate is so dense that it stops most of the incoming photons. Furthermore, this inorganic
scintillating crystals have a strong light yield temperature dependence. Therefore, in orderto achieve a high energy resolution, PHOS is operated under a temperature of −25◦ C, where
the deterioration of the energy resolution due to noise is minimised.

32

Chapter 2. Experimental Setup

Total Weight
Number of SMs
Coverage

EMCAL

DCAL

PHOS

∼ 82 t∼ 36 t12.5 t

6 SMs

3 SMs

2 one-third SMs

2 one-third SMs

1 half SM

80◦ < φ < 187◦260◦ < φ < 327◦

250◦ < φ < 320◦

|η| < 0.7

|η| < 0.7 a|η| < 0.13

0.0143 x 0.0143

0.0143 x 0.0143

0.004 x 0.004

10 SMs∼ 60 x 60 x 246 mm3

Tower size(∆η × ∆φ)Eﬀective Rad.

∼ 60 x 60 x 246 mm3∼ 22 x 22 x 180 mm3

20.1

20.1

20

5.68 g/cm3√
7%/ E ⊕ 1.5%

5.68 g/cm3√
7%/ E ⊕ 1.5%

8.28 g/cm3√
3.3%/ E ⊕ 1.1%

Length X0
Eﬀective density
Energy resolution

Tab 2.2: Specification of ALICE electromagnetic calorimeters
PHOS consists of 3 SMs and 1 half SM. Each SM (half SM) is made up of 56 × 64

(56 × 32) crystals; in all PHOS has 12,544 crystals. The main specifications of EMCAL,DCAL and PHOS are summarised in Tab. 2.2.

EMCAL and DCAL focus on jet physics, where the improvement of jet energy resolution is very desired for the tomographic study of QGP. They improve the charged jetmeasurement by adding the neutral constituents. Furthermore, the association of EMCAL
and DCAL makes hadron-jet and/or jet-jet high precision correlation measurement possible, because of their back-to-back in azimuth layout in agreement with the di-jet topology.
The event display in Fig. 2.13 shows a typical jet-jet event recorded during the 2015 Pb-Pb
run. The primary aim of PHOS is to measure and identify photon and neutral meson fromthe hot QCD matter. It has been designed to detect photons produced over a wide energy
range, up to 100 GeV and reconstruct neutral mesons decaying to photons with very highenergy and position resolutions.
In Fig. 2.14 and Fig. 2.15, the π 0 → γγ invariant mass distribution measured in EMCAL

and PHOS respectively are shown. A clear peak is observed (larger S/B) even in the very
demanding heavy-ion environment.
awith exception: 260◦ < φ < 320◦ , |η| < 0.25

Section 2.2. The ALICE Experiment

33

×103
1.4
1.2

Pb-Pb, sNN=2.76 TeV
Centrality 0-20%
EMCAL
9<pT<10 GeV/c
22.03.2013

1
0.8

Events / 2 MeV/c 2

Events / 7 MeV/c2

Fig 2.13: ALICE event display taken in 2015 Pb-Pb run. [33]

×103
2

1.5

Pb-Pb, s NN = 2.76 TeV

ALICE performance

Centrality 0-10%

03.03.2015

PHOS
4.0 < p < 4.2 GeV/csignal + background
event mixing backgroundTsignal after bkg subtraction

1

0.6
0.5

0.4
0.2

0
0.08

0
0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24
mγ γ (GeV/c2)
ALI−PERF−47199

Fig 2.14: Invariant mass spectrum of photon pairs with pT = 9-10 GeV/c measured in√
EMCAL in sNN = 2.76 TeV Pb-Pb collisions at centrality 0-20%. [33]

0.1

0.12

0.14

0.16

0.18

0.2
0.22
M γ γ (GeV/c 2)

ALI−PERF−91681

Fig 2.15: Invariant mass spectrum of photon
pairs with pT = 4.0-4.2 GeV/c measured in√
PHOS in sNN = 2.76 TeV Pb-Pb collisions
at centrality 0-10%. [33]Chapter 3

ALICE Calorimeter Trigger
Development

During the two-year long shutdown period (LS1) from 2013, LHC accelerator was upgradedto achieve higher beam luminosity and beam energy close to design values. At the sametime, the ALICE experiment took the chance to upgrade some of its detectors to cope with
the new beam conditions and keep improving measurements of QGP properties.
During LS1, a new Electromagnetic calorimeter “DCAL” was installed to enhance theacceptance for neutral particles and measure di-jet energy with charged plus neutral particles. Along with this upgrade, a new online trigger system was deployed to select andenrich dataset with rare events including jets or high pT photons.
In this section, the trigger system which was developed by the author during LS1 for
the ALICE EMCAL/DCAL is presented.

3.1

Overview of Trigger Generation

The trigger inputs from each detector are treated by the Central Trigger Processor (CTP)of the ALICE trigger system. These trigger inputs are grouped into three successive levels(Level-0, Level-1 and Level-2). The trigger inputs from an event of a given bunch crossing
arrive to the CTP with a delay: the trigger input latency amounting to:• 800 ns for L0 triggers• 6,100 ns for L1 triggers• 87,600 ns for L2 triggers
The calorimeters (EMCAL, DCAL and PHOS) are used for L0 and L1 triggering because
their signals are faster than other detectors (e.g. TPC due to its large drift time). Two L1
triggers are generated by calorimeters: L1-photon and L1-Jet to select high-pT photons andjets respectively.
L1 trigger signals are produced by the Summary Trigger Unit (STU) which is displayedon Fig. 3.1. To generate output signals, the STU processes a number of inputs. Trigger
35

36

Chapter 3. ALICE Calorimeter Trigger Development

Fig 3.1: Summary Trigger Unit board (STU).

Region Units (TRU) in charge of triggering at local areas of the detector (1 TRU handles
signals from 1/3 of a SM). TRUs provide a single photon trigger (L0) receiving an analog
sum of each group of 2×2 adjacent towers from the Front End Electronics (FEE) cards.
This group of towers is called “Module” or “FastOR” and is the smallest unit of trigger
calculation. Subsequently, FastOR signal amplitudes are flash digitised in the TRU andused as STU inputs. The relation between each trigger unit is shown in Fig. 3.2.
EMCAL (DCAL) has totally 3,072 (1,344) FastORs and PHOS has 12,544 crystals whichcorresponds to 3,136 FastORs. One FEE card can deal with 8 modules, and one TRU is incharge of 12 FEEs (for EMCAL and DCAL) or 14 FEEs (for PHOS). The TRU coveragein detector coordinate system is shown in Fig. 3.3 and Fig. 3.4. The STU collects FastORs’
amplitudes and produces L1 triggers following its internal trigger algorithm.
The L1 trigger calculation is carried out by a FPGA (Xilinx Virtex-5) mounted on the
STU board. During LHC LS1, the upgrade of the ALICE calorimeter trigger system wasaccomplished by developing an original STU firmware.

Section 3.1. Overview of Trigger Generation37

Fig 3.2: Data flow of L1 trigger production in ALICE calorimeters. In total 7 L1-photon
triggers (3 for PHOS, 2 for DCAL and 2 for EMCAL) and 4 L1-Jet triggers (2 for DCAL
and 2 for EMCAL) are generated.

38

Chapter 3. ALICE Calorimeter Trigger Development

Fig 3.3: EMCAL geometry in terms of trigger production. Each TRU charged area contains
96 FastORs.

Fig 3.4: DCAL+PHOS geometry in terms of trigger production. Each PHOS (DCAL) TRU
contains 112 (96) FastORs respectively.

Section 3.2. L1 Trigger Algorithm39

Fig 3.5: Example of L1-photon patch (= 2 × 2 FastORs). Amplitudes of these patches arecalculated over TRU boundaries.

3.2

L1 Trigger Algorithm

Taking advantage of the freshly commissioned DCAL back-to-back in azimuth to the EMCAL, the new L1 trigger algorithms exploit this two-arm setup by aggregating DCAL and
PHOS regions to estimate the event energy density and thereby correct EMCAL trigger
patches from soft background contamination, and vice versa. The new approach (a.k.a.
median mode), besides providing uniform trigger eﬃciency across event centrality, makes
the calorimeter triggers more self-consistent (using energy measurements only) without relying anymore on the V0 detector to compute a multiplicity-dependent trigger threshold as
implemented during LHC Run1. Furthermore, preliminary Monte-Carlo simulations havealso predicted shaper trigger turn-on curves.
The L1-photon trigger calculation starts from summing up the amplitudes within a 2×2
FastOR trigger patch. The patch slides in units of FastOR and scans the whole detector

40

Chapter 3. ALICE Calorimeter Trigger Development

Fig 3.6: Example of L1-Jet patches (= 2 × 2 or 4 × 4 jet-primitives) in DCAL+PHOS side.
area including TRU boundaries (see Fig. 3.5). This process is running on-the-fly while
receiving TRU data. The same sliding window method is applied for L1-Jet calculation but
with a larger patch size of 8 × 8 (or 16 × 16) FastORs, and a sliding unit of 4 × 4 FastORs
which is called “jet primitive”.

In fact, the optimum threshold, which is made up of only bulk contribution, depends
on underlying event density which fluctuates event-by-event. Thus, the estimated event
background should be subtracted before the comparison with threshold. In this upgrade,
event background is estimated event-by-event using median calculation of background patch(correspond to 2×2 jet-primitives). This estimated background is sent to opposite side STU
in azimuth and used for background subtraction. The calculation flow for L1-Jet is summarised in Fig. 3.7. In addition, the jet patches in DCAL side need to collect the amplitudeof jet-primitives from PHOS due to their respective gain parameters and complicated geometry. (PHOS has been excluded from L1-Jet calculation in physics runs operated in2015 - 2017.)

Section 3.2. L1 Trigger Algorithm41

Fig 3.7: Schematic of event background calculation. Underlying event density estimated bymedian method are swapped between EMCAL STU and DCAL STU.

42

Chapter 3. ALICE Calorimeter Trigger Development

3.3

Trigger Performance

The ALICE calorimeters started operation with the new L1 median mode algorithm for the
first Run2 Pb-Pb run in November 2015. Trigger performances was then evaluated fromthe first data recorded by STUs.
First of all, we validated the principle of background median estimate exchange between
EMCAL and DCAL. Fig. 3.8 shows the correlation of background densities estimated fromevent-by-event median calculation of background patch in EMCAL and DCAL. The clear
positive correlation observed proves firstly that both estimates are consistent and can besafely swapped, and secondly, that the data transfer between EMCAL and DCAL is reliable.
The trigger capability to control event rates for data acquisition is quantified by thetrigger rejection factor defined as the fraction of events passing the trigger condition ina minimum bias events sample. The L1-photon and L1-Jet trigger rejection factors as afunction of trigger threshold are shown in Fig. 3.9 and Fig. 3.10 respectively. A 10 GeV
threshold gives a ∼100 L1-photon trigger rejection, while a 20 GeV threshold results in a∼1000 of L1-Jet trigger rejection. Such trigger rejection factors are used for trigger thresholdsettings to comply with the bandwidth allocated to the calorimeters according to ALICEρ (DCAL) (GeV)

data taking strategy.

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)

Fig 3.8: Correlation of underlying event densities estimated by DCAL and EMCAL STUs.

L1 Trigger Rejection

Section 3.3. Trigger Performance

43

1

ALICE Pb-Pb sNN = 5.02 TeV
L1-Photon Trigger, 2× 2 patch
LHC15o run245793

10−1

EMCAL
DCAL

10−2

10−3
0

5

10

15

20

Trigger Threshold (GeV)HIROKI YOKOYAMA

L1 Trigger Rejection

Fig 3.9: Rejection factor of L1-photon triggers given by DCAL and EMCAL in 2015 Pb-Pb
run.

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)

Fig 3.10: Rejection factor of L1-jet triggers given by DCAL and EMCAL in 2015 Pb-Pb
run.

44

Chapter 3. ALICE Calorimeter Trigger Development

The other important trigger performance to assess is how rapidly full selection eﬃciency
is reached, the so-called turn-on curve. Fig. 3.11 and Fig. 3.12 show the PHOS cluster
spectrum with the L1-photon trigger and minimum bias trigger in diﬀerent event centrality
classes. The ratios of these spectra show clear step-function like shape around the thresholdsetting of 8 GeV . The height of the plateau gives the photon enhancement factor provided
by the trigger system. This value is larger in peripheral collisions than central collisions. The
diﬀerence comes from the fact that the PHOS L1-photon trigger does not implement any
background subtraction, resulting in larger patch energies in central collisions. The trigger
eﬃciency is evaluated by the proportion of jet/photon-trigger events in the minimum-bias
trigger events. Fig. 3.13 and Fig. 3.14 show the L1-photon and L1-Jet trigger eﬃciencies
respectively as a function of trigger patch energy measured in FEE. They also show a sharp
turn-on around the threshold value.
The results shown in the Fig. 3.8 to Fig. 3.14 demonstrate the good performance ofthe new L1-trigger in Pb-Pb collisions. Large event samples have been collected with thistriggers since its commissioning which are now being analysed for paper publication by the
ALICE collaboration.
102

1
10− 1

1
1 dN (GeV/c )-1
Nev dpMB
High
PHOS L1 trigger, threshold = 8 GeV

10− 2

10− 1

10− 4
10− 5
10− 6

10− 3
10− 4
10− 5
10− 6

10− 7

10− 7

efficiency uncorrected
only statistical error

10− 8

1 dN MB
dp
NMB
ev
T

104

103

dN
1
L1
dp
NPHOS
ev
T

PHOS L1/103/

1 dN MB
dp
NMB
ev
T

efficiency uncorrected
only statistical error

10− 8

104

PHOS L1

MB
High
PHOS L1 trigger, threshold = 8 GeV

10− 2

T

10− 3

dN
1
L1
dp
NPHOS
ev
T

ALICE performance
12.03.2016
Pb-Pb, s NN = 5.02 TeV
centrality 60-80 %10T

1 dN (GeV/c )-1
Nev dp102

ALICE performance
12.03.2016
Pb-Pb, s NN = 5.02 TeV
centrality 0-5 %

10

102

10

1

0

ALI−PERF−104944

5

10

15

20

25

30

35
40
p (GeV/c )T

Fig 3.11: (top) pT spectra of clusters reconstructed in PHOS with minimum bias andPHOS L1-photon triggers at 0-5% Pb-Pb collisions. (bottom) The ratio of them. [33]

102

10

1

0

ALI−PERF−104952

5

10

15

20

25

30

35
40
p (GeV/c )T

Fig 3.12: (top) pT spectra of clusters reconstructed in PHOS with minimum bias andPHOS L1-photon triggers at 60-80% Pb-Pb
collisions. (bottom) The ratio of them. [33]

L1 Trigger Efficiency

Section 3.3. Trigger Performance

45

1.4
1.2

ALICE Pb-Pb sNN = 5.02 TeV
L1-Photon Trigger, 2× 2 patch
LHC15o run245793

1
0.8
0.6
0.4

EMCAL L1G Low
EMCAL L1G HighDCAL L1G Low
DCAL L1G High

0.2
0

0

5
HIROKI YOKOYAMA

10

15

20

Photon Trigger Patch Energy (GeV)

L1 Trigger Efficiency

Fig 3.13: EMCAL and DCAL L1-photon trigger eﬃciency in 2015 Pb-Pb run.

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)

Fig 3.14: EMCAL and DCAL L1-Jet trigger eﬃciency in 2015 Pb-Pb run.

Chapter 4

Analysis

This chapter presents the measurement of the inclusive jet nuclear modification factor in√
Pb-Pb collisions at sNN = 5.02 TeV .

4.1

Data Samples

This analysis utilises two types of data samples: (i) experimental data and (ii) Monte-Carlosimulation (MC) data.
The experimental dataset is made of Pb-Pb collisions collected by the ALICE detector in2015. A feature of this dataset was that it was taken with increasing interaction rates (from15 Hz to 7800 Hz depending of beam tuning and filling schemes). The analysis presented
hereafter is based on the lowest interaction rate data. The event statistics is 3.3M after
applying event selection. The data sample was divided into four classes of centrality interval
ranging from very central to peripheral collisions: 0-10%, 10-30%, 30-50% and 50-90%.
The ALICE detector response is modelled by the convolution of Pb-Pb and pp events
generated by HIJING [46] and PYTHIA [47, 48] respectively, with the detector description(geometry, material, calibration. . . ) from a GEANT3-based simulation [49]. The same trackreconstruction code is used for data and simulation. In order to enhance the statistics ofhigh-pT jets, PYTHIA is run in bins of parton scattering transverse momentum in addition
to minimum bias events. These dataset and statistics are summarised in Tab. 4.1.

Expt./MC

system

Expt.

Pb-Pb

HIJING MC

Pb-Pb

PYTHIA MCpp

PYTHIA MC

ppenergy√sNN = 5.02 TeV√
sNN = 5.02 TeV√
s = 5.02 TeV√
s = 5.02 TeV

statistics

remark

3.3M

Minimum Bias Trigger

2.5M
20.4M
670-680k/bin

jet production (10 pthard bins)

Tab 4.1: Dataset used for the analysis.
47

48

Chapter 4. Analysis

this thesis

Nev

N

ev

this thesis
ALICE Pb-Pb sNN = 5.02 TeV

ALICE Pb-Pb sNN = 5.02 TeV

50000

50000

40000

40000

30000

30000

20000

20000

10000

10000

0
− 20

−15

− 10

−5

0

5

10

15

20

0
0

10

20

30

40

50

60

70

80

90 100

v PRI
(cm)
z

centrality (%)

Fig 4.1: Primary vertex position along beam
direction. The events with |vz | < 10cm are
selected.

Fig 4.2: Event centrality distribution calculated with the V0M (= V0A + V0C) estimator.

4.2

Event Selection

The analysis presented in this thesis uses minimum-bias events (MB) triggered by two V0
detectors, requiring a signal in both the V0A and the V0C.
To ensure high tracking eﬃciency the primary vertex is required to be within 10 cm
from nominal ALICE interaction point along the beam axis; |vz | < 10cm. Fig. 4.1 shows
the primary vertex position in beam direction. This requirement rejects ∼ 9% of MB events.
To reject the remaining background events from beam-gas interaction, which generally

show large signal amplitudes in the V0 detector while small track multiplicities in central
barrel, the primary vertex position along the beam axis (z) reconstructed by SPD hits is$$used for additional requirement: $vzPRI − vzSPD $ < 0.1 cm. Fig. 4.3 shows the correlation
between vzSPD − vzPRI and track multiplicity. These events (outlier in Fig. 4.3) have suchsmall numbers of tracks that the resolution of primary vertex position is bad. This event
cut removes ∼ 0.3 % of MB events.

As seen in Fig. 4.2, the centrality distribution after event selection which is defined by

V0 detector amplitude (c.f. section 2.2.1 for the definition) ensures that event cuts did not
introduce any bias.

Section 4.3. Track Selection49

0 - 10 %1

2 9000v SPD- vPRI(cm)zz

ALICE Pb-Pb sNN = 5.02 TeV

2 5000v SPD- vPRI
(cm)
z
z

v SPD
- vPRI
(cm)
z
z

1.5

v SPD
- vPRI(cm)zz

this thesis
2

1.5 8000

1.5
4000

10 - 30 %

1

1

120

1.5

30 - 50 %
7000

0.5

16000

14000

50 - 90 %

100

1
12000

6000

0.5

3

×10

2

0.5

80

0.5

3000
10000

5000

0

0

0

0

− 0.5

−0.5

2000

−0.5

−0.5
6000

3000

−1

−1

− 1.5

−1.5

−1
1000

60
8000

4000

−1

2000

40

4000
20

−2
0

1000

2000

−2 0

3000

4000
0

−1.5 1000

1000

2000

track

N

−2 0

3000

4000
0
track

N

−1.5 2000

1000

2000

−2 0

3000

4000
0
track

N

0

1000

2000

3000

4000
track

N

Fig 4.3: Correlation between vzSPD - vzPRI and track multiplicity for four centrality classes.
The events with bad vertex reconstruction resolution are rejected.

4.3

Track Selection

To avoid biasing jet reconstruction, track selection should provide a uniform η and φ track
acceptance. The tracks are reconstructed in the ALICE central barrel (pseudo-rapidity
region | η | < 0.9) with the ITS in conjunction with TPC. In order to ensure a uniform
tracking eﬃciency in the (η, φ) plane despite some switched oﬀ SPD ladders, a dedicatedtrack selection has been developed, the so-called “hybrid tracks”. The hybrid track sample
is made of two exclusive track types:• global tracks: with at least one hit in the SPD layers and successful inward track
refit through the ITS.

• complementary tracks: which are primary vertex constrained global tracks withno hit in the SPD but still with a successful refit in the ITS.

The azimuthal and pseudo-rapidity distributions of the two component hybrid tracks
with pT > 150 MeV/c are given in Fig. 4.4 and Fig. 4.5 respectively. Hybrid track reconstruction succeeds in making φ distribution uniform. Furthermore, no centrality dependence
are observed in η and φ distribution.
The hybrid track pT distributions shown in Fig. 4.6 show no unusual peaks caused by
hot channels or tracking reconstruction problems.

50

Chapter 4. Analysis

High-pT tracks tend to be aﬀected the ineﬃcient area due to their straight trajectories as
seen in Fig. 4.7 (blue line). The TPC sector boundaries which introduce track ineﬃciencies
are responsible for the bumps observed in the φ distribution of high-pT tracks.
this thesis
ALICE Pb-Pb sNN = 5.02 TeV

180

140

ALICE Pb-Pb sNN = 5.02 TeV

600

Hybrid Tracks
Global Tracks
Complementary Tracks

160

this thesis
700

1/Nev dNtrack /dη

1/Nev dNtrack /dφ200

Hybrid Tracks
Global Tracks
Complementary Tracks

500

120

400

100
300

80
60

200

40
100

20
1

2

3

4

5

φ

track

this thesis

1/Nev dNtrack /dp

T

104
ALICE Pb-Pb sNN = 5.02 TeV

102

centrality
0 - 10 %10

10 - 30 %
30 - 50 %50 - 90 %

1

10−1

−1

−0.5

0

0.5

1

(rad)

Fig 4.4: Track φ distributions for two components of hybrid tracks.

103

0
−1.5

6

10−2

1.5

η trackFig 4.5: Track η distributions for two components of hybrid tracks.
this thesis
105

1/Nev dNtrack /dφ

00

ALICE Pb-Pb sNN = 5.02 TeV

104

0.15 < p (GeV/c) < 2.0T

2.0 < p (GeV/c) < 5.0
T

3

10

5.0 < p (GeV/c)
T

102
10

10−3
10−4

1

−5

10

10−1

10−6
10−7

0

5

10 15 20 25 30 35 40 45 50

p track (GeV/c)T

Fig 4.6: Hybrid track pT distributions forfour centrality classes.

10−2

0

1

2

3

4

5

φ track (rad)6

Fig 4.7: Hybrid track φ distributions forthree transverse momentum classes.

Section 4.3. Track Selection

51

this thesis

Global Tracks

0.04

Complementary TracksT) / p track

σ( p

track

Hybrid Tracks

0.05

0.07
ALICE Pb-Pb sNN = 5.02 TeV

0.06

centrality

0.05

0 - 10 %10 - 30 %0.04

30 - 50 %T

ALICE Pb-Pb sNN = 5.02 TeV

0.06

T

σ( p

track

T

) / p track

this thesis
0.07

50 - 90 %

0.03

0.03

0.02

0.02

0.01

0.01

0 −1
10

1

10

102

p track (GeV/c)T

Fig 4.8: Transverse momentum resolution(σ(pT )/pT ) for two components of hybrid
tracks.
4.3.1

0 −1
10

1

10

102

p track (GeV/c)T

Fig 4.9: Transverse momentum resolution(σ(pT )/pT ) for four centrality classes.

Tracking Resolution

The track transverse momentum resolution is extracted from the track parameter covariancematrix. The pT resolution for two hybrid track components is shown in Fig. 4.8. The global
and complementary track resolutions are similar: the diﬀerence is less than 1 % at least up
to 100 GeV/c . pT resolution centrality dependence shows a small discrepancy smaller than
0.5% across all centrality classes (see Fig. 4.9). The pT resolution of σ(pT )/pT ≃ 0.6% (4%)
at 1 GeV/c (50 GeV/c ) are given respectively.
4.3.2

Tracking Eﬃciency

The tracking eﬃciency of hybrid tracks is evaluated based on MC simulations: PYTHIA
and HIJING events propagated through a GEANT3 detector description. On one hand,the number of generated particles is defined as all charged tracks in the final state (N gen ),emerging from the primary vertex within | η | < 0.8. On the other hand, the reconstructed

tracks are hybrid tracks associated with generated particles (N rec,matched ) within a wider
range of | η | < 0.9 in order to avoid boundary eﬀects at the limit of detector acceptance.
The ratio of above mentioned generated track pT spectra gives the tracking eﬃciency:
genrec(|η| < 0.9) /dpT
1 gen 2 dNmatchedε pT=
dN gen (|η| < 0.8) /dpgen
T

(4.1)

52

Chapter 4. Analysis

this thesis

1.2
ALICE Pb-Pb sNN = 5.02 TeV

1

0.8

0.6
PYTHIA (pp)
HIJING (PbPb)
0 - 10 %0.4

10 - 30 %
30 - 50 %50 - 90 %0.2

0Tracking Efficiency ratio ( PbPb/pp )Tracking Efficiency

this thesis

1.2

ALICE Pb-Pb sNN = 5.02 TeV
1.1

1

0.9
centrality
0 - 10 %10 - 30 %
30 - 50 %50 - 90 %

0.8

0.7

0.6
1

10

1

p track (GeV/c)
T,gen

Fig 4.10: Tracking eﬃciency of hybrid
tracks estimated by PYTHIA (pp) and HIJING (Pb-Pb) events, propagated through
GEANT simulation.

10

p track (GeV/c)
T,gen

Fig 4.11: Ratio of tracking eﬃciency in PbPb collisions to pp collisions.

The tracking eﬃciencies computed from HIJING and PYTHIA, and their ratio: HIJING/PYTHIA are shown in Fig. 4.10 and Fig. 4.11 respectively (for four centrality classes
in HIJING). The tracking eﬃciency increases from about 70% at pT = 200 MeV/c up to
80% at pT = 1 GeV/c with a few percent decrease in central Pb-Pb collisions, mainly due
to larger track multiplicities. For Pb-Pb collisions (HIJING), the tracking eﬃciency is from
2 to 7% smaller than that in pp collisions (PYTHIA) down to 0.5 GeV/c .

4.4

Jet Reconstruction

The jets are reconstructed by feeding the anti-kT sequential clustering algorithm [50] withhybrid tracks lying within | η | < 0.9. Since in the anti-kT algorithm, harder particles are

merged first, it proves to be less sensitive to back-reaction from the soft underlying event
which is particularly well suited for the Pb-Pb environment.
The anti-kT algorithm is controlled by the input parameter named “Resolution Parameter”, R. It is sometimes called as “jet radius” since this parameter usually has a value
close to the radius of the reconstructed jet. The reconstructed jets contain a number ofSection 4.4. Jet Reconstruction

53

Fig 4.12: (top) Jet pT distributions after average background subtraction for diﬀerent pleadTrequirements. (bottom) The ratio to inclusive jet spectrum which shows leading trackpT bias.

particles which don’t originate from the initial hard partons. This phenomenon makes jet
energy resolution worse especially at large R. To minimise this contamination, this analysis
selects R = 0.2 as a resolution parameter. Furthermore, three additional requirements areapplied to improve the quality of the reconstructed jet sample:
1. Jet Direction
Jets whose whole area is expected to stay within the detector acceptance: | ηjet | <0.9 − R.

2. Jet Area
A minimum jet area from anti-kT of 60 % of rigid cone area is required to reduce thefake jet contamination in the low-pT region: Ajet > 0.6 π R2 , where Ajet is jet area
calculated in the anti-kT algorithm.
3. Leading Track Momentum
A minimum transverse momentum of 5 GeV/c is applied to the jet leading track
constituent to cut down the combinatorial jet contamination, which is accidentally

54

Chapter 4. Analysis

reconstructed by tracks from underlying event, at the cost of introducing a fragmentation bias: plead> 5 GeV/c .
T
The average background energy density ρ is calculated on event-by-event basis using kTclusters [51] (for the detail description, see section 4.5). The background is then subtracted
from each anti-kT jet as follows:raw
prec
T,ch jet = pT,ch jet − ρ · Ajet .

(4.2)

The jet pT distributions with diﬀerent leading track pT requirement are shown in Fig. 4.12
for four centrality classes (top), and their ratios to the plead> 0.15 GeV/c case (bottom).
T
As expected, the low-pT jet yield is suppressed up to 35 GeV/c due to the leading trackpT requirement for plead> 5 GeV in the most central collisions, while this bias is negligibleTat higher pT . Furthermore this bias decreases for peripheral collisions in which the jet
fragmentation pattern become harder. Note that the leading track pT requirement reduces
not only combinatorial jets but also true jets with soft fragmentation.
Fig. 4.13 and Fig. 4.14 show prec
T,ch jet > 40 GeV/c reconstructed jet φ and η distributions
respectively. Thanks to hybrid track selection, a fluctuation of ! 20% is achieved over thethis thesis

×10−3

ALICE Pb-Pb sNN = 5.02 TeV

0.7

Anti-kT R = 0.2, Charged Jets|η jet | < 0.7

0.6

p Tlead > 5 GeV/c

0.5
0.4

this thesis

−3

ev

0.8

1 / N dN ch,jet / dη

1 / Nev dN ch,jet / dϕwhole jet acceptance.
3 ×10

ALICE Pb-Pb sNN = 5.02 TeV
2.5

Anti-kT R = 0.2, Charged Jets
p Tlead > 5 GeV/c

2
1.5

0.3

1

0.2
0.5

0.1
0
0

1

2

3

4

5

ϕ

ch,Jet6(rad)Fig 4.13: Reconstructed jet φ distribution
with prec
T,ch jet > 40 GeV/c .

0−1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1

ηch,JetFig 4.14: Reconstructed jet η distribution
with prec
T,ch jet > 40 GeV/c .

Section 4.5. Underlying Event

55

this thesis

ALICE Pb-Pb,

200

pT,track

105

sNN = 5.02 TeV> 0.15 GeV/c
4

10

150

0
0

1000

2000

3000

4000

200

p

T,tracksNN = 5.02 TeV> 0.15 GeV/c

104

100

102

10

50

10

1

0
0

charged track multiplicity

Fig 4.15: Correlation between average background density and charged track multiplicity.

4.5

ALICE Pb-Pb,

103

102

50

250

150

103

100

ρ (GeV/c)

ρ (GeV/c)this thesis

250

10 20 30 40 50 60 70 80 90

1centrality (%)

Fig 4.16: Correlation between average background density and event centrality.

Underlying Event

In high-energy heavy-ion collisions, a number of particles which do not originate fromhard partons should be considered as background for the jet signal of interest. This softbackground fluctuates both from event to event, but also from one location to anotherwithin the same event. As mentioned in section 4.4, the background average pT density parunit area, ρ, is evaluated event-by-event. Local fluctuations of the background density withrespect to the event median cause large uncertainty in the reconstructed jet energy. Thesefluctuations are quantified by known probes (random cones, single high-pT tracks, PYTHIA
jets. . . ) into real Pb-Pb events as explained hereafter. For this local fluctuation within thesame event, statistical correction of the spectrum is available utilising the distribution ofresidual error from average background density.

Average Underlying Event Density
The average background density (ρ) which is used to correct the jet momentum in Eq. 4.2
is estimated as follows:
1. kT clusters are reconstructed with the FastJet kT algorithm using hybrid tracks of56

Chapter 4. Analysis

centrality⟨ρ⟩( GeV/c )0 - 10 %10 - 30 %
30 - 50 %50 - 90 %

146.4
81.4
32.3
3.7

⟨ρ⟩ × πR2 ( GeV/c )(R = 0.2)
18.4
10.2
4.1
0.5

Tab 4.2: The average underlying event density.
pT > 0.15 GeV/c within the ALICE acceptance (|η| < 0.9, 0 < φ < 2 π), and R = 0.2
as resolution parameter.
2. two types of kT clusters are excluded: (i) clusters outside of the fiducial area (|ηjet | >0.9 − R), and (ii) the two highest transverse momentum clusters in order to reducethe influence of true hard jets on the background estimate.

3. the statistical median of the remaining cluster pT,i / Ai ratios is calculated and defined
as background density ρ.
ρ correlation with centrality percentiles and charged track multiplicities are shown in Fig. 4.15
and Fig. 4.16 respectively. It is noticeable that the average background energy density scales
linearly with track multiplicity and shows an amplitude of about 145 GeV/c in the mostcentral collisions (0-10%) which in turn corresponds to 18 GeV/c for R = 0.2 jets. The
mean background densities, ⟨ρ⟩ for four centrality classes are quoted in the Tab. 4.2.
Underlying Event Fluctuation
Region-to-region background energy fluctuations in a heavy-ion collision, δpT , is determinedby randomly placed cones (RC) of radius R as follows:
δpT =

RC
3
i

ptrack− ρ π R2
T,i

(4.3)

where ptrackis the transverse momentum of track i belonging to the RC considered. Fig. 4.17
T,ishows the δpT distributions for two RC definitions:$$• Randomly located cones directing within fiducial area of R = 0.2 jet: ($η RC $ < 0.7).

Section 4.6. Jet Finding Eﬃciency

57

Fig 4.17: δpT distributions for two RC selections and RC in track randomised event.

• RC is apartfrom the leading jet by at least 1 unit in the η-φ plane:
4∆R =(η RC − η lead.jet )2 + (φRC − φlead.jet )2 > 1.

For comparison to purely statistical fluctuations, RC are also thrown throughout randomised
events constructed from real events by cancelling particle correlations.
The right-hand-side tail of the δpT distribution is caused by RC overlapping with theleading jet when the leading jet is not excluded while it is due to high-pT tracks of theleading jet for randomised events. The background fluctuation is characterised by thewidth of the δpT distribution: σ (δpT ). The RMS of the δpT distribution is shown asfunction of track multiplicity in Fig. 4.18. In addition to the RMS, the width of gaussian fitof the left-hand-side region; [µLHS − 3 σ LHS , µLHS + 0.5 σ LHS ], which is independent of theleading jet constituents, is quoted in Fig. 4.17. These results indicate that the backgroundfluctuates within ∼ 5 GeV/c around average background density for R = 0.2 charged jetsin the most central (0-10%) collisions. As expected, a lower fluctuation is observed for
peripheral collisions. The minimum pT limit of measured jet spectrum is typically selected
as 5σ(δpT ), in which σ(δpT ) is the width of δpT distribution. The spectrum collection is
hard below this limit due to poor jet energy resolution (see section 4.7).

4.6

Jet Finding Eﬃciency

Similarly to tracking eﬃciency evaluation, jet finding eﬃciency is estimated from MC simulations (PYTHIA + GEANT). The generator-level jets are reconstructed from generated

58

Chapter 4. AnalysisTσ(δ p )

this thesis
8
random cone7

RC (w/o lead. jet)
RC randomized ηφ6

Poissonian limit

5
4
3
2
1
0
0

500

1000

1500

2000

2500

3000

3500
tracksN

Fig 4.18: The width of δpT distributions for two RC selections and RC in track randomised
event as a function of charged particle multiplicity.

particles, while reconstruction-level jets are made from tracks smeared by the GEANT3 detector response. The jet finding eﬃciency is defined as the fraction of reconstruction-level
jets which match with generator-level jets within | η | < 0.5 as follows:
εjet

5

pgen
T,ch jet6=

recNmatched

N gen (|η gen | < 0.5)

(4.4)

A one-to-one matching between the I-th generator-level jet and the J-th reconstruction-level42
jet established based on the distance in the (η−φ) plane ∆R(i, j) = (ηigen − ηjrec )2 + (φgen− φrecj ) ,i
as follows:

1. for the index j running over all the reconstruction-level jets, find the index j ′ of theclosest generator-level jet.
2. for the index i running over all the generator-level jets, find the index i′ of the closest
reconstruction-level jet.
3. j ′ = J and i′ = I
4. ∆R(I, J) < 0.1

Section 4.7. Unfolding

59

Jet Finding Efficiency

Jet Finding Efficiency

1.4
PYTHIA MB, s = 5.02 TeV, anti-k T , R=0.2

1.2
1
0.8
0.6

1.4

T

1.2
1
0.8
0.6

0.4

p lead> 0.15 GeV/c
T

0.4

0.2

p lead > 5 GeV/c

0.2

0
0

T

20

40

60

80

100

p

(GeV/c)

gen
T

120

Fig 4.19: Jet finding eﬃciency for diﬀerent
plead
requirements.
Ts = 5.02 TeV, anti-k T , R=0.2, p lead > 5 GeV/c00

PYTHIA jet-jet
PYTHIA MB
20

40

60

80

100

p

(GeV/c)

gen
T

120

Fig 4.20: Jet finding eﬃciency for diﬀerent
event samples; PYTHIA MB and PYTHIA
jet-production.

Fig. 4.19 shows the jet finding eﬃciency extracted from a PYTHIA MB dataset forreconstruction-level jets with/without leading track pT cut. The leading track pT cut decreases jet finding eﬃciency since the reconstructed jet doesn’t have constituents withpT > 5 GeV and/or the leading track might not be reconstructed due to tracking ineﬃciency. This result is cross-checked against the jet finding eﬃciency obtained with a
PYTHIA jet production dataset (see Fig. 4.20). The results are in good agreement, sothat the jet finding eﬃciency computed from the PYTHIA jet production sample, are morestatistically precise at high-pT , have been used.

4.7

Unfolding

The measured jet spectra are usually distorted due to finite resolution/tracking eﬃciency ofthe detector and fluctuating background especially in the most central heavy-ion collisions.
An unfolding procedure [52] is performed to revert to true spectrum from the measured
one based on the concept that the measured distribution is described as a convolution of
distortion responses with the true one, which, more specifically, could be written as:
Mm = Gm d · (Gd, t · Tt )
5
6
−1
Tt =
G−1
·
G
d, t
m d · Mm

(4.5)
(4.6)

60

Chapter 4. Analysis

this thesis

140

0.35

(GeV/c)

0.4

200

0.5

ALICE Pb-Pb sNN = 5.02 TeV
Anti-kT R = 0.2, Charged Jets|η | < 0.7, p lead > 5 GeV/cjet
TCentrality: 0-10 %

180
160
140

0.45
0.4
0.35

p

T,ch,jet

160

0.45

gen

ALICE Pb-Pb sNN = 5.02 TeV
Anti-kT R = 0.2, Charged Jets|η | < 0.7, p lead > 5 GeV/cjet
TCentrality: 0-10 %180

T,ch,jetthis thesis
0.5

p

gen

(GeV/c)

200

120

0.3

120

0.3

100

0.25

100

0.25

80

0.2

80

0.2

60

0.15

60

0.15

40

0.1

40

0.1

20

0.05

20

0.05

0

0

0
30

40

50

60

70

80

90

100 110 120

0

20

40

60

80 100 120 140 160 180 200

p rec(GeV/c)T,ch,jetFig 4.21: Response Matrix on backgroundfluctuation in 0-10% centrality class.

0

p rec
(GeV/c)T,ch,jetFig 4.22: Response Matrix on detector eﬀects
in 0-10% centrality class.

where Mm is the measured spectrum, Gm, d (Gd, t ) is the distortion response from background fluctuations (detector resolution/ineﬃciency) and Tt is the true unknown spectrum
to be extracted. Gm, d and Gd, t are called “Response Matrix” on account of their Matrix
format. This analysis utilises the “SVD unfolding” [53] method.
On the one hand, Gm, d (background fluctuation response) is given by the following
procedure:
1. normalise the δpT distribution given in section 4.5 to unity.
2. shift normalised δpT distribution by the pgensuch that the diagonal elements containTthe δpT = 0 bin content (see Fig. 4.21).
On the other hand, Gd, t (response from detector eﬀects) is calculated using a PYTHIA MC
simulation as follows:
1. remove PYTHIA tracks following the tracking eﬃciency defined in section 4.3.2,
2. reconstruct jets with the resulting reduced number of tracks, ,3. match generator-level jets and jets reconstructed in step (2), using the same matchingconditions as those described in section 4.6,
4. fill the response matrix with the pT of the matched jet pairs,

Section 4.7. Unfolding

61

this thesis

this thesis

ALICE Pb-Pb sNN = 5.02 TeV
Anti-kT R = 0.2, Charged Jets|η jet | < 0.7, p lead
> 5 GeV/c
T
Centrality: 0-10 %T,ch,jet

160
140

−10

10

10−11
10−12
−13

10

120

10−14

100

10

80

10

−15
−16

Kinematic Efficiency(GeV/c)

10

180

p gen

1.2

−9

200

0.8
0.6
ALICE Pb-Pb sNN = 5.02 TeV

0.4

−17

10

60

1

Anti-kT R = 0.2, Charged Jets

−18

10

40
20

|η jet | < 0.7, p lead
> 5 GeV/c
T

0.2

−19

10

Centrality: 0-10 %

−20

10

0
30

40

50

60

70

80

90

100 110 120

p rec(GeV/c)T,ch,jet

0
0

10−21

Fig 4.23: Combined Response Matrix for 010% centrality class.

50

100
p gen

150
200
(GeV/c)T,ch jetFig 4.24: Kinematic eﬃciency, the jet yieldfraction lays inside the selected window of
combined response matrix.

5. normalise the projection on the pgenT -axis to unity. (see. Fig. 4.22)
Subsequently, Gm, d · Gd t , called “combined response matrix” is calculated and weighted

by the prior which is the base spectrum of unfolding. The generator-level jet spectrum
passing step (3) of Gd, t construction process is used as a prior. The combined response

0.8|η | < 0.7, p lead > 5 GeV/cjet
TCentrality: 0-10 %

0.7
0.6

Background fluctuation
Detector effectCombined

0.5
0.4

T,jet

T,jet

ALICE Pb-Pb sNN = 5.02 TeV
Anti-kT R = 0.2, Charged Jets

0.9

this thesisσ(p rec ) / p gen

T,jetσ(p rec ) / p gen

T,jetthis thesis

1

1
0.8
0.6
0.4
0.3
0.2

0.1

0.1
40

60

80
p

gen
T,ch jet100
120(GeV/c)Fig 4.25: Jet momentum resolution for 0-10%
centrality class.

Background fluctuation
Detector effectCombined

0.5

0.2

20

|η | < 0.7, p lead > 5 GeV/cjet
TCentrality: 30-50 %

0.7

0.3

0

ALICE Pb-Pb sNN = 5.02 TeV
Anti-kT R = 0.2, Charged Jets

0.9

0

20

40

60

80
p gen

T,ch jet100
120(GeV/c)Fig 4.26: Jet momentum resolution for 3050% centrality class.

62

Chapter 4. Analysis

Jet Yield [a.u.]

this thesis
109

Particle Level
Detector Level
Smeared

108

107

106

105

104

0

20

40

60

80

100

p

jet
T

120

[GeV/c]Fig 4.27: pT distributions used for unfolding performance check; (red) PYTHIA generatorlevel jets, (blue) PYTHIA reconstruction-level jets, (green) and reconstruction-level spectrum after δpT smearing.

matrix in the 0-10% centrality class is shown in Fig. 4.23. The kinematic range of thegenerated pT -axis is wider than the reconstructed pT -axis one in the combined response
matrix in order to allow for feed-in into the measured pT range. The fraction of jets which
will be smeared outside the acceptance of the response matrix, is known as the kinematiceﬃciency (Fig. 4.24) and is taken into account in the unfolding procedure.
Fig. 4.25 and Fig. 4.26 show the jet momentum resolution in Pb-Pb collisions for the
0-10% and 30-50% centrality classes respectively. The momentum resolution is defined asgen
σ (prec
T,ch jet ) / pT,ch jet and derived from the response matrices. The background fluctuations

dominate the detector resolution at low-pT while the opposite happens at high-pT .
The SVD unfolding is controlled by a regularisation parameter k which can be optimisedby the D-vector distribution (for the detail, see [53]). Finally, the unfolded spectra are scaled
down by jet finding eﬃciency to compensate for jets not reconstructed.
4.7.1

Test of Unfolding Performance

The performance of unfolding is benchmarked against a known spectrum given by MC
simulation. The settings of this test are listed below:• the true jet spectrum to be recovered is the PYTHIA generator-level jet spectrum,

Section 4.7. Unfolding

63

this thesis
yield [a.u.]yield [a.u.]

this thesis
1

Generated
10− 1

Unfolded

10− 2Measured−3

10

Refolded

10− 2

10− 4

−3

10

10− 4

−5

10

−5

10

−6

10
−6

−7
1.2
10
0
1.15
1.1

20

40

60

80

100 120 140 160

p

jet
T

180 200[GeV/c]

1.05
1
0.95
0.9
0.85
0.80

20

40

60

80

100 120 140 160

p

gen
T,jet

180 200

Refolded/Measured

Unfolded/Generated

10

−7
1.2
10
30
1.15
1.1

40

50

60

80

90

100

110

120

pjet [GeV/c]
T

1.05
1
0.95
0.9
0.85
0.830

40

50

60

70

80

90

100

110

120

prec [GeV/c]
T,jet[GeV/c]Fig 4.28: (top) Unfolded jet spectrum andgenerator-level jet spectrum. (bottom) The
ratio of these spectra.

70

Fig 4.29:(top) Refolded jet spectrum
and reconstruction-level spectrum after δpT
smearing. (bottom) The ratio of these spectra.

• the detector response is calculated from the same PYTHIA with GEANT simulation,• background Gaussian fluctuations (σ = 4 GeV/c ) are assumed,• the unfolding input jet spectrum is δpT smeared PYTHIA reconstruction-level jet
spectrum.

Fig.4.27 shows each input/output spectrum used in this test. The smearing by the background fluctuations changes the spectrum shape in the low-pT region, while the detector
eﬀects are dominant at higher pT . The unfolded and true jet spectra are shown in Fig. 4.28.
Additionally, the refolded spectrum which is produced by refolding the unfolded spectrumby the same response matrix is shown in Fig. 4.29 along with the smeared input spectrum.
Both results agree with a precision of ∼ 1%.

64

4.7.2

Chapter 4. Analysis

Unfolded Spectrum

The cross section of charged jet with R = 0.2 in Pb-Pb collisions are shown in Fig. 4.30 for
four centrality classes together with the charged jet cross section in pp collisions at same
centre-of-mass energy. In the next chapter, the systematic uncertainties displayed in thisplot are detailed.

Fig 4.30: The cross section of charged jet with R = 0.2 in Pb-Pb and pp collisions at√
sNN = 5.02 TeV .

Chapter 5

Systematic Uncertainties

In this chapter, the main sources of systematic uncertainties aﬀecting the jet spectrum measurement in Pb-Pb collisions presented in this thesis are discussed in detail and estimated.
They can basically be classified into four topical groups (each group sometimes itself broken
down into several uncertainties):
1. the uncertainties due to the unfolding procedure,
2. the uncertainty on the δpT distribution evaluation,
3. the uncertainty on background pT density due to elliptic flow,
4. the uncertainties on tracking eﬃciency and resolution.

5.1
5.1.1

UnfoldingpT Range of the Unfolded Jet Spectrum

The unfolded pT range is chosen to be much wider than the measured pT range in order
to allow bin-to-bin migration likely to occur in the unfolding process. To estimate how
feed-in/out from high/low-pT jets aﬀect the unfolded jet spectrum, the unfolded pT range isvaried around its nominal limits by 10 GeV/c (25 GeV/c ) at low(high) pT . The contribution
to the relative systematic uncertainty in the most central collisions is shown in Fig. 5.1. The
influence of these variations are less than 2% over all centrality classes and pT ranges.
5.1.2

pT Range of the Measured Jet Spectrum

The measured pT range is varied by 5 GeV/c both on the upper and lower limits. At
low-pT , the extension of the pT range enhances the combinatorial background despite theleading track requirement. In the high-pT region, the influence of the limited statistics
recemerges. Fig. 5.2 shows the contribution of the prec
T,min and pT,max cut-oﬀ variations to thesystematic uncertainty on the unfolded jet spectrum.
65

66

Chapter 5. Systematic Uncertainties

this thesis

p true: 10 - 200 [GeV/c]
T

10− 3

p true: 0 - 175 [GeV/c]
T
p true: 0 - 225 [GeV/c]
T

T(Nominal)p meas: 25 - 120 [GeV/c]T
p meas: 30 - 115 [GeV/c]T
p meas: 30 - 125 [GeV/c]
T

10− 5

10− 5

50

60

70

80

1.2
1.1

90

100
110 120
p jet(GeV/c)
T

ratio

10− 4

40

1.3− 630
10

1
0.9

0.8
0.7
30

0.8
0.7
30

50

60

70

80

90 100 110 120

40

50

60

70

80

90

40

50

60

70

80

90 100 110 120

1.2
1.1

1
0.9

40

p meas: 35 - 120 [GeV/c]
T

10− 3

10− 4

1.3− 630
10

p meas: 30 - 120 [GeV/c]
T

jet

jet

1/ N ev dN

ratio[GeV/c](Nominal)

this thesis

10− 2

1/ N ev dN

/d p

T

p true: 0 - 200
T

/d p

10− 2

p Tjet (GeV/c)

Fig 5.1: Unfolded spectra for diﬀerent unfolded jet pT range selections(top), and theirdeviations from nominal selection(bottom),in 0 - 10% centrality class.
5.1.3

100
110 120
p jet(GeV/c)Tp Tjet (GeV/c)

Fig 5.2: Unfolded spectra for diﬀerent measured jet pT range selections(top), and theirdeviations from nominal selection(bottom),in 0 - 10% centrality class.

Unfolding Method

The unfolded spectrum given by the “Bayes Unfolding” is compared to the result of the SVD
unfolding method. In Fig. 5.3, the unfolded spectra and their ratios are shown. Deviations
up to ∼ 5% at low pT are observed for the Bayesian method.
5.1.4

Unfolding Regularisation Parameter

The choice of SVD regularisation parameter k is driven by the D-vector. The regularisation
parameter should be set to coincide with the critical value beyond which the d values drop
to and stick around unity. In order to check that the result does not change dramatically, kis varied around the nominal value, k ± 1. The corresponding variation of the jet spectrum
is shown in Fig. 5.4.

Section 5.1. Unfolding

67

this thesis

10− 2

T

k=4

1/ N ev dN

jet

Bayes

jet

10− 3

10− 4

10− 5

10− 5

1.3− 630
10

40

50

60

70

80

1.2
1.1

90

100
110 120
p jet(GeV/c)T

1.3− 630
10

1
0.9

0.8
0.7
30

0.8
0.7
30

50

60

70

80

90 100 110 120

p Tjet (GeV/c)

Fig 5.3: Unfolded spectra for diﬀerent unfolding method selections(top), and their deviation from nominal selection(bottom), in
0 - 10% centrality class.

5.1.5

40

50

60

70

80

90

40

50

60

70

80

90 100 110 120

1.2
1.1

1
0.9

40

k=6

10− 3

10− 4

ratio

1/ N ev dNratio

k = 5 (Nominal)

/d p

/d p

T

SVD(Nominal)

this thesis

10− 2

100
110 120
p jet(GeV/c)Tp Tjet (GeV/c)

Fig 5.4:
Unfolded spectra for diﬀerents regularisation parameter selections(top),
and their deviations from nominal selection(bottom), in 0 - 10% centrality class.

MC Generator and Prior Selection

The uncertainty related to the choice of the MC event generator is estimated using two
event generations: PYTHIA with a diﬀerent tune (Perugia0) and HERWIG. The diﬀerence of the simulated jet spectrum and fragmentation between the event generators can
induce diﬀerences in the jet response matrix and the prior used for the unfolding. The
method to estimate this uncertainty is based on a fast simulation. We simulate PYTHIA
events, extract the charged final-state particles, apply a parametrised tracking eﬃciency
and pT resolution particle-by-particle and use the FastJet anti-kt algorithm to cluster boththe original generator-level event and the reconstruction-level event to derive the response
matrix. The deviations are shown in Fig. 5.5, resulting in uncertainties of the order of 5%.

68

Chapter 5. Systematic Uncertainties

this thesis

10− 2

/d p

T

PYTHIA:Perugia2011(Nominal)

1/ N ev dN

jet

PYTHIA:Perugia0
HERWIG

10− 3

10− 4

ratio

10− 5

1.3− 6
10

40

50

60

70

80

40

50

60

70

80

90 jet 100 110
p T (GeV/c)

1.2
1.1
1
0.9
0.8
0.7

90

100

110

p Tjet (GeV/c)

Fig 5.5: Unfolded spectra for diﬀerent event generator selections(top), and their deviations
from nominal selection(bottom), in 0 - 10% centrality class.

5.2

Background Fluctuation δpT Estimation

Three random cone selections are used to assess the δpT distribution variation: (i),(ii)excluding the surrounding areas defined by ∆R > 0.5 and 1.5 and (iii) excluding the 1st
and 2nd leading jet neighbourhood of ∆R > 1.0. The resulting δpT distribution widthvariation is of a few hundred MeV/c corresponding to less than 5 % change of the unfolded
spectrum for the most central collisions (see Fig. 5.6).

5.3

Correction for the Elliptic Flow Bias

The sample of jets selected with a leading track cut is biased by elliptic flow in heavy-ion
collisions. The azimuthal dependence with respect to the leading track in the event of
the mean background density departure from the nominal value (full azimuth) is shown in
Fig. 5.7. The azimuthal regions are defined as:Section 5.3. Correction for the Elliptic Flow Bias

69

this thesis

10− 2

/d p

T

RC w/o lead.Jet (∆ r>1.0)

1/ N ev dN

jet(Nominal)
RC w/o lead.Jet (∆ r>0.5)

10− 3

RC w/o lead.Jet (∆ r>1.5)
RC w/o 2 lead.Jet (∆ r>1.0)

10− 4

ratio

10− 5

1.3− 630
10

40

50

60

70

80

90

40

50

60

70

80

90 100 110 120

1.2
1.1

100
110 120
p jet(GeV/c)
T

1
0.9
0.8
0.7
30

p Tjet (GeV/c)

Fig 5.6: Unfolded spectra for diﬀerent δpT definitions(top), and their deviations fromnominal value(bottom), in 0 - 10% centrality class.

⎧⎪⎪[0, π/4 − R]
$
$ ⎪
⎨
$
$
φ
−
φ
=
$ leading track
kT cluster $ ⎪[π/4 + R, 3π/4 − R]⎪⎪⎩
[3π/4 + R, π]: near side
: perpendicular: away side

The diﬀerence of the azimuthal background density to the mean background density inthe full event is 4 GeV/c in the 0-10% centrality class. The uncertainty on the backgrounddensity due to the flow bias is estimated by shifting the δpT distribution by ±4 π R2 GeV/c .
Since the upper and lower variations of the background density due to flow are symmetricwith respect to the nominal value, the systematic uncertainty is also symmetric as seen in
Fig. 5.8. The uncertainty due to the flow bias decreases with pT,jet , from 7% at pT,jet = 40
GeV/c to 4% at pT,jet = 100 GeV/c .

70

Chapter 5. Systematic Uncertainties

this thesis

10− 2

/d p

T

ρ shift: ± 0 GeV/c (Nominal)

1/ N ev dN

43

ρ shift: + 4 GeV/c

10− 3

10− 4

-ρ

2
1
0

10− 5

−1
−2

Near Side
Away Side
Perpendicular

−3
−4
−5
0

10

20

30

40

ratio

ρ

this thesis

5

regionfull event[GeV/c]jetρ shift: - 4 GeV/c50
60Centrality

1.3− 630
10

40

50

60

70

80

90

40

50

60

70

80

90 100 110 120

1.2
1.1

100
110 120
p jet(GeV/c)T1
0.9

Fig 5.7: The azimuthal dependence with respect to the event leading track of averagebackground density deviation from the nominal (full azimuth) value.

0.8
0.7
30

p Tjet (GeV/c)

Fig 5.8:
Unfolded spectra for diﬀerent
average background densities due to flowbias(top), and their deviations from nominal
value(bottom), in 0 - 10% centrality class.

5.4

Tracking Eﬃciency and Resolution

The uncertainty on the tracking eﬃciency is estimated to be 4% based on the track cut
parameters which are applied during track reconstruction, see Fig. 5.9. New detector response matrices are built using a fast simulation including a tracking eﬃciency variationof ±4% around the default eﬃciency. The PYTHIA jet spectrum smeared by the nominal
combined response matrix is unfolded using these variations. The diﬀerence between thenominal unfolded solution and the unfolded spectra with modified tracking eﬃciencies gives∼ 10% systematic uncertainty on the unfolded yield at pT,jet = 100 GeV/c .
Furthermore, the uncertainty related to momentum resolution with much larger variation (±20%) gives a ∼ 5% deviation as shown in Fig. 5.10.

Section 5.5. Summary of Systematic Uncertainties

71

this thesis

10− 2

T
jet

Trk. Eff -4%

1/ N ev dN

Trk.Res. +20%

10− 5

10− 5

50

60

70

80

1.2
1.1

90 jet 100 110
p T (GeV/c)

ratio

10− 4

40

1.3− 6
10

1
0.9

0.8
0.7

0.8
0.7

50

60

70

80

90

100

110

p Tjet (GeV/c)

Fig 5.9: Unfolded spectra for diﬀerent tracking eﬃciency estimation(top), and their deviations from nominal value(bottom), in 0 10% centrality class.

5.5

40

50

60

70

80

40

50

60

70

80

1.2
1.1

1
0.9

40

Trk.Res. -20%

10− 3

10− 4

1.3− 610

ratio

Nominal Trk.Res.

/d p

jet

Trk. Eff +4%

1/ N ev dN

/d p

T

Nominal Trk.Eff

10− 3

this thesis

10− 2

90 jet 100 110
p T (GeV/c)

90

100

110

p Tjet (GeV/c)

Fig 5.10:
Unfolded spectra for diﬀerent
track momentum resolution(top), and theirdeviations from nominal value(bottom), in
0 - 10% centrality class.

Summary of Systematic Uncertainties

In Tab. 5.1 and Tab. 5.2 the breakdown of the present systematic uncertainties for three jet
pT bins are quoted. The final jet cross-section measurement incorporates systematic uncertainties divided into two categories: (i) Spectrum shape uncertainties and (ii) Correlated
uncertainties. The shape uncertainties are anti-correlated or less correlated between binsof the unfolded spectrum: if the yield increases in some bins, it concomitantly decreases in
the other bins or are not correlated. The correlated uncertainty, for their part, result incorrelated changes over the entire spectrum which means that the spectrum shape is almost
conserved.
Contributions to the spectrum shape systematic uncertainties include regularisation
parameter, pT range of the unfolded jet spectrum, pT range of the measured jet spectrum,

72

Chapter 5. Systematic Uncertainties

the unfolding method, and the choice of the generator. The uncertainties are added inquadrature to calculate the total systematic uncertainty.
Correlated uncertainties originate from the uncertainty on the knowledge of the tracking
eﬃciency and resolution, the correction for the flow bias and the background fluctuation
δpT estimation. These contributions are also added quadratically.
In the same tables, the shape and correlated systematic uncertainties are reported.

Section 5.5. Summary of Systematic Uncertainties

pT,ch.jet73

30 - 40 GeV/c

50 - 60 GeV/c

70 - 90 GeV/cpT range unfolded

±1.0

±1.0

±1.0

pT range measured

±2.9

±1.2

±3.7

Unfolding method

±4.4

±4.4

±4.4

Regularisation

±0.4

±2.4

±4.8

Generator/Prior

±5.7

±5.7

±5.7

Total shape uncertainty

±7.8

±7.7

±9.5

δpT

+5.1
−1.8

+2.2
−0.9

Flow bias

+6.6
−6.1

+3.8
−0.9

Tracking eﬃciency

±5.3

±6.8

±8.6

Tracking resolution

±3.4

±3.4

±3.4

Total correlated uncertainty

+10.4
−8.9

+9.7
−8.8

+10.0
−9.8

+4.7
−4.4

+3.2
−3.2

Tab 5.1: Systematic uncertainties for 0 - 10%
pT,ch.jet

20 - 30 GeV/c

40 - 50 GeV/c

60 - 70 GeV/cpT range unfolded

±0.5

±0.5

±0.5

pT range measured

±2.6

±0.8

±2.4

Unfolding method

±1.2

±1.2

±1.2

Regularisation

±0.2

±1.3

±2.4

Generator/Prior

±5.9

±5.9

±5.9

Total shape uncertainty

±6.5

±6.2

±6.9

δpT

+5.0
−1.3

+1.9
−0.6

Flow bias

+9.0
−8.1

+2.5
−0.8

Tracking eﬃciency

±8.9

±8.5

±8.1

Tracking resolution

±3.4

±3.4

±3.4

Total correlated uncertainty

+14.0
−12.6

+10.9
−10.5

+9.9
−9.7

+5.4
−5.1

Tab 5.2: Systematic uncertainties for 30 - 50%

+4.2
−4.2

Chapter 6

Results and Discussion

In this chapter, the jet cross sections and the corresponding nuclear modification factors
are presented. These results will be compared with single particle measurements or jetmeasurements at lower collision energy for systematic understanding of parton energy loss
in the QGP. To go further in the study of parton energy loss, the jet energy loss is extracted
from the results of this work. The jet energy loss, which is the more direct observable ofparton energy loss, helps to assess the relative contributions of the two energy loss mechanisms, gluon radiation (radiative energy loss) and multiple parton scattering (collisionalenergy loss).

6.1

Jet Suppression

To estimate jet quenching in heavy-ion collisions, the jet nuclear modification factor is
calculated as the ratio of charged jet spectrum in heavy-ion collisions to that of pp collisions,normalised by the number of binary collisions:AA⟨Ncoll ⟩ = ⟨TAA ⟩ × σinel

RAA

=

=

AA / dp dη
d 2 σch,jetT
2 pp⟨Ncoll ⟩ d σch,jet / dpT dη
AA / dp dη
1/N ev d 2 Nch,jet
T
pp⟨TAA ⟩ d 2 σch,jet/ dpT dη ,

(6.1)
(6.2)

(6.3)

where ⟨TAA ⟩ and ⟨Ncoll ⟩ are respectively the nuclear overlap function and the number ofbinary collisions given by the Glauber model. The nuclear overlap function, number ofparticipants, and number of binary collisions are reported in Tab. 6.1 for the consideredcentrality classes (and the corresponding impact parameter b).
Fig. 6.1 shows the charged jet spectra after the normalisation by ⟨TAA ⟩. As pp reference

for the RAA calculation, the experimental data collected in 2015 by ALICE are used [33].
The statistics of these data is about 25M events, and the kinematic reach of the jet spectrum
is up to ∼ 60 GeV/c . In order to extend the kinematic reach of RAA measurement, the75

76

Chapter 6. Results and Discussion

Fig 6.1: Charged jet spectra in Pb-Pb collisions after the normalisation by the number of√binary collisions. As a pp reference, the spectrum measured with s = 5.02 TeV pp run
and corresponding simulation result are shown.

spectrum given by the POWHEG MC event generator [54], which is based on next-toleading-order QCD calculations, is adopted as an additional pp reference. pp data and thePOWHEG predictions are in good agreement as it can be seen in Fig. 6.1.
√
Fig. 6.2 shows the charged jet RAA for Pb-Pb collisions at sNN = 5.02 TeV for four
centrality classes, in which the shaded and open boxes represent the shape and correlated
systematic uncertainties respectively. In addition, the red bars at upper-right in the figuresSection 6.1. Jet Suppression

77

centrality

bmin (fm)bmax (fm)⟨Ncoll ⟩⟨Npart ⟩⟨TAA ⟩

0-10%

0

4.96

10-30%

4.96

8.59

1636.0 ± 170.0

359.0 ± 3.0

23.4 ± 0.9

30-50%

8.59

11.1

50-90%

11.1

15

263.5 ± 16.1

108.8 ± 1.4

3.8 ± 0.2

801.0 ± 55.5
38.1 ± 1.6

225.5 ± 2.3
26.8 ± 0.4

11.4 ± 0.4

0.54 ± 0.02

Tab 6.1: Geometrical parameters obtained from Glauber model.

are the uncertainties from the ⟨TAA ⟩ scaling. A strong jet suppression of RAA ∼ 0.4 isobserved in the most central events, while for peripheral collisions the suppression is weaker,
RAA ∼ 0.8. This suppression in central heavy-ion collisions indicates that the full jet energy
is not contained in the reconstructed jets (R = 0.2). This is consistent with a scenario in

which gluons are radiated out-of-cone due to the parton interaction with the dense medium
which results in a decrease of jet-pT . Another reason for a jet nuclear modification factor
lower than unity, could also be that some jets cannot be resolved anymore or melt in theFig 6.2: Charged jet nuclear modification factors of R = 0.2 in Pb-Pb collisions at
5.02 TeV .

√

sNN =

78

Chapter 6. Results and Discussion

Fig 6.3: Comparison of nuclear modification factor between charged particles at√
2.76 TeV and charged jets at sNN = 5.02 TeV .

√

sNN =

background. A RAA rise as function of pT is observed in the low-pT region, while at highpT gently increases or reaches a constant value.

6.2

Comparison to Charged Hadrons

In Fig. 6.3 the jet nuclear modification factor is compared to the single particle nuclear√
modification factor at sNN = 2.76 TeV measured by ALICE [55]. Note that the pT scale,centrality bins and centre-of-mass energy of both measurements are diﬀerent even if therecent results from the ALICE collaboration show no significant diﬀerence between charged√
particle RAA in Pb-Pb collisions at sNN = 2.76 and 5.02 TeV [56].
A single charged particle and a jet of the same pT originate from diﬀerent parton energies.
Naively one expects that the jet catches some or all of the radiated energy resulting in alarger nuclear modification factor for jets compared to the nuclear modification factor forcharged particles. For both measurements, the expected RAA high-pT reach is similar if
the proper upscaling of single particle pT is applied. For charged jets fragmenting in thevacuum, the high pT leading particle carries about 50% of the corresponding jet pT . The
high-pT region observed in the single particle suppression approximately corresponds toSection 6.3. Comparison to the Jet RAA in Pb-Pb Collisions at√

sNN = 2.76 TeV

Fig 6.4: Comparison of charged jet nuclear modification factor between√
and sNN = 5.02 TeV .

√79

sNN = 2.76 TeV

2 × ptrack. The suppression for both high-pT observables at approximately the same partonTenergies is consistent even though diﬀerent centre-of-mass energies are considered.

6.3

Comparison to the Jet RAA in Pb-Pb Collisions at√

sNN = 2.76 TeV

The ALICE measurement of charged jet nuclear modification factor in Pb-Pb collisions at√√
sNN = 5.02 TeV is compared to that at sNN = 2.76 TeV in Fig. 6.4 [57]. The PYTHIA
charged jet spectrum is adopted as pp reference due to the lack of charged jet measurement√√in pp collisions at sNN = 2.76 TeV . The jet suppression in Pb-Pb collisions at sNN =√2.76 TeV is comparable to that at sNN = 5.02 TeV within systematic uncertainties except
for the high-pT region in the most central collision. As an aside, the same comparison
reported by ATLAS with R = 0.4 calorimetric jets at higher-pT is given in Fig. 6.5. A
similar magnitude of jet suppression for the two collision energies is observed.
The magnitude of jet suppression is expected to be stronger in higher centre-of-massenergy since heavy-ion collisions of higher centre-of-mass energy produce hotter/denser
and longer-lived medium, causing larger parton energy loss. Concomitantly, the increaseof collision energy results in a hardening of the jet spectrum shape, which enhances theChapter 6. Results and Discussion

R AA

80

1.5
ATLAS Preliminary
anti-k t R = 0.4 jets

ATLAS, s NN = 5.02 TeV, this analysis

0 - 10 %|y | < 2.1

ATLAS, s NN = 2.76 TeV, arXiv: 1411.2357
1

0.52015 Pb+Pb data, 0.49 nb-1
2015 pp data, 25 pb-1
0

100
0

200

300

400

500

600

900
p [GeV]T

Fig 6.5: Comparison of nuclear modification factor of jets with R = 0.4 measured by√√
ATLAS between sNN = 2.76 TeV and sNN = 5.02 TeV . [58]

nuclear modification factor.
Thus, the consistent RAA measurements despite the increase of energy can be interpreted
as a cancellation between these two eﬀects. In order to quantify each contributions, a direct
measurement of jet energy loss is performed.

6.4

Jet Energy Loss Toy Models

The jet energy loss is defined as the diﬀerence between the pp and Pb-Pb spectra of sameyields. This definition is based on the hypothesis that the jet yield at a given jet momentum
in heavy-ion collisions comes from the overlay of pp collisions with the same total yield.
Note, however, that the actual jet yield at a certain pT is a convolution of the diﬀerent
parton energies.
Three simple energy loss scenarios are considered in this analysis:
1. The jet energy loss is independent to jet pT .
2. The jet energy loss is proportional to jet pT .
3. A certain fraction of jets disappear.
Since the pp reference spectrum doesn’t suﬀer from energy loss, the PYTHIA charged
jet spectrum is used. The spectrum is fitted with a Tsallis function [59] in the m0 → 0 limit

Section 6.4. Jet Energy Loss Toy Models

81

this thesisd2σ / dp T,ch jet dη jet (mb c/GeV)

10−1

PYTHIA data
fitting result−210χ2/NDF = 0.64
PYTHIA sNN = 5.02 TeV

10−3

Anti-kT R=0.2 charged jets|η | < 0.7 p lead
> 5 GeV/c
T

10−4

jet

10−5
10−6

data/fit

10−70
1.4
1.2
1
0.8
0.6
0

20

20

40

40

60

p

60

80
T,ch jet80pT,ch jet

100 120(GeV/c)100
120(GeV/c)Fig 6.6: (top) PYTHIA Charged jet spectrum given by PYTHIA. The black line is Tsallis
fitting result. (bottom) The ratio of data to fitting function.

as:
d 2σ
dpT dη

= pT A(n − 1) (n − 2)
(nC)2

⎡

⎣1 +

pT
nC

⎤−n
⎦

.

(6.4)

where A, n and C are the fitting parameters. The fit shown in Fig. 6.6 performs well downto ∼ 20 GeV/c due to small χ2 /N DF value of 0.64.

The spectra in Pb-Pb collisions are also fitted by the same function, in which pT is

substituted with pT + ∆ for the scenario 1, or pT /(1 − f ) for the scenario 2, and for the
scenario 3, A is substituted with A/(1 − r), where ∆, f and r are respectively the jet energy

loss, the lost energy fraction and the disappeared jet fraction. The parameters A, C andn given by the reference spectrum fitting are set for these fittings. The fitting results forthese scenarios in 0 - 10% centrality are shown in Fig. 6.7 and extracted ∆, f and r values
are summarised in Tab. 6.2 with the fitting χ2 values.
The RAA distributions extracted from the fitting functions are shown in Fig. 6.8, Fig. 6.9

82

Chapter 6. Results and Discussion

Fig 6.7: Comparison of spectrum fitting from three energy loss models, in 0-10 % centrality
class.

and Fig. 6.10 for the three jet energy loss models. The model 1, which assumes a constantenergy loss, is in better agreement with data than the other models as shown in smaller χ2value, particularly in the low-pT region. Therefore, a constant jet energy loss is adopted forthe following sections.

0-10%
jet energy loss, ∆ ( GeV/c )lost energy fraction, f (%)
disappeared jet fraction (%)

jet energy loss, ∆ ( GeV/c )lost energy fraction, f (%)
disappeared jet fraction (%)

value

fitting χ2

9.9+1.6−1.5

4.1 × 10−2

56.3+6.4−5.9

4.3 × 10−1

14.7+2.6−2.1

5.8 × 10−1
30-50%

value

fitting χ2

4.2+1.5−1.3

4.2 × 10−2

32.0+9.9−9.0

3.0 × 10−1

7.2+2.8−2.3

3.7 × 10−1

Tab 6.2: Estimated value of spectrum fitting from three jet energy loss models.

Section 6.4. Jet Energy Loss Toy Models

83

Fig 6.8: Comparison of charged jet nuclear modification with constant energy loss model(black line).

Fig 6.9: Comparison of charged jet nuclear modification with fractional energy loss model(black line).

84

Chapter 6. Results and Discussion

Fig 6.10:

Comparison of charged jet nuclear modification with jet disappearance model(black line).

6.4.1

Path Length Dependence

The jet energy loss strongly depends on the parton path length in the QGP. The observed
strong jet suppression (presented in section 6.1) results from long parton path lengths
throughout the large size system produced in the most central collisions. Therefore, forbetter understanding the study of jet energy loss as a function of parton path length isof crucial importance. However, the observed inclusive jet spectrum is the result of thesuperimposition of all possible parton paths (see Fig. 6.11). The corresponding parton path
length should then be averaged over all possible paths.
In the following, the average path length will be estimated from the Glauber model.
The relation between the impact parameter and the estimated average parton path lengthis shown in Fig. 6.12. Using this relation, the centrality is converted to an average path
length.
Fig. 6.13 and Fig. 6.14 show the jet energy loss as a function of parton path length,
fitted with a linear and quadratic function respectively. The χ2 for the linear function fit
is 3.2 × 10−1 and for the quadratic function is 6.0 × 10−4 . Radiative energy loss is thensupposed to be responsible of the measured ∆pT distribution since it is known (from QCD
calculations, see section 1.3.1) to be proportional to the square of the path length.

Section 6.4. Jet Energy Loss Toy Models

85

parton path length: <L> (fm)this thesis
7
6

Pb+Pb, sNN = 5.02 TeV
RPb = 6.62 fm

5

σNN = 86.0 mb
4
3
2
1
0
0

Fig 6.11: The sketch of heavy-ion collisionin transverse plane. The average parton path
length and overlapped area are estimated by
toy model calculation.
6.4.2

2

4

6

8
10
12
14
impact parameter: b (fm)Fig 6.12:
The estimated average parton
path length as a function of collision impact
parameter b.

Centre-of-Mass Energy Dependence

As the nucleus-nucleus collision centre-of-mass energy increases, the produced QGP reaches
higher energy/particle densities and the system stays longer in the QGP phase. Since
the parton energy loss is correlated with gluon densities and therefore to charged particle
multiplicities (∆Eloss ∝ dNg /dη ∝ dNch /dη ), it is worth evaluating jet energy loss as afunction of dNch /dη .

Fig. 6.15 shows the jet energy loss as a function of charged particle multiplicity par unittransverse area, AT , for three centre-of-mass energies [57, 60]. AT is the overlapped areaof two incoming nuclei and can be estimated by the Glauber model (see Fig. 6.11). The
charged particle multiplicities are given by [61, 62, 63]. There is a significant increase of√energy at the LHC compared to RHIC (Au-Au collisions at sNN = 200 GeV ), such thata denser QGP is expected to be produced resulting in much larger energy loss.

86

Fig 6.13: Average energy loss of charged
jets as a function of estimated parton path
length, with fitting result by linear function.

Chapter 6. Results and Discussion

Fig 6.14: Average energy loss of charged
jets as a function of estimated parton path
length, with fitting result by quadratic function.

Fig 6.15: Average energy loss as a function of charged multiplicity par unit transverse area
in 0 - 10% centrality class for three centre-of-mass energies.

Chapter 7

Summary

The work undertaken in this thesis aims at revealing the properties of a new state of QCD
matter at extreme temperature and/or energy density, the Quark-Gluon Plasma, throughthe inclusive jet measurement. In the QGP, quarks and gluons become weakly coupled, deconfined from nucleons, due to the asymptotic freedom feature of QCD at high temperature.
According to Lattice QCD calculation, a transition from normal nuclear matter to a QGP
should occur when energy density exceeds a critical threshold of εc ∼ 0.18 - 0.5 GeV /fm3

(Tc = 154 ± 9 MeV ). Relativistic heavy-ion collisions, which produce extremely high tem-

peratures and energy densities, are the unique tool to create QGP in the laboratory. Jets,
defined as sprays of hadrons resulting from the fragmentation of high-energy partons, are
one of the most powerful probes to study QGP properties. Such partons are indeed produced at very early stages of the collision and propagate through the medium losing energy
via gluon radiation or multiple scattering. As such, their modification (yield, fragmentation,
shape. . . ) reflects the whole system evolution. This phenomenon, called jet quenching, isconfirmed by several experimental observables measured both at RHIC and LHC.
The LHC (Large Hadron Collider) at CERN started operation from 2009 and sincethen, various collision systems and energies were provided. The ALICE, one of the four
LHC experiments, is optimised for the study of QGP in heavy-ion collisions. During thetwo-year LHC long shutdown period (LS1) from 2013, the LHC accelerator was upgraded toachieve higher beam luminosity and energy. The ALICE experiment seized the opportunityof LS1 to upgrade some of its detectors to cope with the new beam conditions and keep
improving QGP measurements.
During LS1, a new Electromagnetic calorimeter “DCAL” was installed in ALICE toenhance the acceptance for neutral particles and measure di-jet energy with charged andneutral particles. Along with this upgrade, a new online trigger system was deployed toeﬃciently select events containing high energy electromagnetic showers from jets or highpT photon. Taking advantage of back-to-back relation in azimuth between DCAL and EMCAL, the new L1 trigger algorithm implements a median background estimation whichmakes the calorimeter triggers more self-consistent. The trigger calculation is carried out
87

88

Chapter 7. Summary

by a FPGA mounted on the STU (Summary Trigger Unit) board. The new trigger algorithm performance was validated with the data taken in the first Pb-Pb run of the LHC
Run2 period (after LS1).
Using the same Pb-Pb data, jet production was measured at highest-ever centre-of-massenergy of 5.02 TeV provided by the LHC. Jets are reconstructed from charged particles detected in the ALICE central tracking detectors, with jet resolution parameter of R = 0.2.
One of the basic challenge for the jet measurement in heavy-ion collisions is to separate
the jets from the soft underlying event. The average energy contribution from the softunderlying event is quantified on an event-by-event basis and subtracted from the reconstructed jet. The remaining underlying event fluctuations and detector eﬀects are unfolded
at an event-ensemble level. Additionally, a jet leading track transverse momentum cut-oﬀ
of 5 GeV/c is applied to reduce the fake jet contamination.
A strong suppression of jet production is observed in the most central Pb-Pb collisions
and quantified by the measurement of the nuclear modification factor, RAA . The observed
suppression confirms the jet quenching picture established by earlier results. To gain further insight into the parton energy loss mechanism, in this work, the jet energy loss isstudied using spectrum energy shift between AA and pp collisions. The following notableconclusions were drawn:• The measured jet nuclear modification factor is well accounted for with a constantenergy loss model in the considered momentum range (up to ∼ 100 GeV/c ).

• The magnitude of energy loss at LHC energies is larger than at RHIC, which suggeststhat the nuclear collisions of larger centre-of-mass energy produce denser QGP.

• The energy loss as a function of the average parton path length has a quadratic
behaviour which supports the idea that gluon radiation is the dominant source ofparton energy loss in QGP.
To go one step further, a systematic study (as a function of centre-of-mass energy, resolution parameters, leading track pT cut-oﬀ, charged+neutral jet measurement. . . ) should
be carried out. Complementary jet correlation studies (e.g. requiring an away side jet,high-pT photon or high-pT hadron. . . ) would also help to control the parton path length.
Especially, the jet/photon triggers developed in this thesis work will help a lot these latter
analysis to collect the requested large statistics of jets and/or high-pT photons.

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