UNIVERSITA DEGLI STUDI DI PADOVA

Measurement of D0 production in Proton-Proton Collisions at s = 7 TeV with

the ALICE Detector

A Dissertation Presented

By

Xianbao Yuan

to

The Doctoral School in partial fulfillment of the requirements

For the Degree of Doctor of Philosophy in Physics

Supervisors： Viesti Giuseppe，Daicui Zhou

Specialty：Particle physics and nuclear physics

Research Area: Ultra-relativistic heavy-ion collisions

DissertationDissertationDissertationDissertation

MeasurementMeasurementMeasurementMeasurement ofofofof DDDD0000 productionproductionproductionproduction ininininProton-ProtonProton-ProtonProton-ProtonProton-Proton

CollisionsCollisionsCollisionsCollisions atatatat s =7=7=7=7 TeVTeVTeVTeV withwithwithwith thethethetheALICEALICEALICEALICE DetectorDetectorDetectorDetector

ByByByBy

XianbaoXianbaoXianbaoXianbao YuanYuanYuanYuan

SupervisorsSupervisorsSupervisorsSupervisors：VVVVieieieiestistististi GiuseppeGiuseppeGiuseppeGiuseppe，DaicuiDaicuiDaicuiDaicui ZhouZhouZhouZhou

SpecialtySpecialtySpecialtySpecialty：ParticleParticleParticleParticle physicsphysicsphysicsphysics andandandand nuclearnuclearnuclearnuclear physicsphysicsphysicsphysics

ResearchResearchResearchResearchArea:Area:Area:Area: Ultra-relativisticUltra-relativisticUltra-relativisticUltra-relativistic heavy-ionheavy-ionheavy-ionheavy-ion collisionscollisionscollisionscollisions

UNIVERSITAUNIVERSITAUNIVERSITAUNIVERSITADEGLIDEGLIDEGLIDEGLI STUDISTUDISTUDISTUDI DIDIDIDI PADOVAPADOVAPADOVAPADOVA

November 22, 2011

Acknowledgements

The writing of this thesis would not have been possible without the help and encouragement of many

professors and teachers, friends and my family. It is my great pleasure to thank all these people,though it is

difficult to express my gratitude to all of them individually.

First of all, I deeply thank my advisors Prof. Giuseppe Viesti，Prof. Zhou Daicui, Prof. Andrea

Dainese and Prof. Turrisi Rosario, Prof. Antinori Federico who led me to the fascinating world of high energy

physics. I feel fortunate to work under their kind guidance and supports and I will never forget the exciting

moments we have enjoyed in our discussions. All of my supervisors have spent a significant effort and time in

teaching me how to be a good scientist. The remarkable scope of insight with clarity, profound knowledge with

breadth, together with the careful judgments, vitality, precision and enthusiasm inspire me to work harder to

live up to their expectation.

I would like to thank Prof. Cai Xu, Prof. Liu Feng. Inparticular, I would like to thank Prof. Yin

Zhongbao and associate Prof. Wang Yaping for their discussions in our work group.

I would like to thank to Rossi Andrea, Bianchin Chiara, Bombonati Carlo, Caffarri Davide and Meng

Guang. Who give me great help on my work and let me spent a very happy time in Padova. I also thank to Prof.

Daniela Fabris, Prof. Maurizo MOrAndo, Prof. Francesca Soramel, Sandea Maretto, Silvia Pesente, Luca

Stevanato, Nassreldeen Elsheikh,. Who give me a lot of help and encourage me to overcome different troubles

when I stayed in Padova.

Thanks to all the people that I have known or shared my time in Padova, specially Hao Xin, Zhao

Heer, Wang Zhirui, Bao Yiyan, Yao Yuliang, Yang Yong, Wang Jing, Liu Yiliang, Ma Hao, Liu Zheng, Huang

Binbin, Zheng Jian, He Fuben, Su Huaien, Qian Jiyun, Pan Kailin, Cai Yunfan, Zhao Xiaowei ，Song

Yueyan，Shi Wei, Yu Xinyi， Li Tianyu ，Hu Xuexi ，Zhang Ying，Sun Yanwen，Qiu Yaqi and Tong Yan.

For sure I would never forget the great supports from China Scholarship Council (CSC), without its

support, I would have no chance to stay abroad for my PhD.

It is my pleasure to thank all members from the Institute of Particle Physics: Zhang Xiaoming, Wan

Renzhuo, Mao Yaxian, Ma Ke, Ding Hengtong, Xiang Wenchang, Xu Guifang, Zhu Xiangrong, Wang

Mengliang, Wang Dong, Zhang Fan, Zhu Jianling, Zhou Fengchu, Yin Xuan, Luo Jiebin, Zhu Jianhui, Zhu

Hongsheng, Zhang Haitao, Li Shuang, Zhang Yonghong, Dang Ruina, especially the friendship of Jiang

Qingquan, Wang Fei, Feng Bo, Jiang Bing feng, Zhang Zhu Liling, ZhengHua, Zhang Shenghao, Wu Kejun,

Xu Yuanguo, Li Hanling, Chang Qing, …

Finally, I would like to express my great appreciations to my all old friends and my family, especially

my parents and my parents-in-low, my wife Liu Furong, my young sister Yuan Juanjuan and her husband Han

Yongda, My brother Hu Bing. Thank you for your support and understanding.

Yuan Xianbao

CCNU,WuHan

Nov 19, 2011

Abstract

Driven by the curiosity of basic structure of the material world, from the beginning of Daltons

atomic theory in 1808, scientists have been established to explore the microscopic world. Later,

scientists found that atom consists of atomic nuclei and electrons. Until the inelastic electron ex-

periments, scientists realized that the nucleus have basic structure, that is, quarks and gluons. So

far there have not found much smaller structure in electron.The Standard Model of particle physics

is the best tool, currently, to describe the fundamental structure of matter and the fundamental

interaction forces among them. The basic components of this theory are three types of particles:

leptons, quarks and gauge bosons. There are six different leptons and the corresponding antilep-

tons, six different quarks and their corresponding antiquarks and four types of gauge bosons as

the force-carrying particles, which mediate the fundamental interaction force and can be grouped

to the electromagnetic, weak, and strong interactions. The electroweak interactions is described

by the Yang-Mills gauge theory. While the quantum chromodynamics (QCD) is a theory of the

strong interaction (color force), a fundamental force describing the interactions of the quarks and

gluons.

According to the quantum chromodynamics (QCD), a deconfined quark-gluon plasma (QGP)

will be formed at extremely high temperature and/or density. This deconfined phase (QGP)

consists of free quarks and gluons that compose hadronic matter. Quarks are confined in hadronic

matter, but quarks are deconfined in the QGP. In nature, the QGP probably have existed in

the first few microseconds after the Big-Bang and still exists in the cores of heavy neutron stars.

Fortunately, high energy heavy ion collisions provide a unique opportunity to study the properties

of such deconfined QGP and the transition is expected to occur at a temperature of about 175

MeV and an energy density of 0.7 GeV/fm3.

Super Proton Synchrotron (SPS) experiments at CERN first tried to create the QGP using

Pb-Pb collisions (√sNN = 17.6 GeV). Relativistic Heavy Ion Collider (RHIC) keeps this effort

by Au-Au collisions at Brookhaven National Laboratory at√sNN = 200 GeV. Several indirect

evidences for a ‘new state of matter’ (QGP) were announced, for example: collective flow, jet

quenching and J/ψ depression, etc. A Large Ion Collider Experiment (ALICE) is one of the four

experiments at Large Hadron Collider (LHC) the biggest accelerator in the world at the moment.

i

ALICE has been carrying on the experimental heavy-ion program by SPS and RHIC from 2010.

The main target of ALICE is the study the heavy-ion collisions at the center-of-mass energy of 5.5

TeV per nucleon with lead and study the properties of the hadronic matter at the extremely high

energy densities.

In this thesis one focus on charm physics measured with ALICE experiment. This is because

heavy-quarks (charm and bottom) provide a reliable tool to probe the dynamic properties of the

collision system evolution. Heavy quarks are characterized by early production which takes place

on the timescale of the order of 1/mQ according to the pQCD. Thus, their production kinematics is

not influenced by medium effects and due to the long decay length they undergo the thermalization

phase of the quark-gluon plasma. They interact strongly with the hot and dense matter produced in

heavy-ion collisions and lose energy when they transverse the medium. It provides the the system

evolution dynamic information to measure some typical observables. The physics framework is

discussed in chapter 1 and chapter 2, where one summarize the status of the experimental studies

of deconfinement in heavy-ion collisions and present how charm particles can serve as probes of

deconfined matter (QGP). The ALICE experimental framework is described in Chapter 3, along

with layout, main sub-systems and their expected performance. The main studies of this thesis

are summarized in the following two parts.

• The track impact parameter, defined as the distance of closest approach of the particle

trajectory to the primary vertex (see Fig.4.1).The track impact parameter is a critical variable

for the separation of physics signals from backgrounds, especially for the selection of physics

signals which are characterized by the secondary vertex with a small displacement from the

primary vertex. This is, in particular, the case for the detection of particles with open charm

and open beauty, namely D0 (cτ ∼= 123µm), D+ (τ ∼= 315µm) and B mesons (cτ ∼ 500µm),

and so on. The main requirement applied for the selection of such particles is the presence of

one or more daughter tracks (decay products) which are displaced from the primary vertex

(e.g. for D0 → K−π+ two displaced tracks are required, for B → e± +X one electron-tagged

displaced track is required. How to select the fit function and define the fit range is the subject

of section 4.1. In this section the particle track impact parameter distribution and fitting

procedure are introduced. The final measured particles mainly come from two different

parts. Particles coming from the primary vertex have an impact parameter distribution

with gaussian shape. Particles coming from weak decay have an exponential distribution of

impact parameter, as is the case for particles scattered from the detector materials. So, the

ii

fit function, combined by gaussian with exponential tail, was used as the analysis tool and

extract the impact parameter resolution. Section 4.2 focuses on the cause which affect the

impact parameter resolution. The main effects on impact parameter resolution are discussed,

including primary vertex selection and diamond constraint, small-angle multiple scattering

and particle species (particle identification). The resolution of track impact parameter is the

convolution of the resolution of primary vertex with that of tracks. The primary vertex and

the variables associated to the tracks will affect the impact parameter resolution. For the

primary vertex, one mainly discuss two aspects: the ‘diamond constraint’ on primary vertex

distribution and the effect of current track on the primary vertex. The emitted particles

with small transverse momenta will be deflected by many small-angle scatterings (Coulomb

scattering) when the particles traverse the beam pipe, detectors and equipments. The track

impact parameter resolution contributed by the uncertainty of the track fit can be regarded

as a sum of spatial precision of tracking detectors and multiple scattering. The formula

on impact parameter resolution distribution with polar angle was given out, see text for

detail. Within the error range, the result of ESDPID is agreement with that of PDGPID.

The resolution distribution for different kinds of particle have the same trend which is larger

at low pt than at high pt and have clear mass order at low pt. The value of resolution for

protons is the biggest one among three kinds of particle, kaon comes second and it is the

smallest for pion at the same pt. Because the proton has larger mass, so it will undergo more

multiple scattering when it traverse the beam pipe, detector and support equipment. Finally,

one consider the different selection conditions affecting the impact parameter resolution, as

well as magnet and charge effects on the resolution and mean of impact parameter. The

barrel detectors in ALICE are embedded in a large solenoidal magnet providing a magnetic

field < 0.5 T in positive and negative value, and they allow to reconstruct track in the

pseudorapidity range |η| < 0.9. So, the magnetic field and the particle charge will affect the

impact parameter resolution and mean.

• ALICE is a general-purpose heavy-ion experiment designed to study the physics of strongly

interacting matter and the quark gluon-plasma in nucleus-nucleus collisions at the LHC.

The measurement of open charm and open beauty production allows one to investigate the

mechanisms of heavy-quark production, propagation and, at low momenta, hadronisation

in the hot and dense medium formed in high-energy nucleus-nucleus collisions. It is an

important task in ALICE to measure charm production via the exclusive reconstruction of

iii

selected D meson decay channels at central rapidity. The measurement of the cross-section for

charm production in p-p collisions is not only a fundamental reference to investigate medium

properties in heavy-ion collisions, but an key test of pQCD predictions in a new energy domain

as well. In chapter 5, the analysis procedure and the final D0 cross-section for the D0 → K−π+

channel are presented. First, the analysis strategy is recalled, as well as the detailed steps of

analysis are given according to the analysis strategy, see in section 5.1. In p-p collisions, if all

the possible pairs are considered as ‘candidate’ D0, the signal over combinatorial background

ratio is ∼ 10−4. It is then mandatory to preselect the reconstructed tracks and candidates on

the basis of the typical kinematical and geometrical properties characterizing the signal tracks

and reconstructed vertices. Beside two kinds of variables : single track variables and pair

variables, particle identification, in particular for the charged kaon, is applied for background

rejection and improving the ration of signal-to-background, see detail in section 5.2. Then,

the pt-differential cross sections for prompt D0 at LHC√s = 7 GeV, obtained from the

yields extracted by fitting the invariant mass spectra. The fit function used to reproduce the

invariant mass distributions is the sum of a Gaussian for D0 peak and an exponential or second

order polynomial for the background. The amount of signal and background is then extracted

by subtraction of the background fit from the total or by counting the excess of entries in the

histogram with respect to the background function, see in section 5.3. In order to evaluate

the total number of D0 mesons effectively produced and decayed in the D0 → K−π+ channel,

(ND0→K−π+

tot ) the raw signal yield is divided by an efficiency correction factor (ϵ) that accounts

for selection cuts, for PID efficiency, for track and primary vertex reconstruction efficiency,

and for the detector acceptance. The procedure and the tools used to compute the efficiency

corrections is the subject of section 5.4. At LHC energies, a relevant fragmentation fraction of

D0 mesons comes from the decay of B mesons. On average, the reconstructed tracks coming

from ‘secondary’ D0 are well displaced from the primary vertex, because of the relatively long

B lifetime (cτ ≃ 460-490 µm). Thus, the selection further enhances their contribution to the

raw signal yield (up to 15%) and it is important to subtract this fraction. To determine

its amount different methods are available and will be detailed in the text. The best way

is to extract it directly from data exploiting the different shapes of the impact parameter

distribution of secondary D0, but this requires large statistics. Alternatively, or as a cross

check it is possible to rely on Monte Carlo estimates based on pQCD calculations, but this

can add a bias to the measurement, or on the measurement of beauty production at the

iv

LHC, see detail in section 5.5. In the section 5.6, the raw yield, corrected for the efficiency, is

divided by the decay channel branching ratio (BR(D0 → K−π+) = 3.80± 0.09%) to get the

total number of produced D0 mesons ND0

tot . The latter number is divided by the integrated

luminosity LINT to obtain the cross section for D0 meson production. A factor 1/2 must be

considered because both D0 and D0 mesons are reconstructed and a factor 1/(2 ymax) because

the measurement is performed in the rapidity range −ymax < y < +ymax. Several sources of

systematic uncertainties were considered, namely those affecting the signal extraction from

the invariant mass spectra, as well as the statistical uncertainties, the detail see section 5.7.

Finally, the measured D0 meson production cross sections are compared to two theoretical

predictions, namely FONLL and GM-VFNS. Our measurement of D0 at LHC energies are

reproduced by both models within their theoretical uncertainties.

Keywords: QCD, Quark Gluon Plasma, LHC/ALICE experiment, heavy quark, cross-section

v

Contents

1 High energy heavy-ion physics 1

1.1 The basic theory of deconfined matter . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.2 Quantum Chromodynamics(QCD) . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Relativistic heavy-ion collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2.1 p-p collisions and nucleus-nucleus collisions . . . . . . . . . . . . . . . . . . 8

1.2.2 Initial Energy density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.2.3 Space Time Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.2.4 Particle Multiplicities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.3 Existing signals of QGP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.3.1 Collective flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.3.2 High pt physics and Jet Quenching . . . . . . . . . . . . . . . . . . . . . . . 18

1.3.3 J/Ψ suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2 Heavy flavours 31

2.1 Heavy quarks production in P-P collisions . . . . . . . . . . . . . . . . . . . . . . . 31

2.2 Heavy quark production in nucleus-nucleus collisions . . . . . . . . . . . . . . . . . 33

2.2.1 Initial-state effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.2.2 Final-state effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.2.3 Parton energy loss in medium . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.3 Some relevant experimental results about heavy flavour . . . . . . . . . . . . . . . 41

2.3.1 Cross section of heavy flavour in p-p and A-A collision . . . . . . . . . . . . 41

2.3.2 Elliptic flow of heavy flavour . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.3.3 RAA of heavy flavour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

i

2.4 Open charm and open beauty in ALICE at LHC . . . . . . . . . . . . . . . . . . . 44

2.4.1 Momentum fraction x of heavy quarks in ALICE . . . . . . . . . . . . . . . 44

3 The ALICE experiment at the LHC 51

3.1 ALICE physics targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.2 The ALICE detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.2.1 Inner Tracking System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.2.2 Time Projection Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.2.3 Time of Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.3 ALICE analysis tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.3.1 ROOT and AliROOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.3.2 ALICE computing environment . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.4 Event generation and reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.4.1 Description of Event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.4.2 Track reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.4.3 Primary vertex reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4 Vertexing in ALICE: resolution on impact parameter measurement 73

4.1 The strategy to measure the impact parameter resolution . . . . . . . . . . . . . . 74

4.1.1 Data selection and impact parameter calculation . . . . . . . . . . . . . . . 74

4.1.2 Fit function selection and fit range definition . . . . . . . . . . . . . . . . . 75

4.2 Main contribution for the impact parameter resolution . . . . . . . . . . . . . . . . 76

4.2.1 Primary vertex resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.2.2 Effects of small-angle multiple scattering on the impact parameter resolution 77

4.2.3 Magnetic field and charge effects on the resolution and mean of impact pa-

rameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5 Measurement of the cross section for D0 production in pp collision at√s = 7 TeV 85

5.1 Strategy for D0 cross-section measurement . . . . . . . . . . . . . . . . . . . . . . . 85

5.2 Reconstruction of D0 → K−π+ channel . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.2.1 Cut variable selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.2.2 Definition of the cut variable values . . . . . . . . . . . . . . . . . . . . . . 91

5.2.3 Particle identification strategy . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.3 Raw signal yield extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

ii

5.4 Correction for efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.5 Correction for B feed-down . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.5.1 Evaluation of the feed-down contribution with FONLL . . . . . . . . . . . . 98

5.5.2 Fraction of secondary D0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.6 Normalization of the corrected spectrum . . . . . . . . . . . . . . . . . . . . . . . . 100

5.7 Analysis of statistical and systematic errors . . . . . . . . . . . . . . . . . . . . . . 100

5.8 Comparison with pQCD prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

6 Summary and Outlook 110

iii

List of Figures

1.1 The Standard Model of elementary particles, with the gauge bosons in the rightmost

column. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 A summary of αs measurement. Open symbols indicate NLO, and fill symbols

NNLO QCD calculations used in the respective analysis. . . . . . . . . . . . . . . . 5

1.3 Energy density as a function of the temperature for different numbers of degenerate

quark flavours. The curves are the result of a lattice QCD calculation using improved

gauge and staggered fermion actions. . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 A sketch of the phase diagram of QCD for different temperatures T and quark

chemical potential µ [12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 Schematic view of a heavy ion collision at ultra-relativistic energies. The different

stages of the collision are shown: the approaching nuclei, the interpenetration and

creation of a new matter phase, the expansion of a quark gluon plasma, the expansion

of hadronic matter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.6 The space-time diagram of longitudinal coordinate and time of the evolution of

fireball (a) without and (b) with the production of quark-gluon plasma. . . . . . . 12

1.7 Charged-particle pseudo-rapidity density per participant pair for central nucleus-

nucleus and non single-diffractive p-p (p-p) collisions as a function of√sNN . The

solid lines ∝ s0.15NN and ∝ s0.11NN are superimposed on the heavy-ion and p-p (p-p)

data, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.8 Comparison of this measurement with model predictions. Dashed lines group similar

theoretical approaches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.9 Sketch of an almond shaped fireball, where z axis is the beam direction. . . . . . . 16

iv

1.10 The created initial transverse energy density profile and its evolution with time in

coordinate space for a non-central heavy-ion collisions. The z-axis is along the beam

direction, the x-axis is defined by the impact parameter b. . . . . . . . . . . . . . . 16

1.11 Sketch of the formation of anisotropic flow. . . . . . . . . . . . . . . . . . . . . . . 17

1.12 Illustration of the three most common flow phenomena. . . . . . . . . . . . . . . . 17

1.13 (a) v2(pt) for the centrality bin 40-50% from the 2- and 4-particle cumulant methods

for this measurement and for Au-Au collisions at√sNN = 200 GeV. (b) v24 for

various centralities compared to STAR measurements. The data points in the 20-

30% centrality bin are shifted in pt for visibility. . . . . . . . . . . . . . . . . . . . 18

1.14 RAA(pt) measured in central Au-Au at√sNN = 200 GeV for direct γ, π0 and η

mesons [76]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.15 RAB(pt) from Eq 1.9 for minimum bias and central d-Au collisions, and central

Au-Au collisions [77]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.16 Dihadron azimuthal correlations at high pt . Left panel shows correlations for p-

p, central d-Au and central Au-Au collisions (background subtracted) from STAR.

Right panel shows a study from STAR of the high pt dihadron correlation from

20-60% centrality Au-Au collisions [84]. . . . . . . . . . . . . . . . . . . . . . . . . 21

1.17 J/Ψ RAA versus pt for several centrality bins in Au-Au collisions. Mid (forward)

rapidity data are shown with open (solid) circles [87]. . . . . . . . . . . . . . . . . . 23

1.18 J/Ψ RAA as a function of ⟨Npart⟩ in Pb-Pb collisions at√sNN = 2.76 TeV compared

to PHENIX results in Au-Au collisions at√sNN = 200 GeV [93]. . . . . . . . . . . 23

2.1 Some of the processes defined as pair creation, flavour excitation and gluon splitting.

The thick lines correspond to the hard process. . . . . . . . . . . . . . . . . . . . . 32

2.2 The transverse plane of the collision geometry. . . . . . . . . . . . . . . . . . . . . 34

2.3 Ratio of gluon distribution function from different models at Q2 = 5GeV. . . . . . 36

2.4 Parametrization of the shadowing effect in the cc nucleon-nucleon cross-section as

function of the impact parameter. The parametrization is applied for b ≤ 16 fm;

b ≥ 16 fm the constant value σcc = 6.64 mb is considered. . . . . . . . . . . . . . . 37

2.5 Left panel: cc cross-section in Pb-Pb for b < bc . Right panel: number of σcc

processes in different centrality classes b < bc for Pb-Pb collision. In both the plots

the shadowing parametrization is inclouded. . . . . . . . . . . . . . . . . . . . . . . 37

2.6 Typical gluon radiation diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

v

2.7 Transport coefficient as a function of energy density for different media: cold (marker),

massless hot pion gas (dotted curve) and ideal QGP (solid curve). . . . . . . . . . 40

2.8 pt distributions of invariant yields for reconstructed D0, charm decayed prompt µ

and non-photonic electrons in different centralities as observed by STAR. . . . . . 41

2.9 pt distributions of invariant yields of electrons from heavy-flavour decays for different

Au-Au centralities and p-p data measured by PHENIX, compared with theoretical

predictions based on FONLL calculations normalized to p-p data and scaled with

⟨TAA⟩. Error bars (boxes) depict statistical (systematic) uncertainties. The inset

shows the ratio of heavy-flavour to background electrons for minimum bias Au-Au

collisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.10 PHENIX results, see (a): RAA of heavy-favour electrons in 0-10% centrality Au-Au

collisions compared with π0 data and model calculations. (b): v2 of heavy-favour

electrons in minimum bias collisions compared with π0 data. . . . . . . . . . . . . 43

2.11 RAA of heavy-flavour electrons for the integrated pt spectrum (pt > 0.3 GeV/c) and

for pt > 3 GeV/c and of π0 for pt > 4 GeV/c, measured by PHENIX. . . . . . . . 44

2.12 ALICE acceptance in the (x1, x2) plane for heavy flavours in Pb-Pb at 5.5 TeV

(left) and in p-p at 14 TeV (right). The figure is explained in detail in the text. . . 45

2.13 ALICE acceptance in the (x1, x2) plane for heavy flavours at 8.8 TeV in p-Pb (left)

and in Pb-p (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.14 ALICE acceptance in the (x1, x2) plane for charm (left) and beauty (right) at 5.5,

8.8 and 14 TeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.1 Layout of ALICE detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.2 The hierarchical structure of Inner tracking System . . . . . . . . . . . . . . . . . . 55

3.3 CAD sketch of Inner Tracking System . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.4 Disposition of the 10 sectors around the beam pipe. The maximum curvature radii

for which tracks have a possibility to go undetected through the layers are 119 mm

for the first and 475 mm for the second . . . . . . . . . . . . . . . . . . . . . . . . 57

3.5 Sketch of the two-directional SDD with a blow-up of a corner. . . . . . . . . . . . . 58

3.6 The ladders are mounted on a CFRP structure made of a cylinder, two cones and

four support rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.7 Photograph of the SSD in the final configuration . . . . . . . . . . . . . . . . . . . 60

vi

3.8 Schematic view of TPC in ALICE. The central electrode relative position, the di-

rection of field cage and readout chamber are shown. . . . . . . . . . . . . . . . . . 62

3.9 Schematic drawing of the Time Of Flight(TOF) supermodul,consisting of 5 mod-

ules,in the ALICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.10 The CERN Analysis Facility (CAF). . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.11 Data processing framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.12 Scheme adopted for vertex reconstruction with tracks reconstructed in both TPC

and ITS (ITS+TPC), and only in TPC (TPC-only). . . . . . . . . . . . . . . . . 70

4.1 Schematic map of impact parameter for D0 → K−π+ products . . . . . . . . . . . 74

4.2 The impact parameter distribution for primary, secondary, strangeness and charm

or beauty particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.3 An example of the transverse impact parameter distribution in real and Monte Carlo

data. The cave is the fitting result, The detail see in text. . . . . . . . . . . . . . . 76

4.4 Diamond constraint effect on the impact parameter resolution. . . . . . . . . . . . 78

4.5 Impact parameter resolution for different vertex. . . . . . . . . . . . . . . . . . . . 78

4.6 Comparison of impact parameter resolution of real data with MC data. . . . . . . 79

4.7 Impact parameter resolution distribution as function of polar angle at fixed pt . . . 80

4.8 Comparison of the ESDPID and PDGPID result, see text. . . . . . . . . . . . . . . 80

4.9 Comparison of the positive charged particles and negative charged particles. . . . . 81

4.10 Mean value of the transverse impact parameter distribution as a function of pt . . 82

4.11 Transverse impact parameter resolution as the function of pt for the tracks recon-

structed in the min-bias PbPb collisions at 2.76 TeV and compared with the Monte

Carlo and the pp results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.12 The impact parameter resolution distribution with run number. Usually, the reso-

lution should be nearly equal in the same period. If it is far from the mean of the

resolution, it can be remove during the special physics analysis, as the run number

labeled with the red circle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.1 Distance of closest approach (dca, left panel) and cosθ⋆ (right panel) and distri-

butions for background (black circles) and signal (red triangles) candidates. The

different error bar sizes are due to the smaller number of signal than background

candidates. The variables are defined and described in the text. . . . . . . . . . . . 89

vii

5.2 Product of daughter impact parameters (dK0 × dπ0 , right panel) and cosθpoint distri-

butions for background (black circles) and signal (red triangles) candidates. The

different error bar sizes are due to the smaller number of signal than background

candidates. A cut cosθpoint > 0 was applied already at the level of candidates re-

construction: the background distribution shape is almost at in the entire range [3].

The variables are defined and described in the text. . . . . . . . . . . . . . . . . . . 90

5.3 Distance of closest approach dca (top left), cosθ⋆ (top right) distributions for MC

background (red) and data (blue) candidates. . . . . . . . . . . . . . . . . . . . . 90

5.4 Cosθpoint (left) and product of impact parameters dK0 × dπ0 (right) distributions for

MC background (red) and data (blue) candidates. . . . . . . . . . . . . . . . . . . 91

5.5 Significance trend in the two-dimensional space (cosθpointing, dK0 × dπ

0 ) in the range

3 < ptD0

< 4 GeV/c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.6 Invariant mass distributions for ∼ 1.1× 108 minimum bias events with exponential

+ Gaussian fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.7 pt > 2 GeV/c invariant mass spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.8 Sigma of the Gaussian fit of the invariant mass distributions in 5 for ∼ 1.1 × 108

minimum bias events as a function of pt . . . . . . . . . . . . . . . . . . . . . . . . 95

5.9 D0 → K−π+ yield as a function of the transverse momentum for 108 minimum bias

events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.10 Efficiencies for D0 as a function of pt (see text for details). . . . . . . . . . . . . . . 97

5.11 FONLL calculation of the primary and secondary D0 cross-sections in proton proton

collisions at 7 TeV for |η| < 0.5 (left). The relative contribution of secondary D0 is

represented in right panel by the relative ratio 1/(1 +σpriminary

σsecondary). . . . . . . . . . . 98

5.12 Systematic errors summary plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.13 Different methods for signal extraction. . . . . . . . . . . . . . . . . . . . . . . . . 101

5.14 Check on the effect of cut variation. . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.15 Check on the effect of PID efficiency on data and MC. . . . . . . . . . . . . . . . . 102

5.16 D0/D0 raw yield ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.17 Check on the effect of a different pt distribution shape: the efficiencies from prompt

D0 from PYTHIA and FONLL as a function of pt and their ratio are shown . . . . 103

5.18 Ratio of events with a signal in both V0 detectors over the events triggered as

CINT1B as function of run number. . . . . . . . . . . . . . . . . . . . . . . . . . . 105

viii

5.19 pt-differential cross section for prompt D0 in pp collisions at√S = 7TeV compared

with FONLL and GM-VFNS theoretical predictions. . . . . . . . . . . . . . . . . . 106

ix

List of Tables

3.1 Parameters of the six ITS layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.2 LHC parameters for PP and PbPb runs for ALICE . . . . . . . . . . . . . . . . . . 69

5.1 Selection cuts used in the present analysis. . . . . . . . . . . . . . . . . . . . . . . . 93

5.2 Yield of Signal and Background and significance from fit in the 1.1 × 108 events

minimum bias sample for seven pt bins. The considered invariant mass range is of

3σ where σ is reported in Fig 5.8 as a function of pt. . . . . . . . . . . . . . . . . . 96

5.3 Summary of relative systematic errors for D0 cross section. The systematic error

from B feed-down varies in pt. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.4 Production cross section in |y | < 0.5 for prompt D0 in pp collisions at√S = 7 TeV,

in transverse momentum intervals. The normalization systematic error of 7% is not

included in the systematic errors reported in the table. . . . . . . . . . . . . . . . . 106

x

Chapter 1

High energy heavy-ion physics

The goal of high energy heavy ion physics is to study the properties of matter produced in

nucleus-nucleus collisions at the highest mass and energy densities reached in the laboratory, and

to deepen the understanding of these properties in the framework of quantum chromodynamics

(QCD), the fundamental theory of strong interactions.

In the past two decades, high energy heavy-ion collisions have obtained a large number of

outstanding achievements with the increasing of collided energy from the Brook/haven Alternating

Gradient Synchrotron (AGS) with√s < 5 GeV, the CERN Super Proton Synchrotron (SPS) with

√s < 20 GeV and the Brook/Haven Relativistic Heavy Ion Collider (RHIC) with

√s < 200 GeV.

Since 2010, the CERN Large Hadron Collider (LHC) has opened up a new era for high energy

heavy ion physics. Its highest energy (√s < 5.5 TeV for Pb-Pb) is almost a factor 30 higher than

RHIC.

1.1 The basic theory of deconfined matter

High-temperature QCD equilibrium dynamics has been studied non-perturbatively by lattice

calculations, while in the perturbative regime by finite temperature field theory, this last being the

main theoretical tool, with the potential of connecting heavy-ion collisions with first principles of

QCD.

In particular, the most dramatic collective phenomenon, expected in finite temperature QCD,

namely the phase transition to a quark-gluon plasma at a given critical temperature, has been

firmly established in lattice QCD.

1

1.1.1 Standard Model

The Standard Model (SM) of particle physics describes the fundamental structure of matter

and the fundamental forces acting in nature, but gravity.

The basic ingredients of this theory are three types of particles: quarks, leptons and gauge

bosons. There are six different quarks (down, up, strange, charm, bottom and top) and their

corresponding antiquarks, six different leptons (electron, electron neutrino, muon, muon neutrino,

tau and tau neutrino) and the corresponding antileptons and four types of gauge bosons (gluon,

photon, W±/Z-boson). Each boson has an integer spin and mediates one fundamental interaction

force. The W± and Z-bosons carry the weak interaction, the photon the electromagnetic force

and the gluon is the force-carrying particle of the strong force. The electromagnetic and the weak

interaction can be described in one unified theory, the electro-weak interaction.

The Higgs boson is responsible for the existence of mass of the elementary particles in the

Standard Model. The existence of this particle is still to be experimentally confirmed. The model

does not include gravitation and its gauge boson, the graviton. The quarks and leptons are listed

in Fig 1.1. [1] [2] [3] [4].

Quarks and leptons, fermions with spin ±1/2 together with gauge bosons, are assumed to

be fundamental particles, i.e. structureless. One can sort both quarks and leptons into three

different classes, the so-called generations or families. Each generation consists of two quarks, one

with an electric charge of − 13e and the other with one of +2

3e, a charged lepton and a neutrino.

Quarks carry another charge, the so-called color charge, that can have three states (called red,

green, and blue) and the corresponding anti-states. The strong interaction described by quantum

chromodynamics (QCD) is one of the fundamental forces in the standard model, coupling by the

color charge quarks and gluons have the unique property, among gauge particles, to interact each

other with the same force they carry. The coupling constant is the parameter in such quantum

field theories that describes the strength of the interaction. The coupling constant αs of QCD

shows a unique feature, as it depends on the momentum transfer Q2 in a collision of quarks or

gluons. At large momentum transfers, the coupling constant can be approximated as [3]

αs(Q2) ≈ 12π

(33− 2Nf )× ln(Q2/Λ2QCD)

(1.1)

ΛQCD is an experimentally determinded QCD scale parameter, being ΛQCD ≈ 250 MeV/c.

Nf is the number of the accessible quark flavors and can obviously not be larger than 6, however,

virtual quark-antiquark pairs can only be separated for large momentum transfers αs, therefore Nf

2

Figure 1.1: The Standard Model of elementary particles, with the gauge bosons in the rightmost column.

depends on αs and is between 3 and 6. The equation is only valid for momentum transfers that are

large compared to the scale parameter (Q2/Λ2QCD ≫ 1), but it still shows the phenomenon that the

coupling becomes weaker with increasing momentum transfers. Looking at the phenomenological

potential of the strong interaction [2].

Vs(r) = −4

3

αs

r+ k · r (1.2)

one can distinguish two contributions to the overall potential: a Couloumb-like term ∼ 1/r,

dominating at small distances, and a linear term ∼ r, dominating at larger distances. The first

term depends on as which depends on r itself. Because as αs → 0 for r → 0, this leads to the

asymptotic freedom. The second term leads to a confinement of the field lines into small tubes or

strings, which can be explained by gluon-gluon interactions. Therefore it is not possible to observe

single quarks or to separate two quarks. When e.g. a quark-antiquark pair is separated, only new

color-neutral particles are created because it is energetically favored.

1.1.2 Quantum Chromodynamics(QCD)

Quantum chromodynamics (QCD) is the gauge theory to describe the strong interaction among

quarks and gluons. Similar to the form of the Quantum Electrodynamics (QED) lagrangian, its

lagrangian can be written as:

LQCD = ψi(iγµ∂µ −mi)ψi − gGα

µ ψiγµTα

ijψj −1

4Gα

µνGµνα (1.3)

3

where the Ψ is a spin 1/2 fermion field same as charged particle in the QED case, which is a

quark in the QCD case. The G is a massless boson field with spin 1, which is a gluon in QCD. The

g is coupling strength between fermion field Ψ and boson field G. The gluonic field tensor written

in terms of the vector potential, A, is

Fαµν = ∂µA

αν − ∂αµA

αν + Cα

βγAβµA

γν (1.4)

The final term in equation 1.4 is particularly note worthy; it represents self interactions of the

gluon field and has no analogue in QED. Thus in addition to a quark emitting or absorbing a

gluon just as an electron may emit or absorb a photon in QED, QCD allows wholly bosonic gluon

emission and absorption of another gluon as well as direct two gluon interactions. This property

arises from gluons themselves having a non-zero charge equivalent.

Whereas in QED fermions have a quantum number slot that allows them to be positively or

negatively charged, in QCD not only is the ‘charge’ available to the bosons it is also different in

that it may take three values referred to as color. The color labels of red, green and blue (R, G, B)

are a convenient metaphor drawn from the visible spectrum because color neutrality, ‘whiteness’,

can be achieved either via a color-anticolor pair or a triplet of all three colors. These traits are

described by the SU(3) group. In this vocabulary the group has generators, Tαij that are eight 3×3

matrices, complemented by the constants that satisfy their commutation relations, Cαβγ .

In addition to the color quantum number which follows an exact gauge symmetry there is

also a quantum number described by an SU(3) group corresponding to an approximate symmetry

denoting the flavor of the quark. This symmetry holds for the three lightest quarks, u,d and s

due to their similar mass but is broken by the heavy quark flavors c, b, and t. Nevertheless, the

approximate symmetry was the key in developing the map of bound hadronic states, known as the

Eight-Fold Way [5], which led to the development of the parton (and subsequently quark) model.

In analogy with QED, the strength of the coupling constant in the QCD lagrangian is not

constant but is a function of the momentum exchange in the interaction. This dependence is

characterized by the beta function of αs(= g2/4π) which at lowest order for an SU(N) group

theory is:

β(αs) =α2s

2π(2nf3

− 11N

6) (1.5)

where nf is the number of quark flavors. So for the three colors of SU(3) as long as nf <332 , β

4

Figure 1.2: A summary of αs measurement. Open symbols indicate NLO, and fill symbols NNLO QCD calculations

used in the respective analysis.

is negative; this follows from the non-Abelian nature of the group description of the gluons (i.e. the

self interaction term of the Lagrangian) [6] [7]. Or cast as a function of the momentum transfer,

Q :

αs(Q2) = (β0ln(

Q2

Λ2)−1 (1.6)

where perturbation theory requires that q be somewhat larger than the cutoff scale Λ (exper-

imentally found to be ≈ 0.2 GeV and requiring that Q2 be greater than ≈ 1 GeV ) [8]. Fig 1.2

summarizes results for the“running” coupling [9]. It is worth noting that besides having opposite

sign the coupling strength varies much faster than that of QED.

The negative value of β has hugely important implications for the behavior of QCD interactions.

Although it is quite unintuitive, this means that at lower momentum transfer or longer distances

the strong force field’s energy grows larger. This leads to the phenomenon of confinement : free

color charges are never observed as the separation between quarks grows the energy gets so large

that other quarks are created from the vacuum and they bind the attempted escapee into a hadronic

state. This concept explains the failure to observe free quarks attempted experimentally shortly

after the quark model was developed. The long range effects of the strong force that are needed

to describe the bound hadronic states, fall too close (or under) Λ and so can not be calculated

perturbatively. Lattice QCD, in which large scales become calculable by using a discrete lattice

rather than calculating in continuous space [10], has to some extent filled this breach.

5

Figure 1.3: Energy density as a function of the temperature for different numbers of degenerate quark flavours. The

curves are the result of a lattice QCD calculation using improved gauge and staggered fermion actions.

1.1.2.1 Lattice QCD calculation

To investigate this further one turn to the lattice QCD framework, which allows calculations at

high temperature and large coupling strength. In particular, in the search for a phase transition

from hadronic matter into a QGP, lattice QCD can calculate as a proxy for the degrees of freedom

the energy density ϵ divided by the temperature to the fourth power T 4. As shown in Fig 1.3

the quantity ϵ/T 4 rises drastically at a certain temperature, Tc (calculated to be ≈ 170 MeV),

and then remains at as a function of temperature [11]. This behavior indicates a phase transition

from a system of hadrons to a system with partonic degrees of freedom, i.e. QGP. The figure also

shows the Stephan-Boltzmann limit corresponding to an ideal gas of partons, which significantly

surpasses the level of the apparent plateau of the calculated energy density. The failure of the

number of degrees of freedom to reach this limit suggests that even following the phase transition

the QGP phase is still strongly coupled to some degree.

Therefore, one have good reason to expect that at the proper energy density hadronic matter

should undergo a phase transition into strongly coupled partonic matter. This energy density

presumably existed shortly after the Big Bang as the universe began its cooling expansion, it may

also exist in neutron stars, but can we create it under laboratory conditions?

6

Figure 1.4: A sketch of the phase diagram of QCD for different temperatures T and quark chemical potential µ [12].

1.1.2.2 Phase diagram

On the basis of thermodinamical considerations and of QCD calculations, strongly interacting

matter is expected to exist in different states. Its behaviour, as a function of the baryonic chemical

potential µB (a measure of the baryonic density) and of the temperature T , is displayed in the

phase diagram reported in Fig 1.4. At low temperatures and for µB ≃ mp ≃ 940 MeV, weone have

ordinary matter. Increasing the energy density of the system, by ‘compression’ (towards the right)

or by ‘heating’ (upward), a hadronic gas phase is reached in which nucleons interact and form

pions, excited states of the proton and of the neutron (δ resonances) and other hadrons. If the

energy density is further increased, the transition to the deconfined QGP phase is predicted: the

density of partons (quarks and gluons) becomes so high that the confinement of quarks in hadrons

vanishes. The phase transition can be reached along different ‘paths’ on the (µB , T ) plane. In

the primordial Universe, the transition QGP-hadrons, from the deconfined to the confined phase,

took place at µB ≈ 0 (the global baryonic number was approximately zero) as a consequence of

the expansion of the Universe and of the decrease of its temperature (path downward along the

vertical axis) [13]. On the other hand, in the formation of neutron stars, the gravitational collapse

causes an increase in the baryonic density at temperatures very close to zero (path towards the

right along the horizontal axis) [13].

In heavy ion collisions, both temperature and density increase, possibly bringing the system to

the phase transition. In the diagram in Fig 1.4 the paths estimated for the fixed-target SIS and

collider (RHIC, LHC) experiments are shown.

7

1.2 Relativistic heavy-ion collisions

As discussed, a new phase of strongly interacting matter was predicted both by early phe-

nomenological considerations and lattice QCD calculations long time ago. In the extreme condi-

tions where there is a high temperature and pressure, a new phase matter phase would appear:

hadrons would melt- up in a large volume of interacting quarks and gluons. This state of matter

is called Quark Gluon Plasma (QGP). It could have existed in the early universe and could be

reproduced in ultra-relativistic heavy ion collisions, the ‘QGP factory’ in the laboratory. Finding

the QGP and studying its properties are the main goals that the large heavy-ion colliders have

been built for. The early properties of the collision system can be studied by several experimental

signatures, such as particle yields, spectra (momentum distributions), or particle correlations, etc.

1.2.1 p-p collisions and nucleus-nucleus collisions

1.2.1.1 p-p collisions

Most of the heavy-ion observables reviewed require p-p measurements of the same observables

for comparison. This is important in order to identify the genuine collective effects in nucleus-

nucleus collisions and to separate them from phenomena appearing already in p-p collisions. The

general observables in p-p collisions are presented below:

• Particle multiplicities: differences in particle multiplicities between p-p and A-A are related to

the features of parton distributions in the nucleon with respect to those in nuclei (shadowing)

and to the onset of saturation phenomena occurring at small-x [14] [15].

• Particle yields and ratios: particle ratios are indicative of the chemical equilibration achieved

in A-A collisions and should be compared to those in p-p collisions [16-26].

• Slopes of transverse-mass distributions: the comparison of slopes in A-A collisions with those

in p-p allows one to determine the collective effects such as transverse flow present in A-A

and absent in p-p.

• Ratios of momentum spectra: the ratios of transverse momentum spectra at sufficiently high

momenta allow one to discriminate between the different partonic-energy losses of quarks

and gluons [27] [28].

• Jet fragmentation functions: model calculations of medium-induced parton-energy loss pre-

dict a modification (softening) of the jet fragmentation functions [27] [28].

8

• Dilepton spectra: dilepton production from resonance decays yields information on in-medium

modifications in A-A collisions. The determination of the details of the effect relies on com-

parisons to smaller systems and to p-p collisions.

• Strangeness enhancement: strange particle production exhibits a very regular behaviour in p-

p collisions between 10 and 1800 GeV, with an almost constant ratio between newly produced

s and u quarks. On the other hand, a strangeness enhancement is observed in heavy-ion

collisions at rather low centre-of-mass energies between 2 and 10 GeV. In particular, the

K+/π+ ratio becomes more than twice as large as in p-p collisions and then decreases again

towards RHIC energies [29] [30] [31]. Therefore, the comparison of strangeness production in

A-A and p-p collisions at the LHC at comparable center-of-mass energies per nucleon pair is

particularly interesting. Changes in this ratio are indicative of new production mechanisms,

as provided, for example, by new collective effects or by the significant contribution of jet

fragments to total multiplicity.

• Heavy-quark and quarkonium production cross sections: the signals of possible suppression

or enhancement of heavy-quarkonium production, as well as parton-energy losses, have to be

evaluated with respect to the p-p yields measured in the same experiment. In addition, these

yields are not well established and must be determined more precisely.

• Photon spectra: the p-p photon-energy spectrum is needed to calibrate photon production in

order to estimate the background to the thermal photon production in heavy-ion collisions.

Reference values for the γ − jet cross sections in p-p collisions are also important. For the

observables mentioned above the dominant error is often due to the systematics. To minimize

the systematic errors from comparison with the baseline measurements, it is mandatory that

the observables in A-A and p-p collisions be measured in the same detector set-up.

In addition to the benchmark role emphasized in the previous, the study of p-p collisions in

LHC/ALICE addresses some genuinely important aspects of p-p physics. It includes, in partic-

ular, the exploration of a novel range of energies and of Bjorken-x values accessible at the LHC.

More generally, the ALICE p-p programme aims at studying non-perturbative strong-coupling

phenomena related to confinement and hadronic structure.

9

1.2.1.2 Nucleus-nucleus collisions

In a high energy heavy ion collision, the colliding nuclei close to light speed are relativistically

contracted and have the shape of thin disks, Fig 1.5. The highest energy density is reached when

the two disks overlap. After that, a multitude of particles is created. The participating entities and

the interactions between them are a number large enough to allow for the use of thermodynamics

terminology. Size and kinetic energy of the accelerated nuclei determine the initial conditions of

the hot and dense state of matter which is created when they collide.

Several processes contribute to particle production in the collision. In the earliest moments of

the collision, the nucleons of the two incoming nuclei collide as if they were independent particles.

It is in this phase that hard scatterings occur and produce heavy quarks and the most energetic

partons that will later fragment into jets. Multiple collisions among nucleons make them lose

kinetic energy creating a high energy density region, filled with quarks and gluons. The system

tends, after this, to a thermal equilibrium, and if the energy density is high enough the QGP

phase is reached. The energy density causes a pressure which makes the system expand and cool

down. At some point, the temperature drops below the critical one, and partons cannot remain

de-confined anymore. The following hadronization still allows for interactions among the newly

created particles, until the medium cools down even more and the hadrons stop interacting and

leave the region.

Different properties of the system can be probed at different stages of the collision. Since

hadrons interact until the kinetic freeze out of the system, it is difficult to obtain experimental

information on the early stages after thermalization and only model descriptions are available.

Never the less, several properties of the QGP can be studied by the observation of the final state

particles.

1.2.2 Initial Energy density

The initial matter and energy density is the driving parameter for the phase transition from

confined hadronic matter to de-confined quark gluon plasma. The Bjorken method [32] is a simple

way to estimate the initial energy density. It assumes that the particles created at mid-rapidity

result from inelastic processes and after some formation time, τ0, they can undergo re-scattering.

The particles are refereed to as quanta and the model does not distinguish between whether these

particles are hadrons or partons. Fig 1.5 helps illustrate how the energy density is derived. The

formed particles radiating from the thin disk in the yellow region will have a maximum velocity of

10

Figure 1.5: Schematic view of a heavy ion collision at ultra-relativistic energies. The different stages of the collision

are shown: the approaching nuclei, the interpenetration and creation of a new matter phase, the expansion of a

quark gluon plasma, the expansion of hadronic matter.

β = d/τ0, thus the number of particles in this region will have velocities from 0 to β at τ0. For

small values of β, the number of particles is βdN/dβ within volume βτ0A where A is the overlap

area. This gives:

ϵBj =dET

dy

1

τ0A(1.7)

where dET = ⟨mT ⟩, ⟨mT ⟩ being the mean transverse mass with ⟨mT ⟩ =√⟨pt⟩2 +m2

0, where

m0 is the particle rest mass, and dy = dβ. dET /dy is thus total transverse energy carried by the

particles emerging per unit of rapidity at y ∼ 0. The Bjorken model is valid as long as the particles

are formed in volume much bigger than the collision volume i.e. the length τ0c ≫ 2R/γ where R

is heavy-ion radius and γ is the Lorentz contraction factor. Otherwise, particles with the same β

can form in different regions which invalidates the thin disk assumption thus the use of d-A as the

active volume.

The Bjorken energy density has been estimated for central Au-Au collisions with√sNN =

200 GeV using the measured dET /dy ≃ 620 GeV, and an overlap area A ≃ 130 fm2 [33]. The

estimation proceeds as follows [34]. Although τ0 is not directly observable, it was calculated to

be τ0 ≃0.35 fm/c using the uncertainty principle (τ0 = 0.2/⟨mT ⟩ in ~ units of GeV.fm/c) and

the hadron ⟨mT ⟩ =0.57 GeV which is applicable over a wide range of collision energies. With

these values, the Bjorken energy density ϵBj≃ 14 GeV/fm3. This is significantly higher than the

critical energy density, ϵc ∼ 0.7 GeV/fm3, further suggesting that the deconfinement is achieved at

RHIC energies. Finally, although relating the mean final state hadron energy to the mean initial

state parton energy appears questionable, the argument is often made on grounds of entropy

conservation, i .e. the local number density of particles can never decrease during the fireball

11

Figure 1.6: The space-time diagram of longitudinal coordinate and time of the evolution of fireball (a) without and

(b) with the production of quark-gluon plasma.

evolution [35].

1.2.3 Space Time Evolution

Here, one consider the optimal situation, a head-on collision of two heavy nuclei (A and B),

moving with relativistic energies, in the center of mass frame. The dynamics of such a collision can

be described in the space-time picture with the time coordinate t (vertical) and the longitudinal

coordinate z, see Fig 1.6.

Due to their relativistic speeds, the colliding nuclei are Lorentz contracted as disks, shown as

thick lines. The projectile nucleus A with velocity close to speed of light comes from z = −∞ and

collide with the target nucleus, B, coming from z = +∞ with same speed. They overlap at z = 0

and t = 0.

After the collision, if the initial energy of the nuclei speeded-up is not high enough, the energy

density of the system created by collisions, may not reach the critical value and in such a case the

system consists of a gas of hadrons, see Fig 1.6 (a).

However, if the initial energy density of the system is high enough, a new matter state can

be formed, see Fig 1.6 (b). About 1 fm/c after the nuclei collisions, due to the multiple parton-

parton interactions(i.e, the pre-equilibrium periods), a quark-gluon plasma (QGP) is formed, and

12

the QCD system begins to expand rapidly, followed by a quick fall-down of the temperature of

QCD system. During this period, the energy density of system is about ∼ 1 GeV/fm3 When its

temperature drops to a critical value, Tc=175 MeV [36].The system enters into the hadronisation.

Because, the hadron formation requires some finite time, the system should stay some time in the

mixed phase, where quarks, gluons and hadrons co-exist.

The expansion is almost a isothermal process in this mixing phase, and the latent heat is

absorbed for the conversion of the degrees of freedom of quarks and gluons into hadronic degrees

of freedom.

In the hadron gas phase, all the quarks and gluons are confined inside the hadrons. The

expansion of the system continues and at a temperature Tch, the in-elastic collisions between the

hadrons stop. The particle abundances (total number of particle) reach constant value and there is

no further creation and annihilation of particles. This is called the chemical freeze-out, Tch is called

chemical freeze-out temperature. Then, the system keep expending, until the mean free path of the

hadrons exceeds the dynamical size of the system at Tfo (thermal/kinetic freeze-out temperature),

and the hadrons interaction (elastic scattering) will stop. This is called kinetic freeze-out, following

which the hadrons freely stream-out and finally are measured in detectors.

1.2.4 Particle Multiplicities

One can obtain relevant information about the collision dynamics through studying dependen-

cies of the particle multiplicity (or pseudo-rapidity distributions) on collision energy, system size

and centrality, etc.

Particle multiplicity distributions have been used to study the particle production mechanism,

based on binary scaling, participant scaling, two components model [37] and the Color Glass Con-

densate (CGC) [38-43]model. Furthermore, particle pseudo-rapidity distributions coupled with the

measurement of average transverse energy provide information about the energy density achieved

in the collision using the Bjorken estimation [32] and on the properties of the system produced

using hydrodynamics with CGC as the initial condition.

The first physics results from LHC/ALICE were the measurements of pseudo-rapidity density

of charged hadrons, dNch/dη, near mid-rapidity in central Pb-Pb collisions at collision energies of

√sNN=2.76 TeV [44]. In Fig 1.7, this value is compared to the measurements for Au-Au and Pb-

Pb, and non-single diffractive p-p and p-p collisions over a wide range of collision energies [45-60] It

is interesting to note that the energy dependence is steeper for heavy-ion collisions than for p-p and

13

p-p collisions. For illustration, the curves proportional to s0.15NN and ∝ s0.11NN are shown superimposed

on the data. A significant increase, by a factor 2.2, in the pseudo-rapidity density is observed at

√sNN=2.76 TeV for Pb-Pb compared to

√sNN=0.2 TeV for Au-Au. The average multiplicity per

participant pair is found to be a factor 1.9 higher than that for p-p and p-p collisions at similar

energies.

Fig 1.8 compares the measured pseudo-rapidity density to model calculations that describe

RHIC measurements at√sNN=0.2 TeV, and whose predictions at

√sNN=2.76 TeV are available.

Empirical extrapolation from lower energy data [61] significantly underpredicts the measurement.

Perturbative-QCD-inspired Monte Carlo event generators, based on the HIJING model tuned to 7

TeV p-p data without jet quenching [62] , on the dual parton model [63] , are consistent with the

measurement. Models based on initial-state gluon density saturation have a range of predictions

depending on the specific implementation [64-68] and exhibit a varying level of agreement with the

measurement. The prediction of a hybrid model based on hydrodynamics and saturation of final-

state phase space of scattered partons [69] is close to the measurement. A hydrodynamic model

in which multiplicity is scaled from p-p collisions overpredicts the measurement [70] , while a

model incorporating scaling based on Landau hydrodynamics underpredicts the measurement [71].

Finally, a calculation based on modified PYTHIA and hadronic rescattering [72] underpredicts the

measurement.

1.3 Existing signals of QGP

In the past twenty years, a large number of observables with heavy-ion beams (Au-Au and Pb-

Pb) collisions, have been measured successfully. The results show strong nuclear A dependence in

strangeness enhancement, stopping power, hadronic resonance production, collective flow and J/Ψ

meson suppression, etc, from AGS, SPS and RHIC. Here, several critical evidences about the QGP

are discussed: high pt and jet quenching, photons and dileptons, collective flow, event-by-event

fluctuations, identical particle interferometry and J/Ψ suppression.

1.3.1 Collective flow

The collective flow originates from a collective expansion of the system produced in the heavy

ions collisions. The shape of flow depends on the geometry of the overlap region which is determined

by the impact parameter b, the distance between the centers of the nuclei in the transverse plane,

14

Figure 1.7: Charged-particle pseudo-rapidity density per participant pair for central nucleus-nucleus and non single-

diffractive p-p (p-p) collisions as a function of√sNN . The solid lines ∝ s0.15NN and ∝ s0.11NN are superimposed on the

heavy-ion and p-p (p-p) data, respectively.

Figure 1.8: Comparison of this measurement with model predictions. Dashed lines group similar theoretical ap-

proaches.

see Fig 1.9. The plane defined by the the beam direction z (longitudinal direction) and impact

parameter b (transverse direction) is called the reaction plane, see Fig 1.10 [73]. Fig 1.11 shows

15

Figure 1.9: Sketch of an almond shaped fireball, where z axis is the beam direction.

Figure 1.10: The created initial transverse energy density profile and its evolution with time in coordinate space

for a non-central heavy-ion collisions. The z-axis is along the beam direction, the x-axis is defined by the impact

parameter b.

the spatial evolution with time in the transverse plane for a noncentral (b = 0) heavy-ion collision.

At the beginning, the created system has anisotropies in the coordinate-space, which changes

into an asymmetry in momentum-space, due to multiple interactions, see Fig 1.11. Therefore,

anisotropic flow is very sensitive to the properties of the system at an early time of its evolution.

Quantitatively, anisotropic flow is characterized by the coefficients in the Fourier expansion of

the azimuthal dependence of the invariant yield of particles relative to the reaction plane [74]:

Ed3N

d3p=

1

2π

d2N

ptdptdy[1 +

∞∑n=1

2vncos(nϕ)] (1.8)

where ϕ is the azimuthal angle with respect to the reaction plane, vn are the amplitudes of the

16

Figure 1.11: Sketch of the formation of anisotropic flow.

Figure 1.12: Illustration of the three most common flow phenomena.

NTH harmonic. v1 and v2 called directed and elliptic flow, see Fig 1.12.

Fig 1.13 (a) shows the v2(pt) for centrality class 40-50% obtained with different methods. For

comparison, one present STAR measurements [75] for the same centrality from AuAu collisions at

√sNN = 200 GeV, indicated by the shaded area, and Pb-Pb

√sNN = 2.76 TeV by ALICE. The

value of v2(pt) does not change within uncertainties from√sNN = 200 GeV to 2.76 TeV. Fig 1.13

(b) presents v2(pt) obtained with the 4-particle cumulant method for three different centralities,

compared to STAR measurements. The transverse momentum dependence is qualitatively similar

17

Figure 1.13: (a) v2(pt) for the centrality bin 40-50% from the 2- and 4-particle cumulant methods for this measure-

ment and for Au-Au collisions at√sNN = 200 GeV. (b) v24 for various centralities compared to STAR measure-

ments. The data points in the 20-30% centrality bin are shifted in pt for visibility.

for all three centrality classes.

1.3.2 High pt physics and Jet Quenching

Jets are bunches of partons (quarks and gluons) focussed along direction, produced in early

hard scattering during the p-p and nucleus-nucleus collisions. The hard partons will lose their

energy due to elastic collision with the medium and gluon radiation. The energy loss is supposed

to be larger in the deconfined medium (QGP) than hadronic matter. This phenomenon is called

Jet Quenching, which is regarded as one of the main signatures of QGP. Experimentally, one can

test the signal of QGP observing the suppression of partonic jets and high transverse momentum

particles. Fig 1.14 shows the nuclear modification factor RAA( see Eq 1.9) of direct γ, π0 and η

mesons in central√sNN = 200 GeV Au-Au collisions.

RAA(pt) =1

Ncoll

d2NAA/dydpt

d2Npp/dydpt

(1.9)

18

Figure 1.14: RAA(pt) measured in central Au-Au at√sNN = 200 GeV for direct γ, π0 and η mesons [76].

Figure 1.15: RAB(pt) from Eq 1.9 for minimum bias and central d-Au collisions, and central Au-Au collisions [77].

The suppression is clearly observed at high transverse momentum for π0 and η mesons. How-

ever, this phenomenon is not in the γ data because the photons do not take part in the strong

interaction, This indicates that the suppression happens at the parton level.

The STAR collaboration has not found the suppression in the single-particle inclusive spectra

in d-Au collisions at√sNN = 200 GeV, see Fig 1.15. This evidence suggests that the strong

suppression of inclusive spectra observed in central Au-Au collisions happens because of the final

state interactions with the deconfined hot and dense medium that can be formed in A-A collisions

only.

19

Fig 1.16 shows the azimuthal distribution of associated hadrons (pt > 2 GeV/c) relative to

a triggered hadron (ptriggert > 4 GeV/c). On the near side, ∆ϕ = 0, enhanced correlations are

observed in pp, d-Au, and Au-Au collisions. On the away-side, ∆ϕ = π, the correlation is observed

both in p-p collisions and d-Au collision while it almost disappears in central Au-Au collisions.

This again suggests that the suppression is due to the final state interaction of hard-scattered

partons or their fragmentation production in the dense medium generated in Au-Au collisions [77],

if the correlation is indeed the result of jet fragmentation.

Another probe of partonic energy loss is the measurement of high pt dihadron correlations

relative to the reaction plane orientation. Fig 1.16 (right) shows a study from STAR of the high

pt dihadron correlation from 20-60% centrality Au-Au collisions, with the trigger hadron situated

in the azimuthal quadrants centered either in the reaction plane ‘in-plane’) or orthogonal to it

‘out-of-plane’) [78]. The same-side dihadron correlation in both cases is similar to that in pp

collisions.

In contrast, the suppression of the back-to-back correlation depends strongly on the relative

angle between the trigger hadron and the reaction plane. This systematic dependence is consistent

with the picture of partonic energy loss: the path length in medium for a di-jet oriented out of the

reaction plane is longer than in the reaction plane, leading to correspondingly larger energy loss

for out of plane direction. The dependence of parton energy loss on path length is predicted to be

substantially stronger than linear [79].

At the LHC, large production of jets is expected [80]. The comparison of full jet measurements

at RHIC with the LHC will provide a deeper insight into the understanding of jet quenching and

hot QCD matter. Using the first Pb-Pb collisions data at√sNN = 2.76 TeV, ALICE, ATLAS and

CMS have presented the first evidences of jet quenching in this new energy regime [81-83].

1.3.3 J/Ψ suppression

Quarkonium was proposed as a privileged probe to study the properties of the high-density

and hot system formed in the early stages of high-energy heavy-ion collisions. A prediction about

quarkonium suppression in deconfined matter [85], due to color-screening of the heavy-quark po-

tential, has been experimentally tested at the SPS and RHIC [86] [87].

In general, the early produced J/Ψ will be subsequently dissolved by : a) Nuclear absorption;

b) Debye color screening [88]; c) Inelastic scattering on ‘co-moving’ hadrons in the hadron gas

phase of the reaction.

20

Figure 1.16: Dihadron azimuthal correlations at high pt . Left panel shows correlations for p-p, central d-Au and

central Au-Au collisions (background subtracted) from STAR. Right panel shows a study from STAR of the high

pt dihadron correlation from 20-60% centrality Au-Au collisions [84].

The interaction potential exhibited by the bound states of cc system is [89]:

V (r) = σr − αeff

r(1.10)

where σ is the string tension and αeff is the coulomb interaction coupling. The energy of the

bound state, including the c-quark kinetic energy and their rest mass, can be estimated by

E (r) = 2m +1

2mr2+ v(r) (1.11)

So, σ(T ) decreases with the increasing temperature. However, above the deconfinement temperature(T ≥

Tc), the potential because the color-screened coulomb potential, given by [90]

V (r) = −(αeff

r)e

−rrD(T ) (1.12)

where rD(T ) is the Debye screening radius. This potential can still allow bound states to be

formed. Combining equation 1.6 and 1.7 and minimizing E(r), one can get

x(x+ 1)e−x =1

mαeff rD(1.13)

Here, x ≡ r/rD is regarded as the critical parameter for a bound state. Using the LQCD

calculations [91], Matsui and Satz calculated rmaxJ/Ψ /rD = 1.61, the universal coulomb J/Ψ radius

at the last point where such a state is possible.

21

They argued that the existence of cc bound state is excluded down to T/Tc = 1.2. The

formation of a QGP therefore prevents the existence of such a bound state. As a result an ob-

served suppression would imply deconfinement. However, as previously mentioned, J/Ψ′s will also

undergo a ‘normal’ suppression, for example, induced by ordinary nuclear effects.

Systematic study of the J/Ψ and Ψ′ production has been performed at SPS and RHIC [86]

[87]. The NA50 experiment at SPS reported the observation of J/Ψ and Ψ′ suppression in central

heavy-ion collisions [86]. The same was also observed in proton-induced reactions on different

target nuclei [86] [92].

Quarkonium absorption in cold nuclear matter has been hypothesized as the mechanism respon-

sible for quarkonium suppression at mid-rapidity in p-A collisions. After considering the parton

shadowing and Quarkonium absorption in cold nuclear matter, the outcome of this analysis is that

only about 20-30% of the suppression in the most central Pb-Pb collisions at SPS energies is indeed

due to dissociation in hot QCD matter [92]. The PHENIX experiment at RHIC has reported the

observation of J/Ψ suppression in central Au-Au collisions at√sNN = 200 GeV, see Fig 1.17 [87].

As a consequence, J/Ψ suppression is roughly estimated to 40-80%, due to dissociation in hot QCD

matter, in central Au-Au collisions at RHIC. This result could explain higher suppression at RHIC

than that observed at SPS. In addition, the PHENIX observation shows that the suppression at

large rapidity is larger than that observed at mid-rapidity. It was a very interesting observation,

but one have not defined whether the hot or cold nuclear matter effects is the reason behind.

Fig 1.18 shows the J/Ψ RAA at LHC/ALICE comparison with those obtained by the PHENIX

experiment. The J/Ψ RAA at LHC/ALICE has a weaker dependence with centrality than that

observed at RHIC. The RAA (pt > 0, 2.5 < y < 4) for the most central class 0-10% is about a

factor 2 larger than that measured by PHENIX with muons in the forward region; the difference

is smaller, but still significant, when comparing to PHENIX at midrapidity.

22

Figure 1.17: J/Ψ RAA versus pt for several centrality bins in Au-Au collisions. Mid (forward) rapidity data are

shown with open (solid) circles [87].

Figure 1.18: J/Ψ RAA as a function of ⟨Npart⟩ in Pb-Pb collisions at√sNN = 2.76 TeV compared to PHENIX

results in Au-Au collisions at√sNN = 200 GeV [93].

23

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28

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29

30

Chapter 2

Heavy flavours

Heavy quarks (charm and bottom) provide a reliable tool to probe the dynamic properties of

the Pb-Pb collision evolution [1]. Heavy quarks production takes place on the timescale of the

order of 1/mQ , according to pQCD and have long lifetime. Thus, their production kinematics is

not influenced by medium effects and they experience the thermalization phase of the quark-gluon

plasma. They interact strongly with the hot and dense matter produced in heavy-ion collisions and

lose energy when they transverse the medium. The study of heavy quark production in p-p and p-A

collisions is important to extract the information about quark-gluon plasma in A-A collisions [2].

In this chapter, heavy-quark production in p-p collisions and A-A collisions is described. The

main focus is on the generation mechanisms of heavy quark, on the nuclear initial-state effects and

final-state effects. Then, the current results on heavy quark production are presented. In the last

part, the ALICE heavy flavour program is discussed.

2.1 Heavy quarks production in P-P collisions

At ultra-relativistic energies, heavy quarks are mostly produced via pair-creation by gluon-

gluon fusion (gg → QQ), as well as qq annihilation (qq → QQ), at leading-order. However, at

next-to-leading-order, the production of heavy quarks has more complicated topologies. Generally,

according to the number of heavy quarks in the final state of the hard process, the processes are

classified in three classes:

• pair creation: the hard process is one of the leading-order graphs (gg → QQ , qq → QQ); its

final state contains two heavy quarks;

31

Figure 2.1: Some of the processes defined as pair creation, flavour excitation and gluon splitting. The thick lines

correspond to the hard process.

• gluon splitting: no heavy flavour is involved in the hard scattering, but a pair is produced in

the final state from a g → QQ branching.

• flavour excitation: an virtual heavy quark, which comes from a g → QQ splitting in the

Parton distribution function (PDF) of the proton, is put on mass shell by scattering on a

parton of the other beam: qQ→ qQ or gQ→ gQ; this process is characterized by one heavy

quark in the final-state of the hard scattering;

Fig 2.1 shows some topologies for the processes specified above.

Heavy quarks are produced in primary partonic scatterings with large virtuality Q in the early

stage of the collision. According to asymptotic freedom, the QCD coupling constant decreases with

increasing energy. In p-p collisions at the LHC, the QCD coupling constant is small enough and

the cross-section of heavy quarks can be calculated in the framework of collinear factorisation and

pQCD. The single-inclusive differential cross-section for the production of a heavy flavour hadron

HQ can be written as [3]:

dσNN→HQX (√sNN,mQ , µ

2F, µ

2R) =

∑i,j=q,q,g

fi(x1, µ2F)⊗ fj (x2, µ

2F)⊗ dσij→Q(Q){k}

×(αs(µ2R, µ

2F,mQ , x1x2sNN)⊗D

HQ

Q (z , µ2F) (2.1)

where mQ and pt are the heavy quark mass and transverse momentum separately. The sum

runs over all possible sub-processes that generate the heavy flavour hadron. The formula consist

of three different terms explaining as follow:

• Parton distribution function (PDF) fi(xi , µ2F ) gives the probability of finding a quark (or

a gluon) i with a momentum fraction xi of the nucleon. The PDFs are evolved, with the

32

virtuality (four-momentum squared Q2) which has been exchanged in the scattering process,

up to the factorisation scale µF using the DGLAP equations.

• Partonic cross-section dσdpt

(ij → Q(Q)) is related to interactions of partons at high Q2. This

means that it can be described by perturbative QCD.

It is a function related to the heavy-quark mass (mQ) , the parton-parton centre of mass

energy squared (x1x2s) and the quark transverse-momentum (pt). In pQCD, the cross-section

is calculated in a power expansion in terms of αs , the coupling constant which depends on

the µR (renormalisation scale). The total cross-section for heavy-flavour production was

calculated up to next-to-leading order (NLO), which corresponds to O(α3s).

• Fragmentation function DHQ

Q (z , µ2F) which is the probability for the heavy quark Q scattered

to hadronize as a hadron HQ with a momentum fraction z = pHQ/pQ . The fragmentation

function is usually extracted by fitting a phenomenological model to experimentally data in

e+e−.

2.2 Heavy quark production in nucleus-nucleus collisions

Nucleus-nucleus (p-nucleus) collisions, if we neglect the nuclear and medium effects, and no

phase transition occurs, can be regarded as a superposition of independent p-p collisions. The

heavy-quark differential yields of nucleus-nucleus (p-nucleus) collisions can be written as product

between that of pp collisions and the number of inelastic N-N collisions Ncoll (the number of binary

collisions). So, their differential yields can be written as [3]:

d2NHQ

AA(pA)/dpt = Ncoll × d2NHQpp /dptdy (2.2)

The Ncoll is the number of binary collisions between the two nucleons, which can be calculated

with the Glauber model [4] of heavy-ion collisions.

For a collision of two nuclei with atomic numbers A and B, the probability generate n times

binary collision between the two incoming nucleons is written as binomial distribution:

Pm,n =

(m

n

)pn(1− p)m−n (2.3)

where m = AB. p is the probability for occurring a binary collision. n is the number of binary

collision and p is the probability for a binary collision to happen. The p can be calculated by

33

Figure 2.2: The transverse plane of the collision geometry.

combining the interaction cross-section between the two nucleons σNN and the thickness function

TAB (b) which related to the overlapping volume of the two nuclei. With a given collision impact

parameter, the thickness as the following form:

TAB (b) =

∫d2sTA(s)TB (s− b) (2.4)

where the Ti(s) =∫dzρi(s, z ) is the thickness function of the nucleus i(i = A,B) which

integrate the nuclear density ρi over the longitudinal direction z . Here, the nuclear density ρi can

be described by the Woods-Saxon distribution [5]. If the thickness function Ti(s) is integrated

over the all transverse nucleus area, it should be normalized to unity, i.e.∫d2sTi(s) = 1. Fig 2.2

shows the transverse plane of the collision geometry.

For a given impact parameter b, the probability that the two incoming nucleons inside two

nuclei generate one interaction is p(b) = σNN .TAB (b).

The binomial probability Pm,n for n binary interactions have the following formula:

PAB,n(b) =

(AB

n

)(σNNTAB (b))

n(1− σNNTAB (b))AB−n (2.5)

The probability for at least one binary collision to happen at a given impact parameter b can

be written as:dσAB

db= 1− PAB,0 (b) = 1− (1− σNNTAB (b))

AB (2.6)

The inelastic cross-section for a given centrality selection is obtained by integrating the inter-

action probability dσAB

db up to impact parameter bc :

34

σinelAB (bc) =

∫ bc

0

dbdσAB

db= 2π

∫ bc

0

db{1− [1− σNNTAB (b)]AB} (2.7)

For a given impact parameter b, the average number of inelastic collisions ⟨Ninel⟩ is

⟨Ninel⟩ = σNN .ABTAB (b) (2.8)

If one replace the inelastic nucleon-nucleon cross-section σNN with the elementary cross-section

σhardNN which is for a given hard process, one can get the average number of inelastic collisions

⟨N hardinel ⟩ for the given hard process

⟨N hardinel ⟩ = σhard

NN .ABTAB (b) (2.9)

and the cross-section for hard processes for 0 6 b < bc :

σhardAB (bc) = σhard

NN · 2π∫ bc

0

bdbABTAB (b) (2.10)

For minimum-bias collisions,bc = +∞, one can get

σhardAB = σhard

NN AB (2.11)

The ratio of the hard cross-section in nucleus-nucleus collisions, at a given centrality cut b < bc ,

relative to the cross-section in nucleon-nucleon collisions is

f hard(bc) =σhardAB (bc)

σhardNN

= 2π

∫ bc

0

bdbABTAB(b) (2.12)

The yield of hard processes per triggered event is

N hardAB (Bc) =

σhardAB (bc)

σinelAB (bc)

= ℜ(bc).σhardNN (2.13)

where

ℜ(bc) =∫ bc0

bdbABTAB(b)∫ bc0

bdb{1− [1− σNNTAB(b)]AB}(2.14)

2.2.1 Initial-state effects

One of the most important, initial-state-effects is the nuclear shadowing, which affects the

heavy-quark production by modifying the PDF [6] in the nucleus by gluon recombination at small

35

Figure 2.3: Ratio of gluon distribution function from different models at Q2 = 5GeV.

x . Usually, these nuclear effects are classified according to the behavior of the ratio of the PDFs

in the nucleus, f Ai (x ,Q2), with respect to that of the free nucleon, f Ni (x ,Q2). The ratio is

RAi (x ,Q

2) =f Ai (x ,Q2)

f Ni (x ,Q2)(2.15)

where i represents the parton species (valence quark, sea quark, gluon). At small x (x < 0.05−

0.1), a reduction of the hard cross-section producing a suppression of low transverse momentum

particles at mid-rapidity is observed. This behavior is called nuclear shadowing (RAi (x ,Q

2) < 1).

On the contrary, at intermediate x , an anti-shadowing effect (x (x ∼ 0.1− 0.2)) is expected to be

dominant (RAi (x ,Q

2) > 1).

There are various theoretical models to describe initial state nuclear effects. Fig 2.3 shows the

ratios of different models, between the gluon distribution functions for Pb and that of proton, as

function of x for Q2 = 5 GeV 2 which is the threshold for the cc production, Q2 = (2mc)2 ≃

5 GeV2. The bands represent the ranges of x for the cc production with rapidity range |y | ≤ 0.5,

at RHIC (√s = 200 GeV) and LHC (

√s = 5.5 TeV).

In nucleus-nucleus collisions, the nuclear shadowing [7] can be considered by recalculating the

hard cross-section for nucleon-nucleon interactions with nuclear-modified PDFs.

The cross-section of cc production and the number of cc processes per triggered event can be

calculated including the shadowing effect. It depends on the centrality, as follows

36

Figure 2.4: Parametrization of the shadowing effect in the cc nucleon-nucleon cross-section as function of the impact

parameter. The parametrization is applied for b ≤ 16 fm; b ≥ 16 fm the constant value σcc = 6.64 mb is considered.

Figure 2.5: Left panel: cc cross-section in Pb-Pb for b < bc . Right panel: number of σcc processes in different

centrality classes b < bc for Pb-Pb collision. In both the plots the shadowing parametrization is inclouded.

σhardNN = σhardNoshad [C0 + (1− C0)(

b

16)4] (2.16)

where σhardN0Shad is the nucleon-nucleon cross-section for a hard process without the shadowing

effect, which is σccNN = 6.64 mb [8] for charm production. C0 is a parameter, which is 0.65 in case

of charm production according to EKS98 parametrization [9]; b is the impact parameter measured

in fm. In Fig 2.4, shows the parametrization behavior of nuclear shadowing as function impact

parameter b. The cross section for cc production in Pb-Pb and the number of cc processes are

plotted in Fig 2.5.

37

2.2.2 Final-state effects

Final-state effects, such as partonic energy loss [10] [11] and development of anisotropic flow

patterns, due to the interaction of the produced partons with the medium formed in the colli-

sion, are expected to provide information on the properties of the medium (gluon density, volume

and temperature). The in-medium energy loss of massive partons (Charm and beauty quarks) is

expected to be different from that of ‘massless‘ partons (light quarks and gluons).

2.2.3 Parton energy loss in medium

Based on the elastic scattering of high momentum partons from gluons in the QGP, the en-

ergy loss of partons in the Quark-Gluon-Plasma were argued by J.D. Bjorken [12]. The resulting

(collisional) loss has dE/dx ≃ α2s

√ε dependence on the energy density ε of QGP.

However, gluon bremsstrahlung is another important source of energy loss [13]. Due to multiple

scatterings (inelastic) and induced gluon radiation hard partons lose energy and become quenched.

Such radiative loss is considerably larger than the collisional energy loss.

An energetic parton produced in a hard collision radiates a gluon with a probability which is

proportional to the path length L in the dense medium. Fig 2.6 shows that radiated gluons suffer

multiple scatterings with mean free path λ which decreases as the density of the medium increases.

Similarly, the number of scatterings of the radiated gluon is proportional to L. Therefore, the

average energy-loss of the parton is proportional to L2. This is the most unique feature of QCD

energy loss with respect to QED bremsstrahlung energy loss which is proportional to the path

length (∝ L), due to the fact that gluons interact with each other in the medium, while photons

do not. The scale of the energy loss is set by the ‘maximum’ energy of the emitted gluons, which

depends on the properties of the medium [14] and on the path length L:

wc =1

2qL2 (2.17)

where q is the transport-coefficient of the medium, defined as the average transverse-momentum

squared pt transferred to the projectile per unit path length

q =⟨p2

t ⟩medium

λ(2.18)

In the static medium, the distribution of the energy w of the radiated gluons, for w ≪ wc , has

the form:

wdI

dw≃ 2αsCR

π

√wc

2w(2.19)

38

Figure 2.6: Typical gluon radiation diagram.

where CR is the QCD coupling factor (Casimir factor), equal to 3 for gluon-gluon coupling and

to 4/3 for quark-gluon coupling.

The average energy loss of the initial parton can be estimated by integrating of the energy

distribution up to wc , as below

⟨∆E ⟩ =∫ wc

wdI

dwdw ∝ αsCRwc ∝ αsCRqL

2 (2.20)

Therefore, the average energy-loss has the following four features:

• proportional to L2;

• proportional to the transport coefficient of the medium;

• proportional to αsCR and, thus, larger by a factor 9/4 = 2.25 for gluons than for quarks;

• independent of the parton initial energy.

The last point, is peculiar to the BDMPS model [15] [16]. However, there is always an intrinsic

dependence of the radiated energy on the initial energy, determined by the fact that the radiated

energy cannot be larger than the initial energy, i .e. ∆E ≤ E .

The transport coefficient is proportional to the density ρ of the scattering centers and to the

typical momentum transfer in the gluon scattering off these centers. For cold nuclear matter, with

the value estimated in Ref [15]was:

qcold ≃ 0.05 GeV2/fm ≃ 8ρ0 (2.21)

39

Figure 2.7: Transport coefficient as a function of energy density for different media: cold (marker), massless hot

pion gas (dotted curve) and ideal QGP (solid curve).

This value is consistent with the experimental result of gluon kt broadening on J/ψ transverse

momentum distributions [17]

q = (9.4± 0.7)ρ0 (2.22)

However, an estimate for a hot medium, based on perturbative treatment of gluon scattering

in a Quark Gluon Plasma with T ≃ 250 MeV, resulted in the value of the transport coefficient of

about a factor twenty larger than that of cold matter:

qhot ≃ 1 GeV/fm ≃ 20qcold (2.23)

The large difference of transport coefficient between cold matter and hot medium, has two

reasons. First, the higher density of color charges in hot medium than in cold matter, i.e. shorter

mean free path of the probe in the Quark Gluon Plasma. Second, the fact that deconfined gluons in

QGP have harder momenta than confined gluons in cold matter, therefore the typical momentum

transfers are larger.

Fig 2.7 [18] reports the dependence of the transport coefficient q on the energy density for

different equilibrated media. q is expected to be of ∼ 10GeV2/fm for a QGP phase formed at the

LHC with ε ∼ 100 GeV/fm3.

40

Figure 2.8: pt distributions of invariant yields for reconstructed D0, charm decayed prompt µ and non-photonic

electrons in different centralities as observed by STAR.

2.3 Some relevant experimental results about heavy flavour

2.3.1 Cross section of heavy flavour in p-p and A-A collision

The differential cross-section for charm production has been measured at RHIC via the analysis

of hadronic channels and muons or non-photonic electrons,see [19].

The reconstruction of D mesons via hadronic channels gives the cleanest signal and the full

momentum of the initial D meson is reconstructed. STAR reconstructed exclusively D0 → K−π+

decays by an invariant mass analysis of identified opposite charged kaon and pion pairs in Au-Au

and d-Au collisions. However, it is rather difficult to perform this measurement without a vertex

detector, because of the large combinatorial background, especially in Au-Au collisions. Both the

systematic and statistical uncertainties are quite large. The design of the Inner Tracking System

(ITS) detector will allow ALICE to perform this analysis with very good significance.

Fig 2.8, shows the pt-distributions of invariant yields for reconstructed D0, charm-decayed

prompt µ and non-photonic electrons in different centralities in STAR at RHIC [19].

Fig 2.9, shows result measured by PHENIX for the p-p collisions and the Au-Au collisions in

different centralities [20]. The curves are results of FONLL-based calculation. For all centralities,

the Au-Au spectra well agree with the p-p at low pt while a suppression develops towards high pt.

Charm and beauty production has been also measured by the CDF and D0 experiments at

41

Figure 2.9: pt distributions of invariant yields of electrons from heavy-flavour decays for different Au-Au centralities

and p-p data measured by PHENIX, compared with theoretical predictions based on FONLL calculations normalized

to p-p data and scaled with ⟨TAA⟩. Error bars (boxes) depict statistical (systematic) uncertainties. The inset shows

the ratio of heavy-flavour to background electrons for minimum bias Au-Au collisions.

√sNN = 1.96 TeV. The cross-section for charm production has been measured by CDF via the

exclusive reconstruction of D mesons decays in hadronic channels, see [21]

2.3.2 Elliptic flow of heavy flavour

Elliptic flow (v2) is the second Fourier moment of the azimuthal momentum distribution and

is thought to be an important experimental probe that provides information about the thermal-

ization of the medium created in non-central heavy-ion collisions [22] [23] [24]. It results from the

geometrical anisotropy in the transverse plane in non-central collisions, which is largest at early

times. Therefor, v2 is sensitive to the properties of the dense matter, such as its equation of state.

In addition, measurements of elliptic flow at high momentum provide information on the density

and energy loss of partons.

Fig 2.10 [20], shows that the large vHF2 is better reproduced in Langevin-based heavy quark

transport calculations [25] [26]. A calculation which includes elastic scattering mediated by res-

onance excitation (curves II) [25] is in good agreement with both the measured RAA and v2. It

suggests that elliptic flow is built up at partonic stage while radial flow comes from hadronic

scattering at a later stage where charm may have already decoupled.

42

Figure 2.10: PHENIX results, see (a): RAA of heavy-favour electrons in 0-10% centrality Au-Au collisions compared

with π0 data and model calculations. (b): v2 of heavy-favour electrons in minimum bias collisions compared with

π0 data.

Theoretical models used to calculate RAA and v2 simultaneously [27] and can reproduce the

data with parameters (q, diffusion coefficient) typical of a strongly coupled, perfect fluid (no

viscosity) medium.

2.3.3 RAA of heavy flavour

As shown in Fig 2.11 [20], RAA ≈ 1 for all centralities (Npart), for the pt > 0.3 GeV/c integration

region, containing more than a half of the electrons from heavy-flavour decays, in accordance with

the binary scaling of the total heavy flavour yield. For the higher pt integration regions the RAA

decreases with increasing centrality, as expected if heavy quarks lose energy in the medium. In

central collisions, Fig 2.11, the nuclear modification factor is consistent with 1 at low pt and then

reduces at higher pt, reaching, at pt & 4 GeV/c, a value similar to that observed for light hadrons

like π0.

43

Figure 2.11: RAA of heavy-flavour electrons for the integrated pt spectrum (pt > 0.3 GeV/c) and for pt > 3 GeV/c

and of π0 for pt > 4 GeV/c, measured by PHENIX.

2.4 Open charm and open beauty in ALICE at LHC

2.4.1 Momentum fraction x of heavy quarks in ALICE

The LHC will allow us to probe the parton distribution functions of the nucleon and, in the case

of p-A and A-A collisions, also their modifications in the nucleus, down to unprecedentedly low

values of the momentum fraction (Bjorken x). Here, one compare the regimes in x corresponding

to the production of a cc pair at SPS, RHIC and LHC energy and one estimate the x range that

can be accessed with ALICE as far as heavy-flavour production is concerned. Charm and beauty

production cross sections at the LHC are significantly affected by parton dynamics in the small-x

region, as we will discuss in the following sections. Therefore, the measurement of heavy-flavour

production should provide valuable information on the parton densities.

We consider the simple case of the production of a heavy-quark pair QQ through the leading-

order pair-creation process gg → QQ in the collision of two nuclei (A1,Z1) and (A2,Z2). The

x range actually probed depends on the value of the centre-of-mass (c.m.s.) energy per nucleon

pair√sNN, on the invariant mass MQQ of the QQ pair produced in the hard scattering and on

its rapidity yQQ . If the intrinsic transverse momentum of the parton in the nucleon is neglected,

the four-momenta of the two incoming gluons are (x1, 0, 0, x1) · (Z1/A1)√spp/2 and (x2, 0, 0, x2) ·

(Z2/A2)√spp/2, where x1 and x2 are the momentum fractions carried by the gluons, and

√spp is

44

Figure 2.12: ALICE acceptance in the (x1, x2) plane for heavy flavours in Pb-Pb at 5.5 TeV (left) and in p-p at 14

TeV (right). The figure is explained in detail in the text.

the c.m.s. energy for pp collisions (14 TeV at the LHC). The square of the invariant mass of the

QQ pair is given by

M 2QQ = s = x1x2sNN = x1

Z1

A1x2

Z2

A2

√spp (2.24)

and its longitudinal rapidity in the laboratory is

yQQ =1

2ln[

E + pzE− pz

] =1

2ln[

x1x2

· Z1A1

Z2A2] (2.25)

From these two relations one can derive the dependence of x1 and x2 on colliding system, MQQ

and yQQ

x1 =A1

Z1·MQQ√spp

exp(+yQQ) and x2 =A2

Z2·MQQ√spp

exp(−yQQ) (2.26)

which simplifies to

x1 =MQQ√spp

exp(+yQQ) and x2 =MQQ√spp

exp(yQQ) (2.27)

for a symmetric colliding system (A1 = A2, Z1 = Z2). At central rapidities one have x1 ≃ x2

and their magnitude is determined by the ratio of the pair invariant mass to the c.m.s. energy. For

production at threshold (Mcc = 2mc ≃ 2.4 GeV, Mbb = 2mb ≃ 9 GeV). The x regime relevant for

charm production at the LHC (∼ 10−4) is about 2 orders of magnitude lower than at RHIC and 3

orders of magnitude lower than at the SPS. Because of its lower mass, charm allows one to probe

lower x values than beauty. The capability to measure charm and beauty particles in the forward

(or backward) rapidity region (|y | ≃ 4 GeV) gives access to x regimes about 2 orders of magnitude

lower, down to x ∼ 10−6.

45

Fig 2.12 shows the regions of the (x1, x2) plane covered for charm and beauty by the ALICE

acceptance, at 5.5 TeV (the planned Pb-Pb c.m.s. energy) and at 14 TeV (the planned p-p c.m.s.

energy). In this plane the points with equal invariant mass lie on hyperbolae (x1 = M 2QQ

/(x2sNN)),

straight lines in the log-log scale: one show those corresponding to the production of cc and bb

pairs at the threshold; the points with constant rapidity lie on straight lines (x1 = x2e+2yQQ ). The

shadowed regions show the acceptance of the ALICE barrel, covering the pseudorapidity range

|η| < 0.9, and of the muon arm, −4 < η < −2.5.

In the case of asymmetric collisions, e.g. p-Pb and Pb-p, we have a rapidity shift: center of

mass moves with a longitudinal rapidity

yc·m =1

2ln

Z1A2

Z2A1(2.28)

obtained from equation for x1 = x2. The rapidity window covered by the experiment is conse-

quently shifted by

∆y = yc·m (2.29)

corresponding to +0.47 (-0.47) for p-Pb (Pb-p) collisions. Therefore, running with both p-Pb

and Pb-p will allow the largest interval in x to be covered. The c.m.s. energy in this case is 8.8

TeV. Fig 2.13 shows the acceptances for p-Pb and Pb-p, while in Fig 2.14 the coverages in p-p,

Pb-Pb, p-Pb and Pb-p are compared for charm (left) and beauty (right). These figures are meant

to give only an approximate idea of the regimes accessible with ALICE; the simple relations for the

leading-order case were used, the ALICE rapidity acceptance cuts were applied to the rapidity of

the QQ pair, and not to that of the particles actually detected. In addition, no minimum pt cuts

were accounted for: such cuts will increase the minimum accessible value of MQQ , thus increasing

also the minimum accessible x . These approximations, however, are not too drastic, since there is

a very strong correlation in rapidity between the initial QQ pair and the heavy-flavour particles it

produces and the minimum accessible pt for D and B mesons in ALICE is expected to be of order

1-2 GeV/c.

46

Figure 2.13: ALICE acceptance in the (x1, x2) plane for heavy flavours at 8.8 TeV in p-Pb (left) and in Pb-p (right).

Figure 2.14: ALICE acceptance in the (x1, x2) plane for charm (left) and beauty (right) at 5.5, 8.8 and 14 TeV.

47

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49

50

Chapter 3

The ALICE experiment at the

LHC

ALICE (A Large Ion Collider Experiment) [1] is a multipurpose detector dedicated to heavy-

ion collisions at the LHC which focuses on Quantum Chromo-dynamic (QCD) [2], the strong

interaction theory of the Standard Model (SM) [3]. It is the dedicated heavy-ion detector to study

of nucleus-nucleus interactions at the LHC. The physics targets include the study collisions with p-

p, lighter ions and proton-nucleus. From 2008 to this year, it has accumulated data on cosmic-ray,

P-P collision at√s = 900 GeV and

√s = 7 TeV, as well as Pb-Pb collision at

√s = 2.76 TeV. The

whole detector ran effectively and harvested many results. In the future, it will run with P-P at√s = 14 TeV and Pb-Pb at

√s = 5.5 TeV [4]. Some breakthroughs are expected to be discovered.

In section 1, I discuss the physics targets at ALICE. The layout of ALICE detector will be

introduced, as well as the structure of some detectors (ITS, TPC and TOF). In section 2, the

detector performance will be presented in the last section. we will give the calibration, alignment,

tracking, primary vertex reconstruction and the ALICE run status.

3.1 ALICE physics targets

As QCD predicts [2], a transition will happen from confined hadron phase to the deconfined

Quark Gluon Plasma phase at very high temperatures and very high densities. Heavy-ion collisions

are a unique tool to provide this extreme conditions. The Large Hadron Collider (LHC) is the

biggest accelerator in the world at the moment. There are four experiments (ALICE, ATLAS,

51

CMS and LHCb ) with different physics targets.

ATLAS and CMS are dedicated to the search for the Higgs particle and supersymmetric par-

ticles which are manifestations of a broken intrinsic symmetry between fermions and bosons in

extensions of the Standard Model [3]. LHCb will focus on CP-symmetry violating processes. AL-

ICE will investigate the properties of QGP formed at high-energy densities over large volumes

and long timescales obtained in heavy-ion collisions. The physics programmes are not completely

separated, but will have some overlap e.g. in flavor physics, heavy-ion physics, etc.

In addition, ALICE can gain insight into the physics of parton densities close to phase-space

saturation, and their collective dynamical evolution towards hadronization (confinement) in a dense

nuclear environment. In this way, one also expects to probe the structure of the QCD phase diagram

and the properties of the QGP phase. Three momentum regimes can be identified, which have

specific features.

a) Hard processes: They can be calculated via pertubative QCD and probe the very early state

of the reaction. It is the main contribution above pt = 10 GeV/c. Outstanding tracking perfor-

mance will allow an interesting whose program on heavy flavors. The Electro-Magnetic Calorimeter

(EMCAL) can increase the fraction of reconstructed energy and trigger the jets effectively. These

will improve the statistics of reconstructed jets prominently [5].

b) Semi-hard processes: They belong to the intermediate pt regime (2-5/10 GeV/c), which

will contribute to the cross section. In the semi-hard process, the pt-spectra will be dominated by

the presence of mini-jets and the production of open charm is mainly governed by the interaction

of hard process. The thermodynamics of the system produced by initial collision can be explored

with measurement of thermal photons. Because of the dead-cone effect, the intermediate pt heavy

quarks will lose less energy then light quarks when they traverse the dense medium. The nuclear

modification factor ratio between the D mesons (B mesons) and normal hadrons are predicted to

be sensitive to the mass dependence. The central detectors of ALICE provide the tools for accurate

reconstruction of D mesons by hadron decay and B mesons by semi-leptonic decay. Even more,

ALICE can detect sufficient statistics of charmonia and bottomonia produced at midrapidity (in

di-electron channels) and at forward rapidities (in di-muon channels) at LHC energy. In the case

of Υ, due to the higher mass, we can ignore the influence of the recombination of charm quarks.

Hence, the production can be measured by normalization to the quarkonia production.

c) Soft processes: The processes most be described by non-pertubative QCD and probe later

stages of the collision, in the low pt region (0-2 GeV/c). In this pt region, the analysis of collective

52

Figure 3.1: Layout of ALICE detector

phenomena measurement can help to understand the expansion dynamics of the reaction and

study the spacetime evolution of the system as well as the thermal freeze-out condition, e.g. by

particle interferometry. Furthermore, the particle yields offer information on the chemical freeze-

out properties of the reaction. ALICE will measure the charged-particle multiplicity and the

charged-particle pseudo-rapidity distribution using the Forward Multiplicity Detector (FMD) and

the ITS in eight units of pseudo-rapidity. This will help to know the energy density reached in

the early stage of the collision. In the low pt region, ALICE will investigate the chiral symmetry

restoration through the measurement of special resonances which have lifetimes comparable to that

of the QGP phase.

3.2 The ALICE detectors

ALICE consists of the central barrel detector system covering |η| < 0.9 region of pseudo-

rapidity, over the full azimuth, where it is able to measure hadrons, electrons and photons, and a

forward spectrometer to measure muons (−4 < η < −2.4) [6]. Fig 3.1 shows the layout of ALICE

detector.

The beam pipe is built in beryllium which has relatively low atomic number (i.e. low radiation

length, X0 ) and it has an outer radius of 2.9 cm and a thickness of 0.8 mm (corresponding to 0.23

53

of x0) in order to minimize the multiple scattering.

Going from the beam pipe outwards, we find the Inner Tracking System (ITS) [7] composed of

six layers which divide into three sub-detectors (SPD, SDD and SSD) [8] [9] [10] for tracking and

vertex reconstruction, as well as particle identification; a Time Projection Chamber (TPC) [11] for

tracking and particle identification; a Transition Radiation Detector (TRD) [12] for electron identi-

fication, a Time of Flight (TOF) [13] for particle identification, a large acceptance electromagnetic

calorimeter (EMCal) [14] for the measurement of high momentum photons and electrons, and to

improve jet energy resolution; a small-area ring imaging Cherenkov detector(|η| < 0.9) at large dis-

tance for High Momentum Particle Identification (HMPID) [15], and a single-arm electromagnetic

calorimeter of high-density crystals, Photon Spectrometer (PHOS) [16].

The central barrel detector is embedded in a large solenoidal magnet with a magnetic field

B ≤ 0.5 T, with its central axis parallel to the z axis. This field strength is a good compromise

between low momentum acceptance and momentum resolution. In order to detect the decay

products of low-pt hyperons and D (B) mesons, the momentum cut-off value should be as low as

possible (about 100 MeV/c). At high pt the magnetic field determines the particle momentum

resolution, which is essential for the study of high-pt leptons and jet quenching. The best choice

for the high-pt observables the maximum field would be around 0.5 T, while for hadronic physics,

maximizing reconstruction efficiency, 0.2 T would be the ideal choice. However, to assure enough

statistics of high-pt observables, ALICE will run mostly with a higher field option 0.4 T.

The muon spectrometer was designed to measure the spectrum of heavy quark resonances,

namely J/ψ, ψ′, Υ, Υ′ and Υ′′, as well as the ϕ, through µ+µ− decay channel. Combined with

the TRD identification capabilities, it is also possible to measure heavy-flavour production in the

region −2.5 < η < −1 with measurement of e − µ coincidences. It is made up of an absorber,

positioned very close to the vertex, followed by a spectrometer with a dipole magnet and tracking

chambers.

The set-up is completed by a forward photon counting detector, The photon Multiplicity Detec-

tor (PMD) positioned at positive z (2.3 < η < 3.7) and a multiplicity detector, Forward Multiplicity

Detector (FMD) covering the forward pseudo-rapidity region (−3.4 < η < −1.7 and 1.7 < η < 5),

that, in conjunction with the ITS, allows the measurement of the charged multiplicity in the

pseudo-rapidity range (−3.4 < η < 5).

A system of scintillators (V0 detector) and quartz counters (T0 detector) provide fast trigger

signals and timing.

54

ITS barrel

SPD barrel

Sectors (10)

Half-staves(4 on inner, 8 on outer layer)

Modules (2)

SDD-SSD barrel

SDD barrel SSD barel

Layers (2)

Ladders(14 on inner, 22 on outer layer)

Modules(6 on inner, 8 on outer ladders)

Layers (2)

Ladders(34 on inner, 38 on outer layer)

Modules(22 on inner, 25 on outer ladders)

Figure 3.2: The hierarchical structure of Inner tracking System

Owing to their different Z/A values, it is possible to separate in space the neutron and proton

spectators and the beam particles (Z/A ≃ 0.4 for Pb beams) by means of the first LHC dipole.

Therefore, the neutron and proton spectators are detected in two distinct calorimeters, Zero De-

grees Calorimeters (ZDC), made respectively of brass and tantalum with embedded quartz fibers,

located on both sides of the interaction region (about 90m) downstream in the machine tunnel.

3.2.1 Inner Tracking System

The basic functions of the ITS [7] are:

Table 3.1: Parameters of the six ITS layers

Number Active Area Resolution Material

Layer Type r [cm] ±z [cm] of per module budget

modules rφ× z [mm2] rφ× z [µm2] X /X0[%]

1 pixel(ϕ) 3.9 14.1 80 12.8×70.7 12×100 1.14

2 pixel(z) 7.6 14.1 160 12.8×70.7 12×100 1.14

3 drift(ϕ) 15.0 22.2 84 70.17×75.26 35×25 1.13

4 drift(z) 23.9 29.7 176 70.17×75.26 35×25 1.26

5 strip(ϕ) 38.0 43.1 748 73×40 20×830 0.83

6 strip(z) 43.0 48.9 950 73×40 20×830 0.86

55

SPD

SDD

SSD

87

.2 c

m

x

y

z

locz

locy

locx

locf

locq

locy

Figure 3.3: CAD sketch of Inner Tracking System

• determination of the primary vertex and of the secondary vertices with high resolution;

• particle identification and tracking of low-momentum particles which are not detected by

TPC;

• improvement of the momentum and angle resolution of particles detected by TPC.

The geometrical parameters of the layers of the ITS are summarised in Table 3.1. As far

as the material budget is concerned, it should be noted that the values reported in Table 3.1

account for sensor, electronics, cabling, support structure and cooling for particles crossing the

ITS perpendicularly to the detector surfaces. Another 1.3 % of X0 (radiation length) comes from

the thermal shields and supports installed between SPD and SDD barrels and between SDD and

SSD barrels, thus making the total material budget for perpendicular tracks equal to 7.66 % of

X0.

In the following paragraphs, a brief description of the features of each of the three subdetectors

(SPD, SDD and SSD) is done, for more details see [7] . In Fig 3.2, the hierarchical structure of the

three subsystems, driving the definition of the alignment procedure is shown. Each of the objects

itemized in Fig 3.3 is defined as an alignable volume in the software geometry and it can be moved,

to account for the misalignment, by applying a transformation defined by the six independent

alignment degrees of freedom (three translations and three rotations) of the volume.

3.2.1.1 Silicon Pixel Detector (SPD)

The basic building block of the SPD [8] is a module consisting of 2 two-dimensional sensor

matrices of reverse-biased silicon detector diodes bump-bonded to 5 front-end chips. Each sensor

56

Figure 3.4: Disposition of the 10 sectors around the beam pipe. The maximum curvature radii for which tracks

have a possibility to go undetected through the layers are 119 mm for the first and 475 mm for the second

matrix consists of 256 × 160 cells, each measuring 50 µm (rφ) by 425 µm (z). The active area

of each module is 12.8 mm (rφ) × 70.7 mm (z), the thickness of the sensor is 200 µm, while the

readout chip is 150 µm thick. Two modules are mounted together along the z direction to form

a 141.6 µm long half-stave. Two half-staves are attached head-to-head along the z direction to a

carbon-fibre support sector, with cooling lines integrated. Each sector (see Fig 3.4) supports six

staves: two on the inner layer and four on the outer layer. The assembly of half-staves on sectors

provides an overlap of about 2 % of the sensitive area along rφ, while there is no sensor overlap

along z, where, instead, there is 500 µm gap between the two half staves. Five sectors are then

mounted together to form an half-barrel and finally the two (top and bottom) half-barrels are

mounted around the beam pipe to close the full barrel, which is actually composed of 10 sectors.

In total, the SPD includes 60 staves, consisting of 240 modules with 1200 readout chips for a total

of 9.8 × 106 cells.

The spatial precision of the SPD sensor is determined by the pixel cell size and by the track

incidence angle on the detector, as well as by the threshold applied in the readout electronics. The

values of resolution along rφ and z extracted from beam tests are 12 and 100 µm respectively.

57

Figure 3.5: Sketch of the two-directional SDD with a blow-up of a corner.

3.2.1.2 Silicon Drift Detector (SDD)

The basic building block of the ALICE SDD [9] is a module with a sensitive area of 70.17 (rφ)

× 75.26 (z) mm2 divided into two drift regions where electrons move in opposite directions under

a drift field of ≈ 500 V/cm. The SDD modules are mounted on linear structures called ladders.

There are 14 ladders with six modules each on the inner SDD layer (layer 3), and 22 ladders with

eight modules each on the outer SDD layer (layer 4). Modules and ladders are assembled to have

an overlap of the sensitive areas larger than 580 µm in both rϕ and z directions, so as to provide

full angular coverage. Fig 3.5 shows the sketch of the two-directional SDD with a blow-up of a

corner.

The modules are attached to the ladder space frame, which is a lightweight truss made of

Carbon-Fibre Reinforced Plastic (CFRP) with a protective coating against humidity absorption,

using ryton pins. The anode rows parallel to the ladder axis (z). During the assembling phase, the

positions of the detectors were measured with respect to the reference ruby spheres glued to the

ladder feet.

The ladders are mounted on a CFRP structure made of a cylinder, two cones and four support

rings, see Fig 3.6. The cones provide the links to the outer SSD barrel and have windows for

the passage of the SDD services. The support rings are mechanically fixed to the cones and bear

reference ruby spheres for the ladder positioning.

58

Figure 3.6: The ladders are mounted on a CFRP structure made of a cylinder, two cones and four support rings

The z coordinate is reconstructed from the centroid of the collected charge along the anodes.

The position along the drift (rφ) coordinate is reconstructed starting from the measured drift

time with respect to the trigger time. An unbiased reconstruction of the rφ coordinate requires

therefore to know with good precision the drift speed and the time-zero (t0), which is the measured

drift time for particles with zero drift distance.

The drift speed depends on temperature (as T−2.4) and it is therefore sensitive to temperature

gradients in the SDD volumes and to temperature variations with time. Hence, it is important to

calibrate frequently this parameter during the data taking. For this reason, in each of the two drift

regions of an SDD module, 3 rows of 33 MOS charge injectors are implanted at known distances

from the collection anodes. When a dedicated calibration trigger is received, the injector matrix

provides a measurement of the drift speed in 33 positions along the anode coordinate for each SDD

drift region.

Finally, a correction for non-uniformity of the drift field (due to non-linearities in the voltage

divider and for few modules also due to significant inhomogeneities in dopant concentration) has

to be applied: it is extracted from measurements of the systematic deviations between charge

injection position and reconstructed coordinates that was performed on all the 260 SDD modules

with an infrared laser.

The space precision of the SDD detectors, as obtained during beam tests of full-size prototypes

is, on average, 35 µm along the drift direction (x-y) and 25 µm for the anode coordinate (Z).

59

Figure 3.7: Photograph of the SSD in the final configuration

3.2.1.3 Silicon Strip Detector(SSD)

The basic building block of the ALICE SSD [10] is a module composed of one double-sided strip

detector connected to two hybrids hosting the front-end electronics. The sensors are 300 µm thick

and have an active area of 73 × 40 mm2 along z and rφ directions, respectively. Each sensor has

768 strips on each side with a pitch of 95 µm. The stereo angle is 35 mrad which is a compromise

between stereo view and reduction of ambiguities resulting from high particle densities. The strips

are almost parallel to the beam axis (z-direction), to provide the best resolution in the rϕ direction.

The angle of the strips with respect to the beam axis is +7.5 mrad on one side and -27.5 mrad

on the other side. As a result, each strip crosses about 14 strips on the other detector side. The

modules are assembled on ladders of the same design as those supporting the SDD. The innermost

SSD layer (layer 5) is composed of 34 ladders, each of them being a linear array of 22 modules

along the beam direction. Layer 6 (the outermost ITS layer) consists of 38 ladders, each of them

made of 25 modules, see Fig 3.7.

To obtain full pseudo-rapidity coverage, the modules are mounted on the ladders in a way that

the active areas of the modules overlap. For a track crossing an overlap region the two clusters

60

measured on the two neighbouring modules are 600 µm apart radially. The 72 ladders, carrying a

total of 1698 modules, are mounted on Carbon Fibre Composite support cones in two cylinders.

Carbon fiber is lightweight (to minimise the interactions) and, at the same time, it is a stiff material

allowing to minimise the bending due to gravity. The ladders are 120 cm long, but the sensitive

area amounts to 88 cm on layer 5 and to 100 cm on layer 6. For each layer, the ladders are mounted

at two slightly different radii (△ r = 6mm) to ensure a full azimuthal coverage. The acceptance

overlaps, present both along z and rφ, amount to 2% of the SSD sensor surface.

The spatial resolution of the SSD system is determined by the 95 µm pitch of the sensor

readout strips and by the charge-sharing between those strips. Without making use of the analogue

information the r.m.s spatial resolution is 27 µm. Beam tests have shown that a spatial resolution

of better than 20 µm in the rφ direction can be obtained by analyzing the charge distribution

within each cluster. In the direction along the beam the spatial resolution is about 830 µm.

3.2.2 Time Projection Chamber

ALICE chose a large cylindrical TPC [11] as its main tracking device, see Fig 3.8. Its inner

(outer) radius and overall length along the beam direction are 0.85 (2.5) m and 5 m. In a high-

multiplicity environment, the challenge is to achieve high tracking efficiency, good momentum

resolution (a few percent for tracks with momentum below 5 GeV/c and about 10% for 100 GeV/c),

good two-track separation, as well as good dE/dx resolution. This requires high granularity readout

with about 560,000 electronic channels. In addition to its tracking function, the TPC can serve as

a detector for identification up to momenta of about 2.5 GeV/c. Since the drift of the ionization

electrons can take up to 88 µs, the gas must has high purity, the diffusion has to be low as much

as possible and the electrical parameters of the TPC have to be chosen so as to avoid space-charge

problems.

The design of the readout and of the end plates, as well as the choice of the operating gas

is optimized for good two track resolution. The drifting electrons are detected by Multi-wire

proportional chambers (MWPCs) with cathode pad readout.

The TPC will provide Particle Identification (PID) for low-p particles (for example identification

of pions in the range 0.4 < p < 0.5 GeV/c). The control of uncertainties requires an understanding

of space-charge effects and the drift velocity to 0.1%, amongst other parameters. This calibration

is regularly carried out by a laser system.

61

Figure 3.8: Schematic view of TPC in ALICE. The central electrode relative position, the direction of field cage

and readout chamber are shown.

3.2.3 Time of Flight

The Time Of Flight detector (TOF) [13] of ALICE is a large array that covers the central

pseudorapidity |η| < 0.9, see Fig 3.9. It has a modular structure corresponding to 18 sectors in the

global azimuthal angle ϕ (0o − 360o) and 5 segments along the beam direction (z), with an inner

radius of 370 cm and an outer radius of 399 cm. Five modules of three different types are chosen

to cover the full cylinder along the z direction. These modules have the same structure and width

(about 128 cm) but different length. The middlemost module is 1.17 m long, the two intermediate

modules are 1.57 m long and the two external modules are 1.77 m long.

The TOF technology is based on the double-stack Multigap Resistive Plate Chamber (MRPC)

and the active area of the detector is field with the mixed gas C2F4H2/C4H10/SF6. This technol-

ogy makes it possible to identify, on an event-by-event basis, the highest expected charged-particle

multiplicity density (dN ch/dη = 8000 and to identify the particles in the intermediate momentum

range (for pion/kaon in the momentum range below 2.5 GeV/c and proton/kaon in the range below

4 GeV/c). Due to its excellent time resolution (60-80 ps), the separation is better than 3σ both

for pion/kaon and kaon/proton. It is associated with the ITS and TPC for tracking and vertex

reconstruction and for dE/dx measurement in the low momentum range (below 1 GeV/c).

62

Figure 3.9: Schematic drawing of the Time Of Flight(TOF) supermodul,consisting of 5 modules,in the ALICE

3.3 ALICE analysis tools

3.3.1 ROOT and AliROOT

The ALICE offline framework, AliRoot, is based on the the ROOT analysis framework which

is an object oriented package written in C++ [16]. It provides all the tools to reconstruct and

analyze the Monte Carlo (MC) data generated by AliROOT itself and real data.

3.3.2 ALICE computing environment

The distributed computing system GRID, is the adopted solution of processing and storing

huge number of data which could not be completed by a single large computer center on time [17].

According to the type of stored data (Raw data, ESD data and AOD data, see next section),

the computing is hierarchically divided into three levels of so-called Tier centers. The first level

(Tier-0) is at CERN, where the copy of all the raw data is stored. Then, RAW data are copied

and store to regional computing centers (Tier-1). The smaller Tier-2 computing centers are used

to produce MC simulations and files that can be accessed directly by analyzer. The all activity

on GRID is handled by a “Middleware” Alice ENvironment (AliEN), which assigns the computing

resources in a dynamical system of virtual organizations.

A fast response environment for high priority jobs and quick tests is provided by the CERN

63

Figure 3.10: The CERN Analysis Facility (CAF).

Analysis Facility (CAF), see Fig 3.10: it is a computer clusters located at CERN, which adopt the

Parallel ROOT Facility (PROOF) protocol to stretch the use of ROOT on clusters and distributed

computing. Due to the limited storage space, CAF can not access all ALICE data as AliEN, but

can provide a vary fast way for the user to pre-analyze the data.

3.4 Event generation and reconstruction

3.4.1 Description of Event

In the following, the steps of the simulation and reconstruction chain for collision events are

outlined.

3.4.1.1 Event simulation

The kinematics of the particles produced in collisions are simulated through events generators,

like Pythia or HIJING. All the information about the generated particles (e.g. type, momentum,

parent particles and production process, decay products) is organized in a kinematic tree stored

in a file.

64

3.4.1.2 Particle transport in the detector: hits

The generated particles are propagated to the detector where they can interact with the detec-

tor material and be “detected”. During this process particles can decay and produce additional

particles. Using the ROOT geometrical modeler, the detector shape, structure, position and ma-

terial are described in the AliRoot framework as realistically as possible, down to the level of all

mechanical structures and single electronic components. The specialised programmes for particle

transport like Geant3, Geant4 and Fluka, interfaced with the geometry, can reproduce realistic in-

teraction between particles and material. All interactions of particles with sensitive detector parts

are recorded as hits, containing the position, time and energy deposit of the respective interaction.

3.4.1.3 Digitization and raw data

For each hit the corresponding digital output of the detector is simulated and stored taking

into account the detector response function. If the case, noise is then added. The last step consists

in the storing the data in the specific hardware format of the detector, the raw data. The raw

data, representing the response of the detector, constitute the minimum of the physical information

parabola in Fig 3.11. They are the starting point of the reconstruction process, which is identical

for both simulated and real events.

3.4.1.4 Cluster finding

Particles crossing the sensitive part of a detector usually leave a signal in several adjacent

detecting elements, for instance adjacent pixels (strips) on the SPD (SSD). These signals are

combined into a single cluster, which better estimates the position of the traversing particle besides

reducing the effect of random noise.

3.4.2 Track reconstruction

Track reconstruction is one of the most challenging tasks in the ALICE [18] [19] [20]. The

tracking starts from the reconstructed points given by the local reconstruction in each detector.

The general tracking strategy starts from the best tracker device, i.e. the TPC, to extrapolate

the candidate tracks in the ITS and to backpropagate the tracks to the outer detectors, namely

the TRD, TOF, HMPID and PHOS. Three steps make up the tracking procedure: track seeding,

track finding and track fitting. The track seeding consists in the combination of pairs of rec points

belonging to two pad rows located in the external parts of TPC, where the density of particles

65

Figure 3.11: Data processing framework

is lower. These track segments are called “seeds”. Due to the small number of clusters assigned

to a seed, the low precision of its parameters does not allow the extrapolation of the seed in

the outward direction. Instead, the track candidate is propagated towards the primary vertex,

associating whenever possible new points to the track. This is performed using the Kalman filter

method, where the track finding and track fitting procedures are combined.

When the seeds are extrapolated to the inner radius of the TPC, the tracks are prolonged

from TPC to the ITS. In this step, a strict vertex constraint with a resolution of ∼ 100 µm is

imposed. Then, another pass is done without vertex constraint in order to reconstruct the tracks

coming from secondary vertices. In the extrapolation to the ITS multiple scattering effects have

to be taken account and more than one cluster in ITS may be compatible with the track segment

found in TPC. Because of the high track density and the distance ITS-TPC. Therefore, for each

TPC track, a track hypothesis tree is built in the ITS and the most probable path along the tree is

chosen taking into account the χ2 of the track and the possibility that a cluster is shared by several

track candidates. The track is then propagated to the point on the track of minimum distance

from the interaction point and all the track parameters are defined in this point.

A special ITS stand-alone tracking procedure is applied to those clusters which are not assigned

to tracks propagated from the TPC; the aim of this reconstruction algorithm is to recover the tracks

that were not found in the TPC because of the low transverse momentum cut-off of the dead zones

between the TPC sectors and of decays.

66

At this point, the Kalman filter is applied from the vertex to the outward direction. In this way

the track is propagated towards the TRD, TOF, HMPID, PHOS and EMCal. The space point

with large-χ2 contributions are eliminated.

Finally, all the tracks are refitted backwards to the primary vertex. The tracks which passed

the final refit are used for the secondary vertex reconstruction.

The tracks found with Kalman filter are locally defined by the parameters of a helix. A helix

is generally described by six parameters as follows:

x = Rcosφ+ x0

y = Rsinφ+ y0

z = kφ+ z0

where C=(x0, y0)is the center of the circumference in the bending plane, R is the radius, φ is

the azimuthal angle, z0 is the starting point along the z axis and K is the coefficient giving the

proportionality between the z coordinate and φ. An alternative way is to replace R,φ and K by

three components of the momentum, px, px and pz.

In our case,the parameters are defined in the so called reference plane (xr, yr) which is the

plane, defined track by track, parallel to the bending plane (x, y) and rotated in such a way that the

xr axis is oriented along the TPC sector which includes the track. The tracks are always defined

locally, i.e. at a given position X along xr. Therefore, only five parameters (and consequently a

5 × 5 covariance matrix) are needed to locally describe the track, because one parameter (X) is

fixed. The five parameters are:

• y coordinate of the track in the local reference system, corresponding to the position X along

xr;

• z coordinate of the track;

• sinφ, where the φ is the track azimuthal angle defined in the reference system;

• tanλ, where the λ = π/2− θ, θ is the polar angle;

• curvature C = 1/R, where R is the radius of the circumference;

3.4.3 Primary vertex reconstruction

Primary vertex reconstruction is one of the main requirements in the three levels of the data

processing in the ALICE experiment: online, reconstruction and analysis [21] [22] [23] [24]. At the

67

online level, the knowledge of the interaction point is necessary to monitor the beam position and

to measure the beam spread along the three coordinates x, y and z. The spread is expected to

be of the order of 50-200 µm in the transverse plane (x and y coordinates) and of the order of 5

cm in the longitudinal direction (z), for p-p collisions. The Silicon Pixel Detector (SPD), located

in the two innermost layers of the Inner Tracking System (ITS), is the ideal detector to perform

fast vertex measurements and online monitoring because (a) it gives a fast response, (b) it is the

closest detector to the interaction point, and (c) it has an excellent resolution in the transverse

plane, due to its high granularity.

In addition, the SPD is used to provide the primary vertex position for events triggered by the

Forward Muon Spectrometer, without the need of reading and reconstructing the events in the

other barrel detectors.

At the reconstruction level, the position of the primary vertex given by the clusters in the SPD

is needed by the Kalman filter algorithm to perform the tracking in the central barrel.

At the analysis level, a good measurement of the primary vertex improves the resolution on the

impact parameters of the tracks with respect to the interaction point: this is important for studies

of short-lived particles, such as those with open charm and open beauty.

Three algorithms for vertex reconstruction are discussed in this work, which updates and ex-

pands a previous note. The algorithms, included in the ALICE software [2], are listed below:

• VertexerSPDz: it provides the measurement of the z coordinate of the interaction point by

means of the SPD. It requires the knowledge of the x and y coordinates.

• VertexerSPD3D: it provides a three-dimensional measurement of the primary vertex by means

of the SPD.

• VertexerTracks: it provides a three-dimensional measurement of the primary vertex by means

of the reconstructed tracks.

The first two algorithms only require local reconstruction in the SPD, whereas VertexerTracks

can only be used once the reconstructed tracks are available. In the following we summarize the

structure of the event reconstruction “loop” (tracking and vertexing), and we describe the use

of the three algorithms for primary vertex reconstruction. Track reconstruction in the ALICE

central barrel is performed using three subdetectors (here ordered from the inside to the outside):

the Inner Tracking System (ITS), which has an outer radius of ⋍ 45 cm, the Time Projection

Chamber (TPC), with outer radius ⋍ 250 cm, and the Transition Radiation Detector (TRD), with

68

outer radius ⋍ 350 cm. These detectors, which are embedded in a large solenoidal magnet providing

a magnetic field of 0.5 T, allow the track reconstruction in the pseudorapidity range |η| < 0.9. In

Table 3.1 we present the main parameters of the six layers of the ITS, since this is the detector

used for vertex reconstruction. Event reconstruction is performed in the following steps: 1. First

estimate of the position of the interaction vertex using the correlation of tracklets in the SPD.

The vertex position is reconstructed in the three coordinates using VertexerSPD3D; for the events

in which this algorithm fails (mostly events with only one SPD tracklet), only the position along

the beam line (z) is determined, using VertexerSPDz. The run-by-run information on the position

and spread of the interaction region (diamond), if available from the Offline Condition Database

(OCDB), is used by the two algorithms, as we will detail in the following. The reconstructed vertex

is stored in the ESD (Event Summary Data).

2. Track reconstruction in the TPC. Track finding and fitting are performed from outside

inward by means of a Kalman filter. Track candidates (seeds) are created using the information

from the n outermost pad rows (n ⋍ 15) and the position of the primary vertex as reconstructed

with the SPD. A copy of the set of tracks from the TPC reconstruction is propagated to the

primary vertex and stored in the ESD, in order to allow the possibility to perform a TPC-only

analysis.

3. Track reconstruction in the ITS. TPC reconstructed tracks are matched to the outermost

ITS layer and followed in the ITS down to the innermost pixel layer. Track finding is done in two

passes: during the first pass, the position of the primary vertex estimated using the SPD pixels is

used to maximize the efficiency for primary tracks; during the second pass, the vertex information

Table 3.2: LHC parameters for PP and PbPb runs for ALICE

Parameter PP PbPb

√sNN [TeV] 0.9 10 14 5.5

β∗ [m] 10 10 10 0.5

σbunchx,y [µm] 280 84 71 16

σbunchz [cm] 10.5 5.4 7.5 7.5

σvertexx,y [µm] 198 59 50 11

σvertexz [cm] 7.4 3.8 5.3 5.3

Luminosity [cm2s−1] ∽ 1027 ∽ 1029 5× 1032 5× 1026

69

Figure 3.12: Scheme adopted for vertex reconstruction with tracks reconstructed in both TPC and ITS (ITS+TPC),

and only in TPC (TPC-only).

is not used, in order to recover the tracks with large displacement from the vertex.

4. Track back-propagation to the outermost layer of the ITS and then to the outermost radius

of the TPC. Extrapolation to the TRD and track finding in the six layers of this detector. Extrapo-

lation to outer detectors for particle identification. Time-of- Flight (TOF), High-Momentum Parti-

cle Identification Detector (HMPID), Photon Spectrometer (PHOS), Electromagnetic Calorimeter

(EMCal). And matching with hits on these detectors.

5. As a last step, reconstructed tracks are re-fitted inward in TRD, TPC, ITS and are propa-

gated to the primary vertex reconstructed by the SPD.

6. At this stage the set of reconstructed tracks is used to determine the primary vertex position

with the optimal resolution. Also a TPC-only primary vertex is reconstructed from the set of

tracks with TPC-only parameters. These vertices will be used in the subsequent physics analyses.

VertexerTracks is used in both cases, with different criteria. The two sets of tracks are finally

propagated to their respective vertex and stored in the ESD, along with the two vertices.

We mentioned the possibility of using the information on the interaction diamond during ver-

tex reconstruction. This is extremely helpful for checking the data quality and physics analysis.

Fig 3.12 gives the scheme map for vertex reconstruction with tracks.

70

Bibliography

[1] http://aliceinfo.cern.ch/.

[2] R.K.Ellis, W.J.Stirling, QCD and collider physics, FERMILAB-Cof-90/164-T (1990).

[3] http://public.web.cern.ch/public/en/science/StandardModel-en.html;

http://en.wikipedia.org/wiki/Standard-Model; arXiv:hep-ph/0609174v1.

[4] http://pcalimonitor.cern.ch/production/raw.jsp.

[5] Gines Martinez, ALICE, the heavy-ion experiment at LHC, ALICE-PUB-2001-32 (2003).

[6] Thomas Bird, An Overview of the ALICE Experiment, School of Physics and Astronomy

University of Southampton Southampton United Kingdom (2010).

[7] The ALICE Inner Tracking System, Technical Design Report, CERN-LHCC 99-12.

[8] G Anelli, F Antinori, A Boccardi, G E Bruno et al. J. Phys. G: Nucl. Part. Phys. 30 (2004)

S1091CS1095.

[9] D. Nouaisa, S. Beolea, M. Bondilab, V. Bonvicinic, P. Cerelloa, E. Crescio et al. Nuclear

Instruments and Methods in Physics Research A 501 (2003) 119-125.

[10] P. Kuijer, Nuclear Instruments and Methods in Physics Research A 447 (2000) 251-256.

[11] The ALICE Time Projection Chamber, Technical Design Report, CERN-LHCC 2000.

[12] Tariq Mahmoud, The ALICE transition radiation detector, Nuclear Instruments and Methods

in Physics Research A 502 (2003) 127C132.

[13] The ALICE Time-Of Flight system, Technical Design Report, CERN-LHCC 2002-016.

[14] ALICE HMPID Technical Design Report,CERN/LHCC/98-19,1998.

71

[15] D C Zhou, J. Phys. G: Nucl. Part. Phys. 34 (2007) S719CS723.

[16] http://aliweb.cern.ch/Offline/AliRoot/Manual.html and http://root.cern.ch/drupal/.

[17] http://aliweb.cern.ch/Offline/Activities/Analysis/index.html.

[18] P.Kuijer, ALICE Internal Note, ALICE-INT-2003-049 (2003).

[19] A. Badal1, R. Barbera, G. Lo Re, A. Palmeri, G. S. Pappalardo, A. Pulvirenti, F. Riggi,

ALICE Internal Note, ALICE-INT-2001-39 (2001).

[20] ALICE Internal Note, ALICE-INT-2003-011 (2003)

[21] ALICE Internal Note, ALICE-INT-2001-11 (2001).

[22] ALICE Internal Note, ALICE-INT-2001-13 (2001).

[23] ALICE Internal Note, ALICE-INT-2003-27 (2003).

[24] N.Bustreo, M.Lambardi, B.S.Nilsen, R.A.Ricci, L.Vannucci, Finding the primary vertex in

the ALICE experiment without tracking.

72

Chapter 4

Vertexing in ALICE: resolution on

impact parameter measurement

The track impact parameter is defined as the distance of closest approach of the particle tra-

jectory to the primary vertex (see Fig.4.1) [1]. It is a crucial variable for the separation of physics

signals from background, especially for the selection of physics signals which are characterized by a

secondary vertex with a small displacement from the primary vertex [2] [3]. This is, in particular,

the case for the detection of particles with open charm and open beauty, namely D0 (cτ ∼= 123µm),

D+ (τ ∼= 315 µm) and B mesons (cτ ∼ 500 µm) [4]. The main requirement applied for the selec-

tion of such particles is the presence of one or more tracks (decay products) which are displaced

from the primary vertex (e.g. for D0 → K−π+ two displaced tracks are required (see Fig 4.1), for

B → e± +X one electron-tagged displaced track is required.)

The track impact parameter is projected in two different directions, along the beam axis and

in the plane transverse to it. One can write:

d0(rϕ) = ρ−√(xV − x0)2 + (yV − y0)2 and d0(z) = ztrack − zV , (4.1)

where ρ and (x0, y0) are the radius and the center of the track projection in the transverse

plane, (xV , yV , zV ) is the coordinate of the primary vertex, and ztrack is the z position of the

track after it has been propagated to the distance of closest approach with respect to the primary

vertex in the transverse plane. The d0 resolution is the convolution of the track position resolution

and of the primary vertex position resolution.

73

π

pointing angle θpointing

secondary vertexprimary vertex

D reconstructed momentum 0

D flight line0

d

d

0

0

K

K

π

impact parameters ~100 mµ

Figure 4.1: Schematic map of impact parameter for D0 → K−π+ products

4.1 The strategy to measure the impact parameter resolu-

tion

As discussed in section 4 of chapter 3, the central detector (ITS and TPC) [5] [6] will provide

the precise measurement for track and vertex position, the ITS being the closest detector to the

primary vertex. The measurement method on impact parameter resolution will be discussed in

following.

4.1.1 Data selection and impact parameter calculation

Two periods of p-p collisions LHC10b, LHC10c, LHC10d and LHC10e, at√s = 7 TeV and one

period of Pb-Pb collisions, LHC10h at√s = 3.5 TeV are analyzed in this chapter. For comparison,

the sample of simulated p-p collisions is also discussed [2] [7].

The events and the tracks must meet the following requirements. The tracks satisfy the standard

TPC track quality cuts (number of TPC clusters > 70, chi2/cluster < 4, |η| < 0.8) and having the

kITSrefit and 2 points in SPD.

The class ALIROOT/PWG1/ITS/AliAnalysisTaskSEImpParRes.cxx [8]collects the main meth-

ods for the calculation of the impact parameter. It considers the impact parameter not only for

different cuts but also for several special selections. It can analyze the ESD events and AOD

events, for P-P and Pb-Pb collisions.

74

Figure 4.2: The impact parameter distribution for primary, secondary, strangeness and charm or beauty particles.

4.1.2 Fit function selection and fit range definition

The final particles mainly come from two different parts [8]. Particles coming from the primary

vertex have an impact parameter distribution with gaussian shape. Particles coming from weak

decay have an exponential distribution of impact parameter, as is the case for particles scattered

from the detector materials, see Fig 4.2 for an example.

The red points are the impact parameter distribution for all particles. The black and green

points are primary particles produce in the initial collision and the secondary particles that come

from decay and detector materials, separately. The blue and yellow points are products decayed

from open charm/beauty and strange particles. The strange particle decays are the main contri-

bution for the secondary particles. Here, the resolution of primary particles is our interest.

It has been checked that the contribution of secondary particles produces almost negligible

effects on the standard deviation obtained by fitting the impact parameter distribution, if the fit

range is ±2 RMS, with RMS obtained by fitting the total impact parameter distribution [10]. This

standard deviation can be considered a good estimate of the impact parameter resolution. However,

in order to better reproduce the contribution of primary tracks and secondary tracks (including

the effect of multiple scattering), the formula below, which is the combination of gaussian with

exponential tail, was taken as the fit function. The fit function is

75

Figure 4.3: An example of the transverse impact parameter distribution in real and Monte Carlo data. The cave is

the fitting result, The detail see in text.

κ · 1√2πσ

· e−(x−µ)2

2·σ2 + (1− κ) · 1

2λ· e−

(x−µ)2

2·λ (0 ≤ κ ≤ 1) (4.2)

Where κ is the fraction of the primary tracks. The fit range was fixed by selecting the minimum

χ2 per unit d.o.f (degree of freedom). Finally, the fit range was fixed on the ≈ 3 RMS, see Fig 4.3.

4.2 Main contribution for the impact parameter resolution

The main contributions to the track impact parameter are the primary vertex resolution, track-

ing resolution and multiple scattering in the detector and beam pipe material. This part will focus

on the primary vertex effects (including the vertex constraint effect), multiple scattering, the PID

and misalignments effect. Other effects will be discussed in the next section.

4.2.1 Primary vertex resolution

The resolution of track impact parameter is the convolution of the resolution of primary vertex

with that of tracks.

In principle, the two beams are centered and their centers should overlap. The interaction

vertex has a “diamond” shape distribution. In the real situation, it is not true. For the Pb-Pb

collisions, beams will be well focused in the transverse plane, and the transverse position of the

76

vertex will be known from the machine monitoring with a resolution of ≃ 10 µm. However,

in the p-p collisions, the two beams are not focused well. The interaction vertex will spread in

large range 150 µm. So, it will worse the impact parameter resolution. Fig 4.4 shows the impact

parameter resolution as function of transverse momentum, the comparison without “diamond”

constraint and with “diamond” constraint. The result with ”diamond” constraint is better than

without “diamond” constraint.

In addition, the primary vertex will be pulled to the track under consideration if it was used

for the primary vertex determination, especially in the high pt region. This “pull” effect can be

negligible for Pb-Pb collisions, because they have a large multiplicities. p-p collisions have quite

limited multiplicities. The “pull” effect should worsen the real impact parameter. To obtain an

unbiased estimate of the impact parameter, the primary vertex position is recalculated track-by-

track skipping the track under consideration from the computation, see Fig 4.5 [11]. The impact

parameter resolution for vertex which exclude the current track is higher than that for vertex which

include the current track, especially at high pt. It is the reason the current “pull” the vertex to

track itself.

Fig 4.6 presents the distribution of impact parameter resolution as a function of pt for MC

and real data. The impact parameter was calculated using the primary vertex without current

track. The result of real data is in agreement with the MC simulation. It means the ALICE

detectors performance well. The obtained curve is the fitting result with the empirical formula,

which describes well the data

σ(d0) = A+B

pcT(4.3)

The resulting parameter (see Fig 4.6) are very close, although there are slight difference in the

whole pt bin. It maybe the misalignment of detectors for real data.

4.2.2 Effects of small-angle multiple scattering on the impact parameter

resolution

The emitted particles with small transverse momenta will be deflected by many small-angle

scatterings (Coulomb scattering) when the particles traverse the beam pipe, detectors and equip-

ments [12] [13]. The thickness of each layer was minimized to the smallest when the detector

was designed and produced. The small-angle scattering still dominates the track momentum and

position resolutions of low momentum (<1 GeV/c). The track impact parameter resolution con-

tributed by the uncertainty of the track fit can be regarded as a sum of spatial precision of tracking

77

[GeV/c]t

p1 10

m]

m d

0_

reso

lutio

n [

0

50

100

150

200

250

300 With diamond constraint

Without diamond constraintALICE performance

13/11/2011

Figure 4.4: Diamond constraint effect on the impact parameter resolution.

[GeV/c]t

p1 10

m]

m d

0_

reso

lutio

n [

0

50

100

150

200

250

300

350

primary vertex without current track

primary vertex with current track ALICE performance

13/11/2011

Figure 4.5: Impact parameter resolution for different vertex.

detectors and multiple scattering. The formula has the following form

σ(dtrack0 ) = σTD

⊕σMS (4.4)

where the σTD which means the spatial precision of tracking detectors is a constant. It can be

explained as the intrinsic resolution of tracking detector and misalignment. The multiple scattering

contribution σMS to the impact parameter resolution can be expressed as:

78

[GeV/c]t

p1 10

m]

m d

0_

reso

lutio

n [

0

50

100

150

200

250

300

ALICE performance

13/11/2011

Data (LHC10c period)

MC,residual misal.

1.07 t

p49.7=26.5+dataf

1.07t

p47.8=24+MCf

Figure 4.6: Comparison of impact parameter resolution of real data with MC data.

σMS =b√

p2 sin3 θ=

b√p2t sin θ

(4.5)

where p is the track momentum, pt its transverse momentum and θ the track polar angle with

respect to z direction (beam direction). Hence, σ(dtrack0 ) can be written as

σ2(dtrack0 ) = σ2TD +

b2

p2t sin θ= σ2

TD +b2

p2 sin3 θ(4.6)

so that, the total track impact parameter resolution is

σ2(d0) = σ2VD(pt) + σ2

TD +b2

p2t sin θ(4.7)

In Fig 4.6 we use the empirical fit function with linear, instead of quadratic, addition of the

pt-dependent and pt-indenpent terms, which describes better the resolution in both data and

simulation, probably due to the misalignment effect that is present in both. Fig 4.7 shows the

impact parameter resolution distribution as function of polar angle at fixed pt (0.5 GeV < pt < 0.6

GeV). The selected tracks have been divided into 10 polar angle bins between 0.25π and 0.5π. The

obtained curve is the fitting result using the function (4.7).

We use the information of Particle Identification (PID) [9] [14] for pion, kaon and proton.

The combined PID information (ESDPID) of ITS, TPC and TOF [15] can provide high-quality of

particle identification. In Fig 4.8, present PDGPID get from MC information and ESDPID result

79

Figure 4.7: Impact parameter resolution distribution as function of polar angle at fixed pt

Figure 4.8: Comparison of the ESDPID and PDGPID result, see text.

as function of pt for MC and real data. With the error range, the result of ESDPID is agreement

with that of PDGPID. The resolution distribution for different kinds of particle have the same

trend which is larger at low pt than at high pt and have clear mass order at low pt. The value of

resolution for protons is the biggest one among three kinds of particle, kaon comes second and it is

the smallest for pion at the same pt. The proton has larger mass, so it will undergo more multiple

scattering when it traverse the beam pipe, detector and support equipment.

80

[GeV/c]t

p1 10

m]

m d

0_

reso

lutio

n [

0

50

100

150

200

250

300 PostiveTrack

NegativeTrack

PostiveField

NegativeField

ALICE performance

13/11/2011

Figure 4.9: Comparison of the positive charged particles and negative charged particles.

4.2.3 Magnetic field and charge effects on the resolution and mean of

impact parameter

The barrel detectors are embedded in a large solenoidal magnet providing a magnetic field < 0.5

T in positive and negative value, and they allow to reconstruct track in the pseudorapidity range

|η| < 0.9. So, the charged tracks will be deflected from their momenta direction. The magnetic

field and charge which carry by charged particles will affect the impact parameter resolution.

Fig 4.9 and Fig 4.10 show the impact parameter resolution and mean distribution as a function

of pt for different magnetic field scenarios. In Fig 4.10, the green and blue points indicate the

positive magnetic field. The red and black point correspond to negative magnetic field. There is

no difference in resolution between different magnetic fields, as well as for the different charged

particles. But the mean value of impact parameter have a larger difference for two different

magnetic fields. This is under investigation and may be related to lorentz angle correction.

Fig 4.11 shows the impact parameter resolution for the tracks reconstructed in the min-bias

Pb-Pb collisions at 2.76 TeV and compared with the Monte Carlo and the p-p results as the

function of pt. For p-p with two different vertexes (vertex with current track marked with blue

cross and vertex without current track marked with blue diamond) and for Pb-Pb collision using

vertex reconstructed with whole tracks. Because of the bias of vertex resolution is small in Pb-Pb

collisions. As we expected the impact parameter resolution for Pb-Pb data is between the p-p data

81

Figure 4.10: Mean value of the transverse impact parameter distribution as a function of pt

[GeV/c]t

p-110 1 10

m]

m re

solu

tion

[f r 0d

0

50

100

150

200

250

300

Pb-Pb Data (2.76 TeV min. bias)

Pb-Pb MC (Hijing min. bias)

pp Data (7 TeV, track incl. in vertex)

pp Data (7 TeV, track excl. from vertex)

ALICE Performance

01/12/2010

Figure 4.11: Transverse impact parameter resolution as the function of pt for the tracks reconstructed in the min-bias

PbPb collisions at 2.76 TeV and compared with the Monte Carlo and the pp results.

two different vertex situations. The track impact parameter resolution of Pb-Pb data signed by red

circle close to Pb-Pb MC sample signed by black triangle. However, there is still some difference.

Maybe, it is the reason of misalignment.

In addition, the impact parameter resolution can provide a tool to check the quality of data, see

Fig 4.12. The resolution distribution of impact parameter as function of run number should nearly

82

run number

1277

15 12

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95

d0_r

esol

utio

n

0

200

400

600

800

1000 0.26<pt<0.27

1.25<pt<1.3

4.1<pt<5.2

Figure 4.12: The impact parameter resolution distribution with run number. Usually, the resolution should be

nearly equal in the same period. If it is far from the mean of the resolution, it can be remove during the special

physics analysis, as the run number labeled with the red circle.

be flat (i. e. should nearly be equal for different runs) in the same run period. This condition

is used as one of the quality assurance parameters for runs, excluding from the analysis the runs

where it is not met.

83

Bibliography

[1] A.Dainese, PhD thesis, Universit‘a degli Studi di Padova (2003), hep-ph/0311004.

[2] A. Dainese, R.Turrisi, ALICE Internal Note, ALICE-INT-2002-05 (2002)

[3] A. Dainese, R.Turrisi, ALICE Internal Note, ALICE-INT-2003-28 (2003).

[4] D.E.Groom et al, The European Physical Journal C (2001) 1.

[5] The ALICE Inner Tracking System, Technical Design Report, CERN-LHCC 99-12.

[6] The ALICE Time Projection Chamber, Technical Design Report, CERN-LHCC 2000-001.

[7] http://pcalimonitor.cern.ch/production/raw.jsp.

[8] http://alisoft.cern.ch/viewvc/.

[9] ALICE: Physics Performance Report, Volume I and II.

[10] ALICE Internal Note,Performance of the track impact parameter resolution in

ALICE,ALICE-INT-2011 in preparation (2011).

[11] A. Dainese, M.Masera, ALICE Internal Note, ALICE-INT-2003-27 (2003).

[12] Particle physics booklet:http://pdg.lbl.gov/ or http://www.cern.ch.library.

[13] G.Borisov and C.Mariotti, Nuclear Instruments and Methods in Physics Research A 372

(1996) 181-187.

[14] N Carrer, A Dainese and R Turrisi, J. Phys. G: Nucl. Part. Phys. 29 (2003) 575C593.

[15] The ALICE Time-Of Flight system, Technical Design Report, CERN-LHCC 2002-016.

84

Chapter 5

Measurement of the cross section

for D0 production in pp collision

at√s = 7 TeV

The measurement of the cross-section for charm production in p-p collisions is not only a

fundamental reference to investigate medium properties in heavy-ion collisions, but a key test of

pQCD predictions in a new energy domain as well. It is an important task in ALICE to measure

charm production via the exclusive reconstruction of selected D meson decay channels at central

rapidity.

In this chapter, the analysis procedure and the final D0 cross-section for the D0 → K−π+

channel are presented. First, the analysis strategy is recalled. Then, the detailed steps of analysis

are given according to the analysis strategy. Finally, the conclusion of analysis is presented in the

last section.

5.1 Strategy for D0 cross-section measurement

The measurement strategy is based on an invariant mass analysis of those combinational can-

didates of reconstructed tracks that can represent a D0 meson decayed at a secondary vertex

displaced from the primary vertex of interaction. The cross section is calculated from the raw

85

signal yield extracted with the invariant mass analysis, N reco.sel. (pt), using the following formula:

d2σD0

(pt, y)

dydpt

∣∣∣∣∣y<0.5

≈ 1

2

1

2 ymax

fD ·N reco.sel. (pt)||y|<ymax

ϵ · BR · LINT=

1

2

1

2 ymax

fD ·N reco.sel. (pt)||y|<ymax

ϵ · BR ·NppMB

σppMB ,

(5.1)

with ymax ≃ 0.5, possibly dependent on pt. The different terms in the above formula are described

in the following along with the analysis steps.

Raw signal extraction

In pp collisions, if all the possible pairs are considered as “candidate” D0, the signal over com-

binatorial background ratio is ∼ 10−4. It is then mandatory to preselect the reconstructed tracks

and candidates on the basis of the typical kinematical and geometrical properties characterizing

the signal tracks and reconstructed vertices. The D0 decays weakly with a relatively large proper

decay length (cτ ≈ 123 µm). To tag secondary tracks which are displaced by only a few tens of

microns from the primary vertex, a very precise reconstruction of the primary vertex and track

position extrapolation is mandatory and it is provided by the ITS detectors [1]. The transverse

impact parameter (d0), defined as the distance between the projection of a track in the plane trans-

verse to the beam direction and the primary vertex of interaction, is used to identify displaced

tracks. The possibility to resolve the D0 decay vertices and the primary vertex is the key element

to select signal candidates among the huge number of combinatorial background candidates. The

geometrical variables used for the signal selection are described in Section 5.2. Besides topological

cuts, particle identification information, in particular for the charged kaon, is used to improve the

background rejection [1] [2]. The resulting invariant mass distribution is fit to extract the raw

signal yield N reco.sel. , the detail see in Section 5.2.

Efficiency corrections for detector acceptance and cut selection (ϵ)

In order to evaluate the total number of D0 mesons effectively produced and decayed in the

D0 → K−π+ channel, (ND0→K−π+

tot ) the raw signal yield is divided by an efficiency correction factor

ϵ that accounts for selection cuts, for PID efficiency, for track and primary vertex reconstruction

efficiency, and for the detector acceptance. The procedure and the tools used to compute the

efficiency corrections is the subject of section 5.4.

86

Correction for feed–down from B mesons with MC and data-driven methods

At LHC energies, a relevant fraction of D0 mesons comes from the decay of a B meson. On

average, the reconstructed tracks coming from “secondary” D0 are well displaced from the primary

vertex, because of the relatively long B lifetime (cτ ≃ 460-490 µm) [3]. Thus, the selection further

enhances their contribution to the raw signal yield (up to 15%) and it is important to subtract

this fraction. To determine its amount different methods are available and will be detailed in the

following. The best way is to extract it directly from data exploiting the different shapes of the

impact parameter distribution of secondary D0, but this requires large statistics. Alternatively, or

as a cross check it is possible to rely on Monte Carlo estimates based on pQCD calculations, but

this can add a bias to the measurement, or on the measurement of beauty production at the LHC.

Cross section normalization

The raw yield, corrected for the efficiency, is divided by the decay channel branching ratio

(BR(D0 → K−π+) = 3.80 ± 0.09%) [3] to get the total number of produced D0 mesons ND0

tot .

The latter number is divided by the integrated luminosity LINT to obtain the cross section for

D0 meson production. A factor 1/2 must be considered because both D0 and D0 mesons are

reconstructed and a factor 1/(2 ymax) because the measurement is performed in the rapidity range

−ymax < y < +ymax.

5.2 Reconstruction of D0 → K−π+ channel

As shown in Fig 4.1, a typical signature of the D0 → K−π+ decay channel is the presence of two

tracks with opposite charges and with an impact parameter not compatible with zero. For each

pair of tracks a secondary vertex is defined as their point of closest approach. The implementation

and the performance of the vertex finding algorithm are described in detail in Ref [4].

In this section, the cut variables and the particle identification will be applied for background

rejection and improving the ration of signal-to-background.

5.2.1 Cut variable selection

Two kinds of variables are used to enhance the signal-to-background ratio [5] [6]: single track

variables and pair variables. The firsts, related to single track properties, are the impact parameter

and the transverse momentum. A cut on the minimum impact parameter could reduce the number

87

of primary tracks coming from the primary vertex of interaction. However, especially at low pt,

the impact parameter of particles coming from D0 decays is determined mainly by the detector

resolution rather than by the D0 lifetime. Conversely, a cut on the maximum impact parameter can

reject tracks coming from decays of particles with long lifetime, as strange and bottom hadrons, or

produced by the interaction of primary particles with the detector material. Most of the background

are low pt primary tracks and a cut on the minimum transverse momentum rejects a fraction of

them. In the following, the pair-variables used to enhance the signal-to-background ratio are

described.

5.2.1.1 Distance of closest approach between kaon and pion tracks

The distance of closest approach (dca) between the two tracks is the length of the segment

minimizing the distance between the two track helices. For tracks coming from a common point, like

a decay vertex or the primary vertex of interaction (ideal dca=0), the observed dca is determined

by the detector spatial resolution on the track position. In Fig 5.1 (left panel) the dca distributions

for background and signal pairs are shown. Most of the background is made of primary track pairs:

their dca distribution is strongly correlated to the impact parameter resolution, thus to the tracks

transverse momenta. On average, tracks coming from the decay of a D0 meson are reconstructed

with a higher spatial precision because of the higher average transverse momentum. With a cut

on the minimum transverse momentum, background pairs made of primary tracks with relatively

high momentum are selected and the background dca distribution is similar to the signal one.

Therefore, the dca is effective in rejecting background pairs only if a cut on the minimum impact

parameter is applied. In this way background pairs including a secondary track are rejected.

5.2.1.2 Cosine of the decay angle

In the D0 reference system the pion and the kaon are emitted isotropically with three-momenta

p⋆ of equal magnitude p⋆ and opposite direction. The decay angle in the c.m.s. θ⋆ is defined as the

angle between the kaon momentum and the D0 flight line, which is also taken as the boost direction.

For each candidate two values are calculated, one per each mass hypothesis (the D0 [D0] hypothesis

forces the negative (positive) track to be interpreted as the kaon). As it is shown in Fig 5.1 (right

panel), due to the isotropic production in the c.m.s., the cosθ⋆ distribution for signal pairs is almost

flat. Conversely, the background distribution peaks close to ±1. The depletion at cosθ⋆ is related

to the cuts applied in the candidate reconstruction (pt > 0.3 GeV/c and cosθpoint > 0 ) and to

88

dca [cm]0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

0

0.005

0.01

0.015

0.02

0.025

MC info

Signal

Background

*qcos-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0.002

0.004

0.006

0.008

0.01

0.012

Figure 5.1: Distance of closest approach (dca, left panel) and cosθ⋆ (right panel) and distributions for background

(black circles) and signal (red triangles) candidates. The different error bar sizes are due to the smaller number of

signal than background candidates. The variables are defined and described in the text.

detector effects: if the particles are emitted parallel to the D0 momentum, one of the two is boosted

at very low momenta and can go out of the geometrical acceptance.

5.2.1.3 Cosine of the pointing angle cosθpoint

The pointing angle, already defined as the angle between the D0 flight line and the total

momentum of the two daughter tracks. For background pairs there is no correlation between the

momentum direction and the reconstructed flight line, because most of the pairs are composed of

primary tracks and the secondary vertex position is determined only by the finite spatial tracking

resolution. For any flight line associated to a background pair the possible total three-momentum

is distributed isotropically. This implies that the distribution of the cosine of the polar angle with

respect to the flight line (that is, the cosine of the pointing angle) is flat. Conversely, for a signal

pair the flight line direction is effectively determined by the D0 threemomentum direction and the

cosine of the pointing angle distribution is expected to peak at 1. The distributions of cosθpoint

for the signal and background are shown in Fig 5.2 (left panel).

5.2.1.4 Product of track impact parameters

The typical impact parameters for a pion and a kaon track coming from a D0 decay is of

the order of ∼ 100 µm (chapter 4) and have opposite signs due to the opposite charge. Ideally,

their product would be negative. Due to detector resolution the observed distribution (Fig 5.2,

89

Pointqcos0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07 MC info

Signal

Background

]2 [cm0

d´0

d-0.001 -0.0008 -0.0006 -0.0004 -0.0002 0 0.0002 0.0004 0.0006 0.0008 0.001

-410

-310

-210

-110

MC info

Signal

Background

Figure 5.2: Product of daughter impact parameters (dK0 ×dπ0 , right panel) and cosθpoint distributions for background

(black circles) and signal (red triangles) candidates. The different error bar sizes are due to the smaller number of

signal than background candidates. A cut cosθpoint > 0 was applied already at the level of candidates reconstruction:

the background distribution shape is almost at in the entire range [3]. The variables are defined and described in

the text.

dca [cm]0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

]-1

Ent

ries/

0.00

2 [c

m

0

10

20

30

40

50

60

ALICE performance

4/05/2011

Pythia Perugia-0

data LHC10c

<5 GeV/ct

3<p

(strangeness increased, based on data)

= 7TeVs p-p @ +p- K®0D

only single track cuts

*qcos-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Ent

ries/

0.01

-310

-210

-110

1

PW

G3-

D2H

-019

Figure 5.3: Distance of closest approach dca (top left), cosθ⋆ (top right) distributions for MC background (red) and

data (blue) candidates.

right panel) shows both positive and negative values but it is strongly asymmetric with respect to

zero. For background pairs, composed mainly of randomly associated primary tracks with opposite

charges, the distribution is symmetric.

90

pointingqcos0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

Ent

ries/

0.01

0

0

2

4

6

8

10

12

14

ALICE performance

4/05/2011

Pythia Perugia-0

data LHC10c

<5 GeV/ct

3<p

(strangeness increased, based on data)

= 7TeVs p-p @ +p- K®0D

only single track cuts

]2 [cmp0d´

0Kd

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

-310´

]-2

[cm

-3 1

0´

Ent

ries/

0.00

4

1

10

210

310

410

PW

G3-

D2H

-019

Figure 5.4: Cosθpoint (left) and product of impact parameters dK0 × dπ0 (right) distributions for MC background

(red) and data (blue) candidates.

In Fig 5.3 and 5.4 the same cut variables are shown for data and MC (background), in order

to check the agreement between data and simulation.

5.2.2 Definition of the cut variable values

The values of the variables used as cuts are chosen in order to reject as much background

as possible without losing too much signal. The adopted criterion is to maximize the statistical

significance, defined as:

S =S√

S + B=

√S√

1 + 1r

(5.2)

with S and B the signal and background candidates after cuts and r = S/B the signal-to-background

ratio, which depends on the effectiveness of the cuts. The significance quantifies how much the

signal emerges above the fluctuations of the background.

The value used in this analysis are shown in Table 5.1. The choice of the best cut value has

been made according to the higher significance and/or signal over background ratio preferring as

loose cut as possible. The cut values are modulated as a function of the transverse momentum

of the candidate to follow the corresponding pt-dependence of the resolutions on this variables for

our signal.

91

d0d0 [cm^2]

-0.6-0.5

-0.4-0.3

-0.2-0.1

-310´cosThetaPoint

0.70.75

0.80.85

0.90.95

12

12.5

13

13.5

14

14.5

15

Significance wrt d0d0 [cm^2] vs cosThetaPoint (Ptbin4 3.0<pt<4.0)

Figure 5.5: Significance trend in the two-dimensional space (cosθpointing, dK0 × dπ

0 ) in the range 3 < ptD0< 4

GeV/c.

The two most “powerful” cut variables are the cosine of the pointing angle and the product of

the impact parameters. In Fig 5.5 a projection of the significance trend in the two-dimensional

space (dK0 × dπ0 ; cosθpointing) is shown. The high correlation between the two variables for signal

candidates results in a very efficient rejection of background pairs. The cuts optimization is done

using an automatic procedure working both on MC and data. In the former case S and B are

determined from the MC information, while in the latter case S and B are estimated from the fit

of the invariant mass distribution [6].

5.2.3 Particle identification strategy

Kaons and pions are identified via the energy loss deposit in the Time Projection Chamber

and the velocity measurements in the Time Of Flight (see chapter 3). The two detectors are

complementary, since they can well separate kaons and pions from all the other particle species

in different momentum ranges. For both detectors, a track can be identified in units of resolution

of the difference between the measured and expected signals (nσ cut). The particle identification

strategy described below was aimed to identify the single tracks as kaons and pions, reducing the

combinatorial background and without any loss of signal. In particular, in the TPC (see chapter

3), a 2σ cut was applied to identify both pions and kaons. In addition, if the track dE/dx signal

92

was between 2 and 3σ from the expected value, it was kept as non-identified and both the kaon

and pion mass hypothesis were assigned to it. In the momentum range 0.6 < p < 0.8 GeV/c, where

the pion and kaon expectation become closer, the selection applied went down to 1σ. In the whole

momentum range, if a track had an energy loss that differs more than 3σ from the kaon [pion]

curve, it was discarded as kaon [pion]. For the TOF signal, when present, a 3σ cut was applied to

select the kaons. The tracks with momentum p > 1.5 GeV/c, where the kaon and pion signal bands

start to overlap, were considered as non-identified. In order to identify pions, only the information

coming from the TPC was used, while the mass of the kaon was assigned to a track identified as

kaon by at least one of the two detectors. In case TOF and TPC were in contradiction, the track

were kept as non-identified. Both the kaon and pion mass were assigned to all the non-identified

tracks. Two-prong candidates were accepted (as D0, D0 , or both) or rejected, according to the

compatibility with the K∓π± state. The comparison of the invariant mass distributions obtained

without and with particle identification selection showed that this selection reduced by a factor

2-3 the combinatorial background in the low pt region, while preserving close to 100% of the D

meson signal.

Table 5.1: Selection cuts used in the present analysis.

pt bin [GeV/c] pK,πt [GeV/c] |dK,π

0 | [cm] dca [cm] cos θ∗ dK0 × dπ0 [cm2] cos θpointing

0 < pt < 1 > 0.3 < 0.1 < 0.03 < 0.8 < −0.00035 > 0.73

1 < pt < 2 > 0.5 < 0.1 < 0.02 < 0.8 < −0.00025 > 0.73

2 < pt < 3 > 0.5 < 0.1 < 0.02 < 0.8 < −0.00008 > 0.8

3 < pt < 4 > 0.7 < 0.1 < 0.02 < 0.8 < −0.00008 > 0.85

4 < pt < 5 > 0.7 < 0.1 < 0.02 < 0.8 < −0.00008 > 0.85

5 < pt < 6 > 0.7 < 0.1 < 0.0015 < 0.8 < −0.00008 > 0.85

6 < pt < 8 > 0.7 < 0.1 < 0.0015 < 0.8 < −0.00008 > 0.85

8 < pt < 12 > 0.7 < 0.1 < 0.0015 < 0.8 < −0.00005 > 0.85

all pt |d0/δd0 | > 0.5 decl/δdecl > 1 decl > Min(pt × 0.0066 + 0.01, 0.06[cm])

93

]2) [GeV/cpInvariant Mass (K1.75 1.8 1.85 1.9 1.95 2 2.05

2E

ntrie

s / 1

0 M

eV/c

0

100

200

300

400

500

600

0.002±Mean = 1.865

0.002±Sigma = 0.008

1.0 ±) 4.6 sSignificance (3 43 ±) 207 sS (3 22±) 1806 sB (3

ALICE Performance24/09/2010

events 810´ = 7 TeV, 1.1spp

+p- K®0D

< 2 GeV/c0D

t1 < p

]2) [GeV/cpInvariant Mass (K1.75 1.8 1.85 1.9 1.95 2 2.05

2E

ntrie

s / 1

0 M

eV/c

0

50

100

150

200

250

300

350

400

0.002±Mean = 1.866

0.001±Sigma = 0.009

1.0 ±) 6.8 sSignificance (3

37 ±) 261 sS (3 19±) 1215 sB (3

< 3 GeV/c0

D

t 2 < p

]2) [GeV/cpInvariant Mass (K1.75 1.8 1.85 1.9 1.95 2 2.05

2E

ntrie

s / 1

0 M

eV/c

0

50

100

150

200

250

300

350

400

0.001±Mean = 1.868

0.002±Sigma = 0.013

1.1 ±) 9.8 sSignificance (3 48 ±) 446 sS (3 26±) 1619 sB (3

< 4 GeV/c0D

t 3 < p

]2) [GeV/cpInvariant Mass (K

1.75 1.8 1.85 1.9 1.95 2 2.05

2E

ntrie

s / 1

0 M

eV/c

0

20

40

60

80

100

120

140

0.002±Mean = 1.870 0.002±Sigma = 0.016

1.1 ±) 7.9 sSignificance (3 29 ±) 220 sS (3 17±) 560 sB (3

< 5 GeV/c0D

t 4 < p

]2) [GeV/cpInvariant Mass (K1.75 1.8 1.85 1.9 1.95 2 2.05

2E

ntrie

s / 1

0 M

eV/c

0

10

20

30

40

50

60

70

80

90

0.002±Mean = 1.867 0.002±Sigma = 0.018

1.1 ±) 8.7 sSignificance (3 21 ±) 179 sS (3 12±) 244 sB (3

< 6 GeV/c0

D

t5 < p

]2) [GeV/cpInvariant Mass (K1.75 1.8 1.85 1.9 1.95 2 2.05

2E

ntrie

s / 1

0 M

eV/c

0

5

10

15

20

25

30

35

40

0.004±Mean = 1.864 0.005±Sigma = 0.028

1.3 ±) 8.0 sSignificance (3 20 ±) 129 sS (3 11±) 131 sB (3

< 12 GeV/c0

D

t8 < p

]2) [GeV/cpInvariant Mass (K

1.75 1.8 1.85 1.9 1.95 2 2.05

2E

ntrie

s / 1

0 M

eV/c

0

10

20

30

40

50

60

70

0.002±Mean = 1.867 0.002±Sigma = 0.018

1.1 ±) 8.9 sSignificance (3 18 ±) 160 sS (3 10±) 161 sB (3

< 8 GeV/c0

D

t 6 < p

PW

G3-

D2H

-021

Figure 5.6: Invariant mass distributions for ∼ 1.1× 108 minimum bias events with exponential + Gaussian fit.

5.3 Raw signal yield extraction

In this Sections the raw yield extraction results on p-p data will be shown. The fit function

used to reproduce the invariant mass distributions is the sum of a Gaussian for the D0 peak and an

exponential or second order polynomial for the background. The fit is performed in two steps, the

first gives a rough estimation of the background function parameters using the side bands, while

the second include also the signal range and gives the final estimation of all parameters [6]. The

amount of signal and background is then extracted by subtraction of the background fit (in red in

the pictures) from the total fit (in blue) or by counting the excess of entries in the histogram with

respect to the background function.

Fig 5.6 shows the invariant mass distributions for the p-p minimum bias sample (∼ 100× 106

events in the periods LHC10b and LHC10c) in seven bins of pt and Fig 5.7 the invariant mass

for pt > 2 GeV/c after applying the cuts listed in Table 5.1. The distributions are fitted with

a Gaussian + exponential function. The raw yields of signal and background together with the

significance and the S/B ratio are summarized in Table 5.2 in a 3σ range, where σ is the width of

the Gaussian extracted from the fit itself and varies with the pt as shown in Fig 5.8. In Fig 5.9

the differential raw yield in five pt bins is compared to the FONLL calculation scaled to the data

and its shape is in agreement with them.

94

]2) [GeV/cpInvariant Mass (K1.75 1.8 1.85 1.9 1.95 2 2.05

2E

ntrie

s / 1

0 M

eV/c

0

200

400

600

800

1000

0.001±Mean = 1.867

0.001±Sigma = 0.014 1.2 ±) 21.3 sSignificance (2

82 ±) 1486 sS (2

32±) 3380 sB (2

ALICE Performance

13/07/2010

> 2 GeV/c0D

t events, p810´ = 7 TeV, 1.4spp

PW

G3−

D2H

−011

+p− K®0D

PW

G3−

D2H

−011

Figure 5.7: pt > 2 GeV/c invariant mass spectra.

[GeV/c]t

p0 2 4 6 8 10 12 14 16 18

]2 [M

eV/c

s in

varia

nt m

ass

0 D

0

10

20

30

40

50

ALICE Performance

28/09/2010PW

G3-D

2H-0

24

+p- K®0D

PWG3

-D2H

-024

MC (LHC10d3)

Data: LHC10cb (111M events)

Figure 5.8: Sigma of the Gaussian fit of the invariant mass distributions in 5 for ∼ 1.1× 108 minimum bias events

as a function of pt

5.4 Correction for efficiency

95

[GeV/c]t

p0 2 4 6 8 10 12 14

[a

rb. u

nits

]|y

|<0.

5|

tdp

0D

dN

+p- K® 0D

= 7 TeVspp,

min. bias events810

stat. errors only

Calculation: FONLLscaled to integral of data

ALICE Preliminary

PWG

3-Pr

elim

inar

y-01

2

Figure 5.9: D0 → K−π+ yield as a function of the transverse momentum for 108 minimum bias events.

Table 5.2: Yield of Signal and Background and significance from fit in the 1.1 × 108 events minimum bias sample

for seven pt bins. The considered invariant mass range is of 3σ where σ is reported in Fig 5.8 as a function of pt.

pt bin [GeV/c] Sfit BfitS√S+B

in 3σ

1 < pT<2 207± 43 1806± 22 4.6± 1.0

2 < pT<3 261± 37 1215± 19 6.8± 1.1

3 < pT<4 446± 48 1619± 26 < 9.8± 1.1

4 < pT<5 220± 29 560± 17 7.9± 1.1

5 < pT<6 179± 21 244± 12 8.7± 1.1

6 < pT<8 160± 18 161± 10 8.9± 1.1

8 < pT<12 129± 20 131± 11 8.0± 1.3

Fig 5.10 shows the efficiencies calculated with the correction framework for D0 → K−π+ with

all the decay particles in the acceptance |η| < 0.9, the data collection LHC10d. At low pt, the

selection cuts are tighter and the efficiencies are of order 10−3, while for increasing pt the efficiencies

increase and flatten at about 0.1. The efficiency without particle identification selection, shown

for comparison, are the same as those with particle identification for pt > 2 GeV/c, indicating

that this selection is essentially fully efficient for the signal. The efficiencies for D mesons from B

96

Figure 5.10: Efficiencies for D0 as a function of pt (see text for details).

meson decay, also shown for comparison, are larger by a factor about 2, because this feed-down

component is more displaced from primary vertex, due to the large B life time.

5.5 Correction for B feed-down

In order to estimate the number of produced D0 mesons, it is necessary to correct the yield

obtained with the fitting procedure with the efficiency obtained from the correction framework.

Since it provides the efficiencies for primary D0 mesons (from c quark fragmentation) and the raw

yield from the fit includes both primary and secondary (from B meson decays) D0 mesons, an

estimation of the fraction of the feed-down from B is necessary, before applying the corrections.

The best way to estimate the fraction of secondary D0 is relying only on data, but so far the

statistics analyzed is not enough to exploit the method of the impact parameter described in [4]

so, for the time being the theoretical predictions for the beauty production cross section at LHC

have been used. The FONLL prediction has been used following two approaches described in the

following in order to correct the raw yield and to estimate a systematic error on the feed-down

subtraction.

97

[GeV]T

p0 5 10 15 20 25 30

[

pb

/GeV

]|y

|<0.5

|T

dps

d

210

310

410

510

610

710

810

Cacciari-Frixione-Mangano-Nason-Ridolfi collaboration = 7 TeVNNs in p+p collisions at 0D

0D 0 D®B

[GeV]T

p0 5 10 15 20 25 30

(D

))

s d

´ D

)) /

(B

R

® (

B

s d

´1

/ (

1+

R)

wh

ere

R

=

( B

R

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Cacciari-Frixione-Mangano-Nason-Ridolfi collaboration

= 7 TeVNN

s in p+p collisions at +p - K® 0D

Figure 5.11: FONLL calculation of the primary and secondary D0 cross-sections in proton proton collisions at 7

TeV for |η| < 0.5 (left). The relative contribution of secondary D0 is represented in right panel by the relative ratio

1/(1 +σpriminary

σsecondary).

5.5.1 Evaluation of the feed-down contribution with FONLL

The FONLL calculation of the primary and secondary D0 cross-sections in proton proton col-

lisions at 7 TeV for |y | < 0.5 are depicted in Fig 5.11 (left panel). The relative contribution

of secondary D0 to the total D0 cross-section is shown in Fig 5.12 (right panel) represented by

the relative ratio 1/(1 +σpriminary

σsecondary). Here, one consider these FONLL predictions to evaluate the

contribution of secondary D0 in our measurement with two different approaches.

5.5.1.1 Nb method: subtract the FONLL feed-down prediction

The first method relies on the FONLL calculation of the secondary D0 cross-section. It consists

in subtracting from the D0 raw yield the expected secondary raw yield evaluated as the FONLL

cross-section corrected by the acceptance, reconstruction and analysis cuts efficiency and normal-

ized to the analyzed integrated luminosity. The mathematical formulation is quoted in Eq 5.3. The

upper and lower uncertainties of the FONLL calculation are considered to evaluate the feed-down

subtraction uncertainties, that in this case are at most +7% and −10%.

98

d2σc→D

dydpt=

1

L × ϵtrigger × BRc ×∆y× 1

(Acc × ϵ)c→D× (

d2N rawD

dydpt− d2Nraw

B→D

dydpt)

=1

L × ϵtrigger × BRc ×∆y× 1

(Acc × ϵ)c→D× (5.3)

[d2N raw

D

dydpt− (L × ϵtrigger × BRb ×∆y × (Acc × ϵ)B→D)× d2σFONLL

B→D

dydpt]

5.5.1.2 fc method: consider the FONLL primary / secondary calculation

The second method trusts the ratio primary over secondary D0 given by the FONLL calculation.

It depends on the primary and secondary pt distributions and on the ratio of their cross-sections,

but does not rely on their absolute normalization. Here the feed-down contribution is evaluated

estimating the relative primary/secondary D0 raw yields considering the FONLL cross-sections

corrected by the acceptance, reconstruction and analysis cuts efficiency as described in Eq 5.5.

The measured raw yield is then multiplied by this corrective factor to obtain the primary D0

cross-section, see Eq 5.4. The FONLL uncertainties are propagated to evaluate the uncertainty on

the feed-down subtraction considering that primary and secondary estimates are correlated and

that the calculation of the upper (lower) primary contribution corresponds to the upper (lower)

secondary contribution. They are at most +6% and −21%.

d2σc→D

dydpt=

1

L × ϵtrigger × BRc ×∆y× 1

(Acc × ϵ)c→D× d2N raw

D

dydpt× fc(y , pt) (5.4)

fc(y , pt) = 1/(1 +(Acc × ϵ)B→D

(Acc × ϵ)c→D×

d2σFONLLB→D

dydpt

d2σFONLLc→D

dydpt

) (5.5)

5.5.2 Fraction of secondary D0

As the results of the Nb and fc methods differ slightly, see Fig 5.11, one combine them. Since the

FONLL B meson calculations seem to have a better agreement with the existent data measurements

at different energies and rapidities. We consider that the central value of our calculation is the

one given by the Nb method, and the feed-down subtraction uncertainties are defined by the

envelope of the Nb and fc feed-down uncertainties. The procedure is illustrated in Fig 5.11, and

the uncertainties are at most +7% and −24%.

99

[GeV/c]t

p2 3 4 5 6 7 8 9 10 11 12

Rel

ativ

e E

rror

-0.4

-0.2

0

0.2

0.4Total (excl. norm.)Normalization (10%)Feed-down from BTracking efficiencyBranching ratioYield extractionCuts efficiencyPID efficiency

shapet

MC p

DD =

+p - K® 0D-1 = 7 TeV, 1.4 nbspp,

ALICE Performance30/11/2010

Figure 5.12: Systematic errors summary plot.

5.6 Normalization of the corrected spectrum

The raw yield, corrected for the efficiency, is divided by the decay channel branching ratio

(BR(D0 → K−π+) = 3.80 ± 0.09%) to get the total number of produced D0 mesons ND0

tot . The

latter number is divided by the integrated luminosity LINT to obtain the cross section for D0 meson

production. A factor 1/2 must be considered because both D0 and D0 mesons are reconstructed

and a factor 1/(2 ymax) because the measurement is performed in the rapidity range −ymax < y <

+ymax.

5.7 Analysis of statistical and systematic errors

Several sources of systematic uncertainties were considered, namely those affecting the signal

extraction from the invariant mass spectra and all the correction factors applied to obtain the

pt-differential cross sections. A summary of the estimated relative systematic errors is given in

Table 5.3 and Fig 5.12.

The systematic uncertainty on the yield extraction from the invariant mass spectra was deter-

mined by repeating the fit, in each pt interval, in a different mass range, with a different function

(a polynomial) to describe the background and a method based on bin counting. In particular the

latter estimates the signal counting the entries of the invariant mass histograms after the subtrac-

100

Figure 5.13: Different methods for signal extraction.

Figure 5.14: Check on the effect of cut variation.

tion of the background fit. The result is shown in Fig 5.13 where the two series of points are the

signal extracted with two estimation of the background, the gray is using the fit of the side bands

and the red the final background fit.

This gives a systematic error of 15% at 2 < pt < 3 GeV/c and about 5− 6% at higher pt. The

101

Figure 5.15: Check on the effect of PID efficiency on data and MC.

systematic error on the tracking efficiency (including the effect of the track selection) amounts to

2%. A systematic effect can arise due to different features in data and simulation for the variables

used to select the signal D meson candidates. The distributions of these variables were compared

for candidates passing loose topological cuts, i.e. essentially for background candidates, and found

to be well described in the simulation. Some of them were shown in section 5.3. The systematic

effect due to residual differences between data and simulation was quantified by repeating the

analysis with different sets of cuts as reported in Fig 5.14. From the corresponding variation of the

corrected spectra a systematic error was estimated as a function of pt. The systematic error induced

by a different efficiency of the particle identification selection in data and simulation was evaluated

by repeating the analysis without applying this selection or with stricter (2 σ compatibility instead

of 3 σ) selection, see Fig 5.15. Furthermore, the pt-differential yields of particles and anti-particles

were extracted separately and their relative difference was assigned as a systematic error according

to Fig 5.16.

The correct description of the evolution of the experimental conditions with time was verified

by analyzing separately sub-samples of data collected with different detector configuration and

also different orientation of the magnetic field. The results were found to be compatible within

statistical errors. The effect of the shape of the simulated D mesons spectrum within our pt

intervals was estimated from the relative difference in the Monte Carlo efficiencies obtained with

102

[GeV/c]t

p2 3 4 5 6 7 8 9 10 11 12

D0/D

0b

ar

raw

yiled

rati

o

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Figure 5.16: D0/D0 raw yield ratio.

Figure 5.17: Check on the effect of a different pt distribution shape: the efficiencies from prompt D0 from PYTHIA

and FONLL as a function of pt and their ratio are shown

the pt shapes from PYTHIA [7] with Perugia-0 [8] tune and from the FONLL pQCD calculation

and it is shown in Fig 5.17. These two models predict a significantly different slope at high pt,

which however results in a systematic effect on the D meson selection efficiency below 6%.

103

The contribution of D mesons from B decays was evaluated relying on the FONLL prediction,

which describes well bottom production at the Tevatron [9] and at the LHC [10] [11]. In each

pt interval, the theoretical cross section for secondary D mesons, multiplied by the ratio of the

efficiencies of secondary and prompt D mesons, was subtracted from the cross section recovered

using Eq 5.1 with fprompt = 1. The systematic error from this correction was estimated to be at the

level of 10%, from the spread of the results recovered using the minimum and maximum predictions

for secondary D production that were obtained by varying the factorization and re-normalization

scales in the range should specify the range and the b quark mass in the range should specify the

range. The uncertainty on the ratio of the efficiencies yielded a negligible contribution. The cross

section for prompt D production obtained with this method agrees within errors.

Finally, the systematic error on the branching ratios [12] and the 7% uncertainty on the

minimum-bias p-p cross section were considered. The integrated luminosity was computed as

Lint = Npp,MB/σpp,MB , where Npp,MB and σpp,MB are the number and the cross section of p-

p collisions passing the minimum-bias trigger condition. The σpp,MB value, 62.3 ± 0.4(stat) ±

4.3(syst)mb, was obtained relative to the cross section of collisions that give signals in both sides

of the VZERO scintillator detector(σV ZERO−AND), measured with the van der Meer technique [13].

The relative factor, σpp,V ZERO−AND/σpp,MB ≈ 0.87, was found to be stable within 1% over the

analyzed data sample as shown in Fig 5.18.

Table 5.3: Summary of relative systematic errors for D0 cross section. The systematic error from B feed-down varies

in pt.

Low pt High pt

Yield extraction 15% 6.5%

Tracking efficiency 2% 3%

Cut efficiency 10% 10%

PID efficiency 10% 3%

MC pt shape 1.8% 6%

Particle/Antiparticle 8% 8%

Feed-down from B −25%+5%

Branching ration 1.3%

Normalization 7%

104

Figure 5.18: Ratio of events with a signal in both V0 detectors over the events triggered as CINT1B as function of

run number.

5.8 Comparison with pQCD prediction

The pt-differential cross sections for prompt D0, obtained from the yields extracted by fitting

the invariant mass spectra and corrected with the procedure described in this thesis, is shown

in Fig 5.19. The error bars represent the statistical error, while the systematic errors, described

in section 5.7, are plotted as rectangle areas around the data points. The numerical values are

reported in Table 5.4 together with their statistical and systematic uncertainties. The measured D

meson production cross sections are compared to two theoretical predictions, namely FONLL and

GM-VFNS [14]. Our measurement of D0 at LHC energies are reproduced by both models within

their theoretical uncertainties. The central value of the FONLL predictions lies systematically,

as a function of pt, below the measurements. This feature was observed also at√s = 0.2 TeV

(p-p) [16] [17] [18]and 1.96 TeV [19].

105

GeV/c t

p0 2 4 6 8 10 12 14

b/G

eV/c

m

|y|<

0.5

| t /

dpsd

-110

1

10

210

310+p - K® 0D

-1 = 7 TeV, 1.6 nbspp,

PWG

3-Pr

elim

inar

y-02

4

= 62.3 mbMB

s

7% global norm. unc. (not shown)±

ALICE Preliminary

stat. unc.

syst. unc.

FONLL

GM-VFNS

Figure 5.19: pt-differential cross section for prompt D0 in pp collisions at√S = 7TeV compared with FONLL and

GM-VFNS theoretical predictions.

Table 5.4: Production cross section in |y | < 0.5 for prompt D0 in pp collisions at√S = 7 TeV, in transverse

momentum intervals. The normalization systematic error of 7% is not included in the systematic errors reported in

the table.

pt interval(GeV/c) dσ/dpt ± stat ± syst(µb/GeV/c)

2-3 99± 18+20−31

3-4 60± 8+11−15

4-5 19± 3+3−4

5-6 11.8± 1.7± 2

6-8 5.1± 0.7+0.7−1.2

8-12 1.6± 0.3+0.2−0.5

106

Bibliography

[1] B. Alessandro et al. [ALICE Collaboration], J. Phys. G: Nucl. Part. Phys. 32 (2006)

[2] A.Dainese, PhD thesis, Universit‘a degli Studi di Padova (2003), hep-ph/0311004.

[3] C. Amsler et al. [Particle Data Group], Phys. Lett. B 667 (2008) 1-1340.

[4] E. Bruna, A. Dainese, M. Masera, and F. Prino, ALICE Internal Note, ALICE-INT-2009-018

(2009).

[5] A. Rossi, PhD thesis, Universit‘a di Trieste (2009).

[6] C. Bianchin, A. Dainese, C. Di Giglio, A. Rossi, C. Zampolli, ALICE Internal Note, ALICE-

INT-2010-019 (2010)

[7] T. Sj’ostrand, S. Mrenna, P. Skands, J. High Energy Phys. 2006 (2006) 05 026.

[8] P.Z. Skands, arXiv:0905.3418 (2009).

[9] M. Cacciari et al., JHEP 0407 (2004) 033.

[10] R. Aaij et al. [LHCb Coll.], arXiv:1009.2731

[11] V. Khachatryan et al. [CMS Coll.], arXiv:1011.4193

[12] K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010)

[13] S. Van der Meer, ISR-PO/68-31, KEK68-64.

[14] B.A. Kniehl et al., Finite-mass effects on inclusive B-meson hadroproduction Phys. Rev. D77

(2008) 014011.

[15] S. Chekanov et al. [ZEUS Collaboration], Eur. Phys. J. C 44 (2005) 351.

107

[16] A. Adare et al. [PHENIX Coll.], Phys. Rev. Lett. 97 (2006) 252002.

[17] B.I. Abelev et al. [STAR Coll.], Phys. Rev. Lett. 98 (2007) 192301;

[18] W. Xie et al. [STAR Coll.], PoS DIS2010 (2010) 182.

[19] D. Acosta et al. [CDF Coll.], Phys. Rev. D71 (2005) 032001.

108

109

Chapter 6

Summary and Outlook

In this thesis, the cross section of D0 meson was measured in p-p collisions at the ALICE

experiment via the exclusive reconstruction of the decay channel D0 → K−π+. D mesons are

powerful probes of the medium since the charm quark is produced in a very short time scale and

experiences all the evolution of the collision.The measurement of open charm and open beauty

production allows one to investigate the mechanisms of heavy-quark production, propagation and,

at low momenta, hadronization in the hot and dense medium formed in high-energy nucleus-nucleus

collisions. To extract information on the medium properties the measurement performed with Pb-

Pb collisions must be related to the same measurement in p-p collisions, where the formation of

the QGP is not expected.

Charm production at mid-rapidity is measured in ALICE by reconstructing the following D

meson decays: D0 → K−π+, D0 → K−π+π+π−, D+ → K−π+π+, D+s → K+K−π+, D∗+ → D0π+,

and charge conjugates. The D0 → K−π+ channel, which has a fragmentation fraction c → D0

of about 0.6 and a decay branching ratio of 3.8 ± 0.09%, is one of the most promising of these

analyses because, being a two-body decay, it is affected by smaller combinatorial background with

respect to three- and four-body decays.The D0 proper decay length is cτ ≈ 123 µm, hence the

decay (secondary) vertex is displaced by a few hundred microns from the interaction (primary)

vertex. The analysis strategy is based on an invariant mass analysis of those combinations of

reconstructed tracks (“candidates”) that can represent a D0 meson decayed at a secondary vertex

displaced from the primary vertex of interaction. In p-p collisions, if all the possible pairs are

considered as “candidate” D0, the signal over combinatorial background ratio is ∼ 10−4. Most of

the combinatorial background consists of pairs of tracks from particles produced at the primary

110

vertex of interaction. It is then mandatory to preselect the reconstructed tracks and candidates

on the basis of the typical kinematical and geometrical properties characterizing the signal tracks

and reconstructed vertices.

Base on the recalling the existing theatrical, experimental results of high energy heavy-ion

collision and introducing the detector of LHC/ALICE and its physical targets. We measured the

track impact parameter resolution and production cross sections of prompt D0 mesons at central

rapidity in pp collisions at√S = 7 TeV. As discussed in the text, the impact parameter is a

critical variable for the selection of physics signals which are tagged by the secondary vertex with a

small displacement from the primary vertex. In this part, various effects on the impact parameter

are studied, including the primary vertex, multiple scattering, magnetic field (particle charge), and

particle mass. The impact parameter distribution of primary particle has a gaussian shape, and the

secondary particles has a exponential tail shape. So, the function of Gaussian+exponesional tail

was used as tool for extracting the resolution. Because of the limited multiplicity in pp collisions,

the track will pull the primary vertex to themselves and worse the impact parameter resolution.

Hence, the impact parameter resolution was investigated in two different primary-reconstructed

vertex (including current track and excluding current track). The multiple scattering has a big

effect on the impact parameter resolution, especially, at low pt. The resolution distribution for

different kinds of particle have the same trend which is larger at low pt than at high pt and have

clear mass order at low pt. And the other effects on the impact parameter resolution are very

small, despite they have a big difference in mean value of impact parameter.

Finally, the measurement of the production cross sections of prompt D0 meson at central ra-

pidity in p-p collisions at√s = 7 TeV in the interval 2 < pt < 12 GeV/c has been presented.

The pt-differential cross sections for prompt D0, obtained from the yields extracted by fitting the

invariant mass spectra with sum of a Gaussian for D0 peak and an exponential or second order poly-

nomial for the background. D0 mesons is reconstructed from its charged hadronic decay products

in the central rapidity region by exploiting the tracking and particle identification capabilities of

the ALICE central barrel detectors. In order to evaluate the total number of D0 mesons effectively

produced and decayed in the D0 → K−π+ channel, (ND0→K−π+

tot ) the raw signal yield is divided

by an efficiency correction factor (ϵ) that accounts for selection cuts, for PID efficiency, for track

and primary vertex reconstruction efficiency, and for the detector acceptance. Later, a relevant

fragmentation fraction of D0 mesons comes from the decay of B mesons was considered, as well

as decay channel branching ratio, rapidity range −ymax < y < +ymax and A factor 1/2 must be

111

considered because both D0 and D0 mesons are reconstructed. The last number is divided by the

integrated luminosity LINT to obtain the cross section for D0 meson production. The pt-differential

cross section is reproduced within uncertainties by theoretical predictions based on perturbative

QCD, namely FONLL and GM-VFNS.

After measurement of the production cross sections of prompt D0 meson in p-p collisions at√s = 7 TeV, one will measure the production cross sections of prompt D0 meson and v2 of D0

in Pb-Pb collisions. The comparison of heavy flavour production in p-p and Pb-Pb collisions

allows to probe the properties of the high-density QCD medium formed in the latter and to

study the mechanism of in-medium partonic energy loss. A sensitive observable is the nuclear

modification factor, defined, for a particle species h, as RhAA =

dNhAA/dpt

⟨TAA⟩×dσhpp/dpt

, By comparing the

nuclear modification factors of charged pions (Rπ±

AA), mostly originating from gluon fragmentation,

with that of hadrons with charm (RDAA) and beauty (RB

AA) the dependence of the energy loss

on the parton nature (quark/gluon) and mass can be investigated. The azimuthal distribution of

particles in the plane perpendicular to the beam direction is also one of the experimental observables

that is sensitive to the properties of this matter. When nuclei collide at finite impact parameter

(noncentral collisions), the geometrical overlap region and therefore the initial matter distribution

is anisotropic (almond shaped). If the matter is interacting, this spatial asymmetry is converted

via multiple collisions into an anisotropic momentum distribution. The second moment of the final

state hadron azimuthal distribution is called elliptic flow; it is a response of the dense system to

the initial conditions and therefore sensitive to the early and hot, strongly interacting phase of the

evolution.

112

 

List of Publications

• Shengqin Feng，Xianbao Yuan, The feature study on the pion and proton

rapidity distributions at AGS, SPS and RHIC, Science in China Series G 52 (2) (2009) 198-206.

• Xianbao Yuan, D0 cross section in p-p collisions at √s = 7 TeV, measured with ALICE detector, will be published in SLACeConf (2011).

• K. Aamodt, N. Abel…Xianbao Yuan…, First proton-proton collisions at the LHC as observed with the ALICE detector: measurement of the charged particle pseudorapidity density at √s= 900 GeV，Eur. Phys. J. C. 65 (2010) 111-125.

• K. Aamodt, N. Abel…Xianbao Yuan…, Alignment of the ALICE Inner Tracking System with cosmic-ray tracks ， JINST 5 (2010) p03003 (1748-0221).

• K. Aamodt, N. Abel…Xianbao Yuan…, Charged-particle multiplicity measurement in proton-proton collisions at √s = 0.9 and 2.36 TeV with ALICE at LHC，Eur.Phys.J.C. 68 (, 2010) 89-108.

• K. Aamodt, N. Abel…Xianbao Yuan…, Charged-particle multiplicity measurement in p-p collisions at √s = 7 TeV with ALICE at LHC, Eur. Phys. J. C , 68 (2010) 345–354.

• K. Aamodt, N. Abel…Xianbao Yuan…, Midrapidity antiproton-to-proton ratio in pp collisions at √s = 0.9 and 7 TeV measured by the ALICE experiment, Phys. Rev. Lett. 105 (2010), 072002.

• K. Aamodt, N. Abel…Xianbao Yuan…, Two-pion Bose-Einstein correlations in p-p collisions at √s=900 GeV, Phys. Rev. D. 82 (2010), 052001.

• K. Aamodt, N. Abel…Xianbao Yuan…, Transverse momentum spectra of charged particles in proton–proton collisions at √s=900 GeV with ALICE at the LHC, Physics Letters B. 693 (2010) 53–68.

• K. Aamodt, N. Abel…Xianbao Yuan…, Charged-particle multiplicity density at mid-rapidity in central Pb-Pb collisions at √sNN = 2.76 TeV, Phys. Rev. Lett. 105 (2010) 252301.

• K. Aamodt, N. Abel…Xianbao Yuan…, Suppression of Charged Particle Production at Large Transverse Momentum in Central Pb-Pb Collisions at √sNN = 2.76 TeV, Phys. Lett. B. 696 (2011) 30-39.

• K. Aamodt, N. Abel…Xianbao Yuan…, Elliptic flow of charged particles in Pb-Pb collisions at 2.76 TeV, Phys. Rev. Lett. 105 (2011) 252302.

• K. Aamodt, N. Abel…Xianbao Yuan…, Centrality dependence of the charged-particle multiplicity density at mid-rapidity in Pb-Pb collisions at sqrt(sNN) = 2.76 TeV, Phys. Rev. Lett. 106 (2011) 032301.

• K. Aamodt, N. Abel…Xianbao Yuan…, Two-pion Bose-Einstein correlations in central PbPb collisions at √sNN = 2.76 TeV, Phys. Lett. B. 696(4) (2011) 328-337.

LIST OF PUBLICATIONS 

 • K. Aamodt, N. Abel…Xianbao Yuan…, Strange particle production in

proton-proton collisions at √s = 0.9 TeV with ALICE at the LHC, Eur. Phys. J. C. 71(3) (2011) 1594.

• K. Aamodt, N. Abel…Xianbao Yuan…, Rapidity and transverse momentum dependence of inclusive J/psi production in pp collisions at √s =7 TeV, Phys. Lett. B. 704 (2011) 442-455.

• K. Aamodt, N. Abel…Xianbao Yuan…, Higher harmonic anisotropic flow measurements of charged particles in Pb-Pb collisions at 2.76 TeV, Phys. Rev. Lett. 107 (2011) 032301.

• K. Aamodt, N. Abel…Xianbao Yuan…, Production of pions, kaons and protons in p-p collisions at √s = 900 GeV with ALICE at the LHC, Eur. Phys. J. C. 71(6) (2011) 1655.

• K. Aamodt, N. Abel…Xianbao Yuan…, D0 cross section measurement in p-p collisions at √s = 7 TeV, measured with the ALICE experiment. arXiv: hep/ex 1111.1553.