Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
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
Bibliography
[1] http://public.web.cern.ch/public/en/science/StandardModel-en.html;
http://en.wikipedia.org/wiki/Standard-Model.
[2] Perkins, D.H. Introduction to High Energy Physics. Cambridge University Press,Cambridge,
4th edition, 2000.
[3] Povh, Bogdan and Rith, Klaus and Scholz, Christoph and Zetsche, Frank. Teilchen und Kerne.
Eine Einfhrung in die physikalischen Konzepte. Springer,Heidelberg, 6th edition, 2006.
[4] Yagi, Koshuke and Hatsuda, Tetsuo and Miake, Yasuo. Quark-Gluon Plasma.Cambridge Uni-
versity Press,Cambridge, 1st edition, 2008.
[5] M. Gell-Mann. ”The Eightfold Way: A Theory of strong interaction symmetry.” CTSL-20.
[6] D. J. Gross and F. Wilczek. ”Ultraviolet Behavior of Non-Abelian Gauge Theories.” Phys.
Rev. Lett. 30, 1343 (1973).
[7] H. D. Politzer. ”Reliable Perturbative Results for Strong Interactions?” Phys. Rev. Lett. 30,
1346 (1973).
[8] M. E. Peskin and D. V. Schroeder. An Introduction to quantum field theory. Reading, USA:
Addison-Wesley (1995) 842 p.143.
[9] S. Bethke. ”Experimental tests of asymptotic freedom.” Progress in Particle and Nuclear
Physics 58, 351 (2007). ISSN 0146-6410.
[10] K. G. Wilson. ”Confinement of quarks.” Phys. Rev. D 10, 2445 (1974).
[11] F. Karsch. ”Lattice QCD at High Temperature and Density.” In W. Plessas and L. Math-
elitsch, editors, Lectures on Quark Matter, volume 583 of Lecture Notes in Physics, pages
209-249. Springer Berlin/Heidelberg (2002).
24
[12] David Blaschke, THE QUEST FOR THE DENSE MATTER PHASE DIAGRAM AND EOS,
talk on:[email protected](2010).
[13] C. Alcock, The Astrophysics and Cosmology of Quark-Gluon Plasma, in Quark-Gluon Plasma,
Springer-Verlag (1990).
[14] Hebecker A A 2001 Preprint hep-ph/0111092.
[15] Eskola K J, Kajantie K, Ruuskanen P V and Tuominen K Nucl. Phys. B 570 379
[16] Braun-Munzinger P and Stachel J. Nucl. Phys. A 606 320 (1996).
[17] Harris JW and M”uller B Annu. Rev. Nucl. Part. Sci. 46 71 (1996)
[18] Bass S A, Gyulassy M, St”oker H and GreinerW J. Phys. G: Nucl. Part. Phys. 25 R1 (1999)
[19] Satz H. Rep. Prog. Phys. 63 1511 (2000); Stock R. Phys. Lett. B 456 277 (1999); Stock R.
Prog. Part. Nucl. Phys. 42 295 (1999).
[20] Heinz U. Nucl. Phys. A 638 357c (1998); Heinz U. J. Phys. G: Nucl. Part. Phys. 25 263 (1999);
Heinz U. Nucl. Phys. A 661 140c (1999); Heinz U. Nucl. Phys. A 685 414c (2001).
[21] Stachel J. Nucl. Phys. A 654 119c (1999); Redlich K. Nucl. Phys. A 698 94c (2002); Heinz U
and Kolb P F. Nucl. Phys. A 702 269c (2002).
[22] Schnedermann E, Sollfrank J and Heinz U. Particle Production in Highly Excited Matter
(NATO ASI Series vol B303) ed H H Gutbrod and J Rafelski (NewYork: Plenum) p 175
(1993).
[23] Heinz U. Hot Hadronic Matter: Theory and Experiment (NATO ASI Series vol B346) ed J
Letessier et al(NewYork: Plenum) p 413 (1995).
[24] Heinz U. Measuring the Size of Things in the Universe: HBT Interferometry and Heavy Ion
Physics ed S Costa et al (Singapore: World Scientific) p 66 (1999).
[25] Heinz U and Jacob M. Preprint nucl-th/0002042 (2000) and
http://cern.web.cern.ch/CERN/Announcements/2000/ NewStateMatter/.
[26] Braun-Munzinger P, Magestro D, Redlich K and Stachel J. Phys. Lett. B 518 41 (2001).
[27] Seymour M H Preprint hep-ph/0007051 (2000).
25
[28] Affolder T etal . [CDF Collaboration] Phys. Rev. D 65 092002 (2002).
[29] Afanasev S V etal . [NA49 collaboration] Phys. Rev. C 66 054902 (2002).
[30] Adcox K etal . [PHENIX Collaboration] Phys. Rev. Lett. 88 242301 (2002).
[31] Adler C etal . [STAR Collaboration] Phys. Lett. B 595 143 (2004).
[32] J. D. Bjorken. Phys. Rev. D27 140 (1983).
[33] J. Adams. et al. (STAR Collaboration), Phys. Rev. C 70 054907 (2004).
[34] K. Adcox. et al. (PHENIX Collaboration), Nucl. Phys. A 757 184 (2005).
[35] A. Krasnitz, Y. Nara and R. Venugopalan, Nucl. Phys. A 717 268 (2003).
[36] Sourendu Gupta, Xiaofeng Luo, Bedangadas Mohanty, Hans Georg Ritter, Nu Xu. Scale for
the Phase Diagram of Quantum Chromodynamics, Science 332, 1525 (2011);
[37] M. Biyajima et al., Phys. Rev. Lett. B 515 470-476 (2001).
[38] J.J. Marian, J. Phys. G, 30 S751-S758 (2004).
[39] E. Iancu and R. Venugopalan, [arXiv:hep-ph/0303204] (2003).
[40] D. Kharzeev, E. Levin and M. Nardi, [arXiv:hep-ph/0111315] (2001).
[41] D. Kharzeev, E. Levin and M. Nardi, Nucl. Phys. A 730 448 (2004).
[42] J.J. Marian, [arXiv:nucl-th/0212018] (2002).
[43] T. Hirano and Y. Nara, [arXiv:nucl-th/0403029] (2004).
[44] K. Aamodt, B. Abelev et al. Charged particle multiplicity density at midrapidity in central
PbPb collisions at√sNN = 2.76 TeV. PRL 105, 252301 (2010).
[45] M. C. Abreu et al. (NA50), Phys. Lett. B530, 43 (2002).
[46] C. Adler et al. (STAR), Phys. Rev. Lett. 87, 112303 (2001), arXiv:nucl-ex/0106004.
[47] I. G. Bearden et al. (BRAHMS), Phys. Lett. B523, 227 (2001), arXiv:nucl-ex/0108016.
[48] I. G. Bearden et al. (BRAHMS), Phys. Rev. Lett. 88, 202301 (2002), arXiv:nucl-ex/0112001.
[49] K. Adcox et al. (PHENIX), Phys. Rev. Lett. 86, 3500 (2001), arXiv:nucl-ex/0012008.
26
[50] B. B. Back et al. (PHOBOS), Phys. Rev. Lett. 85, 3100 (2000), arXiv:hep-ex/0007036.
[51] B. B. Back et al. (PHOBOS), Phys. Rev. Lett. 87, 102303 (2001), arXiv:nucl-ex/0106006.
[52] B. B. Back et al., Phys. Rev. Lett. 91, 052303 (2003), arXiv:nucl-ex/0210015.
[53] B. Alver et al., (2010), arXiv:1011.1940 [nucl-ex].
[54] C. Albajar et al., Nucl. Phys. B335, 261 (1990).
[55] K. Alpgard et al., Phys. Rev. B112, 183 (1982).
[56] G. J. Alner et al., Z. Phys. C33, 1 (1986).
[57] B. I. Abelev et al., Phys. Rev. C79, 034909 (2003).
[58] F. Abe et al., Phys. Rev. D41, 2330 (1990).
[59] K. Aamodt et al. (ALICE), Eur. Phys. J. C 68, 89 (2010).
[60] V. Khachatryan et al. (CMS), JHEP 02, 041 (2010), arXiv:1002.0621 [hep-ex].
[61] W. Busza, J. Phys. G35, 044040 (2008), arXiv:0710.2293 [nucl-ex].
[62] W.-T. Deng, X.-N. Wang, and R. Xu, (2010), arXiv:1008.1841 [hep-ph].
[63] F. W. Bopp, J. Ranft, R. Engel, and S. Roesler, Phys. Rev. C77, 014904 (2008), arXiv:hep-
ph/0505035.
[64] J. L. Albacete, (2010), arXiv:1010.6027 [hep-ph].
[65] E. Levin and A. H. Rezaeian, Phys. Rev. D82, 054003 (2010), arXiv:1007.2430 [hep-ph].
[66] D. Kharzeev, E. Levin, and M. Nardi, Nucl. Phys. A747, 609 (2005), arXiv:hep-ph/0408050.
[67] D. Kharzeev, E. Levin, and M. Nardi, (2007), arXiv:0707.0811 [hep-ph].
[68] N. Armesto, C. A. Salgado, and U. A. Wiedemann, Phys. Rev. Lett. 94, 022002 (2005),
arXiv:hep-ph/0407018.
[69] K. J. Eskola, P. V. Ruuskanen, S. S. Rasanen, and K. Tuominen, Nucl. Phys. A696, 715
(2001), arXiv:hep-ph/0104010.
[70] P. Bozek, M. Chojnacki, W. Florkowski, and B. Tomasik, Phys. Lett. B694, 238 (2010),
arXiv:1007.2294 [nucl-th].
27
[71] E. K. G. Sarkisyan and A. S. Sakharov, (2010), arXiv:1004.4390 [hep-ph].
[72] T. J. Humanic, (2010), arXiv:1011.0378 [nucl-th].
[73] Peter F. Kolb and Ulrich Heinz. Hydrodynamic description of ultrarelativistic heavy-ion colli-
sions. In R.C. Hwa, editor, Quark gluon plasma, pages 634-714 (2003).
[74] S. Voloshin and Y. Zhang. Flow study in relativistic nuclear collisions by fourier expansion of
azimuthal particle distributions. Z. Phys., C70:665-672 (1996).
[75] K. Aamodt, B. Abelev, et al. Elliptic Flow of Charged Particles in Pb-Pb Collisions at√sNN =
2.76 TeV. Phys. Rev. Lett. 105, 252302 (2010).
[76] S. S. Adler et al. [PHENIX Collaboration], Common suppression pattern of η and π0 mesons
at high transverse momentum in Au+Au collisions at√sNN = 200 GeV, Phys. Rev. Lett. 96,
202301 (2006).
[77] John Adams et al. (STAR Collaboration), Evidence from d+Au measurements for final state
suppression of high pT hadrons in Au+Au collisions at RHIC, Phys. Rev. Lett. 91, 072304
(2003).
[78] John Adams et al. ”Azimuthal anisotropy and correlations at large transverse momenta in p
+ p and Au + Au collisions at√sNN = 200 GeV.” Phys. Rev. Lett., 93:252301, (2004).
[79] Xin-Nian Wang Ben-Wei Zhang Miklos Gyulassy, Ivan Vitev. ”Jet Quenching and Radiative
Energy Loss in Dense Nuclear Matter.”.
[80] P.M. Jacobs and M. van Leeuwen, High pT in Nuclear Collisions at the SPS, RHIC, and
LHC, Nucl. Phys. A 774 237-246 (2006).
[81] J”urgen Schukraft, ”Little Bang” The first 3 weeks..., Talk at ”First results from Heavy Ion
collisions at the LHC (ALICE, ATLAS, CMS)”-CERN 02/12/2010.
[82] B. A. Cole on behalf of the ATLAS Collaboration, Observation of a Centrality-Dependent
Dijet Asymmetry in Lead-Lead Collisions with the ATLAS Detector, Talk at ”First results
from Heavy Ion collisions at the LHC (ALICE, ATLAS,CMS)” CERN 02/12/2010.
[83] B. Wyslouch on behalf of CMS Collaboration , PbPb collisions in CMS, Talk at ”First results
from Heavy Ion collisions at the LHC (ALICE, ATLAS, CMS)” CERN 02/12/2010.
28
[84] J. Adams, et al. STAR Collaboration: Experimental and Theoretical Challenges in the Search
for the Quark Gluon Plasma: The STAR Collaboration’s Critical Assessment of the Evidence
from RHIC Collisions. Nucl.Phys.A757:102-183 (2005)
[85] T. Matsui and H. Satz, Phys. Lett. B 178 (1986) 416.
[86] B. Alessandro et al. NA50 collaboration. Eur. Phys. J. C39, 335 (2005); Eur. Phys. J. C48,
329, (2006); Eur. Phys. J. C49, 559 (2007).
[87] A. Adare et al. PHENIX collaboration. Phys. Rev. Lett. 98, 232301 (2007), nucl-ex/0611020;
arXiv:1010.1246v1 (2010); arXiv:1103.6269v1 (2011).
[88] E.V. Shuryak, Phys. Lett. B 78 (1978) 150.
[89] C. Quigg and J.L. Rosner, Phys. Rep. 56 (1979) 167.
[90] K. Kanaya and H. Satz, Phys. Rev. D 34 (1986) 3193.
[91] N.S. Craigie, Phys. Rep. 47 (1978) 1.
[92] R. Arnaldi et al. NA60 colliboration. Nucl. Phys. A830, 345c (2009), arXiv:0907.5004v2.
[93] Gine’s Marti’nez Garci’a, for ALICE colliboration. talk on QM2011: Quarkonium production
measurements with the ALICE detector at the LHC.
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
Bibliography
[1] A.Dainese, J. Phys. G 31 (2005) S781-S790.
[2] J. Baines, S.P. Baranov, O. Behnke et al. arXiv:hep-ph/06011642v2 (2007).
[3] ALICE: Physics Performance Report, Volume I and II.
[4] R.J.Glauber and G.Matthiae, Nucl. Phys. B21(1970)135.
[5] http://en.wikipedia.org/wiki/Woods-Saxon-potential.
[6] Z. Sullivan, P.M. Nadolsky, arXiv:hep-ph/0111358v1(2001).
[7] N. Armesto, J.Phys.G32:R367-R394(2006) or arXiv:hep-ph/0604108v2.
[8] M.Mangnao, P.Nason and G.Ridolfi, Nucl. Phys. B373(1992)295.
[9] K.J.Eskola, V.J.Kolhinen and C.A.Salgado, Eur.Phys.J9(1999)61,arXiv:hep-ph/9807297.
[10] I.P.Lokhtin, A.M.Snigirev, Phys.Lett. B567 (2003) 39-45.
[11] Ronny Thomas, PhD thesis, Energy Loss of Quarks by Gluon Radiation in Deconfined Matter
(2003).
[12] J.D. Bjorken, FERMILAB-PUB-82-59-THY.
[13] M. Gyulassy and M. Plumer, Phys. Lett. B243 (1990) 432.
[14] C.A. Salgado and U.A. Wiedemann, Phys. Rev. D68 (2003) 014008,arXiv:hep-ph/0302184
(2003);
[15] R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peigne and D. Schiff, Nucl. Phys. B483 (1997)
291.
48
[16] R. Baier, Yu.L. Dokshitzer, A.H. Mueller, S. Peigne and D. Schiff, Nucl.Phys. B483 (1997)
291; ibidem B484 (1997) 265.
[17] D.E. Kharzeev, M. Nardi and H. Satz, Phys. Lett. B405 (1997) 14.
[18] R. Baier, Nucl. Phys. A715 (2003) 209c.
[19] B.I. Abelev et al. [STAR Collaboration] arXiv:nucl-ex/0805.0364v2 (2008).
[20] A. Adare et al. [PHENIX Collaboration] Phys. Rev. Lett.98 (2007) 172301.
[21] D. Acosta et al. [CDF Collaboration] Phys. Rev. Lett. 91 (2003) 241804.
[22] Ante Bilandzic, Raimond Snellings and Sergei Voloshin, Phys. Rev. C 83, (2011) 044913.
[23] S. Voloshin, Y. Zhang, Z.Phys.C70:665-672(1996), arXiv:hep-ph/9407282v1.
[24] A.M.Poskanzer, S.A. Voloshin, Phys.Rev.C58:1671-1678(1998), arXiv:nucl-ex/9805001v2.
[25] H. van Hees, V. Greco, and R. Rapp, Phys. Rev. C 73,034913 (2006).
[26] G. D. Moore and D. Teaney, Phys. Rev. C 71, 064904(2005).
[27] A. Adare et al. [PHENIX Collaboration],Phys. Rev. Lett. 98 (2007) 172301.
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
7724
1277
29 12
7730
1278
15 12
7815
1278
19 12
7820
1278
22 12
7931
1279
33 12
7935
1279
36 12
7937
1280
50 12
8053
1281
75 12
8180
1281
82 12
8183
1281
85 12
8190
1281
91 12
8192
1282
56 12
8257
1282
60 12
8359
1283
66 12
8483
1284
86 12
8495
1285
03 12
8504
1285
06 12
8507
1285
82 12
8589
1285
94 12
8605
1286
09 12
8610
1286
11 12
8615
1286
78 12
8776
1287
77 12
8778
1288
14 12
8818
1288
20 12
8823
1288
33 12
8834
1288
35 12
8836
1288
43 12
8849
1288
55 12
8910
1289
13 12
9041
1295
08 12
9510
1295
13 12
9516
1295
19 12
9520
1295
23 12
9526
1295
27 12
9528
1295
29 12
9540
1295
41 12
9586
1295
97 12
9598
1295
99 12
9639
1296
41 12
9647
1296
48 12
9650
1296
51 12
9653
1296
54 12
9659
1296
65 12
9666
1297
23 12
9725
1297
26 12
9729
1297
31 12
9734
1297
35 12
9736
1297
38 12
9742
1297
44 12
9745
1297
47 12
9748
1297
50 12
9760
1297
63 12
9959
1299
60 12
9962
1299
83 13
0148
1301
58 13
0168
1301
70 13
0178
1303
43 13
0348
1303
53 13
0354
1303
58 13
0369
1304
80 13
0609
1306
20 13
0623
1306
27 13
0628
1306
96 13
0793
1307
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.