UNIVERSIDAD NACIONAL AUTÓNOMA
DE MÉXICO
POSGRADO EN CIENCIAS FÍSICAS
Jets structure in Pb–Pb
collisions at LHC energies
TESIS
QUE PARA OBTENER EL GRADO DE:
DOCTORA EN CIENCIAS (FÍSICA)
PRESENTA:
ISABEL DOMÍNGUEZ JIMÉNEZ
DIRECTORES DE TESIS:
Dr. Guy Paić
Dr. Eleazar Cuautle Flores
MIEMBRO DE COMITÉ TUTORAL:
Dr. Jesús Guillermo Contreras Nuño
MÉXICO, D.F. 2011
 
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Resumen
El objetivo de este trabajo es estudiar las propiedades de la materia densa utilizando
jets en el ambiente de simulación y análisis del experimento ALICE del CERN. Es-
pecı́ficamente, nos hemos enfocado a las modificaciones que pueden sufrir los jets
en un medio de materia nuclear densa. Con dicho propósito, se simularon eventos
de alto pT en colisiones p+ p con PYTHIA , para tomarlos como referencia y eventos
simulados utilizando dos modelos de pérdida de energı́a partónica: PYQUEN y Q-
PYTHIA. Después de simular los eventos, se utilizo un algoritmo de cono, implemen-
tado en el ambiente de simulación del experimento ALIROOT, para la reconstrucción
de los jets. Se estudiaron las modificaciones en la estructura de los jets debido a
la pérdida de energı́a partónica, a través del momento transverso intrı́nseco kT y
el momento transverso con respecto al eje del jet jT . También se llevo a cabo un
análisis de las variables de forma del evento, seleccionando diferentes topologı́as
y observando las modificaciones en tres de ellas: τ , R y Tmin. Con este estudio
se espera poder entender mejor las propiedades de la materia densa creada en
colisiones de Pb+Pb a energı́as de LHC.
i
Abstract
The aim of this work is to study the properties of the dense matter via jets in the
framework of the ALICE experiment in CERN. Specifically we have concentrated on
the aspect of modifications in jet structure in a dense nuclear medium environment.
With this purpose, we simulated high-pT events in p+ p collision, with PYTHIA, as a
baseline, and subsequently these events were passed through two afterburner mo-
dels of energy loss: PYQUEN and Q-PYTHIA, to simulate the effect of a dense
medium. After events simulation, jets were reconstructed in the framework of the
ALICE experiment (ALIROOT) with a jet finding algorithm. Modifications in jet struc-
ture due to parton energy loss, like: the intrinsic transverse momentum kT and the
transverse momentum with respect to the jet axis jT were studied, as well as event
shape analysis, identifying different topologies of the events and the modifications
in three shape variables: τ , R and Tmin. This study helps us to understand the pro-
perties of a dense medium created in Pb+Pb collisions at LHC energies.
ii
Introducción
En los pasados 100 años la idea de los constituyentes fundamentales de la materia
ha evolucionado considerablemente. Se encontró que los átomos estaban consti-
tuidos por electrones y núcleos y que estos últimos están formados por protones y
neutrones, a los que en general se les llama nucleones. A su vez, estos nucleones
se encuentran formados por partı́culas más pequeñas llamadas quarks y gluones.
Los quarks y antiquarks nunca han sido observados como partı́culas libres, siempre
se encuentran, ya sea, en grupos de tres llamados bariones (protones, neutrones,
etc...) o de dos llamados mesones (piones, kaones, etc.). Sin embargo, se cree
que los quarks libres existieron en el universo temprano hasta 40 microsegundos
después del Big Bang. De acuerdo a esta teorı́a, el universo estaba formado por
un gas caliente llamado Plasma de quarks y gluones (QGP). La temperatura de
este plasma era aproximadamente 100 000 veces mayor que la temperatura del sol
(unos 100 x 1010 K); no se sabe si los quarks son verdaderamente elementales,
pero si lo son, el plasma en el universo temprano se debió de haber formado direc-
tamente del Big Bang y conforme el universo se enfrió los quarks y antiquarks se
agruparon en hadrones (mesones y bariones). Al hecho de que los quarks siempre
han sido observados en estados ligados se le llama confinamiento.
La teorı́a que estudia las interacciones entre los quarks y gluones es la Cromodiná-
mica Cuántica (QCD) y ésta predice una transición de la materia hadrónica al plasma
de quarks y gluones libres. La predicción de esta transición de fase ha dado origen a
su búsqueda experimental y desde hace casi 20 años se intenta encontrar y estudiar
sus propiedades en el laboratorio.
Para producir este nuevo estado de la materia se requiere un sistema denso y a alta
temperatura de quarks y gluones y para formarlo, se hacen chocar haces de iones
pesados que viajan con una velocidad cercana a la de la luz. El sistema creado
en estas colisiones pasa por varias etapas y finalmente se emiten partı́culas que
inciden en los detectores, con ellas se tienen que definir los observables que den
indicio de la eventual creación del plasma, es decir, encontrar señales del descon-
finamiento. Una de las señales que se ha estudiado es la pérdida de energı́a que
sufren los quarks y gluones al viajar a través del plasma.
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iv
Se predice que la pérdida de energı́a depende de la velocidad con la que las
partı́culas cargadas se muevan dentro del plasma. El efecto es mayor para aquellos
quarks y gluones que viajan más rápido. Por otra parte hay muchos indicios, conoci-
dos colectivamente como dualidad partón-hadrón, de que los hadrones con mucho
momento provienen de partones que también llevaban mucho momento. Ası́, que la
pérdida de energı́a, se reflejarı́a en una disminución, o incluso en la desaparición,
de las partı́culas con momento grande.
La detección experimental de este fenómeno sufre de varias complicaciones. Por
un lado, el espectro de momentos cae exponencialmente, por lo que en una coli-
sión dada hay muchı́simas más partı́culas con momentos pequeños que grandes.
Por otro lado, la producción de partı́culas es un proceso cuántico por lo que esta
sujeto a fluctuaciones. Además un efecto similar en los espectros de partı́culas
medidas en los detectores podrı́a haber sido causado por otros medios y no sola-
mente por la pérdida de energı́a que sufren los quarks y gluones al viajar a través
del plasma. Ası́, debido a la gran complejidad del problema no hay una señal que
por si misma determine la existencia de la formación de QGP, sino que es la consis-
tencia de muchas señales en diversos tipos de experimentos de las que se deducirá
su existencia.
A la fecha se han medido espectros de partı́culas cargadas producidas en coli-
siones de iones pesados en experimentos localizados en los aceleradores SPS (Su-
per Proton Synchroton) del CERN (European Organisation for Nuclear Research) y
en RHIC (Relativistic Hevy Ion Collider) del BNL (Brookhaven National Laborator).
RHIC ha observado una supresión de partı́culas con mucho momento transversal
con respecto a p+ p. En el LHC (Large Hadron Collider) se espera que la energı́a
de las colisiones sea lo suficientemente grande como para alcanzar el desconfi-
namiento de los quarks y gluones, formando un plasma de éstos.
En colisiones de iones pesados las observables son comparadas con las observ-
ables de colisiones p+ p, ası́, la idea de este trabajo es utilizar simulación Monte-
Carlo de colisiones p+ p y Pb+Pb y la reconstrucción de jets en estos eventos,
para estudiar señales de desconfinamiento, considerando energı́as de ALICE [1, 2],
uno de los cuatro detectores con los que cuenta el LHC.
Jets con momento transverso grande
Jet se refiere a un grupo de hadrones que se originaron de la fragmentación de
colisiones duras de partones. Las partı́culas del jet están contenidas en un cono de
radio R =
√
(∆η )2 +(∆φ)2 y la energı́a y dirección del jet se esperan sean cercanas
a las del partón inicial. Dicho jet moviéndose en un plasma de quark y gluones (esto
es, en un medio con alta densidad de carga), pierde energı́a al interactuar con el
medio, esto es, radia partones quienes se llevan parte de la energı́a original del jet.
iv
v
En 1982 Bjorken [3] sugirió que los partones que viajan rápido a través del plasma
de quarks y gluones pudieran perder grandes cantidades de energı́a por choques
elásticos con los componentes del plasma, dando por resultado la supresión de jets
en el medio altamente denso que se forma en los choques de iones pesados. En
una serie de artı́culos teóricos de los años 90 Gyulassy, Plümer y X.N. Wang [4]
identificaron la supresión de jets como consecuencia de la pérdida de radiación, y
en 1995-1997 Baier , Dokshitzer, Mueller, Peigné y Schiff [5] realizaron un estudio
importante sobre la taza de la pérdida de energı́a como resultado de múltiples inter-
acciones de color del gluón radiado con los componentes coloreados en el plasma.
En el lı́mite de un plasma ópticamente grueso, encontraron que la pérdida de en-
ergı́a ∆E de los partones rápidos, aumenta cuadráticamente con la distancia L que
recorren antes de escaparse y hadronizarse.
∆E ≈ αs
2
µ2
λ
L2, (1)
donde αs es la constante de acoplamiento, µ es el apantallamiento de Debye de las
cargas de color en el plasma y λ el recorrido libre medio del gluón.
Las predicciones para esta pérdida de energı́a fueron mejoradas por Gyulassy,
Levai, Vitev [6] y Wiedemann [7] considerando opacidad finita . Esto conduce a
una dependencia importante de la pérdida de energı́a ∆E del partón rápido y a las
desviaciones de la dependencia cuadrática de la longitud de la trayectoria, para
valores pequeños de L. Con estos resultados mejorados se puede mantener la
esperanza que la pérdida de energı́a se pueda utilizar como punta de prueba cuan-
titativa de la densidad y de la evolución temporal del plasmas de quarks y gluones
creado en colisiones del iones pesados.
Evidencia experimental
Existen 4 experimentos en RHIC (Relativistiv Heavy Ion Collisions) que han estudi-
ado colisiones p+ p y Au+Au a energı́as del centro de masa de
√
sNN = 62.4, 130
y 200 GeV los cuales han mostrado evidencias de la pérdida de energı́a. Se ha
encontrado que las partı́culas con mucho momento trasversal, pT , son altamente
suprimidas en colisiones centrales de Au+Au, además la no supresión de estas
partı́culas en colisiones d +Au confirma que la supresión se puede atribuir a la in-
teracción de los partones con el medio denso formado durante la colisión. Esta
supresión de partı́culas se ha estudiado mediante las correlaciones azimutales.
Las correlaciones azimutales entre hadrones se escriben usualmente como:
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vi
C(∆Φ) =
1
Ntrigger
∫
d∆η
dN
d∆Φd∆η
(2)
donde ∆Φ y ∆η son, respectivamente, el ángulo azimutal y la pseudorapidez entre
la partı́cula con más alto momento y su partı́cula asociada. La correlación azimutal
muestra una estructura de dos picos que es interpretada por STAR [8] como eviden-
cia de jets a nivel partónico. En el caso de colisiones de Au+Au se observa una
disminución importante de estos picos en ∆φ = ±π, lo que es interpretado como
una pérdida de energı́a de los partones al atravesar un medio denso.
Jets en ALICE
El experimento LHC, inicialmente realizó corridas de choques de p+ p a
√
sNN =
900 GeV y 7 TeV. Las colisiones de Pb+Pb se realizaron a una energı́a de
√
sNN =
2.7 TeV y posteriormente se realizarán con una energı́a de
√
sNN = 5.5 TeV. En este
experimento se espera que la energı́a de la colisión sea lo suficientemente grande
para que se lleve a cabo el desconfinamiento de los quarks y gluones, formándose
un plasma de estos componentes fundamentales de la materia. El detector ALICE se
enfoca en el estudio de las propiedades de este plasma.
Producción mediante técnica Monte Carlo
Anticipándose a la toma de datos, se realizan estudios sobre la fı́sica que se espera
poder estudiar en ALICE mediante simulación Monte-Carlo. La estrategia general
para la simulación Monte-Carlo de colisiones Pb+Pb consiste en generar procesos
duros en colisiones p+ p utilizando el generador de eventos PYTHIA 6.2.14 [9], que
serı́a una muestra de jets, esto es, una verdadera señal y mezclarlos con eventos
generados en colisiones Pb+Pb utilizando el generados de HIJING v1.36 [10], que
serı́a ruido.
Los generadores de colisiones p + p han sido adaptados para simular modifica-
ciones nucleares en los estados iniciales y finales. Las modificaciones al estado
inicial han sido incluidos en las funciones de densidad de los partones dentro del
núcleo (PDF’s). Las modificaciones en los estados finales de los jets con momento
transverso grande producidos en colisiones de iones pesados a energı́as de LHC,
se espera que sean dominadas por la perdida de energı́a a través de la radiación
de gluones, debido a la presencia de un medio denso.
No existe hasta la fecha un solo generador para simular este efecto, sin embargo
varias aproximaciones fenomenológicas pueden ayudar a estudiar y entender la
pérdida de energı́a. PYQUEN [11] y Q-PYTHIA [12] como parte del ambiente de
simulación del detector ALICE, ALIROOT [13], han sido utilizados para la simulación
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vii
y estudio de dichas modificaciones en los estados finales.
Una vez que la simulación de la colisión ha sido realizada incluyendo las modifica-
ciones debido a las presencia de un medio denso, se requiere tener control sobre
la producción de eventos en los cuales los jets sean bien identificados. Con este
propósito se utiliza un análisis de la forma del evento (Event Shape Analysis ESA)
[14, 15] y un algoritmo de cono para la reconstrucción de jets [16].
Ası́, el trabajo se divide en 3 etapas:
1. Simulación de eventos a energı́as de LHC incluyendo los modelos de pérdida
de energı́a en el ambiente de simulación de ALICE.
2. Clasificación y reconstrucción de eventos, en base a su topologı́a, utilizando
ESA y un algoritmo de cono
3. Estudio las modificaciones en la estructura de los jets debido a la pérdida
de energı́a partónica, a través del momento transverso intrı́nseco kT y el mo-
mento transverso con respecto al eje del jet jT , ası́ como también los efectos
de un medio nuclear en términos de los factores de supresión RAA en función
de pT y jT y las variables de forma τ , R y Tmin
Todo en un ambiente bajo las condiciones del experimento ALICE.
vii
Contents
1 Introduction 1
2 QCD phase diagram and QGP 3
2.1 QGP: Theoretical overview . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 QGP: Experimental study . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 Experimental programs 16
3.1 Relativistic Heavy Ion Collider . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.1 The ALICE experiment . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Heavy-Ion physics with ALICE . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.1 Soft Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.2 Heavy flavor probes . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.3 High-pT probes . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4 Framework of the ALICE detector: AliROOT 30
4.1 Simulation framework . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1.1 Parametrized generation . . . . . . . . . . . . . . . . . . . . . . 34
4.1.2 Reconstruction Framework . . . . . . . . . . . . . . . . . . . . 35
4.1.3 Event summary data . . . . . . . . . . . . . . . . . . . . . . . . 37
4.1.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
viii
CONTENTS ix
5 Production of high-pT events 40
6 Jet reconstruction 43
6.1 The Cone Jet Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 44
6.1.1 Cone Jet Algorithm for Heavy-Ion Collisions . . . . . . . . . . . 46
6.2 Events with dijets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.3 Event Shape Analysis (ESA) . . . . . . . . . . . . . . . . . . . . . . . 54
6.3.1 Event shape variables . . . . . . . . . . . . . . . . . . . . . . . 54
6.3.2 Azimuthal correlations . . . . . . . . . . . . . . . . . . . . . . . 57
7 Energy loss 59
7.1 PYQUEN model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
7.2 Q-PYTHIA model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
8 Acoplanarity for dijets (kT ) and the transverse momentum of a jet ( jT ) 69
8.1 Acoplanarity for dijets . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
8.2 Transverse momentum jT . . . . . . . . . . . . . . . . . . . . . . . . . 71
9 Event shape analysis in a dense medium 75
9.1 Azimuthal correlations at RHIC energy . . . . . . . . . . . . . . . . . . 75
9.2 Event Shape Analysis (ESA) at LHC energy . . . . . . . . . . . . . . . 75
10 Discussion and Conclusion 82
Bibliography 86
ix
List of Figures
2.1 Energy density ε as a function of temperature . . . . . . . . . . . . . . 4
2.2 Temperature dependence . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Space-time evolution of the quark-gluon plasma . . . . . . . . . . . . 12
3.1 Binary-scaled ratio RAB at
√
sNN = 200 GeV . . . . . . . . . . . . . . . 19
3.2 Dihadron azimuthal correlations at
√
sNN = 200 GeV . . . . . . . . . . 20
3.3 The CERN accelerator complex . . . . . . . . . . . . . . . . . . . . . . 21
3.4 ALICE detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.5 Jets produced in Pb+Pb collisions . . . . . . . . . . . . . . . . . . . . 29
4.1 Data processing framework. . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Simulation framework. . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.3 Reconstruction framework. . . . . . . . . . . . . . . . . . . . . . . . . 36
5.1 pT distribution in p+ p collisions at
√
sNN = 5.5 TeV . . . . . . . . . . . 42
6.1 Cone jet algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.2 Charged jets in the η -φ plane . . . . . . . . . . . . . . . . . . . . . . . 48
6.3 Dihadron azimuthal correlation at
√
sNN = 5.5 TeV . . . . . . . . . . . . 49
6.4 pT distribution for all and leading particles at
√
sNN = 5.5 TeV . . . . . 50
6.5 ET jets as function Rc at
√
sNN = 5.5 . . . . . . . . . . . . . . . . . . . . 52
6.6 Dijet azimuthal correlations with several phard
T . . . . . . . . . . . . . . 53
x
LIST OF FIGURES xi
6.7 Thrust map at
√
sNN = 200 GeV . . . . . . . . . . . . . . . . . . . . . . 56
6.8 Dihadron azimuthal correlations in three regions of thrust map . . . . 58
7.1 pT distribution for PYTHIA and PYQUEN at
√
sNN = 5.5 TeV . . . . . . 64
7.2 Dihadron azimuthal correlations and RAA for PYQUEN . . . . . . . . . . 65
7.3 pT distribution for PYTHIA and Q-PYTHIA at
√
sNN = 5.5 TeV . . . . . . 68
7.4 Dihadron azimuthal correlations and RAA for Q-PYTHIA . . . . . . . . . 68
8.1 Acoplanarity as a function of transverse momentum . . . . . . . . . . 71
8.2 pT,diff and pout for PYQUEN and Q-PYTHIA . . . . . . . . . . . . . . . . . 72
8.3 Ratio of particles yield as function of pT . . . . . . . . . . . . . . . . . 73
8.4 Ratio of particles yield as function of pT at different distances r . . . . 74
8.5 Ratio of particles yield as function of jT . . . . . . . . . . . . . . . . . 74
9.1 Dihadron azimuthal correlations with Q-PYTHIAand ESA cuts . . . . . 76
9.2 Thrust map and dihadron azimuthal correlations with pcut
T in p+ p . . . 78
9.3 Thrust distribution for PYTHIA, PYQUEN and Q-PYTHIA . . . . . . . . . 79
9.4 Recoil distribution for PYTHIA, PYQUEN and Q-PYTHIA . . . . . . . . . 80
9.5 Thrust minor distribution for PYTHIA, PYQUEN and Q-PYTHIA . . . . . . 81
xi
List of Tables
2.1 Experimental facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1 Luminosities expected for different collision systems . . . . . . . . . . 22
3.2 Conditions created in central heavy-ion collisions . . . . . . . . . . . . 22
3.3 Jets produced in Pb+Pb collisions . . . . . . . . . . . . . . . . . . . . 29
5.1 PYTHIA 6.2.14 parameter settings . . . . . . . . . . . . . . . . . . . . . 41
5.2 Weight for each phard
T . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
6.1 Mean pT leading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.2 Settings for cone jet algorithm . . . . . . . . . . . . . . . . . . . . . . . 51
6.3 Thrust map parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 57
7.1 PYQUEN internal model parameters . . . . . . . . . . . . . . . . . . . . 62
7.2 Parametere used in PYQUEN . . . . . . . . . . . . . . . . . . . . . . . 63
8.1 Parameters used in kT the simulation . . . . . . . . . . . . . . . . . . . 70
9.1 Thrust map parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 76
xii
Chapter 1
Introduction
In the past 100 years the idea of the fundamental constituents of the matter has
evolved considerably. It was found that atoms split into electrons and nucleus and
that these last are formed by protons and neutrons, which in generally they are
called nucleons. These nucleons are formed by small particles called quarks and
gluons.
Quarks and antiquarks have never been observed as free particles, they are either
in colorless groups of three so-called baryons (protons, neutrons, etc.) or two-called
mesons (pions, kaons, etc.). However, it is believed that free quarks existed in the
early universe up to 40 microseconds after of the Big Bang. Following this theory,
the universe consisted of a hot gas called Quark and gluon plasma (QGP). The
temperature of this plasma was approximately 100 000 higher than the temperature
of the sun (approximately 100 x 1010 K), it is not known if the quarks are truly elemen-
tary, but if they are, the plasma in the early universe had been formed directly from
the Big Bang and as the universe cooled quarks and antiquarks were coalesscing
into hadrons (baryons and mesons). The fact that quarks has never been observed
is called confinement.
The theory that studies the interactions between quarks and gluons is quantum
chromodynamic and it predicts a transition from color non-conductive to a color con-
ductive hadronic matter plasma of quarks and gluons. The prediction of this phase
transition has given rise to its search for 20 years and study of their properties in
the laboratory. To produce this new state of matter is required a dense system of
high temperature that is reached colliding beams of heavy ions traveling at a speed
close to that of the light. The system created in these collisions passes through
several stages and finally, emitted particles are detected. In them, we try to find
signals of deconfinement. One of the signals that have been studied is the energy
loss suffered by quarks and gluons while traveling through the plasma.
It is predicted that the loss of energy depends on the speed with which the charged
1
2
particle moves inside the plasma. The effect is bigger for quarks and gluons who
travel faster. On the other hand there many indications, known collectively as duality
parton-hadron, hadrons with a high momentum come from partons with much mo-
mentum too. So, the energy loss reflected in a decrease, or even the disappearance
of the particles with large momenta.
Experimental detection of this phenomenon suffers from several complications. The
spectrum of momenta falls exponentially with the momentum, so in a collision there
are many more particles with small momentum than with larger ones. Furthermore
the production of particles is a quantum process so which is subject to fluctuations.
Besides, a similar effect on the spectra of particles measured in the detectors could
have been caused by other means. So, because of the great complexity of the
problem there is not only one signal that by itself determines the formation of QGP,
but it is the union of many signals at different experiments that could give evidence
of it existence.
Spectra of charged particles produced in heavy ion collision experiments located in
the accelerators SPS (Super Proton Synchroton) of CERN (European Organization
for Nuclear Research) and RHIC (Relativistic Heavy Ion Collider) of BNL (Brookhaven
National Laboratory), has been measured. RHIC has observed a suppression of
particles with a lot of transverse momentum with respect to proton - proton. In
the experiment LHC at CERN it is expected that the energy of the collision will be
sufficient to deconfine quarks and gluons, forming a plasma of these fundamental
components of the matter.
In heavy ion collision the observables are compared with the observables measured
in p+ p collisions, so the idea of this work is to use the Monte-Carlo simulation
of p+ p collisions and reconstruction of jets in these events, to study the signs of
desconfinement related to the parton’s intrinsic momentum kT , the transverse mo-
mentum with respect to the jet axis jT and three event shape variables, τ , R and
Tmin, to follow the same analysis in Pb+Pb and compare the two cases. This work
was developed considering the energies of the LHC and the environment of the AL-
ICE detector at the LHC.
The first part of this work is a revision of the current status of the search of the QGP.
In this chapter is explain how to create such plasma in the laboratory, as well as,
signals that are being proposed as a possible indication of formation. Subsequently
are some of the experimental results obtained.
In the second section we worked on simulation and reconstruction of jets and their
modifications due to parton energy loss. Finally we explore the possibility that jT , kT
and three event shape variables, τ , R and Tmin, are used as observable to study the
dense system.
2
Chapter 2
QCD phase diagram and QGP
In quantum chromodynamics (QCD) [17], theory of the strong force, the interac-
tions of hadrons are described in terms of the interaction among the hadronics con-
stituents quarks and gluons (referred as partons). One of the key features of the
theory that has set it, is the property of asymptotic freedom. This term is used to
describe the weakening of effective quark-gluon coupling at short distance.
Based on asymptotic freedom, Collins and Perry [18] suggested that a high tem-
perature or density, matter should be close to ideal gas arguing that in dense matter
constituents are almost always close to each other, and therefore, due to the asymp-
totic freedom, their interaction should be sufficiently weak. This ideal gas was called
quark-gluon plasma (QGP).
The QCD phase diagram, at baryonic density equal to zero, is based on lattice
QCD [19], but for nonzero baryon density it is necessary to interpolate between low-
density hadronic matter, described by low-energy effective theories and high-density
quark-gluon plasma described by perturbative QCD. The result of lattice is shown in
figure 2.1. Near Tc the energy density in units of T 4 changes dramatically by more
than a factor of 10 within a very narrow temperature interval. The critical density of
energy εc is of the order of 1 GeV/f m3 and can be reached heating the matter with
baryonic density zero to temperature of Tc ∼ 170 MeV or compress the nuclear cold
matter to the baryonic density of ρc ∼ 3 -10 ρ0 (where ρ0 = 0.15 f m−3 is the density
of nuclear matter in equilibrium at zero temperature) or by combination of both.
2.1. QGP: Theoretical overview
The deconfinement can be explained in terms similar to the shielding of the electric
force loads. In vacuum, two electric charges interact through the Coulomb potential,
3
2.1. QGP: Theoretical overview 4
  0
  2
  4
  6
  8
 10
 12
 14
 16
100 200 300 400 500 600
T [MeV] 
ε/T
4
εSB/T
4
Tc = (173 +/- 15) MeV 
εc ~ 0.7 GeV/fm
3
 
RHIC  
LHC  
SPS  3 flavour
2 flavour
‘‘2+1-flavour’’
Figure 2.1: Energy density ε as a function of temperature, obtained by numer-
ical evaluation of lattice QCD. ε is divided by T4 to show the sudden increase,
which occurs when the temperature is about 170 MeV (Tc). This behaviour is
typical of phase transition [20].
V0(r) =
(
e2
0
r
)
(2.1)
where r denotes the distance between them. In a dense environment of many other
charges, the potential becomes screened,
V (r) =
(
e2
0
r
)
exp(−µr) (2.2)
where rD = µ−1 is the Debye screening radius of the medium; it decreases as
the charge density of the medium increases. Thus the potential between two test
charges a fixed distance apart becomes weaker with increasing density. This occurs
because the other charges in the medium partially neutralize the test charges and
thereby shorten the range of the interaction.
If a bound state, such as a hydrogen atom, is put into such a medium, the screening
radius rD will for sufficiently high density become less than the binding radius of
the atom. The effective force between proton and electron has become so short-
ranged that the two can no longer bind. Thus insulating matter, consisting of bound
4
2.1. QGP: Theoretical overview 5
electric charges, will at sufficiently high density become conducting: it will undergo a
phase transition, in which charge screening dissolves the binding of the constituents,
leading to a plasma of unbound charges as a new state of matter.
The interaction of quarks in QCD is based on their intrinsic color charge, and in a
dense medium this charge can be screened in much the same way as an electric
charge. Hadrons are color-neutral bound states of colored quarks; hence dilute
hadronic matter is a color insulator. At sufficiently high density, however, we expect
color screening to set in, so that the potential
V0(r) ∼ σr, (2.3)
becomes screened
V (r) ≃ σr
[
1− exp(−µr)
µr
]
(2.4)
as above. The color screening mass µ here is also the inverse of the screening
radius for color charges. The resulting exponential damping of the binding force will
remove all long range effects and in a sufficiently dense medium ‘melt’ hadrons just
as Debye screening dissociated hydrogen atoms. Color screening will thus trans-
form a color insulator into a color conductor, turning hadronic matter into a quark
plasma. The transition from insulator to conductor by charge screening is a collec-
tive effect, so that we expect a phase transition at the point of plasma formation.
When the atomic matter is transformed from an insulator into a conductor, the ef-
fective mass of the conduction electrons is changed. In insulators, the electrons
occur with their physical mass; in the conducting phase, however, they acquire a
different, effective mass, due to the presence of the other conducting electrons, the
periodic field of the charged ions and the lattice vibrations. All these effects combine
to produce a mean background field quite different from the vacuum. As a result, the
insulator-conductor transition is accompanied by a mass shift for the electrons. Sim-
ilarly, the effective quark mass is expected to change between the confined and the
deconfined phase. When confined in hadrons, the basic quarks ‘dress’ themselves
with gluons to acquire an effective constituent quark mass of about 300 MeV (1/3 of
the proton or 1/2 of the ρ-meson mass). On the other hand, the basic bare quarks in
the QCD Lagrangian are almost massless, so that the mass of the constituent quarks
in the confined phase must be generated spontaneously through the confinement in-
teraction. Hence it is likely that when deconfinement occurs, this additional mass is
‘lost’ and the quarks revert to their intrinsic ‘bare’ mass
A Lagrangian with massless fermions (limiting case of the light up and down quarks
5
2.1. QGP: Theoretical overview 6
in the physical Lagrangian) possesses chiral symmetry; this allows a decomposi-
tion of the quarks into independent left- and right-handed massless spin one-half
states, which for massive fermions become mixed. For massless quarks, confine-
ment must thus lead to spontaneous breaking of chiral symmetry, deconfinement to
its restoration. Hence the mass shift transition in QCD is often referred to as chiral
symmetry restoration. It can, but does not need to coincide with deconfinement:
when the hadrons are dissolved into quark constituents, the liberated and hence
now coloured quarks may still interact to form coloured bound states. Thus at low
temperature and high density, the quark triplets in nucleons, once deconfined, might
choose to recombine into massive coloured quark pairs, similar to Cooper pairs in
QED. When the density is increased further, the diquarks would break up into the
massless basic quarks. This results in a three-phase picture of strongly interact-
ing matter, with hadronic matter as confined phase, then deconfinement, followed
by a phase consisting of massive coloured diquark systems, and finally, after chiral
symmetry restoration, a plasma of coloured massless quarks and gluons. Such a
three-phase structure would correspond to the succession of insulator, supercon-
ductor and conductor in atomic matter.
The transition from hadronic matter to quark-gluon plasma can be illustrated in a
simple model. For an ideal gas of massless pions, the pressure as function of the
temperature is given by the Stefan-Boltzmann form
Pπ = 3
π2
90
T 4 (2.5)
where the factor 3 accounts for the three charge states of the pion. The correspond-
ing form for an ideal quark-gluon plasma with two flavours and three colours is
Pqg = {2×8+
7
8
(3×2×2×2)}π2
90
T 4 −B = 37
π2
90
T 4 −B. (2.6)
In equation 2.6, the first temperature term in the curly brackets accounts for the
two spin and eight colour degrees of freedom of the gluons, the second for the
three colour, two flavour, two spin and two particle-antiparticle degrees of freedom
of the quarks, with 7/8 to obtain the correct statistics. The bag pressure B takes
into account the difference between the physical vacuum and the ground state for
quarks and gluons in a medium.
This simple model thus leads to a two-phase picture of strongly interacting matter,
with a hadronic phase up to
6
2.1. QGP: Theoretical overview 7
Tc =
(
45
17π2
)1/4
B1/4 ≃ 0.72 B1/4 (2.7)
and a quark gluon plasma above this critical temperature. From hadron spec-
troscopy, the bag pressure is given by B1/4 ≃ 0.2 GeV, so that we obtain
Tc ≃ 145 MeV (2.8)
as the deconfinement temperature. This simple estimate is close to the value ob-
tained in lattice QCD.
The energy densities of the two phases of our model are given by
επ =
π2
10
T 4 (2.9)
and
εqg = 37
π2
30
T 4 +B (2.10)
From strong interaction thermodynamics, based on QCD as the input dynamics, the
Lagrangian is defined
L = −1
4
Fa
µν Fµν
a − ∑
f
ψ̄ f
α (iγµ∂µ +m f −gγµAµ)
αβ ψ f
β , (2.11)
with
Fa
µν = (∂µAa
ν −∂ν Aa
µ −g f a
bcAb
µAc
ν ) (2.12)
Here Aa
µ denotes the gluon field of colour a (a=1,2,...,8) and ψ f
α the quark field of
colour α (α=1,2,3) and flavour f ; the input (‘bare’) quark masses are given by m f .
With the dynamics thus determined, the corresponding thermodynamics is obtained
from the partition function, which is most suitably expressed as a functional path
integral,
Z(T,V ) =
∫
dA dψ dψ̄ exp
(
−
∫
V
d3x
∫ 1/T
0
dτ L (A,ψ, ψ̄)
)
(2.13)
7
2.1. QGP: Theoretical overview 8
since this form involves directly the Lagrangian density defining the theory. The
spatial integration in the exponent of equation 2.13 is performed over the entire
spatial volume V of the system; in the thermodynamic limit it becomes infinite. The
time component x0 is ’rotated’ to become purely imaginary, τ = ix0, thus turning
the Minkowski manifold, on which the fields A and ψ are originally defined, into a
Euclidean space. The integration over τ in equation 2.13 runs over a finite slice
whose thickness is determined by the temperature of the system.
From Z(T,V ), all thermodynamical observables can be calculated in the usual form.
Thus
ε = (T 2/V )
(
∂ lnZ
∂T
)
V
(2.14)
gives the energy density, and
P = T
(
∂ lnZ
∂V
)
T
(2.15)
the pressure. For the study of critical behaviour, long range correlations and multi-
particle interactions are of crucial importance; hence perturbation theory cannot be
used. The necessary non-perturbative regularization scheme is provided by the
lattice formulation of QCD; it leads to a form which can be evaluated numerically by
computer simulation. The first variable to consider is the deconfinement measure
given by the Polyakov loop
L(T )∼ lim
r→∞
exp{−V (r)/T} (2.16)
where V (r) is the potential between a static quark-antiquark pair separated by a dis-
tance r. In the limit of large input quark mass, V (∞) = ∞ in the confined phase, so
that then L = 0. Colour screening, on the other hand, makes V (r) finite at large r,
so that in the deconfined phase, L does not vanish. It thus becomes an ‘order pa-
rameter’ like the magnetization in the Ising model; this is zero at high temperatures,
but becomes non-zero below the Curie point, when the ‘up-down’ Z2 symmetry of
the Ising Hamiltonian is spontaneously broken. In the large quark mass limit, QCD
reduces to pure SU(3) gauge theory, which is invariant under a global Z3 symmetry.
The Polyakov loop provides a measure of the state of the system under this symme-
try: it vanishes for Z3 symmetric states and becomes finite when Z3 is spontaneously
broken. Hence the critical behaviour of the Ising model (and more generally, ZN spin
systems) as well as that of SU(N) gauge theories is based on the spontaneous
symmetry breaking of a global ZN symmetry.
8
2.1. QGP: Theoretical overview 9
For finite quark mass mq, V (r) remains finite for r → ∞, since the ‘string’ between
the two colour charges ‘breaks’ when the corresponding potential energy becomes
equal to the mass Mh of the lowest hadron; beyond this point, it becomes energet-
ically more favourable to produce an additional hadron. Hence now L no longer
vanishes in the confined phase, but only becomes exponentially small there,
L(T )∼ exp{−Mh/T} (2.17)
here Mh is of the order of the ρ-mass, so that L ∼ 10−2, rather than zero. Decon-
finement is thus indeed much like the insulator-conductor transition, for which the
order parameter, the conductivity σ(T ), also does not really vanish for T > 0, but
with σ(T ) ∼ exp{−∆E/T} is only exponentially small, since thermal ionization (with
ionization energy ∆E) produces a small number of unbound electrons even in the
insulator phase.
Figure 2.2 (left) shows lattice results for L(T ) and the corresponding susceptibility
χL(T )∼
〈
L2
〉
−〈L〉2. The calculations were performed for the case of two flavours of
light quarks, using a current quark mass about four times larger than that needed for
the physical pion mass. We note that L(T ) undergoes the expected sudden increase
from a small confinement to a much larger deconfinement value. The sharp peak of
χL(T ) defines quite well the transition temperature Tc, which we shall shortly specify
in physical units.
The next quantity to consider is the effective quark mass; it is measured by the
expectation value of the corresponding term in the Lagrangian, 〈ψ̄ψ〉(T ). In the
limit of vanishing current quark mass, the Lagrangian becomes chirally symmetric
and 〈ψ̄ψ〉(T ) the corresponding order parameter. In the confined phase, with effec-
tive constituent quark masses Mq ≃ 0.3 GeV, this chiral symmetry is spontaneously
broken, while in the deconfined phase, at high enough temperature, we expect its
restoration. In the real world, with finite pion and hence finite current quark mass,
this symmetry is also only approximate, since 〈ψ̄ψ〉(T ) now never vanishes at finite
T .
The behaviour of 〈ψ̄ψ〉(T ) and the corresponding susceptibility χm ∼ ∂ 〈ψ̄ψ〉/∂mq
are shown in figure 2.2 (right), calculated for the same case as above in figure 2.2
(left). Here the expected sudden drop of the effective quark mass and the associ-
ated sharp peak in the susceptibility. The temperature at which this occurs coincides
with that obtained through the deconfinement measure. We therefore conclude that
at vanishing baryon number density, quark deconfinement and the shift from con-
stituent to current quark mass coincide.
Next we turn to the behaviour of energy density ε and pressure P at deconfinement.
In figure 2.2 (bottom) it is seen that ε/T 4 changes quite abruptly at the above de-
termined critical temperature T = Tc, increasing from a low hadronic value to nearly
9
2.1. QGP: Theoretical overview 10
Figure 2.2: The temperature dependence of the Polyakov loop and the asso-
ciated susceptibility in two-flavour QCD (left) and the temperature dependence
of the chiral condensate, the associated susceptibility in two-flavour QCD (right)
and the temperature dependence of energy density and pressure in two-flavour
QCD (bottom)
10
2.2. QGP: Experimental study 11
that expected for an ideal gas of quarks and gluons. Besides the sudden increase
at deconfinement, there are two further points to note. In the region Tc < T < 2 Tc, ε
and 3P do not yet coincide, as also found in the simple model of the previous section;
much of the difference is presumably due to the difference between physical vacuum
and QCD in-medium ground state. Furthermore the thermodynamic observables do
not quite reach their Stefan-Boltzmann values (marked ’SB’ in figure 2.2 bottom)
even at very high temperatures. These deviations from ideal gas behaviour can be
expressed to a large extent in terms of effective ‘thermal’ masses mth of quarks and
gluons, with mth ∼ gT .
Finally we turn to the value of the transition temperature. Since QCD (in the limit
of massless quarks) does not contain any dimensional parameters, Tc can only be
obtained in physical units by expressing it in terms of some other known observable
which can also be calculated on the lattice, such as the ρ-mass, the proton mass, or
the string tension. In the continuum limit, all different ways should lead to the same
result. Within the present accuracy, they define the uncertainty so far still inherent in
the lattice evaluation of QCD. Using the ρ-mass to fix the scale leads to Tc≃0.15 GeV,
while the string tension still allows values as large as Tc≃0.20GeV. This means that
energy densities of some 1 - 2 GeV/f m3 are needed in order to produce a medium
of deconfined quarks and gluons [21].
2.2. QGP: Experimental study
The predictions made by QCD have led to the production and study of the quark-
gluon plasma in the laboratory. The idea to produce this state of matter experimen-
tally is colliding heavy nuclei with a speed approaching that of light, to increase the
energy density in the medium above the energy of deconfinement
When the nuclei travel at a speed close to speed of light, they suffer a Lorentz
contraction in the direction of movement so in the center of mass reference frame
the collision looks like the collisions of two almost flat nucleons. When the impact
parameter of the collision b, i.e., the distance between the centers of the two nuclei,
is small, we call the collision central and when is large, peripheral. It is expected
that central collisions are those that generate higher energy density and therefore
are candidates for the formation of QGP.
When two nucleons hits, each nucleon may scatter several times and the liber-
ated partons from different nucleon-nucleon collisions rescatter with others before
hadronization. This features change the particle prediction per participating nucleon
but the rescattering process leads to a state of local thermal equilibrium, by redis-
tibuting the energy lost by beam into the statistically most probable configurations.
This rescattering is the thermodynamics pressure acting against the outside vac-
uum which cause the expansion of the reaction zone. The expansion cools and
11
2.2. QGP: Experimental study 12
Figure 2.3: Space-time diagram of longitudinal evolution of the quark-gluon plasma
dilutes the fireball below the critical energy density of the quark-hadron transition, at
which point hadrons are formed from the quarks and gluons (hadronization). Fur-
ther interactions between these hadrons cease once their average distance exceeds
the range of strong interactions, this last phase is called the thermal equilibrium.
Finally these hadrons are detected experimentally. Thus, the temporal evolution
of the system which is formed by the collision can be separated into 4 stages: a
pre-equilibrium, followed by the formation of plasma, then hadronization and finally
thermal equilibrium. This process is shown in the space-time diagram in Figure 2.3.
To estimate the energy density, Bjorken [22] modeled the expansion process as-
suming that the finally observed hadrons have emerged from an initial interaction
volume in free flow i.e., without any collective motion. The resulting initial energy
density in an Au+Au collision is
ε0 =
p0
πR2
Aτ0
(
dNh
dy
)AA
y=0 (2.18)
where p0 denotes the average (local) energy of the emitted secondaries and (dNh/dy)
their multiplicity. The initial interaction volume is determined by the transverse size
RA and the longitudinal extension as obtained from the formalization time τ0, which
is generally taken to be about 1 fm.
For Au+Au collisions
12
2.2. QGP: Experimental study 13
(
dNh
dy
)AA
y=0 = A0.48ln
√
s
2m
(2.19)
then, the initial density is
ε0 =
p0
4
A0.48ln
√
s
2m
[GeV/f m3] (2.20)
If the particles produced are pions p0 = 0.5 GeV. ε0 for different experiments are
shown in table 2.1.
Machine Start Type Beam
√
s εAB
0
[GeV/A] [GeV/fm3]
BNL-AGS 1986 Fixed Target 28Si 5 0.7
CERN-SPS 1986 Fixed Target 16O,32 S 19 1.6
BNL-AGS 1992 Fixed Target 197Au 5 1.5
CERN-SPS 1994 Fixed Target 208Pb 17 3.7
BNL-RHIC 2000 Collider 197Au 200 7.6
CERN-LHC 2010 Collider 208Pb 2760 12.8
Table 2.1: Experimental facilities for high energy nuclear collisions
The experimental investigation of the quark-gluon plasma requires selection of ap-
propriate signals related to its formation. A problem present in the study of this new
state of matter is that the size and lifetime is very short, just few fermis of diameter
and 5 to 10 fm/c of duration, so it is impossible to detect it directly macroscopically.
Besides, plasma signals compete with the signals emitted by the hadron gas and
can be modified by that stage. Despite this, large number of ideas to identify and
study their formation have been proposed
Kinematics probes
The basic concept behind these is the determination of energy density ε, pressure P
and the entropy s as a function of temperature T and baryonic chemical potential µB.
Some observations related to these quantities are average transverse momentum
〈pT 〉 and the distribution of particles or energy as a function of pseudorapidity dN/dη
and dE/dη respectively. In these cases you want to see that the system reached
13
2.2. QGP: Experimental study 14
thermodynamic equilibrium and attempts to extract parameters of its equation of
state.
Also interferometric correlations between particles identities are of interest to study
the size of the system created. For example ππ and KK provide information of
the space-time dynamics of nuclear collisions. Studying correlation between two
particles at different points in space phase, it is possible to obtain information on
size, time life and the flow of plasma until hadronization.
Electromagnetics probes
The most direct signals are those produced by the direct photons, that is, the pho-
tons that are not produced by the decay of hadrons after thermal equilibrium. Since
photons do not feel any strong interaction, because they have no color charge, they
escape the medium without interacting with it. These photons are emitted through
the expansion of plasma and its production is expected to be principally in the initial
hot and dense states. Unfortunately, direct photons are rare, and the photons pro-
duced after thermal equilibrium are many. However, it is predicted that the spectrum
of direct photons is much harder than the photons coming from decays so, their
presence could be measured.
Deconfinement probes
Strangeness was one of the first proposed signatures of the deconfined phase. The
mass of strange quarks and antiquarks is of the same magnitude as the temperature
Tc other hadrons are expected to disolve into quarks. The dominant mechanism
for cooking up strangeness in quark-gluon deconfined matter was found to be the
gluon-fusion reaction gg−→ ss. The strange particles decay into lighter quarks, thus,
strageness-carrying hadrons decay by weak interactions that occur, in general, on a
time scale that is extremely long compared with nuclear-collision times. This make
it relatively easy to detect the strange particle through the tracks left by their decay
products.
Other particles formed in the plasma are hadrons with charm quarks c. Since the
charm quark is about ten times heavier than the strange quark, pairs of charm
quarks can be formed only during the very early stages of the collision, as the nuclei
begin to penetrate each other. At this early stage the colliding particles have the
energy to overcome the high energy threshold. If the QGP phase is formed, these
charmed quark have less chance of forming charmonium states, because the gluons
present within the plasma hinder their binding, or/and break the bound states.
Matsui and Satz suggested that due to the high gluonic density resulting from color
deconfinement, it is posible to produce a potential interactions screening between
14
2.2. QGP: Experimental study 15
pairs of quarks c y c produced during the initial collisions of the nuclei, preventing the
formation of states (cc) J/ψ, ψ’, χc. However, these quarks c, can find other quarks
to form different hadrons with open charm (cq and cq). This leads to the suppression
in the production of bound states weakly bounded , ψ ′ and χc and strongly bound
J/ψ [23].
Parton energy loss
One more of the existing proposals to detect the creation of quark-gluon plasma is
parton energy loss. In 1982 Bjorken [3] suggested that partons traveling with high
speed in the quark-gluon plasma, could lose large amounts of energy by elastic col-
lisions with plasma components. Gyulassy, Plümer and X.N. Wang [4] identified loss
of radiation due to the jet suppression incorporating Landau-Pomeranchuk-Migdal
interface effect. Subsequently Baier, Dokshitzer, Mueller, Peigné and Schiff [5] stud-
ied radiative parton energy loss where multiple parton scattering was modeled by a
screened Coulomb potential. The predictions for this energy loss were improved by
Gyulassy, Levai, Vitev [6] and Wiedemann [7] considering finite opacity.
A simple estimation can be given by the thermal averaged energy transfer νel ≃
q2
T/2ω of the jet parton to a thermal parton with energy ω, qT being the transverse
momentum transfer of the elastic scattering. The resulting energy loss
dEel
dx
=C2
3πα2
s
2
T 2ln
3ET
2µ2
(2.21)
is sensitive to the temperature of the thermal medium but is small compared to
radiative energy loss. Here µ is the Debay screening mass and C2 is the Casimir
factor of the parton.
The radiative parton energy loss in the plasm of size L is estimated as
dErad
dx
=C2
αsµ2
4
L
λ
ln
3E
µL
(2.22)
where λ is the gluon’s mean free-path in the medium. Using this result one can
estimate the total energy loss for a parton with initial energy E = 40 GeV to be about
∆E ≃ 10 GeV after it propagates a distance L = 6 fm in a medium with µ = 0.5
GeV and λ = 1 fm.
This leads to a significant dependence of energy loss ∆E of the fast parton. With
these results improvements can maintain hope that the loss of energy can serve
as quantitative test of the density and temporal evolution of the quark-gluon plasma
created in heavy ions collisions.
15
Chapter 3
Experimental programs
Dedicated programs to create and study the QGP phase have started in early eight-
ies with collisions of heavy-ions at relativistic energies. The search and study of
QGP started first with the Au beam at 1 A.GeV at the Bevalac in Berkeley. The next
milestone came with the acceleration of Au beam at 11.7 AGeV at the BNL-AGS and
Pb beam at 158 A.GeV at the CERN-SPS. First hints of the formation of a new state
of matter has been obtained from the SPS data [24]. The Relativistic Heavy Ion Col-
lider (RHIC) started becoming operational in the year 2000 with Au+Au collisions at√
sNN = 130 GeV and soon after to top Au+Au energies of
√
sNN = 200 GeV [25].
The RHIC experiments bring out highest quality data from p+ p, d+Au, Cu+Cu and
Au+Au at various energies, strong evidence for the production of extreme hot and
dense matter has been seen. RHIC results, in combination with the ones from
AGS and SPS , have enhanced our understandings of the QCD matter at different
temperatures and densities. In October 1990 was proposed the Large Hadron Col-
lider (LHC), emphasized the idea of providing p+ p collisions as well as heavy-ions
[26].
3.1. Relativistic Heavy Ion Collider
The Relativistic Heavy Ion Collider (RHIC) was built to create and investigate strongly
interacting matter. There are four heavy-ion experiments at RHIC which have studied
Au+Au collisions at three center-of-mass energies:
√
sNN = 62.4, 130 and 200 GeV,
the experiments are: BRAHMS (Broad Range Hadron Magnetic Spectrometers Ex-
periment at RHIC), PHOBOS, PHENIX (Pioneering High Energy Nuclear Interaction
Experiment) and STAR (Solenoidal Tracker at RHIC).
The results from the four RHIC experiments demonstrated the capability to reach
extreme conditions during the early stages of nucleus-nucleus collisions, forming
matter that exhibits heretofore unobserved behavior. In particular, evidence for jet
energy loss has been reported: the suppression in the nuclear modification factor
16
3.1. Relativistic Heavy Ion Collider 17
for central Au+Au events RAA, away-side correlations in central Au+Au collisions
compared to p+ p collisions
Figure 3.1 and figure 3.2 show the most significant high pT measurements made at
RHIC. Both figures incorporate measurements of p+ p, d+Au and centrality selected
Au+Au collisions at
√
sNN = 200 GeV, where p+ p and d +Au systems providing
benchmarks for phenomena seen in the more complex Au+Au collisions.
Figure 3.1 shows the nuclear modification factor, RAB, defined as the ratio of the
inclusive momentum spectrum of charged hadrons yields in A+B (either Au+Au or
d +Au) events to a p+ p reference spectrum, scaled to account for the nuclear geo-
metry effects via < Nbin >. The calculated mean number of binary nucleon-nucleon
collisions contributing to each A+B centrality bin:
RAB =
dNAB/dηd2 pT
TABdσNN/dηd2 pT
. (3.1)
where the overlap integral TAB =< Nbin > /σ pp
inelastic.
High-pT hadrons in central Au+Au collisions are suppressed by a factor ∼ 5 relative
to naive (binary scaling) expectations. Conventional nuclear effects, such as nuclear
shadowing of the parton distribution functions and initial state multiple scattering,
cannot account for the suppression. Furthermore, the suppression is not seen in
d +Au but is unique to Au+Au collisions, proving experimentally that it results not
from nuclear effects in the initial state (such as gluon saturation), but rather from the
final state interaction of hard scattered partons or their fragmentation products in the
dense medium generated in Au+Au collisions [27, 28, 29, 8].
This dominant final state interaction in Au+Au is presumably superimposed on a
variety of interesting initial-state effects revealed by the d +Au. The enhancement
seen in figure 3.1 in RdAu for moderate pT and mid-rapidity, known as the Cronin
effect [32], is generally attributed [33, 34, 35] to the influence of multiple parton
scattering through cold nuclear matter prior to the hard scattering that produces the
observed high-pT hadron.
Figure 3.2 shows STAR measurements of correlations between high pT hadrons. The
top panel shows the azimuthal distribution of hadrons with pT>2 GeV/c relative to a
trigger hadron with ptrig
T >4 GeV/c. A hadron pair drawn from a single jet will generate
an enhanced correlation at ∆φ ≈ 0, as observed for p+ p, d +Au and Au+Au. A
hadron pair drawn from back-to-back dijets will generate an enhanced correlation
at ∆φ≈ π, as observed for p+ p and for d +Au with somewhat broader width than
the near-side correlation peak. However, the back-to-back dihadron correlation is
absent in central Au+Au collisions, while for peripheral Au+Au collisions the corre-
17
3.1. Relativistic Heavy Ion Collider 18
lation appears quite similar to that seen in p+ p and d +Au. If the correlation is
indeed the result of jet fragmentation, the suppression is again due to the final state
interaction of hard-scattered partons or their fragmentation products in the dense
medium generated in Au+Au collisions [8]. In this environment, the hard hadrons
we do see (and hence, the near-side correlation peak) would arise preferentially
from partons scattered outward from the surface region of the collision zone, while
the away-side partons must burrow through significant lengths of dense matter.
A more differential probe of partonic energy loss is the measurement of high pT di-
hadron correlations relative to the reaction plane orientation. The bottom panel of
figure 3.2 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’) [31]. The same-side dihadron correlation in both cases is similar to that
in p+ p collisions. In contrast, the suppression of the back-to-back correlation de-
pends 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 dijet oriented out of the reaction plane is longer
than in the reaction plane, leading to correspondingly larger energy loss. The de-
pendence of parton energy loss on path length is predicted linear. The orientation
dependence of the energy loss should be further affected by different rates of matter
expansion in-plane vs. out-of-plane.
While large effects of energy loss in dense matter have been observed, precision
data in a larger pT range are needed to fully explore this phenomena and their con-
nection to properties of the dense matter. The region 2< pT < 6 GeV/c has significant
contributions from non-perturbative processes other than vacuum fragmentation of
partons, perhaps revealing novel hadronization mechanisms. Most studies to date of
azimuthal anisotropies and correlations of jets have by necessity been constrained
to this region, with only the inclusive spectra extending to the range where hard scat-
tering is expected to dominate the inclusive yield. High statistics data sets for much
higher pT hadrons are needed to fully exploit azimuthal asymmetries and correla-
tions as measurements of partonic energy loss. Dihadron measurements probing
the details of the fragmentation process may be sensitive to the energy density, in
addition to the gluon density that is probed with the present measurements.
18
3.1. Relativistic Heavy Ion Collider 19
 [GeV/c]
T
p
1 2 3 4 5
N
u
cl
ea
r 
M
o
d
if
ic
at
io
n
 F
ac
to
r
0.5
1
1.5
d+Au (MB)
Au+Au (0-10%)
=0η
 (GeV/c)Tp
0 1 2 3 4 5 6 7 8 9 10
R
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
=200 GeVNNs
neutral pions 
 - dAu min. bias (PbGl)
dA
R
 - dAu min. bias (PbSc)
dA
R
 - AuAu 0-10% centralAAR
0.5
1
1.5
2
70-100%
0 2 4
0
0.5
1
1.5
20-40%
40-70%
2 4 6
0-20%
d
A
u
R
 (GeV/c)
T
p
0 2
 (GeV/c)Tp
4 6 8 10
0
0.5
1
1.5
2
d+Au FTPC-Au 0-20%
d+Au Minimum Bias
 
T
/c)
Au+Au Central
R
A
B
 (
p
T
)
Figure 3.1: Binary-scaled ratio RAB of charged hadron and π0 inclusive yields
from
√
sNN = 200 GeV Au+Au and d +Au relative to that from p+ p collisions,
from BRAHMS [27] (upper left), PHENIX [28] (upper right), PHOBOS [29] (lower
left) and STAR [8] (lower right). The PHOBOS data points in the lower left frame
are for d +Au, while the solid curve represents PHOBOS central (0-6%) Au+
Au data. The shaded horizontal bands around unity represent the systematic
uncertainties in the binary scaling corrections.
19
3.1. Relativistic Heavy Ion Collider 20
 (radians)φ ∆
-1 0 1 2 3 4
)φ 
∆
 d
N
/d
(
T
R
IG
G
E
R
1
/N
0
0.1
0.2
d+Au FTPC-Au 0-20%
p+p min. bias
Au+Au Central
)φ∆
 d
N
/d
(
T
ri
g
g
e
r
1
/N
 (radians)φ∆
-1 0 2
)-
fl
o
w
  
  
φ
∆
 d
N
/d
(
tr
ig
g
e
r
1
/N 0
0.1
0.2
 p+p
 Au+Au, in-plane
 Au+Au, out-of-plane
1 3 4
{STAR
 data
Figure 3.2: Dihadron azimuthal correlations at high pT . Top panel shows corre-
lations for p+ p, central d +Au and central Au+Au collisions (background sub-
tracted) from STAR [8, 30]. Bottom panel shows the background-subtracted high
pT dihadron correlation for different orientations of the trigger hadron relative to
the Au+Au reaction plane [31].
20
3.2. Large Hadron Collider 21
3.2. Large Hadron Collider
The Large Hadron Collider (LHC) is designed to deliver colliding p+ p beams at
center-of-mass energies of 14 TeV and Pb + Pb beams at
√
sNN = 5.5 TeV. The
p+ p collisions offer the possibility of discovering the Higgs Boson, the missing link
in the standard model and the aim of the heavy-ion physics program is to study QGP.
In the CERN accelerator complex (see figure 3.3), the ions pass into the Low Energy
Ion Ring (LEIR), then proceed to the PS, the SPS and finally to the LHC.
Figure 3.3: The CERN accelerator complex. The ions pass through the LEIR,
then to the PS, the SPS and finally to the LHC.
The typical expected yearly running times of LHC are of the order of 107 seconds for
p+ p collisions and 106 seconds for heavier systems. Table 3.2 gives the center-of-
mass energy and expected luminosity at LHC for some typical collision systems. Due
to the limited rate capability of the ALICE detector, the luminosity for p+ p collisions
will be limited to a maximum of 1031cm−2s−1.
A comparison of some of the basic parameters measured at the SPS and RHIC with
expected values for the LHC are given in table 3.2. The table lists the pseudorapid-
ity density of charged particles (dNch/dη ), formation time of QGP (τ0), the energy
density (ε) for τ0 = 1, the initial temperature in terms of the critical temperature (Tc),
QGP life time (τQGP) and the freezeout time (τ f ) for the top center-of-mass ener-
gies (
√
sNN) of these accelerators. At the LHC, with the increase of beam energy
to about 28 times more compared to that of RHIC, the number of charged particles
from the produced fireball increase by more than three times, the formation time of
the QGP decreases significantly, the matter becomes much hotter, denser and long
lived. All these conditions are conducive to opening up new physics domain at the
LHC.
21
3.2. Large Hadron Collider 22
System
√
sNN(TeV) L0(cm−2s−1) σgeom(b)
p+ p 14.0 1034 0.1
Pb+Pb 5.5 1027 7.7
p+Pb 8.8 1029 1.9
Ar+Ar 6.3 1029 2.7
Table 3.1: Luminosities expected for different collision systems with different
center-of-mass energies [36].
Condition SPS RHIC LHC
√
sNN (GeV) 17.3 200 5500
dNch/dη 450 600 1200−4000
τ0 (fm/c) ∼1 ∼0.2 ∼0.1
ε(GeV/fm3) 2.5 4-5 10-40
T/Tc 1.1 1.9 3−4
τQGP (fm/c) ∼1 2−4 >4
τ f (fm/c) ∼10 ∼20 ∼30
Table 3.2: Conditions created in central heavy-ion collisions at the top energies
of SPS , RHIC and projections for LHC.
The ALICE (A Large Ion Collider Experiment) experiment at the LHC is designed
specifically for heavy-ion physics [1, 2]. The other two major experiments, ATLAS and
CMS, also have heavy ion programs [37, 38]. Both of these experiments will focus
more on jets, photons and muon channels.
3.2.1. The ALICE experiment
ALICE (A Large Ion Collider Experiment) shown in figure 3.4, is a general-purpose
heavy-ion detector focuses on QCD, the strong-interaction sector of the Standard
Model. It is designed to address the physics of strongly interacting matter and
the quark-gluon plasma at extreme values of energy density and temperature in
nucleus-nucleus collisions. Besides running with Pb ions, the physics program
includes collisions with lighter ions, lower energy running and dedicated proton-
nucleus runs. ALICE will also take data with proton beams at the top LHC energy to
collect reference data for the heavy-ion programme and to address several QCD top-
22
3.2. Large Hadron Collider 23
Figure 3.4: Longitudinal view of the ALICE detector.
ics for which ALICE is complementary to the other LHC detectors [39, 40, 41]. The
ALICE detector has been built by a collaboration including currently over 1000 physi-
cists and engineers from 105 institutes in 30 countries. Its overall dimensions are 16
x 16 x 26 m3 with a total weight of approximately 10 000 t. The experiment consists
of 18 different detector systems each with its own specific technology choice and
design constraints, driven both by the physics requirements and the experimental
conditions expected at LHC. The most stringent design constraint is to cope with the
extreme particle multiplicity anticipated in central Pb+Pb collisions. The different
subsystems were optimized to provide high-momentum resolution as well as excel-
lent Particle Identification (PID) over a broad range in momentum, up to the highest
multiplicities predicted for LHC. This will allow for comprehensive studies of hadrons,
electrons, muons, and photons produced in the collision of heavy nuclei.
The detector setup can be broadly described by three groups of detectors: the for-
ward detectors, the muon spectrometer and the central barrel.
The forward detectors
The ALICE experiment is equipped with a set of forward detectors, such as the a For-
ward Multiplicity Detector (FMD), Photon Multiplicity Detector (PMD), Zero Degree
23
3.2. Large Hadron Collider 24
Calorimeters (ZDC), and detectors for trigger and timing (V0, T0). The FMD, consist-
ing of several rings of silicon detectors, covers a very large range in pseudo-rapidity
(-3.4 < η < -1.7 and 1.7 < η < 5.0). The main function of FMD is to provide charged-
particle multiplicity information. The V0 detector consists of two arrays (each array
with 32 segments) of scintillator counters, called V0A and V0C, which are installed
on both sides of the ALICE interaction point. With a time resolution of about 600ps
the detector provides minimum-bias triggers for in p+ p and Pb+Pb collisions. V0
detector helps in monitoring of the beam luminosity and reducing the beam-gas
contributions.
The T0 detector consists of two arrays of Čerenkov counters (12 counters per array)
and has an excellent time resolution (about 50ps). The main purpose of T0 detector
is to provide start time (T0) for the TOF detector. T0 detector also measures the
vertex position and performs several trigger related functions.The Photon Multiplicity
Detector (PMD) measures the multiplicity and spatial distribution of photons event-
by-event in the region 2.3 < η < 3.7. It consists of two planes of gas proportional
counters with cellular honeycomb structure, preceded by two lead converter plates
of 3 radiation lengths each. Two sets of two compact calorimeters each will be
used to measure and trigger on the impact parameter of the collision (Zero Degree
Calorimeter ZDC). They are made of tungsten (neutron calorimeters, ZN) and brass
(proton calorimeters, ZP) with embedded quartz fibres, and located on both sides in
the machine tunnel, about 116m from the interaction region. In addition, two small
electromagnetic calorimeters (ZEM) are installed on one side, 7 m from the vertex,
to improve the centrality selection.
The muon spectrometer
The forward muon arm is primarily designed to measure the production of heavy
quarkonia (J/ψ,ψ′,ϒ,ϒ′,ϒ′′) via their decay in the µ+µ− channel. The spectrometer
acceptance covers the pseudorapidity interval 2 ≤ η ≤ 4 and the resonances can be
detected down to zero transverse momentum. The invariant mass resolution is of
the order of 70 MeV in the J/ψ region. The spectrometer consists of a front absorber
(∼ 10λint) which absorbs hadrons and photons from the interaction vertex, a large
dipole magnet, a highly granular tracking system and a trigger system placed behind
a passive muon filter wall.
The central barrel
The central barrel consists of the Inner Tracking System (ITS), Time Projection
Chamber (TPC), Transition Radiation Detector (TRD), the Time of Flight (TOF) de-
tector and the electromagnetic calorimeter. The design goal is to have low material
budget and low magnetic field (B≤ 0.5 T ) in order to be sensitive to low-pT particles.
24
3.2. Large Hadron Collider 25
The ITS consists of six layers of silicon detectors. The two innermost layers consist
of silicon pixel detectors (which covers up to the |η |< 1.98), followed by two layers of
silicon drift detectors and the last two outer layers are of silicon strip detectors. The
ITS is designed to handle the high particle density expected in Pb+Pb collisions.
The main uses of ITS will be to (i) determine the primary vertex of the collision, (ii)
localize the secondary vertices for decays of hyperons and D and B mesons, (iii)
track and identify particles with momentum below 200 MeV/c, (iv) improve the track-
ing in the central barrel and (v) provide minimum bias and high multiplicity triggers.
The TPC is the main tracking detector of ALICE. It is cylindrical in shape. The active
volume has an inner radius of 85 cm, an outer radius of 250 cm, and an overall length
along the beam direction of 500 cm. With this the coverage of TPC becomes |η | <
0.9. The TPC is made of a large cylindrical field cage, filled with 90 m3 of Ne/CO2/N2
(90/10/5), in which the primary electrons are transported over a distance of up to 2.5
m on either side of the central electrode to the end plates. Multi-wire proportional
chambers with cathode pad readout are mounted into 18 trapezoidal sectors at each
end plate. The TPC is the primary device for obtaining charged-particle momentum
measurements and particle identification. It also provides an independent measure
of primary vertex. The combination of ITS and a large Time Projection Chamber
(TPC) provides powerful tracking with excellent momentum resolutions (about 2%
to 5%) from 100 MeV/c to 100 GeV/c.
The central barrel is equipped with a Transition Radiation Detector (TRD) for electron
identification above 1 GeV/c, where the pion rejection capability from TPC is no
longer sufficient. The TRD, in combination with other central barrel detectors, will
provide sufficient electron identification to measure the production of light and heavy
vector meson resonances and the dilepton continuum produced in p+ p and Pb+
Pb collisions. It consists of 540 individual readout detector modules arranged in 18
super modules. Each module consists of a radiator of 4.8 cm thicknes, a multiwire
proportional readout chamber along with frontend elctronics. The gas mixture in the
readout chamber is Xe/CO2 (85%/15%). The particle identification of hadrons in the
intermediate momentum range (to about 4 GeV/c depending on the particle species)
is improved significantly with the inclusion of a Time-Of-Flight (TOF) system.
The TOF system consists of Multi-gap Resistive-Plate Chambers (MRPC). The key
aspect of these chambers is that the electric field is high and uniform over the whole
sensitive gaseous volume of the detector. Ionization produced by traversing charged
particle starts a gas avalanche process which eventually generates the observed
signals on the pick-up electrodes. The intrinsic time resolution of 40ps has been
achieved with an efficiency of close to 100%.
The central arm includes a High-Momentum Particle Identification Detector (HMPID)
for the identification of hadrons at pT > 1 GeV/c. The detector is based on proximity-
focusing Ring Imaging Cherenkov (RICH) counters and consists of seven modules of
25
3.3. Heavy-Ion physics with ALICE 26
about 1.5 x 1.5 m2 each, mounted in an independent support cradle. The coverage
of HMPID is limited (-0.6 < η < 0.6 with 1.2◦< φ < 58.8◦.
The measurements of low pT direct photons and high-pT π0 are performed by a sin-
gle arm high resolution photon (electromagnetic) spectrometer (PHOS), consisting
of lead-tungstate (PbWO4) crystals. The major requirements of the PHOS include
the ability to identify photons, discriminate direct photons from decay photons and
perform momentum measurements over a wide dynamic range with high energy
and spatial measurements. PHOS covers approximately a quarter of a unit of pseu-
dorapidity -0.12 < η < 0.12, and 100◦in azimuthal angle. The total area is ∼ 8m2.
Recently, an electromagnetic calorimeter (EMCAL), which will be located inside the
L3 magnet, has been included in the ALICE detector, improving the capability for
measurement of high energy jets.
3.3. Heavy-Ion physics with ALICE
The heavy-ion program is focused in the study of hot and dense medium can be
studied by many observables. In ALICE this probes are subdivided into three classes:
soft probes (with the typical momenta pT < 2 GeV/c), heavy-flavor probes (i.e., using
the particles having c and b quarks) and high-pT probes (in the momentum range
above pT > 20 GeV/c).
3.3.1. Soft Probes
ALICE will measure the charged-particle multiplicity and the charged-particle pseudo-
rapidity distribution over almost 8 units of η by means of Forward Multiplicity Detec-
tor (FMD) and the innermost layers of ITS. The way the initial energy is redistributed
over the particles in the final state is strictly linked with such an important thermody-
namical quantity as the energy density ε reached in the early phase of the collision.
Furthermore, the multiplicity information allows one to constrain the hadroproduction
models. Thus, in the phenomenological approach, the measured pseudorapidity
density dNch/dη is expressed as the sum of a term proportional to the number of
participants Npart (soft component) and the number of binary collisions Ncoll (hard
component). Measuring dNch/dη as a function of Npart , one can estimate the relative
number of particles produced in hard and soft scatterings.
Resonances with lifetimes comparable to that of the QGP phase (such as ρ0,K∗(892)0,
φ(1020)) may change their properties (mass, width) when they are produced in the
dense medium. Detection of K∗(892)0 and φ(1020) is especially important because
of the expected overall strangeness enhancement in heavy-ion collisions.
The ALICE detector will be able to register these resonances with sufficient statistics
and with mass resolution of the order of a few MeV.
26
3.3. Heavy-Ion physics with ALICE 27
3.3.2. Heavy flavor probes
When traversing the dense matter created in nucleus-nucleus collisions, the initially-
produced hard partons lose energy mainly on account of medium-induced gluon
radiation. The heavy quarks at intermediate pT will lose less energy as compared
with the light quarks at the same momenta due to the ’dead-cone’ effect [5,6]. The
ratio of the nuclear modification factor for D (and B) mesons to the one for the normal
hadrons is thus suggested to be sensitive to the mass dependence of in-medium
parton energy loss. The D mesons needed for these studies will be topologically
reconstructed in central ALICE detectors, whereas B mesons can be detected in
semi-leptonic decay channels.
Precise detection of the open charm (open beauty) is also needed for the normal-
ization of the quarkonia production. In nucleus-nucleus collisions, quarkonium sup-
pression is expected to occur due to the Debye screening in the deconfined mat-
ter. Increase of the energy density reached in the collisions leads to break up of
first the ψ′ and χc, and finally the J/ψ . Such a suppression pattern was already
observed at SPS. However, at higher energies (RHIC, LHC) the situation becomes
more complicated, because the charmonia can be regenerated in the hot medium
by recombination.
ALICE will be able to measure the charmonia and bottomnia production both at mid-
rapidity (in di-electron channels) and at forward rapidities (in di-muon channels).
The statistics of registered ϒ′s is expected to be enough for the suppression studies.
In this case, due to much higher mass, the influence of the regeneration will be
negligible.
3.3.3. High-pT probes
High-pT partons produced in the initial stage of a nucleus–nucleus collision are ex-
pected to undergo multiple interactions inside the collision region prior to hadroni-
sation. Hereby, the energy of the partons is reduced through collisional energy loss
and medium-induced gluon radiation, the latter being the dominant mechanism in
a QGP. This so-called jet quenching has been suggested to behave very differently
in cold nuclear matter and in QGP, and has been postulated as a tool to probe the
properties of this new state of matter. This is the main motivation for studying jets
as well as high-pT particle spectra and particle correlations in heavy-ion collisions.
As compared to jet physics at RHIC, there are two fundamentally new features in
central Pb+Pb collisions at the LHC: The multi-jet production per event is not re-
stricted to the minijet region ET < 2 GeV but extends to about 20 GeV and jet rates
are high at energies at which jets can be distinguished from the background energy
of the underlying event. Hence, event-by-event reconstruction of jets with reason-
27
3.3. Heavy-Ion physics with ALICE 28
able energy resolution will be possible.
ALICE will study the whole spectrum of jet production ranging from minijets, ET > 2
GeV, to high-ET jets of several hundred GeV. Experimental considerations delin-
eate four distinct energy regions, which are discussed here for the 10% most central
Pb+Pb collisions at
√
sNN = 5.5 TeV. In the region ET < 20 GeV several jets over-
lap in one event within the ALICE acceptance. This means that jet identification in
the traditional sense is not possible and their presence is revealed via studies of
particle correlations. For 20 < ET < 100 GeV the jet rate > 1Hz is high enough so
that, even with a read-out rate limited by the TPC to 20–40Hz, an event sample of
O(104) jets can be collected in one effective month of running (106 s). For ET > 100
GeV triggering will be necessary to collect jet enriched data. Considering that for a
fragmentation function analysis of the order of 104 jet events are needed, the statis-
tics limit is reached at about 250 GeV.
Figure 3.5 and table 3.3.3 show the expected average LHC Pb+Pb luminosity of
5×1026 cm−2s−1, the number of jets produced per effective month of running (106 s)
within the fiducial region |η | < 0.5 for charged jet reconstructed using ALICEcentral
barrel tracking (ITS+TPC) and |η | < 0.3, 83◦ < ϕ < 157◦ for jet reconstruction with
central barrel tracking and Electromagnetic Calorimetry (EMCal). Rates in minimum
bias collisions are compared to those in the 10% most central collisions. The lat-
ter have been obtained by scaling with the average number of binary collisions for
impact parameter b < 5 fm.
In the low-ET -jet region, jet-structure modifications will be studied with inclusive
spectra of identified particles and particle correlations, as shown by the RHIC exper-
iments. These studies require excellent low-pT and PID capabilities and ALICE will
extend them with the electromagnetic calorimeter (EMCAL). The EMCAL will in-
crease the selection efficiency and further reduce the bias on the jet fragmentation.
Furthermore, it will add a jet trigger which is needed to increase the statistics at
high ET . The low- and high-transverse-momentum tracking capabilities combined
with electromagnetic calorimetry represent an ideal tool for jet-structure modifica-
tion studies at the LHC over a wide kinematic region of jet and associated-particle
momenta.
28
3.3. Heavy-Ion physics with ALICE 29
 [GeV]min
TE
20 40 60 80 100 120 140 160 180 200
| 
<
 0
.5
)
η
, 
|
m
in
T
 >
 E
T
#
J
e
ts
/ 
m
o
n
th
 (
E
5
10
610
710
8
10
9
10
10
10
1110
Minimum Bias
10% most central
Figure 3.5: Number of jets with ET > Emin
T and |η |< 0.5 produced in Pb+Pb col-
lisions at
√
sNN = 5.5TeV in one effective month of running (106 s). The minimum
bias rate (solid line) is compared to the rate in the 10% most central collisions
(dashed line).
Emin
T [GeV] TPC fiducial region EMCal fiducial region
20 2.0×109 2.4×108
50 4.8×107 5.8×106
100 2.6×106 3.1×105
150 4.0×105 4.8×104
200 1.0×105 1.2×104
250 2.5×104 3.0×103
Table 3.3: Number of jets with ET > Emin
T produced in one month of Pb+Pb run-
ning within the central barrel (|η | < 0.5) and within the EMCAL acceptance
(|η | < 0.3 and 83◦ < ϕ < 157◦). The acceptance limits assume that a cone size
of Rc = 0.4 is used for jet reconstruction.
29
Chapter 4
Framework of the ALICE detector: AliROOT
In high energy physics, a framework is a set of software tools that enables data
processing. The role of the framework is shown in figure 4.1.
The primary interactions are simulated via event generators, and the resulting kine-
matic tree is then used in the transport package. An event generator produces set
of “particles” with their momenta. The set of particles, where one maintains the
production history (in form of mother-daughter relationship and production vertex),
forms the kinematic tree. The transport package transports the particles through
the set of detectors, and produces hits, i.e., energy deposition at a given point. The
hits contain also information (“track labels”) about the particles that have generated
them.
At the next step, the detector response is taken into account, and the hits are trans-
formed into digits. As mentioned previously, the hits are closely related to the tracks
that generated them. The transition from hits/tracks to digits/detectors is marked on
the picture as “disintegrated response”, the tracks are “disintegrated” and only the
labels carry the Monte-Carlo information.
There are two types of digits: “summable digits”, where one uses low thresholds
and the result is additive, and “digits”, where the real thresholds are used, and the
result is similar to what one would get in the real data taking. In some sense the
“summable digits” are precursors of the “digits”. The noise simulation is activated
when “digits” are produced.
The summable digits are used for the so-called “event merging”, where a signal
event is embedded in a signal-free underlying event. This technique is widely used
in heavy-ion physics and allows reusing the underlying events with substantial econ-
omy of computing resources. Optionally, it is possible to perform the conversion dig-
its to raw data which is used to estimate the expected data size, to evaluate the high
level trigger algorithms and to carry on the so called computing data challenges.
The reconstruction and the HLT algorithms can both work with digits and with raw
30
4.1. Simulation framework 31
data.
After the creation of digits, the reconstruction and analysis chains can be activated
to evaluate the software and the detector performance, and to study some particular
signatures. The reconstruction takes as input digits or raw data, real or simulated
[13].
Figure 4.1: Data processing framework.
4.1. Simulation framework
The simulation framework covers the simulation of primary collisions and generation
of the emerging particles, the transport of particles through the detector, the simula-
tion of energy depositions (hits) in the detector components, their response in form
of so called summable digits, the generation of digits from summable digits with the
optional merging of underlying events and the creation of raw data.
31
4.1. Simulation framework 32
Figure 4.2: Simulation framework.
Generation of Particles
Different generators can be used to produce particles emerging from the collision.
The class AliGenerator is the base class defining the virtual interface to the gener-
ator programs.
Virtual Monte Carlo
A class derived from TVirtualMC performs the simulation of particles traversing the
detector components. The Virtual Monte-Carlo also provides an interface to con-
struct the geometry of detectors. The geometrical modeller TGeo does the task of the
geometry description. The concrete implementation of the Virtual Monte-Carlo
application TVirtualMCApplication is AliMC. The Monte-Carlo used in ALICE are
GEANT.3.21 [42].
Modules and Detectors
A class derived from AliModule describes each module of the ALICE detector. Classes
for active modules (i.e., detectors) are not derived directly from AliModule but from
its subclass AliDetector. These base classes define the interface to the simulation
framework via a set of virtual methods.
32
4.1. Simulation framework 33
Configuration File (Config.C)
The configuration file is a C++ macro that is processed before the simulation starts.
It creates and configures the Monte-Carlo object, the generator object, the magnetic
field map and the detector modules.
Detector Geometry
The Virtual Monte-Carlo application creates and initializes the geometry of the
detector modules by calling the virtual functions CreateMaterials, CreateGeometry,
Init and BuildGeometry.
Vertexes and Particles
In case the simulated event is intended to be merged with an underlying event, the
primary vertex is taken from the file containing the underlying event by using the
vertex generator AliVertexGenFile. Otherwise, the primary vertex is generated ac-
cording to the generator settings. Then the particles emerging from the collision are
generated and put on the stack (an instance of AliStack). The Monte-Carlo ob-
ject performs the transport of particles through the detector. The external decayer
AliDecayerPythia usually handles the decay of particles.
Hits and Track References
The Monte-Carlo simulates the transport of a particle step by step. After each step
the virtual method StepManager of the module in which the particle currently is lo-
cated is called. In this StepManager method, calling AddHit creates the hits in the
detector. Optionally also track references (location and momentum of simulated par-
ticles at selected places) can be created by calling AddTackReference. AddHit has
to be implemented by each detector whereas AddTackReference is already imple-
mented in AliModule. The detector class manages the container and the branch
for the hits and for the (summable) digits via a set of so-called loaders. The rel-
evant data members and methods are fHits, fDigits, ResetHits, ResetSDigits,
ResetDigits, MakeBranch and SetTreeAddress. For each detector methods like
PreTrack, PostTrack, FinishPrimary, FinishEvent and FinishRun are called dur-
ing the simulation when the conditions indicated by the method names are fulfilled.
Summable Digits
Calling the virtual method Hits2SDigits of a detector creates summable digits. This
method loops over all events, creates the summable digits from hits and stores them
in the digits files.
33
4.1. Simulation framework 34
Digitization and Merging
Dedicated classes derived from AliDigitizer are used for the conversion of summable
digits into digits. Since AliDigitizer is a TTask, this conversion is done for the cur-
rent event by the Exec method. Inside this method the summable digits of all input
streams have to be added, combined with noise, converted to digital values taking
into account possible thresholds, and stored in the digits container. An object of
type AliRunDigitizer manages the input streams (more than one in case of merg-
ing) as well as the output stream. The methods GetNinputs, GetInputFolderName
and GetOutputFolderName return the relevant information. The run digitizer is ac-
cessible inside the digitizer via the protected data member fManager. If the flag
fRegionOfInterest is set, only detector parts where summable digits from the sig-
nal event are present should be digitized. When Monte-Carlo labels are assigned
to digits, the stream-dependent offset given by the method GetMask is added to the
label of the summable digit. The detector specific digitizer object is created in the
virtual method CreateDigitizer of the concrete detector class. The run digitizer
object is used to construct the detector digitizer. The Init method of each digi-
tizer is called before the loop over the events is started. A direct conversion from
hits directly to digits can be implemented in the method Hits2Digits of a detector.
The loop over the events takes place inside the method. Of course merging is not
supported in this case.
4.1.1. Parametrized generation
The event generation based on parametrization can be used to produce signal-free
final states. It avoids the dependences on a specific model, and is efficient and
flexible. It can be used to study the track reconstruction efficiency as a function of
the initial multiplicity and occupation.
In many cases, the expected transverse momentum and rapidity distributions of par-
ticles are known. In other cases, the effect of variations in these distributions must
be investigated. In both situations, it is appropriate to use generators that produce
primary particles and their decays sampling from parametrized spectra. To meet
the different physics requirements in a modular way, the parametrizations are stored
in independent function libraries wrapped into classes that can be plugged into the
generator.
It is customary in heavy-ion event generation to superimpose different signals on an
event in order to tune the reconstruction algorithms. This is possible in ALIROOT the
so-called cocktail generator. This creates events from user-defined particle cock-
tails by choosing as ingredients a list of particle generators.
Several event generators are available via the ROOT class [43] that implements the
34
4.1. Simulation framework 35
generic generator interface, TGenerator. By means of implementations of this ab-
stract base class, we wrap Fortran Monte-Carlo codes like PYTHIA [9] and HI-
JING [10] that are thus accessible from the ALIROOT classes. In particular the in-
terface to PYTHIA includes the use of nuclear structure functions of LHAPDF.
PYTHIA 6
PYTHIA is used for simulation of p+ p interactions and for generation of jets in case
of event merging. For more details see section 5
HIJING
HIJING (Heavy-Ion Jet Interaction Generator) combines a QCD-inspired model of jet
production using the Lund model for jet fragmentation. Hard or semi-hard parton
scatterings with transverse momenta of a few GeV are expected to dominate high-
energy heavy-ion collisions. The HIJING model has been developed with special
emphasis on the role of mini jets in p+ p, p+A and Au+Au reactions at collider
energies.
4.1.2. Reconstruction Framework
The global ALICE coordinate is a right-handed coordinate system with the z-axis
coinciding with the beam-pipe axis pointing away from the muon arm, the y-axis
going upward, and its origin defined by the intersection point of the z-axis and the
central membrane-plane of TPC
We briefly summarize the main conceptual terms of the reconstruction framework
(see also section 3.2):
• Digit: This is a digitized signal (ADC count) obtained by a sensitive pad of a
detector at a certain time.
• Cluster: This is a set of adjacent (in space and/or in time) digits that were
presumably generated by the same particle crossing the sensitive element of
a detector.
• Space point (reconstructed): This is the estimation of the position where
a particle crossed the sensitive element of a detector (often, this is done by
calculating the centre of gravity of the ‘cluster’).
• Track (reconstructed): This is a set of five parameters (such as the curvature
and the angles with respect to the coordinate axes) of the particle’s trajectory
together with the corresponding covariance matrix estimated at a given point
in space.
35
4.1. Simulation framework 36
Figure 4.3: Reconstruction framework.
If the input data is provided in format of ROOT trees, either the loaders or directly the
trees are used to access the digits. In case of raw data input, the digits are accessed
via a raw reader. If a galice.root file exists, the run loader will be retrieved from it.
Otherwise the run loader and the headers will be created from the raw data. The
reconstruction cannot work if there is no galice.root file and no raw data input.
The clusters (rec. points) are considered intermediate output and are stored in
ROOT trees handled by the loaders. The final output of the reconstruction is a tree
with objects of type AliESD stored in the file AliESDs.root. This Event Summary
Data (ESD) contains lists of reconstructed tracks/particles and global event proper-
ties.
The first step of the reconstruction is the so-called ”local reconstruction”. It is ex-
ecuted for each detector separately and without exchanging information with other
detectors. Usually the clusterization is done in this step.
The reconstruction of the primary-vertex position in ALICEis done using the informa-
tion provided by the silicon pixel detectors, which constitute the two innermost layers
of the ITS.
The combined track reconstruction tries to accumulate the information from different
detectors in order to optimize the track reconstruction performance. The result of
this is stored in the combined track objects. This is achieved by using just integer
indexes pointing to the specific track objects, which on the other hand makes it
possible to retrieve the full information if needed. The list of combined tracks can
36
4.1. Simulation framework 37
be kept in memory and passed from one reconstruction module to another. The
storage of the combined tracks should be done in the standard way.
After the tracks have been reconstructed and stored in the AliESD object, further
information is added to the ESD. For each detector the method FillESD of the re-
constructor is called. Inside this method e.g. V0s are reconstructed or particles are
identified (PID). For the PID, a Bayesian approach is used.
4.1.3. Event summary data
The classes that are needed to process and analyze the ESD are packaged in
a standalone library (libESD.so) which can be used independently from the ALI-
ROOT framework. Inside each ESD object, the data is stored in polymorphic contain-
ers filled with reconstructed tracks, neutral particles, etc. The main class is AliESD,
which contains all the information needed during the physics analysis:
• fields to identify the event, such as event number, run number, time stamp, type
of event, trigger type (mask), trigger cluster (mask), version of reconstruction,
etc.;
• reconstructed ZDC energies and number of participants;
• primary vertex information: vertex z-position estimated by the T0, primary ver-
tex estimated by the SPD, primary vertex estimated using ESD tracks;
• tracklet multiplicity;
• interaction time estimated by the T0 together with additional time and ampli-
tude information from T0;
• array of ESDtracks;
• arrays of HLT tracks, both from the conformal mapping and from the Hough
transform reconstruction;
• array of MUON tracks;
• array of PMD tracks;
• array of TRD ESDtracks (triggered);
• arrays of reconstructed V0 vertexes, cascade decays and kinks;
• array of calorimeter clusters for PHOS/EMCAL; indexes of the information from
PHOS and EMCAL detectors in the array above.
37
4.1. Simulation framework 38
4.1.4. Analysis
The analysis of experimental data is the final stage of event processing. The Physics
Board coordinates data analysis via the Physics Working Groups (PWGs). At present,
the following PWG have started their activity
• PWG0 first physics
• PWG1 detector performance
• PWG2 global event characteristics: particle multiplicity, centrality, energy den-
sity, nuclear stopping; soft physics: chemical composition (particle and reso-
nance production, particle ratios and spectra, strangeness enhancement), re-
action dynamics (transverse and elliptic flow, HBT correlations, eventbyevent
dynamical fluctuations)
• PWG3 heavy flavors: quarkonia, open charm and beauty production
• PWG4 hard probes: jets, direct photons
In the ALICE Computing Model the analysis starts from the Event Summary Data
(ESD). These are produced during the reconstruction step and contain all the infor-
mation for the analysis. The size of the ESD is about one order of magnitude lower
than the corresponding raw data. The analysis tasks produce Analysis Object Data
(AOD) specific to a given set of physics objectives. Further passes for the specific
analysis activity can be performed on the AODs, until the selection parameter or
algorithms are changed.
A typical data analysis task usually requires processing of selected sets of events.
The selection is based on the event topology and characteristics, and is done by
querying the tag database. The tags represent physics quantities which charac-
terize each run and event, and permit fast selection. They are created after the
reconstruction and contain also the unique identifier of the ESD file.
The next step of a typical analysis consists of a loop over all the events in the list and
calculation of the physics quantities of interest. Usually, for each event, there is a
set of embedded loops on the reconstructed entities such as tracks, V0 candidates,
neutral clusters, etc., the main goal of which is to select the signal candidates. Inside
each loop a number of criteria (cuts) are applied to reject the background combina-
tions and to select the signal ones. The cuts can be based on geometrical quantities
such as impact parameters of the tracks with respect to the primary vertex, distance
between the cluster and the closest track, distance of closest approach between
the tracks, angle between the momentum vector of the particle combination and
the line connecting the production and decay vertexes. They can also be based on
38
4.1. Simulation framework 39
kinematics quantities such as momentum ratios, minimal and maximal transverse
momentum, angles in the rest frame of the combination. Particle identification crite-
ria are also among the most common selection criteria.
The optimization of the selection criteria is one of the most important parts of the
analysis. The goal is to maximize the signal-to-background ratio in case of search
tasks, or another ratio (typically Signal/
√
Signal+Background) in case of measure-
ment of a given property. Usually, this optimization is performed using simulated
events where the information from the particle generator is available.
After the optimization of the selection criteria, one has to take into account the com-
bined acceptance of the detector. This is a complex, analysis-specific quantity which
depends on the geometrical acceptance, the trigger efficiency, the decays of parti-
cles, the reconstruction efficiency, the efficiency of the particle identification and
of the selection cuts. The components of the combined acceptance are usually
parametrized and their product is used to unfold the experimental distributions or
during the simulation of some model parameters.
The last part of the analysis usually involves quite complex mathematical treatments,
and sophisticated statistical tools. Here one may include the correction for system-
atic effects, the estimation of statistical and systematic errors, etc.
The AOD files generated during the scheduled analysis can be used by several sub-
sequent analyses, or by a class of related physics tasks.
The AOD analysis framework implements a set of tools like data readers, converters,
cuts, and other utility classes. The design is based on two main requirements:
flexibility and common AOD particle interface. This guarantees that several analyses
can be done in sequence within the same computing session.
In order to fulfill the first requirement, the analysis is driven by the ‘analysis manager’
class and particular analyses are added to it. It performs the loop over events, which
are delivered by an user-specified reader. This design allows the analyses to be
ordered appropriately if some of them depend on the results of the others.
The cuts are designed to provide high flexibility and performance. A two-level archi-
tecture has been adopted for all the cuts (particle, pair and event). A class repre-
senting a cut has a list of ‘base cuts’. Each base cut implements a cut on a single
property or performs a logical operation (and, or) on the result of other base cuts.
39
Chapter 5
Production of high-pT events
The aim of this work is to study the effects of parton energy loss in a medium un-
der extreme conditions of temperature and density. To achieve that, we simulated
high-pT events in p+ p collision, reconstructed jets with a jet finding algorithm and
performed event shape analysis. p+ p collisions were used as a baseline and the
jets energy loss was simulated using two afterburner Monte-Carlo models. Finally,
modifications in jet structure due to energy loss, were studied.
The PYTHIA program is a standard tool for the generation of high-energy collisions,
comprising a coherent set of physics models for the evolution from a few-body hard
process to a complex multihadronic final state. It contains a library of hard pro-
cesses and models for initial and final state parton showers, multiple parton-parton
interactions, beam remnants, string fragmentation and particle decays, and it also
has a set of utilities and interfaces to external programs. For a complete description
of the physics content we refer to the PYTHIA manual [9].
We focus on high-pT particle production with PYTHIA version 6.2.14 (packaged in
ALIROOT) with tune set A [44] in p + p mode at
√
sNN = 5.5 TeV. In table 5.1, we
report the main list of parameters used for the generation of high-pT events.
The particle production was done to improve the jets production selecting hard pro-
cesses in PYTHIA. A calibration sample of a fixed pT with phard
T = 50 GeV/c (dashed
line in figure 5.1) and, to approach the real spectrum produced in ALICE, events with
phard
T = 30 - 179 GeV/c (solid line in figure 5.1) was produced. The ratio of triggered
to generated jets for a fixed interval of phard
T together with the corresponding hard
cross section given by PYTHIA, determine the weight which we apply to every event
(or jet event) generated for the particular interval. The weights are show in table 5.2.
40
41
Description Parameter Value
Process types QCD jets MSEL 1
ISUB (11) qiq j → qiq j
ISUB (12) qiq̄i → qkq̄k
ISUB (13) qiq̄i → gg
ISUB (28) qig → qig
ISUB (53) gg → qkq̄k
ISUB (68) gg → gg
ISUB (96) semihard QCD 2 → 2
Minimum/maximum CKIN(3) fPtHardMin
parton phard
T [GeV] CKIN(4) fPtHardMax
see Table 5.2
Initial/final state radiation on MSTP(61) 1
MSTP(71) 1
Intrinsic kT from Gaussian (zero mean) MSTP(91) 1
width σ [GeV] PARP(91) 1
upper cut-off (at 5σ) [GeV] PARP(93) 5
Cone jet finder (pycell)
|η | of the “detector” PARU(51) 2
number of cells in η MSTU(51) 274
number of cells in φ MSTU(52) 432
threshold [GeV] PARU(58) 0
seed [GeV] PARU(52) 4
min ET [GeV] PARU(53) 5
radius PARU(54) 1
Table 5.1: PYTHIA 6.2.14 parameter settings for the generation of jets in p+
p collisions at
√
sNN = 5.5 TeV
After event generation, jets were first reconstructed, at the final state particle level,
with PYCELL routine1 and subsequently we used a cone jet algorithm and event
shape analysis, described in the next section, to study jets.
1PYCELL is the internal PYTHIA cone algorithm with Rc =1 which uses all simulated particles to
reconstruct jets
41
42
 (GeV/c)
T
p
0 20 40 60 80 100 120 140 160 180
T
 d
N
/d
p
e
v
1
/N
-610
-510
-410
-310
-210
-110
1
10
210
310 p-p simulation with PYTHIA
 = 5.5 TeV
NN
s 
Charged and neutral particles
>0.3 GeV/c
T
with p
 = 30 - 179 GeV/chard
T
p
 = 50 GeV/chard
T
p
Figure 5.1: pT distribution for charged and neutral particles produced in p+
p collisions at
√
sNN = 5.5 TeV with phard
T = 50 GeV/c (dashed line) and phard
T = 30
- 179 GeV/c (solid line) weighted with respect to the values of table 5.2.
Min. phard
T [GeV/c] Max. phard
T [GeV/c] Weight
30 35 7.007 ·10−4
35 42 4.521 ·10−4
42 50 2.202 ·10−4
50 60 1.151 ·10−4
60 72 5.155 ·10−5
72 86 2.533 ·10−5
86 104 1.238 ·10−5
104 124 5.131 ·10−6
124 149 2.375 ·10−6
149 179 1.006 ·10−6
Table 5.2: Values of the weight for each phard
T .
42
Chapter 6
Jet reconstruction
Jets have been studied for many years in the field of high energy physics at e+e− and
hadron-hadron colliders. The measurement of jets cross sections, has provided
useful tests of quantum chromodynamics.
Although the basic hard scattering processes studied in e+e− and hadron-hadron
collisions are almost the same, the overall event structure is quite different. In the
e+e− case the initial state is purely electromagnetic and the entire final state can be
thought as arising from the short distance interaction of the virtual photon with the
quarks. In this sense all of the hadrons in the final state are associated with the
hard scattering process. In contrast the overall structure of the hadron-hadron case
is more complex. Of the large number of initial state partons, more probably one
“active parton” from each incident hadron participates in the hard scattering pro-
cess. Thus only a fraction of hadrons in the final state are to be associated with the
hard scattering process, with the remainder ascribed to the “underlying event.” This
second contribution corresponds to the soft interactions of the remaining partons in
the incident hadrons and, in first approximation, can be treated as uncorrelated with
the hard process. The active partons also produce additional radiation in the form
of initial state bremsstrahlung that is not present in e+e− events. The underlying
event plus the initial state radiation produce the characteristic “beam jets” of hadron
collisions: particles with small momenta transverse to the beam axis, but possibly
large momenta along the beam axis.
Due to the different event structures in the two cases, different jet definitions and
algorithms to reconstruct them have been developed. The aim of both however, is to
provide a mapping between the observed high-energy hadrons and the initial state
energetic partons which were involved in the hard scattering.
In e+e− collisions is used a jet definition that associates every final-state hadron
uniquely with one of the jets. In hadron-hadron collisions only a small fraction of the
final state hadrons are associated with the high-pT jets, the other particles present in
43
6.1. The Cone Jet Algorithm 44
the event can be thought as associated with the underlying events. To keep the high-
pT jets distinct from the hadronic debris in the underlying events, a cone definition
is used, which was inspired by the theoretical definition for jets in e+e− collisions.
A jet in this definition is a set of particles whose momentum vectors lie within a cer-
tain angular cone. In this kind of definition, one recursively groups sets of particles
with “nearby” momenta, as defined by some measure, into larger sets of particles.
The initial sets consist of just one particle, the final sets are jets [52].
6.1. The Cone Jet Algorithm
Jet algorithm, start from a list of particles that we take to be hadrons at the experi-
mental level, and partons in a perturbative QCD calculation. The role of the algorithm
is to associate clusters of these particles into jets such that the kinematic properties
of the jets can be related to the corresponding properties of the energetic partons
produced in the hard scattering process. Thus the jet algorithm allows us to study
the partons in the hadronic final state.
Differences in the properties of reconstructed jets when going from the parton to
the hadron: Each particle i carries a 4-momentum pµ
i , the algorithm selects a set of
particles which are typically emitted close to each other in angle and combines their
momenta to form the momentum of a jet. The selection process is called the “jet
algorithm” and the momentum addition rule is called the “recombination scheme”.
This two steps are distinct, for example, use one set of kinematic variables in the
jet algorithm to determine the particles in a jet and then construct a separate set of
kinematic variables to characterize the jets that have been identified.
For e+e− annihilation, one wants to emphasize rotational invariance. Thus the natu-
ral variables are energies E and polar angles θ,φ. For hadron-hadron collisions, one
wants to emphasize invariance under boosts along the beam axis since, in fact, the
center of mass frame of the hard scattering is typically moving in the hadron-hadron
center of mass frame. Thus the natural variables are transverse momenta pT or the
corresponding transverse energy ET≡E sinθ, azimuthal angle φ and pseudo-rapidity
η =− ln(tan(θ/2)).
Cone algorithms form jets by associating together particles which trajectories i.e., to-
wers whose centers lie within a circle of specific radius R in η ×φ space. This 2-
dimensional space is natural in pp collisions where the dynamics is spread out in
the longitudinal direction. Starting with a trial geometric center (or axis) for a cone
in η ×φ space, the energy-weighted is calculated including contributions from all
particles within the cone. This new point in η ×φ is then used as the center for a
new trial cone. As this calculation is iterated the cone center “flows” until a “stable”
solution is found, i.e.,, until the centroid of the energy depositions within the cone
44
6.1. The Cone Jet Algorithm 45
is aligned with the geometrical axis of the cone. This leads us to our initial cone
algorithm of scalar ET -weighted centers. The particles are specified by massless 4-
vectors (E i = |pi|,pi) with angles
(
φi,θ i,η i =− ln
(
tan(θ i/2)
))
given by the direction
from the interaction point with unit vector p̂i = pi/E i. The scalar ET for each particle
is E i
T = E i sin(θ i). For a specified geometric center for the cone
(
ηC,φC
)
the particles
i within the cone satisfy
i ⊂C :
√
(η i −ηC)
2
+(φi −φC)
2 ≤ R. (6.1)
a “stable” cone satisfies the constraints
ηC =
∑i⊂C E i
T η i
EC
T
, φC =
∑i⊂C E i
T φi
EC
T
(6.2)
i.e.,, the geometrical center of the previous equation is identical to the ET -weighted
centroid with
EC
T = ∑
i⊂C
E i
T . (6.3)
Naively we can simply identify these stable cones, and the particles inside, as jets,
J =C.
To complete the jet finding process we require a recombination scheme. Using the
stable cone variables:
EJ
T = ∑
i⊂J=C
E i
T = EC
T , (6.4)
η J =
1
EJ
T
∑
i⊂J=C
E i
T η i , (6.5)
φJ =
1
EJ
T
∑
i⊂J=C
E i
T φi . (6.6)
In practice, in order to save computing time, the iterative process of searching for
the “stable” cones in experimental data starts with those cones centered about the
most energetic particles in the event, the so-called “seeds”.
Seed-based cone algorithm offer the advantage of being comparatively efficient in
CPU time. In a typical application, detector towers are sorted according to descend-
ing ET and only towers passing a seed cut,
45
6.1. The Cone Jet Algorithm 46
Etower
T > Eseed
T , (6.7)
are used as starting points for the initial jet cones. This greatly reduces the number
of cones that need to be evaluated in the initial stage. The seed threshold Eseed
T must
be chosen low enough so that variations of Eseed
T lead to negligible variations in any
observable under consideration.
In each seed cone, The ET -weighted centroids are calculated for the particles and
then the centroids are used as centers for new cones in η ×φ space. This procedure
is iterated for each cone until the cone axis coincides with the centroid.
Figure 6.1 shows the flow chart representation of the cone algorithm used at the
CDF experiment [53]. The choice of cone radius is based on the amount of jet
energy contained within the cone and the radius which gives the best resolution.
This optimization differs from experiment to experiment, for example, Rc = 1.0 was
originally used at UA1 but smaller cone sizes of Rc = 0.4 and 0.7 have been used at
CDF.
6.1.1. Cone Jet Algorithm for Heavy-Ion Collisions
Jet reconstruction in heavy ion collisions is affected by the bulk of soft and semi-hard
particles. A cone jet algorithm implemented in the module JETAN of ALIROOT was
used. This algorithm is based on a algorithm developed by the UA1collaboration [54]
and further developed to account for the heavy-ion background.
The input to the algorithm is an energy grid in (η ,φ) filled by a combination of trans-
verse energy .
The algorithm consists of the following steps:
1. Initialize the estimated background level per grid cell ÊBG
T to the average over
all grid cells.
2. Sort cells in decreasing cell energy, E i
T .
3. For at least 2 iterations, and until the change in ÊBG
T between most recent
successive iterations is smaller than a set threshold
(a) Clear the jets list
(b) Flag all cells outside a jet
(c) Execute the jet-finding loop for each cell, starting with the largest:
i. If E i
T − ÊBG
T > Eseed
T , where Eseed
T is a chosen threshold cell energy, and
the cell is flagged as not in a jet, treat it as a jet seed candidate:
46
6.1. The Cone Jet Algorithm 47
Start with list of all towers with
ET ≥ ESeed sorted in
decreasing order of energy
Is the tower list
exhausted?
STOP
Calculate cone centroid, C
around next tower in list
using radius R
Is C within ε
of tower centre?
Iterate this cone
Was this cone
already found?
Remove this cone
Add cone to
list of jets
Y
N
Y
Y
N
Y
N
Figure 6.1: Cone jet algorithm used at the Tevatron at Fermilab, from [53]
47
6.1. The Cone Jet Algorithm 48
Figure 6.2: Charged jets in the η -φ plane for a 100 GeV jet in p+ p (left) and
for the same jet embedded in a central Pb+Pb event (right). In both cases a
particle pcut
T of 0.5 GeV has been applied [55]
A. Set jet centroid (ηC, φC) to the co-ordinates of the jet seed cell ηi,
φi.
B. Using all cells within
√
(η i −ηC)2 +(φi −φC)2 < R of the initial
centroid, calculate the new energy-weighted (E i
T − ÊBG
T ) centroid.
Set the new energy-weighted centroid to be the new initial cen-
troid. Repeat centroid calculation iterations until the centroid does
not shift by more than one cell in subsequent iterations.
C. Store centroid as jet candidate and flag all cells within R of cen-
troid as inside a jet.
(d) Re-calculate the estimated background energy ÊBG
T
(e) For each jet candidate, calculate the energy by summing the energies of
the cells in the cone and subtracting the background. If the jet energy is
greater than EC
T , the minimum allowed cone energy, a jet is found.
Full event simulation performed within the ALIROOT framework, chose HIJING for
the generation of background events, in which PYTHIA events containing jet signals
are merged. The mixed event contains all particles of the signal and as well of
the background event, both, above a pcut
T and within the central ALICE acceptance
of |η | < 0.9 [16]. The initial tower configuration of the cone finder is illustrated in
figure 6.2 for a 100 GeV jet. As the signal sticks out of the background it is possible
to do the analysis only with the jet signal, without taking into account the background.
48
6.1. The Cone Jet Algorithm 49
φ∆
-1 0 1 2 3 4 5
φ∆
 d
N
/
e
v
1
/N
0
5
10
15
20
25
30
35
40
p-p simulation with PYTHIA 
 = 50 GeV/c
hard
T
 = 5.5 TeV with p
NN
s
Charged particles 
>0.3 GeV/c
T
p
>2 GeV/c
T
p
>4 GeV/c
T
p
Figure 6.3: Dihadron azimuthal correlation at
√
sNN = 5.5 TeV and phard
T = 50
GeV/c pcut
T > 0.3 GeV/c (solid line), pcut
T > 2 GeV/c (dashed line) and pcut
T > 4
GeV/c (dotted line)
Choice of the alghorithm parameters
In order to select only hard processes a cut in pT was done. We choose this cut
studying azimuthal correlations between particles.
Two scattered partons propagate nearly back-to-back in azimuth from the collision
point and fragment into jet-like spray of final state particles. The back-to-back az-
imuthal correlations of high pT hadrons is written as
C(∆Φ) =
1
Ntrigger
∫
d∆η
dN
d∆Φd∆η
(6.8)
where ∆φ and ∆η are, respectively, the azimuthal angle and pseudo-rapidity be-
tween a trigger and their associated particles.
Figure 6.3 shows the azimuthal correlation between particles with phard
T = 50 GeV/c .
If the transverse momentum pT > 0.3 GeV/c a huge amount of particles with low
49
6.1. The Cone Jet Algorithm 50
RMS   2.032
 (GeV/c)
T
p
0 10 20 30 40 50
T
 d
N
/d
p
e
v
1
/N
-410
-310
-210
-110
1
10
210
Mean   15. 4
p-p simulation with PYTHIA
 = 50 GeV/c
hard
T
 = 5.5 TeV and p
NN
s 
>0.3 GeV/c
T
with p
Charged and neutral particles
Leading particles
 GeV/chard
T
p
20 40 60 80 100 120 140 160 180 200
>
 (
G
e
V
/c
)
le
a
d
in
g
T
<
p
0
10
20
30
40
50
60
70
80
90
100
p-p simulation with PYTHIA
 = 5.5 TeV  
NN
s 
All particles 
Charged particles
Figure 6.4: pT distribution for neutral and charged particles produced in p+
p collisions at
√
sNN = 5.5 TeV and phard
T = 50 GeV/c. The solid line shows pT dis-
tribution for all particles per event and the dashed line shows the pT distribution
for leading particles only. The right panel show the mean pT leading per bin for all
and charged particles production in p+ p collisions at
√
sNN = 5.5 TeV
pT are present between the the two-peaks (solid line), this particles are considered
like background. With a higher pcut
T this background is reduced (dashes and dotted-
dashed lines). A pcut
T = 2 GeV/c was chosen for further work.
The seed energy of the threshold is the transverse momentum of the leading (or
trigger) particles i.e., the particles with highest momentum in each event. This ’seed
energy’ depends of the phard
T used in the simulation of hard processes. For ex-
ample, figure 6.4 (left) shows the pT distribution for neutral and charged particles
simulated for a phard
T bin of 50 GeV/c. The mean pT of leading particles is about
∼15 GeV/c (dashed line), the initial interaction in cone jet algorithm will be pseed
T =
15 GeV/c and the same procedure for different bin. Figure 6.4 (right) and table 6.1
show the behaviour of mean pleading
T , with increase in phard
T .
The size of the cones used to identify jets were: Rc = 0.4, 0.7 and 1. Other param-
eters used for jet cone algorithm are shown in table 6.2. Once defined the cone
algorithm parameters, jets were reconstructed. Only jets obtained for phard
T = 50
GeV/c and phard
T = 30 - 179 GeV/c with charged particles and pcut
T = 2 GeV/c are
shown, but the results are the same for all particles and different phard
T . Studies in
jets in the CDF experiment [53], show that almost all the energy of the jet is con-
tained in Rc = 0.4, the ideal case is Rc =1, where all the particles are inside the cone
and Rc = 0.7 is a middle case.
50
6.2. Events with dijets 51
phard
T pTleading All pTleading Chg
[GeV/c] [GeV/c] [GeV/c]
30 9.32 7.99
50 15.34 12.69
100 30.37 24.95
150 46.10 37.74
200 61.98 50.84
30-179 12.69 10.52
Table 6.1: Mean pT leading per bin for all and charged particles production in
p+ p collisions at
√
sNN = 5.5 TeV
Description Value
Minimum seed energy [GeV] see Table 6.1 0.0
Particle pcut
T [GeV/c] 2
Radii R 0.4, 0.7,1
Maximum iterations 100
Minimum jet energy [GeV] 5.0
Size in φ 0.05
Size in η 0.05
Table 6.2: The settings used for cone jet algorithm implemented in the module
JETAN of ALIROOT.
Figure 6.5 shows the mean ET vs Rc for jets simulated with phard
T = 50 GeV/c and
phard
T = 30 - 179 GeV/c . Only small differences are observed when changing the
cone radius.
6.2. Events with dijets
Azimuthal correlation between dijets are shown in figures 6.6 for phard
T = 50 GeV/c (top
left), phard
T = 150 GeV/c (top right) and phard
T = 30 - 179 GeV/c (bottom). Here the back-
to-back azimuthal correlations is written as ∆φ = ΦEmax −ΦEmin, where max/min are
the jets with maximum/minimum energy in the same event. We can see that there
exist fake jets reconstructed close to the jet with maximum energy, these jets disap-
pear when the energy of the jets increases since the jets are more collimated (top),
but this fakes jets are more numerous when the cone size is small. For Rc = 0.4
there are fakes jets reconstructed at ∆φ = 0.5 and ∆φ = 5.5 due to part of the energy
of the jet is not inside the cone. These fakes jets are less when the cone size is
51
6.2. Events with dijets 52
cR
0.4 0.5 0.6 0.7 0.8 0.9 1
 >
 (
G
e
V
/c
)
T
<
 E
10
15
20
25
30
35
40
 = 5.5 TeV
NN
sp-p simulation with PYTHIA at 
 > 2 GeV/ccut
t
Jets with charged particles and p
 = 50 GeV/c hard
T
p
 = 30 - 179 GeV/chard
T
p
Figure 6.5: ET jets vs Rc for charged particles with pcut
T > 2 GeV/c, phard
T = 50
GeV/c (solid circles) and phard
T = 30 - 179 GeV/c (open circles).
increasing to an ideal case with Rc = 1. This effect is bigger in the spectrum with all
the phard
T bins together (bottom).
One way to select only real dijets that are opposite in azimuthal angle and with
small difference in energy, is defining an interval in ∆φ of 2.8 rad < ∆φ< 3.4 rad and
ET,max −ET,min/ET,max < 0.3 for dijets with all particles and ET,max −ETmin/ET,max < 0.8
for dijets with charged particles, where max/min are the jets with maximum/minimum
energy in the same event.
Another way to select real jets is using event shape analysis.
52
6.2. Events with dijets 53
minφ-maxφ = φ∆
0 1 2 3 4 5 6
φ∆
 d
N
/d
e
v
1
/N
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2 p-p simulation
with PYTHIA
 = 5.5 TeV
NN
s
 = 50 GeV/chard
T
p
Charged particles
>2 GeV/c
T
p
 = 1cR
 = 0.7cR
 = 0.4cR
minφ-maxφ = φ∆
0 1 2 3 4 5 6
φ∆
 d
N
/d
e
v
1
/N
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5 p-p simulation
with PYTHIA
 = 5.5 TeV
NN
s
 = 150 GeV/chard
T
p
Charged particles
>2 GeV/c
T
p
 = 1cR
 = 0.7cR
 = 0.4cR
minφ-maxφ = φ∆
0 1 2 3 4 5 6
φ∆
 d
N
/d
e
v
1
/N
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
p-p simulation
with PYTHIA
 = 5.5 TeV
NN
s
 = 30 - 179 GeV/chard
T
p
Charged particles
>2 GeV/c
T
p
 = 1cR
 = 0.7cR
 = 0.4cR
Figure 6.6: Dijet azimuthal correlations for charged particles with pcut
T > 2 GeV/c,
phard
T = 50 GeV/c (top left), phard
T = 150 GeV/c (top right) and phard
T = 30 - 179
GeV/c (bottom) for three cone radius: Rc = 1 (solid line), Rc = 0.7 (dashed line)
and Rc = 0.4 (dotted line).
53
6.3. Event Shape Analysis (ESA) 54
6.3. Event Shape Analysis (ESA)
The event shape analysis measures the geometrical properties of the energy flow in
QCD states, its allows us a method to determine areas where one does encounter
special topologies of jets in an event.
Sphericity was used at SLAC to show the evidence for the existence of jets in the
annihilation process: e+e− at energies up to 7.4 GeV in the center of mass. They cal-
culated in each event that direction which minimizes the sum of square of transverse
momentum, calling this quantity the sphericity S. Sphericity approaches 0 for events
with correlated transverse momenta and approaches to 1 for events with large mul-
tiplicity and isotropic particles distribution [56]. In hadron collisions, the contribution
of underlying event and multiple interactions introduce an experimental difficulty not
present in lepton colliders.
In this work, three shape variables are used to describe the topology of the events
in hadron collisions: thrust (T ), recoil (R) and thrust-minor (Tmin), these variables are
defined over particles within the acceptance of the detector [14].
6.3.1. Event shape variables
The thrust variable (T ) is defined using only transverse variables:
T ≡ max
︸︷︷︸
−→n t
∑i |−→p t,i ·−→n t |
∑i |−→p t,i|
(6.9)
where the sum runs over all particles in the final state within the acceptance, −→p t,i
represent the momentum components transverse to the beam and −→n t is the trans-
verse vector that maximizes the ratio. It is common to find the definition:
τ ≡ 1−T ∼ S (6.10)
related with the sphericity S of the event. The range of τ is between 0 and 0.35 [15].
For events with narrow back-to-back jets, τ is close to 0 and for events with a uniform
distribution of momenta τ is close to 0.35
The recoil variable R is defined as the vector sum of the transverse momentum:
R ≡ 1
∑i |−→p t,i|
|∑
i
−→p t,i| (6.11)
54
6.3. Event Shape Analysis (ESA) 55
This quantity measures the balance of momenta of the event. For example for mono-
jets events, i.e., two jets in a event but only one of them inside detector acceptance,
R tends to 1, because there are no vectorial transverse momentum cancellations
between particles. Otherwise, in the case of narrow back-to-back jet inside the ac-
ceptance, R tends to 0 because the vectorial transverse momentum sum is 0.
Tmin is a measure of the momentum out of the plane. Given the thrust axis (−→n t), we
can define it as:
Tmin ≡
∑i |−→p t,i x −→n t |
∑i |−→p t,i|
(6.12)
The event shape analysis starts by plotting a two dimensional distribution (“thrust
map”), with τ (1−T ) in the horizontal axis and R in the vertical axis. This plot allows
to identify different classes of events according with their location in the thrust map.
Figure 6.7 shows the two-dimensional distribution R vs. 1−T obtained using PYTHIA
with minimum bias p+ p collisions at
√
sNN = 200 GeV in the simulation, we require
that all particles be charged primaries and within the pseudorapidity range of |η | ≤ 1.
We also require that the events have at least 3 particles with transverse momentum
satisfying |−→p ⊥,i| ≥ 0.8 GeV/c.
Region A is characterized by dijets events, which occur completely inside the ALICE
acceptance (|η | ≤ 1), in this case, we have in the transverse plane the thrust axis
(−→n t) almost collinear to the direction of the leading particle. So, the ratio defined in
equation 6.9 tends to 1 and the recoil term (equation 6.11) tends to 0.
Region B is populated by monojets. These events have small values of τ and due
to the absence of vectorial cancellations in the numerator of the recoil term will have
the biggest values R.
Region C have the most isotropic events (with high 1−T and small R). This zone
of the thrust map is characterized by the presence of three jet events, called “mer-
cedes” events.
The intermediate region between A and B is populated by the combination of
mono-jets and “incomplete dijets”. Dijets are incomplete due to their high R, many
particles are outside of the acceptance.
The intermediate region between B and C is populated by events were 3 or more
jets are emitted at small angles with respect to the direction of the leading jet.
The line which appears in the high R part of the map is due to the definition of the
variables. For example, suppose that we have one event with a certain thrust axis
−→n t0, and in the event there are N particles. If the vectorial transverse momentum of
55
6.3. Event Shape Analysis (ESA) 56
Figure 6.7: R vs 1−T for a minimum bias sample of p+ p collisions at
√
sNN =
200 GeV [14]
the particle i is −→p t,i, then from the definitions of R and T:
1−T +R = 1− ∑i |−→p t,i ·−→n t0|
∑i |−→p t,i|
+
|∑i
−→p ti|
∑i |−→p t,i|
(6.13)
Now, we use the fact that:
|∑
i
−→p ti| ≤ ∑
i
|−→p t,i| (6.14)
Then:
1−T +R ≤ 1−T +1 (6.15)
56
6.3. Event Shape Analysis (ESA) 57
The maximum value which T can reach is 1, so we find the following restriction:
1−T +R ≤ 1 (6.16)
6.3.2. Azimuthal correlations
For describing the topology of the events we performed an analysis of the azimuthal
correlation between particles using PYTHIA with minimum bias p + p collisions at√
sNN = 200 GeV. The distribution were obtained from the three regions (see ta-
ble 6.3) which are generated by choosing the highest momentum particle in the
event to be at 0 radians. This is shown in the left panel of figure 6.8, where the near
side peaks are well distinguishable for the 3 plots while substantial differences occur
in the away-side. For particles in region (A) we find the usual form of the away-side
peak. For particles in region (B), as expected, there is no sight of a peak in the
away-side. Finally for particles in region (C) we are confronted with a double hump
structure [57], discussed in section 9.
Region Kind of event Variables
A Dijets R ≤ 0.35, τ ≤ 0.03
B Monojets R ≥ 0.9, τ ≤ 0.03
C Mercedes R ≤ 0.4, τ ≥ 0.25
Table 6.3: 1-T and R parameters used for the present analysis.
Adding the three regions (solid line in the right panel of figure 6.8) we compare the
azimuthal distribution with STAR data [8], we obtain a reasonable agreement.
57
6.3. Event Shape Analysis (ESA) 58
 (rad)φ∆
0 1 2 3 4 5 6
−
1
 (
0
.0
5
 r
a
d
)
φ∆
d
N
/d
e
v
1
/N
−5
10
−4
10
−3
10
0 1 2 3−1 4  (rad)φ∆
-1 0 1 2 3 4 5
-1
 (
ra
d
)
φ∆
 d
N
/d
e
v
1
/N
0
0.05
0.1
0.15
0.2
0.25
0.3
 = 200 GeV
NN
sp-p 
 = 10 GeV/chard
t
p
>0.5 GeV/c
t
| < 0.7, pη|
STAR PRL 91, 072304 (2003)
 All events with thrust
Region A
Region B
Region C
Figure 6.8: Dihadron azimuthal correlations for minimum bias p+ p collisions
at
√
sNN = 200 GeV events, in the different regions of the plot R vs 1− T . The
highest momentum particle (leading particle) in the event, located at ∆φ = 0
radians, is not shown. Shown are: events in region (A) (dashed line), events in
region (B) (dotted line), events of region (C) (solid line). In the right panel the
three regions were adding (dashed-dotted line) and compared with STAR data
[8]
58
Chapter 7
Energy loss
It has been predicted that a high-pT parton traversing hot nuclear matter, will expe-
rience collisional energy loss, via scattering, and radiative energy loss, via induced
gluon bremsstrahlung.
Radiative energy loss is expected to dominate over collisional energy loss. The
amount of energy loss, ∆E, is predicted to be proportional to the gluon/energy den-
sity of the medium and a function of the path length of the parton through the
medium. Thus jets, which have lost energy while traversing the medium, can be
used as tools to probe the medium and provide information on its properties and
structure at an early stage
The pQCD based calculations predict that the angular energy distribution for jets
which have undergone energy-loss in a dense QCD medium is very similar to the
energy distribution of jets which fragment in vacuum.
The gluons are radiated at angles close to the jet axis and remain inside the jet cone.
Therefore, measuring the total energy within a cone of radius Rc around the jet axis
will not provide information on jet energy loss since the total energy inside the cone
will include both the final jet energy plus the radiated energy.
However, the momentum distribution of the particles within the jet cone is expected
to be modified for jets which have lost energy due to medium effects. Jet energy loss
is manifested by a shift of the fragmentation function towards low z, as shown by the
increase above unity of low momentum (i.e., low-z)1 particles and the decrease in
the number of high-z particles compared to the case with no energy loss i.e., there
is a shift of particles from high-pT to low-pT . Lower energy jets are more affected
than higher energy jets.
Then, analysis of modifications of the structure of jets produced in nucleus-nucleus
1z = pT /ET jet
59
7.1. PYQUEN model 60
collisions represent a very sensitive tool to study the interactions of partons with the
medium.
In this work, we studied the effects of parton energy loss in a medium under extreme
conditions of temperature and density. To achieve that, we simulate high-pT events
in p + p collision with PYTHIA(see section 5), as a baseline, and events passed
through two afterburner models of energy loss PYQUEN [11] and Q-PYTHIA [12].
7.1. PYQUEN model
PYQUEN (PYthia QUENched) [11] is a fast Monte-Carlo event generator routine im-
plemented to modify standard jets events in PYTHIA 6.2.14. This model simulate re-
scattering, radiative and collisional energy loss of hard partons in expanding quark-
gluon plasma created in ultra-relativistic heavy ion-ion collisions without considering
possible effects of double parton scattering.
The model is based on an accumulating energy loss, the gluon radiation being as-
sociated with each parton scattering in the expanding medium and includes the
interference effect using the modified radiation spectrum dE/dl as a function of de-
creasing temperature T. The kinetic integral equation for the energy loss ∆E as a
function of initial energy E and path length L has the form
∆E(L,E) =
L∫
0
dl
dP(l)
dl
λ (l)
dE(l,E)
dl
,
dP(l)
dl
=
1
λ (l)
exp(−l/λ (l)) , (7.1)
where l is the current transverse coordinate of a parton, dP/dl is the scattering
probability density, dE/dl is the energy loss per unit length, λ = 1/(σρ) is the in-
medium mean free path, ρ ∝ T 3 is the medium density at the temperature T , σ is
the integral cross section for parton interaction in the medium.
The collisional energy loss is due to elastic scattering with high-momentum transfer
taking also into account the low-momentum transfer loss resulting mainly from the
interactions with plasma collective modes. This process does not contribute much
to the total collisional loss in comparison with high-momentum scattering, due to the
absence of a large factor ∼ ln(E/µD) where µD is the Debye screening mass [3].
Then, the collisional part associated with high-momentum transfer has the form:
dE
dl
col
=
1
4Tλσ
tmax∫
µ2
D
dt
dσ
dt
t , (7.2)
60
7.1. PYQUEN model 61
and the dominant contribution to the differential cross section
dσ
dt
∼=C
2πα2
s (t)
t2
E2
E2 −m2
p
, αs =
12π
(33−2N f ) ln(t/Λ2
QCD)
(7.3)
for scattering of a hard parton with energy E and mass mp off the “thermal” parton
with energy (or effective mass) m0 ∼ 3T ≪ E. Here C = 9/4,1,4/9 for gg, gq and
qq respectively, αs is the QCD running coupling constant for N f active quark flavors,
and ΛQCD is the QCD scale parameter which is of the order of the critical temper-
ature, ΛQCD ≃ Tc ≃ 200 MeV. The integrated cross section σ is regularized by the
Debye screening mass squared µ2
D(T )≃ 4παsT 2(1+N f /6). The maximum momen-
tum transfered is tmax = [s− (mp+m0)
2][s− (mp−m0)
2]/s, where s = 2m0E +m2
0 +m2
p.
The medium induced gluon radiation is restricted to BDMS formalism [45, 46]. In the
BDMS framework, the strength of multiple scattering is characterized by the transport
coefficient q̂ = µ2
D/λg (λg is the gluon mean free path), which is related to the elastic
scattering cross section σ . In this simulations, the strength is regulated mainly by
the initial QGP temperature, T0. Then the energy spectrum of coherent medium-
induced gluon radiation and the corresponding dominant part of radiative energy
loss of mass-less parton have the form:
dE
dl
rad
=
2αs(µ2
D)CR
πL
E∫
ωmin
dω
[
1− y+
y2
2
]
ln |cos(ω1τ1)| , (7.4)
ω1 =
√
i
(
1− y+
CR
3
y2
)
κ̄ ln
16
κ̄
with κ̄ =
µ2
Dλg
ω(1− y)
, (7.5)
where τ1 = L/(2λg), y = ω/E is the fraction of the hard parton energy carried away
by the radiated gluon, and CR = 4/3 is the quark color factor. A similar expression for
the gluon jet can be obtained by changing the factor CR = 3 in the square brackets
in equation 7.4.
Another important element of the model is the angular spectrum of in-medium gluon
radiation. Since the detailed calculation of the angular spectrum of emitted gluons
is rather sophisticated and model-dependent, the simple parametrization of gluon
angular distribution over the emission angle θ was used:
dNg
dθ
∝ sinθ exp
(
−(θ −θ0)
2
2θ2
0
)
, (7.6)
where θ0 ∼ 50 is the typical angle of the coherent gluon radiation as estimated in [47].
61
7.1. PYQUEN model 62
The internal model parameters are the initial conditions for the QGP formation ex-
pected for central ion-ion collisions (table 7.1).
Description Parameter Value
Medium-induced ienglu 0 - radiative and collisional
partonic energy loss 1 - radiative
2 - collisional
Initial temperature of Tc 0.2 GeV< Tc < 2 GeV
quark-gluon plasma
Proper time of quark-gluon τ0 0.01 fm/c < τ0 < 10 fm/c
plasma formation
Number of active quark flavors nf 0, 1, 2 or 3
in quark-gluon plasma
Angular distribution of ianglu 0 - small - angular
emitted gluons 1 - wide - angular
2 - collinear
Table 7.1: PYQUEN internal model parameters
The simulation procedure is:
• Generation of the initial parton spectra with PYTHIA (fragmentation off).
• Generation of the jet production vertex at the impact parameter b according to
the distribution
dNjet
dψdr
(b) =
TA(r1)TA(r2)
TAA(b)
, TAA(b) =
2π∫
0
dψ
rmax∫
0
rdrTA(r1)TA(r2) , (7.7)
where r1,2(b,r,ψ) are the distances between the nucleus centers and the jet
production vertex V (r cosψ,r sinψ); rmax(b,ψ) ≤ RA is the maximum possible
transverse distance r from the nuclear collision axis to V ; RA is the radius of the
nucleus A; TA(r) = A
∫
ρA(r,z)dz is the nuclear thickness function with nucleon
density distribution ρA(r,z); TAA(b) is the nuclear overlap function (see ref. [48]
for detailed nuclear geometry explanations).
• Calculation of scattering cross section
• Generation of the displacement between i-th and (i+ 1)-th scatterings, li =
(τi+1− τi) and calculation of the corresponding transverse distance, li pT/E.
62
7.1. PYQUEN model 63
• Reducing the parton energy by collisional and radiative loss per each i-th scat-
tering:
• Calculation of the parton transverse momentum kick due to elastic scattering i
• Formation of the additional (in-medium emitted) gluon with the energy ωi and
the emission angle θi relative to the parent parton.
• Halting the rescattering if (1) the parton escapes the dense zone, or (2) QGP cools
down to Tc=200 MeV, or (3) the parton loses so much energy that its pT (τ )
drops below 2T (τ ).
• At the end of each event, adding new (in-medium emitted) gluons to the PYTHIA par-
ton list and rearrangement of partons to update string formation.
• Formation of the final state particles by PYTHIA (fragmentation on).
The complete study for different PYQUEN parameters values and pT hard was done.
Since the results do not change as function of pT hard, only results with pT hard =50
GeV/c are shown. Similarly, only the important PYQUEN internal parameters used in
p+ p simulation at
√
sNN = 5.5 TeV are shown in table 7.2.
Parameter Value
ienglu 0 - radiative and collisional
1 - radiative
2 - collisional
Tc 1 GeV
2 GeV
τ0 0.01 fm/c
nf 0
iangle 0 - small - angular
Table 7.2: PYQUEN internal parameters used for p+ p collisions at
√
sNN = 5.5 TeV
Figure 7.1 show the transverse momentum distribution, with two temperature, for
charged particles obtained with PYQUEN at
√
sNN = 5.5 TeV and pT hard = 50 GeV/c.
For the collisional part only a transfer momentum and parton transverse momentum
kick due to elastic scattering is calculated. For radiative energy loss, the formation
of the additional radiated gluon with energy ωi and the emission angle θi relative to
the parent parton is generated. Combination of both, collisional and radiative energy
loss, is shown in dashed-dotted line. The result is: more particles with low pT and
less particles with high pT.
63
7.1. PYQUEN model 64
 (GeV/c)
T
p
0 10 20 30 40 50 60 70
T
 d
N
/d
p
e
v
1
/N
-510
-410
-310
-210
-110
1
10
210  = 50 GeV/c
hard
T
 = 5.5 TeV and p
NN
s 
>0.3 GeV/c
T
Charged particles with p
p-p simulation with PYTHIA
 = 1 GeV
c
p-p simulation with PYQUEN T
Collisional energy loss
Radiative energy loss
Collisional and radiative energy loss
Figure 7.1: pT distribution for p+ p collisions at
√
sNN = 5.5 TeV and phard
T = 50
GeV/c simulated only with PYTHIA (solid line) and with PYQUEN with collisional
(dashed line), radiative (dotted line) and both (dashed-dotted line) energy loss
at Tc = 1 GeV.
Figure 7.2 shows the azimuthal correlations between particles in the left panel and
the ratio of particles yields (RAA PYQUEN to PYTHIA) in the right, at
√
sNN = 5.5 TeV with
pT hard = 50 GeV/c for the collisional (top), radiative (middle) and collisional and radia-
tive (bottom) energy loss at two Tc. Since, in real data it is not possible to separate
collisional and radiative energy loss, only the case with both together is studied.
In this plots the formation of particles with low-pT is clear, i.e.,a peak at low-pT in
RAA and more particles in the azimuthal distribution, however, there is no significant
difference with Tc. In the next sections only Tc = 1 GeV is considred.
64
7.1. PYQUEN model 65
φ∆
-1 0 1 2 3 4 5
φ∆
 d
N
/
e
v
1
/N
10
15
20
25
30
35
40
 = 50 GeV/c
hard
T
 = 5.5 TeV and p
NN
s 
>0.3 GeV/c
T
Charged particles with p
p-p simulation with PYTHIA
Pyquen collisional energy loss
 = 1 GeVcT
 = 2 GeVcT
 (GeV/c)
T
p
0 5 10 15 20 25 30 35 40
)
T
 (
p
A
A
R
0
0.5
1
1.5
2
2.5
3
 = 50 GeV/c
hard
T
 = 5.5 TeV and p
NN
s 
>0.3 GeV/c
T
Charged particles with p
Pyquen collisional energy loss
 = 1 GeVcT
 = 2 GeVcT
φ∆
-1 0 1 2 3 4 5
φ∆
 d
N
/
e
v
1
/N
10
15
20
25
30
35
40
 = 50 GeV/c
hard
T
 = 5.5 TeV and p
NN
s 
>0.3 GeV/c
T
Charged particles with p
p-p simulation with PYTHIA
Pyquen radiative energy loss
 = 1 GeVcT
 = 2 GeVcT
 (GeV/c)
T
p
0 5 10 15 20 25 30 35 40
)
T
 (
p
A
A
R
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
 = 50 GeV/c
hard
T
 = 5.5 TeV and p
NN
s 
>0.3 GeV/c
T
Charged particles with p
Pyquen radiative energy loss
 = 1 GeVcT
 = 2 GeVcT
φ∆
-1 0 1 2 3 4 5
φ∆
 d
N
/
e
v
1
/N
10
15
20
25
30
35
40
 = 50 GeV/c
hard
T
 = 5.5 TeV and p
NN
s 
>0.3 GeV/c
T
Charged particles with p
p-p simulation with PYTHIA
Pyquen collisional and radiative energy loss
 = 1 GeVcT
 = 2 GeVcT
 (GeV/c)
T
p
0 5 10 15 20 25 30 35 40
)
T
 (
p
A
A
R
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
 = 50 GeV/c
hard
T
 = 5.5 TeV and p
NN
s 
>0.3 GeV/c
T
Charged particles with p
Pyquen collisional and radiative energy loss
 = 1 GeVcT
 = 2 GeVcT
Figure 7.2: Dihadron azimuthal correlation (left) and RAA (PYQUEN to PYTHIA)
(right) for p + p collisions at
√
sNN = 5.5 TeV and phard
T = 50 GeV/c simulated
with PYQUEN with collisional (top) radiative (middle) and collisional and radiative
(bottom) energy loss and Tc = 1 GeV (dashed line) and Tc = 2 GeV (dashed-
dotted line).
65
7.2. Q-PYTHIA model 66
7.2. Q-PYTHIA model
Q-PYTHIA [12, 49] is a modification of the final state showering routine PYSHOW in
PYTHIA 6.4.18 that introduced a medium-induced term in the splitting probability
function P(z) and a formation time effect as an effective cut-off of the radiation with-
out consider collisional energy loss.
The spectrum for medium-induced gluon radiation is a sum of a vacuum term plus a
medium-induced term
dItot
dzdp2
T
=
dIvac
dzdp2
T
+
dImed
dzdp2
T
. (7.8)
The vacuum term can be related with the standard Dokshitzer-Gribov-Lipatov-Altarelli-
Parisi (DGLAP) splitting functions Pvac(z) [50],
dIvac
dzdp2
T
=
αs
2π
1
p2
T
Pvac(z), Pvac(z)≃
2CR
1− z
. (7.9)
where 1− z is the momentum fraction of the parent parton momentum taken by the
emitted gluon, pT the transverse momentum of the emitted gluon with respect to the
direction of its parent, αs is the QCD running coupling constant and CR the quadratic
Casimir of the color representation of the parent parton.
By matching the medium and the vacuum cases, the corresponding modification to
the splitting probability function is:
Ptot(z) = Pvac(z)→ Ptot(z) = Pvac(z)+∆P(z, t, q̂,L,E), ∆P(z, t, q̂,L,E)≃ 2πt
αs
dImed
dzdt
.
(7.10)
The correction ∆P(z, t, q̂,L,E) depends not only on the energy fraction z but also
on the virtuality t = z(1 − z)p2
T of the radiating parton and its energy E, medium
length L and transport coefficient q̂. The transport coefficient q̂ encodes all possible
information about the medium properties as temperature, density, etc. in a single
parameter, with the interpretation of the average transverse momentum squared
that the gluon gets per mean free path in the medium.
The basic procedure followed by Q-PYTHIA is: given a parton coming from a branch-
ing (or production) point with coordinates (t1,x1), with t1 the virtually and x1 its energy
fraction, compute the coordinates (t2,x2) for the next branching.
The scale t of the evolution in PYTHIA is chosen to be the invariant mass squared
66
7.2. Q-PYTHIA model 67
of the decaying particles. The showering is performed by the creation of pairs of
partons, conserving four-momentum at each step. If, in the course of the evolution,
a parton a reaches a scale ta that is smaller than any minimal mass of any allowed
branching mode, then its mass and its scale will be set to its current mass m0
a and
it will leave the parton shower without further branching. The evolution has a scale
cut-off t0 = Q2
0.
The geometry of a dense medium produced in nucleus–nucleus collision can be
chosen by the user. The simplest is a brick geometry with L = 4.5 fm and q̂ = 5
GeV2/fm and q̂ = 50 GeV2/fm to exemplify the dependence of energy loss with q̂, also
a realistic Glauber-like collision geometry is defined, in this geometry the production
points and the quenching parameters are defined like in the PQM model [51]. The
production points of the hard scatterings are distributed in the nuclear overlapping
area according to the probability of central nucleon-nucleon collisions. Then, q̂ and
in-medium path length L are computed locally through two integrals of the density of
binary nucleon-nucleon collisions along parton trajectories isotropically distributed in
azimuth. In this model the only free parameter is the scale of the transport coefficient
k = 6 ·106 fm, which corresponds to an average 〈q̂〉= 14 GeV2/fm in a 0-10% central
collision.
Figure 7.3 shows the pT distribution and 7.4 the azimuthal correlation between par-
ticles in the left panel and the ratio of particles yields (Q-PYTHIA and PYTHIA) as
function of pT in the right panel, at
√
sNN = 5.5 TeV and phard
T = 50 GeV. Two geom-
etry are used, brick geometry with 2 values of q̂ and the Glauber geometry.
We can see:
• Increase of multiplicity and pT spectrum is harder for PYTHIA than Q-PYTHIA.
• Re-distribution of particles in azimuthal angle, compared with PYTHIA.
Once particle production simulation was made, with and without energy loss, we pro-
ceed to reconstruct jets using a cone jet algorithm (JETAN) and event shape analysis
(ESA). This procedure is described in the next section.
67
7.2. Q-PYTHIA model 68
 (GeV/c)
T
p
0 10 20 30 40 50 60 70
T
 d
N
/d
p
e
v
1
/N
-510
-410
-310
-210
-110
1
10
210  = 50 GeV/c
hard
T
 = 5.5 TeV and p
NN
s 
>0.3 GeV/c
T
Charged particles with p
p-p simulation with PYTHIA
Q-PYTHIA
/fm L = 4 fm
2
 = 5 GeVq
/fm L = 4 fm
2
 = 50 GeVq
fm. b = 0-10%
6
k = 6.10x10
/fm
2
 = 14 GeVq ⇒ 
Figure 7.3: pT distribution for p+ p collisions at
√
sNN = 5.5 TeV and phard
T =
50 GeV/c simulated only with PYTHIA (solid line) and with Q-PYTHIA with L = 4
fm and 2 values of q̂ in brick geometry (dashed and dotted line) and Glauber
geometry (dashed-dotted line)
φ∆
-1 0 1 2 3 4 5
φ∆
 d
N
/
e
v
1
/N
10
15
20
25
30
35
40
 = 50 GeV/c
hard
T
 = 5.5 TeV and p
NN
s 
>0.3 GeV/c
T
Charged particles with p
p-p simulation with PYTHIA
Q-PYTHIA
/fm L = 4 fm2 = 5 GeVq
/fm L = 4 fm
2
 = 50 GeVq
fm. b = 0-10%
6
k = 6.10x10
/fm2 = 14 GeVq ⇒ 
 (GeV/c)
T
p
0 5 10 15 20 25 30 35 40 45
)
T
 (
p
A
A
R
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
 = 50 GeV/c
hard
T
 = 5.5 TeV and p
NN
s 
>0.3 GeV/c
T
Charged particles with p
Q-PYTHIA
/fm L = 4 fm
2
 = 5 GeVq
/fm L = 4 fm2 = 50 GeVq
fm. b = 0-10%
6
k = 6.10x10
/fm
2
 = 14 GeVq ⇒ 
Figure 7.4: Dihadron azimuthal correlation (left) and RAA (right) for p+ p colli-
sions at
√
sNN = 5.5 TeV and phard
T = 50 GeV/c simulated only with PYTHIA (solid
line) and with Q-PYTHIA with L = 4 fm and 2 values of q̂ in brick geometry (dashed
and dotted line) and Glauber geometry (dashed-dotted line)
68
Chapter 8
Acoplanarity for dijets (kT ) and the transverse
momentum of a jet ( jT )
Jet are produced in the hard scattering of two partons. Two partons collides result-
ing in two outgoing partons with roughly opposite high-pT . This outgoing partons
fragment into jets of hadrons one on toward side (trigger) and one on the away side,
in the azimuthal plane (the plane is formed by the two beams and the trigger jet).
Others jets have small-pT and result from the break up of the two partons collides,
usually refereed to as soft hadronic background.
Each of the particle carriers a transverse momentum, this transverse momentum
can arise from two sources: the transverse momentum of partons inside proton,
originally describe as “intrinsic” transverse momentum kT and the transverse mo-
mentum relative to the jet axis jT , given to a particle during the fragmentation of its
parent after scattering.
The two components of the vector kT , kT x and kT y, are Gaussian distributed and
result in different experimentally measurable effects. kT y leads to the acoplanarity of
the dijet pair while kT x makes the momentum of the jets unequal. Also, jT is a two-
dimensional vector. The component of jT projected onto the azimuthal plane, jT y, is
perpendicular to the jet transverse axis. The other component, jT x, is perpendicular
to the jet transverse axis in the longitudinal plane.
The average transverse momentum component of the away side particles pT a is
label as pout and can be obtained by:
〈|pout|〉2 =
〈
|kT y|
〉
x2
E +
〈
| jTy|
〉
(1+ x2
E) (8.1)
where
〈
|kT y|
〉
and
〈
| jTy|
〉
are the average values of the components of transverse
momentum out of the scattering plane and xE =−pT apT t/|pT t|2 represents the frag-
mentation variable of the away-side jet. The magnitude of pout between dijets and
the transverse momentum of particles inside jets can be calculated as well as jT by:
69
8.1. Acoplanarity for dijets 70
pout = |pT a|sin∆φ (8.2)
jT = |pT a|sinφ (8.3)
where ∆φ is the azimuthal angle between jets and φ is the azimuthal angle relative
to the jet axis [58, 59, 60].
We show results obtained for the acoplanarity between dijets and the modifications
of the fundamental properties of jets due to their interaction with a dense medium.
8.1. Acoplanarity for dijets
In order to understand the behavior of kT in hadron collisions, we studied its depen-
dence with the energy of the collision and the transverse momentum of the hard-
pT particles. High-pT particles was produced using the PYTHIA event generator in
p+ p changing the parameters PARP(91) and PARP(93), that control the magnitude
of the intrinsic transverse momentum in the collisions (see table 5.1).
After event generation, jets were reconstructed with cone jet algorithm implemented
in the module JETAN of ALIROOT. Table 8.1 show the parameters used in the simu-
lation.
PYTHIA 6.2 CONE ALGORITHM
√
sNN = 900 GeV, 5.5 TeV and 14 TeV Rc<0.7
phard
T = 30,50,70,100,150,200 GeV/c |η |<0.9
kT =0, 5, 7.5, 10 and 15 GeV/c No pcut
T
IR and FR off/on ET > 0 GeV
Table 8.1: Parameters used in kT the simulation
Figure 8.1 show the acoplanarity between two jets, defined in equation 8.2, as func-
tion of center of mass energy,
√
sNN and phard
T . As expected, the acoplanarity be-
tween two jets increased with the intrinsic kT (left). pout increase with increasing
phard
T and center of mass energy. At higher center of mass energy pout shows a
small dependence on the unknown intrinsic kT due to the dominance of initial state
radiation (rigth).
70
8.2. Transverse momentum jT 71
T, hard
p
20 40 60 80 100 120 140 160 180 200
>
2 o
u
t
<
p
0
2
4
6
8
10
12
Initial and final radiation off
 = 14 TeV
NN
s
 = 0 Gev/c
T
k
 = 5 Gev/cTk
 = 15 Gev/c
T
k
 = 5.5 TeV
NN
s
 = 0 Gev/c
T
k
 = 5 Gev/cTk
 = 15 Gev/c
T
k
 = 900 GeV
NN
s
 = 0 Gev/c
T
k
 = 5 Gev/c
T
k
 = 15 Gev/c
T
k
Graph
T, hard
p
20 40 60 80 100 120 140 160 180 200
>
2 o
u
t
<
p
0
5
10
15
20
25
30
35
Initial and final radiation on
 = 14 TeV
NN
s
 = 0 Gev/c
T
k
 = 5 Gev/cTk
 = 15 Gev/c
T
k
 = 5.5 TeV
NN
s
 = 0 Gev/c
T
k
 = 5 Gev/cTk
 = 15 Gev/c
T
k
 = 900 GeV
NN
s
 = 0 Gev/c
T
k
 = 5 Gev/c
T
k
 = 15 Gev/c
T
k
Graph
Figure 8.1: pout as a function of transverse momentum of the partons is show for
different values of kT and center of mass energies without (left) and with (right)
initial and final radiation
After parton are produced using PYTHIA, they are passed through PYQUEN (sec-
tion 7.1) and Q-PYTHIA (section 7.2), taking into account initial and final state ra-
diation and kT = 5 GeV/c. The system created was under the assumption of Tc =
1 GeV and with collisional and radiative energy loss, for PYQUEN and k = 6 · 106
fm, which corresponds to an average 〈q̂〉 = 14 GeV2/fm in a 0-10% glauber central
collision for Q-PYTHIA.
The left panel of figure 8.2 show the transverse momentum imbalance defined as
the difference between the trigger jet (~pT,t) and the away-side jet (~pT,a) transverse
momentum in the trigger jet-beam plane.
pmax − ppro j = |pTt |− |pTaPro j(pTt)|=
√
2kT x (8.4)
and in the rigth panel is shown the acoplanarity between dijets. Comparing both
models to simulate energy loss, Q-PYTHIA (dashed line) and PYQUEN (dotted line)
with PYTHIA (solid line) the extra kT from partonic interactions with the dense medium
can be observed on top of the initial state radiation.
8.2. Transverse momentum jT
High-pT events were produced using the PYTHIA event generator in p+ p and jets
are reconstructed with UA1 jet cone algorithm implemented in the module JETAN of
ALIROOT. In order to study the ideal case i.e., all the particle inside the jet, jets with
a Rc =1 were reconstructed .
Figure 8.3 shows the ratio of particles yield (RAA) vs pT for two energy loss models.
71
8.2. Transverse momentum jT 72
Mean   12.19
 (GeV/c)
diff
p
0 10 20 30 40 50 60
d
if
f
 d
N
/d
p
e
v
1
/N
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Mean   15.17
Mean   16.98
Jets with charged particles:
 = 5.5
NN
s
 = 50 GeV/chard
t
p
>0.3 GeV/c 
T
 = 0.7 and pcR
PYTHIA
Q-PYTHIA
fm. b = 0-10%
6
k = 6.10x10
/fm2 = 14 GeVq ⇒ 
PYQUEN
Collisional and radiative
energy loss
 = 1 GeVcT
RMS    7.802
 (GeV/c)
out
p
-40 -30 -20 -10 0 10 20 30 40
o
u
t
 d
N
/d
p
e
v
1
/N
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
RMS    8.447
RMS    9.241
Jets with charged particles:
 = 5.5
NN
s
 = 50 GeV/chard
t
p
>0.3 GeV/c 
T
 = 0.7 and pcR
PYTHIA
Q-PYTHIA
fm. b = 0-10%
6
k = 6.10x10
/fm2 = 14 GeVq ⇒ 
PYQUEN
Collisional and radiative
energy loss
 = 1 GeVcT
Figure 8.2: pT,diff (left) and pout (rigth) for charged dijets with Rc= 0.7 and phard
T =
50 GeV/c at
√
sNN = 5.5 TeV with PYTHIA (solid line), PYQUEN (dashed line) with
T0 = 1 GeV and Q-PYTHIA (dotted line).
As expected, a decrease of the number of particles carrying high-pT and an increase
in the number of low-pT particles is observed.
Figure 8.4 shows the ratio of particles yield (RAA) (Q-PYTHIA/PYTHIA in the left panel
and PYQUEN/PYTHIA in the rigth panel) vs pT for three r values. Clear differences
between the two Monte-Carlo in the pattern of increase of low-momentum particles
and depletion of high-momentum particles at different r can be observed. In vacuum
angular ordering rules the pT distribution of particles at different distances r to the
jet axis. High-pT particles are predominantly produced close the jet axis whereas
low-pT particles are found at larger distances. High-pT particles at large distances
from the jet axis are due to hard gluons radiated shortly after the initial hard scatter-
ing. These gluons see the same medium as the leading parton, but having smaller
energies the effect of energy loss should be stronger.
Broadening of the distribution of jet-particle momenta perpendicular to the jet axis,
jT distribution are show in figure 8.5 (left) and the ratio between the two models and
PYTHIA (right). Additional broadening is observed and this is directly related to the
colour density of the traversed medium.
72
8.2. Transverse momentum jT 73
 (GeV/c)
T
p
0 5 10 15 20 25 30 35 40
)
T
 (
p
A
A
R
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Jets with charged particles:
 = 50 GeV/c
hard
t
 = 5.5 TeV p
NN
s
>0.3 GeV/c 
T
 = 1 and pcR
Q-PYTHIA
fm. b = 0-10%
6
k = 6.10x10
/fm
2
 = 14 GeVq ⇒ 
PYQUEN
Collisional and radiative energy loss
 = 1 GeVcT
Figure 8.3: Ratio of particles yield (RAA) vs pT between p+ p and Pb+Pb colli-
sion with phard
T = 50 GeV/c at
√
sNN = 5.5 TeV and |η |< 1.9
73
8.2. Transverse momentum jT 74
 (GeV/c)
T
p
0 5 10 15 20 25 30
)
T
 (
p
A
A
R
-110
1
Jets with charged particles:
 = 50GeV/chard
t
 = 5.5 TeV p
NN
s
>0.3 GeV/c 
T
 = 50 GeV pTR = 1 E
Q-PYTHIA
fm. b = 0-10%
6
k = 6.10x10
/fm2 = 14 GeVq ⇒ 
0.7 < r < 1
0.3 < r < 0.7
0.0 < r < 0.3
 (GeV/c)
T
p
0 5 10 15 20 25 30
)
T
 (
p
A
A
R
-110
1
Jets with charged particles:
 = 50GeV/chard
t
 = 5.5 TeV p
NN
s
>0.3 GeV/c 
T
 = 50 GeV pTR = 1 E
PYQUEN
Collisional and radiative energy loss
 = 1 GeVcT
0.7 < r < 1
0.3 < r < 0.7
0.0 < r < 0.3
Figure 8.4: Ratio of particles yield (RAA) vs pT in Q-PYTHIA and PYTHIA (left)
and PYQUEN and PYTHIA (rigth) at different distances r to the jet axis for p+
p collision with phard
T = 50 GeV/c at
√
sNN = 5.5 TeV and |η |< 1.9
Mean   0.3341
 (GeV/c)
T
j
0 2 4 6 8 10
T
 d
N
/d
j
e
v
1
/N
-410
-310
-210
-110
1
10
210
Mean  0.3679
Mean  0.3185
Jets with charged particles:
 = 50 GeV/c
hard
t
 = 5.5 TeV p
NN
s
>0.3 GeV/c 
T
 = 1 and pcR
PYTHIA
Q-PYTHIA
fm. b = 0-10%
6
k = 6.10x10
/fm
2
 = 14 GeVq ⇒ 
PYQUEN
Collisional and radiative energy loss
 = 1 GeVcT
 (GeV/c)
T
j
0 1 2 3 4 5
)
T
 (
j
A
A
R
0
0.5
1
1.5
2
2.5
3
3.5
4
Jets with charged particles:
 = 50 GeV/c
hard
t
 = 5.5 TeV p
NN
s
>0.3 GeV/c 
T
 = 1 and pcR
Q-PYTHIA
fm. b = 0-10%
6
k = 6.10x10
/fm
2
 = 14 GeVq ⇒ 
PYQUEN
Collisional and radiative energy loss
 = 1 GeVcT
Figure 8.5: jT distribution (left) and ratio of particles yield (RAA) vs jT between
p+ p and Pb+Pb collision (rigth) with phard
T = 50 GeV/c at
√
sNN = 5.5 TeV and
|η |< 1.9
74
Chapter 9
Event shape analysis in a dense medium
Confronted with the double hump structure obtained in section 6.3.2 we have tried
to see what are the predictions of a generator Q-PYTHIA (section 7.2), that takes into
account the effects of parton energy loss in the medium simulating the effects to be
observed in heavy ion collisions.
9.1. Azimuthal correlations at RHIC energy
In figure 9.1 we compare the effect of Q-PYTHIA on the event shape using a sample
of events generated at
√
sNN = 200 GeV with a hard cutoff in pT leading > 10 GeV/c and
a lower pcut
T on the hadrons of 0.5 GeV/c. The curves obtained correspond to three
distinct choices of parameters of Q-PYTHIA: A medium path length of 6 fm with two
choices of q̂, 1 and 5 GeV2/fm. The interest of the results lays in the behavior of the
dependence of the yields in two different parts of the 1−T vs R distribution. While for
low values of R and 1−T we observe a decrease of the probability with increasing
q̂, in the case of high values of 1−T we observe a frank increase of the yield in
the away-side correlation with the double hump. These results remind us very much
of the double hump structures encountered in the RHIC experiments in collisions of
heavy ions.
9.2. Event Shape Analysis (ESA) at LHC energy
At
√
sNN = 5.5 TeV, charged particles for hard processes with phard
T = 50 GeV/c are
simulated. Even though hard processes are simulated, isotropic events are present
(top of figure 9.2). Increasing the pcut
T (middle and bottom of figure 9.2) events
with monojets and dijets are selected and the backgound decreases. This behavior
is clearly seen in the azimuthal distribution (rigth panels), obtained from the three
regions selected with cuts in described in table 9.1.
To study the effect of PYQUEN and Q-PYTHIA in the event shape variables used to
75
9.2. Event Shape Analysis (ESA) at LHC energy 76
 (rad)φ∆
−1 0 1 2 3 4 5
−
1
 (
0
.0
6
 r
a
d
)
φ∆
 d
N
/d
e
v
1
/N
−410
−3
10
−210
−110
 (rad)φ∆
−1 0 1 2 3 4 5
−
1
 (
0
.0
6
 r
a
d
)
φ∆
 d
N
/d
e
v
1
/N
−410
−3
10
−210
−110
Figure 9.1: Dihadron azimuthal correlations for charged particles in region A
(left) and C (right) (see table 6.3) with phard
t = 10 GeV/c (solid line), Q-PYTHIA
with q̂ = 1 GeV2/fm and L = 6 fm (dashed line) and q̂ = 5 GeV2/fm and L = 6 fm
(dotted line), respectively. The chosen bounds for 1−T and R are 1−T < 0.05
and R < 0.2.
Region Kind of event Variables
A Dijets R ≤ 0.35, τ ≤ 0.03
B Monojets R ≥ 0.9, τ ≤ 0.03
C Mercedes R ≤ 0.4, τ ≥ 0.25
Table 9.1: 1-T and R parameters used for the present analysis.
describe the topology of the events, charged particles for hard processes with phard
T
= 50 GeV/c,
√
sNN = 5.5 TeV and three pcuts
T and pT leading > 10 GeV/c, were produced
and passed through these models.
Sphericity of the event, τ ≡ 1−T , the vector sum of the transverse momentum of
the event R and the measure of the momentum out of the plane Tmin, are shown in
figure 9.3, 9.4 and 9.5, respectively.
Due to interaction with the dense medium, there is more particle production with low-
pT with PYQUEN and Q-PYTHIA than PYTHIA. The increment in the particle with low-
pT produce events with a uniform distribution. This is shown in the top and middle
76
9.2. Event Shape Analysis (ESA) at LHC energy 77
panels of figure 9.3. For τpp & 0.8 PYQUEN and Q-PYTHIA particle production is
above PYTHIA production and for τpp . 0.8, they are below PYTHIA production. This
behavior also change recoil and Tmin distribution at low-pT (top and middle panels of
figure 9.4 and figure 9.5). At high-pT (bottom panels in the same figures) there are
no difference between p+ p and Pb+Pb.
77
9.2. Event Shape Analysis (ESA) at LHC energy 78
1-T
0 0.1 0.2 0.3 0.4 0.5
R
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
E
n
tr
ie
s
0
2
4
6
8
10
12
14
16
18
20
p-p simulation with PYTHIA
 = 5.5 TeV
NN
s
 = 50 GeV/chard
T
p
Charged particles with
>0.3 GeV/c and
T
p
>10 GeV/c
Tleading
p
 (rad)φ∆
-1 0 1 2 3 4 5
-1
 (
ra
d
)
φ∆
 d
N
/d
e
v
1
/N
-510
-410
-310
-210
-110
1
10 p-p simulation with PYTHIA
 = 50 GeV/chard
T
 = 5.5 TeV with p
NN
s
Charged particles
>10 GeV/c
Tleading
>0.3 GeV/c and p
T
p
Region A
Region B 
Region C
1-T
0 0.1 0.2 0.3 0.4 0.5
R
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
E
n
tr
ie
s
0
2
4
6
8
10
12
14
16
18
20
p-p simulation with PYTHIA
 = 5.5 TeV
NN
s
 = 50 GeV/chard
T
p
Charged particles with
>2 GeV/c and
T
p
>10 GeV/c
Tleading
p
 (rad)φ∆
-1 0 1 2 3 4 5
-1
 (
ra
d
)
φ∆
 d
N
/d
e
v
1
/N
-510
-410
-310
-210
-110
1
10
p-p simulation with PYTHIA
 = 50 GeV/chard
T
 = 5.5 TeV with p
NN
s
Charged particles
>10 GeV/c
Tleading
>2 GeV/c and p
T
p
Region A
Region B 
Region C
1-T
0 0.1 0.2 0.3 0.4 0.5
R
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
E
n
tr
ie
s
0
2
4
6
8
10
12
14
16
18
20
p-p simulation with PYTHIA
 = 5.5 TeV
NN
s
 = 50 GeV/chard
T
p
Charged particles with
>4 GeV/c and
T
p
>10 GeV/c
Tleading
p
 (rad)φ∆
-1 0 1 2 3 4 5
-1
 (
ra
d
)
φ∆
 d
N
/d
e
v
1
/N
-410
-310
-210
-110
1
10
210 p-p simulation with PYTHIA
 = 50 GeV/chard
T
 = 5.5 TeV with p
NN
s
Charged particles
>10 GeV/c
Tleading
>4 GeV/c and p
T
p
Region A
Region B 
Region C
Figure 9.2: 1 − T vs R (left) and dihadron azimuthal correlations (rigth) for
charged particles produced in p+ p collisions at
√
sNN = 5.5 TeV with phard
T =
50 GeV/c. The cuts used in ESA are: |η |< 0.9, pT leading > 10 GeV/c and pcut
T >
0.3 GeV/c (top), pcut
T > 2 GeV/c (middel) and pcut
T > 4 GeV/c (bottom).
78
9.2. Event Shape Analysis (ESA) at LHC energy 79
0 0.05 0.1 0.15 0.2 0.25 0.3
1
10
 = 50 GeV/c
hard
T
 = 5.5 TeV and p
NN
sp-p 
Charged particles
PYTHIA
Q-PYTHIA
fm. b = 0-10%
6
k = 6.10x10
/fm2 = 14 GeVq ⇒ 
PYQUEN
Collisional and radiative energy loss
 = 1 GeVcT
 >  0.3 GeV/ccut
T
 p
0 0.05 0.1 0.15 0.2 0.25 0.3
τ
 d
N
/d
e
v
1
/N
1
10
210
 >  2 GeV/ccut
T
 p
τ
0 0.05 0.1 0.15 0.2 0.25 0.3
1
10
 >  4 GeV/ccut
T
 p
Figure 9.3: Thrust distribution in PYTHIA (solid line), Q-PYTHIA (dashed line)
and PYQUEN (dotted line) at
√
sNN = 5.5 TeV and pT hard = 50 GeV/c, η | < 0.9,
pT leading > 10 GeV/c and pcut
T > 0.3 GeV/c (top), pcut
T > 2 GeV/c (middle) and
pcut
T > 4 GeV/c (bottom).
79
9.2. Event Shape Analysis (ESA) at LHC energy 80
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1
10
 = 50 GeV/c
hard
T
 = 5.5 TeV and p
NN
sp-p 
Charged particles
PYTHIA
Q-PYTHIA
fm. b = 0-10%
6
k = 6.10x10
/fm2 = 14 GeVq ⇒ 
PYQUEN
Collisional and radiative energy loss
 = 1 GeVcT
 >  0.3 GeV/ccut
T
 p
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
 d
N
/d
R
e
v
1
/N
1
10
210
 >  2 GeV/ccut
T
 p
R
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1
10
 >  4 GeV/ccut
T
 p
Figure 9.4: Recoil distribution in PYTHIA (solid line), Q-PYTHIA (dashed line)
and PYQUEN (dotted line) at
√
sNN = 5.5 TeV and pT hard = 50 GeV/c , η | < 0.9,
pT leading >10 GeV/c and pcut
T > 0.3 GeV/c (top), pcut
T > 2 GeV/c (middle) and pcut
T >
4 GeV/c (bottom).
80
9.2. Event Shape Analysis (ESA) at LHC energy 81
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
1
10  = 50 GeV/c
hard
T
 = 5.5 TeV and p
NN
sp-p 
Charged particles
PYTHIA
Q-PYTHIA
fm. b = 0-10%
6
k = 6.10x10
/fm2 = 14 GeVq ⇒ 
PYQUEN
Collisional and radiative energy loss
 = 1 GeVcT
 >  0.3 GeV/ccut
T
 p
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
m
in
 d
N
/d
T
e
v
1
/N
1
10
 >  2 GeV/ccut
T
 p
minT
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
1
10
 >  4 GeV/ccut
T
 p
Figure 9.5: Thrust minor in PYTHIA (solid line), Q-PYTHIA (dashed line) and
PYQUEN(dotted line) at
√
sNN = 5.5 ’tev and pT hard = 50 GeV/c , η | < 0.9,
pT leading > 10 GeV/c and pcut
T > 0.3 GeV/c (top), pcut
T > 2 GeV/c (middle) and
pcut
T > 4 GeV/c (bottom).
81
Chapter 10
Discussion and Conclusion
In this thesis we present simulation and analysis in the framework of the ALICE ex-
periment in CERN. Specifically we have concentrated on the aspect of jets in proton-
proton and heavy ion collisions and modifications in jets structure, due to parton
energy loss.
We simulated high-pT events in p + p collision, with PYTHIA, as a baseline, and
events passed through two afterburner models of energy loss PYQUEN and Q-PYTHIA.
After events simulation, jets were reconstructed in the framework of the ALICE ex-
periment (ALIROOT) with a jet finding algorithm and event shape analysis. Finally
modifications in jet structure due to energy loss were studied through the variables
kT , jT , RAA, sphericity, recoil and thrust minor, were studied.
The particle production was done to improve the jets production selecting hard pro-
cesses in PYTHIA version 6.2.14 Tune A. A calibration sample of a fixed interval with
phard
T = 50 GeV/c and, to approach the real spectrum produced in ALICE, an interval
with phard
T = 30 - 179 GeV/c were produced.
Even when the full event simulation performed within the ALIROOT framework mixed
event with all particles of the signal, as well as the background, the signal sticks
out of the background, so that, it was possible to do the analysis only with jet sig-
nal, i.e., only with PYTHIA simulation, without taking into account the background
(HIJING simulation).
After event generation, jets were first reconstructed with the internal PYTHIA cone
algorithm routine, PYCELL, and subsequently with a cone jet algorithm implemented
in the module JETAN of ALIROOT.
Notwithstanding only hard processes were simulated, the production of low-pT par-
ticles is present, these particles caused that the cone jet algorithm reconstructed
fake jets. If the particles transverse momentum is greater than 0.3 GeV/c a huge
amount of particles with low-pT are present between the the two-peaks in the par-
82
83
ticles azimuthal correlations, this particles are considered like background. With a
higher transverse momentum cut this background is reduced. A pcut
T > 2 GeV/c was
used.
Another source of fakes jets reconstruction is the jet cone size. Looking at the az-
imuthal correlation between dijets we can see that there exist fake jets reconstructed
close to the jet with maximum energy when the cone size is small, due to part of the
energy of the jet is not inside the cone. One way to select only real dijets that are
opposite in azimuthal angle and with small difference in energy is defining cuts in
this variables. The cuts applied were: 2.8 rad <∆φ<3.4 rad and ∆ET /ET,max < 0.8.
Moreover the cone jet algorithm, combined with the event shape analysis (ESA)
making possible to describe the topology of jets in an the event, since ESA mea-
sures the geometrical properties of the energy flow in QCD states. In this work,
three shape variables were used: thrust T (related with the sphericity S of the event
S ∼ τ ≡ 1−T ), recoil R and thrust-minor Tmin.
The thrust map (τ vs R) allows to identify different classes of events according with
their location. R ≤ 0.35 and τ ≤ 0.03 is characterized by dijets events, R ≥ 0.9 and
τ ≤ 0.03 is populated by monojets and R ≤ 0.4 and τ ≥ 0.25 have the most isotropic
events, called “mercedes”. An extensive work with ESA was reported in [14] and
[15].
Once the jets were selected, with either of the two methods, a study was done in
the structure and distribution of jets and how their properties are affected by the
presence of a dense medium.
It has been predicted that a high-pT parton traversing hot nuclear matter, will expe-
rience collisional energy loss, via scattering, and radiative energy loss, via induced
gluon bremsstrahlung. In this work, we studied the effects of this parton energy loss
with two models: PYQUEN and Q-PYTHIA and using p+ p simulation with PYTHIA as
baseline. There are other models to simulate energy loss, but due to availability in
the ALIROOT framework and the observable under study, only these two were used.
PYQUEN and Q-PYTHIA are fast Monte-Carlo event generator routines implemented
to modify standard events in PYTHIA. PYQUEN is based on an accumulating energy
loss where the multiple scattering strength is regulated mainly by the initial QGP tem-
perature Tc and Q-PYTHIA introduced a medium-induced term in the vacuum term
splitting probability function P(z) where the transport coefficient q̂ encodes all pos-
sible information about the medium properties with the interpretation of the average
transverse momentum squared that the gluon gets per mean free path length L in
the medium. In both models, the main contribution comes from the radiative en-
ergy loss, resulting more particles at low pT and less particles at high pT compared
with PYTHIA, but an important difference between them is that, Q-PYTHIA includes
multiple-soft scattering and which is not the case in PYQUEN.
83
84
In PYQUEN the collisional energy loss due to elastic scattering takes into account
the low-momentum transfer loss resulting from the interactions with plasma, but,
this does not contribute much to the total energy loss in comparison with radiative
energy loss, for this reason, and due to the fact that in real data, it is not possible to
separate collisional and radiative energy loss, only the case with both together was
studied. Since the energy loss is regulated by the initial QGP temperature Tc, two
temperatures were selected but since no significant difference on Tc was observed.
Only Tc = 1 GeV is considered.
In Q-PYTHIA the geometry of a dense medium produced in nucleus–nucleus collision
can be chosen by the user .The simplest brick geometry with L = 4.5 fm and q̂ = 5
GeV2/fm and q̂ = 50 GeV2/fm were studied to exemplify the dependence on the
energy loss with q̂, but in order to compare, either Monte-Carlo (PYQUEN uses the
same geometry) or real data, a realistic Glauber-like collision geometry defined in
the routine, was chosen.
In order to understand the behavior of the intrinsic transverse momentum kT and it
dependence with the energy of the collision and the transverse momentum of the
hard-pT particles, high-pT events were produced in p+ p environment, changing the
parameters that control the magnitude of kT . After event generation, jets were recon-
structed with cone jet algorithm implemented in the module JETAN of ALIROOT and
the acoplanarity (pout) between two jets were calculated.
As expected, the acoplanarity between two jets increased because they were af-
fected by additional transverse momentum contributions from the intrinsic kT but,
due to the dominance of initial state radiation pout shows only small variations.
With a kT = 5 GeV/c, both models to simulate energy loss, Q-PYTHIA and PYQUEN,
were compared with PYTHIA. The magnitude of the extra kT from partonic interac-
tions with the dense medium can be observed on top of the initial state radiation but
this effect is less than the theoretical prediction [61], where the amount of additional
transverse momentum to of the dijet system relative to the p+ p or p+A baseline,
has been proposed as another possibility to measure the transport parameter q̂.
Another variable that was studied was the transverse momentum relative to the jet
axis, jT , given to a particle during the fragmentation of its parent after scattering.
Broadening of the distribution of jet-particle momenta perpendicular to the jet axis
were observed for the two energy loss models. Since this additional is directly re-
lated to the color density of the traversed medium [58, 59, 60].
Additionally, the pT distributions of particles at different distances r inside the jet
were studied. In vacuum angular ordering rules the pT distribution of particles at dif-
ferent distances r to the jet axis. High-pT particles are predominantly produced close
the jet axis whereas low-pT particles are found at larger distances. High-pT particles
84
85
at large distances from the jet axis are due to hard gluons radiated shortly after the
initial hard scattering. These gluons see the same medium as the leading parton,
but having smaller energies the effect of energy loss should be stronger. In the the
ratio of particles yield (RAA) (Q-PYTHIA/PYTHIA and PYQUEN/PYTHIA vs pT for three r
cone sizes clear differences between the two Monte-Carlo in the pattern of increase
of low-momentum particles and depletion of high-momentum particles at different r
can be observed.
Another way to study modifications in jets structure, due to parton energy loss is
through the event shape variables.
At
√
sNN = 200 GeV/c we confronted with the double hump structure obtained in sec-
tion 6.3.2. To see what are the predictions of the generator Q-PYTHIA , that takes into
account the effects of parton energy loss in the medium. The interest of the results
lays in the behavior of the dependence of the yields in two different parts of the τ vs
R distribution. While for low values of R and τ we observe a decrease of the proba-
bility with increasing q̂, in the case of high values of τ we observe a frank increase
of the yield in the away-side correlation with the double hump. These results remind
us very much of the double hump structures encountered in the RHIC experiments
in collisions of heavy ions.
It seems that the studies of the topologies of events may offer a detailed insight in
the mechanism of hadronisation after collisions.
Due to interaction with the dense medium, there are more particles produced in
the low-pT region with PYQUEN and Q-PYTHIA respect to PYTHIA. This increment
produces events with a uniform distribution. This is shown in the top and middle
panels of figure 9.3. For τpp & 0.8 PYQUEN and Q-PYTHIA particle production is
above PYTHIA production and for τpp . 0.8, they are below PYTHIA production. This
behavior also change recoil and Tmin distribution at low-pT . At high-pT there are no
difference between p+ p and Pb+Pb.
We conclude that jets studies on p + p and Pb+ Pb collisions and their structure
can help us to understand the particles energy loss due to a presence of a dense
medium. Either with a complete jet reconstruction or with ESA, it is possible to de-
fine appropriate variables that showing changes due to parton energy loss and con-
sequently the jet structure. As mentioned above, the Monte-Carlo used in this work
are not the only ones, but taking into account their advantages and limitations we
consider them as good tools for the parton energy loss simulation, but only compar-
isons with the real data will determine if the models work correctly and understand
a little more the way the energy loss mechanisms occur.
85
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