na kierunku Fizyka Techniczna w specjalności Fizyka Komputerowa

na kierunku Fizyka Techniczna w specjalności Fizyka Komputerowa

Two-particle angular correlations of pions, kaons and protons in Pb-Pb collisions at √𝑠

= 5.02 TeV registered by the ALICE experiment

Krystian Głuchowski

Numer albumu 284493

promotor

dr inż. Małgorzata Janik

WARSZAWA 2020

In the first place, I would like to thank my supervisor dr Małgorzata Janik, for guiding me through fascinating aspects of high-energy physics and also for Your great patience, sincerity and constant support. Special thanks should also go to dr Łukasz Graczykowski and dr Georgui Kornakov for Your kindness and every piece of advice You gave me during my internship at CERN.

I would also like to thank all my friends. Especially I want to express my gratitude to everyone from KAB(u)MMMMM group: Ania, Bartek, Marta, Martyna, Michał, Mariusz and Mateusz. Special thanks to my close friends from faculty: Aleksandra, Katarzyna, Jakub, Mateusz and Robert. Finally, I want to acknowledge my best friends Krzysztof and Janusz. Thank You everyone for Your great support, for your kindness and for every single moment I have spent in Your great company. You are the best!

Last but certainly not least, I would like to express my gratitude to my family, especially to my siblings Aleksandra and Michał, for words of encouragement, constant and international support; and also to my parents, who believed in me since the very beginning.

I dedicate this work to F. and to M.

Two-particle angular correlations of pions, kaons and protons in Pb-Pb collisions at √𝒔𝑵𝑵

= 𝟓. 𝟎𝟐 TeV registered by the ALICE experiment.

Two-particle angular correlations functions are source of information about particles produced in collisions of hadrons at high energies. They are estimated by differences in pseudorapidity (Δ𝜂) and differences in azimuthal angle (Δ𝜑) of created pairs of particles. Obtained in this way histograms in Δ𝜂Δ𝜑 space can be used to examine physical effects connected with particle creation like: quantum statistics, elliptic flow, “jets” creation and conservation laws.

Main goal of this thesis is to obtain two-particle angular correlation functions for pairs of particles created in Pb-Pb collisions at √𝑠

= 5.02 TeV registered by ALICE experiment in CERN and to compare them with results of analysis for proton-proton collisions at √𝑠 = 7 TeV. In mentioned analysis for pairs proton-proton and antiproton-antiproton in the area Δ𝜂Δ𝜑 = (0,0) anticorrelation was observed, which was not predicted by any theoretical model.

In this thesis there are presented Δ𝜂Δ𝜑 functions for like-sign and unlike-sign pairs of pions, kaons and protons. In order to increase the accuracy of obtained correlation functions corrections were applyed, which come from Monte Carlo generator called AMPT. In this thesis are also presented correlation functions predicted by theoretical model and systematic uncertainty analysis.

Based on obtained results for like-sign pairs of protons simmilar shape of anticorrelation can be observed, as it was reported in proton-proton collisions analysis.

Moreover, obtained correlation functions for theoretical data, did not recreate the anticorrelation shape as well.

Keywords:

CERN, ALICE, angular correlations, Monte Carlo, AMPT

(supervisor’s signature) (student’s signature)

Dwucząstkowe korelacje kątowe pionów, kaonów oraz protonów w zderzeniach Pb-Pb o energii √𝒔𝑵𝑵

= 𝟓. 𝟎𝟐 TeV zarejestrowanych przez eksperyment ALICE

Dwucząstkowe korelacje kątowe są źródłem informacji na temat mechanizmu powstawania cząstek w wyniku zderzeń hadronów przy wysokich energiach. Są wyznaczane przez różnice w pseudopospieszności (Δ𝜂) i różnice w kącie azymutalnym (Δ𝜑) powstałych par cząstek. Otrzymane w ten sposób histogramy Δ𝜂Δ𝜑 mogą służyć do badań nad efektami fizycznymi, związanymi z produkcją cząstek takimi jak:

statystyka kwantowa, przepływ eliptyczny, tworzenie się „jetów” czy prawa zachowania.

Głównym celem tej pracy jest uzyskanie dwucząstkowych korelacji kątowych dla par cząstek powstałych w wyniku zderzeń Pb-Pb przy energii √𝑠

= 5.02 TeV zarejestrowanych przez eksperyment ALICE w CERN i porównanie ich z wynikami analizy dla zderzenia proton-proton przy energii √𝑠 = 7 TeV. We wspomnianej analizie dla par proton-proton i antyproton-antyproton w okolicy Δ𝜂Δ𝜑 = (0,0) została zaobserwowana antykorelacja, która nie została przewidziana przez żaden z modeli teoretycznych.

W tej pracy przedstawione są funkcje Δ𝜂Δ𝜑 dla jednoimiennych i różnoimiennych par pionów, kaonów oraz protonów. W celu zwiększenia dokładności otrzymanych funkcji korelacyjnych, zostały nałożone korekcje pochodzące z danych generatora Monte Carlo o nazwie AMPT. W pracy zostały również przedstawione funkcje korelacyjne dla przewidywań teoretycznych pochodzących z danych Monte Carlo i analiza błędów systematycznych.

Na podstawie uzyskanych wyników dla jednoimiennych par protonów można zauważyć podobny kształt antykorelacji do tego jaki był przedstawiony w analizie zderzeń proton-proton. Ponadto uzyskane przy użyciu modeli teoretycznych funkcje korelacyjne również nie odtworzyły kształtu antykorelacji.

Słowa kluczowe:

CERN, ALICE, korelacje kątowe, Monte Carlo, AMPT

(podpis opiekuna naukowego) (podpis dyplomanta)

Krystian Głuchowski

Fizyka Techniczna

Oświadczenie

Świadomy odpowiedzialności karnej za składanie fałszywych zeznań oświadczam, że niniejsza praca dyplomowa została napisana przeze mnie samodzielnie, pod opieką kierującego pracą dyplomową.

Jednocześnie oświadczam, że:

▪ niniejsza praca dyplomowa nie narusza praw autorskich w rozumieniu ustawy z dnia 4 lutego 1994 roku o prawie autorskim i prawach pokrewnych (Dz.U. z 2006 r. Nr 90, poz. 631 z późn. zm.) oraz dóbr osobistych chronionych prawem cywilnym,

▪ niniejsza praca dyplomowa nie zawiera danych i informacji, które uzyskałem/-am w sposób niedozwolony,

▪ niniejsza praca dyplomowa nie była wcześniej podstawą żadnej innej urzędowej procedury związanej z nadawaniem dyplomów lub tytułów zawodowych,

▪ wszystkie informacje umieszczone w niniejszej pracy, uzyskane ze źródeł pisanych i elektronicznych, zostały udokumentowane w wykazie literatury odpowiednimi odnośnikami,

▪ znam regulacje prawne Politechniki Warszawskiej w sprawie zarządzania prawami autorskimi i prawami pokrewnymi, prawami własności przemysłowej oraz zasadami komercjalizacji.

Oświadczam, że treść pracy dyplomowej w wersji drukowanej, treść pracy dyplomowej zawartej na nośniku elektronicznym (płycie kompaktowej) oraz treść pracy dyplomowej w module APD systemu USOS są identyczne.

Warszawa, dnia 28 stycznia 2020 (czytelny podpis dyplomanta)

Krystian Głuchowski

Fizyka Techniczna

Oświadczam, że zachowując moje prawa autorskie udzielam Politechnice Warszawskiej nieograniczonej w czasie, nieodpłatnej licencji wyłącznej do korzystania z przedstawionej dokumentacji pracy dyplomowej w zakresie jej publicznego udostępniania i rozpowszechniania w wersji drukowanej i elektronicznej

.

Warszawa, dnia 28 stycznia 2020 (czytelny podpis dyplomanta)

1Na podstawie Ustawy z dnia 27 lipca 2005 r. Prawo o szkolnictwie wyższym (Dz.U. 2005 nr 164 poz. 1365) Art. 239.

oraz Ustawy z dnia 4 lutego 1994 r. o prawie autorskim i prawach pokrewnych (Dz.U. z 2000 r. Nr 80, poz. 904, z późn. zm.) Art. 15a. "Uczelni w rozumieniu przepisów o szkolnictwie wyższym przysługuje pierwszeństwo w opublikowaniu pracy dyplomowej studenta. Jeżeli uczelnia nie opublikowała pracy

Politechnika W arszawska

Table of contents

1 Introduction 15

1.1 Standard Model . . . 16

1.2 Quantum Chromodynamics . . . 17

1.3 Heavy-ion collisions . . . 18

2 Experimental setup 20 2.1 CERN . . . 20

2.2 LHC . . . 21

2.3 ALICE . . . 21

2.3.1 Inner Tracking System . . . 23

2.3.2 Time Projection Chamber . . . 23

2.3.3 Time Of Flight . . . 23

3 Two-particle angular correlations 24 3.1 Pseudorapidity and azimuthal angle . . . 24

3.2 ∆η∆ϕ correlation function . . . 25

3.3 Sources of correlations . . . 26

4 Data analysis 28 4.1 Event selection . . . 28

4.2 Track selection . . . 28

4.3 Particle Identification . . . 30

4.4 Corrections . . . 32

4.4.1 Reconstruction efficiency . . . 32

4.4.2 Secondary contamination . . . 33

4.4.3 Correction factor . . . 33

4.5 Purity . . . 34

5 Results 36 5.1 ∆η∆ϕ correlation functions without corrections . . . 36

5.2 ∆η∆ϕ correlation functions with corrections . . . 37

5.3 ∆η∆ϕ correlation functions from MC . . . 37

6 Systematic uncertainties 40 6.1 Comparison of different track selection method . . . 40

6.2 Comparison of different |η| range . . . 42

TABLE OF CONTENTS

6.2.1 Comparison of different PID method . . . 44

6.2.2 Comparison of different Two-Track Cuts . . . 45

6.3 Summary of systematic uncertainties . . . 46

7 Summary 48 A Alice-related material 49 A.1 Analysis software . . . 49

A.2 Event selection . . . 49

A.3 ALICE collision data . . . 49

A.3.1 MC data . . . 50

B ∆η∆ϕ functions for different centrality ranges 50

References 53

List of Figures 55

List of Tables 56

1 Introduction

In the past centuries there were many theories about the nature of the universe. Most of people believed that universe is static and constant, what means that it existed in current state for eternity, or it was created in that state. All of these theories were rejected in 1921 when Edwin Hubble made a fundamental discovery, in which all galaxies in the whole universe are moving away. This discovery was the proof of expanding universe. In 1927 Georges Lemaître presented new theory about beginning of the universe. According to the Hubble’s discovery, billions years ago all existing objects in the universe were accumulated in one extremely dense and hot point, which expansion is considered to be beginning of the universe. This concept was named Big Bang theory and is accepted until this day.

Conditions similar to the early state of universe can be recreated by the collisions of par- ticles accelerated to velocity close to the speed of light. The Large Hadron Collider (LHC), which belongs to European Organization for Nuclear Research (CERN), is capable to accel- erate particles to high energy and collide them to create Quark-Gluon Plasma (QGP). Studies of QGP properties can result in better understanding process of matter creation and interac- tions between particles. One of the tools to study properties of QGP are angular correlation functions. In the article mentioned in Ref. [1] were presented angular correlation functions obtained in proton-proton collisions at the energy √

s = 7 TeV. It was observed, that for the pairs baryon-baryon there appears strange anti-correlation shape around bin ∆η∆ϕ = (0, 0), which is currently not predicted by any theoretical model. Mentioned correlation functions for proton-proton collisions at√

s = 7TeV are presented in Fig. (1-1).

Figure 1-1: ∆η∆ϕ functions for pp collisions at√

s = 7TeV.

Main goal of this thesis is to obtain results of analysis in the Pb-Pb collisions at the en-

1 INTRODUCTION

ergy√

s_{N N} = 5.02TeV registered by the ALICE experiment and check if this mentioned anti- correlation shape is also visible. Corrections of detector inefficiencies and some basic system- atic checks will be also performed.

1.1 Standard Model

The Standard Model (SM) is a theory, which assumes that whole surrounding us matter is made of fundamental particles (quarks and leptons) and also predicts that three of four fundamental forces (strong, weak and electromagnetic) are carried by the other particles called bosons.

Gravitation, as the fourth fundamental force, is not included into Standard Model. Particles included into Standard Model are presented in Fig. (1-2).

Figure 1-2: Table of elementary particles included in Standard Model. From Ref. [20]

SM is divided into two groups: fermions and bosons. Fermions are the particles with the half-integer spin. They are described by Fermi-Dirac statistics and Pauli exclusion principle, in which it is impossible for two or more fermions to be in the same quantum state. To the fermion group are included quarks and leptons. There are six flavours of quarks (up, down, strange, charm, top and beauty) and corresponding to them six flavours of anti-quarks (anti- up, anti-down, etc.). There are also six lepton flavours (electron, electron neutrino, muon, muon neutrino, tau and tau neutrino) and six anti-lepton flavours. All fermions are grouped in three generations. Whole stable matter is made of fermions, which comes from the first

generation. Atoms consist nucleus which is made of up and down quarks (proton - uud, neutron - udd) and surrounding them electrons. Bosons are the particles with integer spin and they are described by the Bose-Einstein statistics. Bosons mentioned in SM are responsible for carrying interactions between particles. Gluon is responsible for strong interactions, bosons W⁺, W⁻ and Z⁰carries weak interactions and photon carry electromagnetic interactions. To the SM was also added the Higgs boson, which carries interaction of particles with Higgs field to give mass to all particles.

In this thesis were considered particles listed below:

 pions

Pions are particles consist of two first generation quarks: up and anti-down for π⁺ or down and anti-up for π⁻.

 kaons

Kaons are particles, which contain a strange quark. The K⁺ is build of up and anti- strange quarks and K⁻are build of anti-up and strange quarks.

 protons

Protons (p) are the combination of three quarks from first generation – two up quarks and one down quark. Anti-protons (p) consists adequate composition of antiquarks (two anti-up and one anti-down).

1.2 Quantum Chromodynamics

Quantum Chromodynamics (QCD) is the theory describing strong interactions between quarks and gluons. QCD assumes that every flavour of quark can occur in one of three colours (red, blue and green) and anti-quark can occur in one of three anti-colour. In this theory quarks exist only in neutral colour combinations. There are two types of this combinations: pair quark - anti- quark for mesons (eg. pions and kaons) and combination of three quarks (or three anti-quarks) for baryons (like protons and anti-protons).

Quantum Chromodynamics theory have two important properties for the colour-charge parti- cles:

 Confinement

Quarks and gluons can not exist as free particles. It is impossible to separate two quarks, because needed energy to this action tends to infinity. If one wanted to separate pair quark – anti-quark in the meson, the energy of the interaction between them would in- crease with the distance. In one moment if the interaction energy is enough high, it would be more energetically advantageous to produce another pair quark – anti-quark.

This type of process is presented in Fig. (1-3).

 Asymptotic freedom

Interaction between colour-charged particles is very weak in the distance comparable

1 INTRODUCTION

with nucleon radius. Because of that, quarks and gluons become asymptotically free. It implies existence of Quark-Gluon Plasma.

Figure 1-3: Creation new mesons due to confinement effect. From Ref. [21]

1.3 Heavy-ion collisions

Quark-Gluon Plasma (QGP) is a state, in which quarks and gluons are not assigned to any hadron and can move freely in the borders of that state. QGP can be obtained in two ways.

First option is squeezing matter to extremely high density, the other one is heating matter to really high temperatures. Although the first method is impossible to do for any laboratory in the world, the second is possible for huge accelerators, which can increase temperature by collisions of heavy ions accelerated to very high energies. There are few characteristic steps for heavy-ions collisions. Firstly, pair of Lorentz-contracted nucleons are moving toward each other and collide. Then is created a non-equilibrium initial state. Next, there is formed quark- gluon plasma. Then starts hadronization, the process of creation hadrons form quarks and gluons. After that takes place chemical freeze-out, when chemical composition of system is fixed. Finally, there happens kinematic freeze-out, what means that particles momentum is fixed and all created particles stop colliding elastically each other. The space-time evolution of heavy-ion collision is presented in Fig. (1-4).

Figure 1-4: The space-time evolution of heavy-ion collision with the phase transition to the QGP. From Ref. [17].

Main goal of heavy-ion collisions is to study properties of quark-gluon plasma. Lattice QCD calculations predicts that there are two types of phase transition between QGP and hadronic matter. If baryon chemical potential is near values typical for the normal matter, then happens first order phase transition. When baryon chemical potential goes to zero, then phase transition becomes cross-over. Point on the phase diagram, with the specific values of the temperature and baryon chemical potential, where first order phase transition changes to cross-over is called the critical point. Some of heavy-ions experiments are searching for the critical point. Phase diagram is presented in the Fig. (1-5). At the time of writing this thesis, experimental existence of critical point have not been proved.

Figure 1-5: The phase diagram of hadronic matter. From Ref. [18].

2 EXPERIMENTAL SETUP

2 Experimental setup

2.1 CERN

CERN (Conseil Européen pour la Recherche Nucléaire) is a European research organization, which is focused on the high energy particle physics and operates the biggest particle acceler- ator in the world LHC. CERN was founded in 1954 and located on Franco-Swiss border near Geneva. The organization currently has 23 member states.

Scientists at CERN use the large and complex tools to study basic nature of the universe. In network of circular accelerators particles are collided at velocity close to speed of light. Due to this process a lot of data is collected, which can give an information about fundamental parti- cles interactions. Research at CERN leads to many discoveries in the field of particle physics, such as confirmation of existence of Higgs boson in 2012. Complex of accelerators at CERN is presented in Fig. (2-6).

Figure 2-6: Complex of accelerators at CERN. From Ref. [19].

2.2 LHC

The Large Hadron Collider (LHC) is the largest and the most powerful accelerator in the world.

It is 27 km long synchrotron located in a 100 m below ground tunnel. Inside the LHC supercon- ducting electromagnets guide the beams of particles and accelerating structures are increasing their energy. Two high energy particle beams travel in opposite directions to collide with the cen- ter mass energy up to 13 TeV (proton-proton collision) in intersection points, where are located four experiments:

 ATLAS (A Toroidal LHC ApparatuS) [5] is the general-purpose detector, which goal is discovering new particles that can be compared with the standard model predictions. It is used also for the research beyond standard model by looking for particles, which could be identified as dark matter.

 CMS (Compact Muon Solenoid) [6] is the general-purpose detector, which has the same scientific goals as ATLAS, but it has different construction. Because of this reason these two detectors can confirm each other discoveries.

 ALICE (A Large Ion Collider Experiment) [7] is the detector used to studing havy-ion collisions and properties of quark-gluon plasma (see section 2.3).

 LHCb (Large Hadron Collider beauty) [8] is the experiment designed to research differ- ences between matter and antimatter by studying decays of particles, which contains beauty quarks.

2.3 ALICE

ALICE is the detector that mainly focuses on heavy-ions collisions. In that type of collisions can be observed quark-gluon plasma (QGP), which is state of matter at very high temprature and density. QGP was one of the states of expanding universe, shortly after Big Bang. The detector ALICE is shown in the Fig. (2-7).

ALICE is built of many sub-detectors, which are designed to particle tracking, particle identi- fication, measure particle energy and provide information about collision. These sub-detectors are listed below:

 ITS – Inner Tracking System

 FMD – Forward Multiplicity Detector

 T0 – Cherenkov counters

 V0 – Segmented scintillator counters

 TPC – Time Projection Chamber

2 EXPERIMENTAL SETUP

Figure 2-7: The ALICE detector. From Ref. [4].

 TRD – Transition Radiation Detector

 TOF – Time Of Flight Detector

 HMPID – High Momentum Particle Identification Detector

 EMCAL – Electromagnetic Calorimeter

 PHOS – Photon Spectrometer

 ACORDE – ALICE Cosmic Ray Detector,

 PMD – Photon Multiplicity Detector

 CPV – Charged Particle Veto detector

 ZDC – Zero Degree Calorimeters

 AD – ALICE Diffractive detector

 muon spectrometer

All mentioned sub-detectors work together to precisely describe properties of QGP. The most important for this analysis are ITS and TPC, which are responsible for track reconstruction, and also TOF, which collected data are necessary to identification of particles created in the collision.

2.3.1 Inner Tracking System

ITS is the closest detector to the beam axis and to the collision point. It determines a position of primary and secondary vertices.This detector has six cylindrical layers of snsitive silicon detectors, which can cover the pseudorapidity range |η| < 0.9. ITS is also a detector used for tracking and identification low-momentum particles.

2.3.2 Time Projection Chamber

TPC is cylindrical gas detector, which main tasks are identification and tracking charged parti- cles. Charged particles ionize atoms of gas during passing through the detector. Due to electric field, electrons from ionization go to one of the readout pads. This process gives an information about momentum, tracks of particles and energy loss dE/dx, which is used to identification of particles.

2.3.3 Time Of Flight

Main task of TOF is measuring time of passing charged particles across this detector to reach the information about its velocity. When the information about momentum of particles can be recorded by other detectors, the calculation of mass is possible due to data collected by TOF.

Value of calculated mass can be used to identify different species of particles.

3 TWO-PARTICLE ANGULAR CORRELATIONS

3 Two-particle angular correlations

The main aim of this thesis is to perform two-particle angular correlation functions. This kind of correlations is calculated by searching differences in pseudorapidity and azimuthal angle of two particles.

3.1 Pseudorapidity and azimuthal angle

Pseudorapidity η is a commonly used quantity in experimental particle physics. It describes production angle of the particle relative to the beam axis. Pseudorapidity is described as:

η = − ln [tan(θ

2)], (1)

where θ is the polar angle between particle momentum p and beam axis. Pseudorapidity has the 0 value for particles created in the perpendicular direction. If θ goes to 0^◦, pseudorapidity tends to infinity. This quantity can be also defined as the function of the particle momentump:

η = 1

2ln (|p| + pL

|p| − pL

), (2)

where p_L is the component of particle momentum along the beam axis. Two-particle angular analysis measure differences in pseudorapidity between two particles, which make possible to compare correlations of particles with different mass. Quantity ∆η is defined as follows:

∆η = η2− η₁. (3)

Azimuthal angle ϕ is the angle between positive x axis and projection of the particle momen- tum vector into XY plane. Quantity ∆ϕ can be expressed as:

∆ϕ = ϕ2− ϕ₁. (4)

Definition of differences in polar and azimuthal angle is presented in Fig. (3-8).

Figure 3-8: Definition of polar angle θ and azimuthal angle ϕ differences used to construct correlation function. From Ref. [13].

3.2 ∆η∆ϕcorrelation function

Two-particle angular correlation function (C(∆η∆ϕ)) is constructed as follows:

C(∆η∆ϕ) = N_pairs^mixed N_pairs^signal

S(∆η∆ϕ)

B(∆η∆ϕ), (5)

where S(∆η∆ϕ) is the signal distribution and B(∆η∆ϕ) is background distribution. The signal distribution is constructed from particle pairs, which come from the same collision (event). It can be expressed as:

S(∆η∆ϕ) = d²N_pairs^signal

d∆ηd∆ϕ, (6)

where N_pairs^signal is number pairs of particles. Background distribution is constructed using event mixing procedure. Each particle in pair come from different event, what means there is no correlation between these two particles. Background distribution contains only detector effects and is defined as follows:

B(∆η∆ϕ) = d²N_pairs^mixed

d∆ηd∆ϕ, (7)

where N_pairs^mixedis number of mixed pairs of particles used in the analysis.

Samples of signal distribution, background distribution and correlation function are presented in Fig. (3-9).

Figure 3-9: Samples of signal distribution (left), background distribution (center) and correlation function (right).

3 TWO-PARTICLE ANGULAR CORRELATIONS

3.3 Sources of correlations

Many physical effects have an influence on the shape of two-particle angular correlation func- tions. Each of them affects the specific area of ∆η∆ϕ functions. The most important of these effects and their influence on the function shape in Pb-Pb collisions are listed below.

 Elliptic flow

Elliptic flow is a collective effect caused by anisotropic fluid-like expansion of the conden- sate matter created right after collision. Elliptic flow is significant effect, which is visible in non-central collisions of heavy ions. This part of nucleons, which take part in collision creates elliptic-shape state of condensate matter, which expansion depends on azimuthal angle to the reaction plane. This effect gives a cos(2∆ϕ) shape to the correlation function.

 Conservation laws

Quantities like energy, momentum, charge, baryon number and strangeness must be conserved in every collision by each fragmentation and in the global scale. Pions are subjected to energy, momentum and charge conservation laws. Kaons, which consist one strange or anti-strange quark, additionally must obey strangeness conservation law, on the other hand protons respect baryon number conservation. Momentum conserva- tion law ensure that for every group of particles going in similar direction there is another group of particles going in opposite direction. This effect gives a specific shape of corre- lation function along ∆ϕ.

 Jets

Jets are collimated streams of particles distributed in one direction. Due to momentum conservation law, when one jet is created, another jet emerges in opposite direction.

This kind of jets are also called back-to-back jets. Pair of particles, which comes from the same jet contribute correlation in near-side peak (∆η∆ϕ ≈ (0, 0)), but pair of particles from back-to-back jets contributes correlation near ∆ϕ ≈ π.

 Quantum statistics effects

Particles with integer spin like pions and kaons, which spin is equal 0, are called bosons and have to obey Bose-Einstein statistics, in which it is very likely for two identical bosons to be created in the same quantum state (the same η and ϕ) and emitted in similar direction. That effect cause additional correlation in near-side peak. Protons and anti- protons have half-integer spin. This type of particles are called fermions and have to obey Fermi-Dirac statistics, in which it is impossible for two fermions to be created in the same quantum state. Fermi-Dirac statistic effect contributes decrease in near-side peak.

 Resonances

Resonances are short lived particles, which nearly immediately after creation decay into new particles. Contribution of produced particles by the decay to correlation function depends on the energy of decay Q. If Q is much lower than transverse momentum of

decayed particle, then particles will be produced with nearly the same values of η and ϕ.

This kind of decay contribute correlation in the area of near-side-peak. However if Q is comparable or larger than transversal momentum or in the case three-body decay (eg.

ω → π⁺π⁰π⁻), then particles are created in different directions and that contributes to correlation function along area ∆η ≈ 0 what is also called longitudinal ridge.

 Photon conversion

Photon conversion is the process, in which photon is converted into pair electron-positron.

This kind of process have to obey energy and momentum conservation laws. For that reason energy of the photon must be higher than 1.022 GeV what correspond to sum of energy of resting electron and its antiparticle. Photon conversion is only possible with attendance of other particle, which can compensate momentum of converted pair. Elec- tron and positron created in this effect goes in the same direction, what means with small angular differences. Photon conversion cause narrow peak in the area (∆η∆ϕ = 0, 0).

 Coulomb interaction

Coulomb interaction is the interaction between charged particles. Particles with the same electric charge repel each other and those with unlike-sign charge attract each other. Electrostatic force depends on the distance between particles and because of that influence on correlation function is visible only in small distance between particles.

Coulomb interaction in like-sign particles cause decrease of peak around (∆η∆ϕ = 0, 0), but unlike-sign particles cause its increase.

Combined contribution of mentioned physical effects to ∆η∆ϕ correlation functions is shown in the Fig. (3-10).

Figure 3-10: Contribution from different sources of correlation. From Ref. [9].

4 DATA ANALYSIS

4 Data analysis

The data used in this analysis comes from Pb-Pb collisions at center of mass energy

√s_{N N} = 5.02TeV registered by experiment ALICE in 2015. Detailed list of runs is presented in appendix A.

4.1 Event selection

The data sample to this analysis was selected by the minimum bias trigger. Selected were only particles, which come from collisions at the center of the ALICE detector. In this analysis correlation functions were calculated for different centrality ranges: (0 − 10%), (10 − 20%), (20 − 40%), (40 − 60%) and (60 − 80%). All presented correlation functions in this thesis were calculated with the centrality range (10 − 20%). Data from the events, in which in very close time happens more than one collision, can be contaminated by particles coming from different collisions. This kind of effect is called "pile-up" and in this analysis such events are rejected by the implemented methods. Due to TPC detector acceptance, only collisions in distance of primary vertex along the z-axis |z_vtx| < 7 cm from the center of TPC were selected.

4.2 Track selection

In this analysis trajectories of particles are reconstructed by the data from ITS and TPC de- tectors. In order to determine, which tracks come from primary particles, the trajectories are extended to find the closest distance between trajectory and primary vertex. This quantity is called Distance of Closest Approach (DCA). This analysis uses the Global track selection method, where are set specific ranges of DCA. To the analysis were selected tracks of particles with the pseudorapidity range |η| <0.8. In aim to avoid contamination coming from secondary particles, to the analysis were selected particles with the following pT ranges:

 Protons: 0.5 < p_T < 2.5GeV/c,

 Kaons: 0.3 < p_T < 2.5GeV/c,

 Pions: 0.2 < p_T < 2.5GeV/c.

In the Fig. (4-11,4-12) there are shown basic Quality Assurance plots (QA) – p_T, η, ϕ distri- butions and 2D plots of ηϕ distributions for all considered particle species created in Pb-Pb collisions at √

sN N = 5.02TeV. The ϕ and η distributions are close to flat structure. It can be observed, that in p_T distribution big decrease appears for the pions and kaons around p_T = 0.5 GeV/c. This drop is mainly due to including TOF detector to the particle identification and that cause decrease of efficiency. In the ηϕ distributions for all particle species appears a visible structure around ηϕ (0, 1.5). This structure is caused by the Photon Spectrometer, which is located in this area, over the TOF detector.

Figure 4-11: η, ϕ, and pT distributions for Pb-Pb collisions at√

sN N = 5.02TeV.

Figure 4-12: ηϕ distributions for Pb-Pb collisions at√

sN N = 5.02TeV.

4 DATA ANALYSIS

4.3 Particle Identification

The PID (Particle IDentification) is necessary in the research of correlation functions for pions, kaons and protons. In ALICE experiment two detectors are used for PID – TPC (Time Projection Chamber) and TOF (Time Of Flight detector). Particle identification was based on N_σ method, where N stands for a number of standard deviations σ around the Gaussian distribution around the theoretical signal - for TPC it is the Bethe-Bloch parametrization of ionization energy loss and for TOF it is expected arrival time. For this analysis cuts in N_σmethod were used as follows:

 Acceptance:

 p_T > 0.5GeV/c → N_σ =pN_{σT P C} + N_{σT OF} < 2.0

 p_T < 0.5GeV/c → N_σ = |N_{σT P C}| < 2.0

 Rejection:

 NσT P C < 3.0

 If the track passes the PID N_σ cuts with above rejection condition for more than one particle species, it is rejected.

Basic QA plots for PID are shown in the figures below. In the Fig. (4-13) there are presented dE/dx distributions from TPC detector. Points on these histograms are placed around the theoretical Bethe-Bloch curves, which inform about the energy loss of particles in the detector for different particle species. TOF detector distributions in Fig. (4-14) present measured signal subtracted by theoretical values. For this reason many points are around 0 value. Distributions NσT P C vs N_{σT OF} presented in Fig. (4-15) show how far from TPC and TOF predictions are detected particles.

Figure 4-13: TPC dE/dx distributions for Pb-Pb collisions at√

sN N = 5.02TeV.

Figure 4-14: TOF distributions for Pb-Pb collisions at√

sN N = 5.02TeV.

4 DATA ANALYSIS

Figure 4-15: Nσ_{T P C} vs Nσ_{T OF} distributions for Pb-Pb collisions at√

sN N = 5.02TeV.

4.4 Corrections

Particle identification made by detectors is not perfectly accurate. It is impossible for the detec- tors to identify each particle generated in the event. To correct this inaccuracy it is necessary to make the same analysis on Monte Carlo (MC) "truth" and "reconstructed" events. The MC

"truth" events contain information about all particles created by the MC model. The MC "re- constructed" events contain detector response for the generated model. Comparing these two models enable getting information about number of properly identified particles, which may be used to correct real data. All correction calculations in this analysis were made on MC data anchored to ALICE experiment data from Pb-Pb collisions at √

s_{N N} = 5.02TeV from AMPT generator [10] with particle transport performed by GEANT3 [11] simulation of the ALICE de- tector.

4.4.1 Reconstruction efficiency

The reconstruction efficiency  is a ratio of the number of measured primary particles to the number of generated particles, which could be measured by the ideal detector. Reconstruction efficiency is defined as:

 = N_primaries^survived

N_primaries^generated. (8)

In Fig. (4-16) is presented dependence of efficiency on the transverse momentum for√ s_{N N} = 5.02 TeV Pb-Pb collisions. The efficiency was calculated separately for each particle species

(π, K, p and Λ). There is an observable decrease in efficiency around argument p_T = 0.5GeV/c because of PID cuts, which require TOF signal for tracks above p_T value 0.5 GeV/c.

Figure 4-16: Reconstruction efficiency plot for Pb-Pb collisions at√

sN N = 5.02TeV, calculated using data from MC AMPT generator.

4.4.2 Secondary contamination

Secondary contamination C shows fraction of detected particles (secondaries), which were not directly generated in the collision, because these ones were produced in the decay of short- living particles. Secondary contamination is expressed as:

C = Nsecondaries^survived

N_primaries^survived + Nsecondaries^survived

. (9)

Contamination from the secondary particles in pp and Pb-Pb collisions is presented in the Fig. (4-17). There is high contamination value for the protons and because of that, in this analysis only protons with p_T range above 0.5 GeV/c were selected.

4.4.3 Correction factor

Efficiency and contamination values can be used to calculate correction factor f as a function of transverse momentum. Correction factor should be applied for signal and background distri- butions of all particle species to minimise detector’s inaccuracy. Correction factor is defined as follows:

f = 1 − C

 . (10)

In the Fig. (4-18) is presented plot of dependence of correction factor on the transverse mo- mentum for Pb-Pb collisions at√

s_{N N} = 5.02TeV.

4 DATA ANALYSIS

Figure 4-17: Secondary contamination plot for Pb-Pb collisions at√

sN N = 5.02TeV, calculated using data from MC AMPT generator.

Figure 4-18: Correction factor plot for Pb-Pb collisions at√

sN N = 5.02TeV, calculated using data from MC AMPT generator

4.5 Purity

In order to check how efficient is PID method, the calculation of the sample purity are made for all considered particle species. Purity of the sample of particles P can be expressed as:

P = 1 − C. (11)

Dependence of purity on transverse momentum are presented in the Fig. (4-19). Purity inte- grated over p_T range for all particle species used in this analysis are listed in table (4.1). It can be seen that used PID method for pions and protons gives over 99% pure sample and for kaons gives over 98% pure sample.

Figure 4-19: Purity plot for Pb-Pb collisions at√

s_{N N} = 5.02TeV, calculated using data from MC AMPT generator.

Particle Purity π⁺ 0.9994 π⁻ 0.9994 K⁺ 0.9838 K⁻ 0.9829

p 0.9962

p 0.9946

Table 4.1: Purity integrated over pT range for all particles used in the analysis in Pb-Pb collisions at

√s_{N N} = 5.02TeV.

5 RESULTS

5 Results

In this section there are presented obtained correlation functions for Pb-Pb collisions data at

√s_{N N} = 5.02 TeV. Due to similarity between correlation functions in all calculated centrality ranges, only plots made for centrality range 10-20% are shown in paragraphs (5.1) and (5.2).

Dependence of collision centrality range on the shape of correlation functions is presented in appendix B. This analysis was performed for different particle pairs, which are listed in the table (5.2).

Like-sign pairs Unlike-sign pairs π⁺π⁺+ π⁻π⁻ π⁺π⁻ K⁺K⁺+ K⁻K⁻ K⁺K⁻

pp + pp pp

Table 5.2: Pairs of particles that were used in this analysis.

5.1 ∆η∆ϕcorrelation functions without corrections Correlation functions for Pb-Pb collisions at √

s_{N N} = 5.02 TeV obtained in this analysis are presented in Fig. (5-20). These correlation functions are raw. Final version of ∆η∆ϕ functions will be obtained after applying efficiency corrections.

Figure 5-20: ∆η∆ϕ functions before corrections for Pb-Pb collisions data at√

sN N = 5.02TeV. Central- ity 10-20%

5.2 ∆η∆ϕcorrelation functions with corrections

In aim to increase accuracy of ∆η∆ϕ functions there were applied corrections, which were mentioned at paragraph (4.4.3). Obtained correlation functions are presented in Fig. (5-21). It can be observed that results have similar structures around area ∆η∆ϕ = (0, 0) as correlation functions from pp collisions at√

s = 7 TeV, but in this case the most of correlation structures are covered by cos(2∆ϕ) shape caused by the elliptic flow effect. Moreover, there is also visible anti-correlation shape in proton-proton correlation function. In unlike-sign protons correlation function appears a decrease in ∆η∆ϕ = (0, 0) bin. This kind of structure is caused by annihila- tion process between protons and anti-protons.

Figure 5-21: ∆η∆ϕ like-sign pairs functions after corrections for Pb-Pb collisions data at√

sN N = 5.02 TeV. Centrality 10-20%.

5.3 ∆η∆ϕcorrelation functions from MC

In Fig. (5-22) ∆η∆ϕ functions for MC truth data are presented. These plots show correla- tions, which are predicted by AMPT model. MC truth data results are different to real data.

Difference is especially visible in proton-proton correlation function. In real data there is visible anti-correlation shape, but in MC truth data it is not.

In the Fig. (5-23) are presented correlation functions for MC reconstructed data after cor- rections. In analysis of this data there were used the same parameters as for the real data.

After applying corrections plots should be the same as for MC truth data, but there are still dif- ferences. To perform accuracy of corrections there was made MC closure test, in which ∆η∆ϕ functions from MC reconstructed are divided by MC truth. Results from MC closure test are

5 RESULTS

presented in the Fig. (5-24).

Figure 5-22: ∆η∆ϕ functions Pb-Pb collisions data at√

sN N = 5.02TeV for MC truth data from AMPT generator.

Figure 5-23: ∆η∆ϕ functions Pb-Pb collisions data at √

s_{N N} = 5.02 TeV for MC reconstructed data from AMPT generator.

Figure 5-24: MC closure test for Pb-Pb collisions data at√

sN N = 5.02TeV for MC reconstructed and MC truth data from AMPT generator.

In the Monte Carlo closure test the biggest difference appears in the unlike-sign kaons and protons. Although there were applied corrections, the difference is < 6%. The smallest dif- ference between MC reconstructed and MC truth is for all pairs of pions, where is less than 1%.

6 SYSTEMATIC UNCERTAINTIES

6 Systematic uncertainties

Many factors like track selection method, PID method or another applied cuts have an influence on uncertainty of two-particle correlation functions. In this section there are presented some systematic check to determine relative uncertainty. Histograms of ∆η∆ϕ functions presented in section (5.1.1) will be compared with other, which were analysed with different parameter change. Comparison is performed as ∆ϕ projection of these pairs of histograms and relative systematic uncertainty plots are calculated as follows:

R = A − B A

where R is relative uncertainty, A is original histogram from section (5.2) and B is adequate histogram with changed parameter in the analysis.

6.1 Comparison of different track selection method

In aim to investigate the differences between various track reconstruction, the analysis was additionally made separately on following track selection cuts:

 TPC-only tracks - the track reconstruction is based only on the TPC data.

 Hybrid tracks - gaps of the information from the ITS detector in Global Tracks are sup- plemented by the information from TPC-only tracks.

The differences between TPC-only and Global tracks are presented in Fig. (6-25). The most visible difference in almost all presented plots appears in ∆ϕ = 0 bin. The relative difference for like-sign pairs is as follows: for pions 0.04%, for kaons 0.07% and for protons 0.37%. The highest difference in unlike-sign pairs histograms of different track selection is observable for protons is 0.17%, for pions uncertainty is less than 0.05% and for kaons 0.1%.

Fig. (6-26) present results of comparison Hybrid and Global tracks. In all uncertainty plots are visible statistic fluctuations, what proves that these two track selection methods are quite similar. Only in pairs of like-sign and unlike-sign pions are visible structures. However, the uncertainties are much lower than 0.01% of correlation functions.

Figure 6-25: Comparison of ∆ϕ projections with TPC only and Global tracks for Pb-Pb collisions data at√

sN N = 5.02TeV. Centrality 10-20%

Figure 6-26: Comparison of ∆ϕ projections with Hybrid and Global tracks for Pb-Pb collisions data at

√sN N = 5.02TeV. Centrality 10-20%

6 SYSTEMATIC UNCERTAINTIES

6.2 Comparison of different |η| range

To estimate influence of pseudorapidity range of accepted particles on correlation functions, the default |η| < 0.8 range was copared separately with settings |η| < 0.9 and |η| < 0.7.

Comparison of these systematic checks are presented in Fig. (6-27) and Fig. (6-28). For the lower pseudorapidity range, uncertainties are estimated as follows. For like-sign pairs of pions uncertainty is less than 0.01%, for kaons 0.03% and protons 0.1%. For unlike-sign pairs the biggest uncertainty is for protons - 0.06%. For pions difference is less than 0.02% and for kaons 0.03%In the case of higher η range than default settings the difference is mainly smaller than in previous one. The relative uncertainty of like-sign pions is 0.02%, for kaons 0.02% and for protons 0.05%. For the unlike-sign pions 0.03%, for kaons 0.02% and protons 0.04%.

Figure 6-27: Comparison of ∆ϕ projections with |η| < 0.7 and |η| < 0.8 for Pb-Pb collisions data at

√sN N = 5.02TeV. Centrality 10-20%

Figure 6-28: Comparison of ∆ϕ projections with |η| < 0.9 and |η| < 0.8 for Pb-Pb collisions data at

√sN N = 5.02TeV. Centrality 10-20%

6 SYSTEMATIC UNCERTAINTIES

6.2.1 Comparison of different PID method

PID method mentioned in section (4.3) may supply to the analysed sample certain amount of contamination of misidentified particles. To perform PID method influence on correlation function, it was compared with other method called double counting. Double counting method is similar to the default one, it uses the N_σ parameters from TPC and TOF detectors. However, in this method there is no second condition of rejection particles. In that method one particle can be counted several times in the analysis as a different particle type. For this reason, there is expected to receive higher reconstruction efficiency, but lower purity. Comparison of these two methods are presented in Fig. (6-29). In all comparison plots appeared structures with the biggest difference around ∆ϕ ≈ 0. Relative difference for like-sign pions is less than 0.03%, for kaons 0.12% and for protons 0.19%. Margin for unlike-sign pairs was estimated as follows: for pions 0.03%, for kaons 0.14% and for protons 0.29%.

Figure 6-29: Comparison of ∆ϕ projections with different PID method N σ and N σ with additional rejec- tion for Pb-Pb collisions data at√

sN N = 5.02TeV. Centrality 10-20%

6.2.2 Comparison of different Two-Track Cuts

Some pairs of tracks can be wrongly selected to the correlation functions. In aim to avoid pair- wise effect, which is responsible for splitting and merging tracks, some additional cuts are used in the analysis. Default cut used in this analysis is "RadialDistance", which rejection condition is based on difference of pseudorapidity ∆η and difference of modified azimuthal angle ∆ϕ^∗ expressed as:

∆ϕ^∗ = ϕ2− ϕ₁+ a sin (−0.3Bz2r

2p_{T 2} ) − a sin (−0.3Bz1r

2p_{T 1} ), (12)

where B is the magnetic field, p_T is momentum of particles, z their charge and r is the radius inside the TPC detector. Quantity ∆ϕ^∗ is calculated in the radius range 0.8 < r < 2.5 m with the radius step 1 cm. Minimum value for ∆η is 0.02 rad and for ∆ϕ^∗ is 0.045 rad. If tracks of selected pair fulfil that condition, this pair is taken to the analysis. In aim to check influence of choose Two-Track Cut method, the analysis was applied cut for merged fraction, into which are selected pairs with ∆η < 0.01 rad. In this method in every radius step calculated is distance d defined as:

d = 2 sin (|∆ϕ^∗|

2 )r. (13)

If d < 0.045 then point is marked. If the ratio of marked points to all of them is less than 0.025, then selected pair passes the cut. Comparison of these two Two-Track cut methods are presented in the Fig. (6-30). The uncertainty for like-sign pions is less than 0.04% of correlation function, for kaons 0.06% and for protons 0.09%. The difference for unlike-sign pairs is as follows: for pions 0.02%, for kaons 0.05% and for the protons 0.06%.

Figure 6-30: Comparison of ∆ϕ projections with different Two-Track-Cuts MergedFraction and RadialD- istance for Pb-Pb collisions data at√

s_{N N} = 5.02TeV. Centrality 10-20%

6 SYSTEMATIC UNCERTAINTIES

6.3 Summary of systematic uncertainties

The summary of contribution of all considered methods to two-particle angular correlation func- tions is presented in the table (6.3). The biggest relative uncertainty was caused by changing the PID method. The smallest difference comes from increasing the pseudorapidity range to

|η| < 0.9.

Pairs of particles Systematic uncertainty

TPC-only tracks Hybrid tracks |η| < 0.7 |η| < 0.9 Double counting MergedFraction

π⁺π⁺+ π⁻π⁻ 0.04% stat. 0.01% 0.02% 0.03% 0.04%

K⁺K⁺+ K⁻K⁻ 0.07% stat. 0.03% 0.02% 0.12% 0.06%

pp + pp 0.37% stat. 0.1% 0.05% 0.19% 0.09%

π⁺π⁻ 0.05% stat. 0.02% 0.03% 0.03% 0.02%

K⁺K⁻ 0.1% stat. 0.03% 0.02% 0.14% 0.05%

pp 0.17% stat. 0.06% 0.04% 0.29% 0.06%

Table 6.3: Relative systematic uncertainties for different sample selection methods.

The maximum uncertainty of correlation functions for all particle pairs is presented in table (6.4). Values were estimated by following formula:

u_total= v u u t

N

X

i

u²_i, (14)

where u_total is summarized relative uncertainty, N is number selected methods, and u_i is the biggest uncertainty of selected method. The highest summarized relative uncertainty is for unlike-sign protons and the lowest is for like-sign kaons.

Particle pairs u_total π⁺π⁺+ π⁻π⁻ 0.06%

K⁺K⁺+ K⁻K⁻ 0.16%

pp + pp 0.43%

π⁺π⁻ 0.07%

K⁺K⁻ 0.18%

pp 0.34%

Table 6.4: Maximum relative systematic uncertainty for different considered pairs.

Fig. (6-31) presents ∆ϕ projections of two-particle angular correlation functions with marked systematic uncertainties. The uncertainty for each bin was calculated as summarized relative uncertainty multiplied by bin value.

Figure 6-31: ∆ϕ projections of angular correlations functions for Pb-Pb collisions data at√

sN N = 5.02 TeV with marked summarized uncertainty. Centrality range 10 − 20%

7 SUMMARY

7 Summary

This thesis presents like-sign and unlike-sign two-particle angular correlation functions of pions, kaons and protons in Pb-Pb collisions at√

s_{N N} = 5.02TeV registered by the ALICE experiment.

Based on Monte Carlo simulations the efficiency and secondary contamination factors were calculated, which were used to obtain correction factor. All correlation functions with applied correction factor have cos(2∆ϕ) shape, which is caused by elliptic flow effect. Also in this analysis the anticorrelation shape appeared in the baryon-baryon pairs as it was in proton- proton collisions at√

s = 7TeV. This kind of anticorrelation shape does not appear in correlation functions from studied Monte Carlo model. In unlike-sign pairs of protons correlation function a decrease in ∆η∆ϕ ≈ (0, 0) was observed, which was caused by annihilation of protons and antiprotons. Systematics checks for data selection like changing track selection method, |∆η|

range, PID method or Two-Track cuts were performed for this analysis. The highest relative uncertainty is for like-sign protons 0.43% and the lowest is for pairs of like-sign pions – 0.06%.

A Alice-related material

A.1 Analysis software

The analysis was performed using AliFemto package, which is part of AliRoot framework.

AliRoot version: 5.34/30

Code directory:PWGCF/FEMTOSCOPY/(AliFemto and AliFemtoUser) Task used: PWGCF/FEMTOSCOPY/macros/Train/AddTaskFemto.C Configuration macros used: PWGCF/FEMTOSCOPY/macros/Train/KG The whole analysis has been made in PWGCF Pb-Pb LEGO Trains.

A.2 Event selection

It was applied following event selection:

 Trigger and rejection of background events have been done with SelectCollisionCandi- dates method from AliAnalysisTaskSE. AliVEvent::kINT7 trigger was set.

 Only events in distance |zvtx| < 7 cm from the center of TPC were selected.

A.3 ALICE collision data

The data used in this analysis comes from Pb-Pb collisions at the energy √

s = 5.02 TeV registered by experiment ALICE in 2015 LHC15o for Pb-Pb collisions. In the analysis were used The Analysis bject Data (AOD). Runs used in this analysis were suggested by Data Processing Group (DPG) for Central Barrel Tracking and hadron PID.

In the analysis have been used following runs:

 Pb-Pb collisions:

 LHC15o:

245683, 245692, 245702, 245705, 245829, 245831, 245833, 245923, 245949, 245952, 245954, 246001, 246003, 246012, 246036, 246037, 246042, 246048, 246049, 246052, 246053, 246087, 246089, 246113, 246115, 246151, 246152, 246153, 246178, 246180, 246181, 246182, 246185, 246217, 246222, 246225, 246271, 246272, 246275, 246276, 246424, 246431, 246434, 246487, 246488, 246493, 246495, 246750, 246751, 246757, 246758, 246759, 246760, 246763, 246765, 246766, 246804, 246805, 246807, 246808, 246809, 246810, 246844, 246845, 246846, 246847, 246851, 246928, 246945, 246948, 246982, 246984, 246989, 246991, 246994

B ∆η∆ϕFUNCTIONS FOR DIFFERENT CENTRALITY RANGES

A.3.1 MC data

In this analysis it was used AMPT General Purpose Monte Carlo productions anchored to the data from dataset LHC15o.

 LHC17i2:

245683, 245692, 245702, 245705, 245829, 245831, 245833, 245923, 245949, 245952, 245954, 246001, 246003, 246012, 246036, 246037, 246042, 246048, 246049, 246052, 246053, 246087, 246089, 246113, 246115, 246151, 246152, 246153, 246178, 246180, 246181, 246182, 246185, 246217, 246222, 246225, 246271, 246272, 246275, 246276, 246424, 246431, 246434, 246487, 246488, 246493, 246495, 246750, 246751, 246757, 246758, 246759, 246760, 246763, 246765, 246766, 246804, 246805, 246807, 246808, 246809, 246810, 246844, 246845, 246846, 246847, 246851, 246928, 246945, 246948, 246982, 246984, 246989, 246991, 246994

B

functions for different centrality ranges

In this appendix are presented correlation functions calculated for following centrality ranges:

0 − 10%, 10 − 20%, 20 − 40%, 40 − 60% and 60 − 80%. In the Fig. (B-32) are shown like-sign pairs correlation functions and in the Fig. (B-33) are shown plots for unlike-sign pairs. It can be observed that change of centrality range of collisions contributes to correlation functions by changing strength of elliptic flow effect.

Figure B-32: ∆η∆ϕ functions for like-sign pairs for Pb-Pb collisions at √

sN N = 5.02 TeV. Different centralities.

B ∆η∆ϕFUNCTIONS FOR DIFFERENT CENTRALITY RANGES

Figure B-33: ∆η∆ϕ functions for unlike-sign pairs for Pb-Pb collisions at√

sN N = 5.02TeV. Different centralities.

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