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(1)Akademia Górniczo-Hutnicza im. Stanisława Staszica Wydział Fizyki i Informatyki Stosowanej Katedra Oddziaływań i Detekcji Cząstek. Rozprawa doktorska. MOśLIWOŚCI POMIARU AZYMUTALNYCH ANIZOTROPII W ZDERZENIACH Pb-Pb W EKSPERYMENCIE ATLAS PRZY AKCELERATORZE LHC. mgr inŜ. Barbara Toczek. Promotor: Prof. dr hab. Barbara Wosiek. Kraków 2008.

(2) Streszczenie Eksperyment ATLAS, dedykowany do pomiaru zderzeń proton-proton na akceleratorze LHC w ośrodku CERN w Szwajcarii, zostanie równieŜ wykorzystany do badania zderzeń jądrowych, głównie zderzeń ołów-ołów przy energii 5.5 TeV w układzie środka masy nukleon-nukleon. Głównym celem badań zderzeń cięŜkich jonów przy relatywistycznych energiach jest poznanie własności silnie oddziaływującej materii o ekstremalnych wartościach temperatury i gęstości oraz testowanie fundamentalnej teorii silnych oddziaływań, Chromodynamiki Kwantowej. Przygotowanie programu fizycznego przez grupę cięŜko-jonową jest oparte na doświadczeniu zdobytym w eksperymentach przy amerykańskim akceleratorze RHIC w ośrodku BNL. W 2005 roku przedstawiły one dowody odkrycia nowego stanu materii, tzw. silnie sprzęŜonej plazmy kwarkowo-gluonowej (sQGP), o własnościach bliskich idealnej cieczy. Wraz z nowymi odkryciami pojawiło się mnóstwo nierozwiązanych kwestii dotyczących charakterystyki materii hadronowej przy ultrarelatywistycznch zderzeniach, co stanowi powaŜne wyzwanie kontynuacji badań dla przyszłych eksperymentów przy zderzaczu LHC. Istnieje wiele sygnatur plazmy kwarkowo-gluonowej. Jedną z nich są azymutalne anizotropie w rozkładach pędów poprzecznych cząstek produkowanych w zderzeniach. Są one czułe na wczesne etapy procesu zderzenia, w których moŜe nastąpić przejście fazowe materii hadronowej do stanu plazmy kwarkowo-gluonowej. Efekty te mogą dostarczyć bezpośredniej informacji o równaniu stanu, które określa ewolucję systemu, są czułe na stopień termalizacji układu oraz na procesy strat energii partonów w gęstym ośrodku. Warto równieŜ dodać, Ŝe to właśnie badania azymutalnych anizotropii przyczyniły się do obalenia teorii, jakoby plazma kwarkowogluonowa przy tak wysokich gęstościach zachowywała się jak gaz swobodnych cząstek, a nie jak udowodniono, prawie idealna ciecz. Jest to jeden z waŜniejszych powodów, dla których kontynuacja badań azymutalnych anizotropii stanowi istotny aspekt programów badawczych eksperymentów z cięŜkimi jonami. Głównym celem pracy jest oszacowanie moŜliwości pomiaru azymutalnych anizotropii w zderzeniach Pb-Pb przy pomocy eksperymentu ATLAS oraz opracowanie algorytmów do rekonstrukcji efektów asymetrii w rozkładach pędów poprzecznych produkowanych cząstek. Badania te stanowią niezwykle istotną część programu fizycznego grupy cięŜko-jonowej przy eksperymencie ATLAS. PoniewaŜ pierwsze zderzenia wiązek cięŜkich jonów są planowane na koniec 2009 roku, badania zostały prowadzone w oparciu o dane symulacyjne, w których są zaimplementowane efekty anizotropii. Równolegle autor pracy był zaangaŜowany w budowę oraz testowanie aparatury Wewnętrznego Detektora podczas eksperymentu z wiązkami testowymi. W rozprawie przedstawiona jest charakterystyka oraz główne wyniki tych badań testowych, szczególnie dotyczące tej części aparatury, która będzie wykorzystywana do pomiaru azymutalnych anizotropii..

(3) Acknowledgments Ta rozprawa doktorska nie powstałaby, gdyby nie pomoc i Ŝyczliwość wielu osób. Na początku chciałabym podziękować mojej pani promotor, profesor Barbarze Wosiek, dzięki której rozpoczęłam pracę dla grupy cięŜkojonowej eksperymentu ATLAS oraz która wdroŜyła mnie w tajniki fizyki cięŜkich jonów. Jej cierpliwość i gotowość do rozwiązywania wielu moich problemów i pytań była nieoceniona podczas tych kilku lat pracy nad doktoratem. Panom z krakowskiej grupy ATLASa: Andrzejowi Olszewskiemu, Adamowi Trzupkowi oraz Krzysztofowi Woźniakowi dziękuję za wiele cennych uwag oraz dyskusji na temat mojej analizy danych. Pani Beata Murzyn zadbała, by praca była poprawna pod względem językowym, za co jestem jej bardzo wdzięczna. Pragnę złoŜyć serdeczne podziękowania dla pani profesor Danuty Kisielewskiej za opiekę podczas studiów doktoranckich i umoŜliwienie mi wielu interesujących wyjazdów naukowych. Jednak nade wszystko dziękuję jej za serce i przyjazne poklepywanie po ramieniu w cięŜkich chwilach. Leszkowi Adamczykowi dziękuję za stworzenie miłej atmosfery w gabinecie i za nieustanną pomoc w rozwikływaniu problemów przy analizie danych. Moim kolegom Jarkowi Łukasikowi oraz Michałowi Gładyszowi jestem wdzięczna za pomoc oraz rozmowy, dające mi siłę do działania. Rafałowi Ziomkowi dziękuję za szczególne wsparcie podczas ostatnich miesięcy, dzięki któremu było moŜliwe skończenie doktoratu. I would like to extend very special thanks to Professor Allan Clark and Didier Ferrere for the guidance and support they have given me during my visits at CERN. My gratitude also goes to Professor Roy Lacey, Roberto Petti and Naomi van der Kolk for helpful suggestions and discussions of various parts of my analysis. I also extend my heartfelt thanks to Miguel Branco, who kept his enthusiasm up over my work on the elliptic flow analysis, although it was constantly delayed by the programming problems. Rozprawę tą dedykuję moim rodzicom i siostrze, których nieustanne wsparcie i poświęcenie sprawiają, Ŝe moja praca i Ŝycie mają sens.. Barbara Toczek, Kraków 2008 This work was supported by Polish MNiSN grant N202 096 32 (2007-2008)..

(4) AGH – University of Science and Technology Faculty of Physics and Applied Computer Science Department of Particle Interaction and Detection Techniques. Diploma Thesis. CAPABILITY OF MEASURING AZIMUTHAL ANISOTROPIES IN Pb-Pb COLLISIONS WITH THE ATLAS DETECTOR AT LHC. mgr inŜ. Barbara Toczek. Supervised by: Professor Barbara Wosiek. Cracow 2008.

(5) Abstract Quantum Chromodynamics predicts that nuclear matter under extreme temperatures and/or densities will undergo a phase change from hadron gas to Quark-Gluon Plasma (QGP), state described with partonic degrees of freedom. One of the most important signatures of QGP are azimuthal anisotropies in transverse momentum distribution of emitted particles in ultrarelativistic heavy-ion collisions. The ATLAS experiment built at LHC accelerator at CERN in Switzerland is dedicated to studies of proton-proton interactions. The detector is also well suited to study heavy-ion collisions, in particular lead-lead collisions at a centre-of-mass energy. s NN = 5.5 TeV. This dissertation consists of the estimation of the. ATLAS experiment capabilities of measuring the azimuthal angle anisotropies and the detailed analysis of the collective flow results from MC data in which the anisotropy effects were implemented. The main results from the Combined Test Beam are also presented in the thesis, with the focus put on these parts of ATLAS detector which will be used in the azimuthal anisotropies studies..

(6) Table of Contents 1. Introduction. 1. 2. Quark-gluon plasma. 4. 2.1. Phase transitions of QCD matter…………………………………….... 4. 2.2. Probes for QGP………………………………………………………... 8. 2.3. Experience from RHIC………………………………………………... 9. 2.4. Conditions for QGP formation at LHC……………………………….. 11. 3. 4. 5. Collective flow. 15. 3.1. Directed flow………………………………………………………….. 18. 3.2. Elliptic flow………………………………………………………….... 20. 3.2.1. Energy dependence of elliptic flow………………………….. 21. 3.2.2. Scaling properties of elliptic flow………………………….... 22. 3.2.3. Viscous hydrodynamics……………………………………... 24. 3.2.4. Predictions for elliptic flow at LHC energy…………………. 25. ATLAS experiment at Large Hadron Collider. 28. 4.1. LHC accelerator……………………………………………………….. 28. 4.2. ATLAS experiment………………………………………………….... 31. 4.2.1. Inner Detector…………………………………………........... 33. 4.2.2. Calorimeters…………………………………………………. 34. 4.2.3. Muon spectrometer……………………………………........... 36. 4.2.4. Forward detectors……………………………………………. 38. 4.2.5. Trigger system………………………………………….......... 38. Heavy-ion physics with the ATLAS detector. 40. 5.1. Global observables……………………………………………………. 40. 5.2. Jet reconstruction and measurements…………………………………. 44. 5.3. Photons and γ-jet correlations…………………………………………. 47.

(7) 6. 5.4. Quarkonia physics…………………………………………………….. 49. 5.5. Summary……………………………………………………………..... 51. Elliptic flow analysis. 52. 6.1. Simulated datasets…………………………………………………….. 52. 6.2. Reaction Plane method………………………………………………... 55. 6.2.1. Estimate of the reaction plane……………………………….. 58. 6.2.2. Charged particle azimuthal angle distributions…………….... 59. 6.2.3. Results for samples with constant flow…………………….... 62. 6.2.4. Differential flow studies……………………………………... 68. 6.2.5. Conclusions………………………………………………….. 71. Two-Particle Azimuthal Correlation method…………………………. 72. 6.3.1. Correlation functions……………………………………….... 73. 6.3.2. Results for samples with constant flow…………………….... 74. 6.3.3. Differential flow studies……………………………………... 76. 6.3.4. Conclusions………………………………………………….. 77. Lee-Yang Zeroes method……………………………………………... 80. 6.4.1. Generating function and integrated flow…………………….. 81. 6.4.2. Statistical errors…………………………………………….... 84. 6.4.3. Results for samples with constant flow…………………….... 86. 6.4.4. Differential flow studies……………………………………... 91. 6.4.5. Conclusions………………………………………………….. 95. Comparison of methods………………………………………………. 95. 6.3. 6.4. 6.5. 6.5.1. 6.5.2 7. Comparison of methods based on results from ATLAS detector………………………………………………………. 96. Comparison of methods based on RHIC experimental data.... 103. Combined Test Beam. 105. 7.1. Testbeam setup………………………………………………………... 105. 7.2. Data preparation………………………………………………………. 110. 7.3. 7.2.1. Validation of data……………………………………………. 110. 7.2.2. Calibration………………………………………………….... 111. 7.2.3. Alignment……………………………………………………. 112. Data analysis…………………………………………………………... 114. 7.3.1. Inner Detector tracking……………………………………… 114.

(8) 7.3.2 7.4 8. Combined tracking…………………………………………... 119. Conclusions…………………………………………………………… 119. Summary and Outlook. 121. Literature. 123. List of Tables. 129. List of Figures. 130.

(9) Chapter 1. Introduction The main goal of ultra-relativistic heavy-ion physics is to test the properties of strongly coupled matter produced in nucleus-nucleus collisions and to develop an understanding of these properties from the first principles of the fundamental theory of strong interactions, the Quantum Chromodynamics (QCD). It is believed that in ultra-relativistic collisions a state of matter may possibly be created in which quarks and gluons are the relevant degrees of freedom, the phenomenon known as deconfinement. Such a state is called Quark-Gluon Plasma (QGP). Standard models explaining the evolution of our universe predict the existence of this state a few microseconds after the Big Bang, when the universe was at a temperature of approximately 150 to 200 MeV. With regard to complexity of nucleus-nucleus dynamics, there is only one way to achieve the progress in the field of QCD, which is to collect data from experiments studying the nuclear matter at the highest energy densities accessible in the laboratory. The experiments (BRAHMS, PHENIX, PHOBOS and STAR*) at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) have been operating since 2000, beginning the new era of ultra-relativistic collisions. RHIC is the first accelerator of counter-circulating ion beams, where copper and gold ions are accelerated to the maximum energy of 100 GeV/nucleon. It leads to the increasingly higher centre-of-mass energies than those provided by the early fixed-target experiments like the BNL-AGS (Alternating Gradient Synchrotron,. s NN ≤ 5. GeV),. and. the. CERN-SPS. (Super. Proton. Synchrotron,. s NN ≤ 20 GeV). The Large Hadron Collider, LHC, at CERN will study the heavy-ion. *. BRAHMS (Broad RAnge Hadron Magnetic Spectrometer), STAR (Solenoidal Tracker At RHIC).

(10) collisions at a centre-of-mass energy. s NN = 5.5 TeV, which is almost a factor 30 times. higher than the maximal collision energy at RHIC. In 2005 a striking set of new phenomena was discovered by experiments studying the ultra-relativistic heavy-ion collisions at RHIC. They have established empirically that a special form of strongly interacting quark-gluon plasma (sQGP) exists with remarkable properties close to ideal fluid with almost zero viscosity. It refutes the theory that at such energy densities the system behaves like partonic gas. In addition, there is growing evidence that its source is well described by a saturated gluon Color Glass Condensate (CGC) initial state. These RHIC discoveries pave a clear path for future systematic studies of these new forms of matter with LHC accelerator, which is expected to produce a quark-gluon plasma with initial energy density roughly an order of magnitude larger than that achieved at RHIC. A scientific research program of the ATLAS (A Toroidal Lhc ApparatuS ) experiment built at LHC accelerator consists of studies of proton-proton interactions at the energy of 14 TeV, and luminosity of 1033 cm-2 s-1. Recently, this program has been extended to the heavyion studies of lead-lead collisions at a centre-of-mass energy. s NN = 5.5 TeV. The ATLAS. heavy-ion program is mostly focused on global observables and hard probes (jets, photons, and quarkonia) of quark-gluon plasma. From the many signatures of the formation of a quark-gluon plasma in the nucleusnucleus collision systems, one of the most important is azimuthal anisotropy in momentum distribution of emitted particles. In particular, the elliptic flow, which is one of the types of the anisotropic flow in non-central collisions, carries the information of the early stage of the system evolution and allows to infer whether the system reached the local thermodynamic equilibrium. One has to emphasize that the results concerning the azimuthal angle anisotropies obtained by the RHIC experiments and their consistency with the relativistic hydrodynamics lead to the conclusion that the new phase of matter has the property of almost ideal liquid. The main goal of the dissertation is the evaluation of the ATLAS experiment capabilities of measuring the azimuthal angle anisotropies in Pb-Pb collisions and development of the algorithms for reconstructing the effects of the asymmetry in momentum distribution of produced particles. Those studies are crucial for the physics program of the ATLAS heavy-ion group. As the first heavy-ion run is planned for 2009/2010, the studies are based on Monte Carlo simulated data in which the anisotropy effects were implemented. Simultaneously with the preparation of the heavy-ion physics program, the author was. 2.

(11) engaged in the beam line tests of the full slice of the ATLAS detector, the so-called Combined Test Beam (CTB). In this thesis, the basic results for the Inner Detector sub-system (ID) of ATLAS are presented. The outline of the dissertation is as follows. First, the properties of quark-gluon plasma and its signatures are discussed in Chapter 2, followed by the recent experimental results from RHIC and the predictions for creation of the QGP state at the LHC energy. Chapter 3 explains the connection between collective flow, particularly, the anisotropic flow, and quark-gluon plasma. Plasma properties deduced from elliptic flow studies at the RHIC experiments, as well as the predictions for flow measurements in the future heavy-ion collisions at LHC are also presented in this chapter. The ATLAS experiment is described in Chapter 4, with special emphasis put on these detector parts which will be used in the studies of heavy-ion collisions. Chapter 5 presents the main issues addressed in the heavy-ion physics program of the ATLAS experiment, while Chapter 6 describes the methods of the elliptic flow measurements together with the detailed discussion of the elliptic flow results obtained from MC data. The Combined Test Beam (CTB) results based on the real data are presented in Chapter 7, focusing mostly on results from the ATLAS Inner Detector which will be the crucial sub-detector for heavy-ion collision studies, in particular for measurements of the azimuthal anisotropies. Finally, Chapter 8 contains summary and conclusions, as well as plans for future analysis of the elliptic flow effects.. 3.

(12) Chapter 2. Quark-gluon plasma The strong nuclear force mediates interactions between the quarks and gluons thought to compose hadronic matter. Quarks interacting at large distances (small momentum transfers, Q2) are strongly coupled. This is the reason why no single quarks have been observed in nature. The phenomenon is known as confinement. Alternatively, if the distance between a quark and anti-quark is decreased (equivalent to large Q2), the coupling weakens, and the quarks effectively move freely. This phenomenon is know as asymptotic freedom. A consequence of asymptotic freedom is that normal nuclear matter (quarks bound in protons and neutrons) will deconfine into a sea of free quarks and gluons if the energy density or temperature of the system is increased sufficiently. This deconfined partonic state is known as the Quark-Gluon Plasma (QGP) [1].. 2.1 Phase transitions of QCD matter There are two regimes of Quantum Chromodynamics (QCD). In the domain of large momentum transfers (hard hadronic physics) the perturbative analytic calculations might be used, while in the nonperturbative regime (soft hadronic physics) the calculations are restricted only to numerical simulations on a discrete space-time lattice (lattice QCD) [2]. Assuming that the state of matter is near thermodynamic equilibrium, lattice QCD. 4.

(13) calculations are based on the equation of state of quark-gluon plasma, EoS*, which allows a description of strongly interacting matter in terms of thermodynamic quantities such as temperature, T, related to energy density, ε, or pressure, p [3]. The values of the parameters for the phase transition depend on the number of quark flavors (nf) assumed in the calculations. Figure 2.1 shows how the energy density varies with temperature using two quark flavors, three quark flavors, and two light and one heavy quark flavor. The energy density rises quickly at the critical temperature, TC, which is calculated to be around 175 MeV (with 20 MeV uncertainty) for the results shown. This is indicative of a phase transition. The curve approaches 80% of the Stefan-Boltzmann limit (marked as a “εSB/T4” term on the plot), meaning that the QGP state should behave like ideal non-interacting partonic gas, which constitutes the original expectations for a weakly interacting plasma. However, the recent results (see Section 2.3) lead to a conclusion that this 20% difference from the StefanBoltzmann limit is the effect of strong residual interactions in a nonperturbative system.. Fig. 2.1. Energy density scaled by T4 as a function of temperature for several lattice QCD calculations with differing quark flavor configurations, from Reference [3].. *. In the transition region, the energy density, ε, changes rapidly, but the pressure, p, varies slowly. The equation. of state is called stiff when the sound velocity,. cS2 = dp / dε , is big and soft when it is small. The quark-gluon. plasma equation is stiff at high temperature and becomes soft near TC.. 5.

(14) The regions in temperature and baryon chemical potential, µB (which increases with baryon density), where the transition to a quark-gluon plasma is expected, are shown schematically in Figure 2.2*. At low temperatures and densities, the system can be described in terms of bound partons in hadrons: hadron gas. However, at high temperatures and/or densities the hadronic matter undergoes the phase transition into partonic matter in the QGP state. This happens above the critical temperature, TC. At high-energy heavy-ion collisions such densities are created providing the conditions favorable for deconfinement. The information gathered from these collisions is important also in astrophysics. It might help constrain the equation of state, depending on the density of matter in neutron stars and supernovae, as well as reproduce the conditions existed in the first microseconds of the early universe. In Figure 2.2, there is also a region indicated at high density and low temperature, where matter is thought to be in a color superconducting phase [5], which is a state in which the quarks near the Fermi surface become correlated in Cooper-like pairs. Due to the extreme densities necessary for its formation, this part of the phase space is out of reach of current collider experiments. The only known place in the universe where the baryon density might possibly be high enough to produce quark matter and where the temperature is low enough for color superconductivity to occur, is the core of neutron star.. Fig. 2.2. Phase diagram of nuclear matter. Figure from Reference [6]. *. Detailed phase diagram is not 2-, but 3-dimentional with additional dependency on quark masses. For details see Reference [4].. 6.

(15) The QGP phase of matter may also provide insights into the understanding of the chiral symmetry [7]. Massless quarks possess a handedness; this chirality is a fundamental symmetry in QCD. Under normal conditions, the chiral symmetry is spontaneously broken, turning the massless quarks into particles with mass, through the presence of quark-antiquark condensates in the QCD vacuum. It is expected that in the QGP phase the chiral symmetry will be partially restored. The most convenient way of studying the properties of QGP are the ultrarelativistic heavy-ion collisions, especially at high-energy colliders, where the long living state of the QGP is produced in a comparatively large volume. The heavy-ion collisions proceed through a number of different stages. In the first stage, the two colliding nuclei pass through each other. This stage of collision is very short because of the relativistic Lorenz contraction of nuclei moving nearly at the speed of light. Immediately following the collision, the two nuclei form a hot region between them, in which the fluctuations of the color field occur that govern the interactions of quarks and gluons. A large amount of energy is transferred into that stage, which will produce quark-anti-quark pairs, converting the collision energy into partons. Because of the high temperature, a very high density of quarks and gluons will build up and the quarks should no longer be confined. Instead, they will roam freely over the hot zone, forming quark-gluon plasma. The multiple scatterings of partons tend to partition the available energy equally among them and keep the system in the equilibrium. A number of phenomena take place providing the information about the plasma’s properties. In later stages, the QGP cools and expands, and below the deconfinement temperature the quarks and gluons condense into a gas of hadrons. At this point most of the observed particles come into existence. The matter is still highly excited and the hadrons scatter one from another, maintaining the pressure and causing further expansion. When the system is sufficiently dilute the hadrons no longer collide with themselves (the phase called freezout) and travel freely outward reaching the detectors. In fact, the picture of heavy-ion collisions is much more complicated and there is no decisive evidence of how each particular stage of the process looks like. Experience from the previous and recently working experiments shows that some of the theoretically proposed features of the QGP mismatch the empirical results. The LHC heavy-ion program is predicted to create the conditions favorable for the study of the hot and dense QCD matter and therefore is expected to solve many of the puzzles concerning the QGP.. 7.

(16) 2.2 Probes for QGP The formation of quark-gluon plasma in the laboratory conditions has many observable consequences. Unfortunately, most of these observations can be explained by other theoretical approaches that do not require the presence of a QGP. However, it is hoped that the sum of the observations will give evidence for the formation of a QGP (for overview see Reference [8]). Among them, those most relevant for studies at the LHC energy, are: •. Direct photons The photons arising from the electromagnetic interactions of the constituents of the plasma, so called direct photons, will provide information on the properties of the plasma [8]. Since photons are not absorbed by the medium, they provide a relatively clean probe to study the state of the earliest and hottest phase of the evolution of the QGP. The measurement of the direct photons is an important aspect of the ATLAS experiment (see Section 5.3), and the ATLAS will provide meaningful results after the subtraction of the photons from hadronic decays.. •. Quarkonium suppression The J/ψ meson, a bound state of cc pair, has a very long lifetime and it decays into dileptons only when it is far away from the collision zone, which makes it a good probe of the very early stages of the collision [9]. In a QGP, the color charge of a quark is subject to a screening due to the presence of quarks, antiquarks and gluons in plasma. This phenomenon is called “Debye screening”. In plasma, the Debye screening will weaken the interaction between c and c preventing the formation of the cc bound state. Furthermore, the string tension between c and c vanishes since quarks. and gluons are deconfined. For these reasons the production of J/ψ particles in QGP is predicted to be suppressed. A similar phenomena is expected for a heavier quarkonium states, bb . The quarkonium suppression studies in ATLAS are presented in Section 5.4.. 8.

(17) •. Suppression of high pT particles – “jet quenching” When a fast quark or gluon travels through dense matter it suffers energy loss either by excitation of the transverse medium or by radiation. Although radiation is a very efficient energy loss mechanism for relativistic particles, it is strongly suppressed in a dense medium by the Landau-Pomeranchuk effect. Adding the two contributions, the stopping power of a fully established QGP is predicted to be higher than that of hadronic matter, leading to suppressed production of high-pT particles [10]. The ATLAS capabilities of jet quenching measurements are described in Section 5.2.. •. Anisotropic flow The connection between anisotropic flow and formation of quark-gluon plasma state is addressed separately in Chapter 3.. 2.3 Experience from RHIC RHIC started regular beam operations in 2000 and its maximum center of mass energy per pair of colliding gold nuclei,. s NN = 200 GeV, has been the largest so far achieved in. nucleus-nucleus collisions under laboratory conditions. Before the “RHIC era”, no decisive proof of QGP formation was found experimentally, although a number of signals suggesting the formation of a very dense state of matter, possibly partonic, was found at the SPS experiments [11]. In 2005 a formation of quark matter was tentatively confirmed by the results obtained at RHIC. The consensus of the four RHIC research groups, described in socalled “white papers” [12], is that they have evidenced a quark-gluon liquid of very low viscosity. This discovery was in sharp contrast to the theoretical expectations that close to the transition temperature the matter should behave like a gas. It is well known by now that hydrodynamical description of the QGP phase supplemented by hadronic cascade models [13] provides excellent description of RHIC data. A number of published experimental papers from RHIC establish the existence of strongly interacting QGP (sQGP) with the hypothetic source in a saturated gluon Color Glass Condensate (CGC) initial state. The notion of those two special limiting forms of QCD matter are explained as follows:. 9.

(18) •. Strongly coupled QGP (sQGP) The system above TC is called plasma because the degrees of freedom carry nonAbelian analog of charge as in ordinary plasmas. Similar to electromagnetic plasma, the quark-gluon plasma has different regimes: weakly and strongly coupled limits. At extremely high temperatures, the asymptotic freedom property of QCD predicts that it is weakly coupled, while for moderate temperatures, accessible at RHIC, the plasma is predicted by nonperturbative lattice techniques to be strongly coupled (see Figure 2.1) [14]. In many publications, the “strongly coupled” refers to the plasma coupling parameter Γ* (often used in the case of electromagnetic EM plasmas). The plasmas where Γ << 1 behave like gases. However, for Γ >> 1 the plasmas are strongly coupled and behave like low viscosity liquids or even like solids (at Γ > 300). Unlike gases and solids, the interplay of local order and randomness at large distances makes liquids difficult to treat theoretically. For liquids neither Boltzmann equation nor hadronic cascade models can be used because particles are strongly correlated with several neighbors at all times.. •. Color Glass Condensate (CGC) In order to extract the properties of the QGP from experimental data, one must supplement the hydrodynamic description by appropriate models for initial conditions of the collision. The results from RHIC experiments indicate the existence of Color Glass Condensate (CGC) as the initial stage. In Reference [15] heavy-ion collisions are visualized as the collision of two sheets of colored glass. Inside the nuclei, the CGC exists as a form of a very dense superposition of tightly packed gluons, similar to Bose condensate. It has properties similar to glass, that is a very slow evolution compared to the natural time scales of constituent interactions. Remarkably, the CGC predictions on the global observables such as the centrality, rapidity and the energy dependences of charged hadron multiplicities agree with the RHIC data [16].. The most restrictive tests of the models based on sQGP and CGC initial states can be done from the measurements of the anisotropic flow effects. The discussion of the anisotropic flow and its relevance for inferring flow properties of the matter created in heavy-ion collisions is included in Chapter 3. *. This coupling parameter is defined as the ratio of the average potential energy over the average kinetic energy and is used as a measure of the interaction strength in EM plasmas.. 10.

(19) 2.4 Conditions for QGP formation at LHC There is no doubt that the experiments at RHIC have revealed a plenty of new phenomena that for the most part have come as a surprise. In this sense, it is clear that the matter that is created at RHIC differs from anything that has been seen before. Therefore, it is extremely difficult to predict the properties of the quark-gluon plasma in the heavy-ion collisions at the forthcoming LHC accelerator. Reference [17] consists of a compilation of such predictions, based both on the generic trends in the data of the previous heavy-ion experiments and their extrapolation to LHC energies, as well as theoretical ideas on new phenomena that might occur during the heavy-ion collisions at LHC. The latter will not be discussed here and only several, apparently universal trends will be presented. •. Multiplicity distributions. In hadronic collisions, event multiplicities and multiplicity distributions are dominated by processes involving small momentum transfers. Although there exist many model approaches, the understanding of multiplicity distributions based on first principles is still missing. However, based on the data from previous heavy-ion experiments, it is possible to draw several characteristic features, which persist over several orders of magnitude in s NN . Firstly, pseudorapidity* distributions, plotted in the rest frame of one of the. colliding nuclei, follow the universal, energy-independent limiting curve in the fragmentation regions (see Figure 2.3). This trend is known as the extended longitudinal scaling. The second trend refers to the factorization of the energy and centrality/Adependence in pseudorapidity distributions. If Pb-Pb data at LHC will follow the same ch limiting fragmentation curve as in the previous experiments, one can expect dN AA / dη ~. 1100, which is indicated in the plot as a solid curve. On the other hand, the recently ch developed saturation models predict the higher value of dN AA / dη ~ 1650 (dashed line in. Figure 2.3).. Pseudorapidity is defined as: η = − ln tan  θ  , where θ is the angle between the particle and the direction of     2  the beam axis, z.. *. 11.

(20) •. Transverse momentum spectra at low and intermediate pT. The transverse momentum dependence of identified hadron spectra is usually discussed as a function of their transverse mass, mT, rather than pT, and is characterized by the. Fig. 2.3. Pseudorapidity distributions of charged particle production in Au-Au collisions at different centerof-mass energies plotted at the rest frame of one of the colliding nuclei. Lines indicate predictions for Pb-Pb collisions at LHC. Figure taken from [17].. inverse-slope parameter, Tinv. For this characteristics, the following rules can be established. At given. s NN , the inverse-slope parameters of pions, kaons and protons. increase linearly with particle rest mass. For hadrons like, Ξ, Ω or the J/Ψ, the value of Tinv is roughly the same. Secondly, the spectra become flatter with increasing. s NN . Most. likely, the results from LHC will follow those trends, however, the real physics issue is to assess whether a genuine collective hydrodynamic mechanism determines the energy dependence of Tinv. •. Single particle high pT spectra. Some major discoveries at RHIC have been made by studying the particle spectra at high pT. A phase space for such measurements is systematically growing with the energy, from. pT ≤ 3-4 GeV/c at the SPS, through the RHIC’s range of pT ≤ 10-20 GeV/c and finally. 12.

(21) the expected range of pT ~ 10 times higher at the LHC than at RHIC. To discuss the generic trends in the measured spectra at high pT, it is useful to use the nuclear h modification factor, R AB , which is the ratio of the yield obtained from nucleus-nucleus. collisions, A-B, to the yield from elementary nucleon-nucleon collisions, scaled with the AB number of binary collisions, N coll :. h R AB. AB → h dN medium dpT dη . = pp → h AB dN vacuum N coll dpT dη. (2.1). In the absence of any nuclear effects the ratio should saturate at unity for high pT, where production is dominated by hard scatterings and is proportional to the number of binary collisions, Ncoll. Figure 2.4 shows the nuclear modification factor as a function of transverse momentum from RHIC data, which exhibits the following features. Firstly, the strong suppression, by a factor of ~5, at high pT is observed, leading to a value of h R AA ≅ 0.2 for pT ≥ 5-10 GeV/c. Within experimental errors, this suppression is pT -. independent for high transverse momenta. Moreover, there is no particle-species dependence of the suppression pattern at high pT. At intermediate range of pT, h h 3 < pT < 5 GeV/c, R AA is smaller for mesons than for baryons. R AA spectra also show the h characteristic centrality dependence. For the most peripheral collisions R AA is consistent h with the absence of medium effects, while with increasing centrality R AA decreases. monotonically. Those characteristics based on RHIC data prove that the suppression of high pT single hadron spectra in nucleus-nucleus collisions is due to a partonic, mediumlength dependent final state effect. To judge if those characteristics persist at the LHC, one has to introduce the jet quenching parameter qˆ (τ ) , which depends on the time τ after the collision. This parameter comes from the parton energy loss models and is the only h medium-sensitive parameter. Once its value is fixed, it will be possible to predict the R AA. behavior at the LHC energies. Some of these predictions are shown in Figure 2.4. However various theoretical models assume significantly different values of qˆ (τ ) , and in h consequence, the predictions for R AA at LHC are uncertain.. 13.

(22) Fig. 2.4. Nuclear modification factor as a function of transverse momentum at mid-rapidity. Data come from RHIC in. s NN = 200 GeV Au-Au collisions. Arrows indicate qualitative predictions for LHC collisions. Figure. taken from [17].. In this section only a few basic predictions were shown (for the detailed discussion on this subject see Reference [17]). However they indicate how hard it is to predict the features of the collision system at the LHC energy. Various models give the orders of magnitude different values even for the basic global observables. If the predictions based on the generic trends from previous experiments, especially from RHIC, turn out to be correct, more than ever any model which claims to explain the phenomena observed in heavy-ion collisions at ultrarelativistic energies, must contain a reliable explanation for the observed trends, over the broad range of systems, energies and rapidities over which the trends are observed. If these predictions turn out to be false, it will be a direct indication of the onset of new phenomena at LHC energies.. 14.

(23) Chapter 3. Collective flow Over the last years, the study of collective flow in nuclear collisions at high energies has attracted the increased attention of both theoreticians and experimentalists. There are several reasons for this: the observation of anisotropic flow at the AGS, SPS and very interesting results from RHIC experiments, progress in the theoretical understanding of the relation between the appearance and development of flow during the collision evolution and the development of new suitable techniques for flow studies at high energies. Although all forms of flow are interrelated and represent only different parts of one global picture, usually the collective flow discussions are divided into longitudinal expansion, isotropic transverse flow and anisotropic transverse flow, of which the most well established are directed flow and elliptic flow [18]. At high energies the longitudinal flow is well decoupled from transverse flow. The flow (polar) angles observed at low energies are relatively large and a rotation of the coordinate system was done in order to analyze the event shape in the plane perpendicular to the main axis of the flow ellipsoid. At high energies the flow angles become very small, so that one does not have to rotate coordinates to account for the flow pattern, but it is possible to use the plane transverse to the beam axis. Thus only transverse flow from the particle pT spectra and azimuthal angle distributions at fixed pseudorapidity will be discussed. In heavy-ion collisions the azimuthal anisotropy has its origin in the initial geometric deformation of the reaction region and in particle rescatterings in the evolving system, which convert the spatial anisotropy into transverse momentum anisotropy. The transition of the system is through the possible novel phases of nuclear matter into the observed final state, consisting of a large number of produced particles. The important insights into the evolution 15.

(24) may be obtained from the study of such an anisotropic flow of particles. This collective flow is the consequence of the pressure and pressure gradients in the evolving system and thereby provides access to the equation of state, EoS (the equation that relates the pressure P, volume. V, and temperature T of a given substance in thermodynamic equilibrium), of the hot and dense matter (“fireball”) formed in the reaction region. This access is indirect since the flow in the final state represents a time integral over the pressure history of the fireball. Different types of transverse flow (radial, direct, elliptic) show different sensitivities to the early and late stages of the collision, so that a combination of flow observables may allow for a more differential investigation of the equation of state. In particular, the elliptic flow is a signature for the early stage of collision: its driving force is the spatial eccentricity of the dense nuclear overlap region which, if thermalized quickly enough, leads to an anisotropy of the pressure gradients which cause the expansion. Since the developing anisotropic flow reduces eccentricity of the fireball, it acts against its own cause and thus shuts itself off after some time. Radial flow, on the other hand, responds to the absolute magnitude of the pressure gradients and not to their anisotropy; it, therefore, exists also in central collisions, despite that in this case the initial spatial deformation is negligible. Anisotropic flow describes the azimuthal angle distribution of particle emission with respect to the reaction plane angle, ΨR, defined by the beam direction and the impact parameter b (see Figure 3.1), when nuclei collide at other than zero impact parameter (noncentral collisions). Anisotropic flow is usually described by the Fourier expansion of the particle distribution in azimuthal angle, φ, measured with respect to the reaction plane, which can be written as [18]:. E. ∞ d 3N 1 d 2N   = 1 + 2v n cos(n(φ − ΨR )) , ∑  3 2π pT dpT dy  n =1 dp . (3.1). where pT is the transverse momentum* of the particle and y is the rapidity**. The sine terms which in general appear in Fourier expansions vanish due to the reflection symmetry with respect to the reaction plane. The factor “2” in front of each vn coefficient is used in order to make the meaning of vn more transparent [19]. *. Transverse momentum is defined as: pT =. **. Rapidity is defined as: y =. particle.. 16. p x2 + p 2y .. 1 E + p z , where z is the direction of the beam and E denotes the energy of the ln 2 E − pz.

(25) The derivation:. d 3N ∫−π cos n(φ − ΨR )E dp 3 dφ = π d 3N E ∫−π dp 3 dφ π. cos n(φ − ΨR ). ∫ cos n(φ − Ψ )(1 + ∑ 2v cos(m(φ − Ψ )))dφ = π π ∫ π (1 + ∑ 2v cos(m(φ − Ψ )))dφ π. ∞. m =1. R. −. m. R. ∞. m =1. −. π. ∫ 2v = π −. where. the. cos 2 n(φ − ΨR )dφ. n. 2π. orthogonality. π ∫ π [cos n(φ − Ψ )cos m(φ − Ψ )] −. R. R. m. m≠ n. R. = vn ,. relation. between. (3.2) Fourier. coefficients. dφ = 0 has been used, in the end gives the definition of. the Fourier coefficients:. v n = cos n(φ − ΨR ) .. (3.3). The first term in the square brackets of Equation 3.1 represents the isotropic radial flow. On the contrary, the coefficients given by Equation 3.3 represent the anisotropic flow; v1 is called directed flow, while the second one, v2, is referred to as the elliptic flow. Figure 3.2 shows the schematic view of those types of anisotropic flow, directed and elliptic flow.. Fig. 3.1. Reaction plane, defined by the initial direction of two colliding nuclei and the impact parameter, b (left), shown also in the transverse plane (right).. 17.

(26) Reaction plane. Fig. 3.2. Major types of azimuthal anisotropies: directed flow (left) and elliptic flow, viewed in the transverse plane (right).. 3.1 Directed flow Directed flow, v1, affects most strongly the particles at forward and backward rapidities. At low energy (below 100AMeV), the interaction is dominated by the attractive nuclear mean field, in which, among others, the projectile nucleons are deflected towards target, resulting in negative directed flow. At higher energies, individual nucleon-nucleon collisions dominate over mean field effects. They produce a positive pressure which deflects the projectile and target fragments away from each other in the center of mass frame, resulting in positive directed flow [20]. The first evidence of directed flow at SPS was reported by the SPS-WA98 collaboration [21], followed by SPS-NA49 [22] experiment. Figure 3.3 displays the typical variation of directed flow with the bombarding energy. The energy dependence of elliptic flow is also shown for comparison (the details will be explained in the next section). At RHIC energies, the observed directed flow pattern is established very early in the collision, since the affected particles quickly leave the central region where the transverse pressure acts. Its natural time scale is given by the passage of the two Lorenz-contracted nuclei, which decreases at high collision energy; this causes a significant decrease of v1 magnitude at high energy collisions. Additionally, directed flow is particularly susceptible to non-flow correlations arising from momentum conservation* [23].. *. Due to the mometum conservation, in the directed flow dependence on rapidity, the gap is observed at y = 0.. However, this result can be corrected for. For example see Reference [23].. 18.

(27) Fig. 3.3. Schematic behavior of the magnitudes of directed flow (top) and elliptic flow (bottom) as a function of the bombarding kinetic energy per nucleon in the laboratory frame for nucleons (solid line) and pions (dashed line). Figure taken from [20].. The typical shape of directed flow as a function of rapidity is shown at left panel of Figure 3.4, where the theoretical UrQMD* calculations for protons, anti-protons and lambdas in minimum bias Au-Au events at the full RHIC energy are presented [24]. Due to the Equation 3.3, directed flow is an odd function of centre-of-mass rapidity in symmetric collisions. It is, therefore, linear near mid-rapidity. Furthermore, a saturation is observed near projectile and target rapidities, resulting in an S-shape curve. Anti-protons show a strong anticorrelation with the protons, which indicates the presence of anti-baryon absorption in nuclear matter even at ultrarelativistic energies. Another interesting feature of results from directed flow studies is presented at right panel of Figure 3.4, where the zoom into the mid-rapidity region is shown for protons and pions in Au-Au reactions at the RHIC energy s NN = 200 GeV. One can see the wiggly shape of proton distribution, which in hydrodynamic calculations is explained by the existence of “antiflow” component of flow , which largely cancels the directed flow from the “bounce-off” of the two nuclei. This antiflow, predicted at RHIC energies by the hydrodynamic. *. Hadronic transport model - Ultra-relativistic Quantum Molecular Dynamics. 19.

(28) Fig. 3.4. Directed flow parameter, v1, of protons, lambdas and anti-protons (left panel) and for protons and pions (right panel) as a function of rapidity in Au-Au minimum bias collisions at the RHIC energy. s NN = 200. GeV, based on the UrQMD calculations [24].. calculations [24], is also present at SPS results [25]. Surprisingly, the directed flow of pions does not follow the same behavior as that of protons, and v1 of pions has the opposite sign to the proton v1 at large rapidity, which is understood as a consequence of pion rescattering on spectator matter. Although many theoretical predictions have been made, the small magnitude and, additionally, big systematic uncertainties caused by non-flow correlations make the directed flow very challenging to measure accurately at RHIC energies, especially at the midrapidity region, where the magnitude of directed flow is less than 1% [26].. 3.2 Elliptic flow In this section the elliptic flow properties will be described, based on the data from previous and recently ongoing experiments, showing the connection between the v2 magnitude and the quark-gluon plasma properties where appropriate. The comparison of the hydrodynamical models with the real data will be also presented. Finally, some predictions will be made based on the generic trends in the elliptic flow data of the previous heavy-ion experiments and their extrapolation to LHC energies, as well as the theoretical models.. 20.

(29) 3.2.1 Energy dependence of elliptic flow. Elliptic flow, v2, is caused by the initial geometric, almond-shape like, deformation of the reaction region in the transverse plane (see Figure 3.2). Over a broad range of beam energies, elliptic flow can be attributed to a delicate balance between (i) the ability of a fast pressure build-up to generate a rapid transverse expansion of nuclear matter and (ii) the passage time for removal of the shadowing effect on participant hadrons by the projectile and target spectators. If the passage time is long compared to the expansion time, spectator nucleons serve to block the path of participant hadrons emitted toward the reaction plane, and nuclear matter is squeezed out perpendicular to this plane giving rise to negative elliptic flow. For shorter passage times, the blocking of participant matter is significantly reduced and preferential in-plane emission or positive elliptic flow is favored because the geometry of the participant region exposes a larger surface area in the direction of the reaction plane. Thus, elliptic flow is predicted and found to be negative for beam energies < 4 AGeV and positive for beam energies > 4 AGeV [20] (see Figure 3.5). Unlike the directed flow, elliptic flow needs time for thermalization, thus it is generated later than directed flow.. Fig. 3.5. Elliptic flow as a function of energy for different experiments. Figure taken from [17].. 21.

(30) Figure 3.5 shows the energy dependence of elliptic flow magnitude and sign for different experiments. The above discussed effects at AGS energy result in negative v2, while at relativistic energies v2 becomes positive and shows the increasing tendency with the beam energy. Predictions of the elliptic flow magnitude at the LHC energies will be discussed in Sub-Section 3.2.4.. 3.2.2 Scaling properties of elliptic flow. Systematic theoretical and experimental studies of the influence of model parameters are now required to gain more quantitative insight into the transport coefficients and the equation of state for the strongly interacting matter. The range of validity of perfect fluid hydrodynamics is affected by the degree of thermalization and the onset of dissipative effects. These questions can be addressed by investigating several scaling properties of perfect fluid hydrodynamics. Recent detailed results from experiments at RHIC on the differential measurements of the elliptic flow for particles produced in Au-Au and Cu-Cu collisions at wide energy range clarify many of these questions. The shape of the overlap region can be characterized by the single parameter, eccentricity ε. Assuming that the minor axis of the overlap ellipse, x, is along the impact parameter vector and the y-axis is perpendicular to that in the transverse plane, the standard. σ y2 − σ x2 , where σx and σy are the RMS widths of the eccentricity is defined by: εstandard = 2 σ y + σ x2 participant nucleon distributions projected on the x and y axes respectively. However, recent results from RHIC-PHOBOS collaboration show that for small systems, or small transverse overlap regions, fluctuations in the nucleon positions frequently create a situation, where the minor axis of the ellipse in the transverse plane formed by the participating nucleons is not along the impact parameter vector. Therefore, a new definition of the eccentricity was proposed, which characterizes the eccentricity through the event-by-event distribution of nucleon-nucleon interaction points obtained from a Glauber Monte-Carlo calculation. Such “participant eccentricity” is defined by [27]:. ε part =. 22. (σ. 2 y. − σ x2. ). 2. + 4(σ xy ). σ y2 + σ x2. 2. .. (3.4).

(31) In this formula, σ xy = xy − x y . The average values of “standard” and “participant” eccentricities are quite similar for all but the most peripheral interactions for large collision systems, like Au-Au. For smaller species such as Cu, however, fluctuations in the nucleon positions become quite important for all centralities and the average eccentricity can vary significantly, depending on how it is calculated. The flow data for Cu-Cu and Au-Au collisions were reconciled only when scaled by participant eccentricity, which is shown in Figure 3.6.. Fig. 3.6. Eccentricity scaled elliptic flow values as a function of centrality. See text for eccentricity definitions. Figure taken from [28].. Another interesting scaling property of the elliptic flow was found by the RHICPHENIX collaboration in the studies of identified particle elliptic flow [29]. Figure 3.7 (left) shows a comparison of the measured anisotropy v2(pT), for several particle species obtained in minimum bias Au-Au collisions at. s NN =200 GeV. The comparison shows a clear particle. ordering at both low and high pT values. At low pT ( pT ≤ 2 GeV/c), one can see rather clear evidence for mass ordering. If this aspect of v2 is driven by a hydrodynamic pressure gradients, the prediction is that the v2 values observed for each particle species should scale with ET (the transverse kinetic energy ET = mT − m , where mT is the transverse mass of the particle). The pressure gradient that drives elliptic flow is directly linked to the kinetic energy of the emitted particles, which is confirmed by the data shown in the middle plot of Figure 3.7. For higher values of pT ( pT ≈ 2 - 4 GeV/c), Figure 3.7 indicates that mass ordering is broken and v2 is more strongly dependent on the quark composition of the particles (nq denotes the number of constituent quarks for mesons, nq = 2, and for baryons, nq = 3) than on. 23.

(32) their mass, which has been attributed to the dominance of the quark coalescence mechanism for pT ≈ 2 - 4 GeV/c.. Fig. 3.7. Elliptic flow dependency on transverse momentum (left), on transverse kinetic energy (middle) and transverse kinetic energy scaled by number of constituents quarks (right). Figure taken from [29].. 3.2.3 Viscous hydrodynamics. As described in Chapter 2, the success of ideal hydrodynamics for the description of the heavy-ion collisions at RHIC energies has led to the idea of a strongly coupled quark-gluon plasma (sQGP), behaving as a perfect fluid. However, by now, it is also known that sQGP is not a perfect fluid and that its nonideality might be explained by viscous effects [30]. There is a well defined measure of the interaction strength. It is the ratio of the shear viscosity, η, (a measure of the mean free path of particles) and its entropy density, s, (measure of the interparticle distances). It is also important to mention that the characteristics of sQGP depend strongly on the initial conditions for a hydrodynamic description of ultrarelativistic heavy-ion collisions. Unfortunately, these are poorly known, so one has to resort to model studies. At present, there exist two main classes of models, which will be referred to as Glauber-type [13] and color-glass-condensate (CGC)-type models [13]. In the following discussion, only Glauber-type models will be used. Figure 3.8 shows the comparison of hydrodynamic model with the set of viscosity ratios with minimum bias data from PHOBOS and STAR. 24.

(33) experiments [30]. The v2(pT) results for data from STAR seem to favor η/s ≅ 0.03 at low transverse momenta, but it could drastically change while considering the significant systematical errors (in Figure 3.8 only statistical uncertainties are shown). In fact, the data from PHOBOS on centrality dependence of the v2 integrated over pT agree with hydrodynamic model with η/s ≅ 0.08 for peripheral collisions (only systematic errors are shown in Figure 3.8). Expectations for η/s also change while considering CGC-type initial conditions, due to the higher eccentricity values for this model. Although many of the scientists are skeptical about magnitude of systematic errors in those studies, one has to admit that η/s is definitely less than 0.2, which makes sQGP the most perfect liquid known.. Fig. 3.8. PHOBOS and STAR data on v2 for charged particles in Au-Au collisions at. s NN =200 GeV. compared to hydrodynamic model with various viscosity ratios, η/s. Figure taken from [30].. 3.2.4 Predictions for elliptic flow at LHC energy. Elliptic flow is one of the strongest manifestations of collective dynamics in heavy-ion collisions. However, there is a lot of complexities in the theoretical description of conditions in which the quark-gluon plasma phase occurs, as well as the QGP properties. Many questions are still not solved, e.g. what are the initial conditions of heavy-ion collisions, is the produced. 25.

(34) matter a perfect fluid, and if not, what is its viscosity, is the thermal equilibrium achieved, what is the exact temperature of freezout and, finally, how do the later stages of the QGP expansion look like. There are many theoretical models explaining some of these questions, but they fail in the description the whole process. Therefore, the QGP properties, followed from the elliptic flow dependency on such variables as collision energy, particle density, pseudorapidity or transverse momentum, are really hard to predict. In this sub-section, some of the predictions discussed in Reference [17] will be described. In Figure 3.5, the generic trend in the elliptic flow dependency on collision energy is shown. Based on the data from the previous experiments, one can see the v2 value steadily rises from SPS to RHIC energies. Thus, the prediction based on those data leads to the conclusion, that v2(y = 0) at mid-central Pb-Pb collisions will be about 0.075. This is indicated as a purple point in Figure 3.5. However, extrapolating models of ideal hydrodynamics from RHIC to LHC, one gets the lower value of v2 [17]. Another generic trend concerns the pT-integrated dependency of elliptic flow on pseudorapidity, v2(η). In contrast to dN / dη (see Section 2.4), it is not trapezoidal, but rather triangular. As seen in Figure 3.9, longitudinal scaling of pT-integrated v2 persists up to midrapidity. In this case one can expect v2(η=0) to be about 0.075. This is the same value as compared with the extrapolation of data shown in Figure 3.5. The last trend discussed in this section concerns the transverse momentum dependence of the elliptic flow value. In general, at transverse momenta below pT ≅ 2.0 GeV/c, where the data are precisely known from SPS and RHIC experiments, v2 is found to approximately linearly rise with pT. On the other hand, the pT–shape of the charge-hadron v2 has a characteristic breaking point. The reason for this is still not fully clarified, as well as its dependency on collision energy. In Reference [14] the elliptic flow magnitude is compared with different hydrodynamical calculations. Although some calculations are not too close to the data, the overall magnitude of the v2 dependence on pT is clearly reproduced. One does not expect a drastic change while moving to LHC energy.. 26.

(35) Fig. 3.9. Elliptic flow v2, averaged over centrality (0%-40%), at various collision energies. Data from PHOBOS and STAR experiments are plotted as function of η-ybeam (full symbols) and reflected across the LHC-ybeam value (open symbols). Figure taken from [17].. 27.

(36) Chapter 4. ATLAS experiment at Large Hadron Collider This chapter contains the short description of the LHC accelerator and ATLAS detector, with a focus on the features of the detector that will allow to perform a systematic study of various aspects of heavy-ion collisions.. 4.1 LHC accelerator The Large Hadron Collider (LHC) [31] is a particle accelerator which is being built at CERN, the European Organization for Nuclear Research, and straddles the Swiss and French borders. The LHC will take the place of CERN's Large Electron Positron (LEP) collider, and will sit in its 27 km long tunnel, about 100m underground. It will accelerate two separate beams of protons up to an energy of 7 TeV, and then bring them into head-on collisions at four points along the ring. The resulting proton interactions will have a center of mass energy of 14 TeV, which will be the highest accessible energy achieved so far in the laboratory conditions. The startup is scheduled for summer 2008. Before being injected into the LHC, proton beams will be pre-accelerated by CERN's existing accelerator complex (see Figure 4.1). This is a succession of machines with increasingly higher injection energies. The acceleration of the protons starts at a dedicated linear collider (LINAC), which accelerates bunches of 1011 protons to an energy of 50 MeV. These bunches are then transferred through the Proton Synchrotron Booster (PSB) and Proton Synchrotron (PS) into the Super Proton Synchrotron (SPS), where they are accelerated to 450. 28.

(37) GeV. Finally, the SPS injects the protons clockwise and counter-clockwise into the LHC rings, where they are accelerated to their final energy of 7 TeV. More than 1200 dipole magnets, installed along the LHC tunnel, keep the protons on track in the ring. The dipoles provide a magnetic field of up to 8.33 Tesla, a value which is made possible by the use of superconductivity (the ability of certain materials, usually at very low temperatures, to conduct electric current without resistance and power losses, and therefore produce high magnetic fields). The LHC will operate at a temperature about 1.9 K. The main parameters of the LHC accelerator are gathered in Table 4.1.. LHC. - Large Hadron Collider. SPS. - Super Proton Synchrotron. PS. - Proton Synchrotron. PSB. - Proton Synchrotron Booster. AD. - Antiproton Decelerator. LEIR. - Low Energy Ion Ring. LINAC - LINear ACcelerator. Fig. 4.1. CERN accelerator complex [31].. 29.

(38) Like its center of mass energy, the luminosity of the LHC is also unprecedented for a proton collider. The luminosity is defined as a number of protons that pass by, per unit area, per unit time. The LHC designed luminosity is 1034 cm-2s-1, which with the bunch spacing of 25 ns gives on average about 27 interactions per bunch crossing. Thus, the number of protonproton interactions per second will be around 109, which gives an excellent opportunity to study many interesting physics processes even with the very small cross sections. The beams will collide at four points, where four detectors are located: ATLAS, CMS, ALICE and LHC-b. ATLAS (A Toroidal Lhc ApparatuS) [32] and CMS (Compact Muon Solenoid) [33] are general purpose detectors designed to cover a wide range of physics, with a special focus on Higgs boson discovery. They will also explore the physics beyond the Standard Model, like supersymmetry, extra dimensions or mini-black holes. The ATLAS experiment will be described in more detail in the next section. The ALICE (A Large Ion Collider Experiment) [34] experiment is devoted to study the heavy-ion collisions, in particular, the quark-gluon plasma properties. The LHC-b (Large Hadron Collider beauty) [35] detector is designed to study CP-violation in the beauty sector, and is therefore optimized for the detection of B-mesons.. PARAMETER. VALUE. UNIT. Circumference. 26659. m. 7. TeV. Injection energy. 0.45. TeV. Number of dipoles. 1232. Dipole field at 7 TeV. 8.33. T. Helium temperature. 1.9. K. Luminosity. 1034. cm-2s-1. Luminosity lifetime. 15. h. Bunch spacing. 25. ns. Proton beam energy. Particles per bunch. 1011. Bunches per beam. 2808. Expected runtime per year. Table. 4.1. Main parameters of the LHC accelerator [31].. 30. 107. s.

(39) The LHC will be able to also run the variety of heavy-ion beams, thus providing nucleus-nucleus and proton-nucleus collisions. It is foreseen that the heavy-ion programme will extend for one month of running per year of the LHC operation. The startup is scheduled for 2009 or 2010 (it depends on the effectiveness of the initial proton-proton operations). Most of the time will be likely devoted to Pb-Pb interactions (the other potential species are In, Kr, Ar, O, He) , with collision energy of 5.5 TeV per colliding nucleon pair, which is almost a factor 30 times higher than the maximal collision energy at the currently operating Brookhaven Relativistic Heavy Ion Collider (RHIC). The designed luminosity for the Pb-Pb collisions is 1027 cm-2s-1 (with the luminosity lifetime of 4 h) and it is significantly limited by the quenching of the magnets. The bunch-crossing will happen in 100 ns intervals. For example, during Pb-Pb operation the ATLAS detector will record roughly 50 events per second, which imposes the high requirements on event selection system.. 4.2 ATLAS experiment The ATLAS detector [32] is the biggest experiment of four detectors constructed at the crossing points at LHC. Like most colliding beam experiments, it has an appropriate cylindrical symmetry and is organized in a central barrel around the beam pipe and two endcaps. Figure 4.2 gives the overall view of the detector with the various sub-systems indicated. The inner-most system is the Inner Detector which detects the tracks of charged particles. The energy of particles and jets are measured by the calorimetric system. Muons, which can traverse all layers of calorimeters, are measured by the outer-most muon spectrometer. For the heavy-ion studies, the additional sub-system (not shown in the picture), the Zero Degree Calorimeter (ZDC) [36], was built with the location in the LHC tunnel. The various sub-systems are described in the next sub-sections. ATLAS is 45 meters long and 22 meters high, which is a direct consequence of the high center of mass energy of the LHC beams. The large volume gives the trackers a long lever arm which improves the momentum resolution, while thick calorimeters are required to fully contain the showers of particles in the calorimetric system and reduce the amount of punch-through into the muon chambers to minimum. The fast electronics, specially dedicated for the LHC experiments, is required to cope with the high bunch-crossing rate.. 31.

(40) Fig. 4.2. Overview of the ATLAS detector [31].. The main advantage of the ATLAS detector is its unprecedented pseudorapidity coverage, which makes it capable of measuring different physics observables over a large phase-space region. The pseudorapidity coverage of the various ATLAS detector components is shown in Figure 4.3 [37]. The calorimeters allow for a measurement of jets over the pseudorapidity interval η < 5 , identify photons over the interval η < 2.4 and charged particles over η < 2.5 . The muon spectrometers, covering η < 2.7 allow for measurements of ϒ states over a range η < 2.5 . A forward luminosity monitoring detector will provide. dN ch / dη measurements over 5.4 < η < 6.1 . The ATLAS ZDC will cover η > 8 for neutral particles, both neutrons and photons. It is important to note that, for jet and photon measurements, the ATLAS calorimeter system coverage (similar to that of CMS) dramatically exceeds that of the ALICE experiment, which is the experiment dedicated for heavy-ion collisions (see Figure 4.4). This is the main reason why the ATLAS heavy-ion physics program was accepted as the complementary program for the LHC quark-gluon plasma studies. The heavy-ion physics program of the ATLAS experiment is described in Chapter 5.. 32.

(41) Fig. 4.3. Pseudorapidity coverage of the various components of the ATLAS detector [37].. Fig. 4.4. Comparison of the pseudorapidity coverage for the ATLAS and ALICE detector calorimetric systems.. 4.2.1 Inner Detector. The ATLAS Inner Detector (ID) [32] is the detector closest to the interaction point. Its task is to reconstruct the trajectories of charged particles that are produced in the proton or ion collisions. It also reconstructs the primary and possible secondary vertices. The latter being. 33.

(42) needed to identify particles, e.g. B-mesons or photon conversions. The Inner Detector has been designed to track charged particles in 5 units of pseudo-rapidity centered around midrapidity. All its sub-systems are installed in a solenoid magnet, which provides a magnetic field of 2 Tesla, allowing for measuring the momentum of the particles by the track curvature. The Inner Detector combines three technologies (see Figure 4.5). Tracking is done with silicon pixel detectors (Pixel) arrayed in a barrel with three layers (B-layer, Layer 1 and Layer 2) and 6 endcap sections located on both sides of the nominal interaction point. This very high granularity system provides three 3-dimensional points per track. The Pixel detector is followed by the Semi-Conductor Tracker (SCT) consisting of double-sided silicon strip sensors arranged in four layers in the barrel, and two sets of 9 endcap disks. SCT provides at least four 3-dimentional spacepoints (the intersection of two stripes in the sensor). The third tracking detector is a Transition Radiation Tracker (TRT) based on drift tubes arranged in a barrel and 2 endcaps. The TRT sub-system provides a large number (about 36) of track coordinate measurements in the bending plane. The ID was designed with a high granularity and very precise position measurements to cope with the high luminosity expected in pp collisions. The granularity turns out to be essential for tracking charged particles produced in the high-multiplicity environment of heavy-ion collisions in a wide pseudorapidity window. The Pixel detector and SCT are expected to experience acceptable occupancies even in central heavy nucleus-nucleus collisions [38]. Contrary to this, the TRT detector, because of its long straws, will suffer from much higher occupancies and may not be able to contribute to tracking in the busy heavy-ion environment. Nevertheless, the Inner Detector is considered to survey the crucial measurements of global event properties which are the start point for all heavy-ion studies.. 4.2.2 Calorimeters. The calorimetric system [32] in the ATLAS detector identifies and measures the energy of particles (both charged and neutral) and jets, as well as missing transverse energy. The calorimeters contain dense materials (absorbers) which cause an incoming particle to initiate a shower. The particles created in this shower are detected in the active material. ATLAS uses two types of active material: liquid argon (LAr) which is cooled by a cryostat,. 34.