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The interplay of thermodynamic properties of strongly interacting matter and its emission of photons is investigated. For this purpose the Lagrangian of the quark meson model (in the literature also dubbed "linear sigma model" or "linear sigma model with quarks") is extended by an electromagnetic sector. Based on this extended Lagrangian both the grand-canonical potential and the generating functional of correlation functions are calculated in a consistent manner. From the former, the phase structure and various thermodynamical properties are determined. Especially, the dependence of certain landmarks (critical point, intersections of the phase boundary with the coordinate axes, etc.) of the phase diagram with respect to the model parameters is investigated in detail. With the help of the generating functional in turn, the photon propagator can be computed whose imaginary part is connected to the emission rate of photons. The leading order of the result with respect to the number of participating particles and the power of the quark-meson coupling is expressed in terms of tree level diagrams, which are calculated likewise. On this basis, the photon emissivity with respect to temperature, chemical potential and photon frequency is calculated and analyzed addressing various questions. The dependence of the particle masses with respect to temperature and chemical potential leaves notable imprints on the emissivities of the individual production processes. Especially a first-order phase transition can easily be identified, since, there, the emissivity may jump - depending on the temperature - by a factor of about ten. Contrarily, within our analysis, we do not find signatures in the photon emissivities that specifically mark a critical end point. Moreover, it is investigated on which parameters the photon emission rate depends in the low- and high-frequency regions. With these results the behavior of the emissivity with respect to temperature and chemical potential can be understood and many peculiarities of the emissivities can be explained. / Das Zusammenspiel der thermodynamischen Eigenschaften von stark wechselwirkender Materie und deren Emission von Photonen wird untersucht. Dazu wird die Lagrangedichte des Quark-Meson-Modells (auch: Linear-Sigma-Modell oder Linear-Sigma-Modell mit Quarks) um einen elektromagnetischen Sektor erweitert. Aus der so erweiterten Lagrangedichte werden auf konsistente Weise sowohl das großkanonische Potential als auch das erzeugende Funktional der Korrelationsfunktionen ermittelt. Aus ersterem werden die Phasenstruktur des Modells sowie zahlreiche thermodynamische Eigenschaften berechnet. Insbesondere wird die Abhänigkeit einiger Orientierungspunkte (kritischer Punkt, Schnittpunkte der Phasengrenze mit den Koordinatenachsen usw.) des Phasendiagramms von den Modellparametern detailiert untersucht. Mit Hilfe des erzeugenden Funktionals wiederum kann der Photonenpropagator bestimmt werden, dessen Imaginärteil mit der Emissionsrate von Photonen zusammenhängt. Die führende Ordnung in einer Entwicklung nach der Anzahl der beteiligten Teilchen und der Potenz der Quark-Meson-Kopplung lässt sich durch Baumgraphen-Diagramme darstellen, die ebenfalls berechnet werden. Auf dieser Basis wird die Photon-Emissivität in Abhängigkeit von Temperatur, chemischem Potential und Photon-Frequenz berechnet und unter verschiedenen Gesichtspunkten analysiert. Die Abhängigkeit der Teilchenmassen von Temperatur und chemischem Potential hinterlässt teilweise ausgeprägte Signaturen in den Emissivitäten der einzelnen sub-Prozesse. Insbesondere ein Phasenübergang erster Ordnung zeigt sich deutlich, da an diesem die Emissivität - abhänging von der Temperatur - um einen Faktor der Größenordnung zehn springen kann. Jedoch finden wir im Rahmen dieser Analyse keine spezifischen Signaturen in den Photonen-Emissivitäten, die einen kritischen Punkt auszeichnen. Des weiteren wird untersucht von welchen Parametern die Photonen-Emissionsrate in den Bereichen niedriger oder hoher Photonen-Frequenzen abhängt. Mit diesen Ergebnissen kann das Verhalten der Emissivität in Abhängigkeit von Temperatur und chemischem Potential gut verstanden und zahlreiche Auffälligkeiten in den Emissivitäten erklärt werden.

<p>Heavy flavor hadrons serve as valuable probes of the transport properties of the quark-gluon plasma (QGP) created in relativistic heavy-ion collisions. In this dissertation, we introduce a comprehensive framework that describes the full-time evolution of heavy flavor in heavy-ion collisions, including its initial production, in-medium evolution inside the QGP matter, hadronization process from heavy quarks to their respective mesonic bound states and the subsequent interactions between heavy mesons and the hadron gas.</p><p>The in-medium energy loss of heavy quarks is studied within the framework of a Langevin equation coupled to hydrodynamic models that simulate the space-time evolution of the hot and dense QGP matter. We improve the classical Langevin approach such that, apart from quasi-elastic scatterings between heavy quarks and the medium background, radiative energy loss is incorporated as well by treating gluon radiation as a recoil force term. The subsequent hadronization of emitted heavy quarks is simulated via a hybrid fragmentation plus recombination model. The propagation of produced heavy mesons in the hadronic phase is described using the ultra-relativistic quantum molecular dynamics (UrQMD) model. Our calculation shows that while collisional energy loss dominates the heavy quark motion inside the QGP in the low transverse momentum (pT) regime, contributions from gluon radiation are found to be significant at high pT. The recombination mechanism is important for the heavy flavor meson production at intermediate energies. The hadronic final state interactions further enhance the suppression and the collective flow of heavy mesons we observe. Within our newly developed framework, we present numerical results for the nuclear modification and the elliptic flow of D mesons, which are consistent with measurements at both the CERN Large Hadron Collider (LHC) and the BNL Relativistic Heavy-Ion Collider (RHIC); predictions for B mesons are also provided.</p><p>In addition, various transport properties of heavy quarks are investigated within our numerical framework, such as the thermalization process of heavy quarks inside the QGP, and how the initial configuration of the QGP as well as its properties affect the final state spectra and the elliptic flow of heavy mesons and their decay electrons. The effects of initial state fluctuations in heavy-ion collisions are also studied and found to enhance the heavy quark energy loss in a (2+1)-dimensional boost invariant scenario. Furthermore, a new set of observables -- heavy-flavor-tagged angular correlation functions -- are explored and found to be potential candidates for distinguishing different energy loss mechanisms of heavy quarks inside the QGP.</p> / Dissertation

O Plasma de Quarks e Glúons (Quark Gluon Plasma ou QGP) criado de forma sistemática em grandes aceleradores de partículas que envolvem colaborações do mundo inteiro, apesar de ter sua descoberta anunciada há bastante tempo ainda apresenta desafios e questões a serem respondidas tanto do ponto de vista experimental como do teórico. O objetivo deste trabalho é estudar a conexão entre as condições iniciais da expansão do QGP (que dependem da interação forte e não são acessíveis ao experimento) com a anisotropia da emissão azimutal das partículas (que por sua vez reflete as condições iniciais e é medida experimentalmente). O modelo hidrodinâmico é descrito inicialmente, com ênfase no programa NeXSPheRIO. Também são apresentadas alguns tipos de observáveis e modelos de condições iniciais (NeXus, MC-KLN e TRENTO). Por fim resultados de simulações para distribuições evento-por-evento do fluxo anisotrópico (facilmente ligadas aos modelos de condições iniciais) são comparadas com dados do LHC e previsões são feitas para a energia mais alta do RHIC. Estas previsões são testadas via a razão $v_2\\{4\\}/v_2\\{2\\}$ para a qual dados existem. / The Quark Gluon Plasma (QGP), created in a systematic way in large particle accelerators which are built by worldwide collaborations, even though its discovery being announced a long time ago it still presents us with challenges and questions to be answered even from the experimental point of view to the theoretical one. The main goal of this work is to study the connection between the initial conditions for the QGP expansion (which depend on strong interactions and are not accesible to the experiments) to the anisotropy in the azimuthal particle emission (which in turn reflects the initial conditions and is measured experimentally). The hydrodynamical model is described initially, with emphasis on the code NeXSPheRIO. Additionally some types of observables and initial condition models (NeXus, MC-KLN and TRENTO) are presented. And at last, results from simulations for event-by-event distributions for the anisotropic flow (easily connected to the initial conditions models) are compared with LHC\'s data and predictions are made for the RHIC\'s top energy. These predictions are tested by the $v_2\\{4\\}/v_2\\{2\\}$ for which data exists.

Nesta dissertação discutimos a medida RAA desenvolvida para análise de observáveis de colisão núcleo-núcleo (AA), tendo em vista sua implementação em colisões próton-próton (pp). No contexto das colisões hadrônicas de altíssimas energias, o RAA compara quantidade de observáveis duros medidos em colisões AA com a quantidade do mesmo observável em colisões pp. As qualidades destas colisões são descritas pela teoria do modelo de Glauber, em que projeção analítica da produção esperada de quarks pesados (observável duro) é realizada para colisões nucleares por meio da sobreposição de colisões pp independentes. Esta projeção analítica é comparada no RAA à medida de quarks pesados em estado final de colisões AA, e desvios em relação à distribuição de momentos da seção de choque calculada teoricamente são interpretados como decorrentes da presença de plasma de quarks e glúons (PQG) na colisão medida. O plasma de quarks e glúons é o objeto de interesse do campo de estudos em que esta pesquisa se insere. Considerado presente em colisões AA centrais desde 2000, o plasma de quarks e glúons é o estado da matéria mais energético possível, em que os pártons produto da colisão se comportam livremente por breves instantes e sofrem expansão hidrodinâmica. Este processo acontece nos estágios inacessíveis da colisão. Algumas das medidas indiretas que indicam formação de plasma em colisões AA são detectadas em colisões de sistemas pequenos, pp e pA desde 2010. Ainda não foi medida supressão de provas duras no PQG. As tentativas de medir PQG em sistemas pequenos pelo método do RAA tem sido feitas por meio da comparação RpA, também definida pelo modelo de Glauber. Na presente pesquisa buscamos extrapolar o funcionamento do RAA para medidas em colisões pp. Como o núcleo em Glauber é formado por sobreposição de prótons, a resolução da descrição da colisão na teoria é discutida. Além disso verificamos que a concepção de que colisões pp não formam ambiente de PQG é importante para o estabelecimento da comparação RAA. Entendemos que as hipóteses sobre a física de estágios inacessíveis da colisão previstas pela teoria de Glauber são diferentes das hipóteses decorrentes de medidas de coletividade em sistemas pequenos. Propomos alternativamente comparações experimentais simples entre quantidades parecidas medidas em colisões pp que podem conter informações sobre supressão de observáveis duros em colisões pp de alta multiplicidade sem o uso de quantidades teóricas. / This master thesis adresses the measurement RAA, developed for the analysis of nucleus-nucleus (AA) collisions, aiming to implement the measure for proton-proton (pp) collisions. In the context of high energy hadronic collisions, RAA compares hard observables measured in AA collisions with the same observable measured in pp collisions. These collisions traits are described by the Glauber model, where an analitical projection of the expected heavy quark production (hard observable) is calculated through the superimposition of independent pp collisions. In RAA, that analitical projection is compared to the actual final state AA collisions measurements, and deviations with relation to the momentum distribution of the theoriticaly calculated cross section are regarded as arising from interaction of the heavy quark with a quark gluon plasma (QGP) formed in the measured collision. The quark gluon plasma is the fields object of interest in which this reasearch is undertaken. Since 2000, QGP is measured and presumed in central AA colissions.The quark gluon plasma is the most energetic state of nuclear matter, in which partons behave as deconfined matter and undergo hydrodynamic expansion. That happends in the first inaccessible stages of the collisions. Some of the indirect measurements that point to the formation of QGP in AA collisions have been detected small systems, pp and pA, since 2010. Is yet to be measured hard probes PQG supression in these systems. Current attempts to evaluate this supression have been made with the RpA comparison, also defined with the Glauber model. In this study, we attempt to extrapolate the RAA operation to pp collision measurements. As the nucleus in Glauber is modeled as a superimposition of pp collisions, the theory\'s resolutuon in describing AA collisions is discussed. We also notice that the concept of pp collisions not formimg QGP is relevant for RAA comparisons. We appreciate that the theoretical hipothesis on the physics of the inaccessible first stages of collisions as foreseen with the Glauber model are different than the hipothesis that stem from collectivity in small systems. We propose alternatively simple experimental comparisons between similar quantities measured in pp collisions without the use of theoretical quantities.

Um novo estado, o Plasma Quark-Gluon (QGP), é formado quando a matéria comum formada por hadrons é submetida a condições extremas de temperatura e/ou densidade. Acredita-se que esse estado esteja presente nos primeiros momentos do universo e que seja relevante para entender propriedades da cromodinâmica quântica. O QGP é criado e caracterizado em aceleradores de partículas por meio de colisões de íons pesados. No entanto, uma estrutura alongada em psedorapidez (\\textit{double ridge}) na distribuição da correlação angular entre duas partículas foi encontrada em sistemas pequenos, como pp e p--Pb. Essa estrutura assemelha-se àquela observada nas colisões com íons pesados, onde sua interpretação está ligada ao comportamento coletivo que gera uma anisotropia azimutal nos produtos finais das colisões. Essa estrutura não era esperada em sistemas pequenos e sua interpretação física ainda está em debate, em particular no que diz respeito ao papel da hidrodinâmica e das condições iniciais. Uma medida para este efeito com partículas provenientes de quarks pesados ainda não haviam sido realizadas no momento em que este trabalho foi iniciado e esta medida poderia esclarecer questões sobre as diferentes interpretações. Os quarks pesados são uma sonda interessante caso o QGP seja formado devido ao seu tempo de formação inicial, reagindo a toda a evolução do meio. Neste trabalho, os quarks pesados são estudados medindo-se os elétrons provenientes dos decaimentos semi-leptônicos de hádrons que contêm quarks \\textit{charm} ou \\textit{beauty} e outros quarks leves (\\textit{open heavy flavor}). Os hadrons não são reconstruídos e usa-se um método de extração de sinal para remover elétrons de outras fontes. As correlações angulares de elétrons de decaimento de hadrons de quarks pesados com partículas carregadas em colisões de p--Pb a $\\sqrt{s_{m NN}}$ = 5,02 TeV medidos com o experimento ALICE em rapidez central ($ | \\eta | <0,8 $) são apresentadas. As distribuições mostram sinais de anisotropias azimutais que são quantificadas pelo coeficiente $ v_2 $. O $ v_2 $ para elétrons provenientes de quarks pesados é positivo com mais de $ 5 \\sigma $ de significância, fornecendo uma forte indicação de anisotropias azimutais similares ao \\textit{double ridge} para partículas contendo quarks pesados em colisões de alta multiplicidade de p--Pb. Esta é a primeira medida do $ v_2 $ para elétrons vindos de quarks pesados em colisões p--Pb. / A new state of mater, the Quark-Gluon Plasma (QGP), is formed when the ordinary hadronic matter is put under extreme temperature and/or density conditions. This state is believed to be present in the first moments of the universe and it is relevant to understand properties of the quantum chromodynamics. The QGP is created and characterized in particle accelerators by colliding heavy ions. However, a double-ridge long-range structure in the two-particle azimuthal correlation distribution was found in small systems, such as pp and p--Pb. This structure resembles the one observed in heavy-ion collisions, where its interpretation is linked to collective behavior that generates an azimuthal anisotropy in the final products of the collisions. This structure was not expected in small systems and its physical interpretation is still in debate, in particular regarding the role of hydrodynamics and initial conditions. A measurement for this effect with particles coming from heavy quarks was not done by the time this work started and this measurement could shed light into the different interpretations. Heavy quarks are an interesting probe in case the QGP is formed due to their early formation time, experiencing the whole evolution of the medium. In this work, heavy quarks are examined by measuring electrons originating from the semi-leptonic decays of hadrons that contain a heavy quark (charm or beauty) and other light quarks (open heavy flavor). The hadrons are not reconstructed and a signal extraction method is used to remove electrons from other sources. The azimuthal angular correlations of heavy-flavour hadron decay electrons with charged particles in p--Pb collisions at $\\sqrt{s_{m NN}}$ = 5.02 TeV measured with ALICE detector at mid-rapidity ($|\\eta| < 0.8$) are studied. The distributions show signs of azimuthal anisotropies which are quantified by the $v_2$ coefficient. The $v_2$ for heavy-flavor electrons is found to be positive with more than $5\\sigma$ significance, providing very strong indication of long-range azimuthal anisotropies for heavy-flavour particles in high multiplicity p--Pb collisions. This is the first measurement of the $v_2$ for electrons coming from heavy-flavor hadron decays in p--Pb collisions.

We investigate charmonium production in the hot medium created by heavy-ion collisions by setting up a framework in which in-medium charmonium properties are constrained by thermal lattice QCD (lQCD) and subsequently implemented into kinetic approaches. A Boltzmann transport equation is employed to describe the time evolution of the charmonium phase space distribution with the loss and gain term accounting for charmonium dissociation and regeneration (from charm quarks), respectively. The momentum dependence of the charmonium dissociation rate is worked out. The dominant process for in-medium charmonium regeneration is found to be a 3-to-2 process. Its corresponding regeneration rates from different input charmquark momentum spectra are evaluated. Experimental data on J/[psi] production at CERN-SPS and BNL-RHIC are compared with our numerical results in terms of both rapidity-dependent inclusive yields and transverse momentum (pt) spectra. Within current uncertainties from (interpreting) lQCD data and from input charm-quark spectra the centrality dependence of J/[psi] production at SPS and RHIC (for both mid-and forward rapidity) is reasonably well reproduced. The J/[psi] pt data are shown to have a discriminating power for in-medium charmonium properties as inferred from different interpretations of lQCD results.