Thermodynamic properties of QCD matter and multiplicity fluctuations
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2019-09-18
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Universidade Estadual Paulista (Unesp)
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Uma característica vital da cromodinâmica quântica (QCD) está relacionada à simetria quiral. Isso é particularmente intrigante devido ao papel crítico da simetria quiral não abeliana dos spinores de Lorentz na física teórica moderna. Muitos esforços teóricos foram dedicados à sua quebra espontânea no vácuo, bem como a restauração da mesma no ambiente extremamente quente ou denso. Além disso, quarks e glúons tornam-se os graus de liberdade relevantes por meio da transição de desconfinamento do estado dos hádrons. O significado desta última está intimamente ligado às implicações da equação de Callan-Symanzik e à teoria do grupo renormalizado. No entanto, em princípio, ambas as transições acima podem ser descritas pela QCD. Os estudos da QCD na rede demonstraram que a transição do sistema é um cruzamento suave com a densidade bariônica nula e a massa de quarks estranhos grandes. No potencial químico finito, por outro lado, uma variedade de modelos prevê a ocorrência de uma transição de fase de primeira ordem entre a fase hadrônica e o plasma de quarks e glúons (QGP). Esses resultados indicam que um ponto crítico (CEP) pode estar localizado em algum lugar no diagrama de fases da QCD no qual a linha de transições de fase de primeira ordem termina. Espera-se que a transição seja de segunda ordem neste caso. De fato, entre outros objetivos estabelecidos, o programa Beam Energy Scan (BES) em andamento no Relativistic Heavy Ion Collider (RHIC) é impulsionado pela busca do CEP. Nesta tese, exploramos alguns tópicos relacionados às propriedades termodinâmicas da matéria QCD no contexto de colisões de íons pesados. Esses estudos são, até certo ponto, motivados a alcançar uma melhor compreensão do diagrama de fases, enquanto fazem parte do esforço de busca pelo CEP. Em particular, investigamos a consistência termodinâmica do modelo de quasipartículas no potencial químico bariônico nulo e não-nulo, bem como as flutuações da razão de partículas e de multiplicidade. Entende-se que uma fase desconfinada de matéria QCD foi atingida no colisor de íons pesados ultra-relativista. Embora o modelo de sacola MIT seja simplificado demais e incapaz de descrever a equação de estado (EoS) de QGP obtida pelas simulações da QCD na rede, os cálculos de QCD perturbativa (pQCD) são confiáveis apenas a temperaturas extremamente altas. Nesse contexto, o modelo de quase-partícula é uma ferramenta valiosa para acomodar tanto a noção de graus efetivos de liberdade quanto os dados da QCD na rede. Como uma abordagem efetiva, o modelo é capaz de descrever as propriedades termodinâmicas do QGP em uma ampla faixa de temperatura $ T $ e potencial químico bariônico $ \mu $. No entanto, como apontado por Gorenstein e Yang, a consistência termodinâmica apresenta um problema, pois coloca uma restrição não trivial à EoS em questão. Sua receita foi proposta a originalmente para o potencial químico bariônico nulo, enquanto vários autores generalizaram a abordagem para o caso com a densidade bariônica finita. Nestas, revisamos a questão relativa à autoconsistência termodinâmica do modelo de quase-partículas, com potencial químico bariônico finito, adaptado aos cálculos da QCD na rede. Aqui, investigamos a possibilidade da massa efetiva de quase-partículas também ser uma função de seu momento, $ k $, além da temperatura $ T $ e do potencial químico $ \mu $. Verifica-se que a consistência termodinâmica pode ser expressa em termos de uma equação integro-diferencial em termos de $ k $, $ T $ e $ \mu $. Discutimos ainda duas soluções especiais, ambas podem ser vistas como condição suficiente para a consistência termodinâmica, enquanto expressas em termos de uma equação diferencial parcial. O primeiro caso mostra-se equivalente aos discutidos anteriormente por Peshier $et~al$. O segundo, obtido por meio de uma suposição $ad~hoc$, é uma solução intrinsecamente diferente em que a massa das partículas é dependente do momento. Essas equações podem ser resolvidas usando a condição de contorno determinada pelos dados da QCD na rede com potencial químico nulo. Pelos cálculos numéricos, mostramos que ambas as soluções podem reproduzir razoavelmente os resultados recentes da QCD na rede das Colaborações Wuppertal-Budapest e HotQCD, e em particular os relativos à densidade bariônica finita. O programa BES realizado no RHIC é dedicado a explorar o diagrama de fases da matéria nuclear que interage fortemente. Em termos de colisões Au+Au com energias relativamente baixas, estão sendo realizadas medidas precisas para a região da matéria QCD com a sua densidade bariônica alta. Intuitivamente, deve-se procurar quantidades sensíveis à física subjacente enquanto acessíveis experimentalmente. Os cumulantes de ordens mais elevantes das cargas conservadas e as suas combinações, como as taxas de cumulantes, nessa conta, tornam-se observáveis focados. Essas quantidades cumprem os requisitos, pois carregam informações vitais no meio primordial criado nas colisões. Além disso, argumentou-se que eles são sensíveis à estrutura de fases da questão QCD e, em particular, ao paradeiro do CEP. Nesse sentido, recentemente, as flutuações da multiplicidade chamaram muita atenção como um dos principais observáveis. Nesta tese, estudamos os aspectos não críticos das flutuações da multiplicidade em colisões de íons pesados, empregando um modelo hidrodinâmico. A abordagem atual é aprimorada principalmente nas abordagens existentes do modelo HRG, que levam em consideração flutuações térmicas, correção de volume finito e decaimento de ressonâncias. Nosso modelo é focado nos aspectos da expansão hidrodinâmica do sistema e nas flutuações de estado inicial evento a evento (EbE). Calculamos as flutuações da razão de partículas de $ K / \pi $, $ K / p $, e $ p / \pi $ usando o código hidrodinâmico SPheRIO com ou sem as condições iniciais (IC) flutuantes EbE. Além disso, também são avaliadas as flutuações de multiplicidade de prótons, kaon líquido e carga líquida. Os resultados obtidos são então comparados com os dos modelos HRG, UrQMD e os dados experimentais da colaboração STAR. Em geral, relativo aos dados existentes, os resultados obtidos pelo SPheRIO são razoáveis em comparação com as demais abordagens. Em particular, observa-se que as IC EbE podem causar um efeito considerável, que pode não apenas ultrapassar as flutuações térmicas, mas também superestimar os dados. Por sua vez, isso implica potencialmente um requisito mais rigoroso para o gerador de eventos em relação às flutuações EbE.
One vital characteristic of the quantum chromodynamics (QCD) is regarding the chiral symmetry. This is particularly intriguing owing to the critical role of non-abelian gauge symmetry of Lorentz spinors in modern theoretical physics. Many theoretical efforts have been devoted concerning its spontaneously breaking in the vacuum, as well as the restoration at the extremely hot or dense environment. Furthermore, quarks and gluons become the relevant degrees of freedom through the deconfinement transition from the hadron state of matter. The significance of the latter is closely connected to the implications of the Callan-Symanzik equation and the theory of the renormalized group. Nonetheless, in principle, both of the above transitions can be described by the QCD. Lattice QCD studies demonstrated that the transition of the system is a smooth crossover at vanishing baryon density and large strange quark mass. At finite chemical potential, on the other hand, a variety of models predict the occurrence of a first-order transition between the hadronic phase and quark-gluon plasma (QGP). These results indicate that a critical endpoint (CEP) might be located somewhere on the QCD phase diagram at which the line of first-order phase transitions terminates. The transition is expected to be of second-order at this point. As a matter of fact, among other established goals, the ongoing Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider (RHIC) is driven by the search for the CEP. In this thesis, we explore a few topics regarding the thermodynamic properties of QCD matter in the context of heavy-ion collisions. These studies are, to a certain extent, motivated to achieve a better understanding of the phase diagram, while being a part of the endeavor to search for the CEP. In particular, we investigate the thermodynamic consistency of the quasi-particle model at both vanishing and non-vanishing baryon chemical potential, as well as the particle ratio and multiplicity fluctuations. It is understood that a deconfined phase of QCD matter has been attained at the ultra-relativistic heavyion collider. While the MIT bag model is oversimplified and unable to describe the equation of state (EoS) of QGP from the lattice QCD simulations, perturbative QCD (pQCD) calculations are reliable only at extremely high temperature. In this context, the quasi-particle model is a valuable tool to accommodate both the notion of effective degrees of freedom and the lattice QCD data. As an effective approach, the model is capable of describing the thermodynamical properties of QGP over a wide range of temperature T and baryon chemical potential µ. However, as pointed out by Gorenstein and Yang, the thermodynamic consistency poses an issue as it places a nontrivial restriction to the EoS in question. Their proposed recipe was originally for vanishing baryon chemical potential, while several authors have generalized the approach to the case of finite baryon density. In this these, we revisit the matter regarding the thermodynamical self-consistency of quasi-particle model at finite baryon chemical potential adapted to lattice QCD calculations. Here, we investigate the possibility where the effective quasi-particle mass is also a function of its momentum, k, in addition to temperature T and chemical potential µ. It is found that the thermodynamic consistency can be expressed in terms of an integro-differential equation concerning k, T, and µ. We further discuss two special solutions, both can be viewed as sufficient condition for the thermodynamical consistency, while expressed in terms of a partial differential equation. The first case is shown to be equivalent to those previously discussed by Peshier et al. The second one, obtained through an ad hoc assumption, is an intrinsically different solution where the particle mass is momentum dependent. These equations can be solved by using boundary condition determined by the lattice QCD data at vanishing baryon chemical potential. By numerical calculations, we show that both solutions can reasonably reproduce the recent lattice QCD results of the Wuppertal-Budapest and HotQCD Collaborations, and in particular, those concerning finite baryon density. The BES program carried out at RHIC is dedicated to exploring the phase diagram of the strongly interacting nuclear matter. In terms of Au+Au collisions at relatively low energies, precise measurements are being carried out for the high baryon density region of the QCD matter. Intuitively, one shall look for quantities that are sensitive to the underlying physics while accessible experimentally. The higher cumulants of conserved charges and combinations of them, such as cumulant ratios, on that account, become such focused observables. These quantities fulfill the requirement as they carry vital information on the primordial medium created in the collisions. Moreover, it has been argued that they are sensitive to the phase structure of the QCD matter, and in particular, the whereabouts of the CEP. In this regard, recently, multiplicity fluctuations have drawn much attention as one of the key observables. In this thesis, we studied the noncritical aspects of the multiplicity fluctuations in heavy-ion collisions by employing a hydrodynamic model. The present approach is mainly improved upon existing HRG model approaches, which take into consideration thermal fluctuations, finite volume correction, and resonance decay. Our model is focused on the aspects of the hydrodynamic expansion of the system and the event-by-event (EbE) initial state fluctuations. We calculated the particle ratio fluctuations of K/π, K/p, and p/π by using the hydrodynamic code SPheRIO with or without the EbE fluctuating initial conditions (IC). Besides, the net-proton, net-kaon, and net-charged multiplicity fluctuations are also evaluated. The obtained results are then compared to those of the HRG, UrQMD models, as well as the experimental data from the STAR Collaboration. Overall, regarding the existing data, the results obtained by SPheRIO are reasonable in comparison with those by using different approaches. In particular, it is observed that the EbE IC may cause a sizable effect, which may not only overwhelm the thermal fluctuations but also overestimate the data. This, in turn, potentially implies a more stringent requirement for the event generator regarding EbE fluctuations
One vital characteristic of the quantum chromodynamics (QCD) is regarding the chiral symmetry. This is particularly intriguing owing to the critical role of non-abelian gauge symmetry of Lorentz spinors in modern theoretical physics. Many theoretical efforts have been devoted concerning its spontaneously breaking in the vacuum, as well as the restoration at the extremely hot or dense environment. Furthermore, quarks and gluons become the relevant degrees of freedom through the deconfinement transition from the hadron state of matter. The significance of the latter is closely connected to the implications of the Callan-Symanzik equation and the theory of the renormalized group. Nonetheless, in principle, both of the above transitions can be described by the QCD. Lattice QCD studies demonstrated that the transition of the system is a smooth crossover at vanishing baryon density and large strange quark mass. At finite chemical potential, on the other hand, a variety of models predict the occurrence of a first-order transition between the hadronic phase and quark-gluon plasma (QGP). These results indicate that a critical endpoint (CEP) might be located somewhere on the QCD phase diagram at which the line of first-order phase transitions terminates. The transition is expected to be of second-order at this point. As a matter of fact, among other established goals, the ongoing Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider (RHIC) is driven by the search for the CEP. In this thesis, we explore a few topics regarding the thermodynamic properties of QCD matter in the context of heavy-ion collisions. These studies are, to a certain extent, motivated to achieve a better understanding of the phase diagram, while being a part of the endeavor to search for the CEP. In particular, we investigate the thermodynamic consistency of the quasi-particle model at both vanishing and non-vanishing baryon chemical potential, as well as the particle ratio and multiplicity fluctuations. It is understood that a deconfined phase of QCD matter has been attained at the ultra-relativistic heavyion collider. While the MIT bag model is oversimplified and unable to describe the equation of state (EoS) of QGP from the lattice QCD simulations, perturbative QCD (pQCD) calculations are reliable only at extremely high temperature. In this context, the quasi-particle model is a valuable tool to accommodate both the notion of effective degrees of freedom and the lattice QCD data. As an effective approach, the model is capable of describing the thermodynamical properties of QGP over a wide range of temperature T and baryon chemical potential µ. However, as pointed out by Gorenstein and Yang, the thermodynamic consistency poses an issue as it places a nontrivial restriction to the EoS in question. Their proposed recipe was originally for vanishing baryon chemical potential, while several authors have generalized the approach to the case of finite baryon density. In this these, we revisit the matter regarding the thermodynamical self-consistency of quasi-particle model at finite baryon chemical potential adapted to lattice QCD calculations. Here, we investigate the possibility where the effective quasi-particle mass is also a function of its momentum, k, in addition to temperature T and chemical potential µ. It is found that the thermodynamic consistency can be expressed in terms of an integro-differential equation concerning k, T, and µ. We further discuss two special solutions, both can be viewed as sufficient condition for the thermodynamical consistency, while expressed in terms of a partial differential equation. The first case is shown to be equivalent to those previously discussed by Peshier et al. The second one, obtained through an ad hoc assumption, is an intrinsically different solution where the particle mass is momentum dependent. These equations can be solved by using boundary condition determined by the lattice QCD data at vanishing baryon chemical potential. By numerical calculations, we show that both solutions can reasonably reproduce the recent lattice QCD results of the Wuppertal-Budapest and HotQCD Collaborations, and in particular, those concerning finite baryon density. The BES program carried out at RHIC is dedicated to exploring the phase diagram of the strongly interacting nuclear matter. In terms of Au+Au collisions at relatively low energies, precise measurements are being carried out for the high baryon density region of the QCD matter. Intuitively, one shall look for quantities that are sensitive to the underlying physics while accessible experimentally. The higher cumulants of conserved charges and combinations of them, such as cumulant ratios, on that account, become such focused observables. These quantities fulfill the requirement as they carry vital information on the primordial medium created in the collisions. Moreover, it has been argued that they are sensitive to the phase structure of the QCD matter, and in particular, the whereabouts of the CEP. In this regard, recently, multiplicity fluctuations have drawn much attention as one of the key observables. In this thesis, we studied the noncritical aspects of the multiplicity fluctuations in heavy-ion collisions by employing a hydrodynamic model. The present approach is mainly improved upon existing HRG model approaches, which take into consideration thermal fluctuations, finite volume correction, and resonance decay. Our model is focused on the aspects of the hydrodynamic expansion of the system and the event-by-event (EbE) initial state fluctuations. We calculated the particle ratio fluctuations of K/π, K/p, and p/π by using the hydrodynamic code SPheRIO with or without the EbE fluctuating initial conditions (IC). Besides, the net-proton, net-kaon, and net-charged multiplicity fluctuations are also evaluated. The obtained results are then compared to those of the HRG, UrQMD models, as well as the experimental data from the STAR Collaboration. Overall, regarding the existing data, the results obtained by SPheRIO are reasonable in comparison with those by using different approaches. In particular, it is observed that the EbE IC may cause a sizable effect, which may not only overwhelm the thermal fluctuations but also overestimate the data. This, in turn, potentially implies a more stringent requirement for the event generator regarding EbE fluctuations
Descrição
Palavras-chave
Equação de estado, Transição de fase QCD, Ponto final crítico, Equation of state, QCD phase transition, Critical end point, fluctuation, Transformações de fase (Física estatística), Flutuação (Física)