The quark-gluon plasma (QGP) is a deconfined phase of strongly interacting matter which can be described by the theory of quantum chromodynamics (QCD). The QGP filled the entire universe in the early moments after the big bang and is believed to exist in the present time in the core of massive neutron stars. Understanding the physical properties of QGP and its non-equilibrium dynamics requires solving the full non-perturbative QCD equations of motion, which is an unsolved problem at this time. Ultra-relativistic heavy ion collisions (URHICs) can be used to reproduce the extreme conditions of the early universe and create a short-lived QGP in the laboratory; in what is called the ``little'' bang. The highly momentum-anisotropic far-from-equilibrium initial state created in these experiments evolves dynamically in three main stages: pre-equilibrium ($\tau < 0.5$ fm/c), thermalization/hydrodynamization ($\tau > 0.5-2$ fm/c), and finally freeze-out/hadronization ($\tau > 10$ fm/c), where 1\,fm/c = \mbox{$3 \times 10^{-24}$ s}. Each of these stages span a different regime of physics, with different relevant degrees of freedom and, therefore, are described by different theoretical models, such as QCD kinetic theory, dissipative hydrodynamics, and hadronic kinetic theory. This dissertation considers the impact of all three of these stages on our understanding of the QGP generated in URHICs, with the focus on better understanding the non-equilibrium dynamics of the QGP, its path to equilibrium and the effect such non-equilibrium dynamics have on our ability to extract fundamental information about the QGP. This dissertation also provides theoretical insights into how to improve URHIC simulations by examining the impact of non-equilibrium corrections present during different stages of QGP evolution.
As mentioned above, the initially out-of-equilibrium QGP expands, cools, and ``hydrodynamizes'' on a timescale of roughly 1 fm/c. The collective behavior of the QGP observed at RHIC has demonstrated that relativistic fluid dynamics plays a major role in URHICs. Dissipative relativistic hydrodynamics models have been successful in describing experimental data for, for example, identified hadron $p_T$-spectra, abundance ratios, and anisotropic flow. Fits of such simulations to experimental data have provided insights into the properties of the QGP such as its transport coefficients like shear and bulk viscosities. In the first part of this dissertation we present model-to-data comparisons using the quasi-particle anisotropic hydrodynamics model (aHydroQP) to make predictions for particle production in URHICs. We compare aHydroQP predictions for a variety experimental observables to data collected at Brookhaven National Laboratory's Relativistic Heavy-Ion Collider by the PHENIX, STAR, and PHOBOS experiments. The aHydroQP results are shown to agree very well with experimental data. Using this model-to-data comparison we provide estimates of the initial central temperature of the QGP ($T_0 = $ 455 MeV) and its shear viscosity to entropy density ratio ($\eta/s= 0.179$).
The aHydroQP equations of motion used in the first part of this dissertation were derived using relativistic kinetic theory in the relaxation-time approximation (RTA), which is based on a near-equilibrium limit for the collisional kernel of the Boltzmann equation. Due to the nature of the initial state at RHIC, the system becomes highly-anisotropic in momentum-space in the local rest frame (far from equilibrium). Therefore, intrinsic non-linearities in more realistic scattering kernels could become important to the dynamical evolution and the associated non-equilibrium attractor. In the second part of this dissertation we make the first attempt to consider a more realistic scattering kernel in the context of aHydro by considering the leading-order (LO) collisional kernel stemming from $2 \leftrightarrow 2$ scattering in massless $\lambda\phi^4$ theory using both classical and quantum (Bose) statistics. The role played by the microscopic interactions of the system in the dynamics was investigated by applying the moment method to a 0+1d Bjorken expanding conformal system. The results provide an apples-to-apples comparison between the RTA and scalar collisional kernels and allows us to compute the quantitative differences in the evolution of the dynamical variables. Finally, we establish the existence of a non-equilibrium attractor when using this non-linear scattering kernel. We also use the emergent dynamical attractor observed in order to better understand differences in the approach to equilibrium when comparing these different collisional kernels.
Phenomenological studies of the QGP have pushed the application of relativistic hydrodynamics to very early times after the initial nuclear pass through ($\tau < 0.25$ fm/c). At these very early times, hydrodynamic models cannot provide reliable information since they are typically based on a set of near-equilibrium assumptions together with a gradient expansion. As a result, a separate set of tools is needed in order to fully understand the hydrodynamization of the QGP created in URHICs. In particular, an understanding of pre-equilibrium dynamics is critical in understanding the unreasonable success of hydrodynamical models in describing data when the system is far from equilibrium and, hence, naively, outside their region of applicability.
The existence of non-equilibrium attractors has been confirmed in a variety of microscopic models. In the third part of this dissertation we make use of a perturbative approach based on QCD effective kinetic theory to understand the equilibration of a high-temperature QGP and to explore hydrodynamization in a larger context than just energy density/pressure attractors. By extracting higher-order moments of the one-particle distribution function, one can probe regions of the momentum phase-space distribution that are sensitive to non-hydrodynamical degrees of freedom. For this work we analyzed the non-equilibrium attractor by comparing the evolution subject to both thermal and non-thermal initial conditions. The initial gluon distribution functions used account for different initial momentum-space anisotropy and thermalization was neither assumed or nor enforced. Our results demonstrated that there exists an early-time non-equilibrium attractor in a high-temperature gluonic plasma. Since publication of this work, we have included quark degrees of freedom in both initial conditions, evolution, and all considered moments, finding that there exists a universal attractor also in this case.
Using the results of our QCD effective kinetic theory simulations we could also assess the efficacy of different freeze-out prescriptions used to convert fluid dynamical degrees of freedom (energy-momentum tensor) into those of a hot hadron gas. It is during this stage of the evolution that one switches to a description in terms of hadronic degrees of freedom, which are subsequently modeled using hadronic relativistic kinetic theory. Since this stage makes use of information obtained from the hydrodynamics stage to sample hadronic degrees of freedom, one needs to take care to ensure that the assumed distribution functions are well-defined (e.g., positive in all of phase space) and agree with expectations from QCD kinetic theory treatments. This dissertation tackles this problem by examining the impact of different freeze-out prescriptions on the extracted one-particle distribution function and comparing moments of the extracted distribution function in each case with our numerical calculations of the moments using QCD effective kinetic theory. We demonstrate that there are important differences between the freeze-out prescriptions considered, particularly for small collision systems such as pPb, pp, and peripheral PbPb in which the QGP's lifetime is short. Our results indicate that the use of a spheroidally-deformed distribution function (Romatschke-Strickland ansatz) provides a superior description of the extracted moments when compared to traditional linearized freeze-out approximations, particularly for higher-order moments of the distribution function which are sensitive to non-hydrodynamic degrees of freedom.