In the field of high-energy nuclear physics, ultrarelativistic heavy-ion collisions serve as a one-of-a-kind laboratory for investigating the extreme properties of matter. These collisions involve massive nuclei, such as lead or gold, colliding with energies in the trillions of electron volts per nucleon range. These collisions produce an environment where the strong force, as described by quantum chromodynamics (QCD), is the dominant force. In particular, the collisions generate a state of matter known as the quark-gluon plasma (QGP), which is characterized by a state of quarks and gluons that is not confined inside hadrons such as protons and neutrons. The QGP is an intriguing state of matter that provides insights into the behavior of dense astrophysical objects and the early universe. It is produced when the energy density of the collision reaches a critical threshold, resulting in the transition from the confined to the unconfined state of quarks and gluons. The QGP is a hot and dense system, with temperatures on the order of trillions of Kelvin and densities several orders of magnitude greater than the density of atomic nuclei in ordinary matter.
In the initial phases of a heavy-ion collision, the system is far from thermal equilibrium and possesses a highly anisotropic pressure. The pressure anisotropy results from the longitudinal expansion being more rapid than the transverse expansion. The dynamics of the system cannot be adequately described by ideal hydrodynamics, which assumes local isotropic thermal equilibrium at all times. To account for the pressure anisotropy and non-equilibrium nature of the QGP, a framework known as anisotropic hydrodynamics has been developed. Anisotropic hydrodynamics (aHydro) is a useful tool for describing the evolution of the QGP, especially during the early non-equilibrium evolution of the QGP. It goes beyond the ideal hydrodynamic limit by incorporating dissipative transport coefficients, such as shear viscosity, which are essential for accurately modeling the system's dynamics. aHydro accounts for the anisotropic character of the pressure tensor and permits a more accurate description of the evolution of the QGP.
In addition, the introduction of the quasiparticle formulation of anisotropic hydrodynamics (aHydroQP) is a recent development in the field. This formulation integrates the concept of quasiparticles and extends the aHydro framework to a full 3+1D framework with a realistic equation of state. Quasiparticles are effective degrees of freedom that arise in the QGP as a result of strong interactions. The aHydroQP method provides a more exhaustive description of the QGP's behavior, enabling a phenomenological analysis of heavy-ion collision data at various energies. Significant emphasis has been placed on conformal theories in hydrodynamics, where the equations of motion exhibit scale invariance. In conformal systems, the existence and properties of hydrodynamic attractors have been the subject of extensive investigation. These attractor solutions are insensitive to the initial conditions of the system and describe the approach of the system towards thermal equilibrium. Understanding the behavior of conformal systems has yielded significant insights into the dynamics of non-equilibrium relativistic systems. However, the study of hydrodynamic attractors in non-conformal kinetic theories remains an open question. Non-conformal systems possess additional scales, thereby destroying the scale invariance of conformal theories. Exploring the behavior of non-conformal systems is crucial for gaining a comprehensive understanding of dynamics in far-from-equilibrium situations that are more phenomenologically realistic.
In this dissertation, the primary objective is to increase our knowledge of the non-equilibrium dynamics of the QGP in ultrarelativistic heavy-ion collisions. Because of that, we intend to develop an improved ansatz for the distribution function in anisotropic hydrodynamics, aiming specifically for a more precise representation of moments with $l=0$. Due to the inadequacy of the early assumption of ideal hydrodynamics and local isotropic thermal equilibrium in capturing the complex dynamics of the QGP, the canonical formulation of aHydro provided adequate descriptions of moments with nonzero longitudinal momentum ($l>0$). However, it failed to describe moments with $l=0$ accurately. This inadequacy was attributed to the limitations of a single ellipsoidal form in representing the two-component nature of exact solutions to the Boltzmann equation in the relaxation time approximation.
To address this limitation, a revised ansatz is proposed that incorporates an explicit separation of free-streaming and equilibrating contributions in the distribution function. This study demonstrates that this improved ansatz yields much better agreement with exact results available in the literature for the evolution of moments, especially those that do not contain power of the longitudinal momentum. By obtaining more precise dynamical equations and extracting the non-equilibrium attractor associated with this enhanced ansatz, a more accurate representation of the non-equilibrium dynamics of the QGP is obtained. As result, this research has the potential to enhance our understanding of the behavior of the QGP and enhance the theoretical frameworks used to investigate ultrarelativistic heavy-ion collisions. By refining the description of non-equilibrium dynamics, it contributes to the development of more precise models and a deeper understanding of the QGP's complex phenomena.
Moreover, experiments conducted at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) are designed to recreate conditions comparable to those in the early universe and during astrophysical mergers. Under these conditions of high temperatures and net baryon densities, nuclear matter undergoes a phase transition from quarks and gluons confined within hadrons to the deconfined QGP state. Calculations based on lattice quantum chromodynamics (LQCD) have determined the temperature at which this deconfinement transition occurs, yielding important insights into the QCD equation of state. For modeling the spatiotemporal dynamics of the QGP in ultrarelativistic heavy-ion collisions, relativistic viscous hydrodynamics has proven to be an indispensable instrument.
For a more accurate description, it became apparent that dissipative transport coefficients, such as shear viscosity, must be included. This resulted in the development of second-order viscous hydrodynamics, which effectively incorporated dissipative effects and allowed for constraints on the shear viscosity to entropy density ratio. However, the application of second-order viscous hydrodynamics to the early phases of the collision, where the system is far from equilibrium and exhibits significant pressure anisotropy along the beam-line direction was problematic. Early on, it was difficult for fixed-order truncations of viscous hydrodynamics to accurately represent the large viscous corrections.
To address these issues, aHydro was used, employing a distribution function that assured probability positivity and non-negativity. The original formulation was centered on boost-invariant conformal Bjorken expansion, but subsequent work has expanded it to incorporate more realistic characteristics associated with heavy-ion collisions. This part of the research endeavor has dual objectives. The first objective of the project is to demonstrate that aHydro automatically includes an infinite series of terms when expanded as a power series in the inverse shear Reynolds number, thereby providing an infinite order resummation of viscous contributions to all orders. The second focus of the research is aHydroQP in a full 3+1D framework, which surpasses traditional approaches and allows for phenomenological applications to heavy-ion collision experiments at RHIC and LHC energies. By refining the theoretical frameworks used in ultrarelativistic heavy-ion collision studies, this research seeks to describe various bulk observables of the QGP using anisotropic hydrodynamics and compare the results with experimental data at different collision energies. This will contribute to a more thorough characterization of the QGP and provide valuable insights into the physics at play.
Understanding the success of aHydro has led researchers to consider the topic of dynamical hydrodynamic attractors. Extensive research has been conducted on the existence of hydrodynamic attractors in conformal theories but less so in non-conformal theories. Important insights into the behavior of relativistic systems have been gleaned from studies of conformal systems. However, the existence of hydrodynamic attractors in non-conformal kinetic theories remains unanswered. This raises the intriguing issue of whether or not hydrodynamic attractor theories extend beyond conformal theories. Exploring the behavior of non-conformal systems is crucial for gaining a comprehensive understanding of dynamics in situations far from equilibrium that are phenomenologically relevant. In addition, the influence of a realistic mass- and temperature-dependent relaxation time on the behavior of an attractor has not been studied in detail. Understanding the interaction between relaxation dynamics and the emergence of attractor solutions can cast light on the evolution of non-conformal systems at the macroscopic level. In addition, we plan to investigate the impact of initial conditions on the time-dependent evolution of integral moments of the one-particle distribution function. We aim to investigate how the initial momentum-space anisotropy and initialization time influence the emergence and persistence of hydrodynamic attractors.
Our findings indicate the existence of an attractor for the scaled longitudinal pressure, but not for the shear and bulk viscous corrections separately. Additionally, our results provide evidence for both early- and late-time attractors for all moments of the one-particle distribution function containing greater than one power of the longitudinal momentum squared. By answering these questions, we aim to shed light on the behavior of non-conformal kinetic theories, reveal the role of relaxation dynamics, and examine the sensitivity of the system to initial conditions. This research contributes not only to the fundamental understanding of far-from-equilibrium dynamics, but also to the description of relativistic systems in diverse physical contexts.