(2+2)D Collective Model based on a relativistic Boltzmann equation in the Isotropization Time Approximation: CoMBolt-ITA

Abstract

A new model based on the relativistic Boltzmann equation in the isotropization time approximation is developed to investigate the collective behavior of the quark-gluon plasma produced in high-energy heavy-ion collisions. The equation is solved in (2+2)D (two spatial and two momentum-space dimensions). This framework couples pre-equilibrium dynamics with hydrodynamic evolution to simulate the dynamics of quasiparticle evolution. A numerical scheme based on the method of characteristics enables the evolution to begin from a specified initial Boltzmann distribution. In this work, the spatial structure of the initial distribution is modeled using the TrENTo framework. Our results show that a medium initialized at $\tau_0$ on the order of 1 [fm/$c$] with a small shear viscosity to entropy density ratio ($\eta/s = 0.008$) evolves consistently with hydrodynamic simulations, such as those performed using the VISH2+1 code, while discrepancies arise for a medium with $\eta/s = 0.8$. Furthermore, when initialized with a highly anisotropic momentum distribution in the longitudinal direction at early times, the system exhibits spatially non-uniform thermalization in the transverse plane, leading to the emergence of a nontrivial hypersurface that marks the onset of hydrodynamic applicability. Finally, we compute the $p_T$-spectra for a non-fluctuating initial condition using the hybrid version of CoMBolt-ITA. In this hybrid setup, the description is switched from quasiparticles to hadrons, and UrQMD is used to model the hadron gas dynamics. We compare these results with those obtained from the hybrid VISH2+1 initialized within the same setup. For a small shear viscosity, $\eta/s = 0.08$, the two results show a good level of consistency, whereas for a larger value, $\eta/s = 0.8$, a noticeable discrepancy emerges.