(3+1)-dimensional anisotropic fluid dynamics with a lattice QCD equation of state

TL;DR

This paper develops a new (3+1)-dimensional anisotropic hydrodynamics framework for non-conformal fluids, incorporating a lattice QCD equation of state, to better model large dissipative effects in relativistic heavy-ion collisions.

Contribution

It introduces a novel dissipative hydrodynamic formulation that non-perturbatively treats large anisotropic and bulk viscous effects using an anisotropic distribution function and lattice QCD data.

Findings

Accurately models early-time pressure anisotropies in heavy-ion collisions.

Demonstrates improved agreement with lattice QCD equations of state.

Provides a computational framework for realistic 3+1D simulations.

Abstract

Anisotropic hydrodynamics improves upon standard dissipative fluid dynamics by treating certain large dissipative corrections non-perturbatively. Relativistic heavy-ion collisions feature two such large dissipative effects: (i) Strongly anisotropic expansion generates a large shear stress component which manifests itself in very different longitudinal and transverse pressures, especially at early times. (ii) Critical fluctuations near the quark-hadron phase transition lead to a large bulk viscous pressure on the conversion surface between hydrodynamics and a microscopic hadronic cascade description of the final collision stage. We present a new dissipative hydrodynamic formulation for non-conformal fluids where both of these effects are treated nonperturbatively. The evolution equations are derived from the Boltzmann equation in the 14-moment approximation, using an expansion around an anisotropic leading-order distribution function with two momentum-space deformation parameters, accounting for the longitudinal and transverse pressures. To obtain their evolution we impose generalized Landau matching conditions for the longitudinal and transverse pressures. We describe an approximate anisotropic equation of state that relates the anisotropy parameters with the macroscopic pressures. Residual shear stresses are smaller and are treated perturbatively, as in standard second-order dissipative fluid dynamics. The resulting optimized viscous anisotropic hydrodynamic evolution equations are derived in 3+1 dimensions and tested in a (0+1)-dimensional Bjorken expansion, using a state-of-the-art lattice equation of state. Comparisons with other viscous hydrodynamical frameworks are presented.