# Second-order dissipative hydrodynamics for plasma with chiral asymmetry and vorticity

## TL;DR

This paper develops a second-order dissipative hydrodynamic framework for chiral plasmas, incorporating quantum effects, axial charge dynamics, and vorticity, based on chiral kinetic theory and Chapman-Enskog expansion.

## Contribution

It introduces a novel Israel-Stewart type formulation for chiral relativistic fluids, including quantum corrections and a symmetric energy-momentum tensor suitable for weakly nonuniform plasmas.

## Key findings

- Derived second-order dissipative hydrodynamic equations for chiral plasma.
- Analyzed the impact of vorticity and velocity fluctuations on chiral vortical waves.
- Established a conserved energy-momentum tensor consistent with quantum corrections.

## Abstract

By making use of the chiral kinetic theory in the relaxation-time approximation, we derive an Israel-Stewart type formulation of the hydrodynamic equations for a chiral relativistic plasma made of neutral particles (e.g., neutrinos). The effects of chiral asymmetry are captured by including an additional continuity equation for the axial charge, as well as the leading-order quantum corrections due to the spin of particles. In a formulation of the chiral kinetic theory used, we introduce a symmetric form of the energy-momentum tensor that is suitable for the description of a weakly nonuniform chiral plasma. By construction, the energy and momentum are conserved to the same leading order in the Planck constant as the kinetic equation itself. By making use of such a chiral kinetic theory and the Chapman-Enskog approach, we obtain a set of second-order dissipative hydrodynamic equations. The effects of the fluid vorticity and velocity fluctuations on the dispersion relations of chiral vortical waves are analyzed.