Chiral hydrodynamics of expanding systems

We obtain equations of motion for the boost-invariant expansion of a system of chiral particles. Our analysis is based on the Boltzmann equation for left- and right-handed massless particles in the relaxation time approximation. We assume Bjorken symmetry, but allow for parity breaking. We generalize the relaxation time approximation to take into account the so-called side-jump effect, but we show that the ensuing correction happens to vanish for Bjorken symmetry. After expressing the conserved currents in terms of chiral moments, we derive equations of motion for these moments from the Boltzmann equation. After a suitable truncation, these equations allow us to study the transition from the early-time collisionless regime to the hydrodynamic regime at late time, where the parity-violating chiral moments decay exponentially. The truncation that we use for the parity-violating moments is shown to be identical to Israel-Stewart's 14-moment approximation. Our final set of equations can be used to calculate the energymomentum tensor, vector, and axial-vector currents with chiral degrees of freedom for possible applications in heavy-ion collisions.