Bulk viscosity of strongly interacting matter in the relaxation time approximation

Abstract

This paper presents how thermal mean field effects are incorporated consistently in the hydrodynamical modelling of heavy-ion collisions. The nonequilibrium correction to the distribution function resulting from a temperature-dependent mass is obtained in a procedure which automatically satisfies the Landau matching condition and is thermodynamically consistent. The physics of the bulk viscosity is studied here for Boltzmann and Bose-Einstein gases within the Chapman-Enskog and 14-moment approaches in the relaxation time approximation. Constant and temperature-dependent masses are considered in turn. It is shown that, in the small mass limit, both methods lead to the same value of the ratio of the bulk viscosity over its relaxation time. The inclusion of a temperature-dependent mass leads to the emergence of the $β_λ$-function in that ratio, and it is of the expected parametric form for the Boltzmann gas, while for the Bose-Einstein case it is affected by the infrared cut-off. This suggests that the relaxation time approximation may be too crude to obtain a reliable form of $ζ/τ_R$ for gases obeying Bose-Einstein statistics.