Quasiparticle theory of shear and bulk viscosities of hadronic matter

Abstract

A theoretical framework for the calculation of shear and bulk viscosities of hadronic matter at finite temperature is presented. The framework is based on the quasi-particle picture. It allows for an arbitrary number of hadron species with point-like interactions, and allows for both elastic and inelastic collisions. Detailed balance is ensured. The particles have temperature dependent masses arising from mean field or potential effects, which maintains self-consistency between the equation of state and the transport coefficients. As an example, we calculate the shear and bulk viscosity in the linear σ model. The ratio of shear viscosity to entropy density shows a minimum in the vicinity of a rapid crossover transition, while the ratio of bulk viscosity to entropy density shows a maximum.

Shear and bulk viscosities of the gluon plasma in a quasiparticle description

“…In local thermal equilibrium, this picture reduces to the quasiparticle model, which was employed successfully to describe lattice QCD equilibrium thermodynamics in [90,[92][93][94]. Thermodynamic self-consistency in this model is a direct consequence of the consistency condition that must be imposed in order to fulfill energy and momentum conservation in the kinetic theory [95,101]. We used expressions for shear and bulk viscosities derived within relaxation-time approximation to the kinetic theory.…”

“…This may be considered as a rather crude approximation [75,77,108]. A more refined approach, employing a momentum-dependent relaxation time including elastic and inelastic scatterings, was recently proposed in [95].…”

“…Concise expressions for the shear and bulk viscosities have been derived systematically in [95] within a quasiparticle framework. In the relaxation-time (τ ) approximation, one can deduce for the (quasi)gluon plasma…”

“…The QPM was successfully employed to quantitatively describe lattice QCD results of equilibrium thermodynamics such as the EoS and related quantities [90][91][92][93][94]. In the following, we apply this model to systems exhibiting small departures from thermal equilibrium by using the results of an effective kinetic-theory approach [71,72] for shear and bulk viscosities derived for a quasiparticle system in [95].…”

Bulk and shear viscosities of hot and dense hadron gas

“…The computation of the transport coefficient of the hadronic mixture is not an easy task. There have been various attempt on this field over last few years involving various approximations like relaxation time approximation, Chapman-Enscog as well as Green Kubo approach to estimate the shear viscosity to entropy ratio using different effective models for hadronic interactions [10,[13][14][15][16].…”