Quasi-Particle Theory of Shear and Bulk Viscosities of Hadronic Matter

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 $\sigma$ 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.