In-medium viscous coefficients of a hot hadronic gas mixture

We estimate the shear and the bulk viscous coefficients for a hot hadronic gas mixture made of pions and nucleons. The viscosities are evaluated in the relativistic kinetic theory approach by solving the transport equation in the relaxation time approximation for binary collisions (ππ,πN, and NN). Instead of the vacuum cross sections usually used in the literature we employ in-medium scattering amplitudes in the estimation of the relaxation times. The modified cross sections for ππ and πN scattering are obtained using one-loop modified thermal propagators for ρ,σ, and Δ in the scattering amplitudes which are calculated using effective interactions. The resulting suppression of the cross sections at finite temperature and baryon density is observed to significantly affect the T and μN dependence of the viscosities of the system.