The nucleon thermal width due to pion-baryon loops and its contribution in Shear viscosity

In the real-time thermal field theory, the standard expression of shear viscosity for the nucleonic constituents is derived from the two point function of nucleonic viscous stress tensors at finite temperature and density. The finite thermal width or Landau damping is traditionally included in the nucleon propagators. This thermal width is calculated from the in-medium self-energy of nucleon for different possible pion-baryon loops. The dynamical part of nucleon-pion-baryon interactions are taken care by the effective Lagrangian densities of standard hadronic model. The shear viscosity to entropy density ratio of nucleonic component decreases with the temperature and increases with the nucleon chemical potential. However, adding the contribution of pionic component, total viscosity to entropy density ratio also reduces with the nucleon chemical potential when the mixing effect between pion and nucleon components in the mixed gas is considered. Within the hadronic domain, viscosity to entropy density ratio of the nuclear matter is gradually reducing as temperature and nucleon chemical potential are growing up and therefore the nuclear matter is approaching toward the (nearly) perfect fluid nature