Shear viscosity of pionic and nucleonic components from their different possible mesonic and baryonic thermal fluctuations

Owing to the Kubo relation, the shear viscosities of pionic and nucleonic components have been evaluated from their corresponding retarded correlators of viscous stress tensor in the static limit, which become non-divergent only for the non-zero thermal widths of the constituent particles. In the real-time thermal field theory, the pion and nucleon thermal widths have respectively been obtained from the pion self-energy for different meson, baryon loops and the nucleon self-energy for different pion-baryon loops. We have found a non-monotonic momentum distributions of pion and nucleon thermal widths, which have been integrated out by their respective Bose-enhanced and Pauli-blocked phase space factors during evaluation of their shear viscosities. The viscosity to entropy density ratio for this mixed gas of pion-nucleon system decreases and approaches toward its lower bound as the temperature and baryon chemical potential increase within the relevant domain of hadronic matter.