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Owing to the Kubo relation, the shear viscosities of pionic and nucleoniccomponents have been evaluated from their corresponding retarded correlators ofviscous stress tensor in the static limit, which become non-divergent only forthe non-zero thermal widths of the constituent particles. In the real-timethermal field theory, the pion and nucleon thermal widths have respectivelybeen obtained from the pion self-energy for different meson, baryon loops andthe nucleon self-energy for different pion-baryon loops. We have found anon-monotonic momentum distributions of pion and nucleon thermal widths, whichhave been integrated out by their respective Bose-enhanced and Pauli-blockedphase space factors during evaluation of their shear viscosities. The viscosityto entropy density ratio for this mixed gas of pion-nucleon system decreasesand approaches toward its lower bound as the temperature and baryon chemicalpotential increase within the relevant domain of hadronic matter.

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