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Bulk viscosity for pion and nucleon thermal fluctuation in the hadron resonance gas model

We have calculated microscopically bulk viscosity of hadronic matter, where equilibrium thermodynamics for all hadrons in medium are described by Hadron Resonance Gas (HRG) model. Considering pions and nucleons as abundant medium constituents, we have calculated their thermal widths, which inversely control the strength of bulk viscosities for respective components and represent their in-medium scattering probabilities with other mesonic and baryonic resonances, present in the medium. Our calculations show that bulk viscosity increases with both temperature and baryon chemical potential, whereas viscosity to entropy density ratio decreases with temperature and with baryon chemical potential, the ratio increases first and then decreases. The decreasing nature of the ratio with temperature is observed in most of the earlier investigations with few exceptions. We find that the temperature dependence of bulk viscosity crucially depends on the structure of the relaxation time. Along the chemical freeze-out line in nucleus-nucleus collisions with increasing collision energy, bulk viscosity as well as the bulk viscosity to entropy density ratio decreases, which also agrees with earlier references. Our results indicate the picture of a strongly coupled hadronic medium.