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

Abstract

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.

Bulk Viscosity Coefficient of Hadronic Matter

“…At µ B = 0, the decreasing nature of our ζ/s(T ) agrees with most of the earlier works as addressed elaborately in Ref. [4]. However, some investigations have reported it to increase with T and some time also have a peak structure near transition temperature [7].…”

“…The m π , m N stand for masses of pion, nucleon and their momenta are denoted by k. The Γ π and Γ N are thermal widths of pion and nucleon, which have been calculated from the imaginary part of their selfenergies (on-shell) at finite temperature. We have considered different mesonic and baryonic loops for pion self-energy, whereas, pion-baryon intermediate states are taken in nucleon self-energy [3,4].…”

Temperature effect on shear and bulk viscosities of QCD matter

“…The situation of the bulk viscosity, ζ, is more complicated. Generally, the ζ is recognized to be very small [25,[31][32][33][34][35], but theoretical studies relating the ζ with the trace anomaly [36][37][38] obtain and explaining recent experiments requires [39,40] a large value. Nevertheless, the relation connecting the bulk viscosity with the trace anomaly [38] is very subtle since it requires particular ansatz for the spectral function [41,42] and sophisticated technique to rule out the non-thermal contributions [31,43].…”

“…Some hadron resonance models and Nambu-Jona-Lasinio model calculations yield convex or concave function [28,31]. Some others give decreasing features [18,26,39,48] or increasing behavior [22]. The quasiparticle model produces a decreasing or convex function depending on the σ-meson mass [12] and recent quasiparticle anisotropic hydrodynamics also gives a convex function [49].…”

“…[26,[35][36][37][38][39]). However, studies relating the ζ with the trace anomaly suggest [40,41] and explaining recent experiments requires [32,42] a large value.…”