Dissipative properties of hot and dense hadronic matter in an excluded-volume hadron resonance gas model

We estimate dissipative properties, viz., shear and bulk viscosities of hadronic matter using relativistic Boltzmann equation in relaxation time approximation within the framework of excluded-volume hadron resonance gas (EHRG) model. We find that at zero baryon chemical potential the shear viscosity to entropy ratio ($\eta /s$) decreases with temperature while at finite baryon chemical potential this ratio shows the same behavior as a function of temperature but reaches close to the Kovtun-Son-Starinets (KSS) bound. Further along the chemical freezeout curve, ratio $\eta /s$ is almost constant apart from small initial monotonic rise. This observation may have some relevance to the experimental finding that the differential elliptic flow of charged hadrons does not change considerably at lower center-of-mass energy. We further find that bulk viscosity to entropy density ($\zeta /s$) decreases with temperature while this ratio has higher value at finite baryon chemical potential at higher temperature. Along the freezeout curve $\zeta /s$ decreases monotonically at lower center-of-mass energy and then saturates.

Figure 1

Top panel shows shear viscosity to entropy density ratio $\eta /s$ for $r_h=0.3$ fm as a function of temperature for different chemical potentials. Middle panel shows $\eta /s$ for $r_h=0.5$ fm. Bottom panel shows the shear viscosity as a function of temperature at different chemical potentials for $r_h=0.5$ fm.

Figure 2

Comparison of $\eta /s$ estimated in our model with the estimations of other models [16, 50, 51] at zero chemical potential.

Figure 3

Left panel shows ratio $\eta T/(\epsilon +P)$ for $r_h=0.3$ fm as a function of temperature for different chemical potentials. Right panel shows $\eta T/(\epsilon +P)$ for $r_h=0.5$ fm.

Figure 4

Left panel shows comparison of $\eta /s$ ($r_h=0.3$ fm) estimated in our model with the estimations of Ref. [50]. Right panel shows comparison of $\eta T/(\epsilon +P)$ with Ref. [50].

Figure 5

Top panel shows bulk viscosity to entropy ratio $\zeta /s$ for $r_h=0.3$ fm as a function of temperature for different chemical potentials. Middle panel shows $\zeta /s$ for $r_h=0.5$ fm. Bottom panel shows the bulk viscosity as a function of temperature at different chemical potentials for $r_h=0.5$ fm.

Figure 6

Comparison of $\zeta /s$ estimated in our model with estimations using SHMC model [16] at zero chemical potential.

Figure 7

Top panel shows $\eta /s$ along the freezeout line for $r_h=0.5$ fm. Middle panel shows $\eta T/(\epsilon +P)$ along the freezeout line. Bottom panel shows $\zeta /s$ along the freezeout line for $r_h=0.5$ fm.