In-medium viscous coefficients of a hot hadronic gas mixture

We estimate the shear and the bulk viscous coefficients for a hot hadronic gas mixture made of pions and nucleons. The viscosities are evaluated in the relativistic kinetic theory approach by solving the transport equation in the relaxation time approximation for binary collisions $(\pi \pi ,\pi N$, and $NN)$. Instead of the vacuum cross sections usually used in the literature we employ in-medium scattering amplitudes in the estimation of the relaxation times. The modified cross sections for $\pi \pi$ and $\pi N$ scattering are obtained using one-loop modified thermal propagators for $\rho ,\sigma$, and $\mathrm{\Delta }$ in the scattering amplitudes which are calculated using effective interactions. The resulting suppression of the cross sections at finite temperature and baryon density is observed to significantly affect the $T$ and ${\mu }_N$ dependence of the viscosities of the system.

Figure 1

$\pi \pi$ cross section as a function of $E_{\mathrm{c}.\mathrm{m}.}$.

Figure 2

$\pi N$ cross section as a function of $E_{\mathrm{c}.\mathrm{m}.}$. The values of temperature $T$ and nucleon chemical potential ${\mu }_N$ are in MeV.

Figure 3

Relaxation time of pions in a hadron gas mixture of pions and nucleons.

Figure 4

Relaxation time of nucleons in a hadron gas mixture of pions and nucleons.

Figure 5

Shear viscosity as a function of $T$ for various ${\mu }_N$ with and without medium effects. Legends 1, 2, 3, and 4 indicate ${\mu }_N=200$, 300, 400, and 500 MeV, respectively. The pion chemical potential ${\mu }_{\pi }=80$ MeV.

Figure 6

Shear viscosity over entropy density as a function of $T$.

Figure 7

Bulk viscosity as a function of $T$ with and without medium effects. Legends 1, 2, 3, and 4 indicate ${\mu }_N=200$, 300, 400, and 500 MeV respectively.

Figure 8

Ratio of bulk viscosity and entropy density vs $T$.