Medium effects on the relaxation of dissipative flows in a hot pion gas

The relaxation times over which dissipative fluxes restore their steady-state values are evaluated for a pion gas using the 14-moment method. The effect of the medium is implemented through a temperature-dependent $\pi \pi$ cross section in the collision integral which is obtained by including one-loop self-energies in the propagators of the exchanged $\rho$ and $\sigma$ mesons. To account for chemical freeze-out in heavy-ion collisions, a temperature-dependent pion chemical potential is introduced in the distribution function. The temperature dependence of the relaxation times for shear and bulk viscous flows as well as the heat flow is significantly affected.

Figure 1

$\pi \pi$ scattering with self-energy corrections.

Figure 2

The $\pi \pi$ cross section as a function of $E_{\mathrm{c}.\mathrm{m}.}$. The dashed line corresponds to scattering in vacuum. The dot-dashed line refers to the in-medium cross section involving only the pion loop for the $\sigma$ and $\rho$ mesons. The solid line corresponds to the additional loops in the $\rho$-meson self-energy.

Figure 3

Relaxation time of the bulk viscous flow as a function of $T$.

Figure 4

Relaxation time of the heat flow as a function of $T$.

Figure 5

Relaxation time of the shear viscous flow as a function of temperature.