Shear viscosity of a pion gas due to rhoππ and σππ interactions

We have calculated the shear viscosity of pion medium, where propagating pion has some finite thermal width due to interaction with the low mass resonances, $\sigma$ and $\rho$. With the help of standard thermal field theoretical technique, the thermal width of the pion has been calculated from the pion self-energy diagram for $\pi\sigma$ and $\pi\rho$ loops, where an effective Lagrangian density has been used for interaction part. We have found a very small value of shear viscosity by entropy density ratio ($\eta/s$), which is very close to the KSS bound.