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Shear viscosity of pion gas due to $ρππ$ and $σππ$ interactions

We have evaluated the shear viscosity of pion gas taking into account its scattering with the low mass resonances, $σ$ and $ρ$ during propagation in the medium. The thermal width (or collisional rate) of the pions is calculated from $πσ$ and $πρ$ loop diagrams using effective interactions in the real time formulation of finite temperature field theory. A very small value of shear viscosity by entropy density ratio ($η/s$), close to the KSS bound, is obtained which approximately matches the range of values of $η/s$ used by Niemi et al. \cite{Niemi} in order to fit the RHIC data of elliptic flow.