Shear viscosity of a pion gas due to $\rho\pi\pi$ and $\sigma\pi\pi$ interactions

TL;DR

This paper calculates the shear viscosity of a pion gas considering interactions with low mass resonances, finding a very small shear viscosity to entropy density ratio close to the KSS bound.

Contribution

It introduces a thermal field theoretical approach to compute pion shear viscosity including $ ho$ and $\sigma$ resonance interactions.

Findings

Shear viscosity to entropy density ratio ($/s$) is very small, near the KSS bound.

Thermal width of pions is computed from self-energy diagrams with effective Lagrangian.

The approach accounts for finite thermal widths due to resonance interactions.

Abstract

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.