On the contribution of plasminos to the shear viscosity of a hot and dense Yukawa-Fermi gas

We determine the shear viscosity of a hot and dense Yukawa-Fermi gas, using the standard Green-Kubo relation, according to which the shear viscosity is given by the retarded correlator of the traceless part of viscous energy-momentum tensor. We approximate this retarded correlator using a one-loop skeleton expansion, and express the bosonic and fermionic shear viscosities, $\eta_{b}$ and $\eta_{f}$, in terms of bosonic and fermionic spectral widths, $\Gamma_{b}$ and $\Gamma_{\pm}$. Here, the subscripts $\pm$ correspond to normal and collective (plasmino) excitations of fermions. We study, in particular, the effect of these excitations on thermal properties of $\eta_{f}[\Gamma_{\pm}]$. To do this, we determine first the dependence of $\Gamma_{b}$ and $\Gamma_{\pm}$ on momentum $p$, temperature $T$, chemical potential $\mu$ and $\xi_{0}\equiv m_{b}^{0}/m_{f}^{0}$, in a one-loop perturbative expansion in the orders of the Yukawa coupling. Here, $m_{b}^{0}$ and $m_{f}^{0}$ are $T$ and $\mu$ independent bosonic and fermionic masses, respectively. We then numerically determine $\eta_{b}[\Gamma_{b}]$ and $\eta_{f}[\Gamma_{\pm}]$, and study their thermal properties. It turns out that whereas $\Gamma_{b}$ and $\Gamma_{+}$ decrease with increasing $T$ or $\mu$, $\Gamma_{-}$ increases with increasing $T$ or $\mu$. This behavior qualitatively changes by adding thermal corrections to $m_{b}^{0}$ and $m_{f}^{0}$, while the difference between $\Gamma_{+}$ and $\Gamma_{-}$ keeps increasing with increasing $T$ or $\mu$. Moreover, $\eta_{b}$ ($\eta_{f}$) increases (decreases) with increasing $T$ or $\mu$. We show that the effect of plasminos on $\eta_{f}$ becomes negligible with increasing (decreasing) $T$ ($\mu$).