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

Abstract

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, $η_{b}$ and $η_{f}$, in terms of bosonic and fermionic spectral widths, $Γ_{b}$ and $Γ_{\pm}$. 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 $η_{f}[Γ_{\pm}]$. To do this, we determine first the dependence of $Γ_{b}$ and $Γ_{\pm}$ on momentum $p$, temperature $T$, chemical potential $μ$ and $ξ_{0}\equiv m_{b}^{0}/m_{f}^{0}$, in a one-loop perturbative expansion in the orders of the Yukawa coupling. Here, $m_{b}^{0}$ and $m_{f}^{0}$ are $T$ and $μ$ independent bosonic and fermionic masses, respectively. We then numerically determine $η_{b}[Γ_{b}]$ and $η_{f}[Γ_{\pm}]$, and study their thermal properties. It turns out that whereas $Γ_{b}$ and $Γ_{+}$ decrease with increasing $T$ or $μ$, $Γ_{-}$ increases with increasing $T$ or $μ$. This behavior qualitatively changes by adding thermal corrections to $m_{b}^{0}$ and $m_{f}^{0}$, while the difference between $Γ_{+}$ and $Γ_{-}$ keeps increasing with increasing $T$ or $μ$. Moreover, $η_{b}$ ($η_{f}$) increases (decreases) with increasing $T$ or $μ$. We show that the effect of plasminos on $η_{f}$ becomes negligible with increasing (decreasing) $T$ ($μ$).