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, ${\eta }_b$ 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) $T$ ($\mu$).

Comments: V1: 25 pages, 18 figures; V2: 26 pages, 18 figures. Discussions improved, references added. Version accepted for publication in PRD