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

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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, ηb and ηf, in terms of bosonic and fermionic spectral widths, Γb and Γ±. Here, the subscripts ± correspond to normal and collective (plasmino) excitations of fermions. We study, in particular, the effect of these excitations on thermal properties of ηf[Γ±]. To do this, we determine first the dependence of Γb and Γ± on momentum p, temperature T, chemical potential μ and ξ₀≡ mb⁰/mf⁰, in a one-loop perturbative expansion in the orders of the Yukawa coupling. Here, mb⁰ and mf⁰ are T and μ independent bosonic and fermionic masses, respectively. We then numerically determine ηb[Γb] and ηf[Γ±], and study their thermal properties. It turns out that whereas Γb and Γ₊ decrease with increasing T or μ, Γ₋ increases with increasing T or μ. This behavior qualitatively changes by adding thermal corrections to mb⁰ and mf⁰, while the difference between Γ₊ and Γ₋ keeps increasing with increasing T or μ. Moreover, ηb (ηf) increases (decreases) with increasing T or μ. We show that the effect of plasminos on ηf becomes negligible with increasing (decreasing) T (μ).