Momentum and its affiliated transport coefficients for a hot QCD matter in a strong magnetic field

Abstract

We have studied the effects of anisotropies on the momentum transport in a QCD matter by shear ($\eta$) and bulk ($\zeta$) viscosities. The anisotropies arise either by the strong magnetic field or by the preferential expansion. This study helps to understand the fluidity and location of transition point of matter through $\eta/s$ and $\zeta/s$ ($s$ is entropy density), respectively, the sound attenuation through the Prandtl number (Pl), the nature of flow by the Reynolds number (Rl), and the competition between momentum and charge diffusions. The viscosities are calculated in the relaxation time approximation of kinetic theory within the quasiparticle model. Compared to isotropic medium, both $\eta$ and $\zeta$ get increased in magnetic field-driven (B-driven) anisotropy, contrary to the decrease in expansion-driven anisotropy. $\eta$ increases with temperature faster in former case than in latter case whereas $\zeta$ in former case decreases with temperature and in latter case, it is meagre and diminishes at a specific temperature. So the viscosities can distinguish aforesaid anisotropies. Thus, $\eta/s$ gets enhanced in former case and in latter case, it becomes smaller than isotropic one. Similarly $\zeta/s$ gets amplified but decreases faster with the temperature in a strong magnetic field. The Prandtl number gets increased in B-induced anisotropy and gets decreased in expansion-induced anisotropy, compared to isotropic one. Since, Pl is found larger than 1, the sound attenuation is governed by momentum diffusion. The B-driven anisotropy makes the Reynolds number smaller than one, whereas the expansion-driven anisotropy makes it larger. The ratio ($\frac{\eta}{s}/\frac{\sigma_{\rm el}}{T}$) gets amplified in B-driven anisotropy whereas it gets reduced in expansion-driven anisotropy. Since, the ratio is always more than one, the momentum diffusion prevails over the charge diffusion.