Momentum transport properties of a hot and dense QCD matter in a weak magnetic field

Abstract

We have studied the momentum transport properties of a hot and dense QCD matter in the presence of weak magnetic field by determining the shear ($\eta$) and bulk ($\zeta$) viscosities in the relaxation time approximation of kinetic theory. The dependence of $\eta$ and $\zeta$ on the temperature has been explored in the presence of weak magnetic field ($B$-field) and finite chemical potential ($\mu$). It is observed that both shear and bulk viscosities get decreased in the presence of a weak magnetic field, whereas the finite chemical potential increases these viscosities, specifically at low temperatures. This study is important to understand the sound attenuation through the Prandtl number (Pr), the nature of the flow through the Reynolds number (Re), the fluidity and location of transition point of the matter through the ratios $\eta/s$ and $\zeta/s$ ($s$ is the entropy density), respectively. The Prandtl number is observed to increase in the weak magnetic field, whereas the presence of a finite chemical potential reduces its magnitude as compared to the scenario of absence of $B$-field and $\mu$. However, Pr still remains larger than unity, indicating that the energy dissipation due to the sound attenuation is mostly governed by the momentum diffusion. It is noticed that the weak magnetic field makes the Reynolds number larger, whereas the chemical potential makes it smaller than that in the absence of $B$-field and $\mu$. We have observed that the ratio $\eta/s$ decreases in the weak magnetic field regime, whereas the finite chemical potential increases its value, but the ratio $\zeta/s$ is found to decrease in the presence of weak magnetic field as well as finite chemical potential.