Eur. Phys. J. C (2021) 81: 139
https://doi.org/10.1140/epjc/s10052-021-08931-1

Regular Article – Theoretical Physics

Viscous properties of hot and dense QCD matter in the presence of a magnetic field

Department of Physics, Indian Institute of Technology Roorkee, 247667, Roorkee, India

^a srath@ph.iitr.ac.in

Received: 7 October 2020
Accepted: 30 January 2021
Published online: 9 February 2021

Abstract

We have studied the effect of strong magnetic field on the viscous properties of hot QCD matter at finite chemical potential by calculating the shear viscosity ($\eta$) and the bulk viscosity ($\zeta$). The viscosities have been calculated using the relativistic Boltzmann transport equation within the relaxation time approximation. The interactions among partons are incorporated through their quasiparticle masses at finite temperature, strong magnetic field and finite chemical potential. From this study, one can understand the influence of strong magnetic field and the influence of chemical potential on the sound attenuation through the Prandtl number (Pl), on the nature of the flow by the Reynolds number (Rl), and on the relative behavior between the shear viscosity and the bulk viscosity through the ratio $\zeta /\eta$. We have observed that, both shear and bulk viscosities get increased in the presence of a strong magnetic field and the additional presence of chemical potential further enhances their magnitudes. With the increase of temperature, $\eta$ increases for the medium in the presence of a strong magnetic field as well as for the isotropic medium in the absence of magnetic field, whereas $\zeta$ is found to decrease with the temperature, contrary to its increase in the absence of magnetic field. We have observed that, the Prandtl number gets increased in the presence of strong magnetic field and finite chemical potential as compared to that in the isotropic medium, but it always remains larger than unity, thus instead of the thermal diffusion, the momentum diffusion largely affects the sound attenuation in the medium and this is more vigorous in the presence of both strong magnetic field and finite chemical potential. However, the Reynolds number becomes lowered than unity in an ambience of strong magnetic field and even gets further decreased in an additional presence of chemical potential, thus it implies the dominance of kinematic viscosity over the characteristic length scale of the system. Finally, the ratio $\zeta /\eta$ is amplified to the value larger than unity, contrary to its value in the absence of magnetic field and chemical potential where it is less than unity, thus it is inferred that the bulk viscosity prevails over the shear viscosity for the hot and dense QCD matter in the presence of a strong magnetic field.