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

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 ($η$) and bulk ($ζ$) viscosities. The viscosities are calculated using kinetic theory in the relaxation time approximation. The interactions are incorporated through the quasiparticle masses of partons at strong magnetic field and finite chemical potential. From this study, one can understand the effects of strong magnetic field and 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 shear viscosity and bulk viscosity through the ratio $ζ/η$. We have found that, $η$ and $ζ$ get increased in a strong magnetic field and the additional presence of chemical potential further enhances their magnitudes. With the increase of temperature, $η$ increases in a strong magnetic field as well as in the absence of magnetic field, whereas $ζ$ decreases 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 chemical potential as compared to the isotropic one, but it always remains larger than 1, thus the momentum diffusion largely affects the sound attenuation in the medium. The Reynolds number gets lowered than 1 in a strong magnetic field and it becomes further decreased in an additional presence of chemical potential, so the kinematic viscosity dominates over the characteristic length scale of the system. Finally, $ζ/η$ becomes larger than 1, contrary to its value in the absence of magnetic field and chemical potential where it is less than 1, so the bulk viscosity prevails over the shear viscosity for the hot and dense QCD matter in the presence of a strong magnetic field.