Viscous effects of a hot QGP medium in time dependent magnetic field and their phenomenological significance

Abstract

In this work, we have studied, for the first time, the impact of a realistic picture of a time dependent electric and magnetic field on the shear and bulk viscosities of the medium. Both the electric and magnetic fields are considered to be exponentially decaying with time, and the study is valid in the regime where the magnetic field strength is weak ($eB\ll T^2$). The evaluation has been done in the kinetic theory framework wherein we have solved the relativistic Boltzmann transport equation within the relaxation time approximation collision kernel. We have shown that the constant weak field results as well as the $B=0$ results in the literature can be obtained as special cases of our general results. We have observed that the shear and bulk viscosities increase with time or equivalently, decrease with the strength of the magnetic field. To connect these observations with experiments, we have calculated the thermalization time, shear viscosity to entropy ratio ($\eta /s$), and bulk viscosity to entropy ratio ($\zeta /s$).