One particle distribution function and shear viscosity in magnetic field: A relaxation time approach

.We calculate the f correction to the one particle distribution function in the presence of magnetic field and non-zero shear viscosity within the relaxation time approximation. The f correction is found to be electric charge dependent. Subsequently, we also calculate one longitudinal and four transverse shear viscous coefficients as a function of the dimensionless Hall parameter H in the presence of the magnetic field. We find that a proper linear combination of the shear viscous coefficients calculated in this work scales with the result obtained from Grad's moment method in [#!Denicol:2018rbw!#]. The calculation of the invariant yield of - in a simple Bjorken expansion with cylindrical symmetry shows no noticeable change in spectra due to the f correction for realistic values of the magnetic field and relaxation time. However, when transverse expansion is taken into account using a blast wave type flow field we found noticeable change in spectra and elliptic flow coefficients due to the f correction. The f is also found to be very sensitive to the magnitude of magnetic field. Hence we think it is important to take into account the f correction in more realistic numerical magnetohydrodynamics simulations.