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

We calculate the \( \delta f\) correction to the one particle distribution function in the presence of magnetic field and non-zero shear viscosity within the relaxation time approximation. The \( \delta f\) 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 \( \chi_{H}\) 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 \( \pi^{-}\) in a simple Bjorken expansion with cylindrical symmetry shows no noticeable change in spectra due to the \( \delta f\) 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 \( \delta f\) correction. The \( \delta f\) is also found to be very sensitive to the magnitude of magnetic field. Hence we think it is important to take into account the \( \delta f\) correction in more realistic numerical magnetohydrodynamics simulations.