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تسجيل مستخدم جديدOne particle distribution function and shear viscosity in magnetic field: a relaxation time approach
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We calculate the $delta f$ correction to the one particle distribution function in 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 dimensionless Hall parameter $chi_{H}$ in 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 Grads moment method in cite{Denicol:2018rbw}. Calculation of 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 on 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.
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