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

TL;DR

This paper computes the charge-dependent correction to particle distribution functions and shear viscosity in magnetic fields, revealing significant effects on spectra and flow in realistic hydrodynamic models.

Contribution

It introduces a charge-dependent $ ext{delta}f$ correction and shear viscosity coefficients in magnetic fields, enhancing the realism of hydrodynamic simulations in heavy-ion collisions.

Findings

$ ext{delta}f$ correction depends on electric charge.

Shear viscous coefficients scale with the Hall parameter $oldsymbol{ ext{chi}_H}$.

Noticeable impact on spectra and elliptic flow when transverse expansion is included.

Abstract

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 Grad's 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.