Charge-dependent directed flows in heavy-ion collisions by Boltzmann-Maxwell equations

Abstract

We have calculated the directed flow ${v}_{1}$ and charge-dependent directed flow $\mathrm{\ensuremath{\Delta}}{v}_{1}$ of pions and protons in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{NN}}=200$ GeV by solving the coupled Boltzmann-Maxwell equations self-consistently. Our numerical results show that ${v}_{1}$ for pions and protons are all negative in the positive midrapidity region and have similar behavior and magnitude. In contrast we find a quite different behavior in $\mathrm{\ensuremath{\Delta}}{v}_{1}$ for pions and protons. The difference lies in that $\mathrm{\ensuremath{\Delta}}{v}_{1}$ for protons mainly comes from pressure gradients of the medium, while the dominant contribution to $\mathrm{\ensuremath{\Delta}}{v}_{1}$ for pions is from electromagnetic fields. Our results indicate that the effect of the electric field will slightly exceed that of the magnetic field and lead to a small negative slope of $\mathrm{\ensuremath{\Delta}}{v}_{1}$ for pions.