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

We have calculated the directed flow v1 and charge-dependent directed flow Av1 of pions and protons in Au+Au collisions at ,/sNN = 200 GeV by solving the coupled Boltzmann-Maxwell equations self-consistently. Our numerical results show that v1 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 Av1 for pions and protons. The difference lies in that Av1 for protons mainly comes from pressure gradients of the medium, while the dominant contribution to Av1 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 Av1 for pions.