Charge-dependent Flow Induced by Magnetic and Electric Fields in Heavy Ion Collisions

We investigate the charge-dependent flow induced by magnetic and electric fields in heavy ion collisions. We simulate the evolution of the expanding cooling droplet of strongly coupled plasma hydrodynamically, using the iEBE-VISHNU framework, and add the magnetic and electric fields as well as the electric currents they generate in a perturbative fashion. We confirm the previously reported effect of the electromagnetically induced currents, that is a charge-odd directed flow $\Delta v_1$ that is odd in rapidity, noting that it is induced by magnetic fields (\`a la Faraday and Lorentz) and by electric fields (the Coulomb field from the charged spectators). In addition, we find a charge-odd $\Delta v_3$ that is also odd in rapidity and that has a similar physical origin. We furthermore show that the electric field produced by the net charge density of the plasma drives rapidity-even charge-dependent contributions to the radial flow $\langle p_T \rangle$ and the elliptic flow $\Delta v_2$. Although their magnitudes are comparable to the charge-odd $\Delta v_1$ and $\Delta v_3$, they have a different physical origin, namely the Coulomb forces within the plasma.