Interplay of drag by hot matter and electromagnetic force on the directed flow of heavy quarks

Rapidity-odd directed flow in heavy ion collisions can originate from two very distinct sources in the collision dynamics i. an initial tilt of the fireball in the reaction plane that generates directed flow of the constituents independent of their charges, and ii. the Lorentz force due to the strong primordial electromagnetic field that drives the flow in opposite directions for constituents carrying unlike sign charges. We study the directed flow of open charm mesons $D^0$ and $\overline{D^0}$ in the presence of both these sources of directed flow. The drag from the tilted matter dominates over the Lorentz force resulting in same sign flow for both $D^0$ and $\overline{D^0}$, albeit of different magnitudes. Their average directed flow is about ten times larger than their difference. This charge splitting in the directed flow is a sensitive probe of the electrical conductivity of the produced medium. We further study their beam energy dependence; while the average directed flow shows a decreasing trend, the charge splitting remains flat from $\sqrt{s_{NN}}=60$ GeV to $5$ TeV.