Charge dependent directed flow splitting from baryon inhomogeneity and electromagnetic field

This work aims to understand the recent experimental data from the STAR collaboration on the system size dependence of directed flow splitting between oppositely charged hadrons [arXiv:2412.18326]. Previously, we have studied the role of baryon inhomogeneity on charge dependent directed flow. We now incorporate the effects of the electromagnetic (EM) field albeit perturbatively, as implemented in Ref. [arXiv:1806.05288]. This enables us to compare the relative contributions between baryon inhomogeneity and EM field on charge dependent directed flow. Our model calculation describes the experimental data on the centrality and system size dependence of the mid-rapidity directed flow slope splitting, $\Delta dv_1/dy$, between protons and anti-protons. Our results indicate that in central collisions, where the EM field strength is negligible, the inclusion of EM field effects does not influence the splitting between protons and anti-protons. This suggests that the observed system size dependence of $\Delta dv_1/dy (p-\bar{p})$ in central collisions arises solely from enhanced baryon stopping in larger collision systems. However, in semi-central and peripheral collisions, both baryon diffusion and EM field effects contribute to the splitting. Furthermore, the centrality dependence of $\Delta dv_1/dy (p-\bar{p})$ is highly sensitive to the electrical conductivity of the medium, making it a potential probe for extracting this transport coefficient in the QCD medium through model-to-data comparisons. However, achieving this requires a precise determination of the background baseline originating from baryon diffusion. Additionally, further investigation is needed to understand $\Delta dv_1/dy$ for oppositely charged kaons and pions, particularly by incorporating the diffusion of other conserved charges.