Directed flow of D mesons at RHIC and LHC: non-perturbative dynamics, longitudinal bulk matter asymmetry and electromagnetic fields

We present a study of the directed flow $v_1$ for $D$ mesons discussing both the impact of initial vorticity and electromagnetic field. Recent studies predicted that $v_1$ for $D$ mesons is expected to be surprisingly much larger than that of light charged hadrons; we clarify that this is due to a different mechanism leading to the formation of a directed flow with respect to the one of the bulk matter at both relativistic and non-relativistic energies. We point out that the very large $v_1$ for $D$ mesons can be generated only if there is a longitudinal asymmetry between the bulk matter and the charm quarks and if the latter have a large non-perturbative interaction in the QGP medium. A quite good agreement with the data of STAR and ALICE is obtained if the diffusion coefficient able to correctly predict the $R_{AA}(p_T)$, $v_{2}(p_T)$ and $v_{3}(p_T)$ of $D$ meson is employed. Furthermore, the mechanism for the build-up of the $v_1(y)$ is associated to a quite small formation time that can be expected to be more sensitive to the initial high-temperature dependence of the charm diffusion coefficient. We discuss also the splitting of $v_1$ for $D^0$ and $\bar D^0$ due to the electromagnetic field that is again much larger than the one observed for charged particles and in agreement with the data by STAR that have however still error bars comparable with the splitting itself, while at LHC standard electromagnetic profile assuming a constant conductivity is not able to account for the huge splitting observed.