Ballistic diffusion of heavy quarks in the early stage of relativistic heavy ion collisions at RHIC and LHC

We study the diffusion of charm quarks in the early stage of high energy nuclear collisions at the RHIC and the LHC. The main novelty of the present study is the introduction of the color current carried by the heavy quarks that propagate in the evolving Glasma (Ev-Glasma), that is responsible of the energy loss via polarization of the medium. We compute the transverse momentum broadening, $sigma_p$, of charm in the pre-thermalization stage, and the impact of the diffusion on the nuclear modification factor in nucleus-nucleus collisions. The net effect of energy loss is marginal in the pre-thermalization stage. The study is completed by the calculation of coordinate spreading, $sigma_x$, and by a comparison with Langevin dynamics. $sigma_p$ in Ev-Glasma overshoots the result of standard Langevin dynamics at the end of the pre-hydro regime. We interpret this as a result of memory of the color force acting on the charm quarks that implies $sigma_ppropto t^2$. Moreover, $sigma_xpropto t^2 $ in the pre-hydro stage shows that the charm quark in the Ev-Glasma is in the regime of ballistic diffusion.