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

Abstract

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 (EG), which is responsible of the energy loss via polarization of the medium. We compute the transverse momentum broadening, ${\ensuremath{\sigma}}_{p}$, of charm in the prethermalization 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 prethermalization stage. The study is completed by the calculation of coordinate spreading, ${\ensuremath{\sigma}}_{x}$, and by a comparison with Langevin dynamics. ${\ensuremath{\sigma}}_{p}$ in EG overshoots the result of standard Langevin dynamics at the end of the prehydro regime. We interpret this as a result of memory of the color force acting on the charm quarks that implies ${\ensuremath{\sigma}}_{p}\ensuremath{\propto}{t}^{2}$. Moreover, ${\ensuremath{\sigma}}_{x}\ensuremath{\propto}{t}^{2}$ in the prehydro stage shows that the charm quark in the EG is in the regime of ballistic diffusion.