Heavy quarks in the early stage of high energy nuclear collisions at RHIC and LHC: Brownian motion versus diffusion in the evolving Glasma

We study the transverse momentum, $p_T$, broadening of charm and beauty quarks in the early stage of high energy nuclear collisions. We aim to compare the diffusion in the evolving Glasma fields with that of a standard, Markovian-Brownian motion in a thermalized medium with the same energy density of the Glasma fields. The Brownian motion is studied via Langevin equations with diffusion coefficients computed within perturbative Quantum Chromodynamics. We find that for small values of the saturation scale, $Q_s$, the average $p_T$ broadening in the two motions is comparable, that suggests that the diffusion coefficient in the evolving Glasma fields is in agreement with the perturbative calculations. On the other hand, for large $Q_s$ the $p_T$ broadening in the Langevin motion is smaller than that in the Glasma fields. This difference can be related to the fact that heavy quarks in the latter system experience diffusion in strong, coherent gluon fields that leads to a faster momentum broadening due to memory, or equivalently to a strong correlation in the transverse plane.