Memory effects on energy loss and diffusion of heavy quarks in the quark-gluon plasma

Abstract

We study the dynamics of heavy quarks in a thermalized quark-gluon plasma with a time-correlated thermal noise, $\ensuremath{\eta}$. In this case, it is said that $\ensuremath{\eta}$ has memory. We use an integro-differential Langevin equation in which the memory enters via the thermal noise and the dissipative force. We assume that the time correlations of the noise decay exponentially on a timescale, $\ensuremath{\tau}$, which we treat as a free parameter. We compute the effects of $\ensuremath{\tau}\ensuremath{\ne}0$ on the thermalization time of the heavy quarks, on their momentum broadening, and on the nuclear modification factor. We find that overall memory slows down the momentum evolution of heavy quarks: In fact, transverse momentum broadening and the formation of ${R}_{AA}$ are slowed down by memory and the thermalization time of the heavy quarks become larger. The potential impact on other observables is discussed briefly.