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

We study the dynamics of heavy quarks in a thermalized quark-gluon plasma with a time-correlated thermal noise, η. In this case, it is said that η 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, τ, which we treat as a free parameter. We compute the effects of τ≠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 RAA are slowed down by memory and the thermalization time of the heavy quarks become larger. The potential impact on other observables is discussed briefly.