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

TL;DR

This paper investigates how memory effects in thermal noise influence the energy loss, diffusion, and thermalization of heavy quarks in a quark-gluon plasma, revealing that memory generally slows down their momentum evolution.

Contribution

It introduces an integro-differential Langevin equation with exponential memory decay to study heavy quark dynamics in quark-gluon plasma, highlighting the impact of memory on thermalization and momentum broadening.

Findings

Memory effects slow down heavy quark momentum evolution.

Thermalization time of heavy quarks increases with memory.

Momentum broadening and $R_{AA}$ formation are delayed by memory.

Abstract

We study the dynamics of heavy quarks in a thermalized quark-gluon plasma with a time-correlated thermal noise, $\eta$. In this case it is said that $\eta$ 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 time scale, $\tau$, that we treat as a free parameter. We compute the effects of $\tau\neq 0$ 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.