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

Marco Ruggieri, Pooja Khowal+2 more|arXiv (Cornell University)|Mar 13, 2022

High-Energy Particle Collisions Research64 references40 citations

TL;DR

This paper investigates the impact of memory effects—time-correlated thermal noise—on heavy quark dynamics in the quark-gluon plasma using a generalized Langevin equation with an exponential memory kernel. It finds that memory slows down momentum equilibration, increases thermalization time, reduces momentum broadening, and delays the evolution of the nuclear modification factor RAA, implying stronger quark-medium interactions are needed to fit experimental data.

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, $ au$, that we treat as a free parameter. We compute the effects of $ au eq 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.

Motivation & Objective

• To study the influence of time-correlated thermal noise (memory) on heavy quark energy loss and diffusion in the quark-gluon plasma.
• To extend standard Langevin approaches by replacing white noise with colored noise decaying over a finite memory time τ.
• To quantify how memory affects key observables: thermalization time, momentum broadening, and the nuclear modification factor RAA.
• To explore the phenomenological implications for heavy quark dynamics in relativistic heavy-ion collisions.

Proposed method

• Uses an integro-differential Langevin equation with a memory kernel in both the dissipative force and thermal noise.
• Models the thermal noise with an exponential correlator ⟨η(t1)η(t2)⟩ = 2D f(t1−t2), where f(t) = (1/(2τ)) e^(-|t|/τ), introducing a finite memory time τ.
• Applies the Fluctuation-Dissipation Theorem to relate the memory kernel to the noise correlator.
• Employs Laplace transforms to analytically solve for the momentum evolution and compute ⟨p(t)⟩ and σp.
• Numerically evaluates the thermalization time and RAA evolution for varying τ, treating τ as a free parameter.
• Uses pQCD and quasiparticle model (QPM) for diffusion and drag coefficients at high and low temperatures, respectively.

Experimental results

Research questions

• RQ1 How does the presence of memory in the thermal noise affect the thermalization time of heavy quarks in the QGP?
• RQ2 To what extent does memory reduce momentum broadening in heavy quark dynamics?
• RQ3 How does memory influence the time evolution of the nuclear modification factor RAA?
• RQ4 What is the impact of memory on the effective interaction strength required to reproduce experimental RAA data?
• RQ5 Can memory effects explain slower equilibration and delayed RAA formation in heavy-ion collisions?

Key findings

• Memory slows down the momentum evolution of heavy quarks, increasing the thermalization time compared to the Markovian (τ=0) case.
• Transverse momentum broadening is reduced due to memory, as the momentum relaxation becomes slower.
• The nuclear modification factor RAA evolves more slowly with memory, requiring larger diffusion coefficients to match experimental data.
• For τ ≪ 1/γ, the pre-thermalization regime shows quadratic decay ⟨p(t)⟩ ≈ p₀(1 − γt²/(2τ)) instead of linear decay, indicating delayed equilibration.
• The full solution of the Langevin equation with memory kernel confirms that thermalization is slower than in the white noise limit.
• The results suggest that memory effects may lead to larger elliptic flow v₂ for heavy quarks if stronger interactions are assumed.