A path integral for heavy-quarks in a hot plasma

TL;DR

This paper develops a quantum mechanical path integral model for heavy-quark propagation in a hot plasma, using numerical and semi-analytical methods to analyze spectral functions and medium interactions.

Contribution

It introduces a novel path integral approach for heavy-quark dynamics in a quark-gluon plasma, incorporating medium effects via a hard thermal loop approximation and employing Monte Carlo and Maximum Entropy techniques.

Findings

Path integral formulation of heavy-quark propagation.

Numerical Monte Carlo calculation of spectral functions.

Semi-analytical one-loop analysis of quark-plasma coupling.

Abstract

We propose a model for the propagation of a heavy-quark in a hot plasma, to be viewed as a first step towards a full description of the dynamics of heavy quark systems in a quark-gluon plasma, including bound state formation. The heavy quark is treated as a non relativistic particle interacting with a fluctuating field, whose correlator is determined by a hard thermal loop approximation. This approximation, which concerns only the medium in which the heavy quark propagates, is the only one that is made, and it can be improved. The dynamics of the heavy quark is given exactly by a quantum mechanical path integral that is calculated in this paper in the Euclidean space-time using numerical Monte Carlo techniques. The spectral function of the heavy quark in the medium is then reconstructed using a Maximum Entropy Method. The path integral is also evaluated exactly in the case where the mass of the heavy quark is infinite; one then recovers known results concerning the complex optical potential that controls the long time behavior of the heavy quark. The heavy quark correlator and its spectral function is also calculated semi-analytically at the one-loop order, which allows for a detailed description of the coupling between the heavy quark and the plasma collective modes.