A path integral for heavy-quarks in a hot plasma

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.

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• Heavy quark bound states in a quark-gluon plasma: dissociation and recombination
• Bottomonium above deconfinement in lattice nonrelativistic QCD
• $T$-matrix Approach to Quark-Gluon Plasma
• Phase transitions and gluodynamics in 2-colour matter at high density
• S wave bottomonium states moving in a quark-gluon plasma from lattice NRQCD
• The Imaginary Part of the Static Potential in Strongly Coupled Anisotropic Plasma
• The Imaginary Potential of Heavy Quarkonia Moving in Strongly Coupled Plasma
• Strong Diffusion Effect of Charm Quarks on $J/\psi$ Production in Pb-Pb collisions at the LHC
• Heavy Quark Momentum Broadening in a Non-Abelian Plasma away from Thermal Equilibrium
• From Complex to Stochastic Potential: Heavy Quarkonia in the Quark-Gluon Plasma
• News on hadrons in a hot medium
• Bottomonium from lattice QCD as a probe of the Quark-Gluon Plasma
• Heavy Quark and Quarkonium Transport in High Energy Nuclear Collisions
• Dissipative effects on quarkonium spectral functions