Real and imaginary-time $Q\bar{Q}$ correlators in a thermal medium

Abstract

We investigate the behavior of a pair of heavy fermions, denoted by $Q$ and $\bar{Q}$, in a hot/dense medium. Although we have in mind the situation where $Q$ and $\bar{Q}$ denote heavy quarks, our treatment will be limited to simplified models, which bear only some general similarities with QCD. We study in particular the limiting case where the mass of the heavy fermions is infinite. Then a number of results can be derived exactly: a Schrödinger equation can be established for the correlator of the heavy quarks; the interaction effects exponentiate, leading to a simple instantaneous effective potential for this Schrödinger equation. We consider simple models for the medium in which the $Q\bar{Q}$ pair propagates. In the case where the medium is a plasma of photons and light charged fermions, an imaginary part develops in this effective potential. We discuss the physical interpretation of this imaginary part in terms of the collisions between the heavy particles and the light fermions of the medium; the same collisions also determine the damping rate of the heavy fermions. Finally we study the connection between the real-time propagator of the heavy fermion pair and its Euclidean counterpart, and show that the real part of the potential entering the Schrödinger equation for the real-time propagator is the free energy calculated in the imaginary-time formalism.

32 pages, 8 figures

References in corpus (35)

• JaxoDraw: A graphical user interface for drawing Feynman diagrams
• Effective field theories for heavy quarkonium
• Real-time static potential in hot QCD
• The Quark-Gluon Plasma: Collective Dynamics and Hard Thermal Loops
• $J/\psi$ and ${\eta }_c$ in the Deconfined Plasma from Lattice QCD
• Behavior of Charmonium Systems after Deconfinement
• Quarkonium Feed-Down and Sequential Suppression
• Towards a Theory of Binary Bound States in the Quark-Gluon Plasma
• Quarkonium Interactions in Hadronic Matter
• Color Screening Melts Quarkonium
• Heavy Quarkonia in Quark-Gluon Plasma
• Quarkonium correlators and spectral functions at zero and finite temperature
• Charmonium at high temperature in two-flavor QCD
• Can quarkonia survive deconfinement ?
• String Breaking and Quarkonium Dissociation at Finite Temperatures
• Damping rates for moving particles in hot QCD
• A resummed perturbative estimate for the quarkonium spectral function in hot QCD
• J/Psi Suppression in an Equilibrating Parton Plasma
• Thermal imaginary part of a real-time static potential from classical lattice gauge theory simulations
• Lifetimes of quasiparticles and collective excitations in hot QED plasmas
• Heavy quark bound states above $T_c$
• Bottomonium Production at RHIC and LHC
• Quarkonia in the deconfined phase: effective potentials and lattice correlators
• Hadronic Modes and Quark Properties in the Quark-Gluon Plasma
• Dissociation of a Heavy Quarkonium at High Temperatures
• The Bloch-Nordsieck propagator at finite temperature
• The widths of quarkonia in quark gluon plasma
• Quarkonium-hadron interactions in QCD
• Potential models and lattice correlators for quarkonia at finite temperature
• Non-perturbative Quarkonium Dissociation in Hadronic Matter
• Damping Rate of a Yukawa Fermion at Finite Temperature
• Dissociation of Heavy Quarkonia in the Quark-Gluon Plasma
• Quarkonia and Quark Drip Lines in Quark-Gluon Plasma
• Describing Charmonium Correlation Functions in Euclidean Time
• Quarkonium correlators at finite temperature and potential models

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