Free energy versus internal energy potential for heavy quark systems at finite temperature

TL;DR

This paper compares free energy and internal energy potentials for heavy quark systems at finite temperature, showing that the free energy potential accurately predicts the decreasing wave function strength of J/psi with temperature, resolving a long-standing debate.

Contribution

It demonstrates that the free energy potential aligns with lattice and Schrödinger equation results, clarifying which potential to use for heavy quark systems at finite temperature.

Findings

J/psi wave function strength decreases with temperature above transition

Free energy potential matches Schrödinger equation results

Internal energy potential predicts increased wave function strength

Abstract

Using the QCD sum rule with its operator product expansion reliably estimated from lattice calculations for the pressure and energy density of the quark-gluon plasma, we calculate the strength of the wave function of J/psi at the origin and find that it decreases with temperature above the transition temperature. This result is shown to follow exactly that obtained from the solution of the Schr\"odingier equation for a charm and anticharm quark pair using the free energy from lattice calculations as the potential and is in sharp contrast to that using the deeper potential associated with the internal energy, which shows an enhanced strength of the J/psi wave function at the origin. Our result thus has resolved the long-standing question of whether the free energy potential or the internal energy potential should be used in analyzing the spectrum of heavy quark systems at finite temperature.