D meson mass and heavy quark potential at finite temperature

Philipp Gubler,Su Houng Lee,Taesoo Song

doi:10.1103/physrevd.101.114029

Abstract

Based on the observation that the heavy quark-antiquark potential value at infinity corresponds to twice the D meson mass, we constrain the asymptotic value of the heavy quark potential in a hot medium through a QCD sum rule calculation of the D meson at finite temperature. We find that to correctly reproduce the QCD sum rule results as well as a recent model calculation for the D meson mass near the critical temperature, the heavy quark potential should be composed mostly of the free energy with an addition of a small but nontrivial fraction of the internal energy. Combined with a previous study comparing potential model results for the $J/\psi$ to a QCD sum rule calculation, we conclude that the composition of the effective heavy quark potential should depend on the inter-quark distance. Namely, the potential is dominated by the free energy at short distance, while at larger separation, it has a fraction of about 20% of internal energy.

Highlights

Quarkonium is a colorless and flavorless bound state of a heavy quark and its antiquark
Combined with our previous results for the heavy quark potential obtained by comparing the potential model result for the J=ψ to the quantum chromodynamics (QCD) sum rule calculation, we conclude that the effective heavy quark potential is dominated by the free energy at short distance, while at larger separation, it has a non-negligible fraction of the internal energy
We find that fitting the results in the potential model to the D meson mass obtained from QCD sum rules with either a constant or temperature dependent Borel window requires the heavy quark potential to be composed of 18% and 21% of internal energy potentials, respectively, with the remaining contribution coming from the free energy potential

Summary

INTRODUCTION

Quarkonium is a colorless and flavorless bound state of a heavy quark and its antiquark. The solutions from the internal energy potential significantly overestimate both quantities This comparison led to the conclusion that the free energy is the appropriate choice for the heavy quark potential at finite temperature rather than the internal energy, which is consistent with recent lattice results extracted from the spectral functions of Wilson line correlators [9]. Combined with our previous results for the heavy quark potential obtained by comparing the potential model result for the J=ψ to the QCD sum rule calculation, we conclude that the effective heavy quark potential is dominated by the free energy at short distance, while at larger separation, it has a non-negligible fraction of the internal energy.

D MESON MASS FROM HEAVY QUARK POTENTIAL

D MESON MASS FROM QCD SUM RULES

MATCHING THE HEAVY QUARK POTENTIAL TO QCD SUM RULES

Findings

SUMMARY AND CONCLUSIONS