$J/\psi$ near $T_c$

TL;DR

This paper investigates the mass shift and thermal decay width of the $J/\psi$ meson near the QCD transition temperature, combining Schrödinger equation solutions and QCD sum rule constraints to predict its melting point.

Contribution

It introduces a novel combined approach using Schrödinger equation and QCD sum rules to analyze $J/\psi$ properties near $T_c$, providing new insights into its melting behavior.

Findings

$J/\psi$ melts slightly above $T_c$ at around 1.09$T_c$

Binding energy and thermal width become comparable at this temperature

Sum rule analysis becomes unstable above this temperature

Abstract

We calculate the mass shift and thermal decay width of the $J/\psi$ near the QCD transition temperature $T_c$ by imposing two independent constraints on these variables that can be obtained first by solving the Schr\"odinger equation and second from the QCD sum rule approach. While the real part of the potential is determined by comparing the QCD sum rule result for charmonium and the D meson to that from the potential model result, the imaginary potential is taken to be proportional to the perturbative form multiplied by a constant factor, which in turn can be determined by applying the two independent constraints. The result shows that the binding energy and the thermal width becomes similar in magnitude at around $T=1.09T_c$, above which the sum rule analysis also becomes unstable, strongly suggesting that the $J/\psi$ will melt slightly above $T_c$.