# Wilson coefficients of dimension 6 gluon operators with spin indices in the heavy quark current correlation functions

## TL;DR

This paper computes the Wilson coefficients of dimension 6 gluon operators with spin indices in heavy quark current correlation functions, enhancing the understanding of QCD sum rules near the critical temperature.

## Contribution

It completes the list of Wilson coefficients for gluon operators up to dimension 6 in heavy quark current correlation functions, aiding in QCD sum rule analyses.

## Key findings

- Including dimension 6 operators improves sum rule stability.
- Sum rules break down slightly above T_c.
- J/ψ sum rule remains stable to higher temperatures.

## Abstract

We calculate the Wilson coefficients of dimension 6 gluon operators with spin indices in the two point correlation function of the heavy scalar, pseudoscalar, and axialvector currents. Our result completes the list of all Wilson coefficients of gluon operators up to dimension 6 for the correlation functions between heavy quark currents without derivatives. We then use the result to investigate the stability of the QCD sum rule results for the $\eta_c$, $J/\Psi$, $\chi_{c0}$, and $\chi_{c1}$ mesons near $T_c$. While the inclusion of the dimension 6 operators increases the stability of the sum rules for all currents, all of them break down slightly above $T_c$ with that for the $J/\psi$ persisting to relatively highest temperature.