OPE of the energy-momentum tensor correlator and the gluon condensate operator in massless QCD to three-loop order

TL;DR

This paper extends the operator product expansion of the gluonic operator correlator in massless QCD to three-loop order, providing more precise Wilson coefficients crucial for understanding QGP transport and glueball sum rules.

Contribution

It presents the first three-loop order calculation of the Wilson coefficient for the gluon condensate operator in the energy-momentum tensor correlator in massless QCD.

Findings

Extended the OPE to three-loop order for the gluonic correlator.

Provided analytical expressions for Wilson coefficients at higher loop orders.

Enhanced the precision of theoretical tools for QGP and glueball studies.

Abstract

The correlator of two gluonic operators plays an important role for example in transport properties of a Quark Gluon Plasma (QGP) or in sum rules for glueballs. In [1] an operator product expansion (OPE) at zero temperature was performed for the correlators of two scalar operators $O_1=-\frac{1}{4} G^{\mu \nu}G_{\mu \nu}$ and two QCD energy-momentum tensors $T^{\mu\nu}$. There we presented analytical two-loop results for the Wilson coefficient $C_1$ in front of the gluon condensate operator $O_1$. In this paper these results are extended to three-loop order. The three-loop Wilson coefficient $C_0$ in front of the unity operator $O_0=1$ was already presented in [1] for the $T^{\mu\nu}$-correlator. For the $O_1$-correlator the coefficient $C_0$ is known to four loop order from [2]. For the correlator of two pseudoscalar operators $\tilde{O}_1=\varepsilon_{\mu\nu\rho\sigma} G^{\mu \nu} G^{\rho \sigma}$ both coefficients $C_0$ and $C_1$ were computed in [3] to three-loop order. At zero temperature $C_0$ and $C_1$ are the leading Wilson coefficients in massless QCD.