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

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 ${\tilde{O}}_1={\epsilon }_{\mu \nu \rho \sigma }{G}^{\mu \nu }{G}^{\rho \sigma }$ 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.

Comments: v2: typos fixed: sign error in (2.18) and (2.19) corrected; all calculated results stay untouched; Note added about the origin of the contact terms in the scalar gluonic correlator