OPE of the pseudoscalar gluonium correlator in massless QCD to three-loop order

TL;DR

This paper computes higher order quantum corrections to the operator product expansion of the pseudoscalar gluonium correlator in massless QCD, providing three-loop results and extending some coefficients to four-loop accuracy in the MSbar scheme.

Contribution

It presents the first three-loop calculations of the Wilson coefficients for the pseudoscalar gluonium correlator and extends some results to four-loop order, enhancing precision in QCD analyses.

Findings

The Wilson coefficient C_1 is finite at three-loop order.

Contact terms appear in C_0 and C_1 coefficients.

Results are provided in the MSbar scheme at zero temperature.

Abstract

In this paper analytical results are presented for higher order corrections to coefficient functions of the operator product expansion (OPE) for the correlator of two pseudoscalar gluonium operators \tilde{O}_1=G^{\mu \nu}\tilde{G}_{\mu \nu}. The Wilson coefficient in front of the scalar gluon condensate operator O_1=-1/4 G^{\mu \nu}G_{\mu \nu} is given at three-loop accuracy. The leading coefficient C_0 in front of the unity operator O_0=1 has been calculated up to three-loop order some time ago but has been checked independently in this work. It is interesting to see that the coefficient C_1 in the pseudoscalar case is finite, whereas contact terms appear in C_0 in this case and in both coefficients C_0 and C_1 in the cases of the scalar gluonium correlator and the energy momentum tensor correlator. For the corresponding Renormalization Group invariant Wilson coefficients which are also constructed the results are partially extended to four-loop accuracy. All results are given in the MSbar-scheme at zero temperature.