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

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 $ {{\mathop{O}\limits^{\sim}}_1}={G^{{\mu v}}}\;{{\mathop{G}\limits^{\sim}}_{{\mu v}}} $ . The Wilson coefficient in front of the scalar gluon condensate operator $ {O_1}=-\frac{1}{4}{G^{{\mu v}}}{G_{{^{{\mu v}}}}} $ 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 [1] 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 [2]. 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 $ \overline{\mathrm{MS}}-\mathrm{scheme} $ at zero temperature.