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

A bstract 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 = − 1 4 G μ ν G μ ν and two QCD energy-momentum tensors T μ ν . 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 = was already presented in [ 1 ] for the T μ ν -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 Õ 1 = ε μνρσ G μ ν G ρσ 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.