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 μν. 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 μν-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 μν 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.
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Zoller, M.F. OPE of the energy-momentum tensor correlator and the gluon condensate operator in massless QCD to three-loop order. J. High Energ. Phys. 2014, 169 (2014). https://doi.org/10.1007/JHEP10(2014)169
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DOI: https://doi.org/10.1007/JHEP10(2014)169