Three-Loop OPE Wilson Coefficients of Dimension-Four Operators for (Axial-)Vector and (Pseudo-)Scalar Current Correlators

We calculate the three-loop Wilson coefficients of all physically relevant dimension-four operators, i.e. $G_{\mu \nu }^a{G}^{a,\mu \nu }$, $m_i{\bar{q}}_j{q}_j$ and $m_i{m}_j{m}_k^2$, in the short-distance expansion of the time-ordered product of a pair of gauge-singlet vector, axial-vector, scalar and pseudo-scalar currents. The results are given for a general non-Abelian gauge theory with arbitrary (compact semi-simple) gauge group and $n_f$ light fermion flavors (quarks) in a common arbitrary representation of the gauge group, which includes QCD as a special case. In particular, we allow for arbitrary flavor contents of each of the currents. For the axial-vector current the included contributions from so-called singlet diagrams are consistent with the one-loop axial anomaly.