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

TL;DR

This paper computes three-loop Wilson coefficients for dimension-four operators in the short-distance expansion of current correlators in a general non-Abelian gauge theory, including QCD, with detailed flavor and gauge group considerations.

Contribution

It provides the first complete three-loop calculation of Wilson coefficients for all relevant dimension-four operators in a general gauge theory, extending previous lower-order results.

Findings

Results applicable to QCD and other non-Abelian gauge theories.

Consistent inclusion of axial anomaly contributions.

Provides explicit formulas for Wilson coefficients at three-loop order.

Abstract

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.