Three-loop OPE Wilson coefficients of dimension-four operators for (axial-)vector and (pseudo-)scalar current correlators

A bstract We calculate the three-loop Wilson coefficients of all physically relevant dimension-four operators, i.e. $$ {G}_{\mu \nu}^a{G}^{a,\mu \nu} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>G</mml:mi> <mml:mi>μν</mml:mi> <mml:mi>a</mml:mi> </mml:msubsup> <mml:msup> <mml:mi>G</mml:mi> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>μν</mml:mi> </mml:mrow> </mml:msup> </mml:math> , $$ {m}_i{\overline{q}}_j{q}_j $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:msub> <mml:mover> <mml:mi>q</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>j</mml:mi> </mml:msub> <mml:msub> <mml:mi>q</mml:mi> <mml:mi>j</mml:mi> </mml:msub> </mml:math> and $$ {m}_i{m}_j{m}_k^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mi>k</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> , 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.