Amplitudes for the n = 3 moment of the Wilson operator at two loops in the RI/'SMOM scheme

Abstract

The renormalization of the third moment of the twist-2 flavour non-singlet Wilson operator is given to two loops in the RI'/SMOM renormalization scheme. This involves renormalizing the operator itself and the two total derivative operators into which it mixes by inserting it into a quark 2-point function and evaluating the amplitudes at the symmetric subtraction point. The corresponding two loop conversion functions are derived from which the three loop Landau gauge anomalous dimension is deduced. The full set of amplitudes for the two loop Green's function for each of the operators are given in both the MSbar and RI'/SMOM schemes.

arXiv comment33 latex pages, 1 figure and anc directory containing txt file with anomalous dimensions, conversion functions and amplitudes in analytic form

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• Bilinear quark operators in the RI/SMOM scheme at three loops
• Nonperturbative Renormalization in Lattice QCD with three Flavors of Clover Fermions: Using Periodic and Open Boundary Conditions
• Two loop renormalization of the n = 2 Wilson operator in the RI'/SMOM scheme
• Moments $n=2$ and $n=3$ of the Wilson twist-two operators at three loops in the RI${}^{\prime }$/SMOM scheme
• Renormalization of non-singlet quark operator matrix elements for off-forward hard scattering
• Three-loop vertex integrals at symmetric point
• Renormalization of three-quark operators at two loops in the RI${}^{\prime }$/SMOM scheme
• Basis transformation properties of anomalous dimensions for hard exclusive processes