| Summary: | We calculate non-singlet quark operator matrix elements of deep-inelastic scattering in the chiral limit including operators with total derivatives. This extends previous calculations with zero-momentum transfer through the operator vertex which provides the well-known anomalous dimensions for the evolution of parton distributions, as well as calculations in off-forward kinematics utilizing conformal symmetry. Non-vanishing momentum-flow through the operator vertex leads to mixing with total derivative operators under renormalization. In the limit of a large number of quark flavors nf and for low moments in full QCD, we determine the anomalous dimension matrix to fifth order in the perturbative expansion in the strong coupling αs in the MS‾-scheme. We exploit consistency relations for the anomalous dimension matrix which follow from the renormalization structure of the operators, combined with a direct calculation of the relevant diagrams up to fourth order.
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