Renormalization of non-singlet quark operator matrix elements for off-forward hard scattering

TL;DR

This paper computes the renormalization and anomalous dimensions of non-singlet quark operators in off-forward deep-inelastic scattering, extending previous work to include operators with total derivatives and high-order perturbative results.

Contribution

It provides the first calculation of the anomalous dimension matrix for off-forward matrix elements including total derivatives up to fifth order in perturbation theory.

Findings

Anomalous dimension matrix determined to fifth order in $ar{MS}$ scheme.

Extension of previous zero-momentum transfer calculations to off-forward kinematics.

Identification of operator mixing with total derivatives under renormalization.

Abstract

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 $n_f$ and for low moments in full QCD, we determine the anomalous dimension matrix to fifth order in the perturbative expansion in the strong coupling $\alpha_s$ in the $\overline{\mbox{MS}}$-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.