Moments $n=2$ and $n=3$ of the Wilson twist-two operators at three loops in the RI${}^{\prime }$/SMOM scheme

Abstract

We study the renormalization of the matrix elements of the twist-two non-singlet bilinear quark operators, contributing to the $n=2$ and $n=3$ moments of the structure functions, at next-to-next-to-next-to-leading order in QCD perturbation theory at the symmetric subtraction point. This allows us to obtain conversion factors between the $\overline{\mathrm{MS}}$ scheme and the regularization-invariant symmetric momentum subtraction (RI/SMOM, RI${}^{\prime }$/SMOM) schemes. The obtained results can be used to reduce errors in determinations of moments of structure functions from lattice QCD simulations. The results are given in Landau gauge.

14 pages, 1 figure, minor changes, references added, matches journal version

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Cited by in corpus (7)

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• Renormalization of non-singlet quark operator matrix elements for off-forward hard scattering
• Three-loop vertex integrals at symmetric point
• Moments of Nucleon Unpolarized, Polarized, and Transversity Parton Distribution Functions from Lattice QCD at the Physical 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