Bilinear quark operators in the RI/SMOM scheme at three loops

Abstract

We consider the renormalization of the matrix elements of the bilinear quark operators $\bar{\psi }\psi$, $\bar{\psi }{\gamma }_{\mu }\psi$, and $\bar{\psi }{\sigma }_{\mu \nu }\psi$ 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) scheme. The obtained results can be used to reduce the errors in determinations of quark masses from lattice QCD simulations. The results are given in Landau gauge.

Comments: 9 pages, 1 figure, minor changes, matches journal version