One-loop hybrid renormalization matching kernels for quasiparton distributions

Abstract

Large-momentum effective theory allows extraction of hadron parton distribution functions in lattice QCD by matching them to quark bilinear matrix elements of hadrons with large momenta. We calculate the matching kernels for the unpolarized, helicity, and transversity-isovector parton distribution functions and skewless generalized parton distributions of all hadrons in the hybrid-regularization-invariant momentum subtraction (RI/MOM) scheme. This renormalization scheme uses RI/MOM when the Wilson line length is less than ${z}_{s}$, otherwise a mass subtraction scheme is used. By design, the nonhybrid scheme is recovered as ${z}_{s}\ensuremath{\rightarrow}\ensuremath{\infty}$. In the opposite limit, ${z}_{s}\ensuremath{\rightarrow}0$, the self-renormalization scheme is obtained. When the parameters ${p}_{z}^{R}=0$ and ${\ensuremath{\mu}}^{R}{z}_{s}\ensuremath{\ll}1$, the hybrid-RI/MOM scheme coincides with the hybrid-ratio scheme times the charge of the PDF. We also discuss the subtlety related to the commutativity of Fourier transform and $\ensuremath{\epsilon}$ expansion in the $\overline{\mathrm{MS}}$ scheme.