One-Loop Matching for Generalized Parton Distributions

TL;DR

This work derives the one-loop matching conditions between spacelike quasi-GPDs and light-cone GPDs for nonsinglet quarks, covering unpolarized ($H$ and $E$) and polarized ($\tilde H$ and $\tilde E$) distributions. The authors show that the matching for $H$ and $\tilde H$ is nontrivial and encodes the UV behavior consistent with the light-cone evolution kernels, while the matching for $E$ and $\tilde E$ is trivial at this order, enabling a smooth large-$p^z$ limit from the quasi to the light-cone distributions. They provide explicit one-loop factorization kernels $Z_H$ and, via crossing, $Z_\phi$ for the pion distribution amplitude, including their regional (DGLAP/ERBL) structures and plus-prescription features. The results support lattice QCD extraction of light-cone GPDs from quasi-GPDs and extend to the pion distribution amplitude, offering a practical framework for obtaining $H,\tilde H$ and $\phi$ from Euclidean simulations. Overall, the paper clarifies which GPDs require nontrivial matching and which can be approached directly in the large-momentum limit, with implications for phenomonology and lattice studies.

Abstract

We present the one-loop matching condition for the unpolarized and polarized generalized quark distributions in the non-singlet case. The matching condition links the quasi distributions defined in terms of spacelike correlators at finite nucleon momentum to the light-cone distributions, and is useful for extracting the latter from the former in a lattice QCD calculation. Our results show that at one-loop and leading power accuracy the matching for the light-cone generalized quark distribution $H$ ($\tilde H$) is non-trivial, whereas no matching is required for $E$ ($\tilde E$). Therefore, $E$ ($\tilde E$) can be smoothly approached by its quasi counterpart in the large momentum limit. We also present the matching for the distribution amplitude of the pion.

Figures (1)

• Figure 1: One-loop diagrams for GPDs in the axial gauge.