Connecting Euclidean to light-cone correlations: From flavor nonsinglet in forward kinematics to flavor singlet in non-forward kinematics

TL;DR

This paper develops a comprehensive framework for connecting Euclidean lattice correlators to light-cone distributions like GPDs, PDFs, and DAs, enabling more accurate extraction of partonic structures from lattice QCD.

Contribution

It derives the next-to-leading-order hard-matching kernels for both flavor singlet and non-singlet cases in various kinematic regimes, unifying the perturbative connection between Euclidean and light-cone correlations.

Findings

Provides explicit NLO matching kernels for GPDs, PDFs, and DAs.

Clarifies issues in perturbative GPD matching literature.

Offers a complete manual for lattice extraction of leading-twist distributions.

Abstract

We present a unified framework for the perturbative factorization connecting Euclidean correlations to light-cone correlations. Starting from nonlocal quark and gluon bilinear correlators, we derive the relevant hard-matching kernel up to the next-to-leading-order, both for the flavor singlet and non-singlet combinations, in non-forward and forward kinematics, and in coordinate and momentum space. The results for the generalized distribution functions (GPDs), parton distribution functions (PDFs), and distribution amplitudes (DAs) are obtained by choosing appropriate kinematics. The renormalization and matching are done in a state-of-the-art scheme. We also clarify some issues raised on the perturbative matching of GPDs in the literature. Our results provide a complete manual for extracting all leading-twist GPDs, PDFs as well as DAs from lattice simulations of Euclidean correlations in a state-of-the-art strategy, either in coordinate or in momentum space factorization approach.