Factorization Theorem Relating Euclidean and Light-Cone Parton Distributions

TL;DR

This paper proves a factorization theorem linking Euclidean Wilson line matrix elements from lattice QCD to light-cone parton distributions using LaMET, with explicit one-loop matching coefficients and scheme dependence analysis.

Contribution

It provides a rigorous proof of the large-momentum factorization in LaMET and extends the theorem to Ioffe-time distributions, including explicit coefficient calculations.

Findings

Established the large-momentum factorization theorem for quasi-PDFs.

Derived explicit one-loop matching coefficients in the $ar{MS}$ scheme.

Showed the scheme dependence of matching coefficients on partonic momentum.

Abstract

In a large-momentum nucleon state, the matrix element of a gauge-invariant Euclidean Wilson line operator accessible from lattice QCD can be related to the standard light-cone parton distribution function through the large-momentum effective theory (LaMET) expansion. This relation is given by a factorization theorem with a non-trivial matching coefficient. Using the operator product expansion we prove the large-momentum factorization of the quasi-parton distribution function in LaMET, and show that the more recently discussed Ioffe-time distribution approach also obeys an equivalent factorization theorem. Explicit results for the coefficients are obtained and compared at one-loop. Our proof clearly demonstrates that the matching coefficients in the $\overline{\rm MS}$ scheme depend on the large partonic momentum rather than the nucleon momentum.