Resummation for Lattice QCD Calculation of Generalized Parton Distributions at Nonzero Skewness

TL;DR

This paper develops a resummation method for large-momentum effective theory calculations of generalized parton distributions at nonzero skewness, improving the reliability of lattice QCD predictions by addressing multi-scale logarithmic effects.

Contribution

The authors derive a threshold factorization formula and propose a resummation approach for off-forward matrix elements at nonzero skewness in LaMET, enhancing the precision of GPD calculations.

Findings

Resummation improves the reliability of LaMET predictions for GPDs.

The method is self-consistent and prevents nonperturbative effects from contaminating perturbative regions.

Numerical tests confirm the effectiveness of the resummation approach.

Abstract

Large-momentum effective theory (LaMET) provides an approach to directly calculate the $x$-dependence of generalized parton distributions (GPDs) on a Euclidean lattice through power expansion and a perturbative matching. When a parton's momentum becomes soft, the corresponding logarithms in the matching kernel become non-negligible at higher orders of perturbation theory, which requires a resummation. But the resummation for the off-forward matrix elements at nonzero skewness $\xi$ is difficult due to their multi-scale nature. In this work, we demonstrate that these logarithms are important only in the threshold limit, and derive the threshold factorization formula for the quasi-GPDs in LaMET. We then propose an approach to resum all the large logarithms based on the threshold factorization, which is implemented on a GPD model. We demonstrate that the LaMET prediction is reliable for $[-1+x_0,-\xi-x_0]\cup[-\xi+x_0,\xi-x_0]\cup[\xi+x_0,1-x_0]$, where $x_0$ is a cutoff depending on hard parton momenta. Through our numerical tests with the GPD model, we demonstrate that our method is self-consistent and that the inverse matching does not spread the nonperturbative effects or power corrections to the perturbatively calculable regions.