Kernel methods for evolution of generalized parton distributions

TL;DR

This paper introduces finite element methods to efficiently compute the scale evolution of generalized parton distributions (GPDs) in momentum space, facilitating their integration into machine learning frameworks for hadron structure analysis.

Contribution

It develops and benchmarks a finite element-based approach for fast, differentiable GPD evolution in Q^2, enabling improved computational tools for hadron structure studies.

Findings

Finite element methods achieve high accuracy in GPD evolution.

The approach is faster and more differentiable than existing codes.

Code is publicly available for community use.

Abstract

Generalized parton distributions (GPDs) characterize the 3-dimensional structure of hadrons, combining information about their internal quark and gluon longitudinal momentum distributions and transverse position within the hadron. The dependence of GPDs on the factorization scale $Q^2$ allows one to connect hard exclusive processes involving GPDs at disparate energy and momentum scales, which is needed in global analyses of experimental data. In this work we explore how finite element methods can be used to construct fast and differentiable $Q^2$ evolution codes for GPDs in momentum space, which can be used in a machine learning framework. We show numerical benchmarks of the methods' accuracy, including a comparison to an existing evolution code from PARTONS/APFEL++, and provide a repository where the code can be accessed.