Unraveling Generalized Parton Distributions Through Lorentz Symmetry and Partial DGLAP Knowledge

TL;DR

This paper demonstrates that generalized parton distributions can be uniquely reconstructed across their entire support from low-skewness data using Lorentz symmetry, with practical methods like neural networks and finite elements, aiding experimental and lattice QCD analyses.

Contribution

It introduces a method to extend GPDs from low to full skewness using polynomiality and Lorentz covariance, validated with neural networks and finite-element techniques.

Findings

Accurate GPD reconstructions at skewness as low as 20%.

Validation against standard models confirms the method's effectiveness.

Potential application in experimental and lattice QCD data analysis.

Abstract

Relying on the polynomiality property of generalized parton distributions, which roots on Lorentz covariance, we prove that it is enough to know them at vanishing- and low-skewness within the DGLAP region to obtain a unique extension to their entire support up to a D-term. We put this idea in practice using two methods: Reconstruction using artificial neural networks and finite-elements methods. We benchmark our results against standard models for generalized parton distributions. In agreement with the formal expectation, we obtain a very accurate reconstructions for a maximal value of the skewness as low as 20% of the longitudinal momentum fraction. This result might be relevant for reconstruction of generalized parton distribution from experimental and lattice QCD data, where computations are for now, restricted in skewness.