Sum Rules for Nucleon GPDs and Border Function Formulation

TL;DR

This paper introduces a novel approach to modeling nucleon GPDs using double distributions, deriving sum rules that relate border functions to full GPDs, and analyzing their connection to parton densities.

Contribution

It presents a new representation-based method for GPD sum rules, emphasizing border functions and their relation to parton densities.

Findings

Border functions H(x,x) receive significant contributions from additional terms.

Derived sum rules enable using border functions instead of full GPDs in scattering calculations.

Relation between border functions and parton densities is clarified.

Abstract

The newy developed approach to model nucleon generalized parton distributions (GPDs) H and E$ is based on two types of their representation in terms of double distributions. Within this approach, we re-consider the derivation of GPD sum rules that allow to use border functions H(x,x) and E(x,x) instead of full GPDs H(x,\xi) and E(x,\xi) in the integrals producing Compton form factors of deeply virtual Compton scattering. Using factorized DD Ansatz to model GPDs, we discuss the relation between the border functions and underlying parton densities. We find that a substantial contribution to H(x,x) border function comes from the extra term required by new DD representations and related to E(x,\xi) GPD.