Generalized Parton Distributions and Their Singularities

TL;DR

This paper introduces a novel approach to modeling generalized parton distributions (GPDs) using a single-double distribution formalism, addressing singularities at zero momentum fraction and ensuring finite, continuous GPDs at the border point.

Contribution

It develops a new method for constructing GPD models that regulate singularities at zero and introduces a separation technique for deriving GPD sum rules.

Findings

Regulated singularities at β=0 using dispersion relations.

Constructed finite, continuous GPDs at the border point x=ξ.

Derived GPD sum rules relating forward distributions and D-term.

Abstract

A new approach to building models of generalized parton distributions (GPDs) is discussed that is based on the factorized DD (double distribution) Ansatz within the single-DD formalism. The latter was not used before, because reconstructing GPDs from the forward limit one should start in this case with a very singular function f({\beta})/{\beta} rather than with the usual parton density f({\beta}). This results in a non-integrable singularity at {\beta}=0 exaggerated by the fact that f({\beta})'s, on their own, have a singular {\beta}^{-a} Regge behavior for small {\beta}. It is shown that the singularity is regulated within the GPD model of Szczepaniak et al., in which the Regge behavior is implanted through a subtracted dispersion relation for the hadron-parton scattering amplitude. It is demonstrated that using proper softening of the quark-hadron vertices in the regions of large parton virtualities results in model GPDs H(x,{\xi}) that are finite and continuous at the "border point" x={\xi}. Using a simple input forward distribution, we illustrate implementation of the new approach for explicit construction of model GPDs. As a further development, a more general method of regulating the {\beta}=0 singularities is proposed that is based on the separation of the initial single DD f({\beta}, {\alpha}) into the "plus" part [f({\beta},{\alpha})]_{+} and the D-term. It is demonstrated that the "DD+D" separation method allows to (re)derive GPD sum rules that relate the difference between the forward distribution f(x)=H(x,0) and the border function H(x,x) with the D-term function D({\alpha}).