A fresh look at the generalized parton distributions of light pseudoscalar mesons

TL;DR

This paper introduces a symmetry-preserving method to derive generalized parton distributions (GPDs) of light pseudoscalar mesons like pions and kaons in Euclidean space, ensuring key theoretical properties are maintained.

Contribution

It develops a novel Euclidean-space scheme that automatically includes essential contributions for GPDs, satisfying polynomiality and sum rules, and compatible with Dyson-Schwinger equations.

Findings

GPDs match the double distribution form

Sum rules and polynomiality are satisfied

Method applicable within continuum approaches like Dyson-Schwinger equations

Abstract

We present a symmetry-preserving scheme to derive the pion and kaon generalized parton distributions (GPDs) in Euclidean space. The key to maintaining crucial symmetries under this approach is the treatment of the scattering amplitude, such that it contains both the traditional leading-order contributions and the scalar/vector pole contribution automatically, the latter being necessary to ensure the soft-pion theorem. The GPD is extracted analytically via the uniqueness and definition of the Mellin moments and we find that it naturally matches the double distribution; consequently, the polynomiality condition and sum rules are satisfied. The present scheme thus paves the way for the extraction of the GPD in Euclidean space using the Dyson-Schwinger equation framework or similar continuum approaches.