On the equivalence of GPD representations

TL;DR

This paper reviews the mathematical equivalences between different representations of generalized parton distributions (GPDs), aiding in better understanding and modeling of hadron structure from experimental data.

Contribution

It demonstrates the equivalence between conformal partial wave and double distribution representations of GPDs, providing insights for flexible GPD modeling.

Findings

Establishes mathematical equivalence between GPD representations

Facilitates development of more versatile GPD models

Enhances interpretation of experimental data

Abstract

Phenomenological representations of generalized parton distributions (GPDs) implementing the non-trivial field theoretical requirements are employed in the present day strategies for extracting of hadron structure information encoded in GPDs from the observables of hard exclusive reactions. Showing out the equivalence of various GPD representations can help to get more insight into GPD properties and allow to build up flexible GPD models capable of satisfactory description of the whole set of available experimental data. We review the mathematical aspects of establishing equivalence between the the double partial wave expansion of GPDs in the conformal partial waves and in the $t$-channel ${\rm SO}(3)$ partial waves and the double distribution representation of GPDs.