From Bethe-Salpeter Wave Functions to Generalised Parton Distributions

TL;DR

This paper reviews the modeling of Generalised Parton Distributions using Dyson-Schwinger equations, emphasizing covariant methods, theoretical constraints, and the potential of lightcone wave functions for covariant GPD models.

Contribution

It provides a comprehensive review of covariant GPD modeling within the Dyson-Schwinger formalism, including impulse approximation limitations and lightcone wave function approaches.

Findings

Covariant computations fulfill most GPD theoretical constraints.

Impulse approximation has limitations, especially beyond the forward case.

Overlap of lightcone wave functions offers advantages for covariant GPD modeling.

Abstract

We review recent works on the modelling of Generalised Parton Distributions within the Dyson-Schwinger formalism. We highlight how covariant computations, using the impulse approximation, allows one to fulfil most of the theoretical constraints of the GPDs. Specific attention is brought to chiral properties and especially the so-called soft pion theorem, and its link with the Axial-Vector Ward-Takahashi identity. The limitation of the impulse approximation are also explained. Beyond impulse approximation computations are reviewed in the forward case. Finally, we stress the advantages of the overlap of lightcone wave functions, and possible ways to construct covariant GPD models within this framework, in a two-body approximation.