A Nakanishi-based model illustrating the covariant extension of the pion GPD overlap representation and its ambiguities

TL;DR

This paper presents a covariant extension model for pion GPDs using Nakanishi-inspired light-front wave functions, illustrating the model-building process and addressing ambiguities via the soft-pion theorem.

Contribution

It introduces a systematic covariant extension of pion GPDs based on Nakanishi representations, highlighting how to constrain ambiguities with physical theorems.

Findings

The model successfully extends GPDs from DGLAP to ERBL regions.

Ambiguities in the covariant extension can be constrained by the soft-pion theorem.

The approach provides a practical framework for modeling pion GPDs with theoretical consistency.

Abstract

A systematic approach for the model building of Generalized Parton Distributions (GPDs), based on their overlap representation within the DGLAP kinematic region and a further covariant extension to the ERBL one, is applied to the valence-quark pion's case, using light-front wave functions inspired by the Nakanishi representation of the pion's Bethe-Salpeter amplitudes (BSA). This simple but fruitful pion's GPD model illustrates the general model building technique and, in addition, allows for the ambiguities related to the covariant extension, grounded on the Double Distribution (DD) representation, to be constrained by requiring a soft-pion theorem to be properly observed.