The Pion-Photon Transition Distribution Amplitudes in the Nambu-Jona Lasinio Model

TL;DR

This paper develops a covariant formalism for pion-photon transition distribution amplitudes within the Nambu-Jona Lasinio model, verifying key theoretical properties and exploring chiral limit behaviors.

Contribution

It introduces a covariant Bethe-Salpeter based approach to define TDAs and applies it to the NJL model, confirming sum rules, polynomiality, and chiral limit features.

Findings

TDAs satisfy sum rules and polynomiality.

Odd polynomial coefficients vanish in the chiral limit.

Pion pole and PCAC effects are explicitly demonstrated.

Abstract

We define the pion-photon Transition Distribution Amplitudes (TDA) in a field theoretic formalism from a covariant Bethe-Salpeter approach for the determination of the bound state. We apply our formalism to the Nambu - Jona Lasinio model, as a realistic theory of the pion. The obtained vector and axial TDAs satisfy all features required by general considerations. In particular, sum rules and polynomiality condition are explicitly verified. We have numerically proved that the odd coefficients in the polynomiality expansion of the vector TDA vanish in the chiral limit. The role of PCAC and the presence of a pion pole are explicitly shown.