Transversity Form Factors and Generalized Parton Distributions of the pion in chiral quark models

TL;DR

This paper calculates the transversity Generalized Parton Distributions and form factors of the pion using chiral quark models, showing good agreement with lattice QCD data and emphasizing the role of chiral symmetry.

Contribution

It provides a comprehensive evaluation of pion transversity GPDs and form factors in both local and nonlocal chiral quark models, aligning with lattice QCD results.

Findings

tGPDs satisfy formal theoretical constraints

Form factors agree with lattice QCD after QCD evolution

Chiral symmetry influences pion transversity structure

Abstract

The transversity Generalized Parton Distributions (tGPDs) and related transversity form factors of the pion are evaluated in chiral quark models, both local (Nambu--Jona-Lasinio) and nonlocal, involving a momentum-dependent quark mass. The obtained tGPDs satisfy all a priori formal requirements, such as the proper support, normalization, and polynomiality. We evaluate generalized transversity form factors accessible from the recent lattice QCD calculations. These form factors, after the necessary QCD evolution, agree very well with the lattice data, confirming the fact that the spontaneously broken chiral symmetry governs the structure of the pion also in the case of the transversity observables.