Generalized Quark Transversity Distribution of the Pion in Chiral Quark Models

TL;DR

This paper calculates the pion's transversity generalized parton distributions using chiral quark models, demonstrating consistency with lattice QCD data after QCD evolution, highlighting the role of chiral symmetry.

Contribution

It introduces a comprehensive calculation of pion tGPDs in nonlocal and local chiral quark models, including QCD evolution and comparison with lattice results.

Findings

Distributions satisfy support and polynomiality conditions.

QCD evolution aligns model results with lattice data.

Chiral symmetry is crucial in transversity observables.

Abstract

The transversity generalized parton distributions (tGPDs) of the the pion, involving matrix elements of the tensor bilocal quark current, are analyzed in chiral quark models. We apply the nonlocal chiral models involving a momentum-dependent quark mass, as well as the local Nambu--Jona-Lasinio with the Pauli-Villars regularization to calculate the pion tGPDs, as well as related quantities following from restrained kinematics, evaluation of moments, or taking the Fourier-Bessel transforms to the impact-parameter space. The obtained distributions satisfy the formal requirements, such as proper support and polynomiality, following from Lorentz covariance. We carry out the leading-order QCD evolution from the low quark-model scale to higher lattice scales, applying the method of Kivel and Mankiewicz. We evaluate several lowest-order generalized transversity form factors, accessible from the recent lattice QCD calculations. These form factors, after evolution, agree properly with the lattice data, in support of the fact that the spontaneously broken chiral symmetry is the key element also in the evaluation of the transversity observables.