Generalized quark transversity distribution of the pion in chiral quark models

Abstract

The transversity generalized parton distributions (tGPDs) of 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.

Transversity Form Factors and Generalized Parton Distributions of the Pion in Chiral Quark Models

“…3 we compare the result in the NJL model (left panel) and the nonlocal instanton model (right panel). Except for different end-point behavior (see [29] for details), the results are qualitatively very similar. In conclusion we wish to stress that the absolute predictions for the multiplicatively evolved B 10 and B 20 agree remarkably well with the lattice results, supporting the assumptions of numerous calculations following the same "chiral-quark-model + QCD evolution" scheme.…”

“…This presentation is based on our two recent papers [13,29], where more results and details may be found. The tGPDs are the least-explored Generalized Parton Distributions (for extensive reviews see [3,6,31] and references therein).…”

“…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.This presentation is based on our two recent papers [13,29], where more results and details may be found. The tGPDs are the least-explored Generalized Parton Distributions (for extensive reviews see [3,6,31] and references therein).…”

“…Some of them (n = 1, 2) have been calculated on Euclidean lattices [7]. The details concerning the chiral quark models and parameters used have been presented in [13,29]. The calculation of the tFFs and tGPDs is made through the use of standard techniques at the one-quark-loop level, which corresponds to the large-N c limit with confinement neglected.…”

Pseudoscalar meson transition form factors in nonperturbative QCD approach

“…The available full-QCD lattice results [62] Within the effective nonlocal model one gets from the triangle diagram corresponding to (10) the transversity pion form factors (see [63,64], where notations are explained)…”