The leading-twist pion and kaon distribution amplitudes from the QCD instanton vacuum

We investigate the leading-twist light-cone distribution amplitudes for the pion and kaon, based on the nonlocal chiral quark model from the instanton vacuum. Effects of explicit flavor SU(3)-symmetry breaking are taken into account. The Gegenbauer moments are computed, analyzed and compared with those of other models. The one-loop QCD evolution of the moments is briefly discussed. The transverse momentum distributions are also discussed for the pion and kaon light-cone wave functions.Comment: 17 pages, 12 figures. Accepted for publication in Physical Review

Photon distribution amplitudes and light-cone wave functions in chiral quark models

The leading- and higher-twist distribution amplitudes and light-cone wave functions of real and virtual photons are analyzed in chiral quark models. The calculations are performed in the nonlocal quark model based on the instanton picture of QCD vacuum, as well as in the spectral quark model and the Nambu--Jona-Lasinio model with the Pauli-Villars regulator, which both treat interaction of quarks with external fields locally. We find that in all considered models the leading-twist distribution amplitudes of the real photon defined at the quark-model momentum scale are constant or remarkably close to the constant in the $x$ variable, thus are far from the asymptotic limit form. The QCD evolution to higher momentum scales is necessary and we carry it out at the leading order of the perturbative theory for the leading-twist amplitudes. We provide estimates for the magnetic susceptibility of the quark condensate $\chi_m$ and the coupling $f_{3\gamma}$, which in the nonlocal model turn out to be close to the estimates from QCD sum rules. We find the higher-twist distribution amplitudes at the quark model scale and compare them to the Wandzura-Wilczek estimates. In addition, in the spectral model we evaluate the distribution amplitudes and light-cone wave functions of the $\rho$-meson.Comment: 24 pages, 15 figure

Generalized Quark Transversity Distribution of the Pion in Chiral Quark Models

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.Comment: 17 pages, 17 figures, regular pape