Quasi-distribution amplitudes for pion and kaon via the nonlocal chiral-quark model

Abstract

We investigate the pseudoscalar (PS) meson ([Formula: see text] and [Formula: see text]) quasi-distribution amplitude (QDA), which is supposed to be an asymptotic analog to the meson distribution amplitude (DA) [Formula: see text] in the limit of the large longitudinal PS-meson momentum, i.e. [Formula: see text], in the non-perturbative (NP) region. For this purpose, we employ the nonlocal chiral-quark model (NLChQM) in the light-front (LF) formalism with a minimal Fock-state for the mesons [Formula: see text][Formula: see text][Formula: see text] at the low-energy scale parameter of the model [Formula: see text][Formula: see text][Formula: see text][Formula: see text]1 GeV. As a trial, we extract the transverse-momentum distribution amplitude (TMDA) from the light-front wave function (LFWF) within the model, and convert it to QDA with help of the virtuality-distribution amplitude (VDA). By doing that, we derive an analytical expression for the NP QDA with the current-quark mass correction up to [Formula: see text]. Numerically, we confirm that the obtained TMDA reproduces the experimental data for the photon-pion transition form factor [Formula: see text] at the low-[Formula: see text] qualitatively well. We also observe that the obtained QDA approaches to DA as [Formula: see text] increases, showing the symmetric and asymmetric curves with respect to [Formula: see text] for the pion and kaon, respectively, due to the current-quark mass difference [Formula: see text]. Assigning [Formula: see text], the moments [Formula: see text] are computed, using the pion and kaon QDAs, and there appear only a few percent deviations in the moments for [Formula: see text] in comparison to the values calculated directly from DAs. It turns out that the higher moments are more sensitive to the change of [Formula: see text], whereas the lower ones depend less on it.