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

Abstract

We investigate the pseudoscalar (PS) meson ($\pi$ and $K$) quasi-distribution amplitude (QDA), which is supposed to be an asymptotic analog to the meson distribution amplitude (DA) ${\varphi }_{\pi ,K}(x)$ in the limit of the large longitudinal PS-meson momentum, i.e. $p_3\to \infty$, in the nonperturbative region. For this purpose, we employ the nonlocal chiral-quark model (NLChQM) in the light-front formalism with a minimal Fock-state for the mesons $\sim q\bar{q}$ at the low-energy scale parameter of the model $\Lambda \sim 1$ GeV. As a trial, we extract the transverse-momentum distribution amplitude (TMDA) from the light-front wave function within the model, and convert it to QDA with help of the virtuality-distribution amplitude. By doing that, we derive an analytical expression for the nonperturbative QDA with the current-quark mass correction up to $\mathcal{O}(\Delta m_q)$. Numerically, we confirm that the obtained TMDA reproduces the experimental data for the photon-pion transition form factor $F_{\gamma {\gamma }^{\ast }{\pi }^0}(Q^2)$ at the low-$Q^2$ qualitatively well. We also observe that the obtained QDA approaches to DA as $p_3$ increases, showing the symmetric and asymmetric curves with respect to $x$ for the pion and kaon, respectively, due to the current-quark mass difference $m_{u,d}\ll m_s$. Assigning $\xi \equiv 2x-1$, the moments $⟨{\xi }^n{⟩}_{\pi ,K}$ are computed, using the pion and kaon QDAs, and there appear only a few percent deviations in the moments for $p_3\gtrsim 30\Lambda$ in comparison to the values calculated directly from DAs. It turns out that the higher moments are more sensitive to the change of $p_3$, whereas the lower ones depend less on it.

Comments: 12 pages, 8 figures, accepted for publication via Mod. Phys. Lett. A