Distribution Amplitudes of Pseudoscalar Mesons within the Light-Front Quark Model

Abstract

In this paper, we investigate the distribution amplitudes (DAs) of pseudoscalar mesons within the light-front quark model (LFQM), and the $n$-th Gegenbauer moment $a_n(\mu)$, $\xi$-moment $\langle \xi^n\rangle$ and transverse moment $\langle \mathbf{k}^n_\perp\rangle$ are also studied. Two parameter sets are adopted by fitting to mesonic decay constants or mass spectra, leading to distinct schemes for numerical analysis. Our results reveal several key insights: (1) Under scheme-I, the second Gegenbauer moment for the pion, $a_{2,\pi} = 0.054$, is in excellent agreement with predictions from the platykurtic model and the nonlocal chiral quark model (NL$\chi$QM). Meanwhile, scheme-II yields $a_{2,\pi} = 0.126$, which is consistent with lattice QCD (LQCD), Dyson-Schwinger equation (DSE) and data-driven light-cone sum rules (LCSR) analyses. Furthermore, we observe that $\phi_{2,\pi} = \phi^P_{3,\pi}$ with the replacement $M \to M_0$. (2) Flavor symmetry breaking effects are found to be more significant in higher-twist DAs, with a notable relation $a_1^P\approx 2 a_1$ emerging in heavy meson systems. (3) Interestingly, numerical analysis indicates that the transverse moment $\langle \mathbf{k}^n_\perp\rangle$ is twist-independent with the replacement $M\to M_0$. Additionally, we propose an empirical scaling relation $\frac{\Delta m^{0.61}}{\beta^{1.10}}x_p=0.67$ to effectively describe the shape of DAs for heavy mesons. Collectively, these results demonstrate that mass asymmetry remarkably influences DAs and kinds of moments, these theoretical predictions will be tested in future experiments.