Distribution amplitudes of pseudoscalar mesons within the light-front quark model

In this paper, we investigate the distribution amplitudes (DAs) of pseudoscalar mesons within the light-front quark model, and the n th Gegenbauer moment a n ( μ ) , ξ moment ⟨ ξ n ⟩ , and transverse moment ⟨ k ⊥ n ⟩ 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 , π = 0.054 , is in excellent agreement with predictions from the platykurtic model and the nonlocal chiral quark model. Meanwhile, scheme II yields a 2 , π = 0.126 , which is consistent with lattice QCD, Dyson-Schwinger equation, and data-driven light-cone sum rules analyses. Furthermore, we observe that ϕ 2 , π = ϕ 3 , π P with the replacement M → M 0 . (2) Flavor symmetry breaking effects are found to be more significant in higher-twist DAs, with a notable relation a 1 P ≈ 2 a 1 emerging in heavy meson systems. (3) Interestingly, numerical analysis indicates that the transverse moment ⟨ k ⊥ n ⟩ is twist independent with the replacement M → M 0 . Additionally, we propose an empirical scaling relation Δ m 0.61 β 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.