In this paper, we investigate the distribution amplitudes (DAs) of pseudoscalar mesons within the light-front quark model, and the $n$th Gegenbauer moment $a_n(\mu )$, $\xi$ moment $⟨{\xi }^n⟩$, and transverse moment $⟨{\mathbf{k}}_{\perp }^n⟩$ 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, $a_{2,\pi }=0.054$, is in excellent agreement with predictions from the platykurtic model and the nonlocal chiral quark model. Meanwhile, scheme II yields $a_{2,\pi }=0.126$, which is consistent with lattice QCD, Dyson-Schwinger equation, and data-driven light-cone sum rules analyses. Furthermore, we observe that ${\varphi }_{2,\pi }={\varphi }_{3,\pi }^P$ 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 $a_1^P\approx 2a_1$ emerging in heavy meson systems. (3) Interestingly, numerical analysis indicates that the transverse moment $⟨{\mathbf{k}}_{\perp }^n⟩$ is twist independent with the replacement $M\to M_0$. Additionally, we propose an empirical scaling relation $\frac{\mathrm{\Delta }{m}^{0.61}}{{\beta }^{1.10}}{x}_p=0.67$ 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.

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• Quark model