Revisiting D-meson twist-2, 3 distribution amplitudes

Owing to the significant difference between the experimental measurements and the theoretical predictions of the standard model (SM) for the value of \begin{document}$ {\cal{R}}(D) $\end{document} of the semileptonic decay \begin{document}$ B\to D\ell\bar{\nu}_{\ell} $\end{document}, researchers speculate that this decay may be evidence of new physics beyond the SM. Usually, the D-meson twist-2, 3 distribution amplitudes (DAs) \begin{document}$ \phi_{2;D}(x,\mu) $\end{document}, \begin{document}$ \phi_{3;D}^p(x,\mu) $\end{document} , and \begin{document}$ \phi_{3;D}^\sigma(x,\mu) $\end{document} are the main error sources when perturbative QCD factorization and light-cone QCD sum rules are used to study \begin{document}$ B\to D\ell\bar{\nu}_{\ell} $\end{document}. Therefore, it is important to obtain more reasonable and accurate behaviors for these DAs. Motivated by our previous work Phys. Rev. D 104, no.1, 016021 (2021)] on pionic leading-twist DA, we revisit D-meson twist-2, 3 DAs \begin{document}$ \phi_{2;D}(x,\mu) $\end{document}, \begin{document}$ \phi_{3;D}^p(x,\mu) $\end{document}, and \begin{document}$ \phi_{3;D}^\sigma(x,\mu) $\end{document}. New sum rule formulae for the \begin{document}$\xi $\end{document}-moments of these three DAs are suggested for obtaining more accurate values. The light-cone harmonic oscillator models for the DAs are improved, and their parameters are determined by fitting the values of ξ-moments via the least squares method.