\begin{document}$ D^+ \to \pi^+\nu\bar\nu $\end{document} using an approach based on QCD sum rules. First, the pion twist-2, 3 distribution amplitude (DA) moments \begin{document}$ \langle\xi_{2;\pi}^n\rangle|_\mu $\end{document} and \begin{document}$ \langle \xi_{3;\pi}^{(p,\sigma),n}\rangle|_\mu $\end{document} are calculated up to the tenth and fourth orders, respectively, in the QCD sum rules according to the background field theory. After constructing the light-cone harmonic oscillator model for the pion twist-2, 3 DAs, we obtain their behaviors by matching the calculated ξ-moments. Then, the \begin{document}$ D\to \pi $\end{document} transition form factors (TFFs) are calculated using an approach based on QCD light-cone sum rules. The vector form factor at the large recoil region is \begin{document}$ f_+^{D\to\pi}(0) = 0.627^{+0.120}_{-0.080} $\end{document}. Using the rapidly converging simplified series expansion of \begin{document}$ z(q^2,t) $\end{document}, we present the TFFs and corresponding angular coefficients in the whole squared momentum transfer physical region. Based on non-standard neutrino interactions, the \begin{document}$ D^+ \to \pi^+ \nu\bar\nu $\end{document} decay can be related to the \begin{document}$ \bar D^0 \to \pi^+ e\bar \nu_e $\end{document} decay indirectly. Thus, we first describe the semileptonic decay process \begin{document}$ \bar D^0 \to \pi^+ e\bar \nu_e $\end{document}, differential decay widths, and branching fraction with \begin{document}$ {\cal B}(\bar D^0\to\pi^+e\bar\nu_e) = 0.308^{+0.155}_{-0.066} \times 10^{2} $\end{document}. The \begin{document}$ \bar D^0\to\pi^+e\bar\nu_e $\end{document} differential/total predictions for forward-backward asymmetry, \begin{document}$ q^2 $\end{document}-differential flat terms, and lepton polarization asymmetry are also reported. The prediction for the \begin{document}$ D^+ \to \pi^+ \nu\bar\nu $\end{document} branching fraction is \begin{document}${\cal B}(D^+ \to \pi^+ {\nu }{\bar\nu}) = $\end{document}\begin{document}$ 1.85^{+0.93}_{-0.46}\times10^{-8}$\end{document}."> <inline-formula><tex-math id="M1">\begin{document}$ { \boldsymbol D^{\bf +} \boldsymbol\to \boldsymbol\pi^{\bf +} \boldsymbol\nu\bar{\boldsymbol\nu}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/cpc/article/app/id/2707e739-87eb-43c7-8b02-7c7f2c8c81b6/CPC-2024-0020_M1.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/cpc/article/app/id/2707e739-87eb-43c7-8b02-7c7f2c8c81b6/CPC-2024-0020_M1.png"/></alternatives></inline-formula> decay process within the QCDSR approach -
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