decay process within the QCDSR approach*

Abstract

In the paper, we investigate the charmed meson rare decay process $D^+ \to \pi^+\nu\bar\nu$ by using the QCD sum rules approach. Firstly, the pion twist-2, 3 distribution amplitudes (DA) moments $\langle\xi_{2;\pi}^n\rangle|_\mu$ and $\langle \xi_{3;\pi}^{(p,\sigma),n}\rangle|_\mu$ are calculated up to 10th-order and fourth-order in the QCD sum rules under background field theory respectively. After constructing the light-cone harmonic oscillator model for pion twist-2, 3 DAs, we get their behaviors by matching the calculated $\xi$-moments. Then, the $D\to \pi$ transition form factors (TFFs) are calculated by using QCD light-cone sum rules approach. The vector form factor at large recoil region is $f_+^{D\to\pi}(0) = 0.627^{+0.120}_{-0.080}$. By taking the rapidly $z(q^2,t)$ converging simplified series expansion, we present the TFFs and the corresponding angular coefficients in the whole squared momentum transfer physical region. Based on the Non-standard neutrino interactions, the $D^+ \to \pi^+ \nu\bar\nu$ decay can be related to $\bar D^0 \to \pi^+ e\bar \nu_e$ decay indirectly. Thus, we firstly display the semileptonic decay process $\bar D^0 \to \pi^+ e\bar \nu_e$ differential decay widths and branching fraction with ${\cal B}(\bar D^0\to\pi^+e\bar\nu_e) = 0.308^{+0.155}_{-0.066} \times 10^{2}$. The $\bar D^0\to\pi^+e\bar\nu_e$ differential/total predictions for forward-backward asymmetry, $q^2$-differential flat terms and lepton polarization asymmetry are also given. Then, prediction for the $D^+ \to \pi^+ \nu\bar\nu$ branching fraction is ${\cal B}(D^+ \to \pi^+ {\nu }{\bar\nu}) = 1.85^{+0.93}_{-0.46}\times10^{-8}$. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.