Investigation for $D^+ \to π^+ ν\barν$ decay process within QCDSR approach

In the paper, we investigate the charmed meson rare decay process $D^+ \to π^+ν\barν$ by using QCD sum rules approach. Firstly, the pion twist-2 and twist-3 distribution amplitude $ξ$-moments $\langleξ_{2;π}^n\rangle|_μ$ up to 10th-order and $\langle ξ_{3;π}^{(p,σ),n}\rangle|_μ$ up to fourth-order are calculated by using QCD sum rule under background field theory. After constructing the light-cone harmonic oscillator model for pion twist-2, 3 DAs, we get their behaviors by matching the calculated $ξ$-moments. Then, the $D\to π$ transition form factors are calculated by using QCD light-cone sum rules approach. The vector form factor at large recoil region is $f_+^{D\toπ}(0) = 0.627^{+0.120} _{-0.080}$. 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. Furthermore, we display the semileptonic decay process $\bar D^0 \to π^+ e\bar ν_e$ differential decay widths and branching fraction with ${\cal B}(\bar D^0\toπ^+e\barν_e) = 0.308^{+0.155}_{-0.066} \times 10^{2}$. The $\bar D^0\toπ^+e\barν_e$ differential/total predictions for forward-backward asymmetry, $q^2$-differential flat terms and lepton polarization asymmetry are also given. After considering the non-standard neutrino interactions, the predictions for the $D^+ \to π^+ ν\barν$ branching fraction is ${\cal B}(D^+ \to π^+ {ν}{\barν}) = 1.85^{+0.93}_{-0.46}\times10^{-8}$.

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