The $D\to \ddot{I}$ semileptonic and radiative decays within the light-cone sum rules

Abstract

The measured branching ratio of the $D$ meson semileptonic decay $D\to \ddot{I}e^{+}\hat{I}{½}_e$, which is based on the $0.82\mathrm{f}{\mathrm{b}}^{-1}$ CLEO data taken at the peak of $\ddot{I}ˆ(3770)$ resonance, disagrees with the traditional SVZ sum rules analysis by about three times. In the paper, we show that this discrepancy can be eliminated by applying the QCD light-cone sum rules (LCSR) approach to calculate the $D\to \ddot{I}$ transition form factors $A_{1,2}(q^2)$ and $V(q^2)$. After extrapolating the LCSR predictions of these TFFs to whole $q^2$-region, we obtain $1/|V_{\mathrm{cd}}{|}^2\times \hat{I}“(D\to \ddot{I}e\hat{I}{½}_e)=(55.45_{-9.41}^{+13.34})\times 10^{-15}\mathrm{GeV}$. Using the CKM matrix element and the $D^0(D^{+})$ lifetime from the Particle Data Group, we obtain $\mathcal{B}(D^0\to \ddot{I}{}^{-}{e}^{+}\hat{I}{½}_e)=(1.749_{-0.297}^{+0.421}\pm 0.006)\times 10^{-3}$ and $\mathcal{B}(D^{+}\to \ddot{I}{}^0{e}^{+}\hat{I}{½}_e)=(2.217_{-0.376}^{+0.534}\pm 0.015)\times 10^{-3}$, which agree with the CLEO measurements within errors. We also calculate the branching ratios of the two $D$ meson radiative processes and obtain $\mathcal{B}(D^0\to \ddot{I}{}^0{\hat{I}}^3)=(1.744_{-0.704}^{+0.598})\times 10^{-5}$ and $\mathcal{B}(D^{+}\to \ddot{I}{}^{+}{\hat{I}}^3)=(5.034_{-0.958}^{+0.939})\times 10^{-5}$, which also agree with the Belle measurements within errors. Thus we think the LCSR approach is applicable for dealing with the $D$ meson decays.

12 pages, 7 figures, version to be published in EPJC