The $D\to \rho$ semileptonic and radiative decays within the light-cone sum rules

Abstract

The measured branching ratio of the $D$ meson semileptonic decay $D\to \rho e^{+}{\nu }_e$, which is based on the $0.82\mathrm{f}{\mathrm{b}}^{-1}$ CLEO data taken at the peak of $\psi (3770)$ 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 $D\to \rho$ 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 $1/|V_{\mathrm{cd}}{|}^2\times \Gamma (D\to \rho e{\nu }_e)=(55.45_{-9.41}^{+13.34})\times 10^{-15}\mathrm{GeV}$. Using the CKM matrix element and the $D^0(D^{+})$ lifetime from the Particle Data Group, we obtain $\mathcal{B}(D^0\to {\rho }^{-}{e}^{+}{\nu }_e)=(1.749_{-0.297}^{+0.421}\pm 0.006)\times 10^{-3}$ and $\mathcal{B}(D^{+}\to {\rho }^0{e}^{+}{\nu }_e)=(2.217_{-0.376}^{+0.534}\pm 0.015)\times 10^{-3}$, which agree with the CLEO measurements within errors. We also calculate the branching ratios of the two $D$ meson radiative processes and obtain $\mathcal{B}(D^0\to {\rho }^0\gamma )=(1.744_{-0.704}^{+0.598})\times 10^{-5}$ and $\mathcal{B}(D^{+}\to {\rho }^{+}\gamma )=(5.034_{-0.958}^{+0.939})\times 10^{-5}$, which also agree with the Belle measurements within errors. Thus we think the LCSR approach is applicable for dealing with the $D$ meson decays.

arXiv comment12 pages, 7 figures, version to be published in EPJC

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