LAUSR

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