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

Abstract

Abstract The measured branching ratio of the D meson semileptonic decay $$D \rightarrow \rho e^+ \nu _e$$ D→ρe+νe , which is based on the $$0.82~{\mathrm{fb}^{-1}}$$ 0.82fb-1 CLEO data taken at the peak of $$\psi (3770)$$ ψ(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 $$D\rightarrow \rho $$ D→ρ transition form factors $$A_{1,2}(q^2)$$ A1,2(q2) and $$V(q^2)$$ V(q2) . After extrapolating the LCSR predictions of these TFFs to whole $$q^2$$ q2 -region, we obtain $$1/|V_{\mathrm{cd}}|^2 \times \Gamma (D \rightarrow \rho e \nu _e) =(55.45^{+13.34}_{-9.41})\times 10^{-15}~\mathrm{GeV}$$ 1/|Vcd|2×Γ(D→ρeνe)=(55.45-9.41+13.34)×10-15GeV . Using the CKM matrix element and the $$D^0(D^+)$$ D0(D+) lifetime from the Particle Data Group, we obtain $$\mathcal{B} (D^0\rightarrow \rho ^- e^+ \nu _e) = (1.749^{+0.421}_{-0.297}\pm 0.006)\times 10^{-3}$$ B(D0→ρ-e+νe)=(1.749-0.297+0.421±0.006)×10-3 and $$\mathcal{B} (D^+ \rightarrow \rho ^0 e^+ \nu _e) = (2.217^{+0.534}_{-0.376}\pm 0.015)\times 10^{-3}$$ B(D+→ρ0e+νe)=(2.217-0.376+0.534±0.015)×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 $$\mathcal{B}(D^0\rightarrow \rho ^0 \gamma )= (1.744^{+0.598}_{-0.704})\times 10^{-5}$$ B(D0→ρ0γ)=(1.744-0.704+0.598)×10-5 and $$\mathcal{B}(D^+ \rightarrow \rho ^+ \gamma ) = (5.034^{+0.939}_{-0.958})\times 10^{-5}$$ B(D+→ρ+γ)=(5.034-0.958+0.939)×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.