D Meson Leading-Twist Distribution Amplitude from B → D l ν ̄ l $B\to Dl\bar {\nu }_{l}$ Semi-Leptonic Decay

The D-meson leading-twist distribution amplitude (DA) is an universal physical quantity for applying QCD light-cone sum rules or perturbative QCD method to exclusive processes involving D-meson. Although several models have been used in the literature, we do not have enough knowledge to determine it. Inversely, one expects that the D-meson DA can be constrained in principle by the processes containing D-meson. In this paper, we try to extract the information of D-meson DA’s behavior from the experimental data of B → D semi-leptonic decay. A revised light-cone harmonic oscillator model has been suggested. It can mimic most of the suggested D-meson DA behaviors, whose parameters can be fixed by the constraints from the processes involving D-meson. By combining the D-meson decay channel $D\to \mu \bar {\nu }$ , the semi-leptonic decay $B\to Dl\bar {\nu }_{l}$ and the constrain that the probability of finding the leading Fock-state $|\bar {c}q>$ in the D-meson Fock state expansion, we restrict the parameter BD in our DA model as BD ∈ [0.00, 0.23]. In order to improve the complexity of the evolution of the oscillator model, we give the fitting formulas for the evolution of the model parameters. Then we calculate the branching ratios ${\mathscr{B}}(\overline {B}^{0}\to D^{+}l\nu _{l})$ and ${\mathscr{B}}(B^{-}\to D^{0}l\bar {\nu }_{l})$ , which agree with the experimental data.