Abstract
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.
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This work was supported in part by the Natural Science Foundation of China under Grants No.11765007; the Project of Guizhou Provincial Department of Science and Technology under Grant No.KY[2017]1089 and No.KY[2019]1171.
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Zhong, T., Li, K., Zhang, Y. et al. D Meson Leading-Twist Distribution Amplitude from \(B\to Dl\bar {\nu }_{l}\) Semi-Leptonic Decay. Int J Theor Phys 59, 2562–2571 (2020). https://doi.org/10.1007/s10773-020-04525-x
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DOI: https://doi.org/10.1007/s10773-020-04525-x