Application of the light-front holographic wavefunction for heavy-light pseudoscalar meson in $B_{d,s}\to D_{d,s}P$ decays

In this paper we extend our analyses of the decay constant and distribution amplitude with an improved holographic wavefunction to the heavy-light pseudoscalar mesons. In the evaluations, the helicity-dependence of the holographic wavefunction is considered; and an independent mass scale parameter is employed to moderate the strong suppression induced by the heavy quark. Under the constraints from decay constants and masses of pseudoscalar mesons, the $\chi^2$-analyses for the holographic parameters exhibit a rough consistence with the results obtained by fitting the Regge trajectory. With the fitted parameters, the results for the decay constants and distribution amplitudes are presented. We then show their application in evaluating the $B_{d,s}\to D_{d,s}P$ decays, in which the power-suppressed spectator scattering and weak annihilation corrections are first estimated. Numerically, the spectator scattering and weak annihilation corrections present a negative shift of about $0.7\%$ on the branching fractions; while, the predictions are still larger than the experimental data. Such small negative shift confirms the estimation based on the power counting rules.