Correlated PQCD Analysis of the Semileptonic Decays ${\overline{B}}^0\to D^{(\ast )+}{\ell }^{-}{\bar{\nu }}_{\ell }$ and the Nonleptonic Decays ${\overline{B}}^0\to D^{(\ast )+}{\pi }^{-}$

Abstract

We present a unified analysis of ${\overline{B}}^0\to D^{(\ast )+}{\ell }^{-}{\bar{\nu }}_{\ell }$ and ${\overline{B}}^0\to D^{(\ast )+}{\pi }^{-}$ decays using the perturbative QCD (PQCD) approach. The $B\to D^{(\ast )}$ transition form factors are calculated at low $q^2$ and extrapolated to the high-$q^2$ region using the latest lattice QCD results via a model-independent $z$-expansion. This hybrid method provides a precise form factor description across the full kinematic range. We then predict the branching fractions and the lepton flavor universality ratios $R(D)=0.336_{-0.013}^{+0.014}$ and $R(D^{\ast })=0.271_{-0.010}^{+0.010}$, which are consistent with the latest experimental averages. Furthermore, we perform a correlated study of the nonleptonic ${\overline{B}}^0\to D^{(\ast )+}{\pi }^{-}$ decays, calculating both factorizable and nonfactorizable amplitudes. To reduce hadronic uncertainties, we introduce and calculate the differential ratio $R_{\pi /\ell }^{(\ast )}(q^2)$, defined between nonleptonic and semileptonic decay rates, providing a sensitive test of factorization and possible new physics effects. The predictions presented here can be directly tested in ongoing Belle II and LHCb experiments.

25 pages, 6 figures,