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

Abstract

We present a unified analysis of $\overline{B}^0 \to D^{(*)+}\ell^-\bar{\nu}_\ell$ and $\overline{B}^0 \to D^{(*)+}\pi^-$ decays using the perturbative QCD (PQCD) approach. The $B \to D^{(*)}$ 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 $R(D) = 0.336^{+0.014}_{-0.013}$ and $R(D^*) = 0.271^{+0.010}_{-0.010}$, which are consistent with the latest experimental averages. Furthermore, we perform a correlated study of the nonleptonic $ \overline{B}^0 \to D^{(*)+}\pi^-$ decays, calculating both factorizable and nonfactorizable amplitudes. To reduce hadronic uncertainties, we introduce and calculate the differential ratio $R^{(*)}_{\pi/\ell}(q^2)$, 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.