Eur. Phys. J. C (2025) 85: 1450
https://doi.org/10.1140/epjc/s10052-025-15203-9

Regular Article - Theoretical Physics

Correlated PQCD analysis of the semileptonic decays ${\overline{B}}^0\to D_{}^{(\ast )+}{\ell }^{-}{\overline{\nu }}_{\ell }$ and the nonleptonic decays ${\overline{B}}^0\to D_{}^{(\ast )+}{\pi }^{-}$

Department of Physics, Yantai University, 264005, Yantai, China

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Received: 10 November 2025
Accepted: 10 December 2025
Published online: 21 December 2025

Abstract

We present a unified analysis of ${\overline{B}}^0\to D_{}^{(\ast )+}{\ell }^{-}{\overline{\nu }}_{\ell }$ 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.