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

Mao-Jing Liu, Ying Li, Zhi-Tian Zou

TL;DR

This paper develops a unified perturbative QCD (PQCD) framework to describe both semileptonic and nonleptonic $\overline B^0\to D^{(*)+}$ transitions. Low-$q^2$ form factors are computed in PQCD and smoothly matched to high-$q^2$ lattice QCD results using a model-independent $z$-expansion, enabling accurate predictions across the full kinematic range and precise LFU ratios $R(D)$ and $R(D^*)$. The authors also compute nonleptonic $\overline B^0\to D^{(*)+}\pi^-$ amplitudes including factorizable and nonfactorizable contributions, and introduce the differential ratio $R^{(*)}_{\pi/\ell}(q^2)$ to reduce hadronic uncertainties and test factorization. The results show reasonable agreement with current data, provide insight into hadronic dynamics, and offer observables well suited for upcoming Belle II and LHCb measurements to probe for new physics beyond the Standard Model.

Abstract

We present a unified analysis of $\overline{B}^0 \to D^{(*)+}\ell^-\barν_\ell$ and $\overline{B}^0 \to D^{(*)+}π^-$ 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^{(*)+}π^-$ decays, calculating both factorizable and nonfactorizable amplitudes. To reduce hadronic uncertainties, we introduce and calculate the differential ratio $R^{(*)}_{π/\ell}(q^2)$, 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.

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

TL;DR

This paper develops a unified perturbative QCD (PQCD) framework to describe both semileptonic and nonleptonic transitions. Low- form factors are computed in PQCD and smoothly matched to high- lattice QCD results using a model-independent -expansion, enabling accurate predictions across the full kinematic range and precise LFU ratios and . The authors also compute nonleptonic amplitudes including factorizable and nonfactorizable contributions, and introduce the differential ratio to reduce hadronic uncertainties and test factorization. The results show reasonable agreement with current data, provide insight into hadronic dynamics, and offer observables well suited for upcoming Belle II and LHCb measurements to probe for new physics beyond the Standard Model.

Abstract

We present a unified analysis of and decays using the perturbative QCD (PQCD) approach. The transition form factors are calculated at low and extrapolated to the high- region using the latest lattice QCD results via a model-independent -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 and , which are consistent with the latest experimental averages. Furthermore, we perform a correlated study of the nonleptonic decays, calculating both factorizable and nonfactorizable amplitudes. To reduce hadronic uncertainties, we introduce and calculate the differential ratio , 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.

Paper Structure

This paper contains 11 sections, 56 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Framework
  3. Brief Review of PQCD Approach
  4. Wave Function of Meson
  5. Wave Functions and Decay Constants of Light Pseudoscalar Mesons
  6. The Semi-leptonic Decays $\overline B^0 \to D^{(*)+} \ell^- \bar{\nu}_\ell$
  7. $B \to D^{(*)}$ Form Factors
  8. The Semileptonic Decays $\overline{B}^0 \to D^{(*)+}\ell^-\bar{\nu}_\ell$
  9. The Non-leptonic Decays $\overline B^0 \to D^{(*)+} \pi^-$
  10. Correlation Between $\overline{B}^0 \to D^{(*)+}\ell^-\bar{\nu}_\ell$ and $\overline{B}^0 \to D^{(*)+}\pi^-$ Decays
  11. Summary

Figures (6)

  • Figure 1: The lowest order Feynman diagrams for the semileptonic decays $\overline{B}^0 \to D^{(*)+}\ell^-\bar{\nu}_\ell$ in PQCD.
  • Figure 2: The theoretical predictions for the $q^2$-dependence of the form factors for $B \to (D,D^*)$ transitions in the PQCD approach (the blue solid curves) , the "PQCD + Lattice" method (the red solid curves), error varying with $\omega_B$ (shaded in lightred) and with $cd$ (shaded in lightyellow)
  • Figure 3: PQCD predictions for the $q^2$-dependence of the differential decay widths $d\Gamma(B \to D^{(*)} \ell \bar{\nu}_\ell)/dq^2$. The solid curves denote the central values, while the larger uncertainties stem from the parameter $\omega_B$, and the thinner uncertainties from the parameter $C_{D^{(*)}}.$
  • Figure 4: PQCD predictions for the ratios $R_D(q^2)$ and $R_{D^*}(q^2)$ defined in Eq. \ref{['DRDdef']}. The bands showing the uncertainties from $\omega_B$.
  • Figure 5: The topologies (a)[(c)] factorizable emission [annihilation] and (b)[(d)] nonfactorizable effects for the decays $B\to D^{(*)+} \pi^{-}$.
  • ...and 1 more figures