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Non-Leptonic Weak Decays of B Mesons

Matthias Neubert, Berthold Stech

TL;DR

The paper establishes a generalized factorization framework for non-leptonic two-body B decays, linking hadronic amplitudes to current matrix elements and exploiting heavy-quark symmetry to reduce form-factor uncertainties for class I decays. It analyzes both perturbative ( Wilson coefficients and 1/Nc expansion) and non-perturbative (non-factorizable corrections, final-state interactions) effects, concluding that energetic B decays are well described with a nearly universal a1^eff and a mildly process-dependent a2^eff. By fitting to data, the authors extract a1^eff ≈ 1.08 and a2^eff ≈ 0.21–0.29, with ζ ≈ 0.44–0.46, and demonstrate that factorization tests via semileptonic comparisons support the approach. They also show that decay constants such as f_Ds and f_Ds* can be determined from non-leptonic decays and find results consistent with leptonic measurements, underscoring the practical utility of factorization in heavy-flavor phenomenology.

Abstract

We present a detailed study of non-leptonic two-body decays of B mesons based on a generalized factorization hypothesis. We discuss the structure of non-factorizable corrections and present arguments in favour of a simple phenomenological description of their effects. To evaluate the relevant transition form factors in the factorized decay amplitudes, we use information extracted from semileptonic decays and incorporate constraints imposed by heavy-quark symmetry. We discuss tests of the factorization hypothesis and show how unknown decay constants may be determined from non-leptonic decays. In particular, we find f_{Ds}=(234+-25) MeV and f_{Ds*}=(271+-33) MeV.

Non-Leptonic Weak Decays of B Mesons

TL;DR

The paper establishes a generalized factorization framework for non-leptonic two-body B decays, linking hadronic amplitudes to current matrix elements and exploiting heavy-quark symmetry to reduce form-factor uncertainties for class I decays. It analyzes both perturbative ( Wilson coefficients and 1/Nc expansion) and non-perturbative (non-factorizable corrections, final-state interactions) effects, concluding that energetic B decays are well described with a nearly universal a1^eff and a mildly process-dependent a2^eff. By fitting to data, the authors extract a1^eff ≈ 1.08 and a2^eff ≈ 0.21–0.29, with ζ ≈ 0.44–0.46, and demonstrate that factorization tests via semileptonic comparisons support the approach. They also show that decay constants such as f_Ds and f_Ds* can be determined from non-leptonic decays and find results consistent with leptonic measurements, underscoring the practical utility of factorization in heavy-flavor phenomenology.

Abstract

We present a detailed study of non-leptonic two-body decays of B mesons based on a generalized factorization hypothesis. We discuss the structure of non-factorizable corrections and present arguments in favour of a simple phenomenological description of their effects. To evaluate the relevant transition form factors in the factorized decay amplitudes, we use information extracted from semileptonic decays and incorporate constraints imposed by heavy-quark symmetry. We discuss tests of the factorization hypothesis and show how unknown decay constants may be determined from non-leptonic decays. In particular, we find f_{Ds}=(234+-25) MeV and f_{Ds*}=(271+-33) MeV.

Paper Structure

This paper contains 11 sections, 89 equations, 3 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Effective Hamiltonian
  3. Factorization
  4. Corrections to Factorization and the 1$/N_c$ Expansion
  5. Final-State Interactions
  6. Decay Constants
  7. Transition Form Factors
  8. Theoretical Predictions, Comparison with Experiment and Determination of $a_1^{\rm eff}$ and $a_2^{\rm eff}$
  9. Tests of Factorization and Extraction of Decay Constants
  10. $B$ Decays to Baryons
  11. Summary

Figures (3)

  • Figure 1: Hard-gluon corrections giving rise to the Wilson coefficients $c_1(\mu)$ and $c_2(\mu)$ in the effective weak Hamiltonian.
  • Figure 2: The ratio $a_2/a_1$ as a function of the running coupling constant evaluated at the factorization scale. The bands indicate the phenomenological values of $a_2/a_1$ extracted from $\bar{B}\to D\pi$ and $D\to K\pi$ decays.
  • Figure 3: Flavour flow diagram for a $B$ decay into a baryon-antibaryon pair.