QCD factorization for exclusive, non-leptonic B meson decays: General arguments and the case of heavy-light final states

TL;DR

This paper establishes a rigorous QCD-based factorization framework for exclusive non-leptonic B decays in the heavy-quark limit, showing that amplitudes can be written as convolutions of universal form factors, light-cone distribution amplitudes, and perturbatively calculable hard kernels. It demonstrates that, for decays with a heavy-light final state, non-factorizable corrections are dominated by hard gluon exchange and that soft contributions decouple via color transparency, yielding a factorization formula valid up to Λ_QCD/m_b corrections. The authors prove factorization at two-loop order for heavy-light final states, derive explicit one-loop and two-loop results for B→Dπ, and compute the leading QCD corrections to class-I amplitudes, finding a near-universal a1 ≈ 1.05 with small perturbative uncertainty. They then apply the framework to B→D^{(*)}L decays, extract a1 predictions, and compare with experimental data, observing good agreement within current uncertainties and outlining power-suppressed effects such as annihilation and spectator interactions. Finally, the work situates factorization relative to prior phenomenological and dynamical approaches, arguing that their formalism provides a theoretically controlled, predictive basis for studying CP violation and exclusive hadronic B decays, while highlighting areas for further development, including two-light-meson final states and higher-order corrections.

Abstract

We provide a rigorous basis for factorization for a large class of non-leptonic two-body $B$-meson decays in the heavy-quark limit. The factorization formula incorporates elements of the naive factorization approach and the hard-scattering approach, but allows us to compute systematically radiative (``non-factorizable'') corrections to naive factorization for decays such as $B\to Dπ$ and $B\to ππ$. We discuss the factorization formula for a general final state from a general point of view. We then consider factorization for decays into heavy-light final states (such as $B\to Dπ$) in more detail, including a proof of the factorization formula at two-loop order. Explicit results for the leading QCD corrections to factorization are presented and compared to existing measurements of branching fractions and final-state interaction phases.

Figures (30)

• Figure 1: Graphical representation of the factorization formula. Only one of the two form-factor terms in (\ref{['fff']}) is shown for simplicity.
• Figure 2: Kinematics and notation.
• Figure 3: Leading contributions to the $B\to M_1$ form factor in the hard-scattering approach. The dashed line represents the weak current. The two lines to the left belong to the $B$ meson, the ones to the right to the recoil meson $M_1$.
• Figure 4: Leading-order contribution to the hard-scattering kernel $T^I_{ij}(u)$. The weak decay of the $b$ quark through a four-fermion operator (of current-current or penguin type) is represented by the black square. See text and Fig. \ref{['fig2']} for further notation.
• Figure 5: Diagrams at order $\alpha_s$ that need not be calculated.