Comments on Color-Suppressed Hadronic B Decays

Recent experimental results on the color-suppressed nonleptonic decays B̄0 → D(∗)0π0 provide evidence for a failure of the naive factorization model and for sizeable relative strong-interaction phases between class-1 and class-2 B̄ → D(∗)π decay amplitudes. The allowed regions for the corresponding ratios of (complex) isospin amplitudes and a2/a1 parameters are determined. The results are interpreted in the context of QCD factorization for the related class-1 amplitudes in the heavy-quark limit. The problem of understanding nonperturbative strong-interaction effects in exclusive nonleptonic weak decays of hadrons has always been a challenge to theorists. Only in a few cases model-independent results based on controlled expansions in QCD can be obtained. In the absence of a quantitative theoretical description various attempts have been made to obtain simple, predictive parameterizations of decay amplitudes based on simple phenomenological assumptions. The most common of these approaches is the “naive” (or “generalized”) factorization model, in which the decay amplitudes are estimated by replacing hadronic matrix elements of four-quark operators in the effective weak Hamiltonian by products of current matrix elements determined in terms of meson decay constants and semileptonic form factors. “Nonfactorizable” strong-interaction effects are parameterized by phenomenological coefficients ai, which depend on the color and Dirac structure of the operators but otherwise are postulated to be universal [1, 2, 3]. One distinguishes class-1 and class-2 decay topologies, which refer to the cases where a charged (class-1) or a neutral (class-2) final-state meson can be produced from the quarks contained in the four-quark operators of the effective Hamiltonian. For instance, in decays based on the quark transition b → cūd mesons with quark content (ūd) or (ūc) can be produced in that way. The decay B̄ → Dπ is a class-1 process, in which the pion can be generated at the weak vertex, whereas B̄ → Dπ is a class-2 process, in which the D meson can be directly produced. The corresponding amplitudes are then expressed as A(B̄ → Dπ) = i GF √ 2 VcbV ∗ ud (m 2 B −mD) fπ F 0 (mπ) a1(Dπ) , √ 2A(B̄ → Dπ) = i GF √ 2 VcbV ∗ ud (m 2 B −mπ) fD F 0 (mD) a2(Dπ) , (1) where F 0 (q ) are B → M form factors at momentum transfer q. In other processes such as B− → Dπ both topologies can contribute and interfere. (Such processes are sometimes called class-3 decays.) In fact, isospin symmetry implies that A(B → Dπ) = A(B̄ → Dπ) + √ 2A(B̄ → Dπ) . (2) The large-Nc counting rules of QCD show that a1(Dπ) = O(1) and a2(Dπ) = O(1/Nc), which is why the class-2 decays are often referred to as “color suppressed”. In the naive factorization model one postulates that for a large class of energetic, twobody (or quasi two-body) B decays the coefficients a1 and a2 are process-independent phenomenological parameters. These parameters are assumed to be real, ignoring the possibility of relative strong-interaction phases between class-1 and class-2 amplitudes. Surprisingly, despite their crudeness these assumptions seemed to be supported by experimental data [2, 3]. Within errors, the class-1 decays B̄ → DM with M = π, ρ, a1, Ds, D ∗ s can be described using a universal value |a1| ≈ 1.1 ± 0.1, whereas the class-2 decays B̄ → K̄M with M = J/ψ, ψ(2S) suggest a nearly universal value |a2| ≈ 0.2–0.3 (which is more uncertain due to the uncertainty in the B → K form factors). Moreover, the class-3 decays B− → DM with M = π, ρ, which are sensitive to the interference of the two decay topologies, could be explained by a real, positive