Abstract
Exclusive non-leptonic two-body decays of B mesons have been studied extensively in the past two decades within the framework of factorization. However, the exploration of the corresponding three-body case has only started recently, in part motivated by new data. We consider here the simplest non-leptonic three-body B decays from the point of view of factorization, namely heavy-to-heavy transitions. We provide a careful derivation of the SCET/QCDF factorized amplitudes to NNLO in αs, and discuss the numerical impact of NLO and NNLO corrections. We then study the narrow-width limit, showing that the three-body amplitude reproduces analytically the known quasi-two-body decay amplitudes, and compute finite-width corrections. Finally, we discuss certain observables that are sensitive to perturbative NLO and NNLO corrections and to higher Gegenbauer moments of the dimeson LCDAs. This is the first study of non-leptonic three-body B decays to NNLO in QCD.
Highlights
The extension of the QCDF/SCET approach beyond two-body decays, discussed already early on [23, 24], has only been pursued relatively recently [25]
The factorization of the three-body amplitude B → M M1M2 in the region where the invariant mass of the pair (M1M2) is small is virtually identical to that of the two-body decay, the only difference arising in some of the form factors and light-cone distribution amplitudes (LCDAs) appearing in the factorization formula, which must be generalized to B → M1M2 form factors and dimeson LCDAs
This amplitude is under more theoretical control than other three-body decays to light mesons where there are two more terms depending on generalized B → M1M2 form factors and the B-meson LCDA
Summary
Θπ is defined as the angle between the three-momenta of the neutral pion (k2) and the B-meson (p) in the (M π) rest frame, in which k = 0 holds. This defines all momenta in terms of the two kinematic variables (k2, θπ), which parameterize the phase space. The partial wave expansion cannot converge for values of k2 where cross-channel resonance contributions such as B → D∗+M − are relevant. This issue may be addressed by the isobar method, for example, a subject we will not comment on any further Which will be useful when checking the narrow-width limit
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