Charmless B→VV decays in QCD factorization implications of recent measurement

Abstract

In the heavy quark limit, both vector mesons in the charmless B → VV decay should have zero helicity and the corresponding amplitude is proportional to the form factor difference ( A 1 − A 2 ). The first observed charmless B → VV mode, B→φK ∗ , indicates that the form factors A 1 ( q 2 ) and A 2 ( q 2 ) cannot be very similar at low q 2 as shown in some form-factor models. The approach of QCD-improved factorization implies that the nonfactorizable correction to each partial-wave or helicity amplitude is not the same; the effective parameters a i vary for different helicity amplitudes. The leading-twist nonfactorizable corrections to the transversely polarized amplitudes vanish in the chiral limit and hence it is necessary to take into account twist-3 distribution amplitudes of the vector meson in order to have renormalization scale and scheme independent predictions. Branching ratios of B → VV decays are calculated in two different models for form factors, and the predicted decay rates are different by a factor of 1.5∼2. Owing to the absence of ( S − P )( S + P ) penguin contributions to the W -emission amplitudes, tree-dominated decays tend to have larger branching ratios than the penguin-dominated ones.