Flavor SU(3) Symmetry and Factorization in B Decays to Two Charmless Vector Mesons

Abstract

We first present a model-independent analysis using flavor SU(3) symmetry with SU(3) breaking effects in $B$ decays to two charmless vector mesons ($VV$) in the final state. In order to bridge the flavor SU(3) symmetry approach and the factorization approach in $B \to VV$ decays, we explicitly show how to translate each SU(3) amplitude into a corresponding amplitude in factorization. Various decay modes, including $B \to K^* \phi$ which is so far the only $B \to VV$ mode having some experimental evidence, are discussed in both the SU(3) symmetry and factorization approaches. Within the generalized factorization approximation, the flavor SU(3) amplitudes and SU(3) breaking effects are numerically estimated as a function of the parameter $\xi \equiv 1/ N_c$ ($N_c$ the effective number of color).