Branching ratios and CP asymmetries in the decay B-->VV.

Abstract

We carry out a systematic study of branching ratios, angular correlations, and $\mathrm{CP}$ asymmetries in the decay of neutral and charged $B$ mesons to final states consisting of two vector mesons. The renormalization-group-improved effective Hamiltonian is evaluated in the vacuum insertion (factorization) approximation. Okubo-Zweig-Iizuka suppressed and annihilation terms are neglected. Current matrix elements are evaluated using the wave functions of Bauer, Stech, and Wirbel. Branching ratios and angular correlations among subsequent decays of the vector mesons are calculated for 34 channels and a comparison is made with the data. As a first approximation, the calculational scheme provides a useful framework with which to organize the data. Interesting direct $\mathrm{CP}$ asymmetries are particularly evident in ${K}^{*}\ensuremath{\omega}$ and ${K}^{*}\ensuremath{\rho}$ final states, where branching ratios are moderate. They are excellent probes of penguin term influence on decay amplitudes. Even larger direct asymmetries are present in $\ensuremath{\omega}\ensuremath{\rho}$ and $\ensuremath{\rho}\ensuremath{\rho}$ final states where, however, branching ratios are low and results are very model dependent. We show how ${B}^{0}\ensuremath{-}{\overline{B}}^{0}$ mixing phases are influenced by phases in the direct amplitudes. The effect is particularly strong for ${\overline{K}}^{*0}{\overline{D}}^{*0}$ final states.