Charmless Hardronic Decays $B_u\to VV$: Angular Distributions, Direct CP Violation and Determination of the Unitary Triangle

Abstract

Two-body charmless nonleptonic decays of $B_u\to VV$ are studied within the generalized factorization approach using a recent calculation of the effective Wilson coefficients $c_i^{eff}$, which are not only renormalization-scale and -scheme independent but also gauge invariant and infrared finite. After making a universal ansatz for the nonfactorizable contributions, we parametrize these effects in terms of $N_c^{eff}(LL)$ and $N_c^{eff}(LR)$, the effective numbers of colors arising from $(V-A)(V-A)$ and $(V-A)(V+A)$ four-quark operators, respectively. Three different schemes for these contributions are considered: (i) the naive factorization, (ii) the large-N_c improved factorization, and (iii) our preferred choice: $(N_c^{eff}(LL),N_c^{eff}(RR))=(2,5)$. We present the full angular distribution of all charmless $B_u\to VV$ decays in both transversity and helicity frames.Direct CP violation in these normalized angular correlation coefficients is not negligible in $B_u^{-}\to K^{\ast -}{\rho }^0,K^{\ast -}\omega$, and direct CP violation in the partial rate difference for $B_u^{-}\to K^{\ast -}\omega ,K^{\ast -}\rho$ and ${\rho }^{-}\omega$ can be as large as 45%, 25%, -10%, respectively. Due to the sizable QCD penguin contributions in ${\rho }^{-}\omega$, the determination of the unitary triangle $\alpha$ via this decay mode is more promising than via ${\rho }^{-}{\rho }^0$. It is also encouraging to determine the unitary triangle $\gamma$ through $B_u^{-}\to K^{\ast -}\rho$ because of $N_c$-insensitivity and the not-so-small tree contribution. The impacts of a negative $\rho$ on the branching ratios and CP violation are studied. We also comment on the theoretical uncertainties and their possible impacts.

14 pages, Latex