A precise determination of $\alpha$ using $B^0\to {\rho }^{+}{\rho }^{-}$ and $B^{+}\to K^{\ast 0}{\rho }^{+}$

Abstract

The effect of the penguin amplitude on extracting $\alpha$ from CP asymmetries in $B^0\to {\rho }^{+}{\rho }^{-}$ decays is studied using information on the SU(3)-related penguin amplitude in $B^{+}\to K^{\ast 0}{\rho }^{+}$. Conservative bounds on non-factorizable SU(3) breaking, small amplitudes, and the strong phase difference between tree and penguin amplitudes, are shown to reduce the error in $\alpha$ in comparison with the one obtained using isospin symmetry in $B\to \rho \rho$. Current measurements imply $\alpha =[90\pm 7f\exp {)}_{-5}^{+2}(\mathrm{th}){]}^{\circ }$.

Comments: 12 pages. 2 figures, to be published in Physics Letters B; v2: Added "Note added in proof" to account for latest experimental results