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

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 $B^+\to K^{*0}\rho^+$. 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 $\alpha = [90 \pm 7 f{\rm exp})^{+2}_{-5} ({\rm th})]^\circ$.