Comment on extracting alpha from B -> rho rho

Abstract

Recent experimental results on $B\toρρ$ decays indicate that the CP asymmetry $S_{ρ^+ρ^-}$ will give an interesting determination of $α=\arg[-(V_{td}V_{tb}^*)/(V_{ud}V_{ub}^*)]$. In the limit when the $ρ$ width is neglected, the $B\toππ$ isospin analysis can also be applied to $B\toρρ$, once an angular analysis is used to separate transversity modes. The present bound on the shift of $S_{ρ^+ρ^-}$ from the true $\sin2α$ is already stronger than it is for $S_{π^+π^-}$. We point out a subtle violation of the isospin relations when the two $ρ$ mesons are observed with different invariant masses, and how to constrain this effect experimentally.