Comment on extracting alpha from B -> rho rho

Abstract

Recent experimental results on $B\to \rho \rho$ decays indicate that the CP asymmetry $S_{{\rho }^{+}{\rho }^{-}}$ will give an interesting determination of $\alpha =\arg [-(V_{td}{V}_{tb}^{\ast })/(V_{ud}{V}_{ub}^{\ast })]$. In the limit when the $\rho$ width is neglected, the $B\to \pi \pi$ isospin analysis can also be applied to $B\to \rho \rho$, once an angular analysis is used to separate transversity modes. The present bound on the shift of $S_{{\rho }^{+}{\rho }^{-}}$ from the true $\sin 2\alpha$ is already stronger than it is for $S_{{\pi }^{+}{\pi }^{-}}$. We point out a subtle violation of the isospin relations when the two $\rho$ mesons are observed with different invariant masses, and how to constrain this effect experimentally.

Comments: 12 pages, minor changes