Comment on extracting $\alpha$ from $\overrightarrow{B}\rho \rho$

Recent experimental results on $\overrightarrow{B}\rho \rho$ decays indicate that the CP asymmetry $S_{{\rho }^{+}{\rho }^{-}}$ will give an interesting determination of $\alpha =\arg \left[-{(V}_{\mathrm{td}}{V}_{\mathrm{tb}}^{*}{)/(V}_{\mathrm{ud}}{V}_{\mathrm{ub}}^{*}\right)].$ In the limit when the $\rho$ width is neglected, the $\overrightarrow{B}\pi \pi$ isospin analysis can also be applied to $\overrightarrow{B}\rho \rho ,$ 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.