The extraction of Cabibbo-Kobayashi-Maskawa matrix element information from hadronic $B$ decays generally suffers from discrete ambiguities, hampering the diagnosis of physics beyond the standard model. We show that a measurement of the rate asymmetry, which is $\mathrm{CP}$ violating, in $B^{\pm }\to {\rho }^{\pm }{\rho }^0\left(\omega \right)\to {\rho }^{\pm }{\pi }^{+}{\pi }^{-}$, where the invariant mass of the ${\pi }^{+}{\pi }^{-}$ pair is in the vicinity of the $\omega$ resonance, can remove the $\mathrm{mod}\left(\pi \right)$ uncertainty in $\alpha \equiv \arg [{-V}_{\mathrm{td}}{V}_{\mathrm{tb}}^{*}/(V_{\mathrm{ud}}{V}_{\mathrm{ub}}^{*}\left)\right]$ present in standard analyses.

• Received 28 May 1997

DOI:https://doi.org/10.1103/PhysRevLett.80.1834