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Extracting Weak Phase Information from B -> V_1 V_2 Decays

We describe a new method for extracting weak, CP-violating phase information, with no hadronic uncertainties, from an angular analysis of B -> V_1 V_2 decays, where V_1 and V_2 are vector mesons. The quantity $\sin^2 (2 ϕ_1 + ϕ_3)$ (ϕ_1=βand ϕ_3=γ) can be cleanly obtained from the study of decays such as B_d^0(t) -> D^{*\pm} ρ^\mp, D^{*\pm} a_1^{\mp}, D^{*0} K^{*0}, etc. Similarly, one can use B_s^0(t) -> D_s^{*\pm} K^{*\mp} or even B\pm -> D^{*0}K^*\pm to extract $\sin^2 ϕ_3$. There are no penguin contributions to these decays. It is possible that $\sin^2 (2ϕ_1 + ϕ_3)$ will be the second function of CP phases, after $\sin 2ϕ_1$, to be measured at B-factories.