Extracting Weak Phase Information fromB→V1V2Decays

We describe a new method for extracting weak, $\mathrm{CP}$-violating phase information, with no hadronic uncertainties, from an angular analysis of $B\to V_1{V}_2$ decays, where $V_1$ and $V_2$ are vector mesons. The quantity ${sin}^2(2\beta +\gamma )$ can be cleanly obtained from the study of decays such as $B_d^0\left(t\right)\to D^{*\pm }{\rho }^{\mp }$, $D^{*\pm }{a}_1^{\mp }$, $\stackrel{\left(¯\right)}{D}{}^{*0}\stackrel{\left(¯\right)}{K}{}^{*0}$, etc. Similarly, one can use $B_s^0\left(t\right)\to D_s^{*\pm }{K}^{*\mp }$ to extract ${sin}^2\gamma$. There are no penguin contributions to these decays. It is possible that ${sin}^2(2\beta +\gamma )$ will be the second function of $\mathrm{CP}$ phases, after $\sin 2\beta$, to be measured at $B$ factories.