Determining $\alpha$ and $\gamma$ from direct $\mathrm{CP}$ violation in $B_u,$ $B_d,$ and $B_s$ decays to two vector mesons

A method for the clean determination of the unitarity angles $\alpha$ and $\gamma$ is proposed that uses only direct $\mathrm{CP}$ violation and does not require any time dependent measurements. The method takes advantage of the helicity amplitudes for $B_u,$ $B_d,$ and $B_s$ decay to two vector mesons and can be used, at any B facility, in conjunction with a large number of modes. It also allows for experimental tests of the theoretical approximations involved.