Extracting CKM phases from angular distributions of $B_{d,s}$ decays into admixtures of CP eigenstates

The time-dependent angular distributions of certain B/sub d, s/ decays into final states that are admixtures of CP-even and CP-odd configurations provide valuable information about CKM phases and hadronic parameters. We present the general formalism to accomplish this task, taking also into account penguin contributions, and illustrate it by considering a few specific decay modes. We give particular emphasis to the decay B/sub d/ to J/ psi rho /sup 0/, which can be combined with B/sub s/ to J/ psi phi to extract the B /sub d//sup 0/-B/sub d//sup 0/ mixing phase and-if penguin effects in the former mode should be sizeable-also the angle gamma of the unitarity triangle. As an interesting by-product, this strategy allows us to take into account also the penguin effects in the extraction of the B/sub s//sup 0/-B/sub s//sup 0/ mixing phase from B /sub s/ to J/ psi phi . Moreover, a discrete ambiguity in the extraction of the CKM angle beta can be resolved, and valuable insights into SU(3)-breaking effects can be obtained. Other interesting applications of the general formalism presented in this paper, involving B/sub d/ to rho rho and B/sub s, d/ to K*K* decays, are also briefly noted. (26 refs).