New, Efficient and Clean Strategies to Explore CP Violation Through Neutral B Decays

We point out that decays of the kind $B_d\to D_\pm K_{S(L)}$ and $B_s\to D_\pm\eta^{(')},D_\pm\phi, ...$, where $D_+$ and $D_-$ denote the CP-even and CP-odd eigenstates of the neutral D-meson system, respectively, provide very efficient, theoretically clean determinations of the angle $\gamma$ of the unitarity triangle. In this new strategy, we use the $B^0_q$--$\bar{B^0_q}$ ($q\in\{d,s\}$) mixing phase $\phi_q$ as an input, and employ only ``untagged'' and mixing-induced CP-violating observables, which satisfy a very simple relation, allowing us to determine $\tan\gamma$. Using a plausible dynamical assumption, $\gamma$ can be fixed in an essentially unambiguous manner. The corresponding formalism can also be applied to $B_d\to D_\pm\pi^0,D_\pm\rho^0, >...$ and $B_s\to D_\pm K_{S(L)}$ decays. Although these modes appear less attractive for the extraction of $\gamma$, they provide interesting determinations of $\sin\phi_q$. In comparison with the conventional $B_d\to J/\psi K_{S(L)}$ and $B_s\to J/\psi\phi$ methods, these extractions do not suffer from any penguin uncertainties, and are theoretically cleaner by one order of magnitude.