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 $B_s\to D_\pmη^{(')},D_\pmϕ, ...$, 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 $γ$ of the unitarity triangle. In this new strategy, we use the $B^0_q$--$\bar{B^0_q}$ ($q\in\{d,s\}$) mixing phase $ϕ_q$ as an input, and employ only ``untagged'' and mixing-induced CP-violating observables, which satisfy a very simple relation, allowing us to determine $\tanγ$. Using a plausible dynamical assumption, $γ$ can be fixed in an essentially unambiguous manner. The corresponding formalism can also be applied to $B_d\to D_\pmπ^0,D_\pmρ^0, >...$ and $B_s\to D_\pm K_{S(L)}$ decays. Although these modes appear less attractive for the extraction of $γ$, they provide interesting determinations of $\sinϕ_q$. In comparison with the conventional $B_d\to J/ψK_{S(L)}$ and $B_s\to J/ψϕ$ methods, these extractions do not suffer from any penguin uncertainties, and are theoretically cleaner by one order of magnitude.

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