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

Abstract

We point out that decays of the kind $B_d\to D_{\pm }{K}_{S(L)}$ and $B_s\to D_{\pm }{\eta }^{{(}^{\prime })},D_{\pm }\varphi ,...$, 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 $B_q^0$--$\overline{B_q^0}$ ($q\in \{d,s\}$) mixing phase ${\varphi }_q$ 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 $\sin {\varphi }_q$. In comparison with the conventional $B_d\to J/\psi K_{S(L)}$ and $B_s\to J/\psi \varphi$ methods, these extractions do not suffer from any penguin uncertainties, and are theoretically cleaner by one order of magnitude.

14 pages, no figures, sign error in factorization prediction for cos(delta) corrected and numerical examples modified accordingly, conclusions unchanged

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