New Strategies to Obtain Insights into CP Violation Through $B_s\to D_s^{\pm }{K}^{\mp },D_s^{\ast \pm }{K}^{\mp },...$ and $B_d\to D^{\pm }{\pi }^{\mp },D^{\ast \pm }{\pi }^{\mp },...$ Decays

Abstract

Decays of the kind $B_s\to D_s^{\pm }{K}^{\mp },D_s^{\ast \pm }{K}^{\mp },...$ and $B_d\to D^{\pm }{\pi }^{\mp },D^{\ast \pm }{\pi }^{\mp },...$ allow us to probe ${\varphi }_s+\gamma$ and ${\varphi }_d+\gamma$, respectively, involving the angle $\gamma$ of the unitarity triangle and the $B_q^0$--${\bar{B}}_q^0$ mixing phases ${\varphi }_q$ ($q\in \{d,s\}$). Analysing these modes in a phase-convention-independent way, we find that their mixing-induced observables are affected by a subtle $(-1{)}^L$ factor, where $L$ denotes the angular momentum of the $B_q$ decay products, and derive bounds on ${\varphi }_q+\gamma$. Moreover, we emphasize that ``untagged'' rates are an important ingredient for efficient determinations of weak phases, not only in the presence of a sizeable width difference $\Delta {\Gamma }_q$; should $\Delta {\Gamma }_s$ be sizeable, the combination of untagged with tagged $B_s\to D_s^{\pm }{K}^{\mp },D_s^{\ast \pm }{K}^{\mp },...$ observables provides an elegant and unambiguous extraction of $\tan ({\varphi }_s+\gamma )$, whereas the conventional determination of ${\varphi }_s+\gamma$ is affected by an eightfold discrete ambiguity. Finally, we propose a combined analysis of $B_s\to D_s^{\pm }{K}^{\mp },D_s^{\ast \pm }{K}^{\mp },...$ and $B_d\to D^{\pm }{\pi }^{\mp },D^{\ast \pm }{\pi }^{\mp },...$ modes, which has important advantages, offering various interesting new strategies to extract $\gamma$ in an essentially unambiguous manner.

Comments: 27 pages, 3 figures, sign error in factorization section corrected and comment on new BaBar result added