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

Abstract

Decays of the kind $B_s\to D_s^{\pm}K^\mp, D_s^{\ast\pm}K^\mp, ...$ and $B_d\to D^{\pm}π^\mp, D^{\ast\pm}π^\mp, ...$ allow us to probe $ϕ_s+γ$ and $ϕ_d+γ$, respectively, involving the angle $γ$ of the unitarity triangle and the $B^0_q$--$\bar B^0_q$ mixing phases $ϕ_q$ ($q\in\{d,s\}$). 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 $ϕ_q+γ$. 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 $ΔΓ_q$; should $ΔΓ_s$ 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 $\tan(ϕ_s+γ)$, whereas the conventional determination of $ϕ_s+γ$ 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 $B_d\to D^{\pm}π^\mp, D^{\ast\pm}π^\mp, ...$ modes, which has important advantages, offering various interesting new strategies to extract $γ$ in an essentially unambiguous manner.