Bd0(t)→DPP time-dependent Dalitz plots, CP-violating angles 2β, 2β+γ, and discrete ambiguities

We study CP-violation in resonant three-body Bd→DPP decays, where PP stands for either D̄π, D̄KS, ππ or πKS. Analogously to the Bd→3π channel and the extraction of 2α, the first three channels are shown to measure cos2β in addition to sin2β, thus allowing to resolve the β→π2−β ambiguity, while the DπKS final state leads to a measurement of 2β+γ. As cos2β and cos(2β+γ) are CP-conserving quantities, their determination is possible without tagging the flavor of the Bd meson. The Bd0(t)→D+D−π0 channel via the interference between D∗∗ orbitally excited resonances is taken as an example, although this Cabibbo-suppressed decay suffers from irreducible penguin uncertainties. Then two penguin-free and Cabibbo-dominant modes are proposed: Bd0(t)→D+D−KS with the Ds∗∗ resonances, and Bd0(t)→D0CPπ+π− with the D∗∗ plus the ρ. Finally, the Bd0(t)→D±π∓KS channel with the Ds∗∗ and K∗ resonances provides a new clean method to measure the unusual angle 2β+γ. We present in all cases a crude estimate of the number of cos2β (respectively 2β+γ) sensitive events. We show that this number is an increasing function of the resonance mass, a favorable situation compared to the more extensively studied three-pion Dalitz plot. However, the poor detection efficiency of the D mesons could pose a problem. As an annex and speculative application of these Dalitz plot based methods, the penguin-dominated Bd0(t)→KSKSKL decay also measures 2β.