M ar 1 99 8 B 0 d ( t ) → DPP time - dependent Dalitz plots , CP - violating angles 2 β , 2 β + γ , and discrete ambiguities

B 0 d (t) → DP P time-dependent Dalitz plots, CP-violating angles 2β, 2β + γ, and discrete ambiguities Abstract We study CP-violation in resonant three-body B d → DP P decays, where P P stands for either ¯ Dπ, ¯ DK S , ππ or πK S. Analogously to the B d → 3π channel and the extraction of 2α, the first three channels are shown to measure cos 2β in addition to sin 2β, thus allowing to resolve the β → π 2 − β ambiguity, while the DπK S final state leads to a measurement of 2β + γ. As cos 2β and cos(2β + γ) are CP-conserving quantities, their determination is possible without tagging the flavor of the B d meson. The B 0 d (t) → D + D − π 0 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: B 0 d (t) → D + D − K S with the D * * s resonances, and B 0 d (t) → D 0 CP π + π − with the D * * plus the ρ. Finally, the B 0 d (t) → D ± π ∓ K S channel with the D * * s 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 cos 2β (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 B 0 d (t) → K S K S K L decay also measures 2β.