B0 -> DPP time-dependent Dalitz plots, CP-violating angles 2beta, 2beta+gamma, and discrete ambiguities

We study \CP-violation in resonant three-body $B_d\to DPP$ decays, where $PP$ stands for either $\bar D\pi$, $\bar DK$, $\pi\pi$ or $\pi K$. Analogously to the $B_d\to 3\pi$ channel and the extraction of $2\alpha$, the first three channels are shown to measure $\cos 2\beta$ in addition to $\sin 2\beta$, thus allowing to resolve the $\beta\to \frac \pi 2 -\beta$ ambiguity, while the $D\pi K$ final state leads to a measurement of $2\beta+\gamma$. As $\cos2\beta$ and $\cos(2\beta+\gamma)$ are \CP-conserving quantities, their determination is possible without tagging the flavor of the $B_d$ meson. The $B_d^0(t)\to D^+ D^- \pi^0$ channel via the interference between $D^{\ast\ast}$ 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: $B_d^0(t)\to D^+D^-K_S$ with the $D_s^{\ast\ast}$ resonances, and $B_d^0(t)\to D^0_{\CP} \pi^+\pi^-$ with the $D^{\ast\ast}$ plus the $\rho$. Finally, the $B_d^0(t)\to D^{\pm} \pi^{\mp} K_S$ channel with the $D_s^{\ast\ast}$ and $K^*$ resonances provides a new clean method to measure the unusual angle $2\beta + \gamma$. We present in all cases a crude estimate of the number of $\cos 2\beta$ (respectively $2\beta+\gamma$) 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 $B_d^0(t)\to K_SK_SK_L$ decay also measures $2\beta$.