First determination of the $CP$ content of $D to pi^+pi^-pi^+pi^-$ and updated determination of the $CP$ contents of $D to pi^+pi^-pi^0$ and $D to K^+K^-pi^0$

Quantum-correlated $psi(3770) to Dbar{D}$ decays collected by the CLEO-c experiment are used to perform a first measurement of $F_+^{4pi}$, the fractional $CP$-even content of the self-conjugate decay $D to pi^+pi^-pi^+pi^-$, obtaining a value of $0.737 pm 0.028$. An important input to the measurement comes from the use of $D to K^0_{rm S}pi^+pi^-$ and $D to K^0_{rm L}pi^+pi^-$ decays to tag the signal mode. This same technique is applied to the channels $D topi^+pi^-pi^0$ and $D to K^+K^-pi^0$, yielding $F_+^{pipipi^0} = 1.014 pm 0.045 pm 0.022$ and $F_+^{KKpi^0} = 0.734 pm 0.106 pm 0.054$, where the first uncertainty is statistical and the second systematic. These measurements are consistent with those of an earlier analysis, based on $CP$-eigenstate tags, and can be combined to give values of $F_+^{pipipi^0} = 0.973 pm 0.017$ and $F_+^{KKpi^0} = 0.732 pm 0.055$. The results will enable the three modes to be included in a model-independent manner in measurements of the unitarity triangle angle $gamma$ using $B^mp to DK^mp$ decays, and in time-dependent studies of $CP$ violation and mixing in the $Dbar{D}$ system.

Measuring $CP$ violation and mixing in charm with inclusive self-conjugate multibody decay modes

Time-dependent studies of inclusive charm decays to multibody self-conjugate final states can be used to determine the indirect $CP$-violating observable $A_Gamma$ and the mixing observable $y_{CP}$, provided that the fractional $CP$-even content of the final state, $F_+$, is known. This approach can yield significantly improved sensitivity compared with the conventional method that relies on decays to $CP$ eigenstates. In particular, $D to pi^+pi^-pi^0$ appears to be an especially powerful channel, given its relatively large branching fraction and the high value of $F_+$ that has recently been measured at charm threshold.

First determination of the CP content of D->pi+pi-pi0 and D->K+K-pi0

Quantum-correlated psi(3770)->DDbar decays collected by the CLEO-c experiment are used to perform first measurements of F+, the fractional CP-even content of the self-conjugate decays D->pi+pi-pi0 and D->K+K-pi0. Values of 0.968 +/- 0.017 +/- 0.006 and 0.731 +/- 0.058 +/- 0.021 are obtained for pi+pi-pi0 and K+K-pi0, respectively. It is demonstrated how modes of this sort can be cleanly included in measurements of the unitarity triangle angle gamma using B+/- -> D K+/- decays. The high CP-even content of D -> pi+pi-pi0, in particular, makes this a promising mode for improving the precision on gamma.

New determination of the D0->K-pi+pi0 and D0->K-pi+pi+pi- coherence factors and average strong-phase differences

Measurements of the coherence factors (R_Kpipi0 and R_K3pi) and the average strong-phase differences (delta^Kpipi0_D and delta^K3pi_D) for the decays D0-> K-pi+pi0 and D0->K-pi+pi+pi- are presented. These parameters are important inputs to the determination of the unitarity triangle angle gamma in B+/- -> DK+/- decays, where D designates a D0 or D0bar meson decaying to a common final state. The measurements are made using quantum correlated DDbar decays collected by the CLEO-c experiment at the psi(3770) resonance, and augment a previously published analysis by the inclusion of new events in which the signal decay is tagged by the mode D-> K0Spi+pi-. The measurements also benefit from improved knowledge of external inputs, namely the D0D0bar mixing parameters, r_D^Kpi and several D-meson branching fractions. The measured values are R_Kpipi0 = 0.82 +- 0.07, delta_D^Kpipi0 = (164+20-14) deg., R_K3pi = 0.32+0.20-0.28 and delta^K3pi_D = (225+21_-78) deg. Consideration is given to how these measurements can be improved further by using the larger quantum-correlated data set collected by BESIII.