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.
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.
Simulation studies are performed to assess the sensitivity of a model-independent analysis of the flavour-tagged decays $D^0 to K^0_{rm S}pi^+pi^-$ and $D^0 to K^0_{rm S}K^+K^-$ to mixing and CP violation. The analysis takes as input measurements of
the $D$ decay strong-phase parameters that are accessible in quantum-correlated $D-bar{D}$ pairs produced at the $psi(3770)$ resonance. It is shown that the model-independent approach is well suited to the very large data sets expected at an upgraded LHCb experiment, or future high luminosity $e^+e^-$ facility, and that with 100M $K^0_{rm S}pi^+pi^-$ decays a statistical precision of around 0.01 and $0.7^circ$ is achievable on the CP violation parameters $r_{CP}$ and $a_{CP}$, respectively. Even with this very large sample the systematic uncertainties associated with the strong-phase parameters will not be limiting, assuming that full use is made of the available $psi(3770)$ data sets of CLEO-c and BES-III. Furthermore, it is demonstrated that large flavour-tagged samples can themselves be exploited to provide information on the strong-phase parameters, a feature that will be beneficial in the measurement of the CKM angle $gamma/phi_3$ with $B^- to DK^-$ decays.
We present the first search for the decay $D^+_{s}to omega e^{+} u$ to test the four-quark content of the $D^+_{s}$ and the $omega$-$phi$ mixing model for this decay. We use 586 $mathrm{pb}^{-1}$ of $e^{+}e^{-}$ collision data collected at a center-o
f-mass energy of 4170 MeV. We find no evidence of a signal, and set an upper limit on the branching fraction of $mathcal{B}(D^+_{s}toomega e^+ u)<$0.20% at the 90% confidence level.
