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S. Malde; C. Thomas; G. Wilkinson; P. Naik; C. Prouve; J. Rademacker; J. Libby; M. Nayak; T. Gershon; R.A. Briere (2015)
Publisher: Elsevier
Journal: Physics Letters B
Languages: English
Types: Article
Subjects: CP violation, QC, Physics, High Energy Physics - Experiment, Quantum correlations, QC1-999, Charm decay, Nuclear and High Energy Physics
Quantum-correlated $\psi(3770) \to D\bar{D}$ decays collected by the CLEO-c experiment are used to perform a first measurement of $F_+^{4\pi}$, 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 $D \to\pi^+\pi^-\pi^0$ and $D \to K^+K^-\pi^0$, yielding $F_+^{\pi\pi\pi^0} = 1.014 \pm 0.045 \pm 0.022$ and $F_+^{KK\pi^0} = 0.734 \pm 0.106 \pm 0.054$, 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 $F_+^{\pi\pi\pi^0} = 0.973 \pm 0.017$ and $F_+^{KK\pi^0} = 0.732 \pm 0.055$. 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 $D\bar{D}$ system.
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