We propose a novel method to measure flavor-oscillations and charge-parity (CP) violation in charm mixing. The approach uses multibody charm decays, such as $D^0to K_S^0pi^+pi^-$, and avoids the need for a fit of the decay amplitudes while suppressing biases due to nonuniform signal-reconstruction efficiencies as functions of phase space and decay time. Data are partitioned in decay-time and Dalitz-plot regions (bins). The Dalitz-plot bins are symmetric with respect to the principal bisector and chosen to ensure nearly constant values of the strong-interaction phases in each. The ratios of signal yields observed in each symmetric bin pair are fit as functions of decay time, using independent auxiliary measurements of the strong-interaction phases as constraints, to determine the relevant physics parameters. Simulation shows that this approach improves the sensitivity to the normalized charm-eigenstate mass difference by 35% with respect to existing model-independent methods. In addition, we introduce a parametrization of oscillation and CP-violation effects in charm mixing that has attractive statistical properties and may find wider applicability.
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