Search for Charm Mixing with Flavor Tagged Dalitz Plots from $\psi(3770) \to D\bar D$

A quantum correlated ($C$=-1) $D\bar D$ state is produced from $\psi(3770) \to D\bar D$. Reconstructing one of the $D$ mesons as a $CP$ eigenstate, $y=\Delta \Gamma/2\Gamma$ can be determined by measuring the flavor specific branching ratios of the other meson. The flavor tag width is independent of the $CP$ quantum number however the branching ratio is inversely proportional to the total width. Consequently, charm threshold experiments have time-integrated sensitivity to $y$. Several multi-body $D^0$ decays proceed through intermediate states that are $CP$ eigenstates, such as $D^0 \to K^0_S f_0, f_0 \to \pi\pi$ and $D^0 \to \rho \pi^0, \rho \to \pi\pi$. The presence of mixing through $y$ would introduce an intensity modulation across the Dalitz plot (for flavor tagged $D$'s relative to the Dalitz plot observed in uncorrelated production) as a function of the $CP$ of the contributing amplitudes. We present a study of the sensitivity to $y$ with the anticipated CLEO-c data set.