Probing the ∆U = 0 rule in three body charm decays

CP violation in charm decay was observed in the decays D⁰→ P^±P^∓ of a D⁰ meson to two pseudoscalars. When interpreted within the SM, the results imply that the ratio of the relevant rescattering amplitudes has a magnitude and phase that are both of O(1). We discuss ways to probe similar ratios in D⁰→ V^±P^∓ decays, where V is a vector that decays to two pseudoscalars, from the Dalitz-plot analysis of time-integrated three-body decays. Compared to two-body decays, three-body decays have the advantage that the complete system can be solved without the need for time-dependent CP violation measurements or use of correlated (Formula presented.) production. We discuss the decays D⁰→ π⁺π⁻π⁰ and D⁰→ K⁺K⁻π⁰ as examples by considering a toy model of only two overlapping charged resonances, treating the underlying pseudo two-body decays in full generality.