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 $$ {D}^0-{\overline{D}}^0 $$ 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.