Probing the ∆U = 0 rule in three body charm decays
Avital Dery, Yuval Grossman, Stefan Schacht, A. Soffer
Abstract
A bstract CP violation in charm decay was observed in the decays D 0 → P ± P ∓ of a D 0 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 D 0 → 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 $$ {D}^0-{\overline{D}}^0 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:mo>−</mml:mo> <mml:msup> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mn>0</mml:mn> </mml:msup> </mml:math> production. We discuss the decays D 0 → π + π − π 0 and D 0 → K + K − π 0 as examples by considering a toy model of only two overlapping charged resonances, treating the underlying pseudo two-body decays in full generality.