Probing the $\Delta U=0$ Rule in Three Body Charm Decays

TL;DR

This paper explores methods to analyze CP violation in three-body charm decays, focusing on the $ riangle U=0$ rule, using Dalitz-plot analysis to probe rescattering amplitude ratios without requiring time-dependent measurements.

Contribution

It proposes a novel approach to study rescattering amplitude ratios in three-body charm decays through Dalitz-plot analysis, avoiding the need for time-dependent CP violation measurements.

Findings

Demonstrates the feasibility of analyzing three-body decays with a toy model of overlapping resonances.

Shows that Dalitz-plot analysis can probe rescattering ratios without time-dependent data.

Provides a framework for future experimental studies of CP violation in charm decays.

Abstract

CP violation in charm decay was observed in the decays $D^0\rightarrow P^{\pm}P^{\mp}$ 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 $D^0\rightarrow V^{\pm}P^{\mp}$ 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 $D^0\rightarrow \pi^+\pi^-\pi^0$ and $D^0\rightarrow K^+K^-\pi^0$ as examples by considering a toy model of only two overlapping charged resonances, treating the underlying pseudo two-body decays in full generality.