Relative phases in Dalitz plot amplitudes for $D^0 \to K_S \pi^+ \pi^-$ and $D^0 \to \pi^0 K^+ K^-$

TL;DR

This paper investigates the relative phases in $D^0$ meson decays to three-body final states, comparing experimental data with flavor-symmetric predictions, and finds discrepancies in certain decay modes.

Contribution

It extends the analysis of phase relations in $D^0$ decays to new channels and discusses potential reasons for observed disagreements with theoretical predictions.

Findings

Good agreement in some decay modes like $D^0 o K^- ho^+$

Discrepancies observed in $D^0 o K_S ho^+$ and $D^0 o ho^0 K^+$ decays

Suggestions offered for resolving the discrepancies

Abstract

Relative phases of amplitudes for $D$ meson decays to a light pseudoscalar meson $P$ and a light vector meson $V$ decaying to two pseudoscalar mesons will lead to characteristic interferences on the three-body Dalitz plot. These phases may be compared with predictions of a flavor-symmetric treatment which extracts contributing amplitudes and their relative phases from a fit to $D \to PV$ decay rates. Good agreement was found previously for the cases of $D^0 \to K^- \pi^+ \pi^0$ and $D^0 \to \pi^+ \pi^- \pi^0$. The present work is devoted to the decays $D^0 \to K_S \pi^+ \pi^-$ and $D^0 \to \pi^0 K^+ K^-$, for which agreement is not found. Several suggestions are offered for this discrepancy.