Cross ratios between Dalitz plot amplitudes in three-body $D^0$ decays

TL;DR

This paper investigates flavor symmetry relations in three-body $D^0$ decays, extending previous analyses to include $D^0 o K^- ho^+ o K^- o ho^+ o ext{final states}$, and compares theoretical predictions with experimental data.

Contribution

It introduces an SU(3) flavor symmetry approach to relate amplitude ratios across different $D^0$ decay modes, highlighting the need for updated Dalitz plot analyses.

Findings

Experimental Dalitz plot ratios largely obey SU(3) symmetry predictions.

Discrepancies suggest the need for refined decay amplitude models.

Supports flavor symmetry as a useful tool in charm meson decay analysis.

Abstract

A recent study of $D^0 \to \pi^0 K^+ K^-$ and $D^0 \to K_S \pi^+\pi^-$ describes a flavor-symmetric approach to calculate relative amplitudes and phases, for characteristic interferences between $D$ decays to a light pseudoscalar $P$ and a light vector $V$, on Dalitz plots for $D \to PPP$ decays. The flavor-symmetric approach used an earlier fit to $D \to P V$ decay rates and was found to agree fairly well with experiments for $D^0 \to \pi^0 \pi^+ \pi^-$ but not as well for $D^0 \to \pi^0 K^+ K^-$ and $D^0 \to K_S \pi^+\pi^-$. The present work extends this investigation to include $D^0 \to K^- \pi^+ \pi^0$. We use an SU(3) flavor symmetry relationship between ratios of Cabibbo-favored (CF) $D \to P V$ amplitudes in $D^0 \to K^- \pi^+ \pi^0$ and ratios of singly- Cabibbo-suppressed (SCS) $D \to P V$ amplitudes in $D^0 \to \pi^0 K^+ K^-$ and $D^0 \to \pi^0 \pi^+ \pi^-$. We observe that experimental values for Dalitz plot cross ratios obey this relationship up to discrepancies noted previously. The need for an updated Dalitz plot analysis of $D^0 \to K^- \pi^+ \pi^0$ is emphasized.