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

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 $D\to PV$ 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) $D\to PV$ amplitudes in $D^0\to K^{-}{\pi }^{+}{\pi }^0$ and ratios of singly- Cabibbo-suppressed (SCS) $D\to PV$ 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.

Comments: 9 pages, one figure. Submitted to Phys. Rev. D (Brief Reports). Additional comparisons with previous results