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.

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

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• Two-body hadronic charmed meson decays
• Evidence for direct CP violation in the decay B->D(*)K, D->KsPi+Pi- and measurement of the CKM phase phi3
• Measurement of D0-antiD0 mixing parameters using D0 -> K0S pi+ pi- and D0 -> KS0 K+ K- decays
• Isospin analysis of D0 decay to three pions
• Dalitz Plot Structure in $D^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$
• Relative phases in Dalitz plot amplitudes for $D^0\to K_S{\pi }^{+}{\pi }^{-}$ and $D^0\to {\pi }^0{K}^{+}{K}^{-}$
• Study of the D0 --> pi+ pi- pi0 decay at BABAR

Cited by in corpus (3)

• Nonleptonic Charm Decays and CP Violation
• Flavor-SU(3) tests from $D^0\to K^0{K}^{-}{\pi }^{+}$ and $D^0\to {\bar{K}}^0{K}^{+}{\pi }^{-}$ Dalitz plots
• Determination of Weak Amplitudes using Bose Symmetry and Dalitz Plots