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

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.

Comments: 11 pages, 3 figures, to be published in Phys. Rev. D. Additonal figure, text, and references; minor corrections