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Relative Phases in $D^0\to K^0 K^-π^+$ AND $D^0\to\ok K^+π^-$ Dalitz Plots

The processes $D^0\to K^0 K^-π^+$ and $D^0\to\ok K^+π^-$ involve intermediate vector resonances whose amplitudes and phases are related to each other via flavor SU(3) symmetry. A closer look at Dalitz plots for these two processes is expected to shed light on our understanding of the usefulness of flavor SU(3) symmetry in studying charm decays. In the present work we use data from the BaBar Collaboration's publication in 2002. The goal is to reproduce Dalitz plot amplitudes and phases assuming flavor SU(3) symmetry and compare them with experiment. While an SU(3) fit is able to account for the relative magnitudes of the amplitudes for the decays $D^0 \to K^{*-}K^+$ and $D^0 \to K^{*+}K^-$, the current BaBar sample (based on an integrated luminosity of only 22 fb$^{-1}$) provides only 1--$2 σ$ evidence for the decays $D^0\to K^{*0}\ok$ and $D^0 \to \oks K^0$, with magnitudes and phases not in accord with predictions. The CLEO collaboration could potentially produce an analysis using data with better statistics, and an analysis based on the full BaBar sample (more than 20 times the 2002 value) should definitively settle the question.