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Flavor-SU(3) tests from $D^0 \to K^0 K^- π^+$ and $D^0 \to \bar K^0 K^+ π^-$ 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. Dalitz plots for these two processes can shed light on the usefulness of this symmetry in studying charm decays. Until this year the only available data on this process came from a conference report in 2002 by the BaBar Collaboration, but now an independent data sample of higher statistics has become available from the CLEO Collaboration. The goal is to predict Dalitz plot amplitudes and phases assuming flavor-SU(3) symmetry and compare them with experiment. An SU(3) fit can account for the relative magnitudes of the amplitudes for the decays $D^0 \to K^{*-}K^+$ and $D^0 \to K^{*+}K^-$, but neither the current BaBar sample (based on an integrated luminosity of 22 fb$^{-1}$) nor the CLEO analysis has significant evidence for the decays $D^0\to K^{*0}\ok$ and $D^0 \to \oks K^0$. At this level one is unable to compare magnitudes and phases with theoretical predictions. The purpose of this Letter is to advocate an analysis using the full BaBar sample (more than 20 times the 2002 value). It should definitively determine whether predicted magnitudes and phases agree with experiment. A similar analysis should be possible with an even larger sample of events collected by the Belle Collaboration at KEK-B.