Dalitz analysis of D0→K−π+η decays at Belle

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Abstract

We present the results of the first Dalitz plot analysis of the decay ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}\ensuremath{\eta}$. The analysis is performed on a data set corresponding to an integrated luminosity of $953\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected by the Belle detector at the asymmetric-energy ${e}^{+}{e}^{\ensuremath{-}}$ KEKB collider. The Dalitz plot is well described by a combination of the six resonant decay channels ${\overline{K}}^{*}(892{)}^{0}\ensuremath{\eta}$, ${K}^{\ensuremath{-}}{a}_{0}(980{)}^{+}$, ${K}^{\ensuremath{-}}{a}_{2}(1320{)}^{+}$, ${\overline{K}}^{*}(1410{)}^{0}\ensuremath{\eta}$, ${K}^{*}(1680{)}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ and ${K}_{2}^{*}(1980{)}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$, together with $K\ensuremath{\pi}$ and $K\ensuremath{\eta}$ S-wave components. The decays ${K}^{*}(1680{)}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}\ensuremath{\eta}$ and ${K}_{2}^{*}(1980{)}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}\ensuremath{\eta}$ are observed for the first time. We measure ratio of the branching fractions, $\frac{\mathcal{B}({D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}\ensuremath{\eta})}{\mathcal{B}({D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+})}=0.500\ifmmode\pm\else\textpm\fi{}0.002(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.020(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}0.003({\mathcal{B}}_{\mathrm{PDG}})$. Using the Dalitz fit result, the ratio $\frac{\mathcal{B}({K}^{*}(1680)\ensuremath{\rightarrow}K\ensuremath{\eta})}{\mathcal{B}({K}^{*}(1680)\ensuremath{\rightarrow}K\ensuremath{\pi})}$ is measured to be $0.11\ifmmode\pm\else\textpm\fi{}0.02{(\mathrm{stat})}_{\ensuremath{-}0.04}^{+0.06}(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}0.04({\mathcal{B}}_{\mathrm{PDG}})$; this is much lower than the theoretical expectations ($\ensuremath{\approx}1$) made under the assumption that ${K}^{*}(1680)$ is a pure ${1}^{3}{D}_{1}$ state. The product branching fraction $\mathcal{B}({D}^{0}\ensuremath{\rightarrow}[{K}_{2}^{*}(1980{)}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}\ensuremath{\eta}]{\ensuremath{\pi}}^{+})=(2.{2}_{\ensuremath{-}1.9}^{+1.7})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ is determined. In addition, the $\ensuremath{\pi}{\ensuremath{\eta}}^{\ensuremath{'}}$ contribution to the ${a}_{0}(980{)}^{\ifmmode\pm\else\textpm\fi{}}$ resonance shape is confirmed with $10.1\ensuremath{\sigma}$ statistical significance using the three-channel Flatt\'e model. We also measure $\mathcal{B}({D}^{0}\ensuremath{\rightarrow}{\overline{K}}^{*}(892{)}^{0}\ensuremath{\eta})=(1.4{1}_{\ensuremath{-}0.12}^{+0.13})%$. This is consistent with, and more precise than, the current world average $(1.02\ifmmode\pm\else\textpm\fi{}0.30)%$, deviates with a significance of more than $3\ensuremath{\sigma}$ from the theoretical predictions of (0.51--0.92)%.

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