Dalitz analysis of $D^{0}to K^{-}pi^{+}eta$ decays at Belle

We present the results of the first Dalitz plot analysis of the decay $D^{0}to K^{-}pi^{+}eta$. The analysis is performed on a data set corresponding to an integrated luminosity of 953 $rm{fb}^{-1}$ collected by the Belle detector at the asymmetric-energy $e^{+}e^{-}$ KEKB collider. The Dalitz plot is well described by a combination of the six resonant decay channels $bar{K}^{*}(892)^0eta$, $K^{-}a_0(980)^+$, $K^{-}a_2(1320)^+$, $bar{K}^{*}(1410)^0eta$, $K^{*}(1680)^-pi^{+}$ and $K_2^{*}(1980)^-pi^{+}$, together with $Kpi$ and $Keta$ S-wave components. The decays $K^{*}(1680)^{-}to K^{-}eta$ and $K_{2}^{*}(1980)^{-}to K^{-}eta$ are observed for the first time. We measure ratio of the branching fractions, $frac{mathcal{B}(D^{0}to K^{-}pi^{+}eta)}{mathcal{B}(D^{0}to K^{-}pi^{+})}=0.500pm0.002{rm(stat)}pm0.020{rm(syst)}pm0.003{rm (mathcal{B}_{PDG})}$. Using the Dalitz fit result, the ratio $frac{mathcal{B}(K^{*}(1680)to Keta)}{mathcal{B}(K^{*}(1680)to Kpi)}$ is measured to be $0.11pm0.02{rm(stat)}^{+0.06}_{-0.04}{rm(syst)}pm0.04{rm(mathcal{B}_{text{PDG}})}$; this is much lower than the theoretical expectations ($approx1$) made under the assumption that $K^{*}(1680)$ is a pure $1^{3}D_1$ state. The product branching fraction $mathcal{B}(D^0to [K_2^{*}(1980)^-to K^{-}eta]pi^{+})=(2.2^{+1.7}_{-1.9})times10^{-4}$ is determined. In addition, the $pieta^{prime}$ contribution to the $a_0(980)^{pm}$ resonance shape is confirmed with 10.1$sigma$ statistical significance using the three-channel Flatt{e} model. We also measure $mathcal{B}(D^0tobar{K}^{*}(892)^0eta)=(1.41^{+0.13}_{-0.12})%$. This is consistent with, and more precise than, the current world average $(1.02pm0.30)%$, deviates with a significance of more than $3sigma$ from the theoretical predictions of (0.51-0.92)%.