Dalitz analysis of $D^0\to K^{-}\ddot{I}{€}^{+}\hat{I}\cdot$ decays at Belle

Abstract

We present the results of the first Dalitz plot analysis of the decay $D^0\to K^{-}\ddot{I}{€}^{+}\hat{I}\cdot$. The analysis is performed on a data set corresponding to an integrated luminosity of 953 ${\mathrm{fb}}^{-1}$ 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 ${\bar{K}}^{\ast }(892{)}^0\hat{I}\cdot$, $K^{-}{a}_0(980{)}^{+}$, $K^{-}{a}_2(1320{)}^{+}$, ${\bar{K}}^{\ast }(1410{)}^0\hat{I}\cdot$, $K^{\ast }(1680{)}^{-}\ddot{I}{€}^{+}$ and $K_2^{\ast }(1980{)}^{-}\ddot{I}{€}^{+}$, together with $K\ddot{I}€$ and $K\hat{I}\cdot$ S-wave components. The decays $K^{\ast }(1680{)}^{-}\to K^{-}\hat{I}\cdot$ and $K_2^{\ast }(1980{)}^{-}\to K^{-}\hat{I}\cdot$ are observed for the first time. We measure ratio of the branching fractions, $\frac{\mathcal{B}(D^0\to K^{-}\ddot{I}{€}^{+}\hat{I}\cdot )}{\mathcal{B}(D^0\to K^{-}\ddot{I}{€}^{+})}=0.500\pm 0.002(\mathrm{stat})\pm 0.020(\mathrm{syst})\pm 0.003({\mathcal{B}}_{\mathrm{PDG}})$. Using the Dalitz fit result, the ratio $\frac{\mathcal{B}(K^{\ast }(1680)\to K\hat{I}\cdot )}{\mathcal{B}(K^{\ast }(1680)\to K\ddot{I}€)}$ is measured to be $0.11\pm 0.02{(\mathrm{stat})}_{-0.04}^{+0.06}(\mathrm{syst})\pm 0.04({\mathcal{B}}_{\text{PDG}})$; this is much lower than the theoretical expectations ($\approx 1$) made under the assumption that $K^{\ast }(1680)$ is a pure $1^3{D}_1$ state. The product branching fraction $\mathcal{B}(D^0\to [K_2^{\ast }(1980{)}^{-}\to K^{-}\hat{I}\cdot ]\ddot{I}{€}^{+})=(2.2_{-1.9}^{+1.7})\times 10^{-4}$ is determined. In addition, the $\ddot{I}€\hat{I}{\cdot }^{\prime }$ contribution to the $a_0(980{)}^{\pm }$ resonance shape is confirmed with 10.1$\ddot{I}ƒ$ statistical significance using the three-channel Flatté model. We also measure $\mathcal{B}(D^0\to {\bar{K}}^{\ast }(892{)}^0\hat{I}\cdot )=(1.41_{-0.12}^{+0.13})\%$. This is consistent with, and more precise than, the current world average $(1.02\pm 0.30)\%$, deviates with a significance of more than $3\ddot{I}ƒ$ from the theoretical predictions of (0.51-0.92)%.

11 pages, 2 figures