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

Abstract

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 ${\mathrm{fb}}^{-1}$ 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 ${\bar{K}}^{\ast }(892{)}^0\eta$, $K^{-}{a}_0(980{)}^{+}$, $K^{-}{a}_2(1320{)}^{+}$, ${\bar{K}}^{\ast }(1410{)}^0\eta$, $K^{\ast }(1680{)}^{-}{\pi }^{+}$ and $K_2^{\ast }(1980{)}^{-}{\pi }^{+}$, together with $K\pi$ and $K\eta$ S-wave components. The decays $K^{\ast }(1680{)}^{-}\to K^{-}\eta$ and $K_2^{\ast }(1980{)}^{-}\to K^{-}\eta$ are observed for the first time. We measure ratio of the branching fractions, $\frac{\mathcal{B}(D^0\to K^{-}{\pi }^{+}\eta )}{\mathcal{B}(D^0\to K^{-}{\pi }^{+})}=0.500\pm 0.002(\mathrm{stat})\pm 0.020(\mathrm{syst})\pm 0.003({\mathcal{B}}_{\mathrm{PDG}})$. Using the Dalitz fit result, the ratio $\frac{\mathcal{B}(K^{\ast }(1680)\to K\eta )}{\mathcal{B}(K^{\ast }(1680)\to K\pi )}$ 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 $\mathcal{B}(D^0\to [K_2^{\ast }(1980{)}^{-}\to K^{-}\eta ]{\pi }^{+})=(2.2_{-1.9}^{+1.7})\times 10^{-4}$ is determined. In addition, the $\pi {\eta }^{\prime }$ contribution to the $a_0(980{)}^{\pm }$ resonance shape is confirmed with 10.1$\sigma$ statistical significance using the three-channel Flatté model. We also measure $\mathcal{B}(D^0\to {\bar{K}}^{\ast }(892{)}^0\eta )=(1.41_{-0.12}^{+0.13})\%$. This is consistent with, and more precise than, the current world average $(1.02\pm 0.30)\%$, deviates with a significance of more than $3\sigma$ from the theoretical predictions of (0.51-0.92)%.

arXiv comment11 pages, 2 figures

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• Measurement of branching fractions and search for $CP$ violation in $D^0\to {\pi }^{+}{\pi }^{-}\eta$, $D^0\to K^{+}{K}^{-}\eta$, and $D^0\to \varphi \eta$ at Belle
• Low-mass enhancement of kaon pairs in $B^{+}\to {\bar{D}}^{(\ast )0}{K}^{+}{\bar{K}}^0$ and $B^0\to D^{(\ast )-}{K}^{+}{\bar{K}}^0$ decays
• The hybrid nonet of ${\pi }_1(1600)$ and ${\eta }_1(1855)$: analysis and predictions for the kaonic members
• Phenomenological studies on the ${\bar{B}}^0\to [K^{-}{\pi }^{+}{]}_{S/V}[{\pi }^{+}{\pi }^{-}{]}_{V/S}\to K^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-}$ decay
• Roles of $a_0(980)$ and $a_0(1710)$ in Cabibbo-suppressed process $D^{+}\to {\pi }^0{\pi }^{+}\eta$
• CP violation in quasi-two-body $D\to VP$ decays and three-body $D$ decays mediated by vector resonances