Observation of $\ddot{I}ˆ(3686)\to {\hat{I}}^3\hat{I}\cdot (1405)$ via $\hat{I}\cdot (1405)\to f_0(980)\ddot{I}{€}^0$

Abstract

The decay $\ddot{I}ˆ(3686)\to {\hat{I}}^3\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ is studied using a sample of $(2712.4\pm 14.3)\times 10^6$ $\ddot{I}ˆ(3686)$ events collected with the BESIII detector. The decay $\hat{I}\cdot (1405)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ is observed for the first time in $\ddot{I}ˆ(3686)$ decays via the intermediate state $f_0(980)$ and the product branching fraction $\mathcal{B}(\ddot{I}ˆ(3686)\to {\hat{I}}^3\hat{I}\cdot (1405))\times \mathcal{B}(\hat{I}\cdot (1405)\to f_0(980)\ddot{I}{€}^0)\times \mathcal{B}(f_0(980)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-})$ is determined to be $(3.77\pm 0.43\pm 0.29)\times 10^{-7}$, where the first uncertainty is statistical and the second is systematic. The isospin-violating decay of $\ddot{I}ˆ(3686)\to {\hat{I}}^3{f}_1(1285)\to {\hat{I}}^3{f}_0(980)\ddot{I}{€}^0\to {\hat{I}}^3\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ has been observed with signal significance of $2.9\ddot{I}ƒ$. And the branching fraction $\mathcal{B}(\ddot{I}ˆ(3686)\to {\hat{I}}^3{f}_1(1285)\to {\hat{I}}^3{f}_0(980)\ddot{I}{€}^0\to {\hat{I}}^3\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0)$ is determined to be $(7.36\pm 2.25\pm 2.26)\times 10^{-8}$. Since no $\hat{I}{\cdot }_c$ signal is evident in either the $\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ or $f_0(980)\ddot{I}{€}^0$ mass spectrum, upper limits are set to be $\mathcal{B}(\ddot{I}ˆ(3686)\to {\hat{I}}^3\hat{I}{\cdot }_c)\times \mathcal{B}(\hat{I}{\cdot }_c\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0)<3.09\times 10^{-7}$ and $\mathcal{B}(\ddot{I}ˆ(3686)\to {\hat{I}}^3\hat{I}{\cdot }_c)\times \mathcal{B}(\hat{I}{\cdot }_c\to f_0(980)\ddot{I}{€}^0)\times \mathcal{B}(f_0(980)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-})<7.97\times 10^{-8}$ at 90\% confidence level, respectively.

11 pages, 3 figures