Search for $\ddot{I}ˆ(3686)\to {\hat{I}}^3\hat{I}{\cdot }_c(\hat{I}\cdot (1405))\to {\hat{I}}^3\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$

Abstract

Using a sample of $448.1\times 10^6$ $\ddot{I}ˆ(3686)$ events collected with the BESIII detector, a search for the isospin violating decay $\hat{I}{\cdot }_c\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ via $\ddot{I}ˆ(3686)\to {\hat{I}}^3\hat{I}{\cdot }_c$ is presented. No signal is observed, and the upper limit on $\mathcal{B}(\ddot{I}ˆ(3686)\to {\hat{I}}^3\hat{I}{\cdot }_c\to {\hat{I}}^3\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0)$ is determined to be $1.6\times 10^{-6}$ at the $90\%$ confidence level. In addition, a search for $\hat{I}\cdot (1405)\to f_0(980)\ddot{I}{€}^0$ in $\ddot{I}ˆ(3686)$ radiative decays is performed. No signal is observed, and the branching fraction $\mathcal{B}(\ddot{I}ˆ(3686)\to {\hat{I}}^3\hat{I}\cdot (1405)\to {\hat{I}}^3{f}_0(980)\ddot{I}{€}^0\to {\hat{I}}^3\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0)$ is calculated to be less than $5.0\times 10^{-7}$ at the $90\%$ confidence level.