Search for hadronic transition $\ddot{I}{‡}_{cJ}\to \hat{I}{\cdot }_c\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and observation of $\ddot{I}{‡}_{cJ}\to K\bar{K}\ddot{I}€\ddot{I}€\ddot{I}€$

Abstract

Hadronic transitions of $\ddot{I}{‡}_{cJ}\to \hat{I}{\cdot }_c\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ (J=0, 1, 2) are searched for using a sample of $1.06\times 10^8$ $\ddot{I}ˆ(3686)$ events collected with the BESIII detector at the BEPCII storage ring. The $\etac$ is reconstructed with $K_S^0{K}^{+}\ddot{I}{€}^{-}+c.c.$ and $K^{+}{K}^{-}\ddot{I}{€}^0$ final states. No signals are observed in any of the three $\ddot{I}{‡}_{cJ}$ states in either $\etac$ decay mode. At the 90% confidence level, the upper limits are determined to be $\BR(χ_{c0}\to η_{c}π^{+}π^{-})<0.07%$, $\BR(χ_{c1}\to η_{c}π^{+}π^{-})<0.32%$, and $\BR(χ_{c2}\to η_{c}π^{+}π^{-})<0.54%$. The upper limit of $\BR(χ_{c1}\to η_{c}π^{+}π^{-}$ is lower than the existing theoretical prediction by almost an order of magnitude. The branching fractions of $\ddot{I}{‡}_{cJ}\to K_S^0{K}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}+c.c.$, $K^{+}{K}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$, $\ddot{I}‰K^{+}{K}^{-}$ and $\ddot{I}•\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ (J=0, 1, 2) are measured for the first time.