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Search for hadronic transition $χ_{cJ}\toη_{c}π^{+}π^{-}$ and observation of $χ_{cJ}\to K\bar{K}πππ$

Hadronic transitions of $χ_{cJ}\to η_{c}π^{+}π^{-}$ (J=0, 1, 2) are searched for using a sample of $1.06\times 10^{8}$ $ψ(3686)$ events collected with the BESIII detector at the BEPCII storage ring. The $\etac$ is reconstructed with $K_{S}^{0}K^{+}π^{-}+c.c.$ and $K^{+}K^{-}π^{0}$ final states. No signals are observed in any of the three $χ_{cJ}$ 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 $χ_{cJ}\to K_{S}^{0}K^{+}π^{-}π^{+}π^{-}+c.c.$, $K^{+}K^{-}π^{+}π^{-}π^{0}$, $ωK^{+}K^{-}$ and $ϕπ^{+}π^{-}π^{0}$ (J=0, 1, 2) are measured for the first time.