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Using a data sample of 106 million $psi(3686)$ events collected with the BESIII detector operated at the BEPCII storage ring, we study for the first time the decay $chi_{cJ}tophi K^{0}_S K^{pm}pi^{mp}$ and $chi_{cJ}tophi K^{+} K^{-}pi^{0}$ in the E1 radiative transition $psi(3686)togammachi_{cJ}$. The decays are dominated by the three-body decay $chi_{cJ}to phi K^*(892)bar{K}$. We measure branching fractions for this reaction via the neutral and charged $K^*(892)$ and find them consistent with each other within the expectation of isospin symmetry. In the $Kbar{K}pi$ invariant mass distribution a structure near the $K^*(892)bar{K}$ mass threshold is observed, and the corresponding mass and width are measured to be $1412pm4(mathrm{stat.})pm8(mathrm{sys.}) mathrm{MeV}/c^2$ and $Gamma$ = $84pm12(mathrm{stat.})pm40(mathrm{sys.}) mathrm{MeV}$, respectively. The observed state favors an assignment to the $h_1(1380)$, considering its possible $J^{PC}$ and comparing its mass, width and decay mode to those reported in the Particle Data Group.
We search for the M1 radiative transition psi(3686) to gammaeta_{c}(2S) by reconstructing the exclusive eta_{c}(2S) to K_{S}^{0}K^{pm}pi^{mp}pi^{+}pi^{-} decay using 1.06 times 10^8 psi(3686) events collected with the BESIII detector. The signal is o bserved with a statistical significance of greater than 4 standard deviations. The measured mass of the eta_{c}(2S) is 3646.9 pm 1.6(stat) pm 3.6(syst) MeV/c^2, and the width is 9.9 pm 4.8(stat) pm 2.9(syst) MeV/c^2. The product branching fraction is measured to be B(psi(3686) to gammaeta_{c}(2S)) times B(eta_{c}(2S) to K_{S}^{0}K^{pm}pi^{mp}pi^{+}pi^{-}) = (7.03 pm 2.10(stat) pm 0.70(syst)) times 10^{-6}. This measurement complements a previous BESIII measurement of psi(3686) to gammaeta_{c}(2S) with eta_{c}(2S) to K_{S}^{0} K^{pm}pi^{mp} and K^{+}K^{-}pi^{0}.
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