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Decays of the chi_{cJ} states (J=0,\ 1,\ 2) to \Lambda \Lambda bar\ pi^{+} \pi^{-}, including processes with intermediate \Sigma(1385), are studied through the E1 transition psi’–>\gamma chi_{cJ} using 106 million psi’ events collected with the BESIII detector at BEPCII. This is the first observation of chi_{cJ} decays to the final state \Lambda\Lambda bar \pi^{+}\pi^{-}. The branching ratio of the intermediate process chi_{cJ}–>\Sigma(1385)^{+/-} \bar{\Sigma}(1385)^{-/+} is also measured for the first time, and the results agree with the theoretical predictions based on the color-octet effect.

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