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We measured the branching fractions of the decays for the first time using the final states . The data sample exploited here is events collected with BESIII. We find $(\chi_{cJ}\rightarrow\Sigma^{-}\bar{\Sigma}^{+}) = (51.3\pm2.4\pm4.1)\times10^{-5},, (5.7\pm1.4\pm0.6)\times10^{-5},, \rm{and}~ (4.4\pm1.7\pm0.5)\times10^{-5}J=0,1,2$, respectively, where the first uncertainties are statistical and the second systematic.

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