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Using a data sample of $(1310.6 \pm 7.0) \times 10^{6}$ $J/\psi$ events takenwith the BESIII detector at the center-of-mass energy of 3.097 GeV, we searchfor the first time for the lepton number violating decay $\Sigma^{-} \to pe^{-} e^{-}$ and the rare inclusive decay $\Sigma^{-} \to \Sigma^{+} X$, where$X$ denotes any possible particle combination. The $\Sigma^-$ candidates aretagged in $J/\psi \to \bar{\Sigma}(1385)^+\Sigma^-$ decays. No signalcandidates are found, and the upper limits on the branching fractions at the90\% confidence level are determined to be $\mathcal{B}(\Sigma^{-} \to p e^{-}e^{-}) < 6.7 \times 10^{-5}$ and $\mathcal{B}(\Sigma^{-} \to \Sigma^{+} X) <1.2 \times 10^{-4}$.

Search for the lepton number violating decay $\Sigma^{-} \to p e^{-} e^{-}$ and the rare inclusive decay $\Sigma^{-} \to \Sigma^{+} X$