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In this work, the lepton-number-violating processes in $|\Delta L|=2$ decays of $\Lambda_b^0$ baryon, $\Lambda_b^0 \to p \pi^+\mu^- \mu^-$ and $\Lambda_b^0 \to \Lambda_c^+ \pi^+\mu^- \mu^-$, are investigated for the first time, via an intermediate on-shell Majorana neutrino $N$ with a mass in the GeV scale.
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