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In this work, the lepton-number-violating processes in $|\Delta L|=2$ decaysof $\Lambda_b^0$ 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 anintermediate on-shell Majorana neutrino $N$ with a mass in the GeV scale. Weexplore the experimental sensitivity of these dimuon channels at the LHCb andCMS experiments, in which heavy neutrino lifetimes in the accessible ranges of$\tau_N = [1, 100, 1000]$ ps are considered. For a integrated luminositycollected of 10 and 50 fb${}^{-1}$ at the LHCb and 30, 300 and 3000 fb${}^{-1}$at the CMS, we found significant sensitivity on branching fractions of theorder ${\rm BR}(\Lambda_b^0 \to p \pi^+\mu^- \mu^-) \lesssim\mathcal{O}(10^{-9} - 10^{-8})$ and ${\rm BR}(\Lambda_b^0 \to \Lambda_c^+\pi^+\mu^- \mu^-) \lesssim \mathcal{O}(10^{-8} - 10^{-7})$. Exclusion regionson the parameter space ($m_N,|V_{\mu N}|^{2}$) associated with the heavyneutrino are presented and compared with those from $K^- \to \pi^+\mu^-\mu^-$(NA48/2) and $B^- \to \pi^+\mu^-\mu^-$ (LHCb) as well as by different searchstrategies such as NA3, CHARMII, NuTeV, Belle, and DELPHI.

Exploring GeV-scale Majorana neutrinos in lepton-number-violating $\Lambda_b^0$ baryon decays