Search for heavy Majorana neutrinos at muon-proton colliders via lepton-number-violating signals

We propose a novel search strategy for heavy Majorana neutrinos based on the lepton-number-violating process $\mu^{-}p \to jN \to j(\ell^{+}W^{-})$ at future muon-proton ($\mu p$) colliders equipped with 1 TeV muon beams and 7 TeV proton beams, yielding a center-of-mass energy of approximately 5.3 TeV. For heavy neutrinos with masses in the range $200~\text{GeV} \lesssim m_N \lesssim 1000~\text{GeV}$, this analysis targets the decay chain $N \to \ell^{+}W^{-} \to \ell^{+}jj$, producing a characteristic final state consisting of one charged lepton and three well-resolved jets. For TeV-scale Majorana neutrinos, the $W$ boson is highly boosted, such that its hadronic decay products coalesce into a prominent fat-jet ($J$) signature. We conduct comprehensive signal and background analyses that account for realistic detector effects to assess the search sensitivity. We derive the projected $2\sigma$ exclusion limits on the neutrino mixing parameter $|V_{\ell N}|^2$ based on two typical integrated luminosity scenarios of $100~\text{fb}^{-1}$ and $1~\text{ab}^{-1}$. The results demonstrate that the proposed search strategy can achieve constraints substantially superior to the existing bounds from the LHC and other high-energy colliders. This study demonstrates that future $\mu p$ colliders can provide competitive sensitivity for probing heavy Majorana neutrinos over the mass range $200~\text{GeV} \leq m_N \leq 3000~\text{GeV}$.