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

Abstract: We propose a novel search strategy for heavy Majorana neutrinos based on the lepton-number-violating process $$μ^{-}p \to jN \to j(\ell<sup>{+}W<sup>{-})$$ at future muon-proton ($μp$) 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 $$N \to \ell^{{+}W^{-}} \to \ell<sup>{+}jj$$, 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 $2σ$ exclusion limits on the neutrino mixing parameter $|V_{\ell N}|<sup>2$ based on two typical integrated luminosity scenarios of $100~\text{fb}<sup>{-1}$ and $1~\text{ab}<sup>{-1}$. 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 $μp$ colliders can provide competitive sensitivity for probing heavy Majorana neutrinos over the mass range $200~\text{GeV} \leq m_N \leq 3000~\text{GeV}$.

• The paper demonstrates that resolved three-jet and boosted fat-jet searches can probe heavy Majorana neutrinos from 200 GeV to 3 TeV through lepton-number-violating production and decay.
• The analysis projects 2σ limits on |VℓN|² of 1.3 × 10⁻⁶ to 7.4 × 10⁻⁶ below 1 TeV and 8.8 × 10⁻⁵ at 3 TeV with 1 ab⁻¹ of data.
• The results indicate that a 5.3 TeV muon-proton collider could outperform several proposed facilities, although higher-order corrections, systematic uncertainties, detector design, and collider feasibility require further study.

Overview

This paper presents a phenomenological study of heavy Majorana neutrino searches at a future muon-proton ($\mu p$) collider with a 1 TeV muon beam and a 7 TeV proton beam, corresponding to $\sqrt{s} \approx 5.3$ TeV. The analysis targets the lepton-number-violating (LNV) process $\mu^{-}p \to jN \to j(\ell^{+}W^{-})$, with $\ell = e, \mu$, covering heavy-neutrino masses from 200 GeV to 3000 GeV. Two complementary final states are analyzed: a resolved topology with one charged lepton plus three jets for $200~\text{GeV} \leq m_N \leq 1000$ GeV, and a boosted fat-jet topology for $m_N \geq 1000$ GeV. The study employs full simulation chains including detector effects and derives projected $2\sigma$ exclusion limits on the mixing parameter $|V_{\ell N}|^2$.

Theoretical framework

The analysis is based on the minimal Type-I seesaw extension of the Standard Model, implemented through the $SM\_HeavyN\_LO$ UFO model. Three gauge-singlet right-handed neutrinos $N_{1,2,3}$ are introduced, mixing with active leptons via the parameter $\sqrt{s} \approx 5.3$0 in their couplings to the $\sqrt{s} \approx 5.3$1, $\sqrt{s} \approx 5.3$2, and Higgs bosons. The benchmark scenario assumes a single light heavy neutrino $\sqrt{s} \approx 5.3$3 with flavor-symmetric mixing $\sqrt{s} \approx 5.3$4 and vanishing coupling to tau flavor; the remaining two heavy neutrinos are decoupled at 10 TeV. For $\sqrt{s} \approx 5.3$5, the branching ratios approach the asymptotic ratio $\sqrt{s} \approx 5.3$6, making the charged-current channel dominant.

The LNV signature arises because the Majorana nature of $\sqrt{s} \approx 5.3$7 permits both $\sqrt{s} \approx 5.3$8 and its charge-conjugate decay, shifting lepton number by two units ($\sqrt{s} \approx 5.3$9). This provides a direct test of the Majorana hypothesis, complementing low-energy probes such as neutrinoless double beta decay.

Resolved three-jet analysis

For $\mu^{-}p \to jN \to j(\ell^{+}W^{-})$0 GeV, the signal cross section decreases monotonically with mass due to phase-space suppression; at $\mu^{-}p \to jN \to j(\ell^{+}W^{-})$1 GeV with $\mu^{-}p \to jN \to j(\ell^{+}W^{-})$2, it is approximately 1.83 fb. Events are generated with MadGraph5_aMC@NLO using NNPDF23L01 PDFs, passed through Pythia 6 showering, Delphes 3.4.2 fast detector simulation (with a dedicated $\mu^{-}p \to jN \to j(\ell^{+}W^{-})$3 detector card), anti-$\mu^{-}p \to jN \to j(\ell^{+}W^{-})$4 jet clustering ($\mu^{-}p \to jN \to j(\ell^{+}W^{-})$5), and analyzed within MadAnalysis 5.

Four sequential cuts are applied: single-lepton selection with mass-dependent $\mu^{-}p \to jN \to j(\ell^{+}W^{-})$6 thresholds (50 GeV below 500 GeV, 1000 GeV above), jet multiplicity and $\mu^{-}p \to jN \to j(\ell^{+}W^{-})$7 requirements, missing transverse energy $\mu^{-}p \to jN \to j(\ell^{+}W^{-})$8 GeV, and an invariant-mass window $\mu^{-}p \to jN \to j(\ell^{+}W^{-})$9 GeV. The cut flow demonstrates strong background suppression: after all cuts, the total background falls to the level of $\ell = e, \mu$0–$\ell = e, \mu$1 fb across all benchmark masses, while retaining 0.57, 0.36, and 0.114 fb of signal for $\ell = e, \mu$2, 600, and 900 GeV respectively. With 1 ab$\ell = e, \mu$3 of integrated luminosity, the resulting $\ell = e, \mu$4 exclusion limits on $\ell = e, \mu$5 range from $\ell = e, \mu$6 to $\ell = e, \mu$7 over 200 GeV to 1 TeV — substantially stronger than existing LHC bounds and competitive with or superior to projections for FCC-hh, FCC-eh, ILC, CLIC, and a 3 TeV muon collider in this mass range.

Fat-jet analysis

For TeV-scale neutrinos, the $\ell = e, \mu$8 boson from the $\ell = e, \mu$9 decay is highly boosted, and its hadronic decay products merge into a single large-radius jet. Fat jets are reconstructed with the Cambridge-Aachen algorithm at $200~\text{GeV} \leq m_N \leq 1000$0. A direct comparison with the FCC-eh ($200~\text{GeV} \leq m_N \leq 1000$1 TeV, $200~\text{GeV} \leq m_N \leq 1000$2 polarized 60 GeV electron beam) shows a marked advantage for the $200~\text{GeV} \leq m_N \leq 1000$3 option: at $200~\text{GeV} \leq m_N \leq 1000$4 GeV with $200~\text{GeV} \leq m_N \leq 1000$5, the cross section is 0.14 fb at the $200~\text{GeV} \leq m_N \leq 1000$6 collider versus $200~\text{GeV} \leq m_N \leq 1000$7 fb at the FCC-eh, a factor of roughly twenty improvement attributable to the higher partonic energy available in muon-initiated collisions.

Five cuts are applied, including a fat-jet mass window $200~\text{GeV} \leq m_N \leq 1000$8 GeV, $200~\text{GeV} \leq m_N \leq 1000$9 GeV, and $m_N \geq 1000$0. After the full selection, the total background is reduced to approximately 0.0043 fb for $m_N \geq 1000$1 GeV, $m_N \geq 1000$2 fb for 2000 GeV, and $m_N \geq 1000$3 fb for 3000 GeV, with the dilepton process $m_N \geq 1000$4 emerging as the dominant residual background. The projected sensitivities are:

$m_N \geq 1000$5 [GeV]	$m_N \geq 1000$6 limit on $m_N \geq 1000$7, $m_N \geq 1000$8 fb$m_N \geq 1000$9	$2\sigma$0 fb$2\sigma$1
1000	$2\sigma$2	$2\sigma$3
2000	—	—
3000	$2\sigma$4	$2\sigma$5

Notably, even with only 100 fb$2\sigma$6, the $2\sigma$7 sensitivity exceeds the global indirect constraints on heavy-neutrino mixing across the entire 1–3 TeV range, and surpasses the projected reaches of CLIC (4 ab$2\sigma$8), a 3 TeV muon collider (1 ab$2\sigma$9), and FCC-eh (up to 3 ab$|V_{\ell N}|^2$0) for masses below 3 TeV.

Limitations and open questions

Several assumptions qualify these results. The analysis assumes leading-order cross sections computed with MadGraph5_aMC@NLO; next-to-leading-order QCD corrections and their impact on both signal acceptance and background normalization are not assessed. The flavor structure is restricted to equal electron and muon mixing with $|V_{\ell N}|^2$1, so sensitivities under alternative flavor hypotheses remain unexplored. Detector performance relies on a Delphes fast-simulation card specific to a hypothetical $|V_{\ell N}|^2$2 detector rather than a fully designed experimental concept, and no systematic uncertainties on backgrounds or luminosity are included in the significance calculation, which uses the asymptotic formula of Cowan et al. The collider itself remains conceptual: beam parameters, achievable luminosity, and pile-up conditions for a multi-TeV $|V_{\ell N}|^2$3 facility have not been established experimentally. Finally, the study does not address lepton-number-conserving channels or displaced-vertex signatures, which could extend sensitivity to smaller mixings at low masses.

Conclusion

This work establishes that a future $|V_{\ell N}|^2$4 collider with $|V_{\ell N}|^2$5 TeV offers a competitive and complementary probe of heavy Majorana neutrinos between 200 GeV and 3 TeV. Exploiting on-shell single production via $|V_{\ell N}|^2$6-channel $|V_{\ell N}|^2$7 exchange and both resolved and fat-jet topologies, the proposed searches would constrain $|V_{\ell N}|^2$8 down to $|V_{\ell N}|^2$9 at low masses and $SM\_HeavyN\_LO$0 at 3 TeV with 1 ab$SM\_HeavyN\_LO$1, improving on current LHC limits and outperforming projections for other proposed facilities in overlapping mass regions. The results position the $SM\_HeavyN\_LO$2 collider as a credible option for testing the Majorana nature of heavy neutral leptons through clean $SM\_HeavyN\_LO$3 signatures.