Sensitivity prospects for lepton-trijet signals in the νSMEFT at the LHeC

The observation of neutrino oscillations and masses motivates the extension of the standard model with right-handed neutrinos, leading to heavy neutrino states possibly in the electroweak scale, which could be impacted by new high-scale weakly coupled physics. A systematic tool for studying these interactions is the neutrino-extended standard model effective field theory ν ν SMEFT. In this work we study the prospects of the future LHeC electron-proton collider to discover or constrain the ν ν SMEFT interactions, performing the first dedicated and realistic analysis of the well known lepton-trijet signals, for both the lepton flavor violating p ~ e⁻ → μ ⁻ + 3 j p e - → μ - + 3 j (LFV) and the lepton number violating p ~ e⁻ → μ ⁺ + 3 j p e - → μ + + 3 j (LNV) channels, for HNLs masses in the electroweak scale range: 100 ~GeV ≤ mN ≤ 500 ~GeV 100 GeV ≤ m N ≤ 500 GeV . The obtained sensitivity prospects show that the LHeC with 100 ~fb⁻¹ 100 fb - 1 luminosity could be able to probe the scenario of a heavy N and constrain the effective couplings to a region of the parameter space as tight as the bounds that are currently considered for the O(10) O ( 10 ) GeV scale masses, with effective couplings of O(10⁻¹) O ( 10 - 1 ) for NP scale Λ =1 \,TeV Λ = 1 TeV .