The see-saw portal at future Higgs factories: the role of dimension six operators

We study an extension of the Standard Model with electroweak scale right-handed singlet fermions N that induces neutrino masses, plus a generic new physics sector at a higher scale Lambda. The latter is parametrized in terms of effective operators in the language of the nu SMEFT. We study its phenomenology considering operators up to d = 6, where additional production and decay modes for N are present in addition to those arising from the mixing with the active neutrinos. We focus on the production with four-Fermi operators and we identify the most relevant additional decay modes to be N -> nu gamma and N -> 3f. We assess the sensitivity of future Higgs factories on the nu SMEFT in regions of the parameter space where the new states decay promptly, displaced or are stable on detector lengths. We show that new physics scale up to 5-60 TeV can be explored, depending on the collider considered.