The extension of the standard model with right-handed neutrinos is motivated by the observation of neutrino oscillations and masses. These lead to heavy neutrino states possibly in the electroweak scale, which could be impacted by new high-scale weakly coupled physics. These interactions can be studied with a systematic tool like the neutrino-extended standard model effective field theory $\nu$SMEFT.

We present here some sensitivity prospects for future $e^+e^-$ and $e^-p$ colliders like the ILC and LHeC to a simplified benchmark scenario where we consider only one heavy neutrino $N$ and parameterize all the dim-6 effective couplings by the same numerical value, in an agnostic approach that takes into account possible operator-mixing, and captures the rich phenomenology of the heavy neutrino effective interactions.

The obtained exclusion plots show that both the LHeC and the ILC, with near $100 fb^{−1}$ 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 $O(10)$ GeV scale masses, with effective couplings of $O(10^{-1})$ for NP scale $\Lambda = 1$ TeV.