Searching for type I seesaw mechanism in a two Heavy Neutral Leptons scenario at FCC-ee

This paper investigates the search for heavy neutral leptons (HNL) in the type I seesaw mechanism at the Future Circular Collider in its $e^+e^-$ stage (FCC-ee), considering a luminosity of 125 ab$^{-1}$ collected at $\sqrt{s}=$91.2 GeV. The study examines two generations of heavy neutral leptons produced in association with Standard Model (SM) neutrinos and decaying to a purely leptonic final state. This theoretical framework can explain neutrino oscillations and other open questions of the SM, providing a broader perspective on the relevance of this experimental search. The analysis is performed using a fast simulation of the IDEA detector concept to study potential HNL interactions at the FCC-ee. The sensitivity contours are obtained from a selection of kinematic variables aimed at improving the signal-to-background ratio for the prompt production case. In the case of long-lived HNLs, the background can be almost fully eliminated by exploiting their displaced decay vertices. The study shows that the FCC-ee has a significant sensitivity to observing these objects in a region of the phase space not accessible by other experiments.