Clues on the Majorana scale from scalar resonances at the LHC

In order to address the observation of the neutrino oscillations and the metastability of the Standard Model, we extend the fermion sector with two right-handed (i.e. sterile) neutrinos, and the scalar sector of the SM with a real scalar, the Hill field. The latter takes the role of a Majoron and generates the Majorana masses for the neutrino sector, such that the particle spectrum features two CP-even scalars $h_1$ and $h_2$, and also two heavy, mass degenerate neutrinos. When the $h_1$ is identified with the scalar resonance at ~125 GeV and the condition is imposed that the $h_1$ self coupling and its running vanish at the Planck scale, the scalar mixing and the vacuum expectation value of the Hill field are fixed by the $h_2$ mass. The $h_2$ can be searched for at the LHC, and it has prospects of being discovered for the target integrated luminosities of the HL-LHC and the Future Circular hadron Collider (FCC-hh) when its mass is on the weak scale. The knowledge of the $h_2$ mass and its decay properties can yield an insight into its coupling to the heavy neutrinos, and thus also on the heavy neutrino mass scale. This yields an interesting connection between potentially detectable heavy scalars in high-energy proton collisions and the mass scale of the heavy neutrinos that is testable at the LHC and at future colliders.