Riding the Seesaw. What Higgsstrahlung may reveal about massive neutrinos

We investigate if the projected high-precision measurements of the cross section of the Higgsstrahlung process $e^{+}{e}^{-}$ → Zh at a future electron-positron collider can be utilised to indirectly probe the fermionic Seesaw models. We consider the two centre-of-mass energies $\sqrt{s}$ = 240 GeV and 365 GeV, and compare the collider reaches to constraints from electroweak observables, probes of lepton flavour universality and the existing and prospective bounds from searches for lepton flavour violation. For the analysis we assume the limit of an exactly conserved lepton-number symmetry. We find that while any appreciable correction to the Higgsstrahlung cross section is already strictly constrained in the Type-I Seesaw model, effects of up to $O$(10%) are possible within Type-III Seesaw.