New physics in the $ZZh$ vertex: One-loop contributions from a radiative seesaw model

Precision Higgs physics offers a sensitive window into physics beyond the Standard Model. In parallel, neutrino-oscillation experiments have established the existence of nonzero neutrino masses, thus implying the presence of new physics. Motivated by these facts, we investigate the one-loop contributions of light and heavy Majorana neutrinos to the $ZZh$ vertex within a variant of the type-I seesaw mechanism in which light-neutrino masses vanish at tree level and are then generated radiatively. We analyze the $CP$-conserving and $CP$-violating anomalous couplings which characterize the $ZZh$ vertex and study their phenomenological implications in two relevant kinematic scenarios at future lepton colliders: Higgsstrahlung production and Higgs production via neutral-current vector-boson fusion. We find that $CP$-conserving effects can reach magnitudes of order ${10}^{-3}$, potentially within projected future experimental sensitivities, whereas $CP$-violating contributions are strongly suppressed, lying well beyond such projections.