Probing Scalar-Mediated Sterile Neutrinos with Gravitational Wave and Colliders Signals

We propose a UV-complete extension of the Standard Model in which a gauge-singlet scalar S acquires a vacuum expectation value, generates a Majorana mass for a sterile neutrino N, and mixes with the Higgs field. This framework addresses neutrino masses via a seesaw mechanism and, for sufficiently large scalar mixing, can also drive a strong first-order electroweak phase transition, producing gravitational-wave (GW) signals potentially detectable by GW observatories. The Higgs-S mixing also enhances sterile-neutrino pair production at colliders through s-channel exchange of the Higgs and S. Owing to the small active-sterile mixing angle, N is generically long-lived, yielding characteristic displaced-vertex signatures. The combination of GW observations and displaced-vertex searches at colliders provides complementary cross-checks of the model parameter space.