$WWh$ anomalous couplings at one loop from a seesaw variant of radiatively-induced neutrino masses

After the successful measurement of the Higgs-like particle at the Large Hadron Collider, the determination of whether it corresponds to either the minimal version of the Higgs scalar, provided by the Standard Model, or to some new physics, so far unknown, has become a main objective of the high-energy-physics community. In particular, the investigation of the couplings of this particle with the rest of the Standard-Model field content is a central task. To this aim, in the present paper we consider a variant of the seesaw neutrino-mass-generating mechanism in which the masses of light neutrinos are generated via radiative corrections of the neutrino 2-point function. In this framework, we calculate the contributions from virtual Majorana neutrinos to the $WWh$ vertex, at one loop. A set of anomalous couplings, some of them $CP$-even and the others $CP$-odd, emerge from this calculation. We perform numerical estimations of these anomalous couplings by taking into account the role of the $WWh$ vertex in (1) $Wh$ production from $pp$ collisions and (2) in Higgs production by vector-boson fusion, occurring in some lepton collider. Our estimations show that all the generated anomalous couplings are beyond current experimental sensitivity. However, we note that $CP$-conserving anomalous couplings could be as large as $\sim10^{-3}$, which would be near the reach of the high-luminosity phase of the Large Hadron Collider. On the other hand, $CP$-odd effects, amounting to $\sim10^{-4}$, turn out to be well below expectations for the Compact Linear Collider by about 2 orders of magnitude.