  Contrary to the see-saw models, extended Higgs sectors leading to
radiatively-induced neutrino masses do require the extra particles to be at the
TeV scale. However, these new states have often exotic decays, to which
experimental LHC searches performed so far, focused on scalars decaying into
pairs of same-sign leptons, are not sensitive. In this paper we show that their
experimental signatures can start to be tested with current LHC data if
dedicated multi-region analyses correlating different observables are used. We
also provide high-accuracy estimations of the complicated Standard Model
backgrounds involved. For the case of the Zee-Babu model, we show that regions
not yet constrained by neutrino data and low-energy experiments can be already
probed, while most of the parameter space could be excluded at the 95 % C.L. in
a high-luminosity phase of the LHC.

High Energy Physics - Phenomenology;High Energy Physics - Experiment