Abstract
In the $\it{\mbox{type II seesaw}}$ model, if spontaneous violation of the lepton number conservation prevails over that of explicit violation, a rich Higgs sector phenomenology is expected to arise with light scalar states having mixed charged-fermiophobic/neutrinophilic properties. We study the constraints on these light CP-even ($h^0$) and CP-odd ($A^0$) states from LEP exclusion limits, combined with the so far established limits and properties of the $125-126$~GeV ${\cal H}$ boson discovered at the LHC. We show that, apart from a fine-tuned region of the parameter space, masses in the $\sim 44$ to $80$ GeV range escape from the LEP limits if the vacuum expectation value of the Higgs triplet is $\lesssim {\cal O}(10^{-3})$GeV, that is comfortably in the region for 'natural' generation of Majorana neutrino masses within this model. In the lower part of the scalar mass spectrum the decay channels ${\cal H} \to h^0 h^0, A^0 A^0$ lead predominantly to heavy flavor plus missing energy or to totally invisible Higgs decays, mimicking dark matter signatures without a dark matter candidate. Exclusion limits at the percent level of these (semi-)invisible decay channels would be needed, together with stringent bounds on the (doubly-)charged states, to constrain significantly this scenario. We also revisit complementary constraints from ${\cal H} \to \gamma \gamma$ and ${\cal H} \to Z \gamma$ channels on the (doubly)charged scalar sector of the model, pinpointing non-sensitivity regions, and carry out a likeliness study for the theoretically allowed couplings in the scalar potential.