Type II Seesaw Higgsology and LEP/LHC constraints

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In the 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 (h⁰) and CP-odd (A⁰) states from LEP exclusion limits, combined with the so far established limits and properties of the 125-126 GeV H boson discovered at the LHC. We show that, apart from a fine-tuned region of the parameter space, masses in the 44 to 80 GeV range escape from the LEP limits if the vacuum expectation value of the Higgs triplet is 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 H → h⁰ h⁰, A⁰ A⁰ 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 H → γγ and H → Z γ 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.