We study a model, in which lepton number violation is solely triggered by a dimension 4 hard breaking term in the scalar potential. A minimal model which contains a SU (2) triplet with hypercharge Y = 2, and a pair of singlet doubly charged scalar fields in addition to the Standard Model (SM) Higgs doublet is constructed. The model is technically natural in the sense that lepton number is preserved in the limit that the hard term vanishes. SM phenomenology restricts the vacuum expectation value of the triplet scalar field vT < 5.78 GeV. Neutrino masses controlled by vT are generated at the two loop level and are naturally to the sub-eV range. In general they exhibit normal hierarchy structure. Here the neutrino mass term does not dominate neutrinoless double beta decays of nuclei. Instead the short distance physics with doubly charged Higgs exchange gives the leading contribution. We expect weak scale singly and doubly charged Higgs bosons to make their appearances at the LHC and the ILC.
Motivated by the discovery hint of the Standard Model (SM) Higgs mass around 125 GeV at the LHC, we study the vacuum stability and perturbativity bounds on Higgs scalar of the SM extensions including neutrinos and dark matter (DM). Guided by the SM gauge symmetry and the minimal changes in the SM Higgs potential we consider two extensions of neutrino sector (Type-I and Type-III seesaw mechanisms) and DM sector (a real scalar singlet (darkon) and minimal dark matter (MDM)) respectively. The darkon contributes positively to the β function of the Higgs quartic coupling λ and can stabilize the SM vacuum up to high scale. Similar to the top quark in the SM we find the cause of instability is sensitive to the size of new Yukawa couplings between heavy neutrinos and Higgs boson, namely, the scale of seesaw mechanism. MDM and Type-III seesaw fermion triplet, two nontrivial representations of SU (2) L group, will bring the additional positive contributions to the gauge coupling g 2 renormalization group (RG) evolution and would also help to stabilize the electroweak vacuum up to high scale.
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