Abstract
When a small vacuum expectation value of Higgs triplet (\U0001d710∆) in the type-II seesaw model is required to explain neutrino oscillation data, a fine-tuning issue occurs on the mass-dimension lepton-number-violation (LNV) scalar coupling. Using the scotogenic approach, we investigate how a small LNV term is arisen through a radiative correction when an Z2-odd vector-like lepton (X) and an Z2-odd right-handed Majorana lepton (N) are introduced to the type-II seesaw model. Due to the dark matter (DM) direct detection constraints, the available DM candidate is the right-handed Majorana particle, whose mass depends on and is close to the mX parameter. Combing the constraints from the DM measurements, the h → γγ decay, and the oblique T -parameter, it is found that the preferred range of v∆ is approximately in the region of 10−5−10−4 GeV; the mass difference between the doubly and the singly charged Higgs is less than 50 GeV, and the influence on the h → Z γ decay is not significant. Using the constrained parameters, we analyze the decays of each Higgs triplet scalar in detail, including the possible three-body decays when the kinematic condition is allowed. It is found that with the exception of doubly charged Higgs, scalar mixing effects play an important role in the Higgs triplet two-body decays when the scalar masses are near-degenerate. In the non-degenerate mass region, the branching ratios of the Higgs triplet decays are dominated by the three-body decays.
Highlights
It is known that the ∆ VEV is dictated by the lepton-number softly breaking term μ∆HT iτ2∆†H, which appears in the scalar potential
We investigate how a small LNV term is arisen through a radiative correction when an Z2-odd vector-like lepton (X) and an Z2-odd right-handed Majorana lepton (N ) are introduced to the type-II seesaw model
In order to naturally obtain a small μD parameter in the type-II seesaw model, in this study, we consider that μ∆HT iτ2∆†H is suppressed at the tree level due to the leptonnumber symmetry; the necessary μ∆ term is radiatively induced through the scotogenic mechanism [39,40,41]
Summary
In addition to the SM particles, we add one Higgs triplet ∆, one vector-like lepton doublet XR,L, and one SU(2) singlet heavy neutrino into the SM, where their representations in SU(2)L × U(1)Y are given in table 1. In order to avoid the Dirac neutrino mass term, we require that X and N are Z2-odd states and that the others are Z2-even; the lightest neutral particles of X and N could be the DM candidate. In order to dynamically generate the finite dimension-3 lepton-number violating term in the scalar potential, we assign that XL(R), N and ∆ carry the lepton numbers as 0(1), 0 and 2, respectively, where the lepton number symmetry is softly broken by the X Dirac mass term. The Higgs doublet, vector-like lepton doublet, and Higgs triplet are respectively expressed as: G+. The VEVs and scalar masses are determined by the scalar potential
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