Abstract
The extension of the Standard Model (SM) with two Higgs triplets offers an appealing way to account for both tiny Majorana neutrino masses via the type-II seesaw mechanism and the cosmological matter-antimatter asymmetry via the triplet leptogenesis. In this paper, we classify all possible accidental symmetries in the scalar potential of the two-Higgs-triplet model (2HTM). Based on the bilinear-field formalism, we show that the maximal symmetry group of the 2HTM potential is SO(4) and eight types of accidental symmetries in total can be identified. Furthermore, we examine the impact of the couplings between the SM Higgs doublet and the Higgs triplets on the accidental symmetries. The bounded-from-below conditions on the scalar potential with specific accidental symmetries are also derived. Taking the SO(4)-invariant scalar potential as an example, we investigate the vacuum structures and the scalar mass spectra of the 2HTM.
Highlights
Pauli matrices with the transpose “T” acting only on the three-dimensional representation space.1 After the neutral components of the Higgs triplets and th√e Standard Model (SM) Higgs doublet acquire their vacuum expectation values, namely, √
We mainly focus on the accidental symmetries of the scalar potential, the symmetry transformations should in the first place keep the kinetic terms invariant
Since the accidental symmetries of the scalar potential in the 2HTM exist only in the flavor space of two Higgs triplets, it is evident that all the terms proportional to HTiσ2σ · φiH should violate all these symmetries except the SO(2)j symmetry, as well as the Z2 symmetry related to the exchange of φ1 and φ2 when μ1 = μ2
Summary
Let us first briefly recall the basic structure of the 2HTM, in particular the scalar potential, and the bilinear-field formalism [29,30,31], in order to establish our notations and conventions. As in the type-II seesaw model, the minimization of the full scalar potential gives rise to the vev’s of the neutral components of the Higgs triplets, leading to tiny Majorana neutrino masses. To this end, the trilinear coupling terms μ1HTiσ2σ · φ1H and μ2HTiσ2σ · φ2H in the doublet-triplet mixing potential VHφ in eq (2.3) are crucially important. Where all the four components of Φ transform in the same way under the SU(2)L gauge group This is the direct consequence of the pure imaginary representation matrices (ti)jk = −i ijk such that φ(i∗) → exp(−itjαj)φ(i∗), where αj (for j = 1, 2, 3) are the spacetimedependent real parameters.
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