Abstract
We investigate unitarity bounds in the most general two Higgs doublet model without a discrete Z2 symmetry nor CP conservation. S-wave amplitudes for two-body elastic scatterings of Nambu–Goldstone bosons and physical Higgs bosons are calculated at high energies for all possible initial and final states (14 neutral, 8 singly-charged and 3 doubly-charged states). We obtain analytic formulae for the block-diagonalized scattering matrix by the classification of the two body scattering states using the conserved quantum numbers at high energies. Imposing the condition of perturbative unitarity to the eigenvalues of the scattering matrix, constraints on the model parameters can be obtained. We apply our results to constrain the mass range of the next-to-lightest Higgs state in the model.
Highlights
The Higgs boson was discovered at LHC in 2012 [1, 2], and its mass and coupling constants turned out to be consistent with the predictions in the standard model (SM) [3, 4]
The unitarity bound was mainly studied for the model with a discrete Z2 symmetry [10] with CP-conservation [11,12,13,14,15]
Analyses in the most general two Higgs doublet model (THDM) without the Z2 symmetry is getting important as an effective description of more various new physics scenarios, such as supersymmetric SMs with non-holomorphic Yukawa couplings [34] and general models with CP-violation [35] which is required for successful scenario of electroweak baryogenesis [36,37,38]
Summary
The most general Higgs potential under the SU (2)L × U (1)Y gauge symmetry is given by. By using the U (1)Y invariance and rephasing the doublet fields, the vacuum expectation values (VEVs) of the two doublet fields can be taken to be real without loss of generality [42,43,44]. The two doublet fields are described in terms of the component fields as. By introducing tan β v2/v1, two VEVs are described by v and as the usual notation. In the following, both the VEVs are assumed to be non-zero, except for the case of the inert doublet model discussed in Appendix. The three neutral states h′1, h′2 and h′3 are not the mass eigenstates at this stage, which generally mix with each other
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