Emergent two-Higgs doublet models

We investigate origin of three features that are often assumed in analysis of two-Higgs doublet models: (i) softly broken Z2 symmetry, (ii) CP invariant Higgs potential, and (iii) degenerated mass spectra. We extend electroweak gauge symmetry, introducing extra gauge symmetry and extra scalars, and we show that our models effectively derive two-Higgs dou- blet models at low energy which naturally hold the three features. We also find that the models can solve the strong CP problem.


CP invariance in Higgs potential
2 Review of two-Higgs doublet models In this section, we review the two-Higgs doublet model with the softly broken Z 2 symmetry widely discussed. We have two Higgs fields, Φ 1 and Φ 2 , charged under SU(2) L ×U(1) Y . In general the Higgs potential at the renormalizable level is given as follows: Four parameters, m 2 3 , λ 5 , λ 6 , and λ 7 , can be complex, and they are CP violating. Now, we impose a softly broken Z 2 symmetry to the Higgs fields: (Φ 1 , Φ 2 ) → (Φ 1 , −Φ 2 ). The Z 2 symmetry forbids λ 6 and λ 7 terms. The m 2 3 term breaks the Z 2 symmetry softly, but can shift the scalar masses. Let us define the vacuum expectation values (VEVs) of the Higgs fields as and then the relation with the Fermi constant is We also define β as follows: (2.4) JHEP08(2016)0 2 Review of two-Higgs doublet models In this section, we review the two-Higgs doublet model with the softly broken Z 2 symmetry widely discussed. We have two Higgs fields, Φ 1 and Φ 2 , charged under SU(2) L ×U(1) Y . In general the Higgs potential at the renormalizable level is given as follows: Four parameters, m 2 3 , λ 5 , λ 6 , and λ 7 , can be complex, and they are CP violating. Now, we impose a softly broken Z 2 symmetry to the Higgs fields: (Φ 1 , Φ 2 ) → (Φ 1 , −Φ 2 ). The Z 2 symmetry forbids λ 6 and λ 7 terms. The m 2 3 term breaks the Z 2 symmetry softly, but can shift the scalar masses. Let us define the vacuum expectation values (VEVs) of the Higgs fields as and then the relation with the Fermi constant is We also define β as follows: Review of two-Higgs doublet models n this section, we review the two-Higgs doublet model with the softly broken Z 2 symmetry idely discussed. We have two Higgs fields, Φ 1 and Φ 2 , charged under SU(2) L ×U(1) Y . In eneral the Higgs potential at the renormalizable level is given as follows: our parameters, m 2 3 , λ 5 , λ 6 , and λ 7 , can be complex, and they are CP violating. Now, we mpose a softly broken Z 2 symmetry to the Higgs fields: (Φ 1 , Φ 2 ) → (Φ 1 , −Φ 2 ). The Z 2 ymmetry forbids λ 6 and λ 7 terms. The m 2 3 term breaks the Z 2 symmetry softly, but can hift the scalar masses. Let us define the vacuum expectation values (VEVs) of the Higgs elds as nd then the relation with the Fermi constant is Review of two-Higgs doublet models n this section, we review the two-Higgs doublet model with the softly broken Z 2 symmetry idely discussed. We have two Higgs fields, Φ 1 and Φ 2 , charged under SU(2) L ×U(1) Y . In eneral the Higgs potential at the renormalizable level is given as follows: our parameters, m 2 3 , λ 5 , λ 6 , and λ 7 , can be complex, and they are CP violating. Now, we mpose a softly broken Z 2 symmetry to the Higgs fields: (Φ 1 , Φ 2 ) → (Φ 1 , −Φ 2 ). The Z 2 ymmetry forbids λ 6 and λ 7 terms. The m 2 3 term breaks the Z 2 symmetry softly, but can hift the scalar masses. Let us define the vacuum expectation values (VEVs) of the Higgs elds as nd then the relation with the Fermi constant is 3) e also define β as follows: v d v u 2 Review of two-Higgs doublet models In this section, we review the two-Higgs doublet model with the softly broken Z 2 symmetry widely discussed. We have two Higgs fields, Φ 1 and Φ 2 , charged under SU(2) L ×U(1) Y . In general the Higgs potential at the renormalizable level is given as follows: Four parameters, m 2 3 , λ 5 , λ 6 , and λ 7 , can be complex, and they are CP violating. Now, we impose a softly broken Z 2 symmetry to the Higgs fields: (Φ 1 , Φ 2 ) → (Φ 1 , −Φ 2 ). The Z 2 symmetry forbids λ 6 and λ 7 terms. The m 2 3 term breaks the Z 2 symmetry softly, but can shift the scalar masses. Let us define the vacuum expectation values (VEVs) of the Higgs fields as and then the relation with the Fermi constant is We also define β as follows: complex parameters：m 3 , λ 5 , λ 6 , λ 7 absent in Z 2 symmetric model ：λ 6 , λ 7 (m 3 breaks Z 2 symmetry softly)

CP is violated in general
However, in many cases, CP invariance is assumed for simplicity

Origin of the three assumptions?
They are reasonable assumptions, but are there origin of them?

Model
Review: SM Higgs with matrix rep.
• introduce vector-like fermions • see-saw • details are discussed in the paper [TA, Omura ʼ16]