The Two-Higgs doublet model (2HDM)

Abstract

The gauge boson and fermion sectors of the Standard Model of the electroweak interactions have been extremely well probed phenomenologically; yet, its scalar sector has not yet been directly explored. The 2HDM consists of two-complex hypercharge-one scalar doublets ?1 and ?2. Of the eight initial degrees of freedom, three are eaten and provide masses for the W± and Z, and the remaining five correspond to physical scalars: a charged Higgs pair, H±, and three neutral scalars h1, h2 and h3. In contrast to the SM, where the Higgs-sector is CP-conserving, the 2HDM allows for Higgs-mediated CP-violation. Of the various models suggested for 2HDM, the type II model as supersymmetric and Peccei–Quinn models are all of type II, the type II model is the most studied one.

Introduction

The gauge boson and fermion sectors of the Standard Model of the electroweak interactions have been extremely well probed phenomenologically; yet, its scalar sector has not yet been directly explored. In the Standard Model (SM) the simplest possible scalar structure – just one SU(2) doublet – is assumed 1–2; on the contrary, the fermion structure, with more than one family and with family mixing, is not simple at all.

For an arbitrary Higgs sector, the tree-level ?-parameter is given by

…… (1)

where VT,Y ? <?(T, Y )> defines the vacuum expectation values (vevs) of each neutral Higgs field, and T and Y specify the total SU(2) isospin and the hypercharge of the Higgs representation to which it belongs.

Y is normalized such that the electric charge of the scalar field is Q = T3 + Y/2, and……… (2)

The 2HDM consists of two-complex hypercharge-one scalar doublets 3 ?1 and ?2. Of the eight initial degrees of freedom, three are eaten and provide masses for the W± and Z, and the remaining five correspond to physical scalars: a charged Higgs pair, H±, and three neutral scalars h1, h2 and h3. In contrast to the SM, where the Higgs-sector is CP-conserving 4, the 2HDMallows for Higgs-mediated CP-violation. If CP is conserved, the three scalars can be classified as two CP-even scalars, h and H (where mh < mH) and a CP-odd scalar A. Thus, new features of the 2HDM include Charged Higgs bosons, a CP-odd Higgs boson (if CP is conserved in the Higgs sector), Higgs-mediated CP-violation (and neutral Higgs states of indefinite CP)

2HDM MODELS

Two-Higgs-doublet models can introduce Flavor-changing neutral currents which have not been observed so far. The Glashow-Weinberg condition, requiring that each group of fermions (up-type quarks, down-type quarks and charged leptons) couples exactly to one of the two doublets, is sufficient to avoid the prediction of flavor-changing neutral currents. Depending on which type of fermions couples to which doublet ? {displaystyle Phi }, one can divide two-Higgs-doublet models into a number of classes 5, few of them have been briefly described here.

Models with natural flavour conservation

The most serious potential problem facing all 2HDMs1 is the possibility of tree level flavour-changing neutral currents (FCNC). For example, the Yukawa couplings of the Q = ?1/3 quarks will, in general, be

…..(3)

where i, j are generation indices. The mass matrix is then

…..(4)

In the Standard Model, diagonalizing the mass matrix automatically diagonalizes the Yukawa interactions; therefore there are no tree-level FCNC. However, generally in 2HDMs, y1 and y2 will not be simultaneously diagonalizable, and thus the Yukawa couplings will not be flavour diagonal. Neutral Higgs scalars ? will mediate FCNC of the form, for example, ds?.

The inert Higgs model

The inert Higgs model is a 2HDM with an unbroken Z2 symmetry under which one of the doublets transforms nontrivially, viz. ?2 ? -?2, and all other SM fields are invariant. This ‘parity’ imposes natural flavour conservation. In the inert Higgs model the Higgs doublet ?2 – the inert doublet – does not couple to matter and acquires no vacuum expectation value, leaving the Z2 symmetry unbroken. The scalar spectrum consists of the SM-like Higgs obtained from ?1and one charged and two neutral states from ?2.

Models with tree-level flavour-changing neutral currentsThe type III 2HDM

As it was shown that one can eliminate the potentially dangerous tree-level FCNC through a discrete symmetry. Suppose, however, that we reject any such symmetry. The tree-level FCNC can certainly be suppressed by making the neutral scalars extremely heavy, but scalar masses in the multi-TeV range (or higher) seem unnatural. Here, the constraints from FCNC and show that a reasonable Ansatz for the neutral flavour-changing couplings allows for scalar masses well below the TeV scale were studied. It is easiest to discuss the tree-level FCNC in the Higgs basis. In that basis, the scalar doublets are rotated so that the vev is entirely in the first doublet, while the second doublet has zero vev. The general Yukawa couplings can be written as

…(5)

where H1 and H2 are the two scalar doublets. In the Higgs basis those doublets have been rotated so that only H1 has a vev, i.e.

…(6)

Models without tree-level FCNC

The differences among the various 2HDMs concern the Yukawa couplings to fermions. Production and decay of the charged Higgs in each of the four models viz, Type II model, Type I model, The Lepton-Specific model, and The flipped 2HDM can be explained.

Let us consider the Type II model. According to this, as supersymmetric and Peccei–Quinn models are all of type II, the type II model is the most studied one. From the Yukawa couplings data, one can see that the coupling of the charged Higgs to the top and bottom quarks is governed by either the bottom-quark mass times tan ?, which may be large, or by the top quark mass times cot ?. As a result, one expects potentially large virtual effects in b-quark decays and mixing. In fact, one of the major motivations for the B factories was the possibility of New Physics coupling strongly to the third generation; the type II 2HDM is the simplest example.

Conclusions

The Glashow-Weinberg condition, requiring that each group of fermions (up-type quarks, down-type quarks and charged leptons) couples exactly to one of the two doublets, is sufficient to avoid the prediction of flavor-changing neutral currents. A large number of models have been proposed for particle physics. Of the various models till proposed for 2HDM, it can be concluded that as supersymmetric and Peccei–Quinn models are all of type II, the type II model is the most studied one.

References:

1 P.W. Higgs, Phys. Rev. Lett. 13 (1964) 508.

2 G.S. Guralnik, C.R. Hagen, T.W.B. Kibble, Phys. Rev. Lett. 13 (1964) 585.

3 Gunion, J.; H. E. Haber; G. L. Kane; S. Dawson (1990). The Higgs Hunters Guide. Addison-Wesley.

4 R.D. Peccei, H.R. Quinn, Phys. Rev. Lett. 38 (1977) 1440

5 Branco, G. C.; Ferreira, P.M.; Lavoura, L.; Rebelo, M.N.; Sher, Marc; Silva, João P. (July 2012), “Theory and phenomenology of two-Higgs-doublet models”, Physics Reports, Elsevier.