Two-Higgs-doublet model explained

The two-Higgs-doublet model (2HDM) is an extension of the Standard Model of particle physics.^{[1] [2]} 2HDM models are one of the natural choices for beyond-SM models containing two Higgs doublets instead of just one. There are also models with more than two Higgs doublets, for example three-Higgs-doublet models etc.^[3]

The addition of the second Higgs doublet leads to a richer phenomenology as there are five physical scalar states viz., the CP even neutral Higgs bosons and (where is heavier than by convention), the CP odd pseudoscalar and two charged Higgs bosons . The discovered Higgs boson is measured to be CP even, so one can map either or with the observed Higgs. A special case occurs when

\cos(\beta - \alpha) → 0 , the alignment limit, in which the lighter CP even Higgs boson has couplings exactly like the SM-Higgs boson.^[4] In another limit such limit, where \sin(\beta - \alpha) → 0 , the heavier CP even boson, i.e. is SM-like, leaving to be the lighter than the discovered Higgs; however, it is important to note that experiments have strongly pointed towards a value for \sin(\beta - \alpha) that is close to 1.^[5]

Such a model can be described in terms of six physical parameters: four Higgs masses (

m _{\rm} , m _{\rm} , m _{\rm} , m _{H ^{\pm}} ), the ratio of the two vacuum expectation values (\tan \beta ) and the mixing angle (\alpha ) which diagonalizes the mass matrix of the neutral CP even Higgses. The SM uses only 2 parameters: the mass of the Higgs and its vacuum expectation value.

The masses of the H and A bosons could be below 1 TeV and the CMS has conducted searches around this range but no significant excess above the standard model prediction has been observed.^{[6] [7]}

Classification

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

\Phi , one can divide two-Higgs-doublet models into the following classes:^{[8] [9]}

Type	Description	up-type quarks couple to	down-type quarks couple to	charged leptons couple to	remarks
Type I	Fermiophobic	\Phi _{2}	\Phi _{2}	\Phi _{2}	charged fermions only couple to second doublet
Type II	MSSM-like	\Phi _{2}	\Phi _{1}	\Phi _{1}	up- and down-type quarks couple to separate doublets
X	Lepton-specific	\Phi _{2}	\Phi _{2}	\Phi _{1}
Y	Flipped	\Phi _{2}	\Phi _{1}	\Phi _{2}
Type III		\Phi _{1,} \Phi _{2}	\Phi _{1,} \Phi _{2}	\Phi _{1,} \Phi _{2}	Flavor-changing neutral currents at tree level
Type FCNC-free		\Phi _{1,} \Phi _{2}	\Phi _{1,} \Phi _{2}	\Phi _{1,} \Phi _{2}	By finding a matrix pair which can be diagonalized simultaneously. ^[10]

By convention,

\Phi _{2} is the doublet to which up-type quarks couple.

See also

• Alternatives to the Standard Model Higgs
• Composite Higgs models
• Preon

Notes and References

1. https://thesis.library.caltech.edu/4505/ "Higgs Scalars and the Nonleptonic Weak Interactions"
2. Book: Gunion. J.. H. E. Haber . G. L. Kane . S. Dawson . The Higgs Hunters Guide. Addison-Wesley . 1990.
3. Keus. Venus. King. Stephen F.. Moretti. Stefano. 2014-01-13. Three-Higgs-doublet models: symmetries, potentials and Higgs boson masses. Journal of High Energy Physics. en. 2014. 1. 52. 10.1007/JHEP01(2014)052. 1029-8479. 2014JHEP...01..052K. 1310.8253. 118482476.
4. 1305.2424. N.. Craig. J.. Galloway. Searching for Signs of the Second Higgs Doublet. Thomas. S.. 2013. hep-ph.
5. 1809.10733. CMS. Collaboration. Combined measurements of Higgs boson couplings in proton–proton collisions at √s=13 TeV . The European Physical Journal C . 2019. 79 . 5 . 421 . 10.1140/epjc/s10052-019-6909-y . 31178657 . 6528832 .
6. Web site: Hunting the Higgs boson siblings with top quarks CMS Experiment . 2023-09-02 . cms.cern.
7. Web site: CMS-PAS-TOP-22-010 . 2023-09-02 . cms-results.web.cern.ch . en-US.
8. Craig . N. . Thomas . S. . 2012 . Exclusive Signals of an Extended Higgs Sector . . 1211 . 11 . 083 . 10.1007/JHEP11(2012)083 . 1207.4835 . 2012JHEP...11..083C . 119312000 .
9. Branco . G. C. . Theory and phenomenology of two-Higgs-doublet models . Physics Reports . 516 . 1 . 1–102 . Elsevier . July 2012 . 10.1016/j.physrep.2012.02.002. 2012PhR...516....1B . 1106.0034 . Ferreira . P.M. . Lavoura . L. . Rebelo . M.N. . Sher . Marc . Silva . João P. . 119214990 .
10. Botella. Francisco J.. Cornet-Gomez. Fernando. Nebot. Miguel. 2018-08-30. Flavor conservation in two-Higgs-doublet models. Physical Review D. en. 98. 3. 035046. 10.1103/PhysRevD.98.035046. 1803.08521 . 2018PhRvD..98c5046B . 2470-0010. free.