Two-Higgs-doublet model

Currently, experimental data seems to match well with the predictions of the Standard Model (SM). However, there is a widespread belief that due to many unanswered questions like dark matter, neutrino masses, the hierarchy problem, and the strong CP-problem, physics beyond the SM must exist. The Two-Higgs-doublet model (2HDM) is one of the simplest extensions of the SM.[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 ${\displaystyle h}$ and ${\displaystyle H}$ (where ${\displaystyle H}$ is heavier than ${\displaystyle h}$ by convention), the CP odd pseudoscalar ${\displaystyle A}$ and two charged Higgs bosons ${\displaystyle H^{\pm }}$. The discovered Higgs boson is measured to be CP even, so one can map either ${\displaystyle h}$ or ${\displaystyle H}$ with the observed Higgs. A special case occurs when ${\displaystyle \cos(\beta -\alpha )\rightarrow 0}$, the alignment limit, in which the lighter CP even Higgs boson ${\displaystyle h}$ has couplings exactly like the SM-Higgs boson.[4] In another limit such limit, where ${\displaystyle \sin(\beta -\alpha )\rightarrow 0}$, the heavier CP even boson, i.e. ${\displaystyle H}$ is SM-like, leaving ${\displaystyle h}$ to be the lighter than the discovered Higgs.

Such a model can be described in terms of has six physical parameters: four Higgs masses (${\displaystyle m_{h},m_{H},m_{A},m_{H^{\pm }}}$), the ratio of the two vacuum expectation values (${\displaystyle \tan \beta }$) and the mixing angle (${\displaystyle \alpha }$) 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.

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 ${\displaystyle \Phi }$, one can divide two-Higgs-doublet models into the following classes:[5][6]

Type	Description	up-type quarks couple to	down-type quarks couple to	charged leptons couple to	remarks
Type I	Fermiophobic	${\displaystyle \Phi _{2}}$	${\displaystyle \Phi _{2}}$	${\displaystyle \Phi _{2}}$	charged fermions only couple to second doublet
Type II	MSSM-like	${\displaystyle \Phi _{2}}$	${\displaystyle \Phi _{1}}$	${\displaystyle \Phi _{1}}$	up- and down-type quarks couple to separate doublets
X	Lepton-specific	${\displaystyle \Phi _{2}}$	${\displaystyle \Phi _{2}}$	${\displaystyle \Phi _{1}}$
Y	Flipped	${\displaystyle \Phi _{2}}$	${\displaystyle \Phi _{1}}$	${\displaystyle \Phi _{2}}$
Type III		${\displaystyle \Phi _{1},\Phi _{2}}$	${\displaystyle \Phi _{1},\Phi _{2}}$	${\displaystyle \Phi _{1},\Phi _{2}}$	Flavor-changing neutral currents at tree level
Type FCNC-free		${\displaystyle \Phi _{1},\Phi _{2}}$	${\displaystyle \Phi _{1},\Phi _{2}}$	${\displaystyle \Phi _{1},\Phi _{2}}$	By finding a matrix pair which can be diagonalized simultaneously. [7]

By convention, ${\displaystyle \Phi _{2}}$ is the doublet to which up-type quarks couple.

References

1. "Higgs Scalars and the Nonleptonic Weak Interactions," Christopher T. Hill, (1977); see pg. 100.
2. Gunion, J.; H. E. Haber; G. L. Kane; S. Dawson (1990). The Higgs Hunters Guide. Addison-Wesley.
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. 2014 (1): 52. arXiv:1310.8253. Bibcode:2014JHEP...01..052K. doi:10.1007/JHEP01(2014)052. ISSN 1029-8479. S2CID 118482476.
4. Craig, N.; Galloway, J.; Thomas, S. (2013). "Searching for Signs of the Second Higgs Doublet". arXiv:1305.2424 [hep-ph].
5. Craig, N.; Thomas, S. (2012). "Exclusive Signals of an Extended Higgs Sector". Journal of High Energy Physics. 1211 (11): 083. arXiv:1207.4835. Bibcode:2012JHEP...11..083C. doi:10.1007/JHEP11(2012)083. S2CID 119312000.
6. 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. 516 (1): 1–102. arXiv:1106.0034. Bibcode:2012PhR...516....1B. doi:10.1016/j.physrep.2012.02.002. S2CID 119214990.CS1 maint: ref=harv (link)
7. Botella, Francisco J.; Cornet-Gomez, Fernando; Nebot, Miguel (2018-08-30). "Flavor conservation in two-Higgs-doublet models". Physical Review D. 98 (3): 035046. doi:10.1103/PhysRevD.98.035046. ISSN 2470-0010.