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 h and H (where H is heavier than h by convention), the CP odd pseudoscalar A and two charged Higgs bosons H^±. The discovered Higgs boson is measured to be CP even, so one can map either h or 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 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. H is SM-like, leaving h to be the lighter than the discovered Higgs; however, it is important to note that experiments have strongly pointed towards a value for ${\displaystyle \sin(\beta -\alpha )}$ that is close to 1.^[5]

Such a model can be described in terms of six physical parameters: four Higgs masses (${\displaystyle m_{\rm {h)),m_{\rm {H)),m_{\rm {A)),m_{\mathrm {H} ^{\pm ))}$), 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.

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 ${\displaystyle \Phi }$, 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	${\displaystyle \Phi _{2))$	${\displaystyle \Phi _{2))$	${\displaystyle \Phi _{2))$	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. [10]

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