Two-Higgs-doublet model

The two-Higgs-doublet model (2HDM) is an extension of the Standard Model of particle physics. 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.

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 $$\cos(\beta - \alpha) \rightarrow  0$$, the alignment limit, in which the lighter CP even Higgs boson $h$ has couplings exactly like the SM-Higgs boson. In another limit such limit, where $$\sin(\beta - \alpha) \rightarrow 0$$, 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 $$\sin(\beta - \alpha)$$ that is close to 1.

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

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:

By convention, $$\Phi_2$$ is the doublet to which up-type quarks couple.