Two-Higgs-doublet model

In particle physics, a two-Higgs-doublet model (2HDM) is an extension of the Standard Model (SM) with an additional Higgs doublet with same quantum numbers. The philosophy is that why we have just one Higgs doublets, in principle there can be many. Therefore 2HDM are one of the simplest models of beyond SM physics, which contains two Higgs doublets instead of one. There are also models with more than two Higgs doublets example three Higgs doublet models etc. However in this page, we shall be confining ourselves to discussion of the 2HDMs.

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 $H^{\pm }$. Now as we have discovered 125-GeV Higgs Boson at the Large Hadron Collider at both ATLAS and CMS detectors, the immediate question which arises is that which of the scalar amongst these five will correspond to the discovered scalar? Since the discovered Higgs is measured to be CP even, we can map either $h$ or $H$ with the observed Higgs.

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

A special case is when $\cos(\beta -\alpha )\rightarrow 0$, the so-called alignment limit, in which the lighter CP even Higgs boson $h$ has couplings like the Higgs boson of the Standard Model. In another limit where $\sin(\beta -\alpha )\rightarrow 0$, the heavier CP even boson i.e. $H$ is SM-like and leaving $h$ to be the lighter than the discovered Higgs.

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:

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.

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