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 Template:Math and Template:Math (where Template:Math is heavier than Template:Math by convention), the CP odd pseudoscalar Template:Math and two charged Higgs bosons Template:Math. The discovered Higgs boson is measured to be CP even, so one can map either Template:Math or Template:Math with the observed Higgs. A special case occurs when $\cos (\beta -\alpha )\to 0$, the alignment limit, in which the lighter CP even Higgs boson Template:Math has couplings exactly like the SM-Higgs boson. In another limit such limit, where $\sin (\beta -\alpha )\to 0$, the heavier CP even boson, i.e. Template:Math is SM-like, leaving Template:Math 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 ($m_{\mathrm{h}},m_{\mathrm{H}},m_{\mathrm{A}},m_{{\mathrm{H}}^{\pm }}$), 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 $\mathrm{\Phi }$, 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	${\mathrm{\Phi }}_2$	${\mathrm{\Phi }}_2$	${\mathrm{\Phi }}_2$	charged fermions only couple to second doublet
Type II	MSSM-like	${\mathrm{\Phi }}_2$	${\mathrm{\Phi }}_1$	${\mathrm{\Phi }}_1$	up- and down-type quarks couple to separate doublets
X	Lepton-specific	${\mathrm{\Phi }}_2$	${\mathrm{\Phi }}_2$	${\mathrm{\Phi }}_1$
Y	Flipped	${\mathrm{\Phi }}_2$	${\mathrm{\Phi }}_1$	${\mathrm{\Phi }}_2$
Type III		${\mathrm{\Phi }}_1,{\mathrm{\Phi }}_2$	${\mathrm{\Phi }}_1,{\mathrm{\Phi }}_2$	${\mathrm{\Phi }}_1,{\mathrm{\Phi }}_2$	Flavor-changing neutral currents at tree level
Type FCNC-free		${\mathrm{\Phi }}_1,{\mathrm{\Phi }}_2$	${\mathrm{\Phi }}_1,{\mathrm{\Phi }}_2$	${\mathrm{\Phi }}_1,{\mathrm{\Phi }}_2$	By finding a matrix pair which can be diagonalized simultaneously.

By convention, ${\mathrm{\Phi }}_2$ is the doublet to which up-type quarks couple.

See also

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