Two-Higgs-doublet model

The two-Higgs-doublet model (2HDM) is an extension of the Standard Model of particle physics.[https://thesis.library.caltech.edu/4505/ "Higgs Scalars and the Nonleptonic Weak Interactions"], Christopher T. Hill, (1977); see pg. 100.{{cite book| last1=Gunion| first1=J.|author2=H. E. Haber |author3=G. L. Kane |author4=S. Dawson |title=The Higgs Hunters Guide| publisher=Addison-Wesley |year=1990}} 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.{{Cite journal|last1=Keus|first1=Venus|last2=King|first2=Stephen F.|last3=Moretti|first3=Stefano|date=2014-01-13|title=Three-Higgs-doublet models: symmetries, potentials and Higgs boson masses|journal=Journal of High Energy Physics|language=en|volume=2014|issue=1|pages=52|doi=10.1007/JHEP01(2014)052|issn=1029-8479|bibcode=2014JHEP...01..052K|arxiv=1310.8253|s2cid=118482476}}

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 {{Math|h}} and {{Math|H}} (where {{Math|H}} is heavier than {{Math|h}} by convention), the CP odd pseudoscalar {{Math|A}} and two charged Higgs bosons {{Math|H^±}}. The discovered Higgs boson is measured to be CP even, so one can map either {{Math|h}} or {{Math|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 {{Math|h}} has couplings exactly like the SM-Higgs boson.{{cite arXiv|eprint=1305.2424|first1=N.|last1=Craig|first2=J.|last2=Galloway|title=Searching for Signs of the Second Higgs Doublet|last3=Thomas|first3=S.|year=2013|class=hep-ph}} In another limit such limit, where $\sin(\beta - \alpha) \rightarrow 0$ , the heavier CP even boson, i.e. {{Math|H}} is SM-like, leaving {{Math|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.{{cite journal|arxiv=1809.10733|first1=CMS|last1=Collaboration|title=Combined measurements of Higgs boson couplings in proton–proton collisions at √s=13 TeV |journal=The European Physical Journal C |year=2019|volume=79 |issue=5 |page=421 |doi=10.1140/epjc/s10052-019-6909-y |pmid=31178657 |pmc=6528832 }}

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 experiment has conducted searches around this range but no significant excess above the standard model prediction has been observed.{{Cite web |title=Hunting the Higgs boson siblings with top quarks {{!}} CMS Experiment |url=https://cms.cern/news/hunting-higgs-boson-siblings-top-quarks |access-date=2023-09-02 |website=cms.cern}}{{Cite web |title=CMS-PAS-TOP-22-010 |url=https://cms-results.web.cern.ch/cms-results/public-results/preliminary-results/TOP-22-010/index.html |access-date=2023-09-02 |website=cms-results.web.cern.ch |language=en-US}}

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:{{cite journal

|last1=Craig

|first1=N.

|last2=Thomas

|first2=S.

|year=2012

|title=Exclusive Signals of an Extended Higgs Sector

|journal=Journal of High Energy Physics

|volume=1211 |issue=11

|pages=083

|doi=10.1007/JHEP11(2012)083

|arxiv = 1207.4835

|bibcode = 2012JHEP...11..083C |s2cid=119312000

}}{{cite journal

| last1 = Branco

| first1 = G. C.

| title = Theory and phenomenology of two-Higgs-doublet models

| journal = Physics Reports

| volume = 516

| issue = 1

| pages = 1–102

| publisher = Elsevier

| date = July 2012

| doi = 10.1016/j.physrep.2012.02.002

|bibcode = 2012PhR...516....1B |arxiv = 1106.0034

| last2 = Ferreira

| first2 = P.M.

| last3 = Lavoura

| first3 = L.

| last4 = Rebelo

| first4 = M.N.

| last5 = Sher

| first5 = Marc

| last6 = Silva

| first6 = João P.

| s2cid = 119214990

}}

class="wikitable"

! Type

! Description

! up-type quarks couple to

! down-type quarks couple to

! charged leptons couple to

! remarks

Type I

| Fermiophobic