# Minkowski space structure of the Higgs potential in the two-Higgs-doublet model

## Abstract

The Higgs potential of 2HDM keeps its generic form under the group of transformation GL(2,C), which is larger than the usually considered reparametrization group SU(2). This reparametrization symmetry induces the Minkowski space structure in the orbit space of 2HDM. Exploiting this property, we present a geometric analysis of the number and properties of stationary points of the most general 2HDM potential. In particular, we prove that charge-breaking and neutral vacua never coexist in 2HDM and establish conditions when the most general explicitly CP-conserving Higgs potential has spontaneously CP-violating minima. We also define the prototypical model of a given 2HDM, which has six free parameters less than the original one but still contains all the essential physics. Our analysis avoids manipulation with high-order algebraic equations.

- Authors:

- Istituto Nazionale di Fisica Nucleare, Gruppo collegato di Cosenza, I-87036 Arcavacata di Rende, Cosenza (Italy)
- (Belgium) and Sobolev Institute of Mathematics, academician Koptyug avenue 4, 630090, Novosibirsk (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 21011004

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevD.75.035001; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CP INVARIANCE; HIGGS BOSONS; HIGGS MODEL; MINKOWSKI SPACE; POTENTIALS; QUANTUM FIELD THEORY; SU GROUPS; SYMMETRY; TRANSFORMATIONS

### Citation Formats

```
Ivanov, I. P., and Physique theorique fondamentale, Departement de Physique, Universite de Liege, Allee du 6 Aout 17, batiment B5a, B-4000 Liege.
```*Minkowski space structure of the Higgs potential in the two-Higgs-doublet model*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.035001.

```
Ivanov, I. P., & Physique theorique fondamentale, Departement de Physique, Universite de Liege, Allee du 6 Aout 17, batiment B5a, B-4000 Liege.
```*Minkowski space structure of the Higgs potential in the two-Higgs-doublet model*. United States. doi:10.1103/PHYSREVD.75.035001.

```
Ivanov, I. P., and Physique theorique fondamentale, Departement de Physique, Universite de Liege, Allee du 6 Aout 17, batiment B5a, B-4000 Liege. Thu .
"Minkowski space structure of the Higgs potential in the two-Higgs-doublet model". United States.
doi:10.1103/PHYSREVD.75.035001.
```

```
@article{osti_21011004,
```

title = {Minkowski space structure of the Higgs potential in the two-Higgs-doublet model},

author = {Ivanov, I. P. and Physique theorique fondamentale, Departement de Physique, Universite de Liege, Allee du 6 Aout 17, batiment B5a, B-4000 Liege},

abstractNote = {The Higgs potential of 2HDM keeps its generic form under the group of transformation GL(2,C), which is larger than the usually considered reparametrization group SU(2). This reparametrization symmetry induces the Minkowski space structure in the orbit space of 2HDM. Exploiting this property, we present a geometric analysis of the number and properties of stationary points of the most general 2HDM potential. In particular, we prove that charge-breaking and neutral vacua never coexist in 2HDM and establish conditions when the most general explicitly CP-conserving Higgs potential has spontaneously CP-violating minima. We also define the prototypical model of a given 2HDM, which has six free parameters less than the original one but still contains all the essential physics. Our analysis avoids manipulation with high-order algebraic equations.},

doi = {10.1103/PHYSREVD.75.035001},

journal = {Physical Review. D, Particles Fields},

number = 3,

volume = 75,

place = {United States},

year = {Thu Feb 01 00:00:00 EST 2007},

month = {Thu Feb 01 00:00:00 EST 2007}

}