# Minimal $SU\left(3\right)\times SU\left(3\right)$ symmetry breaking patterns

## Abstract

Here, we study the vacua of an $$SU(3)\times SU(3)$$-symmetric model with a bifundamental scalar. Structures of this type appear in various gauge theories such as the Renormalizable Coloron Model, which is an extension of QCD, or the Trinification extension of the electroweak group. In other contexts, such as chiral symmetry, $$SU(3)\times SU(3)$$ is a global symmetry. As opposed to more general $$SU(N)\times SU(N)$$ symmetric models, the $N=3$ case is special due to the presence of a trilinear scalar term in the potential. We find that the most general tree-level potential has only three types of minima: one that preserves the diagonal $SU(3)$ subgroup, one that is $$SU(2)\times SU(2)\times U(1)$$ symmetric, and a trivial one where the full symmetry remains unbroken. The phase diagram is complicated, with some regions where there is a unique minimum, and other regions where two minima coexist.

- Authors:

- Univ. of Wisconsin, Madison, WI (United States). Dept. of Physics
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States). Theoretical Physics Dept.

- Publication Date:

- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1426512

- Alternate Identifier(s):
- OSTI ID: 1426671

- Report Number(s):
- FERMILAB-PUB-17-401-T; arXiv:1710.01456

Journal ID: ISSN 2470-0010; PRVDAQ; 1628658; TRN: US1802449

- Grant/Contract Number:
- AC02-07CH11359; SC0017647

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 5; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; extensions of gauge sector

### Citation Formats

```
Bai, Yang, and Dobrescu, Bogdan A.
```*Minimal SU(3)×SU(3) symmetry breaking patterns*. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.97.055024.

```
Bai, Yang, & Dobrescu, Bogdan A.
```*Minimal SU(3)×SU(3) symmetry breaking patterns*. United States. doi:10.1103/PhysRevD.97.055024.

```
Bai, Yang, and Dobrescu, Bogdan A. Fri .
"Minimal SU(3)×SU(3) symmetry breaking patterns". United States. doi:10.1103/PhysRevD.97.055024.
```

```
@article{osti_1426512,
```

title = {Minimal SU(3)×SU(3) symmetry breaking patterns},

author = {Bai, Yang and Dobrescu, Bogdan A.},

abstractNote = {Here, we study the vacua of an $SU(3)\times SU(3)$-symmetric model with a bifundamental scalar. Structures of this type appear in various gauge theories such as the Renormalizable Coloron Model, which is an extension of QCD, or the Trinification extension of the electroweak group. In other contexts, such as chiral symmetry, $SU(3)\times SU(3)$ is a global symmetry. As opposed to more general $SU(N)\times SU(N)$ symmetric models, the $N=3$ case is special due to the presence of a trilinear scalar term in the potential. We find that the most general tree-level potential has only three types of minima: one that preserves the diagonal $SU(3)$ subgroup, one that is $SU(2)\times SU(2)\times U(1)$ symmetric, and a trivial one where the full symmetry remains unbroken. The phase diagram is complicated, with some regions where there is a unique minimum, and other regions where two minima coexist.},

doi = {10.1103/PhysRevD.97.055024},

journal = {Physical Review D},

issn = {2470-0010},

number = 5,

volume = 97,

place = {United States},

year = {2018},

month = {3}

}

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