# Vacuum stability and perturbativity of SU(3) scalars

## Abstract

We calculate the vacuum stability conditions and renormalisation group equations for the extensions of standard model with a higher colour multiplet scalar up to the representation 15' that leaves the strong interaction asymptotically free. In order to find the vacuum stability conditions, we calculate the orbit spaces for the self-couplings of the higher multiplets, which for the representations 15 and 15' of SU(3) _{c} are highly complicated. However, if the scalar potential is linear in orbit space variables, it is sufficient to know the convex hull of the orbit space. Knowledge of the orbit spaces also facilitates the minimisation of the potentials. In contrast to the self-couplings of other multiplets, we find that the scalar quartic couplings of the representations 3 and 8 walk rather than run, remaining nearly constant and perturbative over a vast energy range. We describe the conditions for walking couplings using a schematic model. With these technical results at hand we revise earlier results of generation of new scales with large SU(3) _{c} scalar multiplets. Our results are easily extendable to models of new physics with additional SU(3) or SU(N) gauge symmetries.

- Authors:

- Univ. of Helsinki (Finland). Helsinki Inst. of Physics. Dept. of Physics
- National Inst. of Chemical Physics and Biophysics, Tallinn (Estonia)
- Southern Methodist Univ., Dallas, TX (United States). Dept. of Physics

- Publication Date:

- Research Org.:
- Southern Methodist Univ., Dallas, TX (United States); National Inst. of Chemical Physics and Biophysics, Tallinn (Estonia); Univ. of Helsinki (Finland)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Estonian Research Council; Estonian Ministry of Education and Research; Academy of Finland; European Regional Development Fund (ERDF)

- OSTI Identifier:
- 1501929

- Grant/Contract Number:
- SC0010129; PUT799; IUT23-6; 267842; TK133

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 10; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Beyond Standard Model; renormalization group

### Citation Formats

```
Heikinheimo, Matti, Kannike, Kristjan, Lyonnet, Florian, Raidal, Martti, Tuominen, Kimmo, and Veermäe, Hardi. Vacuum stability and perturbativity of SU(3) scalars. United States: N. p., 2017.
Web. doi:10.1007/jhep10(2017)014.
```

```
Heikinheimo, Matti, Kannike, Kristjan, Lyonnet, Florian, Raidal, Martti, Tuominen, Kimmo, & Veermäe, Hardi. Vacuum stability and perturbativity of SU(3) scalars. United States. doi:10.1007/jhep10(2017)014.
```

```
Heikinheimo, Matti, Kannike, Kristjan, Lyonnet, Florian, Raidal, Martti, Tuominen, Kimmo, and Veermäe, Hardi. Tue .
"Vacuum stability and perturbativity of SU(3) scalars". United States. doi:10.1007/jhep10(2017)014. https://www.osti.gov/servlets/purl/1501929.
```

```
@article{osti_1501929,
```

title = {Vacuum stability and perturbativity of SU(3) scalars},

author = {Heikinheimo, Matti and Kannike, Kristjan and Lyonnet, Florian and Raidal, Martti and Tuominen, Kimmo and Veermäe, Hardi},

abstractNote = {We calculate the vacuum stability conditions and renormalisation group equations for the extensions of standard model with a higher colour multiplet scalar up to the representation 15' that leaves the strong interaction asymptotically free. In order to find the vacuum stability conditions, we calculate the orbit spaces for the self-couplings of the higher multiplets, which for the representations 15 and 15' of SU(3) c are highly complicated. However, if the scalar potential is linear in orbit space variables, it is sufficient to know the convex hull of the orbit space. Knowledge of the orbit spaces also facilitates the minimisation of the potentials. In contrast to the self-couplings of other multiplets, we find that the scalar quartic couplings of the representations 3 and 8 walk rather than run, remaining nearly constant and perturbative over a vast energy range. We describe the conditions for walking couplings using a schematic model. With these technical results at hand we revise earlier results of generation of new scales with large SU(3) c scalar multiplets. Our results are easily extendable to models of new physics with additional SU(3) or SU(N) gauge symmetries.},

doi = {10.1007/jhep10(2017)014},

journal = {Journal of High Energy Physics (Online)},

number = 10,

volume = 2017,

place = {United States},

year = {2017},

month = {10}

}

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