# NLO perturbativity bounds on quartic couplings in renormalizable theories with ${\Phi}^{4}$ -like scalar sectors

## Abstract

The apparent breakdown of unitarity in low order perturbation theory is often is used to place bounds on the parameters of a theory. In this work we give an algorithm for approximately computing the next-to-leading order (NLO) perturbativity bounds on the quartic couplings of a renormalizable theory whose scalar sector is Φ ^{4} -like. And by this we mean theories where either there are no cubic scalar interactions, or the cubic couplings are related to the quartic couplings through spontaneous symmetry breaking. Furthermore, the quantity that tests where perturbation theory breaks down itself can be written as a perturbative series, and having the NLO terms allows one to test how well the series converges. We also present a simple example to illustrate the effect of considering these bounds at different orders in perturbation theory. For example, there is a noticeable difference in the viable parameter when the square of the NLO piece is included versus when it is not.

- Authors:

- Brookhaven National Lab. (BNL), Upton, NY (United States). Dept. of Physics

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

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

- OSTI Identifier:
- 1377050

- Alternate Identifier(s):
- OSTI ID: 1375510

- Report Number(s):
- BNL-114193-2017-JA

Journal ID: ISSN 2470-0010; PRVDAQ; KA2401012

- Grant/Contract Number:
- SC00112704; SC0012704

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 3; 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; NLO; scalar; sectors; quartic; coupling; S-matrix

### Citation Formats

```
Murphy, Christopher W.
```*NLO perturbativity bounds on quartic couplings in renormalizable theories with Φ4 -like scalar sectors*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevD.96.036006.

```
Murphy, Christopher W.
```*NLO perturbativity bounds on quartic couplings in renormalizable theories with Φ4 -like scalar sectors*. United States. doi:10.1103/PhysRevD.96.036006.

```
Murphy, Christopher W. Thu .
"NLO perturbativity bounds on quartic couplings in renormalizable theories with Φ4 -like scalar sectors". United States.
doi:10.1103/PhysRevD.96.036006. https://www.osti.gov/servlets/purl/1377050.
```

```
@article{osti_1377050,
```

title = {NLO perturbativity bounds on quartic couplings in renormalizable theories with Φ4 -like scalar sectors},

author = {Murphy, Christopher W.},

abstractNote = {The apparent breakdown of unitarity in low order perturbation theory is often is used to place bounds on the parameters of a theory. In this work we give an algorithm for approximately computing the next-to-leading order (NLO) perturbativity bounds on the quartic couplings of a renormalizable theory whose scalar sector is Φ 4 -like. And by this we mean theories where either there are no cubic scalar interactions, or the cubic couplings are related to the quartic couplings through spontaneous symmetry breaking. Furthermore, the quantity that tests where perturbation theory breaks down itself can be written as a perturbative series, and having the NLO terms allows one to test how well the series converges. We also present a simple example to illustrate the effect of considering these bounds at different orders in perturbation theory. For example, there is a noticeable difference in the viable parameter when the square of the NLO piece is included versus when it is not.},

doi = {10.1103/PhysRevD.96.036006},

journal = {Physical Review D},

number = 3,

volume = 96,

place = {United States},

year = {Thu Aug 17 00:00:00 EDT 2017},

month = {Thu Aug 17 00:00:00 EDT 2017}

}