## Low-energy effective field theory below the electroweak scale: anomalous dimensions

## Abstract

We compute the one-loop anomalous dimensions of the low-energy effective Lagrangian below the electroweak scale, up to terms of dimension six. The theory has 70 dimension-five and 3631 dimension-six Hermitian operators that preserve baryon and lepton number, as well as additional operators that violate baryon number and lepton number. The renormalization group equations for the quark and lepton masses and the QCD and QED gauge couplings are modified by dimension-five and dimension-six operator contributions. We compute the renormalization group equations from one insertion of dimension-five and dimension-six operators, as well as two insertions of dimension-five operators, to all terms of dimension less than or equal to six. As a result, the use of the equations of motion to eliminate operators can be ambiguous, and we show how to resolve this ambiguity by a careful use of field redefinitions.

- Authors:

- Univ. of California at San Diego, La Jolla, CA (United States). Dept. of Physics

- Publication Date:

- Research Org.:
- Univ. of California, San Diego, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1503683

- Grant/Contract Number:
- SC0009919

- 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: 2018; Journal Issue: 1; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective Field Theories; Renormalization Group

### Citation Formats

```
Jenkins, Elizabeth E., Manohar, Aneesh V., and Stoffer, Peter. Low-energy effective field theory below the electroweak scale: anomalous dimensions. United States: N. p., 2018.
Web. doi:10.1007/jhep01(2018)084.
```

```
Jenkins, Elizabeth E., Manohar, Aneesh V., & Stoffer, Peter. Low-energy effective field theory below the electroweak scale: anomalous dimensions. United States. doi:10.1007/jhep01(2018)084.
```

```
Jenkins, Elizabeth E., Manohar, Aneesh V., and Stoffer, Peter. Thu .
"Low-energy effective field theory below the electroweak scale: anomalous dimensions". United States. doi:10.1007/jhep01(2018)084. https://www.osti.gov/servlets/purl/1503683.
```

```
@article{osti_1503683,
```

title = {Low-energy effective field theory below the electroweak scale: anomalous dimensions},

author = {Jenkins, Elizabeth E. and Manohar, Aneesh V. and Stoffer, Peter},

abstractNote = {We compute the one-loop anomalous dimensions of the low-energy effective Lagrangian below the electroweak scale, up to terms of dimension six. The theory has 70 dimension-five and 3631 dimension-six Hermitian operators that preserve baryon and lepton number, as well as additional operators that violate baryon number and lepton number. The renormalization group equations for the quark and lepton masses and the QCD and QED gauge couplings are modified by dimension-five and dimension-six operator contributions. We compute the renormalization group equations from one insertion of dimension-five and dimension-six operators, as well as two insertions of dimension-five operators, to all terms of dimension less than or equal to six. As a result, the use of the equations of motion to eliminate operators can be ambiguous, and we show how to resolve this ambiguity by a careful use of field redefinitions.},

doi = {10.1007/jhep01(2018)084},

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

number = 1,

volume = 2018,

place = {United States},

year = {2018},

month = {1}

}