# Low-energy effective field theory below the electroweak scale: operators and matching

## Abstract

The gauge-invariant operators up to dimension six in the low-energy effective field theory below the electroweak scale are classified. There are 70 Hermitian dimension-five and 3631 Hermitian dimension-six operators that conserve baryon and lepton number, as well as ΔB = ±ΔL = ±1, ΔL = ±2, and ΔL = ±4 operators. The matching onto these operators from the Standard Model Effective Field Theory (SMEFT) up to order 1/Λ ^{2} is computed at tree level. SMEFT imposes constraints on the coefficients of the low-energy effective theory, which can be checked experimentally to determine whether the electroweak gauge symmetry is broken by a single fundamental scalar doublet as in SMEFT. Furthermore our results, when combined with the one-loop anomalous dimensions of the low-energy theory and the one-loop anomalous dimensions of SMEFT, allow one to compute the low-energy implications of new physics to leading-log accuracy, and combine them consistently with high-energy LHC constraints.

- 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:
- 1503685

- Grant/Contract Number:
- SC0009919

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- Journal Volume: 2018; Journal Issue: 3; 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: operators and matching*. United States: N. p., 2018.
Web. doi:10.1007/jhep03(2018)016.

```
Jenkins, Elizabeth E., Manohar, Aneesh V., & Stoffer, Peter.
```*Low-energy effective field theory below the electroweak scale: operators and matching*. United States. doi:10.1007/jhep03(2018)016.

```
Jenkins, Elizabeth E., Manohar, Aneesh V., and Stoffer, Peter. Tue .
"Low-energy effective field theory below the electroweak scale: operators and matching". United States. doi:10.1007/jhep03(2018)016. https://www.osti.gov/servlets/purl/1503685.
```

```
@article{osti_1503685,
```

title = {Low-energy effective field theory below the electroweak scale: operators and matching},

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

abstractNote = {The gauge-invariant operators up to dimension six in the low-energy effective field theory below the electroweak scale are classified. There are 70 Hermitian dimension-five and 3631 Hermitian dimension-six operators that conserve baryon and lepton number, as well as ΔB = ±ΔL = ±1, ΔL = ±2, and ΔL = ±4 operators. The matching onto these operators from the Standard Model Effective Field Theory (SMEFT) up to order 1/Λ2 is computed at tree level. SMEFT imposes constraints on the coefficients of the low-energy effective theory, which can be checked experimentally to determine whether the electroweak gauge symmetry is broken by a single fundamental scalar doublet as in SMEFT. Furthermore our results, when combined with the one-loop anomalous dimensions of the low-energy theory and the one-loop anomalous dimensions of SMEFT, allow one to compute the low-energy implications of new physics to leading-log accuracy, and combine them consistently with high-energy LHC constraints.},

doi = {10.1007/jhep03(2018)016},

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

issn = {1029-8479},

number = 3,

volume = 2018,

place = {United States},

year = {2018},

month = {3}

}