# Baryon number, lepton number, and operator dimension in the Standard Model

## Abstract

In this study, we prove that for a given operator in the Standard Model (SM) with baryon number ΔB and lepton number ΔL, that the operator's dimension is even (odd) if (ΔB - ΔL)/2 is even (odd). Consequently, this establishes the veracity of statements that were long observed or expected to be true, but not proven, e.g., operators with ΔB - ΔL = 0 are of even dimension, ΔB - ΔL must be an even number, etc. These results remain true even if the SM is augmented by any number of right-handed neutrinos with ΔL = 1.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1253939

- Alternate Identifier(s):
- OSTI ID: 1285778

- Grant/Contract Number:
- de-sc0009919; SC0009919

- Resource Type:
- Published Article

- Journal Name:
- Physics Letters B

- Additional Journal Information:
- Journal Name: Physics Letters B Journal Volume: 758 Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- Netherlands

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; conservation

### Citation Formats

```
Kobach, Andrew. Baryon number, lepton number, and operator dimension in the Standard Model. Netherlands: N. p., 2016.
Web. https://doi.org/10.1016/j.physletb.2016.05.050.
```

```
Kobach, Andrew. Baryon number, lepton number, and operator dimension in the Standard Model. Netherlands. https://doi.org/10.1016/j.physletb.2016.05.050
```

```
Kobach, Andrew. Fri .
"Baryon number, lepton number, and operator dimension in the Standard Model". Netherlands. https://doi.org/10.1016/j.physletb.2016.05.050.
```

```
@article{osti_1253939,
```

title = {Baryon number, lepton number, and operator dimension in the Standard Model},

author = {Kobach, Andrew},

abstractNote = {In this study, we prove that for a given operator in the Standard Model (SM) with baryon number ΔB and lepton number ΔL, that the operator's dimension is even (odd) if (ΔB - ΔL)/2 is even (odd). Consequently, this establishes the veracity of statements that were long observed or expected to be true, but not proven, e.g., operators with ΔB - ΔL = 0 are of even dimension, ΔB - ΔL must be an even number, etc. These results remain true even if the SM is augmented by any number of right-handed neutrinos with ΔL = 1.},

doi = {10.1016/j.physletb.2016.05.050},

journal = {Physics Letters B},

number = C,

volume = 758,

place = {Netherlands},

year = {2016},

month = {7}

}

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https://doi.org/10.1016/j.physletb.2016.05.050

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Cited by: 7 works

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