# Families from supergroups and predictions for leptonic CP violation

## Abstract

As was shown in 1984 by Caneschi, Farrar, and Schwimmer, decomposing representations of the supergroup SU( *M*| *N*), can give interesting anomaly-free sets of fermion representations of SU( *M*) × SU( *N*) × U(1). It is shown here that such groups can be used to construct realistic grand unified models with non-abelian gauged family symmetries. A particularly simple three-family example based on SU(5) × SU(2) × U(1) is studied. The forms of the mass matrices, including that of the right-handed neutrinos, are determined in terms of SU(2) Clebsch coefficients; and the model is able to fit the lepton sector and predict the Dirac CP-violating phase of the neutrinos. Models of this type would have a rich phenomenology if part of the family symmetry is broken near the electroweak scale.

- Authors:

- Univ. of Delaware, Newark, DE (United States)

- Publication Date:

- Research Org.:
- Univ. of Delaware, Newark, DE (United States)

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

- OSTI Identifier:
- 1512470

- Grant/Contract Number:
- SC0013880

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- 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; GUT

### Citation Formats

```
Barr, S. M., and Chen, Heng-Yu.
```*Families from supergroups and predictions for leptonic CP violation*. United States: N. p., 2017.
Web. doi:10.1007/jhep10(2017)128.

```
Barr, S. M., & Chen, Heng-Yu.
```*Families from supergroups and predictions for leptonic CP violation*. United States. doi:10.1007/jhep10(2017)128.

```
Barr, S. M., and Chen, Heng-Yu. Thu .
"Families from supergroups and predictions for leptonic CP violation". United States. doi:10.1007/jhep10(2017)128. https://www.osti.gov/servlets/purl/1512470.
```

```
@article{osti_1512470,
```

title = {Families from supergroups and predictions for leptonic CP violation},

author = {Barr, S. M. and Chen, Heng-Yu},

abstractNote = {As was shown in 1984 by Caneschi, Farrar, and Schwimmer, decomposing representations of the supergroup SU(M|N), can give interesting anomaly-free sets of fermion representations of SU(M) × SU(N) × U(1). It is shown here that such groups can be used to construct realistic grand unified models with non-abelian gauged family symmetries. A particularly simple three-family example based on SU(5) × SU(2) × U(1) is studied. The forms of the mass matrices, including that of the right-handed neutrinos, are determined in terms of SU(2) Clebsch coefficients; and the model is able to fit the lepton sector and predict the Dirac CP-violating phase of the neutrinos. Models of this type would have a rich phenomenology if part of the family symmetry is broken near the electroweak scale.},

doi = {10.1007/jhep10(2017)128},

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

issn = {1029-8479},

number = 10,

volume = 2017,

place = {United States},

year = {2017},

month = {10}

}