# Massive neutrinos in almost-commutative geometry

## Abstract

In the noncommutative formulation of the standard model of particle physics by Chamseddine and Connes [Commun. Math. Phys. 182, 155 (1996), e-print hep-th/9606001], one of the three generations of fermions has to possess a massless neutrino. [C. P. Martin et al., Phys. Rep. 29, 363 (1998), e-print hep-th-9605001]. This formulation is consistent with neutrino oscillation experiments and the known bounds of the Pontecorvo-Maki-Nakagawa-Sakata matrix (PMNS matrix). But future experiments which may be able to detect neutrino masses directly and high-precision measurements of the PMNS matrix might need massive neutrinos in all three generations. In this paper we present an almost-commutative geometry which allows for a standard model with massive neutrinos in all three generations. This model does not follow in a straightforward way from the version of Chamseddine and Connes since it requires an internal algebra with four summands of matrix algebras, instead of three summands for the model with one massless neutrino.

- Authors:

- Centre de physique theorique, CNRS-Luminy, Case 907, 13288 Marseille Cedex 9 (France)

- Publication Date:

- OSTI Identifier:
- 20929648

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 2; Other Information: DOI: 10.1063/1.2437854; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; COMMUTATION RELATIONS; GEOMETRY; MASS; MATRICES; NEUTRINO OSCILLATION; NEUTRINOS; STANDARD MODEL; YANG-MILLS THEORY

### Citation Formats

```
Stephan, Christoph A.
```*Massive neutrinos in almost-commutative geometry*. United States: N. p., 2007.
Web. doi:10.1063/1.2437854.

```
Stephan, Christoph A.
```*Massive neutrinos in almost-commutative geometry*. United States. doi:10.1063/1.2437854.

```
Stephan, Christoph A. Thu .
"Massive neutrinos in almost-commutative geometry". United States.
doi:10.1063/1.2437854.
```

```
@article{osti_20929648,
```

title = {Massive neutrinos in almost-commutative geometry},

author = {Stephan, Christoph A.},

abstractNote = {In the noncommutative formulation of the standard model of particle physics by Chamseddine and Connes [Commun. Math. Phys. 182, 155 (1996), e-print hep-th/9606001], one of the three generations of fermions has to possess a massless neutrino. [C. P. Martin et al., Phys. Rep. 29, 363 (1998), e-print hep-th-9605001]. This formulation is consistent with neutrino oscillation experiments and the known bounds of the Pontecorvo-Maki-Nakagawa-Sakata matrix (PMNS matrix). But future experiments which may be able to detect neutrino masses directly and high-precision measurements of the PMNS matrix might need massive neutrinos in all three generations. In this paper we present an almost-commutative geometry which allows for a standard model with massive neutrinos in all three generations. This model does not follow in a straightforward way from the version of Chamseddine and Connes since it requires an internal algebra with four summands of matrix algebras, instead of three summands for the model with one massless neutrino.},

doi = {10.1063/1.2437854},

journal = {Journal of Mathematical Physics},

number = 2,

volume = 48,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}