Massive neutrinos in almostcommutative geometry
Abstract
In the noncommutative formulation of the standard model of particle physics by Chamseddine and Connes [Commun. Math. Phys. 182, 155 (1996), eprint hepth/9606001], one of the three generations of fermions has to possess a massless neutrino. [C. P. Martin et al., Phys. Rep. 29, 363 (1998), eprint hepth9605001]. This formulation is consistent with neutrino oscillation experiments and the known bounds of the PontecorvoMakiNakagawaSakata matrix (PMNS matrix). But future experiments which may be able to detect neutrino masses directly and highprecision measurements of the PMNS matrix might need massive neutrinos in all three generations. In this paper we present an almostcommutative 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, CNRSLuminy, 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; YANGMILLS THEORY
Citation Formats
Stephan, Christoph A. Massive neutrinos in almostcommutative geometry. United States: N. p., 2007.
Web. doi:10.1063/1.2437854.
Stephan, Christoph A. Massive neutrinos in almostcommutative geometry. United States. doi:10.1063/1.2437854.
Stephan, Christoph A. Thu .
"Massive neutrinos in almostcommutative geometry". United States.
doi:10.1063/1.2437854.
@article{osti_20929648,
title = {Massive neutrinos in almostcommutative 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), eprint hepth/9606001], one of the three generations of fermions has to possess a massless neutrino. [C. P. Martin et al., Phys. Rep. 29, 363 (1998), eprint hepth9605001]. This formulation is consistent with neutrino oscillation experiments and the known bounds of the PontecorvoMakiNakagawaSakata matrix (PMNS matrix). But future experiments which may be able to detect neutrino masses directly and highprecision measurements of the PMNS matrix might need massive neutrinos in all three generations. In this paper we present an almostcommutative 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}
}

We extend a classification of irreducible, almost commutative geometries whose spectral action is dynamically nondegenerate to internal algebras that have four simple summands.

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