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Title: 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:
 [1]
  1. 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}
}
  • We extend a classification of irreducible, almost commutative geometries whose spectral action is dynamically nondegenerate to internal algebras that have four simple summands.
  • In this paper, we will classify the finite spectral triples with KO-dimension 6, following the classification found in Iochum, B., Schuecker, T., and Stephan, C. A., J. Math. Phys. 45, 5003 (2004); Jureit, J.-H. and Stephan, C. A., J. Math. Phys. 46, 043512 (2005); Schuecker, T. (unpublished); Jureit, J.-H., Schuecker, T., and Stephan, C. A., J. Math. Phys. 46, 072302 (2005). with up to four summands in the matrix algebra. Again, heavy use is made of Krajewski diagrams [Krajewski, T., J. Geom. Phys. 28, 1 (1998).] This work has been inspired by the recent paper by Connes (unpublished) and Barrettmore » (unpublished). In the classification, we find that the standard model of particle physics in its minimal version fits the axioms of noncommutative geometry in the case of KO-dimension 6. By minimal version, it is meant that at least one neutrino has to be massless and mass-terms mixing particles and antiparticles are prohibited.« less
  • We extend a classification of irreducible almost-commutative geometries, whose spectral action is dynamically nondegenerate, to internal algebras that have six simple summands. We find essentially four particle models: an extension of the standard model by a new species of fermions with vectorlike coupling to the gauge group and gauge invariant masses, two versions of the electrostrong model, and a variety of the electrostrong model with Higgs mechanism.
  • The authors give a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case (q [yields] 1 limit). The Lie derivative and the contraction operator on forms and tensor fields are found. A new, explicit form of the Cartan-Maurer equations is presented. The example of a bicovariant differential calculus on the quantum group GL[sub q](2) is given in detail. The softening of a quantum group is considered, and they introduce q-curvatures satisfying q-Bianchi identifies, a basic ingredient for the construction of q-gravity and q-gauge theories.
  • Some noncommutative space-time standard model features and possible LHC signatures are presented. The spin effects on the modified noncommutative Altarelli-Parisi splitting functions for polarized partons are also discussed.