Massive Neutrinos in Almost-Commutative Geometry

Abstract

In the noncommutative formulation of the standard model of particle physics by A. Connes and A. Chamseddine [1] one of the three generations of fermions has to possess a massless neutrino. 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-precission measurements of the PMNS matrix might need massive neutrinos in all three generations. In this publication 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 straight forward way from Connes' and Chamseddine's version since it requires an internal algebra with four summands of matrix algebras, instead of three summands for the model with one massless neutrino.

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Cited by in corpus (4)

• New Scalar Fields in Noncommutative Geometry
• On a Classification of Irreducible Almost-Commutative Geometries V
• The Inverse Seesaw Mechanism in Noncommutative Geometry
• Krajewski diagrams and the Standard Model