Massive Neutrinos in Almost-Commutative Geometry

TL;DR

This paper introduces a modification of the noncommutative geometric standard model that accommodates massive neutrinos in all three generations, addressing limitations of previous models with massless neutrinos.

Contribution

It presents an almost-commutative geometry model that allows for three massive neutrinos, requiring an internal algebra with four summands, extending prior formulations.

Findings

Model supports massive neutrinos in all generations.

Requires internal algebra with four summands.

Compatible with neutrino oscillation data.

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.