Going beyond the Standard Model with noncommutative geometry

TL;DR

This paper explores constraints on particle physics models derived from noncommutative geometry, showing the Standard Model's limitations and proposing extensions that satisfy these geometric demands, including implications for neutrinos and supersymmetry.

Contribution

It introduces geometric constraints on fermionic content, demonstrating the Standard Model's need for right-handed neutrinos and proposing extended models compatible with noncommutative geometry.

Findings

Standard Model requires right-handed neutrinos per generation.

Extending the SM with a (1, 2, 1/2) representation satisfies geometric constraints.

The minimal supersymmetric Standard Model does not meet these constraints.

Abstract

The derivation of the full Standard Model from noncommutative geometry has been a promising sign for possible applications of the latter in High Energy Physics. Many believe, however, that the Standard Model cannot be the final answer. We translate several demands whose origin lies in physics to the context of noncommutative geometry and use these to put constraints on the fermionic content of models. We show that the Standard Model only satisfies these demands provided it has a right-handed neutrino in each 'generation'. Furthermore, we show that the demands can be met upon extending the SM with a copy of the representation (1, 2, 1/2), but this has consequences for the number of particle generations. We finally prove that the Minimal Supersymmetric Standard Model is not among the models that satisfy our constraints, but we pose a solution that is a slight extension of the MSSM.