Dirac Neutrino Masses in NCG

TL;DR

This paper investigates the incorporation of Dirac neutrino masses into Noncommutative Geometry (NCG) models, finding that current models cannot simultaneously include right-handed neutrinos while satisfying key physical constraints, suggesting fundamental modifications are needed.

Contribution

It demonstrates the incompatibility of right-handed neutrinos with existing NCG models under specific physical constraints, highlighting the need for new theoretical developments.

Findings

No existing NCG model with right-handed neutrinos satisfies both constraints.

Fundamental changes to NCG may be necessary to incorporate Dirac neutrino masses.

Current models cannot simultaneously include right-handed neutrinos and satisfy Poincaré duality and anomaly freedom.

Abstract

Several models in NCG with mild changes to the standard model(SM)are introduced to discuss the neutrino mass problem. We use two constraints, Poincar$\acute{e}$ duality and gauge anomaly free, to discuss the possibility of containing right-handed neutrinos in them. Our work shows that no model in this paper, with each generation containing a right-handed neutrino, can satisfy these two constraints in the same time. So, to consist with neutrino oscillation experiment results, maybe fundamental changes to the present version of NCG are usually needed to include Dirac massive neutrinos.