Fermion masses in noncommutative geometry

TL;DR

This paper explores how noncommutative geometry constrains fermion masses in the Standard Model, especially neutrinos, and discusses scenarios to satisfy these constraints, highlighting the need for new fermions.

Contribution

It analyzes the impact of Poincare duality in noncommutative geometry on fermion mass constraints and proposes scenarios involving new fermions to resolve these issues.

Findings

Poincare duality constrains massless quarks and neutrinos to be unequal in NCG.

Introducing new fermions can satisfy the duality constraints.

The study provides possible models to incorporate massive neutrinos in NCG.

Abstract

Recent indications of neutrino oscillations raise the question of the possibility of incorporating massive neutrinos in the formulation of the Standard Model (SM) within noncommutative geometry (NCG). We find that the NCG requirement of Poincare duality constrains the numbers of massless quarks and neutrinos to be unequal unless new fermions are introduced. Possible scenarios in which this constraint is satisfied are discussed.