Rethinking Connes' approach to the standard model of particle physics via non-commutative geometry

TL;DR

This paper presents a simplified reformulation of Connes' non-commutative geometry framework for the standard model, revealing an extended model with an extra gauge symmetry and scalar field that address Higgs mass discrepancies.

Contribution

It introduces a unified, simpler axiomatic reformulation of NCG that provides new insights into symmetries and extends the standard model with additional gauge and scalar fields.

Findings

Identifies an extension of the standard model with a $U(1)_{B-L}$ gauge symmetry.

Proposes a new scalar field $\sigma$ with cosmological implications.

Offers a potential solution to the Higgs mass discrepancy.

Abstract

Connes' non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. In a previous paper, we suggested a reformulation of this framework that is: (i) simpler and more unified in its axioms, and (ii) allows the Lagrangian for the standard model of particle physics (coupled to Einstein gravity) to be specified in a way that is tighter and more explanatory than the traditional algorithm based on effective field theory. Here we explain how this same reformulation yields a new perspective on the symmetries of a given NCG. Applying this perspective to the NCG traditionally used to describe the standard model we find, instead, an extension of the standard model by an extra $U(1)_{B-L}$ gauge symmetry, and a single extra complex scalar field $\sigma$, which is a singlet under $SU(3)_{C}\times SU(2)_{L}\times U(1)_{Y}$, but has $B-L=2$. This field has cosmological implications, and offers a new solution to the discrepancy between the observed Higgs mass and the NCG prediction.