Higgs Mass and Noncommutative Geometry

TL;DR

This paper demonstrates that noncommutative geometry models of electroweak interactions do not impose specific relations between the Higgs mass and other parameters, highlighting the importance of a gauge-invariant term in the Lagrangian.

Contribution

It reveals the existence of a gauge-invariant linear curvature term in noncommutative geometry that affects the relations between physical parameters.

Findings

No special Higgs mass relations in noncommutative geometry models

Existence of a nontrivial gauge-invariant linear curvature term

Standard model Lagrangian with full parameter freedom

Abstract

We show that the description of the electroweak interactions based on noncommutative geometry of a continuous and a discrete space gives no special relations between the Higgs mass and other parameters of the model. We prove that there exists a gauge invariant term, linear in the curvature, which is trivial in the standard differential geometry but nontrivial in the case of the discrete geometry. The relations could appear only if one neglects this term, otherwise one gets the Lagrangian of the Standard model with the exact number of free parameters.