Standard Model With Higgs As Gauge Field On Fourth Homotopy Group

TL;DR

This paper proposes a novel Standard Model extension where the Higgs field is interpreted as a gauge field on the fourth homotopy group, using non-commutative geometry, leading to a stable Higgs mechanism without extra parameter constraints.

Contribution

It introduces a new gauge-theoretic framework for the Higgs field based on the fourth homotopy group, unifying it with gauge potentials and ensuring quantum stability.

Findings

Higgs field emerges naturally as a gauge field on the fourth homotopy group.

No additional parameter constraints at the tree level.

Higgs stability is maintained against quantum corrections.

Abstract

Based upon a first principle, the generalized gauge principle, we construct a general model with $G_L\times G'_R \times Z_2$ gauge symmetry, where $Z_2=\pi_4(G_L)$ is the fourth homotopy group of the gauge group $G_L$, by means of the non-commutative differential geometry and reformulate the Weinberg-Salam model and the standard model with the Higgs field being a gauge field on the fourth homotopy group of their gauge groups. We show that in this approach not only the Higgs field is automatically introduced on the equal footing with ordinary Yang-Mills gauge potentials and there are no extra constraints among the parameters at the tree level but also it most importantly is stable against quantum correlation.