Electroweak interaction beyond the Standard Model and Dark Matter in the Tangent Bundle Quantum Field Theory

TL;DR

This paper develops a generalized electroweak theory based on tangent bundle geometry, predicting new particles and dark matter candidates, and unifies known quantum numbers with additional charges explaining particle families.

Contribution

It introduces a novel geometric framework using tangent bundle symmetries to extend the electroweak interaction beyond the Standard Model, predicting new gauge bosons and dark matter particles.

Findings

Predicts additional gauge bosons and particles beyond the Standard Model.

Provides a geometric interpretation linking electroweak theory with gravity.

Explains the origin of particle families through extra quantum numbers.

Abstract

A generalized theory of electroweak interaction is developed based on the underlying geometrical structure of the tangent bundle with symmetries arising from transformations of tangent vectors along the fiber axis at a fixed space-time point, leaving the scalar product invariant. Transformations with this property are given by the $SO(3,1)$ group with the little groups $SU(2),E^{c}(2)$ and $SU(1,1)$ where the group $E^{c}(2)$ is the central extended group of the Euclidian group $E(2).$ Electroweak interaction beyond the standard model (SM) is described by the transformation group $SU(2)\otimes E^{c}\mathbf{(}2)$ without a priori introduction of a phenomenologically determined gauge group. The Laplacian on this group yields the known internal quantum numbers of isospin and hypercharge, but in addition the extra $E^{c}$-charge $\varkappa $ and the family quantum number $n$ which explains the existence of families in the SM. The connection coefficients deliver the SM gauge potentials but also hypothetical gauge bosons and other hypothetical particles as well as candidate Dark Matter particles are predicted. It is shown that the interpretation of the $SO(3,1)$ connection coefficients as elctroweak gauge potentials is compatible with teleparallel gauge gravity theory based on the translational group.