Extension of the standard model of electroweak interaction and Dark Matter in the tangent bundle geometry

Abstract

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 spacetime point given by the SO(3,1) group. Electroweak interaction beyond the standard model (SM) is described by the little groups $$ SU(2)\otimes E^{c}(2)$$SU(2)⊗Ec(2) ($$E^{c}(2)$$Ec(2) is the central extended Euclidian group) which includes the group $$SU(2)\otimes U(1)$$SU(2)⊗U(1) as a limit case. In addition to isospin and hypercharge, two additional quantum numbers arise which explain the existence of families in the SM. The connection coefficients yield the SM gauge potentials but also hypothetical gauge bosons and other hypothetical particles as a Higgs family as well as candidate Dark Matter particles are predicted. Several important consequences for the interaction between dark fermions, dark scalars or dark vector gauge bosons with each other and with SM Higgs and Z-bosons are described.