Extended Standard Model in multi-spinor field formalism: Visible and dark sectors

I. S. Sogami

doi:10.1093/ptep/ptt103

Abstract

To generalize the Standard Model so as to include dark matter, we formulate a theory of multi-spinor fields on the basis of an algebra that consists of triple-tensor products of elements of the Dirac algebra. Chiral combinations of multi-spinor fields form reducible representations of the Lorentz group possessing component fields with spin 1/2, which we interpret as expressing three ordinary families and an additional fourth family of quarks and leptons. Apart from the gauge and Higgs fields of the Standard Model interacting with the fermions of the three ordinary families, we assume the existence of additional gauge and Higgs fields interacting exclusively with the fermions of the fourth family. While the fields of the Standard Model organize the “visible sector” of our universe, the fields related with the fourth family are presumed to generate a “dark sector” that can contain dark matter. The two sectors possess a channel of communication through the bi-quadratic interaction between visible and dark Higgs fields. After experiencing a common inflationary phase, the two sectors follow a reheating period and weak-coupling paths of thermal histories. We propose scenarios for dark matter that have a tendency to take relatively broad interstellar distributions and examine methods for the detection of the main candidate particles of dark matter. The exchange of superposed fields of the visible and dark Higgs bosons induces weak reaction processes between the fields of the visible and dark sectors, which enables us to have a glimpse of the dark sector.

Highlights

Quarks and leptons exist in threefold family modes with color and electroweak symmetries
The triplet algebra AT can be decomposed into three mutually commutative subalgebras, i.e., an external algebra defining the external properties of fermions and two internal algebras that have the respective roles of prescribing family and color degrees of freedom
We choose the external algebra so that it is isomorphic to the Dirac algebra Aγ and all of its elements are separately invariant under the action of the permutation group S3, which works to exchange the order of Aγ elements in the tensor product

Summary

Introduction

Quarks and leptons exist in threefold family modes with color and electroweak symmetries. We demand that the triple mode of the L-field (R-field) is composed of left-handed doublets (right-handed singlets) of the electroweak symmetry SUL (2) and that the electroweak hypercharges Y of the gauge group UY (1) are assigned so as to cancel chiral anomalies in each family. There is no experimental evidence for the existence of fermions other than three families of ordinary quarks and leptons This means that, if the additional fermions belonging to the single mode exist in the range of energy that is presently attainable by experiment, they are sterile with respect to the interactions mediated by the gauge and Higgs fields related to the SM symmetry. If the ordinary mechanism of confinement based on the color SUc(3) symmetry were applied to both family modes, there might emerge exotic hadrons bearing hybrid quantum numbers of gauge symmetries GEW = SUL (2) × UY (1) and GEW = SUR(2) × UY (1).

Triplet algebra and external subalgebra

Subalgebra for family degrees of freedom

Subalgebra for color degrees of freedom

Triplet fields

Gauge symmetries G and G in multi-spinor field formalism

Multi-spinor field theory for G and G symmetries

Breakdowns of GEW and GEW symmetries

Dark matter

Scenarios for dark matter

Detection of the effects of the dark hadron

Discussion