Quark horizontal flavor symmetry and two-Higgs doublet in (7+1)-dimensional extended spin space

Abstract

An extended spin-space model in $7+1$ dimensions is presented that describes the standard-model electroweak quark sector. Up to four generations of massless and massive quarks and two-Higgs doublets derive from the associated representation space, in addition to the W- and Z-vector bosons. Other mass operators are obtained that put restrictions on additional non-Higgs scalars and their vacuum expectation value. After symmetry breaking, the scalar components give rise to a hierarchy effect vertically (within doublets) associated to the Higgs fields, and horizontally (within generations) associated to the non-Higgs elements.