Linking the geometric mass hierarchy with threefold family replication

Abstract

A link is established between the observed (approximate) geometric mass hierarchy of quarks and leptons and the triangular structure of their tenable flavour representations. This singles out SU (3)H as the horizontal flavour group, thereby linking the Fermi mass hierarchy with the threefold family replication. These linkages are exploited within a flavour-chiral SU (3)H model, with fermions and Higgs bosons in the 3 ⊕ 6* representation. The model is left-right symmetric and utilizes the universal see-saw mechanism with a geometric mass suppression pattern. Given certain assumptions, the model produces the following mass-ratio (rather than square-mass-ratio) mixing angle relations Vcb = -Vts..