Towards a canonical fermi mass matrix for a pure generation structure

Abstract

Vertical constraints on the horizontal generation structure are discussed. The minimal electro/nuclear scheme for which the generation structure must be pure is identified to be the partially unified Pati-Salam SU(4) C×SU(2) L×SU(2) R. SO(10) type unification furthermore requires the horizontal group factor to be axial. This in turn crucially affects the Yukawa couplings in such a way that a minimal Higgs system with only two conventional scalars is capable of uniquely giving rise to the ‘canonical’ Fritzsch-type mass matrix, for any arbitrary number of fermionic families. The anomaly-free equations then provide the desired one-to-one correspondence between the mass matrices in the two charged quark sectors. The derived horizontal quantum numbers suggest that the maximal horizontal group factor be SU(2), with the generations furnishing two neighbor j and j + 1 2 representations. Finally, a careful phase analysis shows that the tree-level soft and superwork CP-violation solely reflects the non-abelian character of the horizontal group, representing an induced internal rotation which is triggered by the phase elimination performed in the vertical sector.