Three families from SU(4)A⊗SU(3)C⊗SU(2)L⊗U(1)XSM-like chiral models

Abstract

We give a detailed description of the model construction procedures about our new approach to the family structure of the standard model. SM-like chiral fermion spectra, largely ``derivable'' from the gauge anomaly constraints, are formulated in an $\mathrm{SU}(N)\ensuremath{\bigotimes}\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(2)\ensuremath{\bigotimes}\mathrm{U}(1)$ symmetry framework as an extension of the SM symmetry. The $N=4$ case gives naturally three families as a result, with U${(1)}_{Y}$ nontrivially embedded into the $\mathrm{SU}(4{)}_{A}\ensuremath{\bigotimes}\mathrm{U}(1{)}_{X}.$ Such a spectrum has extra vectorlike quarks and leptons. We illustrate how an acceptable symmetry-breaking pattern can be obtained through a relatively simple scalar sector which gives naturally hierarchical quark mass matrices. Compatibility with various FCNC constraints and some interesting aspects of the possible phenomenological features are discussed, from a non-model-specific perspective. The question of incorporating supersymmetry without putting in the Higgs bosons as extra supermultiplets is also addressed.