Unification via intermediate symmetry breaking scales with the quartification gauge group

The idea of quark-lepton universality at high energies has been introduced as a natural extension to the standard model. This is achieved by endowing leptons with new degrees of freedom—leptonic color, an analogue of the familiar quark color. Grand and partially unified models which utilize this new gauge symmetry $SU(3{)}_{\ell }$ have been proposed in the context of the quartification gauge group $SU(3{)}^4$. Phenomenologically successful gauge coupling constant unification without supersymmetry has been demonstrated for cases where the symmetry breaking leaves a residual $SU(2{)}_{\ell }$ unbroken. Though attractive, these schemes either incorporate ad hoc discrete symmetries and nonrenormalizable mass terms, or achieve only partial unification. We show that grand unified models can be constructed where the quartification group can be broken fully [i.e. no residual $SU(2{)}_{\ell }$] to the standard model gauge group without requiring additional discrete symmetries or higher dimension operators. These models also automatically have suppressed nonzero neutrino masses. We perform a systematic analysis of the renormalization-group equations for all possible symmetry breaking routes from $SU(3{)}^4\to SU(3{)}_q\otimes SU(2{)}_L\otimes U(1{)}_Y$. This analysis indicates that gauge coupling unification can be achieved for several different symmetry breaking patterns and we outline the requirements that each gives on the unification scale. We also show that the unification scenarios of those models which leave a residual $SU(2{)}_{\ell }$ symmetry are not unique. In both symmetry breaking cases, some of the scenarios require new physics at the TeV scale, while others do not allow for new TeV phenomenology in the fermionic sector.