Abstract
We consider the possibility of grand unification of the $\mathrm{ SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ model in an SU(6) gauge unification group. Two possibilities arise. Unlike other conventional grand unified theories, in SU(6) one can embed the $\mathrm{ SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ model as a subgroup such that different multiplets appear with different multiplicities. Such a scenario may emerge from the flux breaking of the unified group in an E(6) F-theory GUT. This provides new ways of achieving gauge coupling unification in $\mathrm{ SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ models while providing the radiative origin of neutrino masses. Alternatively, a sequential variant of the $\mathrm{ SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ model can fit within a minimal SU(6) grand unification, which in turn can be a natural E(6) subgroup. This minimal SU(6) embedding does not require any bulk exotics to account for the chiral families while allowing for a TeV scale $\mathrm{ SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ model with seesaw-type neutrino masses.
Highlights
The discovery of the Higgs boson established the existence of spin-0 particles in nature and this opened up the new era in looking for extensions of the Standard Model (SM) at accelerators
We find that the anomaly free representations of the SVS 331 model can all be embedded in a combination of anomaly free representations of SU(6), which in turn can be potentially embedded in the fundamental and adjoint representations of the group E(6) motivated by F-theory Grand Unified Theory (GUT) with matter and bulk exotics obtained from the flux breaking mechanism [22,23,24,25]
In this paper we have considered the possibility of conventional non-supersymmetric grand unification of extended electroweak models based upon the SU(3)c ⊗ SU(3)L ⊗ U(1)X gauge framework within an SU(6) gauge unification group
Summary
The discovery of the Higgs boson established the existence of spin-0 particles in nature and this opened up the new era in looking for extensions of the Standard Model (SM) at accelerators. In order to drive symmetry breaking and generate the charged fermion masses, we assume a Higgs sector and vevs similar to the SVS 331 model.. If we further assume X + Z X − Z , we can identify the 44 and 55 entries as the heaviest in the mass matrix given in Eq (12) and these rotated isodoublet states form a pair of heavy quasi Dirac neutrinos with mass of the order of the SU(3)c ⊗ SU(3)L ⊗ U(1)X symmetry breaking scale. Up to second order in perturbation theory we obtain two Dirac states with mass of the order of the electroweak symmetry breaking scale ±u = ± y1k0 and a light seesaw Majorana neutrino with mass 2u(z − x)/(X + Z ) With this we see that the model has enough flexibility to account for the observed pattern of fermion masses. These SM scale heavy neutrinos may be searched for through production via SM W and Z processes but this is suppressed by their admixture with the light neutrinos
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