Abstract
We propose the $SU(3)_C\times SU(3)_L\times U(1)_X$ model arising from $SU(6)$ breaking. One family of the Standard Model (SM) fermions arises from two $\bar{6}$ representations and one $15$ representation of $SU(6)$ gauge symmetry. To break the $SU(3)_C\times SU(3)_L\times U(1)_X$ gauge symmetry down to the SM, we introduce three $SU(3)_L$ triplet Higgs fields, where two of them come from the $\bar{6}$ representation while the other one from the $15$ representation. We study the gauge boson masses and Higgs boson mass in detail, and find that the vacuum expectation value (VEV) of the Higgs field for $SU(3)_L\times U(1)_X$ gauge symmetry breaking is around 10 TeV. The neutrino masses and mixing can be generated via the littlest inverse seesaw mechanism. In particular, we have normal hierarchy for neutrino masses and the lightest active neutrino is massless. Also, we consider constraints from the charged lepton flavor changing decays as well. Furthermore, introducing two $SU(3)_L$ adjoint fermions, one $SU(3)_C$ adjoint scalar, and one $SU(3)_L$ triplet scalar, we can achieve gauge coupling unification within 1\%. These extra particles can provide a dark matter candidate as well.
Highlights
The Standard Model (SM) has made a great achievement in explaining the experimental result
To break the SUð3ÞC × SUð3ÞL × Uð1ÞX gauge symmetry down to the SM, we introduce three SUð3ÞL triplet Higgs fields, where two of them come from the 6 ̄ representation while the other one from the 15 representation
We have proposed a new SUð3ÞC × SUð3ÞL × Uð1ÞX model, in which gauge symmetry can be realized from SUð6Þ breaking
Summary
The Standard Model (SM) has made a great achievement in explaining the experimental result. P1ffiffi [9,21–25], there are at least three scalars [see the following Eq (2.12)] in Higgs sector in order to break SUð3ÞL to Uð1ÞEM and generate all the SM fermion and gauge vector masses at tree level. Introducing two SUð3ÞL adjoint fermions, one SUð3ÞC adjoint scalar, and one SUð3ÞL triplet scalar, we can achieve gauge coupling unification within 1% These extra particles can give us a dark matter candidate as well. For gauge structure of SUð3ÞL=SUð3ÞC, since the number of fermion multiplets in 3 representation equals to the number of fermion multiplets in 3 ̄ representation for every generation, it is anomaly free. We do not include all the gauge invariant terms in Eq (2.21)
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