331 Models and Grand Unification: From Minimal SU(5) to Minimal SU(6)

Abstract

We consider the possibility of grand unification of the $\mathrm{SU}(3{)}_{\mathrm{c}}\otimes \mathrm{SU}(3{)}_{\mathrm{L}}\otimes \mathrm{U}(1{)}_{\mathrm{X}}$ model in an SU(6) gauge unification group. Two possibilities arise. Unlike other conventional grand unified theories, in SU(6) one can embed the $\mathrm{SU}(3{)}_{\mathrm{c}}\otimes \mathrm{SU}(3{)}_{\mathrm{L}}\otimes \mathrm{U}(1{)}_{\mathrm{X}}$ 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 $\mathrm{SU}(3{)}_{\mathrm{c}}\otimes \mathrm{SU}(3{)}_{\mathrm{L}}\otimes \mathrm{U}(1{)}_{\mathrm{X}}$ models while providing the radiative origin of neutrino masses. Alternatively, a sequential variant of the $\mathrm{SU}(3{)}_{\mathrm{c}}\otimes \mathrm{SU}(3{)}_{\mathrm{L}}\otimes \mathrm{U}(1{)}_{\mathrm{X}}$ 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 $\mathrm{SU}(3{)}_{\mathrm{c}}\otimes \mathrm{SU}(3{)}_{\mathrm{L}}\otimes \mathrm{U}(1{)}_{\mathrm{X}}$ model with seesaw-type neutrino masses.

arXiv comment22 pages, 6 figures

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Cited by in corpus (19)

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• A theory for scotogenic dark matter stabilised by residual gauge symmetry
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• Towards gauge coupling unification in left-right symmetric $\mathrm{SU}(3{)}_{\mathrm{c}}\times \mathrm{SU}(3{)}_{\mathrm{L}}\times \mathrm{SU}(3{)}_{\mathrm{R}}\times \mathrm{U}(1{)}_{\mathrm{X}}$ theories
• Fermion masses and mixings and some phenomenological aspects of a 3-3-1 model with linear seesaw mechanism
• Lepton Flavor Violation Induced by Dark Matter
• Axion model with the $\mathrm{SU}(6)$ unification
• Scotogenic neutrino masses with gauged matter parity and gauge coupling unification
• Muon Anomalous Magnetic Moment and Higgs Potential Stability in the 331 Model from $SU(6)$
• Probing Heavy Neutrino Magnetic Moments at the LHC using Long-Lived Particle Searches
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• Bottom quark and tau lepton masses in a toy $\mathrm{SU}(6)$
• An extended 3-3-1 model with two scalar triplets and linear seesaw mechanism
• A Stronger Case for Superunification Post Higgs Boson Discovery
• Generalized 331 models
• A two-generational $\mathrm{SU}(7)$ model with extended weak sector: mass hierarchies, mixings, and the flavor non-universality
• Flipped SU(6) Unification of the $SU(3{)}_c\times SU(3{)}_L\times U(1{)}_X$ Model