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.

22 pages, 6 figures

References in corpus (7)

• Big-Bang Nucleosynthesis
• Proton decay matrix elements with domain-wall fermions
• Connection of $g-2_{\mu }$, electroweak, dark matter, and collider constraints on 331 models
• Proton lifetime bounds from chirally symmetric lattice QCD
• Radiative neutrino mass in 331 scheme
• Small neutrino masses and gauge coupling unification
• Lepton masses and mixing in $SU(3{)}_C\otimes SU(3{)}_L\otimes U(1{)}_X$ models with a $S_3$ flavor symmetry

Cited by in corpus (3)

• From the trees to the forest: a review of radiative neutrino mass models
• A Stronger Case for Superunification Post Higgs Boson Discovery
• Generalized 331 models