Abstract
We present a model based on the $SU(3)_C\otimes SU(3)_L\otimes U(1)_X$ gauge symmetry that relates the mass hierarchy of the fermions with the solution to the strong CP problem through the $U(1)_{PQ}$ Peccei-Quinn symmetry. This last symmetry arises accidentally with the imposition of a discrete $Z_9$ symmetry, which also secludes the different scales in the double seesaw mechanism taking place in the neutrino sector. The symmetry breakdown is performed by three scalar triplets plus a scalar singlet hosting an axion field, whose particle excitation can be a component of dark matter. We show a mechanism where a small effective vev is generated for a scalar triplet which is supposed to have a bare mass above the energy scale where the $SU(3)_L\otimes U(1)_X$ symmetry is broken. Combined with the energy scale in which the $U(1)_{PQ}$ is broken, such a mechanism gives rise to a natural hierarchy to the fermions. Beyond the Standard Model particle content, the model predicts an invisible axion, $a$, three GeV neutrinos, $N_{iL}$, plus several new particles at the TeV scale which are: five vector bosons, $U^\pm$, $V^0$, $V^{0\dagger}$, and $Z^\prime$; one up-type $U$, and two down-type $D_a$ quarks; and at least a CP-even, $H_1$, plus non-hermitian neutral, $\phi^0$, $\phi^{0\dagger}$, scalar bosons. The model may be tested by looking for the possible production of such particles at the LHC.
Highlights
Despite the great experimental success, the Standard Model (SM) of particle physics leaves unanswered many pressing questions
We present a model based on the SUð3ÞC ⊗ SUð3ÞL ⊗ Uð1ÞX gauge symmetry that relates the mass hierarchy of the fermions with the solution to the strong CP problem through the Uð1ÞPQ Peccei-Quinn symmetry
We show a mechanism where a small effective vacuum expectation value is generated for a scalar triplet which is supposed to have a bare mass above the energy scale where the SUð3ÞL ⊗ Uð1ÞX symmetry is broken
Summary
Despite the great experimental success, the Standard Model (SM) of particle physics leaves unanswered many pressing questions. In addition to the Standard Model particle content, the model predicts five vector bosons: a singly charged UÆ; a neutral non-Hermitian pair V0, V0†; and a real Z0 The masses of these vector bosons are expected to be at the TeV scale, according to our scheme for generating hierarchical masses to the fermions. Other recent studies have tackled the question of fermion mass hierarchy in 3-3-1 models [21,22,23,24,25,26], but from another perspective In such works, the observed mass hierarchies follow from the imposition of different discrete flavor symmetries alongside several new scalar fields.
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