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We study the trinified model, SU(3)_C x SU(3)_L x SU(3)_R x Z_3, with the minimal Higgs sector required for symmetry breaking. There are five Higgs doublets, and gauge-coupling unification results if all five are at the weak scale, without supersymmetry. The radiative see-saw mechanism yields sub-eV neutrino masses, without the need for intermediate scales, additional Higgs fields, or higher-dimensional operators. The proton lifetime is above the experimental limits, with the decay modes p -> bar u K^+ and p -> mu^+ K^0 potentially observable. We also consider supersymmetr
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The flipped trinification, a framework for unifying the 3-3-1 and left-right symmetries, has recently been proposed in order to solve profound questions, the weak parity violation and the number of families, besides the implication for neutrino mass generation and dark matter stability. In this work, we argue that this gauge-completion naturally provides flavor-changing neutral currents in both quark and lepton sectors. The quark flavor changing happens at the tree-level due to the nonuniversal couplings of $Z_{L,R}$, while the lepton flavor changing $lrightarrow lgamma$ starts from the one loop level contributed significantly by the new charged currents of $Y_{L,R}$, which couple ordinary to exotic leptons. These effects disappear in the minimal left-right model, but are present in the framework characterizing a flipped trinification symmetry.
We propose a model which unifies the Left-Right symmetry with the $SU(3)_L$ gauge group, called flipped trinification, and based on the $SU(3)_Cotimes SU(3)_Lotimes SU(3)_Rotimes U(1)_X$ gauge group. The model inherits the interesting features of both symmetries while elegantly explaining the origin of the matter parity, $W_P=(-1)^{3(B-L)+2s}$, and dark matter stability. We develop the details of the spontaneous symmetry breaking mechanism in the model, determining the relevant mass eigenstates, and showing how neutrino masses are easily generated via the seesaw mechanism. Viable dark matter candidates can either be a fermion, a scalar or a vector, leading to potentially different dark matter phenomenology.
Models with spontaneously broken parity symmetry can solve the strong $CP$ problem in a natural way. We construct such a model in the context of $SU3^3$ unification. Parity has the conventional meaning in this model, and the gauge group is unified.
We propose a low-scale renormalizable trinification theory that successfully explains the flavor hierarchies and neutrino puzzle in the Standard Model (SM), as well as provides a dark matter candidate and also contains the necessary means for efficient leptogenesis. The proposed theory is based on the trinification $SU{3}{C}times SU{3}{L}times SU{3}{R}$ gauge symmetry, which is supplemented with an additional flavor symmetry $U{X}times Z_{2}^{(1)} times Z_{2}^{(2)}$. In the proposed model the top quark and the exotic fermions acquire tree-level masses, whereas the lighter SM charged fermions gain masses radiatively at one-loop level. In addition, the light active neutrino masses arise from a combination of radiative and type-I seesaw mechanisms, with the Dirac neutrino mass matrix generated at one-loop level.
We consider a non-supersymmetric $E_6$ Grand Unified Theory (GUT) with intermediate trinification symmetry $SU(3)_C times SU(3)_L times SU(3)_R times D$ (D denoted as D-parity for discrete left-right symmetry) and study the effect of one-loop threshold corrections arising due to every class of superheavy particles (scalars, fermions and vectors). It is observed that, the intermediate mass scale $M_I$ and $sin^2theta_W$ remain unaffected by GUT threshold contributions. The threshold modified unification mass scale $M_U$ is in excellent agreement with the present experimental proton decay constraint. The novel feature of the model is that GUT threshold uncertainty of $M_U$ is found to be controlled by superheavy scalars only, leading to a very predictive scenario for proton decay, which can be verifiable within the foreseeable experiments.
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