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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.
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New superstrong forces, analogous to QCD but featuring a larger mass scale, should they exist, would offer new possibilities for addressing the strong P, T, problem. One can implement the massless quark solution in a phenomenologically acceptable way, by using a massless quark that is always confined within superheavy particles, and is therefore effectively superheavy: a cryptoquark. Assuming confinement and chiral symmetry breaking from the superstrong dynamics, we find a new mechanism to generate an axion field without introducing new fundamental scalar fields.
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
Current upper bounds of the neutron electric dipole moment constrain the physically observable quantum chromodynamic (QCD) vacuum angle $|bartheta| lesssim 10^{-11}$. Since QCD explains vast experimental data from the 100 MeV scale to the TeV scale, it is better to explain this smallness of $|bartheta|$ in the QCD framework, which is the strong CaPa problem. Now, there exist two plausible solutions to this problem, one of which leads to the existence of the very light axion. The axion decay constant window, $10^9 {gev}lesssim F_alesssim 10^{12} gev$ for a ${cal O}(1)$ initial misalignment angle $theta_1$, has been obtained by astrophysical and cosmological data. For $F_agtrsim 10^{12}$ GeV with $theta_1<{cal O}(1)$, axions may constitute a significant fraction of dark matter of the universe. The supersymmetrized axion solution of the strong CaPa problem introduces its superpartner the axino which might have affected the universe evolution significantly. Here, we review the very light axion (theory, supersymmetrization, and models) with the most recent particle, astrophysical and cosmological data, and present prospects for its discovery.
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.
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