Embedding Standard Model Symmetries into K(E10)
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In a context of a unified vectorlike gauge theory based on the group SU(6) proposed previously by the present authors, various breaking patterns of the gauge symmetry are discussed. It is found that a pattern SU(6) →SU(3)c ×SU(3) ×U(1) →SU(3)c ×SU(2) ×U(1) ×U(1) →S(3)c ×U(1) has very interesting features. In this case, weak and electromagnetic interactions are described by the SU(2) ×U(1) ×U(1) gauge theory and small parity violation in atomic physics is explained by a reasonable assumption. The strength of CP-violating interactions is naturally understood by large violation of SU(3)c ×SU(3) ×U(1) symmetry to SU(3)c ×SU(2) ×U(1) ×U(1).
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We study the symmetry-breaking pattern of SO(10) grand unified theories using the {210}-dimensional Higgs representation. We conclude that there exist finite ranges of parameters of the Higgs potentials such that the minima of the potentials break SO(10) to either SU(2)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}SU(4) or SU(2)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}U(1)\ifmmode\times\else\texttimes\fi{}SU(3). In the first symmetry-breaking pattern, D parity (or charge conjugation) is necessarily broken and this reflects in the mass spectrum of the Higgs boson. In the second case, D parity is conserved as expected. When supersymmetry is imposed on the Higgs superpotential, {210} can no longer break SO(10) to either SU(2)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}SU(4) or SU(2)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}U(1)\ifmmode\times\else\texttimes\fi{}SU(3) without breaking supersymmetry. The implication of our result to the ``Michel's conjecture'' is discussed.
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Dine, Fischler, and Srednicki have proposed a solution to the strong $\mathrm{CP}$ puzzle in which the mass and couplings of the axion are suppressed by an inverse power of a large mass. We construct an explicit SU(5) model in which this mass is the vacuum expectation value which breaks SU(5) down to SU(3) \ensuremath{\bigotimes} SU(2) \ensuremath{\bigotimes} U(1).
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In recent analyses the existence of $SU(2)_L\times\SU(2)_R\times\SU(4)_C(g_{2L}\ne g_{2R})$ intermediate gauge symmetry has been ruled out in SUSY SO(10) model at one-loop level, although the left-right symmetric intermediate gauge group has been shown to exist with certain light scalar superfields near 1 TeV.We show,how the asymmetric gauge group is allowed with an intermediate scale $M_I=10^10- 10^13$ GeV by including two-loop and threshold effects.
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The dual preon with a quasi-simple gauge group G=SU hc(7)⊗SU hf(7) is studied. It automatically has a global symmetry UX(1) of Peccei and Quinn, with an invisible composite axion. The group for the anomaly condition is taken to be the symmetry group at preon confinement, which is further enlarged to a classification group of massless composite fermions. By taking it to be SU(5)⊗UX(1), four generations of 5*⊗ 10 are obtained. Numerical estimates of some scales of the model are also given.
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