Symmetry breaking and intermediate mass scales in the SO(10) grand unified theory
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Abstract
An attempt is made to fill in the particle-mass gap between the ordinary masses of a few hundred GeV and the grand unification mass of ${10}^{15}$ GeV by incorporating two and three stages of spontaneous symmetry breaking in the various descents of SO(10) to the low-energy symmetry $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(3)}_{c}$. It is shown that intermediate masses of order ${10}^{10}$ GeV can exist in the particle-mass gap. Values lower than ${10}^{10}$ GeV can only be achieved at the expense of pushing the grand unifying mass to the Planck mass. Also similarities in the gauge structure and differences in the Higgs-scalar and fermion representations of the $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{R}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(4)}_{c}$-based Pati-Salam model and its synthesis into SO(10) are pointed out.