Abstract
We extend the nonsupersymmetric SO(10) grand unification theories by adding a horizontal symmetry, which connects the three generations of fermions. Without committing to any specific symmetry group, we investigate the 1-loop renormalization group evolutions of the gauge couplings with one and two intermediate breaking scales. We find that depending on the SO(10) breaking chains, gauge coupling unification is compatible with only a handful of choices of representations of the Higgs bosons under the horizontal symmetry.
Highlights
The quest for the unification of fundamental forces remains to be a major motivation over the last few decades for investigating theories beyond the Standard Model
We find that depending on the SO(10) breaking chains, gauge coupling unification is compatible with only a handful of choices of representations of the Higgs bosons under the horizontal symmetry
III, we introduce the various chains of symmetry breaking, indicating the Higgs boson representation whose vacuum expectation value (VEV) is responsible for each breaking, and the masses of the scalar bosons
Summary
We consider the possibility that the three fermion generations form a multiplet under some horizontal symmetry group H that appears as a direct product with SO(10). We will examine the unification of the gauge coupling constants of the Standard Model (SM) into SO(10) In this pursuit, we do not need to assume anything specific about the nature of H. In most of those cases, the horizontal symmetry is imposed on the fermion mass matrix to generate the required texture Despite these attempts, it is fair to say that the flavor problem has not yet been solved, and at the moment there is nothing close to what may be called the Standard Model of flavor physics.
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