Abstract
We suggest simple ways of implementing Peccei-Quinn (PQ) symmetry to solve the strong CP problem in renormalizable SUSY SO(10) models with a minimal Yukawa sector. Realistic fermion mass generation requires that a second pair of Higgs doublets survive down to the PQ scale. We show how unification of gauge couplings can be achieved in this context. Higgsino mediated proton decay rate is strongly suppressed by a factor of (MPQ/MGUT)2, which enables all SUSY particles to have masses of order TeV. With TeV scale SUSY spectrum, pto overline{v}{K}^{+} decay rate is expected to be in the observable range. Lepton flavor violating processes μ → eγ decay and μ − e conversion in nuclei, induced by the Dirac neutrino Yukawa couplings, are found to be within reach of forthcoming experiments.
Highlights
Breaking of the U(1)PQ leads to a near massless scalar, the axion [24,25,26,27,28,29], which may constitute a fraction or the entire dark matter in the universe
The decay rate of the proton would be suppressed by a factor of (MPQ/MGUT)2 compared to the results of ref. [20] in the SUSY SO(10) with PQ symmetry that we present here
We focus on the PQ symmetry which needs to be broken around this intermediate scale, MPQ ≈ vR, these two symmetries are a priori unrelated
Summary
In our set-up the symmetry breaking proceeds in three steps (Chain A): SO(10) × U(1)PQ −−54−H−−, −21−0−H→ SU(3)c × SU(2)L × U(1)Y × U(1)B−L × U(1)PQ. If only the (1, 1, 15) ⊂ 210H field acquires a VEV at the GUT scale, symmetry breaking proceeds via the left-right symmetric vacuum: SO(10) → SU(3)c × SU(2)L × SU(2)R × U(1)B−L × D. This symmetry may be broken at an intermediate scale MI when (1, 1, 3, 0) multiplet (under the LR symmetric gauge symmetry) from 210H acquires VEV In this scenario, bi-doublets (1, 2, 2, 0) from 10H and 126H should be at the intermediate scale to generate correct fermion mass. The U(1)R × U(1)B−L symmetry is left unbroken by the 54H field, but is broken by the 126H + 126H fields This scenario would lead to pseudo-Goldstone Higgs multiplets carrying SM quantum numbers with masses of order ∼ vR2 /MGUT ∼ 1010 GeV. From the above analysis it is clear that our choice of the symmetry breaking chain given in eq (2.15) (Chain A) is the only one that generates a realistic fermion mass spectrum, while being consistent with gauge coupling unification without relying on excessive threshold effects
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