Abstract
We study the correlation between proton lifetime and leptonic CP violation in a class of renormalizable supersymmetric SO(10) grand unified theories (GUTs) with 10, 126 and 120 Higgs fields, which provides a unified description of all fermion masses and a possible resolution for the strong CP problem. This specific model is unique in that it can so far be compatible with current proton lifetime limits for a supersymmetry (SUSY) breaking scale as low as 5 TeV due to the presence of a specific Yukawa texture. Our investigation reveals that a discovery of leptonic CP violation in neutrino oscillations would lead to substantial reduction of the parameter space of the model and the potential ruling out of type-II dominance in the neutrino mass seesaw. Furthermore, the previously predicted proton partial lifetimes are sufficiently long for only certain values of the leptonic CP phase.
Highlights
Mass hierarchy, presence of CP violation, and Dirac vs Majorana nature, it is important to sharpen the predictions of various theories of neutrino masses, so that a clearer picture of the direction of physics beyond the standard model can be determined
We study the correlation between proton lifetime and leptonic CP violation in a class of renormalizable supersymmetric SO(10) grand unified theories (GUTs) with 10, 126 and 120 Higgs fields, which provides a unified description of all fermion masses and a possible resolution for the strong CP problem
Grand unified theories [8, 9] are a surprisingly appropriate setting for the seesaw mechanism for a number of reasons: (i) SO(10) theories [10, 11] have B −L as a subgroup, which is naturally associated with the seesaw scale; (ii) the matter spinor of SO(10) automatically contains the right-handed neutrino field as a symmetry partner to the quarks and leptons of the standard model; (iii) SO(10) theories relate the Dirac mass of neutrinos to the up-like quark masses, leading to a seesaw scale near the GUT scale, which connects it to the scale of coupling unification as well
Summary
The supersymmetric SO(10) model we consider has 10-, 126-, and 120-dimensional Higgs fields with renormalizable Yukawa couplings contributing to fermion masses. Where Ψi is the 16-dimensional matter spinor containing superfields of all the SM fermions (of one generation) plus the right-handed neutrino, and i is the generation index Additional multiplets such as 126(∆), 210(Φ) and 54(S) are needed to break the GUT symmetry and maintain supersymmetry below the GUT scale down to TeV scale. Note that in the original model of this type with 120, we could always choose hii to be real, but to make fij real and gij imaginary, we have to rely on some extra assumptions We could view this choice as a way to fit observations; we argue below that this choice for the mass matrix parameters could arise from an underlying symmetry of the theory. We show that in this case, the θ-parameter is zero only at the tree level due to Hermiticity of the quark mass matrices; we defer a detailed discussion of this issue to a latter paper
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