Abstract
Supersymmetric SO(10) models with Yukawa coupling matrices involving only a 10H and a {overline{126}}_H of Higgs fields can lead to a predictive and consistent scenario for fermion masses and mixings, including the neutrino sector. However, when coupled minimally to a symmetry breaking sector that includes a 210H and a 126H, these models lead either to an unacceptably small neutrino mass scale, or to non-perturbative values of the gauge couplings. Here we show that with the addition of a 54H to the symmetry breaking sector, the successful predictions of these models for fermion masses and mixings can be maintained. The 54H enables a reduction of the B − L symmetry breaking scale to an intermediate value of order 1012 GeV, consistent with the observed neutrino mass spectrum, while preserving perturbative gauge coupling unification. We obtain an excellent fit to all fermion masses and mixings in this framework. We analyze carefully the prediction of the model for CP violation in neutrino oscillations. Consistency with proton lifetime, however, requires a mini-split SUSY spectrum with the squarks and sleptons having masses of order 100 TeV, accompanied by TeV scale gauginos and Higgsinos. Such a spectrum may arise from pure gravity mediation, which would predict the partial lifetime for the decay pto overline{nu}{K}^{+} to be an order of magnitude above the current experimental limit.
Highlights
The 10H and 126H are complex chiral superfields, resulting in the Yukawa superpotential: WSYOu(k1a0w)a = 16T Y10 10H + Y126126H 16
In addition to the Yukawa couplings, the fermion mass matrices will involve 3 ratios of vacuum expectation values (VEVs), with one ratio remaining complex. This leads to a total of 12 real parameters and 7 phases.) It is remarkable that this minimal setup is able to reproduce the full fermion mass spectrum, including large leptonic mixing angles along with small quark mixing angles [2,3,4,5,6,7,8,9,10,11,12], a nontrivial feat in any quark-lepton unified framework
In this paper we have resurrected the minimal Yukawa sector of SUSY SO(10), which explains the entirety of fermion masses and mixings in terms of two symmetric Yukawa matrices
Summary
While the minimal model was found to be very successful in fitting fermion data, it was realized soon thereafter that it faced some hurdles once the symmetry breaking constraints are included [8, 17,18,19]. We show explicitly the severity of this constraint in the minimal model (without a 120H ), if all the SUSY particles have masses around a TeV Both of these problems, too small a scale for neutrino masses and too short a lifetime for the proton with TeV superparticles, could in principle be solved in a split-SUSY scenario [25,26,27] with the gaugino-Higgsino masses around 100 TeV and the squark-slepton masses around 1013 GeV [12]. Too small a scale for neutrino masses and too short a lifetime for the proton with TeV superparticles, could in principle be solved in a split-SUSY scenario [25,26,27] with the gaugino-Higgsino masses around 100 TeV and the squark-slepton masses around 1013 GeV [12] This would allow for an increase in the light neutrino masses, because the gauge couplings can be kept smaller for higher energies before the bosonic threshold is reached. The reactor neutrino mixing angle, large, was not large enough in [12].3 Third, there may be issues with stability of the spectrum with such large values of the bosonic masses [30], this may be an issue of naturalness only
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