SO(10) as a framework for natural supersymmetry

We consider an SO(10) grand unified theory in which the ratio of the SU(2)W and SU(3)c gaugino masses satisfy M2/M3 ≈ 3, which results in the realization of natural supersymmetry. In the MSSM parameter space this relation looks artificial, but in the SO(10) case it results from a field with a designated vacuum expectation value. We consider two models, namely M1: M2: M3 = −1/5: 3 : 1 (Case I), and M1 : M2 : M3 = −5 : 3 : 1 (Case II). Focusing on ameliorating the little hierarchy problem, we explore the parameter space of these models which yield small fine-tuning measuring parameters (natural supersymmetry) at the electroweak scale (ΔEW) as well as at the high scale (ΔHS). Although both models allow for the solution of the little hierarchy problem, the predicted sparticle spectra can differ markedly in the two cases. Depending on the ratio of the bino mass to the other gaugino masses, Case I leads to stau lepton masses of around a 100 GeV, while in Case II, the stau slepton masses are in the several TeV range. In Case I, the bino-like neutralino can be as light as 90 GeV, while the gluino is heavier than 2 TeV or so. In Case II, due to gluino-bino near degeneracy, the bino cannot be lighter than a TeV or so. Having a light neutralino with sizable bino-higgsino mixture in Case I allows the direct dark matter search experiments to test this class of models.