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Yukawa-unified natural supersymmetry

Previous work on t-b-τYukawa-unified supersymmetry, as expected from SUSY GUT theories based on the gauge group SO(10), tended to have exceedingly large electroweak fine-tuning (EWFT). Here, we examine supersymmetric models where we simultaneously require low EWFT ("natural SUSY") and a high degree of Yukawa coupling unification, along with a light Higgs scalar with m_h\sim125 GeV. As Yukawa unification requires large tanβ\sim50, while EWFT requires rather light third generation squarks and low μ\sim100-250 GeV, B-physics constraints from BR(B\to X_sγ) and BR(B_s\to μ+μ-) can be severe. We are able to find models with EWFT Δ\lesssim 50-100 (better than 1-2% EWFT) and with Yukawa unification as low as R_yuk\sim1.3 (30% unification) if B-physics constraints are imposed. This may be improved to R_yuk\sim1.2 if additional small flavor violating terms conspire to improve accord with B-constraints. We present several Yukawa-unified natural SUSY (YUNS) benchmark points. LHC searches will be able to access gluinos in the lower 1-2 TeV portion of their predicted mass range although much of YUNS parameter space may lie beyond LHC14 reach. If heavy Higgs bosons can be accessed at a high rate, then the rare H, A\to μ+μ- decay might allow a determination of tanβ\sim50 as predicted by YUNS models. Finally, the predicted light higgsinos should be accessible to a linear e+e- collider with \sqrt{s}\sim0.5 TeV.