Perturbative λ -supersymmetry and small κ -phenomenology

For minimal λ -supersymmetry, the theory stays perturbative to the GUT scale for λ≤0.7 . This upper bound is relaxed when one either takes the criterion that all couplings are close to ∼ 4 π for non-perturbation or one allows for new fields at the intermediate scale between the weak and GUT scale. We show that a hidden U(1)X gauge sector with spontaneously broken scale ∼ 10 TeV improves this bound as λ≤1.23 instead. This may induce significant effects on the Higgs physics, such as decreasing fine tuning involving the Higgs scalar mass, as well as on the small κ -phenomenology