Perturbative

For minimal $$\lambda $$-supersymmetry, the theory stays perturbative to the GUT scale for $$\lambda \le 0.7$$. This upper bound is relaxed when one either takes the criterion that all couplings are close to $$\sim $$4$$\pi $$ 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 $$\sim $$10 TeV improves this bound as $$\lambda \le 1.23$$ 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 $$\kappa $$-phenomenology