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For the minimal $\lambda$-supersymmetry, it stays perturbative to the GUTscale for $\lambda \leq 0.7$. This upper bound is relaxed when one either takesthe criteria that all couplings close to $\sim 4\pi$ for non-perturbation orallows new fields at the intermediate scale between the weak and GUT scale. Weshow that a hidden $U(1)_X$ gauge sector with spontaneously broken scale$\sim10$ TeV improves this bound as $\lambda\leq1.23$ instead. This may inducesignificant effects on Higgs physics such as decreasing fine tuning involvingthe Higgs scalar mass, as well as on the small $\kappa$-phenomenology.

Perturbative $\lambda$-Supersymmetry and Small $\kappa$-Phenomenology