A heavy gluino can push the physical stop mass above LHC bounds while the underlying stop mass parameter stays near the electroweak scale, solving the little fine-tuning problem when higher-order corrections are resummed.
The fine-tuning price of LEP
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abstract
We quantify the amount of fine tuning of input parameters of the Minimal Supersymmetric Extension of the Standard Model (MSSM) that is needed to respect the lower limits on sparticle and Higgs masses imposed by precision electroweak measurements at LEP, measurements of $b\to X_s\gamma$, and searches at LEP 2. If universal input scalar masses are assumed in a gravity-mediated scenario, a factor of $\gappeq180$ is required at $\tan\beta\sim1.65$, decreasing to $\sim20$ at $\tan\beta\sim10$. The amount of fine tuning is not greatly reduced if non-universal input scalar Higgs masses are allowed, but may be significantly reduced if some theoretical relations between MSSM parameters are assumed.
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Little hierarchies solve the little fine-tuning problem: a case study in supersymmetry with heavy guinos
A heavy gluino can push the physical stop mass above LHC bounds while the underlying stop mass parameter stays near the electroweak scale, solving the little fine-tuning problem when higher-order corrections are resummed.