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Radiative corrections with new heavy particles coupling to Higgs doubletsdestabilize the electroweak scale and require an ad-hoc counterterm cancellingthe large loop contribution. If the mass scale m1 of these new particles in inthe TeV range, this feature constitutes the "little fine-tuning problem". Weconsider the case that the new-physics spectrum has a little hierarchy with twoparticle mass scales m1, m2 and m2 = O(10 m1) and no tree-level couplings ofthe heavier particles to Higgs doublets. As a concrete example we study the(next-to-)minimal supersymmetric standard model ((N)MSSM) for the case that thegluino mass M3 is significantly larger than the stop mass parameters m_{L,R}and show that the usual one-loop fine-tuning analysis breaks down. If m_{L,R}is defined in the dimensional-reduction (DR-bar) or any other fundamentalscheme, corrections enhanced by powers of M3^2/m_{L,R}^2 occur in all higherloop orders. After resumming these terms we find the fine-tuning measuresubstantially improved compared to the usual analyses with M3 <~ m_{L,R}. Inour hierarchical scenario the stop self-energies grow like M3^2, so that thestop masses m_{L,R}^{OS} in the on-shell (OS) scheme are naturally much largerthan their DR-bar counterparts m_{L,R}^{DR-bar}. This feature permits a novelsolution to the little fine-tuning problem: DR-bar stop masses are close to theelectroweak scale, but radiative corrections involving the heavy gluino pushthe OS masses, which are probed in collider searches, above their experimentallower limits. As a byproduct, we clarify which renormalization scheme must beused for squark masses in loop corrections to low-energy quantities such as theB-B-bar mixing amplitude.

Little hierarchies solve the little fine-tuning problem: a case study in supersymmetry with heavy guinos