  Radiative corrections with new heavy particles coupling to Higgs doublets
destabilize the electroweak scale and require an ad-hoc counterterm cancelling
the large loop contribution. If the mass scale m1 of these new particles in in
the TeV range, this feature constitutes the "little fine-tuning problem". We
consider the case that the new-physics spectrum has a little hierarchy with two
particle mass scales m1, m2 and m2 = O(10 m1) and no tree-level couplings of
the heavier particles to Higgs doublets. As a concrete example we study the
(next-to-)minimal supersymmetric standard model ((N)MSSM) for the case that the
gluino 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 fundamental
scheme, corrections enhanced by powers of M3^2/m_{L,R}^2 occur in all higher
loop orders. After resumming these terms we find the fine-tuning measure
substantially improved compared to the usual analyses with M3 <~ m_{L,R}. In
our hierarchical scenario the stop self-energies grow like M3^2, so that the
stop masses m_{L,R}^{OS} in the on-shell (OS) scheme are naturally much larger
than their DR-bar counterparts m_{L,R}^{DR-bar}. This feature permits a novel
solution to the little fine-tuning problem: DR-bar stop masses are close to the
electroweak scale, but radiative corrections involving the heavy gluino push
the OS masses, which are probed in collider searches, above their experimental
lower limits. As a byproduct, we clarify which renormalization scheme must be
used for squark masses in loop corrections to low-energy quantities such as the
B-B-bar mixing amplitude.
