We consider the prospects for natural SUSY models consistent with current
data. Recent constraints make the standard paradigm unnatural so we consider
what could be a minimal extension consistent with what we now know. The most
promising such scenarios extend the MSSM with new tree-level Higgs interactions
that can lift its mass to at least 125 GeV and also allow for flavor-dependent
soft terms so that the third generation squarks are lighter than current bounds
on the first and second generation squarks. We argue that a common feature of
almost all such models is the need for a new scale near 10 TeV, such as a scale
of Higgsing or confinement of a new gauge group. We consider the question
whether such a model can naturally derive from a single mass scale associated
with supersymmetry breaking. Most such models simply postulate new scales,
leaving their proximity to the scale of MSSM soft terms a mystery. This
coincidence problem may be thought of as a mild tuning, analogous to the usual
mu problem. We find that a single mass scale origin is challenging, but suggest
that a more natural origin for such a new dynamical scale is the gravitino
mass, m_{3/2}, in theories where the MSSM soft terms are a loop factor below
m_{3/2}. As an example, we build a variant of the NMSSM where the singlet S is
composite, and the strong dynamics leading to compositeness is triggered by
masses of order m_{3/2} for some fields. Our focus is the Higgs sector, but our
model is compatible with a light stop (with the other generation squarks heavy,
or with R-parity violation or another mechanism to hide them from current
searches). All the interesting low-energy mass scales, including linear terms
for S playing a key role in EWSB, arise dynamically from the single scale
m_{3/2}. However, numerical coefficients from RG effects and wavefunction
factors in an extra dimension complicate the otherwise simple story.Comment: 32 pages, 3 figures; version accepted by JHE
