Single-Scale Natural SUSY
  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. 
Lisa Randall and Matthew Reece
hep-ph