Mitchell Institute for Fundamental Physics & Astronomy
College Station, Texas 77843
We show that the condition that determines the value of the Z boson mass in the MSSM in terms of weak scale parameters allows one to define a quantity $Delta_EW$ that depends essentially on just the particle spectrum, and serves as a bound on the naturalness measure for any underlying model that leads to the same spectrum. A low value of $Delta_ EW$ is a necessary, though not sufficient, condition for naturalness. We compare $\Delta_EW$ with measures of finetuning in the literature, and argue that a low magnitude of the mu parameter is more basic to naturalness considerations than light stops (in that we can find models with low $Delta_EW$ and stops in the 1-2 TeV range). Turning to the phenomenology of low $\mu$ models, we point out a novel SS di-boson signature that allows for a SUSY greater reach at the high luminosity LHC than the canonical missing $E_T$ search for gluinos, if gaugino mass unification is assumed. Confirmatory signals may be present in other multi-lepton channels. After a brief mention of the prospects for detection of neutralino dark matter, we conclude by emphasizing that ILC600 will conclusively explore natural SUSY models with no worse than 3% fine-tuning.