Electroweak versus high scale finetuning in the 19-parameter SUGRA model
Recently, two measures of electroweak finetuning (EWFT) have been introduced for SUSY models: \Delta_{EW} compares the Z mass to each separate weak scale contribution to m_Z while \Delta_{HS} compares the Z mass to high scale input parameters and their consequent renormalizaton group evolution (1/\Delta is the % of fine tuning). While the paradigm mSUGRA/CMSSM model has been shown to be highly finetuned under both parameters (\Delta_{EW}> 10^2 and \Delta_{HS}> 10^3), the two-parameter non-universal Higgs model (NUHM2) in the context of radiatively-driven natural SUSY (RNS) enjoys \Delta_{EW} as low as 10, while \Delta_{HS} remains > 10^3. We investigate finetuning in the 19-free-parameter SUGRA model (SUGRA19). We find that with 19 free parameters, the lowest \Delta_{EW} points are comparable to what can be achieved in NUHM2 with just 6 free parameters. However, in SUGRA19, \Delta_{HS} can now also reach as low as 5-10. The conditions which lead to low \Delta_{HS} include m_{H_u} m_Z at the high scale, with non-universal gaugino masses M_{1,2}>> M_3 also at m_{GUT}. The low \Delta_{HS} models are severely constrained by b\to s\gamma branching fraction. In both cases of low \Delta_{EW} and \Delta_{HS}, the superpotential \mu parameter should be \sim 100-300 GeV. While SUSY models with low EWFT may or may not be discoverable at LHC, the predicted light higgsinos must show up at a linear e^+e^- collider with \sqrt{s}> 2|\mu |.