How conventional measures overestimate electroweak fine-tuning in supersymmetric theory
The lack of evidence for superparticles at the CERN LHC, along with the rather high value of the Higgs mass, has sharpened the perception that supersymmetric model parameter space is highly electroweak fine-tuned (EWFT). We compare three measures of fine-tuning in SUSY models. 1. \Del_HS measures a terms containing large log contributions to m_Z that are inevitable in models defined at scales much higher than the electroweak scale. 2. \Del_BG measures variation in m_Z against variation of model parameters and allows for correlations among high scale parameters which are not included in \Del_HS. 3. The model-independent \Del_EW measures how naturally a model can generate the measured value of m_Z=91.2 GeV in terms of weak scale parameters alone. We hypothesize an overarching Ultimate Theory (UTH) wherein the high scale soft terms are all correlated. The UTH might be contained within the more general effective SUSY theories popular in the literature. For \Del_HS, EWFT can be overestimated by neglecting additional non-independent terms which lead to large cancellations. For \Del_BG, EWFT can be overestimated by applying the measure to the effective theories instead of to the UTH. The measure \Del_EW allows for the possibility of parameter correlations which should be present in the UTH and, since it is model-independent, provides the same value of EWFT for the effective theories as should occur for the UTH. We find that the well-known mSUGRA/CMSSM model is fine-tuned under all three measures so that it is unlikely to contain the UTH. The non-universal Higgs model NUHM2 appears fine-tuned with \Del_HS,BG > 10^3. But since \Del_EW can be as small as 7 (corresponding to 14% fine-tuning), it may contain the UTH for parameter ranges which allow for low true EWFT.