SUSY models under siege: LHC constraints and electroweak fine-tuning

Recent null results from LHC8 SUSY searches along with the discovery of a SM-like Higgs boson with mass m(h) ~ 125.5 GeV indicates sparticle masses in the TeV range, causing tension with conventional measures of electroweak fine-tuning. We propose a simple Fine-tuning Rule which should be followed under any credible evaluation of fine-tuning. We believe that overestimates of electroweak fine-tuning by conventional measures all arise from violations of this rule. We show that to gain accord with the Fine-tuning Rule, then both Higgs mass and the traditional \Delta_{BG} fine-tuning measures reduce to the model-independent electroweak fine-tuning measure \Delta_{EW}. This occurs by combining dependent contributions to m(Z) or m(h) into independent units. Then, using \Delta_{EW}, we evaluate EW fine-tuning for a variety of SUSY models including mSUGRA, NUHM1, NUHM2, mGMSB, mAMSB, hyper-charged AMSB and nine cases of mixed moduli-anomaly (mirage) mediated SUSY breaking models (MMAMSB) whilst respecting LHC Higgs mass and B-decay constraints (we do not impose LHC8 sparticle mass constraints due to the possibility of compressed spectra within many of these models). We find mSUGRA, mGMSB, mAMSB and MMAMSB models all to be highly fine-tuned. The NUHM1 model is moderately fine-tuned while NUHM2 which allows for radiatively-driven naturalness (RNS) allows for fine-tuning at a meager 10% level in the case where m(higgsinos) ~ 100-200 GeV and the TeV-scale top squarks are well-mixed. Models with RNS may or may not be detect at LHC14. A \sqrt{s} ~ 500 GeV e^+e^- collider will be required to make a definitive search for the requisite light higgsinos.