Post-LHC7 fine-tuning in the minimal supergravity/CMSSM model with a 125 GeV Higgs boson

The recent discovery of a 125 GeV Higgs-like resonance at LHC, coupled with the lack of evidence for weak scale supersymmetry (SUSY), has severely constrained SUSY models such as minimal supergravity (mSUGRA)/CMSSM. As LHC probes deeper into SUSY model parameter space, the little hierarchy problem---how to reconcile the Z and Higgs boson mass scale with the scale of SUSY breaking---will become increasingly exacerbated unless a sparticle signal is found. We evaluate two different measures of fine-tuning in the mSUGRA/CMSSM model. The more stringent of these, ΔHS, includes effects that arise from the high-scale origin of the mSUGRA parameters while the second measure, ΔEW, is determined only by weak scale parameters: hence, it is universal to any model with the same particle spectrum and couplings. Our results incorporate the latest constraints from LHC7 sparticle searches, LHCb limits from Bₛ→μ⁺μ^- and also require a light Higgs scalar with mₕ~123--127 GeV. We present fine-tuning contours in the m₀ vs m1/2 plane for several sets of A₀ and tanβ values. We also present results for ΔHS and ΔEW from a scan over the entire viable model parameter space. We find a ΔHS10³, or at best 0.1%, fine-tuning. For the less stringent electroweak fine-tuning, we find ΔEW10², or at best 1%, fine-tuning. Two benchmark points are presented that have the lowest values of ΔHS and ΔEW. Our results provide a quantitative measure for ascertaining whether or not the remaining mSUGRA/CMSSM model parameter space is excessively fine-tuned and so could provide impetus for considering alternative SUSY models.