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

TL;DR

This paper assesses the degree of fine-tuning in the mSUGRA/CMSSM supersymmetry model after the Higgs discovery, considering recent experimental constraints, and finds that the model remains highly fine-tuned, motivating exploration of alternative models.

Contribution

It introduces two measures of fine-tuning, _{HS} and _{EW}, and evaluates their values across the mSUGRA/CMSSM parameter space with current experimental constraints.

Findings

_{HS} > 10^3 indicating extreme high-scale fine-tuning.

_{EW} > 10^2 showing significant electroweak fine-tuning.

Identifies benchmark points with minimal fine-tuning within the model.

Abstract

The recent discovery of a 125 GeV Higgs-like resonance at LHC, coupled with the lack of evidence for weak scale supersymmetry (SUSY), have severely constrained SUSY models such as 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, \Delta_{HS}, includes effects that arise from the high scale origin of the mSUGRA parameters while the second measure, \Delta_{EW}, 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 B_s ->\mu^+\mu^- and also require a light Higgs scalar with m_h ~123-127 GeV. We present fine-tuning contours in the m_0 vs. m_{1/2} plane for several sets of A_0 and tan(\beta) values. We also present results for \Delta_{HS} and \Delta_{EW} from a scan over the entire viable model parameter space. We find a \Delta_{HS} > 10^3, or at best 0.1% fine-tuning. For the less stringent electroweak fine tuning, we find \Delta_{EW} > 10^2, or at best 1% fine-tuning. Two benchmark points are presented that have the lowest values of \Delta_{HS} and \Delta_{EW}. 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.