A Natural SUSY Higgs Near 125 GeV
  The naturalness of a Higgs boson with a mass near 125 GeV is explored in a variety of weak-scale supersymmetric models. A Higgs mass of this size strongly points towards a non-minimal implementation of supersymmetry. The Minimal Supersymmetric Standard Model now requires large A-terms to avoid multi-TeV stops. The fine-tuning is at least 1% for low messenger scales, and an order of magnitude worse for high messenger scales. Naturalness is significantly improved in theories with a singlet superfield S coupled to the Higgs superfields via \lambda\ S H_u H_d. If \lambda\ is perturbative up to unified scales, a fine-tuning of about 10% is possible with a low mediation scale. Larger values of \lambda, implying new strong interactions below unified scales, allow for a highly natural 125 GeV Higgs boson over a wide range of parameters. Even for \lambda\ as large as 2, where a heavier Higgs might be expected, a light Higgs boson naturally results from singlet-doublet scalar mixing. Although the Higgs is light, naturalness allows for stops as heavy as 1.5 TeV and a gluino as heavy as 3 TeV. Non-decoupling effects among the Higgs doublets can significantly suppress the coupling of the light Higgs to b quarks in theories with a large \lambda, enhancing the \gamma \gamma\ and WW signal rates at the LHC by an order one factor relative to the Standard Model Higgs. 
Lawrence J. Hall, David Pinner, Joshua T. Ruderman
hep-ph