A natural SUSY Higgs near 125 GeV

The naturalness of a Higgs boson with a mass near 125GeV 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 SHuHd. 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-ecoupling 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.