O-4 - NNLO absolute stability of the SM vacuum up to the Planck scale requires Mh above 129.4 GeV, excluded at 98 percent CL by the measured Higgs mass
Inputs: Mt = 173.1 +- 0.7 GeV (Tevatron+LHC average), as(MZ) = 0.1184 +- 0.0007, Mh = 125.5 +- 0.5 GeV from ATLAS/CMS. Ingredients: three-loop RG equations, two-loop effective potential, and the first complete two-loop QCD+Yukawa threshold correction to lambda at the weak scale. The NNLO corrections shift the critical Mh by about +0.5 GeV relative to NLO and lower the instability scale by a factor ~2 at Mh ~ 125 GeV.
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Why this is evidence
H-42 (exact stability) predicts the measured Higgs mass should land in the potential’s absolute-stability region; H-31 (false vacuum) is what the calculation instead indicates — the measured mass falls below the NNLO stability bound, so within the SM-to-Planck-scale extrapolation the potential develops a deeper minimum. Directly disfavours H-42, conditional on no new fields altering the running.