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We present the first complete next-to-next-to-leading order analysis of theStandard Model Higgs potential. We computed the two-loop QCD and Yukawacorrections to the relation between the Higgs quartic coupling (lambda) and theHiggs mass (Mh), reducing the theoretical uncertainty in the determination ofthe critical value of Mh for vacuum stability to 1 GeV. While lambda at thePlanck scale is remarkably close to zero, absolute stability of the Higgspotential is excluded at 98% C.L. for Mh < 126 GeV. Possible consequences ofthe near vanishing of lambda at the Planck scale, including speculations aboutthe role of the Higgs field during inflation, are discussed.

Higgs mass and vacuum stability in the Standard Model at NNLO