Abstract
Abstract We present the first complete next-to-next-to-leading order analysis of the Standard Model Higgs potential. We computed the two-loop QCD and Yukawa corrections to the relation between the Higgs quartic coupling (λ) and the Higgs mass (M h ), reducing the theoretical uncertainty in the determination of the critical value of M h for vacuum stability to 1 GeV. While λ at the Planck scale is remarkably close to zero, absolute stability of the Higgs potential is excluded at 98 % C.L. for M h < 126 GeV. Possible consequences of the near vanishing of λ at the Planck scale, including speculations about the role of the Higgs field during inflation, are discussed.
Highlights
102 104 106 108 1010 1012 1014 1016 1018 1020 RGE scale Μ in GeV the top Yukawa coupling and the Higgs anomalous dimension have been computed in [20]
As pointed out in [18], the most important missing NNLO piece for the vacuum stability analysis are the two-loop threshold corrections to λ at the weak scale due to QCD and top Yukawa interactions, because such couplings are sizable at low energy
Will the answer affect our understanding of the mechanism for EW breaking, but it will determine our strategy for future directions in theoretical physics
Summary
A full NNLO computation of the Higgs potential requires three main ingredients: 1) the two-loop effective potential; 2) three-loop beta functions for all the relevant couplings; 3) two-loop matching conditions to determine the initial values of the couplings at the electroweak scale. As anticipated in the introduction, all these ingredient are available for the QCD, Yukawa and Higgs quartic couplings. We first discuss the structure of the two-loop potential and the numerical inputs at the electroweak scale, and present the final numerical results for the stability condition in the Mh–Mt plane
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