30 Sep 2013 | Giuseppe Degrassi, Stefano Di Vita, Joan Elias-Mir, José R. Espinosa, Gian F. Giudice, Gino Isidori, Alessandro Strumia
This paper presents the first complete next-to-next-to-leading order (NNLO) analysis of the Standard Model (SM) Higgs potential. The study focuses on the relationship between the Higgs quartic coupling $ \lambda $ and the Higgs mass $ M_h $, and how these parameters influence the vacuum stability of the SM. The authors compute the two-loop QCD and Yukawa corrections to this relationship, reducing the theoretical uncertainty in the determination of the critical value of $ M_h $ for vacuum stability to 1 GeV.
The analysis shows that the Higgs quartic coupling $ \lambda $ at the Planck scale is remarkably close to zero, but absolute stability of the Higgs potential is excluded at 98% confidence level for $ M_h < 126 $ GeV. The paper discusses the implications of the near vanishing of $ \lambda $ at the Planck scale, including speculations about the role of the Higgs field during inflation.
The authors derive the two-loop threshold correction to $ \lambda(\mu) $, which is crucial for understanding the evolution of $ \lambda $ up to high energies. They find that the two-loop corrections to the Higgs mass are significant and reduce the theoretical error on $ M_h $ from $ \pm2 $ GeV to $ \pm0.7 $ GeV. The final result for the condition of absolute stability up to the Planck scale is given by:
$$ M_h[\mathrm{GeV}] > 129.4 + 1.4\left(\frac{M_t[\mathrm{GeV}] - 173.1}{0.7}\right) - 0.5\left(\frac{\alpha_s(M_Z) - 0.1184}{0.0007}\right) \pm 1.0_{\mathrm{th}}. $$
Combining this with experimental errors on $ M_t $ and $ \alpha_s $, the authors conclude that vacuum stability of the SM up to the Planck scale is excluded at 2σ (98% C.L. one-sided) for $ M_h < 126 $ GeV.
The paper also discusses the implications of the results for Planck scale physics, including the possibility that the Higgs field played a role during inflation. The authors find that the smallness of $ \lambda $ around the Planck scale is quite remarkable and that the SM parameters lie at the critical border between stability and metastability. The dominant uncertainties in the evaluation of the minimum $ M_h $ value ensuring absolute vacuum stability are primarily experimental, with the measurement of $ M_t $ being the largest source of uncertainty. The paper concludes that improved top quark mass measurements could provide valuable insights into the structure of the vacuum and the ultimate fate of our universe.This paper presents the first complete next-to-next-to-leading order (NNLO) analysis of the Standard Model (SM) Higgs potential. The study focuses on the relationship between the Higgs quartic coupling $ \lambda $ and the Higgs mass $ M_h $, and how these parameters influence the vacuum stability of the SM. The authors compute the two-loop QCD and Yukawa corrections to this relationship, reducing the theoretical uncertainty in the determination of the critical value of $ M_h $ for vacuum stability to 1 GeV.
The analysis shows that the Higgs quartic coupling $ \lambda $ at the Planck scale is remarkably close to zero, but absolute stability of the Higgs potential is excluded at 98% confidence level for $ M_h < 126 $ GeV. The paper discusses the implications of the near vanishing of $ \lambda $ at the Planck scale, including speculations about the role of the Higgs field during inflation.
The authors derive the two-loop threshold correction to $ \lambda(\mu) $, which is crucial for understanding the evolution of $ \lambda $ up to high energies. They find that the two-loop corrections to the Higgs mass are significant and reduce the theoretical error on $ M_h $ from $ \pm2 $ GeV to $ \pm0.7 $ GeV. The final result for the condition of absolute stability up to the Planck scale is given by:
$$ M_h[\mathrm{GeV}] > 129.4 + 1.4\left(\frac{M_t[\mathrm{GeV}] - 173.1}{0.7}\right) - 0.5\left(\frac{\alpha_s(M_Z) - 0.1184}{0.0007}\right) \pm 1.0_{\mathrm{th}}. $$
Combining this with experimental errors on $ M_t $ and $ \alpha_s $, the authors conclude that vacuum stability of the SM up to the Planck scale is excluded at 2σ (98% C.L. one-sided) for $ M_h < 126 $ GeV.
The paper also discusses the implications of the results for Planck scale physics, including the possibility that the Higgs field played a role during inflation. The authors find that the smallness of $ \lambda $ around the Planck scale is quite remarkable and that the SM parameters lie at the critical border between stability and metastability. The dominant uncertainties in the evaluation of the minimum $ M_h $ value ensuring absolute vacuum stability are primarily experimental, with the measurement of $ M_t $ being the largest source of uncertainty. The paper concludes that improved top quark mass measurements could provide valuable insights into the structure of the vacuum and the ultimate fate of our universe.