Higgs mass and vacuum stability in the Standard Model at NNLO

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 (lambda) and the Higgs mass (Mh), reducing the theoretical uncertainty in the determination of the critical value of Mh for vacuum stability to 1 GeV. While lambda at the Planck scale is remarkably close to zero, absolute stability of the Higgs potential is excluded at 98% C.L. for Mh < 126 GeV. Possible consequences of the near vanishing of lambda at the Planck scale, including speculations about the role of the Higgs field during inflation, are discussed.

• The paper presents a complete NNLO calculation that significantly reduces the uncertainty in the critical Higgs mass for vacuum stability.
• It incorporates two-loop QCD and top Yukawa corrections to precisely determine the Higgs quartic coupling and its near-null behavior at the Planck scale.
• The study shows that current Higgs mass measurements suggest a marginally metastable Standard Model vacuum, prompting further high-precision investigations.

Higgs Mass and Vacuum Stability in the Standard Model at NNLO

The paper authored by Giuseppe Degrassi and collaborators presents a comprehensive next-to-next-to-leading-order (NNLO) analysis of the Higgs potential within the Standard Model (SM). The focus of this research is on the stability of the vacuum state as defined by the parameters emerging from the Higgs sector and their interaction with other SM fields, primarily at energy scales approaching the Planck scale.

Key Contributions

This paper's primary contribution is the precise determination of the Higgs quartic coupling $\lambda$ in relation to the Higgs mass ($M_h$). This is achieved through the incorporation of the two-loop QCD and top Yukawa corrections, which critically improve the theoretical precision concerning the critical Higgs mass value needed for vacuum stability. These corrections reduced uncertainty in the critical $M_h$ for vacuum stability to approximately 1 GeV. Additionally, the analysis explores the implications of $\lambda$ being nearly zero at the Planck scale.

Results and Discussion

Vacuum Stability Analysis:

1. Two-loop Corrections: The work provides the first complete calculation of two-loop QCD and Yukawa contributions to the Higgs quartic coupling threshold corrections. The importance of these calculations is underscored by the reduction in the theoretical error on the critical $M_h$ required for vacuum stability.
2. Higgs Mass Measurements: At the current experimentally determined value of $M_h \approx 125.5 \pm 0.5$ GeV from ATLAS and CMS data, the predictions suggest that absolute vacuum stability within the SM is marginal, with vacuum stability ruled out at approximately 98% confidence level for $M_h < 126$ GeV.
3. Running of Couplings: The paper illustrates how $\lambda$ and other SM couplings evolve according to the renormalization group equations (RGE). A detailed discussion of the running couplings indicates the importance of $\lambda$'s behavior near high energy scales, particularly its minor deviation from zero at the Planck scale, suggesting a metastable state.

Theoretical Implications:

1. Boundary Conditions at the Planck Scale: The research explores potential theoretical reasons for $\lambda$'s approach to zero around the Planck scale, signifying interest due to the coinciding vanishing of $\beta_{\lambda}$, the beta function of $\lambda$.
2. Inflationary Scenarios: Consequences for cosmology, particularly inflationary models involving the Higgs boson, are considered. The findings suggest constraints on models where the Higgs acts as the inflaton, especially when these models violate perturbative unitarity without further stochastic intervention.
3. Supersymmetry and Beyond Standard Model Physics: The paper briefly addresses how the precision findings might interact with various supersymmetric models and scenarios suggesting new physics, given the observed slight negativity of $\lambda$ at the Planck scale limit.

Future Directions

The future undertakings could include further refinement of SM and beyond SM theories exploring the peculiar near-criticality of $\lambda$ and broader implications on the stability outcomes evidenced by varying $M_h$. Moreover, additional experimental determinations of top quark mass and strong coupling constant could crucially affect theoretical predictions based on this examination.

In summary, this research serves as a crucial refinement for understanding the stability landscape of the SM vacuum. The challenging yet promising theoretical narrative provided by the slight negativity of $\lambda$ at ultra-high energies remains a stimulating call for further exploration in theoretical physics and beyond.