Stability of the Higgs Potential in the Standard Model and Beyond

Abstract

The question of stability of the Higgs potential in the Standard Model is revisited employing advanced theoretical precision and recent experimental results. We show that the top mass and strong coupling constants are key observables in order to reach or refute absolute stability. We highlight new physics scenarios that lead to a decisive stabilisation of the Higgs sector. These proceedings summarise findings first reported in~[1,2].

Figures (4)

• Figure 1: Schematic depiction of the effective potential $V_\text{eff}$ as a function of the Higgs field value $h$ in the SM. The electroweak vacuum $h=v$ is marked in green, a global minimum $h \gg v$ is shown in orange.
• Figure 2: Effective quartic interaction $\alpha_{\lambda,\text{eff}}(h) \equiv\lambda_\text{eff}(h)/ (4\pi)^2$ of the quantum-improved potential as a function of the Higgs field $h$. Several choices for the top pole mass are shown, including the PDG central value of $M_t^\sigma$ (solid blue) and $M_t^\text{MC}$ (solid orange) as well as their respective $\pm2\sigma$ uncertainty (shaded blue and orange), and the $-5\sigma$ value of $M_t^\text{MC}$ (dashed orange). Other observables are taken as PDG central values ParticleDataGroup:2024cfk. Only potentials that remain above the red line at $\alpha_{\lambda,\text{eff}} = 0$ for all values of $h$ are stable.
• Figure 3: Stability region for the SM Higgs effective potential as a function of the top pole mass $M_t$ and the strong coupling constant $\alpha_s^{(5)}(M_Z)$. An absolutely stable potential is marked in green, while red signifies meta- and rapid instability. Central values from the PDG ParticleDataGroup:2024cfk are marked with a dot, with $1\sigma$ uncertainties of the observables added in quadrature are denoted as rings. We distinguish the top mass $M_t^\sigma$ from cross-section measurements (black) and the Monte Carlo mass $M_t^\text{MC}$ (blue). Uncertainty rings for the Monte Carlo mass uncertainty ATLAS:2024dxp are drawn as dashed blue lines.
• Figure 4: Stability region (green) for the SM Higgs effective potential as a function of the top pole mass $M_t$ and the strong coupling constant $\alpha_s^{(5)}(M_Z)$. PDG central values (using $M_t^\sigma$) ParticleDataGroup:2024cfk with uncorrelated $1\sigma$ uncertainties added in quadrature (solid rings) are compared with the CMS study CMS:2019esx (dashed uncertainty regions) with a correlation $\rho = 0.31$. Figure adopted from Hiller:2024zjp.