Extreme Sensitivity of Standard Model Vacuum Stability to Enhanced Scalar Couplings: Implications from Renormalization Group Equations and Radiatively Broken Electroweak Symmetry Scenario

TL;DR

This work shows that Standard Model vacuum stability is extraordinarily sensitive to the Higgs quartic coupling: a mere $3\%$ increase beyond the SM value can pivot the theory from metastability to absolute stability, accompanied by UV Landau poles and strong dynamics near the GUT scale. Using three-loop renormalization group equations and a parameter $k=\lambda_{\rm enhanced}/\lambda_{\rm SM}$, the authors map a phase structure with a critical threshold $k_{\rm crit}=1.03$ and demonstrate that the radiative electroweak symmetry breaking prediction $k\approx7.2$ sits deep in the absolutely stable regime, yielding a UV pole at $\Lambda_{\rm UV}\sim10^{16}$–$10^{18}$ GeV and perturbativity loss near $10^{14}$ GeV. The results imply that precision Higgs measurements probing the self-coupling could reveal beyond-Standard-Model physics, linking electroweak scale phenomena to high-scale compositeness, asymptotic safety, or other UV completions. The analysis emphasizes the universality of the high-energy phenomenology across BSM scenarios and motivates non-perturbative studies for large $k$ values. Overall, the scalar sector emerges as a highly sensitive probe of new physics that could reshape our understanding of electroweak symmetry breaking and high-energy dynamics.

Abstract

We demonstrate that Standard Model vacuum stability exhibits extreme sensitivity to the Higgs quartic coupling: a mere 3\% enhancement represents the critical threshold separating metastability from absolute stability with UV Landau poles. Using three-loop renormalization group equations, we systematically investigate enhancement factors $k = λ_{\rm enhanced}/λ_{\rm SM}$ ranging from $k=1.0$ (Standard Model) to $k=7.2$ (radiative electroweak symmetry breaking prediction). We identify $k_{\rm crit} = 1.03$ as the marginal case where the coupling transitions from negative to positive evolution at high energies. For $k > 1.03$, the theory exhibits absolute vacuum stability and develops UV poles at $Λ_{\rm UV} \sim 10^{16}$--$10^{18}$ GeV, signaling effective field theory breakdown and the onset of strong dynamics. The radiative symmetry breaking scenario with $k \approx 7.2$ falls deep in this regime, naturally connecting the electroweak scale to compositeness or other strong-coupling physics near the GUT scale. Our results reveal that the 125 GeV Higgs mass, lying near the metastability boundary, makes the scalar sector an exceptionally sensitive probe of beyond-Standard-Model physics.

Figures (1)

• Figure 1: High-energy sensitivity of the Higgs quartic coupling to initial enhancement. The horizontal axis shows $\ln(\mu^2/{\rm GeV}^2)$ and vertical axis shows $\lambda(\mu)$. Standard Model ($k=1.0$, blue dashed) exhibits metastability with $\lambda \to 0$ at $\ln(\mu^2/{\rm GeV}^2) \approx 46$ ($\mu \approx 10^{10}$ GeV). Critical case ($k=1.03$, solid red) represents marginal stability with $\lambda$ approaching but not crossing zero. Enhanced scenarios ($k=3.0$, green; $k=5.0$, purple; $k=7.2$, orange dot-dashed) show absolute stability with runaway growth toward UV poles at $10^{16}$--$10^{18}$ GeV.