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 paper shows that the stability of the Standard Model vacuum is extremely sensitive to small increases in the Higgs quartic coupling, with significant implications for high-energy physics and potential new physics near the GUT scale.

Contribution

It provides a detailed analysis of how slight enhancements in the Higgs coupling affect vacuum stability and the emergence of UV Landau poles using three-loop renormalization group equations.

Findings

A 3% increase in Higgs coupling shifts the vacuum from metastable to stable.

Enhanced couplings lead to UV poles at 10^{16}-10^{18} GeV, indicating strong dynamics.

Radiative electroweak symmetry breaking predicts large coupling enhancements deep in the stable regime.

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 $k = \lambda_{\rm enhanced}/\lambda_{\rm SM}$ 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 $\Lambda_{\rm UV} \sim 10^{16}$--$10^{18}$ 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.