Sensitivity of Standard Model Vacuum Stability to Enhanced Scalar Couplings: A Coupling Scan and its Implications for Radiatively Broken Electroweak Symmetry

Abstract

We study how Standard Model vacuum stability depends on the Higgs quartic coupling at the electroweak matching scale, parameterized through a dimensionless enhancement factor $k = \lambda_{\rm enhanced}(M_t)/\lambda_{\rm SM}(M_t)$, with the observed Higgs mass held fixed at $M_h = 125$~GeV. This is a scan of the coupling itself, treated as a free parameter set by physics beyond the Standard Model, and is distinct from the Higgs-mass scan that underlies the conventional stability bound. Using the complete three-loop renormalization group equations including all gauge and Yukawa couplings, we find a critical threshold $k_{\rm crit} \approx 1.076$ separating the metastable Standard Model trajectory from absolutely stable trajectories. At this threshold the matching-scale coupling is $\lambda(M_t) \approx 0.135$, which reproduces the established three-loop absolute-stability boundary, providing an internal consistency check of the framework. The instability scale is highly sensitive to $k$ near the threshold, with a logarithmic susceptibility $d\ln\Lambda_I/d\ln k$ of order $10^3$ as $k \to k_{\rm crit}^-$, larger by two to three orders of magnitude than the analogous susceptibility of $\Lambda_{\rm QCD}$ to $\alpha_s(M_Z)$. For $k > k_{\rm crit}$ the vacuum is absolutely stable and $\lambda$ develops an ultraviolet Landau pole whose scale falls rapidly with increasing $k$: for moderate enhancement the pole lies near the Planck scale, while for the large enhancement $k \approx 7.2$ associated with radiative electroweak symmetry breaking the matching-scale coupling is $\lambda(M_t) \approx 0.9$ and perturbative validity is lost by $\sim 10^5$~GeV.