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

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.