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

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 $k={\lambda }_{\mathrm{e}\mathrm{n}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{d}}\mathrm{/}{\lambda }_{\mathrm{S}\mathrm{M}}$ ranging from $k=1.0$ (Standard Model) to $k=7.2$ (radiative electroweak symmetry breaking prediction). We identify $k_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}=1.03$ 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 ${\mathrm{\Lambda }}_{\mathrm{U}\mathrm{V}}\sim {10}^{16}$–${10}^{18}$ 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.