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 $k = λ_{\rm enhanced}/λ_{\rm SM}$ 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.