Improved Higgs Mass Stability Bound in the Standard Model and Implications for Supersymmetry

We re-examine the lower bound on the mass of the Higgs boson, $M_H$, from Standard Model vacuum stability including next-to-leading-log radiative corrections. This amounts to work with the full one-loop effective potential, $V(\phi)$, improved by two-loop RGE, and allows to keep control of the scale invariance of $V$ in a wide range of the $\phi$-field. Our results show that the bound is ${\cal O}\ (10\ GeV)$ less stringent than in previous estimates. In addition we perform a detailed comparison between the SM lower bounds on $M_H$ and the supersymmetric upper bounds on it. It turns out that depending on the actual value of the top mass, $M_t$, the eventually measured Higgs mass can discard the pure SM, the Minimal Supersymmetric Standard Model or both.