Vacuum (Meta)Stability Beyond the MSSM

Abstract

We study the stability of the Higgs potential in the framework of the effective Lagrangian beyond the MSSM. While the leading nonrenormalizable operators can shift the Higgs boson mass above the experimental bound, they also tend to render the scalar potential unbounded from below. The destabilization is correlated with the Higgs mass increase, so that if quantum corrections are small the problem is severe. We show that a supersymmetric sub-leading correction stabilizes the potential within the domain of validity of the effective theory. Constraints on MSSM parameters as well as on higher dimensional operators are derived, ensuring that our vacuum has a lifetime longer than the present age of the universe. In addition we show that when effective operators are responsible for evading the LEP bound, stability constraints imply an upper bound on the scale of new physics in the few TeV range.