IMPROVED METASTABILITY BOUNDS ON THE STANDARD MODEL HIGGS MASS

Abstract

Depending on the Higgs-boson and top-quark masses, $M_H$ and $M_t$, the effective potential of the Standard Model at finite (and zero) temperature can have a deep and unphysical stable minimum $\langle ϕ(T)\rangle$ at values of the field much larger than $G_F^{-1/2}$. We have computed absolute lower bounds on $M_H$, as a function of $M_t$, imposing the condition of no decay by thermal fluctuations, or quantum tunnelling, to the stable minimum. Our effective potential at zero temperature includes all next-to-leading logarithmic corrections (making it extremely scale-independent), and we have used pole masses for the Higgs-boson and top-quark. Thermal corrections to the effective potential include plasma effects by one-loop ring resummation of Debye masses. All calculations, including the effective potential and the bubble nucleation rate, are performed numerically, and so the results do not rely on any kind of analytical approximation. Easy-to-use fits are provided for the benefit of the reader. Conclusions on the possible Higgs detection at LEP-200 are drawn.