A Review of the Instability of Hot Electroweak Theory and its Bounds on $m_h$ and $m_t$

Abstract

[Talk presented at the International Seminar Quarks `92, Zvenigorod, Russia, May 11-17, 1992.] The electroweak vacuum need not be absolutely stable. For certain top and Higgs masses in the Minimal Standard Model, it is instead metastable with a lifetime exceeding the present age of the Universe. The decay of our vacuum may be nucleated at low temperature by quantum tunneling or at high temperature in the early Universe by thermal excitation. I briefly review the constraints on top and Higgs masses from requiring that the electroweak vacuum be sufficiently stable to have survived to the present day.