and

An unavoidable condition for consistency of the standard model is that all quarks must be lighter than some critical mass. A precise determination f this bound necessitates a complete renormalization group analysis of the scalar potential. Our results, that this critical condition is Mq < 80 GeV + 0.54 Mtligg~, differs markedly from previous investigations. It has been known for some time that radiative corrections to the scalar potential of a quantum field theory can play an important role in determining the properties of its vacuum. In their pioneering paper, Coleman and Weinberg [1] developed the techniques necessary for the evaluation of the O(h) terms in the effective potential. In addition to directly writing down the leading log approximation (valid for small couplings and small field fluctuations), they showed how one can use the properties of the renormaliza-tion group to sum all leading logs, thus obtaining an expression valid over a wider range of field values. In the context of the perturbative electroweak model, it was subsequently found [2--4] that heavy fermions destabilize our vacuum. For a given Higgs mass, there are corresponding upper bounds on quark and lepton masses. Should states which violate these bounds be observed experimentally at forthcoming machines, then the standard model would be bereft of life and new physics would have to come into play. There are other phenomena which lead to mass re-strictions, but these require a precision measurement [5] or are dependent on unknown hadronic matri