Implications of a Higgs Discovery at LEP

If the Higgs boson has a mass below 130 GeV, then the standard model vacuum is unstable; if it has a mass below 90 GeV (i.e. within reach of LEP within the next two years), then the instability will occur at a scale between 800 GeV and 10 TeV. We show that precise determinations of the Higgs and top quark masses as well as more detailed effective potentialcalculations will enable one to pin down the location of the instability to an accuracy of about 25 percent. It is often said that ``the standard model must break down'' or ``new physics must enter'' by that scale. However, by considering a toy model for the new physics, we show that the lightest new particle (or resonance) could have a mass as much as an order of magnitude greater than the location of the instability, and still restabilize the vacuum.