  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.
