  The requirement that the supersymmetric scalar potential be stable in the
minimal supergravity (mSUGRA) model imposes an upper bound on the universal
gaugino mass $m_{1/2}$ as function of the common scalar mass $m_0$. Combining
this with the experimental lower bound on $m_{1/2}$ from LEP data, we find a
new lower bound on $m_0$, stronger than the one that comes from experimental
data alone. If the corresponding upper and lower limits on the superparticle
masses, presented in this letter, are found to be violated at Tevatron Run II
or at the LHC, it would imply that we are living on a false vacuum. Special
attention has been paid in estimating the uncertainties in these predictions
due to the choice of the renormalization scale. The implications of our limits
for the constraints obtained by indirect methods(SUSY dark matter, g - 2 of the
muon, $ b \to s \gamma$....) are briefly discussed.
