NEW CONSTRAINTS ON SUPERPARTNER MASSES

We consider the Minimal Supersymmetric Standard Model (MSSM) without i mposing relations on the superpartner masses that arise in grand unifi ed theories. Given an arbitrary pattern of superpartner masses (consis tent with experimental constraints), it may happen that the scalar pot ential is actually unstable, even though all scalar masses-squared are positive at the weak scale M(W). This is most likely to happen if the running mass-squared in a ''flat'' direction in field space becomes n egative at some scale Q(O) which is well below the GUT scale. In this case, either this pattern of masses is ruled out, or there must be new physics (beyond the MSSM) at or below the scale Q(O).