NATURALNESS, WEAK SCALE SUPERSYMMETRY, AND THE PROSPECT FOR THE OBSERVATION OF SUPERSYMMETRY AT THE FERMILAB TEVATRON AND AT THE CERN LHC -ART. NO. 096004

Naturalness bounds on weak scale supersymmetry in the context of radia tive breaking of the electroweak symmetry an analyzed. In the case of minimal supergravity it is found that for low tan beta and for low val ues of fine-tuning Phi, where Phi is defined essentially by the ratio mu(2)/M-Z(2) where mu is the Higgs mixing parameter and M-Z is the Z b oson mass, the allowed values of the universal scalar parameter m(0), and the universal gaugino mass m(1/2) lie on the surface of an ellipso id with radii fixed by Phi leading to tightly constrained upper bounds similar to root Phi. Thus for tan beta less than or equal to 2(less t han or equal to 5) it is found that the upper limits for the entire se t of sparticle masses lie in the range < 700 GeV (< 1.5 TeV) for any r easonable range of fine-tuning (Phi less than or equal to 20). However , it is found that there exist regions of the parameter space where th e fine-tuning does not tightly constrain m(0) and m(1/2). Effects of n onuniversalities in the Higgs boson sector and in the third generation sector on naturalness bounds are also analyzed and it is found that n onuniversalities can significantly affect the upper bounds. It is also found that achieving the maximum Higgs boson mass allowed in supergra vity unified models requires a high degree of fine-tuning. Thus a heav y sparticle spectrum is indicated if the Higgs boson mass exceeds 120 GeV. The prospect for the discovery of supersymmetry at the Fermilab T evatron and at the CERN LHC in view of these results is discussed. [S0 556-2821(98)01819-0]