Naturalness, weak scale supersymmetry, and the prospect for the observation of supersymmetry at the Fermilab Tevatron and at the CERN LHC

Naturalness bounds on weak scale supersymmetry in the context of radiative breaking of the electroweak symmetry an analyzed. In the case of minimal supergravity it is found that for low tan beta and for low values 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 boson 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 ellipsoid 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 than or equal to 5) it is found that the upper limits for the entire set of sparticle masses lie in the range < 700 GeV (< 1.5 TeV) for any reasonable range of fine-tuning (Phi less than or equal to 20). However, it is found that there exist regions of the parameter space where the fine-tuning does not tightly constrain m(0) and m(1/2). Effects of nonuniversalities in the Higgs boson sector and in the third generation sector on naturalness bounds are also analyzed and it is found that nonuniversalities can significantly affect the upper bounds. It is also found that achieving the maximum Higgs boson mass allowed in supergravity unified models requires a high degree of fine-tuning. Thus a heavy sparticle spectrum is indicated if the Higgs boson mass exceeds 120 GeV. The prospect for the discovery of supersymmetry at the Fermilab Tevatron and at the CERN LHC in view of these results is discussed. [S0556-2821(98)01819-0]