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 are 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 $\sim \sqrt{\Phi }.$ Thus for $\tan \beta <~2(<~5)$ it is found that the upper limits for the entire set of sparticle masses lie in the range $<700\mathrm{}\hspace{0.5em}\mathrm{GeV}\hspace{0.5em}(<\mathrm{}1.5\mathrm{}\hspace{0.5em}\mathrm{TeV})$ for any reasonable range of fine-tuning $(\Phi <~20).$ 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.