Study of constrained minimal supersymmetry

Taking seriously the phenomenological indications for supersymmetry we have made a detailed study of unified minimal SUSY, including many effects at the few percent level in a consistent fashion. We report here a general analysis of what can be studied without choosing a particular gauge group at the unification scale. Firstly, we find that the encouraging SUSY unification results of recent years do survive the challenge of a more complete and accurate analysis. Taking into account effects at the 5-10% level leads to several improvements of previous results and allows us to sharpen our predictions for SUSY in the light of unification. We perform a thorough study of the parameter space and look for patterns to indicate SUSY predictions, so that they do not depend on arbitrary choices of some parameters or untested assumptions. Our results can be viewed as a fully constrained minimal SUSY standard model. The resulting model forms a well-defined basis for comparing the physics potential of different facilities. Very little of the acceptable parameter space has been excluded by CERN LEP or Fermilab so far, but a significant fraction can be covered when these accelerators are upgraded. A number of initial applications to the understanding of the values of $m_h$ and $m_t$the SUSY spectrum, detectability of SUSY at LEP II or Fermilab, $B(b\to s\gamma )$, $\Gamma (Z\to b\overline{b})$, dark matter, etc., are included in a separate section that might be of more interest to some readers than the technical aspects of model building. We formulate an approach to extracting SUSY parameters from data when superpartners are detected. For small $tan\beta$ or large $m_t$ both $m_{\frac{1}{2}}$ and $m_0$ are entirely bounded from above at Å 1 TeV without having to use a fine-tuning constraint.