Reach of CERN LEP2 and Fermilab Tevatron upgrades for Higgs bosons in supersymmetric models

Luminosity upgrades of the Fermilab Tevatron $p\overline{p}$ collider have been shown to allow experimental detection of a standard model (SM) Higgs boson up to ${m}_{{H}_{\mathrm{SM}}}\ensuremath{\sim}120\mathrm{GeV}$ via ${\mathrm{WH}}_{\mathrm{SM}}\ensuremath{\rightarrow}l\ensuremath{\nu}b\overline{b}$ events. This limit nearly saturates the parameter space for many models of weak scale supersymmetry (SUSY) with a minimal particle content. It is therefore interesting to examine the SUSY Higgs reach of future Tevatron experiments. Contours are presented of Higgs boson reach for CERN LEP2 and Tevatron luminosity upgrades for three models of weak scale SUSY: the minimal supersymmetric standard model, the minimal supergravity model and a simple gauge mediated SUSY breaking model. In each case we find a substantial gain in reach at the Tevatron with integrated luminosity increasing from $10{\mathrm{fb}}^{\mathrm{\ensuremath{-}}1}$ to $25--30{\mathrm{fb}}^{\mathrm{\ensuremath{-}}1}.$ With the larger integrated luminosity, a Higgs boson search at the Tevatron should be able to probe essentially the entire parameter space of these models. While a discovery would be very exciting, a negative result would severely constrain our ideas about how weak scale supersymmetry is realized.