A study of SUSY signatures at the Tevatron in models with near mass degeneracy of the lightest chargino and neutralino

For some choices of soft SUSY--breaking parameters, the LSP is a stable neutralino $\cnone$, the NLSP is a chargino $\cpmone$ almost degenerate in mass with the LSP ($\dmchi\equiv\mcpmone-\mcnone\sim \mpi-$few GeV), and all other sparticles are relatively heavy. In this case, detection of sparticles in the usual, mSUGRA--motivated signals will be difficult, since the decay products in $\cpmone\to\cnone...$ will be very soft, and alternative signals must be considered. Here, we study the viability of signatures at the Tevatron based on highly--ionizing charged tracks, disappearing charged tracks, large impact parameters, missing transverse energy and a jet or a photon, and determine the mass reach of such signatures assuming that only the $\cpmone$ and $\cnone$ are light. We also consider the jet+$\etmiss$ and $\gamma+\etmiss$ signatures assuming that the gluino is also light with $\mgl\sim \mcpmone$. We find that the mass reach is critically dependent upon $\dmchi$ and $\mgl-\mcpmone$. If $\dmchi$ is sufficiently big that $c\tau(\cpmone)\lsim$few cm and $\mgl$ is large, there is a significant possibility that the limits on $\mcpmone$ based on LEP2 data cannot be extended at the Tevatron. If $c\tau(\cpmone)>$few cm, relatively background--free signals exist that will give a clear signal of $\cpmone$ production (for some range of $\mcpmone$) even if $\mgl$ is very large.