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

For some choices of soft supersymmetry (SUSY)-breaking parameters, the lightest supersymmetric particle (LSP) is a stable neutralino ${\tilde{\chi }}_1^0,$ the NLSP is a chargino ${\tilde{\chi }}_1^{\pm }$ almost degenerate in mass with the LSP $\left(\Delta m_{{\tilde{\chi }}_1}\equiv m_{{\tilde{\chi }}_1^{\pm }}-m_{{\tilde{\chi }}_1^0}\sim m_{\pi }-\mathrm{few}\mathrm{}\mathrm{GeV}\right),$ and all other sparticles are relatively heavy. In this case, detection of sparticles in the usual, supergravity (MSUGRA)-motivated signals will be difficult, since the decay products in ${\tilde{\chi }}_1^{\pm }\to {\tilde{\chi }}_1^0\dots$ will be very soft, and alternative signals must be considered. Here, we study the viability of signatures at the Fermilab 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 ${\tilde{\chi }}_1^{\pm }$ and ${\tilde{\chi }}_1^0$ are light. We also consider the $\mathrm{jet}+E_T$ and $\gamma +E_T$ signatures assuming that the gluino is also light with $m_{\tilde{g}}\sim m_{{\tilde{\chi }}_1^{\pm }}.$ We find that the mass reach is critically dependent upon $\Delta m_{{\tilde{\chi }}_1}$ and $m_{\tilde{g}}-m_{{\tilde{\chi }}_1^{\pm }}.$ If $\Delta m_{{\tilde{\chi }}_1}$ is sufficiently big that $c\tau \left({\tilde{\chi }}_1^{\pm }\right)\lesssim \mathrm{few}\mathrm{}\mathrm{cm}$ and $m_{\tilde{g}}$ is large, there is a significant possibility that the limits on $m_{{\tilde{\chi }}_1^{\pm }}$ based on CERN LEP2 data cannot be extended at the Fermilab Tevatron. If