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 <(chi)over tilde>(0)(1), the NLSP is a chargino <(chi)over tilde>(+/-)(1) almost degenerate in mass with the LSP (Delta m(<(chi)over tilde>1) = m<(chi)over tilde>(+/-)(1) m<(chi)over tilde>(0)(1)similar to m(pi)-few GeV), and all other sparticles are relatively heavy. In this case, detection of sparticles in the usual, supergravity (MSUGRA)-motivatep signals will be difficult, since the decay products in <(chi)over tilde>(+/-)(1) --><(chi)over tilde>(0)(1)... 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 <(chi)over tilde>(+/-)(1) and <(chi)over tilde>(0)(1) are light. We also consider the jet+ E-T and gamma+ E-T signatures assuming that the gluino is also light with m (g) over bar similar to m<(chi)over tilde>(+/-)(1). We find that the mass reach is critically dependent upon Delta m<(chi)over tilde>(1) and m (g) over bar-m<(chi)over tilde>(+/-)(1). If Delta m<(chi)over tilde>(1) is sufficiently big that c tau(<(chi)over tilde>(+/-)(1))less than or similar to few cm and m (g) over bar is large, there is a significant possibility that the limits on m<(chi)over tilde>(+/-)(1) based on CERN LEP2 data cannot be extended at the Fermilab Tevatron. If c tau(<(chi)over tilde>(+/-)(1)) >few cm, relatively background-free signals exist that will give a clear signal of <(chi)over tilde>(+/-)(1) production (for some range of m<(chi)over tilde>)(1)(+/-) even if m (g) over bar is very large.