Phenomenology of light top squarks at the Fermilab Tevatron

We consider the possibility that one of the supersymmetric partners of the t quark (the t${\mathrm{̃}}_1$) is considerably lighter than all the other squarks as well as lighter than the top. We show that t${\mathrm{̃}}_1$ will decay into a chargino and a bottom quark if this decay is kinematically accessible; otherwise, it decays via t${\mathrm{̃}}_1$→c+Z${\mathrm{̃}}_1$, where Z${\mathrm{̃}}_1$, the lightest neutralino, is also the lightest supersymmetric particle (LSP). We then show that a t${\mathrm{̃}}_1$ with a mass just larger than ${\mathit{M}}_{\mathit{Z}}$/2 could easily have escaped detection at the Fermilab Tevatron. Such a t${\mathrm{̃}}_1$ can completely alter the decay patterns of the top quark; if ${\mathit{m}}_{\mathit{t}}$${\mathit{M}}_{\mathit{W}}$+${\mathit{m}}_{\mathit{b}}$, the t dominantly decays via t→t${\mathrm{̃}}_1$+Z${\mathrm{̃}}_1$ when this decay is kinematically accessible. This then invalidates any bounds on ${\mathit{m}}_{\mathit{t}}$ obtained from searches for isolated leptons. We show that if the LSP mass is around 10 GeV, it is possible that a top as light as 60 GeV could have escaped detection even via the missing-E${\mathrm{?}}_{\mathit{T}}$ analysis of the Collider Detector at Fermilab Collaboration. Finally, we evaluate the prospects for t${\mathrm{̃}}_1$ detection in future Tevatron runs and also examine how signals for a heavy t may be modified if there is a light t${\mathrm{̃}}_1$.