  F-theory GUT models favor a relatively narrow range of soft supersymmetry
breaking parameters in the MSSM Lagrangian. This leads to the specific
predictions that a 10-100 MeV mass gravitino is the LSP, and the NLSP is
quasi-stable, with a lifetime between a second to an hour. In a wide range of
parameter space, the NLSP turns out to be a stau, though a bino-like lightest
neutralino is also possible. Focusing on F-theory GUTs with a stau NLSP, we
study the discovery potential at the LHC for such scenarios. Models with a
quasi-stable stau predict a striking signature of a heavy charged particle
passing through the detector. As a function of the parameters of minimal
F-theory GUTs, we study how many of such events to expect, and additional
signatures correlated with the presence of quasi-stable staus. We also study
the prospects for staus to become stopped in or near the detector, as well as
potential ways to distinguish such models from minimal gauge mediation models
with similar spectra.
