  Nearly-sterile neutrinos with masses in the MeV range and below would be
produced in the beam of the Short-Baseline Neutrino (SBN) program at Fermilab.
In this article, we study the potential for SBN to discover these particles
through their subsequent decays in its detectors. We discuss the decays which
will be visible at SBN in a minimal and non-minimal extension of the Standard
Model, and perform simulations to compute the parameter space constraints which
could be placed in the absence of a signal. We demonstrate that the SBN program
can extend existing bounds on well constrained channels such as $N \rightarrow
\nu l^+ l^-$ and $N \rightarrow l^\pm \pi^\mp$ while, thanks to the strong
particle identification capabilities of liquid-Argon technology, also place
bounds on often neglected channels such as $N \rightarrow \nu\gamma$ and $N
\rightarrow \nu \pi^0$. Furthermore, we consider the phenomenological impact of
improved event timing information at the three detectors. As well as
considering its role in background reduction, we note that if the
light-detection systems in SBND and ICARUS can achieve nanosecond timing
resolution, the effect of finite sterile neutrino mass could be directly
observable, providing a smoking-gun signature for this class of models. We
stress throughout that the search for heavy nearly-sterile neutrinos is a
complementary new physics analysis to the search for eV-scale oscillations, and
would extend the BSM program of SBN while requiring no beam or detector
modifications.
