  The super-weak force is a minimal, anomaly-free U(1) extension of the
standard model (SM), designed to explain the origin of (i) neutrino masses and
mixing matrix elements, (ii) dark matter, (iii) cosmic inflation, (iv)
stabilization of the electroweak vacuum and (v) leptogenesis. We discuss the
neutrino sector of this model in detail and study the allowed parameter space
of the neutrino Yukawa matrices and mixing matrix elements. The model generates
nonstandard neutrino interactions, whose allowed experimental limits are used
to constrain the parameter space of the model. We provide benchmark points in
the relevant parameter space that fall within the sensitivity region of the
SHiP and MATHUSLA experiments.
