  We propose an explanation of the LSND evidence for electron antineutrino
appearance based on neutrino decay. We introduce a heavy neutrino, which is
produced in pion and muon decays because of a small mixing with muon neutrinos,
and then decays into a scalar particle and a light neutrino, predominantly of
the electron type. We require values of $g m_4\sim$ few eV, $g$ being the
neutrino--scalar coupling and $m_4$ the heavy neutrino mass, e.g. $m_4$ in the
range from 1 keV to 1 MeV and $g \sim 10^{-6} - 10^{-3}$. Performing a fit to
the LSND data as well as all relevant null-result experiments, we show that all
data can be explained within this decay scenario. In the minimal version of the
decay model, we predict a signal in the upcoming MiniBooNE experiment
corresponding to a transition probability of the same order as seen in LSND. In
addition, we show that extending our model to two nearly degenerate heavy
neutrinos it is possible to introduce CP violation in the decay, which can lead
to a suppression of the signal in MiniBooNE running in the neutrino mode. We
briefly discuss signals in future neutrino oscillation experiments, we show
that our scenario is compatible with bounds from laboratory experiments, and we
comment on implications in astrophysics and cosmology.
