Ultra High Energy Cosmic Rays & Super-heavy Dark Matter
  We reanalyse the prospects for upcoming Ultra-High Energy Cosmic Ray
experiments in connection with the phenomenology of Super-heavy Dark Matter. We
identify a set of observables well suited to reveal a possible anisotropy in
the High Energy Cosmic Ray flux induced by the decays of these particles, and
quantify their performance via Monte Carlo simulations that mimic the outcome
of near-future and next-generation experiments. The spherical and circular
dipoles are able to tell isotropic and anisotropic fluxes apart at a confidence
level as large as $4\sigma$ or $5\sigma$, depending on the Dark Matter profile.
The forward-to-backward flux ratio yields a comparable result for relatively
large opening angles of about 40~deg, but it is less performing once a very
large number of events is considered. We also find that an actual experiment
employing these observables and collecting 300~events at 60~EeV would have a
$50\%$ chance of excluding isotropy against Super-heavy Dark Matter at a
significance of at least $3\sigma$
