Explaining the ANITA Anomaly with Inelastic Boosted Dark Matter

We propose a new physics scenario in which the decay of a very heavy dark-matter candidate which does not interact with the neutrino sector could explain the two anomalous events recently reported by ANITA. The model is composed of two components of dark matter, an unstable dark-sector state, and a massive dark gauge boson. We assume that the heavier dark-matter particle of EeV-range mass is distributed over the galactic halo and disintegrates into a pair of lighter -- highly boosted -- dark-matter states in the present universe which reach and penetrate the Earth. The latter scatters {\it in}elastically off a nucleon and produces a heavier dark-sector unstable state which subsequently decays back to the lighter dark matter along with hadrons, which induce Extensive Air Showers, via on-/off-shell dark gauge boson. Depending on the mass hierarchy within the dark sector, either the dark gauge boson or the unstable dark-sector particle can be long-lived, hence transmitted significantly through the Earth. We study the angular distribution of the signal and show that our model favors emergence angles in the range $\sim 25^\circ -35^\circ$ if the associated parameter choices bear the situation where the mean free path of the boosted incident particle is much larger than the Earth diameter while its long-lived decay product has a decay length of dimensions comparable to the Earth radius. Our model, in particular, avoids any constraints from complementary neutrino searches such as IceCube or the Auger observatory.