Indirect searches of dark matter via polynomial spectral features

We derive the spectra arising from non-relativistic dark matter annihilations or decays into intermediary particles with arbitrary spin, which subsequently produce neutrinos or photons via two-body decays. Our approach is model independent and predicts spectral features restricted to a kinematic box. The overall shape within that box is a polynomial determined by the polarization of the decaying particle. We illustrate our findings with two examples. First, with the neutrino spectra arising from dark matter annihilations into the massive Standard Model gauge bosons. Second, with the gamma-ray and neutrino spectra generated by dark matter annihilations into hypothetical massive spin-2 particles. Our results are in particular applicable to the 750 GeV diphoton excess observed at the LHC if interpreted as a spin-0 or spin-2 particle coupled to dark matter. We also derive limits on the dark matter annihilation cross section into this resonance from the non-observation of the associated gamma-ray spectral features by the H.E.S.S. telescope.