Ultrahigh energy neutrino absorption by neutrino dark matter

If the dark matter in the Universe consists of massive neutrinos (${m}_{{\ensuremath{\nu}}_{i}}\ensuremath{\simeq}30\ensuremath{-}100$ eV, $i=\ensuremath{\mu}, \ensuremath{\tau}$), a cosmic ray ${\ensuremath{\nu}}_{i}$ of ultrahigh energies may be absorbed at large redshifts, or even while crossing galactic halos, due to their annihilation with the dark matter neutrinos. These processes can become very important for ${E}_{\ensuremath{\nu}}\ensuremath{\simeq}\frac{{M}_{Z}^{2}}{2{m}_{\ensuremath{\nu}}}\ensuremath{\simeq}5\ensuremath{-}10\ifmmode\times\else\texttimes\fi{}{10}^{19}$ eV, for which the $Z$-exchange cross section is resonant, and may lead to a dip in the cosmic ray neutrino spectrum. I compute all the relevant contributions to the $\ensuremath{\nu}$ cross section and use them to evaluate the absorption redshift at ultrahigh energies and to analyze the absorption probability at large redshifts as well as in halos of galaxies. If the determination of the neutrino spectrum at those energies were to become experimentally feasible, the observation of the features discussed here would provide a clear indication of the nature of the dark matter.