Determination of Absolute Neutrino Masses from Bursts of Z Bosons in Cosmic Rays

Ultrahigh energy neutrinos $\left(\mathrm{UHE}\nu \right)$ scatter on relic neutrinos $\left(\mathrm{R}\nu \right)$ producing Z bosons, which can decay hadronically producing protons (Z burst). We compare the predicted proton spectrum with the observed ultrahigh energy cosmic ray (UHECR) spectrum and determine the mass of the heaviest $\mathrm{R}\nu$ via a maximum likelihood analysis. Our prediction depends on the origin of the powerlike part of the UHECR spectrum: $m_{\nu }{=2.75\mathrm{}}_{-0.97\mathrm{}}^{+1.28\mathrm{}}\mathrm{eV}$ for Galactic halo and ${0.26}_{-0.14\mathrm{}}^{+0.20\mathrm{}}\mathrm{eV}$ for extragalactic origin. The necessary $\mathrm{UHE}\nu$ flux should be detected in the near future.