Bounds on relic neutrino masses in the Z-burst model

Neutrinos from far-away sources annihilating at the Z-resonance on relic neutrinos may give origin to the extreme-energy cosmic rays (EECR). If 'Z-bursts' are responsible for the EECR events, then we show that the non observation of cosmic ray events at energies above 2x1020 eV by the AGASA Collaboration implies a lower bound ∼0.3 eV on the relic neutrino mass. Since this mass exceeds the mass-squared differences inferred from oscillation physics, the bound in fact applies to all three neutrino masses. Together with the upper bound provided by comparisons of the CMB anisotropy with large-scale structure, this bound leaves only a small interval for neutrino masses around 0.3 eV,if Z-bursts are to explain the existing EECR events