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 2 x 10^20 eV by the AGASA Collaboration implies a lower bound around 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.