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 nonobservation of cosmic ray events at energies above $2\times {10}^{20}\mathrm{e}\mathrm{V}$ by the AGASA Collaboration implies a lower bound $\sim 0.3\mathrm{e}\mathrm{V}$ 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.

• Received 30 April 2004

DOI:https://doi.org/10.1103/PhysRevD.70.113005