Bounds on Relic Neutrino Masses in the Z-burst Model

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Neutrinos from far away sources annihilating at the Z resonance on relic neutrinos may give origin to the ultrahigh-energy cosmic rays (UHECR). If "Z-bursts" are responsible for the UHECR events, then we show that the non-observation of cosmic ray events at energies above 2 × 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 UHECR events. The mass limit may be weakened to about 0.1 eV if very large extragalactic magnetic fields exist, for such fields remove the photon content of the Z-burst, which would otherwise be dominant above 10^20 eV.

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