A Lower Bound on Neutrino Mass and Its Implication on The Z-burst Scenario

We show that the cascade limit on ultra high energy cosmic neutrino (UHEC$\nu$) flux imposes a lower bound on the neutrino mass provided that super-GZK events of ultra high energy cosmic rays (UHECRs) are produced from Z-bursts. Based on the data from HiRes and AGASA, the obtained neutrino mass lower bound violates its existing cosmological upper bound. We conclude that the Z-bursts cannot be the dominant source for the observed super-GZK UHECR events. This is consistent with the recent ANITA-lite data.