Are Z-bursts responsible for the super-GZK ultra high energy cosmic rays?

We show that the cascade limit on ultra high energy cosmic neutrino (UHECν) 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 data from HiRes and AGASA, the lower bound obtained on neutrino mass violates its existing cosmological upper bound. We conclude that Z-bursts cannot be the dominant source for the observed super-GZK UHECR events. This is consistent with the recent ANITA-lite data.