Reduction of ultra-high energy neutrino flux for spacelike neutrinos from extragalactic sources

Assuming that neutrinos are spacelike (tachyonic) fermions, we calculate width for the kinematically allowed, lepton number conserving, three-body decay ${\nu }_{\alpha }\to {\nu }_{\alpha }{\nu }_{\beta }{\overline{\nu }}_{\beta }$ in the Standard Model. Decays of tachyonic neutrinos over cosmological distances can lead to a reduction of the neutrino flux in the high-energy end of the spectrum. We estimate upper limits on the spacelike neutrino mass based on the PeV-energy cosmological neutrino events observed in the IceCube experiment. These limits are close to those deduced from the measurements of $m_{\nu }^2$ in the tritium-decay experiment KATRIN.