  The emission of a charged light lepton pair by a superluminal neutrino has
been identified as a major factor in the energy loss of highly energetic
neutrinos. The observation of PeV neutrinos by IceCube implies their stability
against lepton pair Cerenkov radiation. Under the assumption of a
Lorentz-violating dispersion relation for highly energetic superluminal
neutrinos, one may thus constrain the Lorentz-violating parameters. A
kinematically different situation arises when one assumes a Lorentz-covariant,
space-like dispersion relation for hypothetical tachyonic neutrinos, as an
alternative to Lorentz-violating theories. We here discuss a hitherto neglected
decay process, where a highly energetic tachyonic neutrinos may emit other
(space-like, tachyonic) neutrino pairs. We find that the space-like dispersion
relation implies the absence of a q^2 threshold for the production of a
tachyonic neutrino-antineutrino pair, thus leading to the dominant additional
energy loss mechanism for an oncoming tachyonic neutrino in the medium-energy
domain. Surprisingly, the small absolute value of the decay rate and energy
loss rate in the tachyonic model imply that these models, in contrast to the
Lorentz-violating theories, are not pressured by the cosmic PeV neutrinos
registered by the IceCube collaboration.
