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The IceCube experiment (IC) has recently observed 2 cascade events withenergies between 1 and 10 PeV. This energy combined with the fact that nomuon-track events are observed may be interpreted as a cosmogenic $\bar \nu_e$interacting in IC via the Glashow resonance (GR) $\bar \nu_e e \to W^-\to$(hadrons or $\bar \nu_e e$). We point out a unique, background-free signatureof the GR, a single isolated muon unaccompanied by any shower activity from theinteraction $\bar \nu_e e \to W^-\to \bar \nu_\mu \mu^-$, and propose it as atest of this interpretation. We calculate the event numbers and find that asingle such event is expected over about a three-year period in IC. We alsoshow that, if event rates remain at their current levels then, even with theGR, standard cosmogenic fluxes cannot easily explain the observations.Moreover, if muon-tracks remain conspicuous by their absence, then new physicsneeds to be invoked. As example scenarios in conformity with the observations,we calculate event rates for neutrino decay and Lorentz-invariance violation.

On the interpretation of IceCube cascade events in terms of the Glashow resonance