Mind the gap on Icecube: Cosmic neutrino spectrum and muon anomalous magnetic moment in the gauged L_{mu} - L_{tau} model

The energy spectrum of cosmic neutrinos, which was recently reported by the IceCube collaboration, shows a gap between 400 TeV and 1 PeV. An unknown neutrino interaction mediated by a field with a mass of the MeV scale is one of the possible solutions to this gap. We examine if the leptonic gauge interaction L_{mu} - L_{tau} can simultaneously explain the two phenomena in the lepton sector: the gap in the cosmic neutrino spectrum and the unsettled disagreement in muon anomalous magnetic moment. We illustrate that there remains the regions in the model parameter space, which account for both the problems. Our results also provide a hint for the distance to the source of the high-energy cosmic neutrinos.