Cosmic neutrino spectrum and the muon anomalous magnetic moment in the gaugedLμ−Lτmodel

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 whether the leptonic gauge interaction ${L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}$ can simultaneously explain the two phenomena in the lepton sector: the gap in the cosmic neutrino spectrum and the unsettled disagreement in the muon anomalous magnetic moment. We illustrate that there remain regions in the model parameter space which account for both of the problems. Our results also provide a hint to the distance to the source of the high-energy cosmic neutrinos.