Mind the Gap on IceCube: Cosmic neutrino spectrum and muon anomalous magnetic moment

The high energy cosmic neutrino spectrum reported by the IceCube collaboration shows a gap in the energy range between 500 TeV and 1 PeV. In this presentation, we illustrate that the IceCube gap is reproduced by the neutrino interaction mediated by the new gauge boson associated with a certain combination of the lepton avour number. The gauge interaction also explains the other long-standing gap in the lepton phenomenology: the gap between theory and experiment in the muon anomalous magnetic moment. (paper)