Evidence for a break in the spectrum of astrophysical neutrinos

The announcement by the IceCube Collaboration of the observation of 53 astrophysical neutrino candidates in the energy range 0.03 \alt E_\nu/PeV \alt 2 has been greeted with a great deal of justified excitement. Herein we provide fits of single and a broken power-law energy-spectra to these high-energy starting events (HESEs). By comparing our statistical results from fits to (background-free) shower HESE data with the spectral shape of muon neutrinos recently reported by the IceCube Collaboration, we show that there is (3 \sigma) evidence for a break in the spectrum of astrophysical neutrinos. After that we use the fitted result to predict the rate of Glashow events (in the ~ 6.3 PeV region) and double-bang tau neutrino events (in the PeV region) just at the threshold of IceCube detection.