Use of ANTARES and IceCube Data to Constrain a Single Power-law Neutrino Flux

We perform the first statistical combined analysis of the diffuse neutrino flux observed by ANTARES (nine-year) and IceCube (six-year) by assuming a single astrophysical power-law flux. The combined analysis reduces by a few percent the best-fit values for the flux normalization and the spectral index. Both data samples show an excess in the same energy range (40-200 TeV), suggesting the presence of a second component. We perform a goodness-of-fit test to scrutinize the null assumption of a single power-law, scanning different values for the spectral index. The addition of the ANTARES data reduces the p-value by a factor . In particular, a single power-law component in the neutrino flux with the spectral index deduced by the six-year up-going muon neutrinos of IceCube is disfavored with a p-value smaller than 10−2.