Evidences of unconventional cosmic ray propagation in gamma-ray and neutrino astronomy

Several independent analyses of Fermi-LAT results found evidences of a spatial dependence of the cosmic ray (CR) proton spectral index which is not accounted for conventional models of CR transport in the Galaxy. We show that these results may have a relevant impact on the gamma-ray and neutrino diffuse emissions of the Galaxy above the TeV. Indeed a phenomenological model which adopts a spatial dependent diffusion coefficient, so to account for those features, also re- produces the gamma-ray excess, at 15 TeV, found by Milagro and H.E.S.S. measurements in the inner Galactic plane. The same model predicts a neutrino emission from that region which is sig- nificantly larger than expected on the basis of conventional models. This emission is compatible with ANTARES and IceCube results and it is a natural target for KM3NeT.