Anomalies in the gamma-ray diffuse emission of the Galaxy and implications for the interpretation of IceCube results

Several independent analyzes of Fermi-LAT results found evidences of an excess of $\gamma$-ray diffuse emission along the inner Galactic plane and of a related spatial dependence of the cosmic ray (CR) proton spectral index. These features are not accounted for by conventional models of CR transport. We show that a phenomenological model accounting for those results in terms of spatial dependent CR transport also reproduces the $\gamma$-ray excess found by Milagro at 15 TeV in the inner Galactic plane and by H.E.S.S. in the Galactic center. We then use that model to compute the neutrino emission along the Galactic plane finding that is significantly larger than expected on the basis of conventional models. This emission is compatible with ANTARES upper limits and may soon be detected by IceCube or, more likely, by Km3NeT.