Abstract Diffuse γ -ray emission between 10 and 1000 TeV from the Galactic plane was recently measured by the Large High Altitude Air Shower Observatory (LHAASO). These observations will help tremendously in constraining the propagation and interaction of cosmic rays in the Milky Way. Additionally, new measurements of cosmic-ray spectra reach a very high precision of up to 100 TeV energies, revealing multiple spectral structures of various species. In this work, based on up-to-date measurements of local cosmic-ray spectra and a simplified propagation setup, we confront a model prediction of diffuse γ -ray emission with measurements of diffuse γ -rays. To better constrain the low-energy part of the model, we analyze the 14.6 yr of Fermi Large Area Telescope (Fermi-LAT) data to extract the Galactic diffuse emission between 1 and 500 GeV from the same sky regions of LHAASO, after subtracting the contribution from known sources and the isotropic diffuse γ -ray background. The joint Fermi-LAT and LHAASO spectra thus cover a very wide energy range from 1 GeV to 1 PeV with small gaps from 0.5 to 10 TeV. Compared with the prediction, we find that clear excesses between several GeV and ∼60 TeV of the diffuse emission exist. Possible reasons to explain the excesses may include unresolved sources or more complicated propagation models. We illustrate that an exponential cutoff power-law component with an index of −2.40 and a cutoff energy of ∼30 TeV is able to account for such excesses.
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