The cosmic-ray sea explains the diffuse Galactic gamma-ray and neutrino emission from GeV to PeV

The LHAASO collaboration has recently released the spectrum and the angular distribution of the $\gamma$-ray Galactic diffuse emission from 1 TeV to 1 PeV measured with the Kilometer-2 Array (KM2A) and Water Cherenkov Detector Array (WCDA). We show that these data are in remarkably good agreement with a set of models that assume the emission to be produced by the Galactic population of cosmic rays if its spectral shape traces that measured by CALET and DAMPE as well as KASCADE at higher energies. No extra-components besides the CR sea is needed to explain LHAASO results. Accounting for unresolved sources, we consistently reproduce Tibet AS$\gamma$ as well as a wide set of $\gamma$-ray data at lower energy. To do this, we consider two different transport setups: a conventional one and a $\gamma$-optimized spatial-dependent one (a development of the widely adopted KRA$_\gamma$ model). We demonstrate that both setups are compatible with LHAASO results. However, the latter is preferred if one takes into account Fermi-LAT gamma-ray data and neutrino measurements. In fact, we also compute the associated Galactic neutrino diffuse emission finding that the contribution from sources cannot be dominant and showing that spatial-dependent propagation models closely match the ANTARES and IceCube best fits for the Galactic Center Ridge and the Galactic Plane emissions. We argue that our $\gamma$-optimized model should be used as a template for future analyses of upcoming data from the Global Neutrino Network.