The Origin of the Very-High-Energy Diffuse $\gamma$-Ray Emission: The Case for Galactic Source Cocoons

The secondary/primary cosmic-ray ratios and the diffuse backgrounds of gamma rays and neutrinos provide us with complementary information about the transport of Galactic cosmic rays~(CRs). We used the recent measurement of the diffuse gamma ray background in the $\sim \rm TeV -\rm PeV$ range by LHAASO and of the very high-energy diffuse neutrino background from the Galactic disc by IceCube to show that CRs may be accumulating an approximately energy independent grammage $X\sim 0.4\, \rm g \, \rm cm^{-2}$, in regions where gamma rays and neutrinos are produced with a hard spectrum, resembling the source spectrum. We speculate that this grammage reflects the early stages of cosmic ray transport around sources, in what are referred to as cocoons, where particles spend $\sim 0.3\, \rm Myr$ before starting their journey in the Galactic environment.