Pion decay model of TIBET-ASγ PeV gamma-ray signal

Tibet-AS$\gamma$ collaboration has recently reported a measurement of diffuse $\gamma$-ray flux from the outer Galactic disk in the energy range reaching PeV. We complement this measurement with the Fermi/LAT measurement of the diffuse flux from the same sky region and study the pion decay model of the combined Fermi/LAT+Tibet-AS$\gamma$ spectrum. We find that within such a model the average cosmic ray spectrum in the outer Galactic disk has the same characteristic features as the local cosmic ray spectrum. In particular, it experiences a hardening at several hundred GV rigidity and a knee feature in the PV rigidity range. The slope of the average cosmic ray spectrum above the break is close to the locally observed slope of the helium spectrum $\gamma\simeq 2.5$, but is harder than the slope of the local proton spectrum in the same rigidity range. Although the combination of Fermi/LAT and Tibet-AS$\gamma$ data points to the presence of the knee in the average cosmic ray spectrum, the quality of the data is not yet sufficient for the study of knee shape and cosmic ray composition.