“…The top panel is for K = 1 (pγ) and the bottom panel is for K = 2 (pp). In each panel, we show the current 90% CL upper limits on the integrated photon flux over the whole energy range from 10 GeV to 10 8 GeV, obtained from a combination of various experiments, such as CASA-MIA [129], MILARGO [130], Fermi-LAT [131], GRAPES [132], KASCADE [133,134], ARGO [135] and HAWC [136]. We also adopted a combined best fit [137] in the 1-100 TeV region for the upper bound on photon flux based on the diffuse electron flux limit from AMS-02 [138], DAMPE [139], Fermi-LAT [140], MAGIC [141], HESS [142], and VERITAS [143], since air showers from electrons, positrons and photons behave the same.…”