Production cross sections of gamma-rays, electrons, and positrons in p-p collisions

Because the production cross sections of gamma-rays, electrons, and positrons made in p-p collisions, $sigma_{pprightarrow gamma}$ and $sigma_{pprightarrow {e}^pm}$, respectively, are kinematically equivalent with respect to the parent pion-production cross section $sigma_{pprightarrow pi}$, we obtain $sigma_{pprightarrow {e}^pm}$ directly from the machine data on $sigma_{pprightarrow gamma}$. In Sato et al. (2012), we give explicitly $sigma_{pprightarrow gamma}$, reproducing quite well the accelerator data with LHC, namely $sigma_{pprightarrow {e}^pm}$ is applicable enough over the wide energy range from GeV to 20,PeV for projectile proton energy. We dicuss in detail the relation between the cross sections, and present explicitly $sigma_{pprightarrow {e}^pm}$ that are valid into the PeV electron energy.