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, $σ_{pp\rightarrow γ}$ and $σ_{pp\rightarrow {e}^\pm}$, respectively, are kinematically equivalent with respect to the parent pion-production cross section $σ_{pp\rightarrow π}$, we obtain $σ_{pp\rightarrow {e}^\pm}$ directly from the machine data on $σ_{pp\rightarrow γ}$. In Sato et al. (2012), we give explicitly $σ_{pp\rightarrow γ}$, reproducing quite well the accelerator data with LHC, namely $σ_{pp\rightarrow {e}^\pm}$ 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 $σ_{pp\rightarrow {e}^\pm}$ that are valid into the PeV electron energy.

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