Cross Sections for Two-Pair Production at Infinite Energy

Abstract

We give here the total cross sections for the following three high-energy processes: (i) $\gamma +\gamma \to e^{+}+e^{+}+e^{-}+e^{-}$, (ii) $\gamma +\gamma \to {\pi }^{+}+{\pi }^{+}+{\pi }^{-}+{\pi }^{-}$, and (iii) $\gamma +\gamma \to {\pi }^{+}+{\pi }^{-}+e^{+}+e^{-}$. Up to the eighth order, all of them approach constants in the high-energy limit. These constants are 6.5, 0.23×${10}^{-5\mathrm{}}$, and 0.26×${10}^{-3\mathrm{}}$ μb, respectively, for (i), (ii), and (iii). The corresponding photon-photon elastic scattering amplitudes in the forward direction are also given. The creation of $\mu$ pairs is also briefly discussed.