High-Energy Relations Between Elastic Scattering Amplitudes of Particles and Antiparticles

We find conditions under which the ratio of particle and antiparticle total scattering cross sections ${\sigma _{+}(s)}/ {\sigma _{-}(s)}\to 1$ as $s \to \infty $. If the forward elastic scattering amplitudes become purely real asymptotically, then their ratio tends to $- 1$. We prove ${\sigma _{+}(s)}/ {\sigma _{-}(s)}\cong 1$, where $\sigma _{+}(s)\gg {\pi }/{m_\pi ^2}$, $m_\pi $ is the $\pi $-meson mass. We show that the asymptotic relations obtained have finite-energy analogues for some processes.