Helicity amplitudes for the small angle lepton pair production in e^+e^- or μ^+ μ^- collisions

Abstract

The lepton pair production $e^{-}{e}^{+}\to e^{-}{e}^{+}{l}^{-}{l}^{+}$ or ${\mu }^{-}{\mu }^{+}\to {\mu }^{-}{\mu }^{+}{l}^{-}{l}^{+}$ is studied in the dominant cross section region of scattering angles $m_j/E_j\stackrel{<}{\sim }{\theta }_j\ll 1$. An analytical expression is found for all 64 helicity amplitudes of these processes. The accuracy of the obtained formulae is given omitting only terms of the order of $m_j^2/E_j^2$, ${\theta }_j^2$ and ${\theta }_j{m}_j/E_j$. The result has a compact form convenient both for analytical and numerical calculations of various cross sections in this dominating scattering regime.

19 pages, Latex