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 $μ^- μ^+ \to μ^- μ^+ l^- l^+ $ is studied in the dominant cross section region of scattering angles ${m_j}/{E_j} \stackrel{<}{\sim} θ_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 ${m_j^2}/{E_j^2}$, $θ_j^2$ and $ θ_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.