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

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 $m_j\mathrm{/}{E}_j{\theta }_j\ll 1$. 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 $m_j^2\mathrm{/}{E}_j^2$, ${\theta }_j^2$ and ${\theta }_j{m}_j\mathrm{/}{E}_j$. The result has a compact form convenient both for analytical and numerical calculations of various cross sections in this dominating scattering regime.