Small-angle electron-positron scattering with a per mille accuracy☆

Abstract The elastic and inelastic high-energy small-angle electron-positron scattering is considered. All radiative corrections to the cross section with the relative accuracy δσ / σ = 0.1% are explicitly taken into account. According to the generalized eikonal representation for the elastic amplitude, in higher orders only diagrams with one exchanged photon may be considered. Single-photon emission with radiative corrections and next-to-leading two-photon and pair production diagrams are evaluated, together with leading three-loop corrections. All contributions have been calculated analytically. We integrate the calculated distributions over typical for LEP 1 experiments intervals of angles and energies. To the leading approximation, the results are shown to be described in terms of kernels of electron structure functions. Some numerical results are presented.