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

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-leadiding 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. (orig.)