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 \delta\sigma/ \sigma = 0.1 \% are explicitly taken into account. According to the generalized eikonal representation for the elastic amplitude, only diagrams with one exchanged photon are considered. Single photon emission with radiative corrections as well as next-to-leading two-photon and pair production diagrams are evaluated, together with leading three-loop corrections. All contributions have been calculated analytically. We define an experimentally measurable cross-section by integrating the calculated distributions over suitable 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.