Small-Angle Electron-Positron Scattering with a Per Mille Accuracy

TL;DR

The paper presents a complete analytic calculation of the small-angle e+e- (Bhabha) scattering cross-section with per mille accuracy, including all relevant QED radiative corrections up to O(alpha^2) and leading three-loop effects under LEP1 kinematics. By adopting a generalized eikonal representation and Sudakov-type factorization, the authors compute single and double hard-photon emission, soft/virtual corrections, and e+e- pair production (with emphasis on the collinear/semi-collinear regions) and demonstrate cancellation of auxiliary parameters, yielding a cross-section expressible in terms of electron structure-function kernels. They integrate the distributions over LEP-like angular and energy intervals and provide numerical results with a claimed total theoretical uncertainty of about 0.006%, highlighting the dominance of scattering-type diagrams and the viability of a structure-function approach for precision luminosity calibration. The work provides analytic expressions and a Monte Carlo–friendly framework (via kernels and Sudakov factors) aiding precise luminosity determination and Standard Model parameter extraction at LEP energies.

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. PACS numbers 12.15.Lk, 12.20.--m, 12.20.Ds, 13.40.--f