Second order contributions to elastic large-angle Bhabha scattering cross-section

TL;DR

The paper addresses precise calculations of elastic large-angle Bhabha scattering cross-sections at high energies, focusing on radiative corrections up to O(α^2 L^2) and O(α^2 L). It systematically assembles known two-loop vertex contributions, computes the squares of one-loop amplitudes (vertex and box types), and adds soft- and double-soft photon emission corrections. It provides explicit analytic expressions for the second-order corrections Δ1, Δ2, Δ3 and the soft-virtual and double-soft terms, demonstrating infrared cancellation and compatibility with renormalization-group expectations. The work also discusses the status of two-loop box contributions and suggests extensions to Möller scattering and experimental calibrations.

Abstract

The cross-section of (quasi-)elastic large-angle electron-positron scattering at high energies is calculated. Radiative corrections of the orders O(α^2 L^2) and O(α^2 L), besides pure two-loop box contributions, are explicitly calculated. In the second order we considered the following sources of corrections: 1) Virtual photonic corrections coming from squares of 1-loop level amplitudes and their relevant interferences (vertex-type and box-type Feynman diagrams). 2) Double soft photon emission and one-loop corrections to single soft photon emission. The results are presented in an analytical form.

Figures (2)

• Figure 1: Vertex diagrams up to 2--loop level.
• Figure 2: Box diagrams up to 2--loop level.