[Paper Review] Second order contributions to the elastic large-angle Bhabha scattering cross-section. I: all except 2-loop box diagrams

A. B. Arbuzov, É. A. Kuraev+1 more|arXiv (Cornell University)|Jun 1, 1998

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper calculates second-order radiative corrections to the elastic large-angle Bhabha scattering cross-section at high energies, including virtual photon corrections from squared one-loop amplitudes, interference terms (vertex and box types), and double soft photon emission. The results are presented in analytical form, covering O(α²L²) and O(α²L) contributions beyond pure two-loop box diagrams.

ABSTRACT

The cross-section of (quasi-)elastic large-angle electron-positron scattering at high energies is calculated. Radiative corrections of the orders O(\alpha^2 L^2) and O(\alpha^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.

Motivation & Objective

• To compute second-order radiative corrections to the elastic large-angle Bhabha scattering cross-section at high energies.
• To include virtual photonic corrections from squared one-loop amplitudes and their interferences, such as vertex and box-type diagrams.
• To account for double soft photon emission and one-loop corrections to single soft photon emission.
• To present results in analytical form for precision QED calculations in high-energy e⁺e⁻ scattering.
• To extend the understanding of higher-order QED corrections beyond pure two-loop box diagrams.

Proposed method

• Employed quantum electrodynamics (QED) to compute virtual corrections from squares of one-loop amplitudes.
• Included interference terms between one-loop amplitudes and their squared counterparts, specifically vertex-type and box-type Feynman diagrams.
• Treated double soft photon emission as a source of second-order corrections, including their interference with virtual corrections.
• Calculated one-loop corrections to single soft photon emission processes, contributing to the O(α²L) terms.
• Used analytical techniques to derive closed-form expressions for the cross-section contributions.
• Systematically excluded pure two-loop box diagrams, focusing on all other second-order contributions.

Experimental results

Research questions

• RQ1 What are the contributions to the large-angle Bhabha scattering cross-section from virtual photon corrections at O(α²L²) and O(α²L)?
• RQ2 How do interference terms between one-loop amplitudes and their squared versions affect the cross-section at second order?
• RQ3 What is the role of double soft photon emission in second-order radiative corrections to Bhabha scattering?
• RQ4 How do one-loop corrections to single soft photon emission contribute to the O(α²L) terms?
• RQ5 What analytical structure emerges for non-box second-order contributions in high-energy Bhabha scattering?

Key findings

• The paper derives analytical expressions for all second-order contributions to the large-angle Bhabha scattering cross-section except for pure two-loop box diagrams.
• Virtual corrections from squared one-loop amplitudes, including vertex and box-type interference terms, contribute significantly to the O(α²L²) and O(α²L) terms.
• Double soft photon emission contributes to the second-order cross-section, with its amplitude and interference terms explicitly calculated.
• One-loop corrections to single soft photon emission are found to contribute to the O(α²L) terms, completing the second-order correction structure.
• The results are presented in a closed analytical form, enabling precise theoretical predictions for high-energy e⁺e⁻ scattering experiments.
• The exclusion of pure two-loop box diagrams allows for a focused analysis on non-box second-order contributions, clarifying their role in radiative corrections.