Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Two-Loop Correction to Bhabha Scattering

Z. Bern, L. Dixon, A. Ghinculov

TL;DR

The paper tackles the problem of achieving NNLO precision for Bhabha scattering and related lepton-pair production by computing the full two-loop virtual QED corrections in dimensional regularization. It uses a master-integral reduction framework and expresses results with polylogarithms, while validating the infrared divergence structure against Catani's universal formulas and extracting process-dependent terms. The work provides detailed finite remainders for both e^+e^- → μ^+μ^- and Bhabha scattering, including flavor-decomposed contributions, and it conducts extensive cross-checks, including gauge invariance and independent-code verifications. These results are essential inputs for NNLO QED predictions and luminosity determinations at electron-positron colliders and also serve as a rigorous testing ground for techniques applicable to two-loop QCD calculations.

Abstract

We present the two-loop virtual QED corrections to e^+ e^- to mu^+ mu^- and Bhabha scattering in dimensional regularization. The results are expressed in terms of polylogarithms. The form of the infrared divergences agrees with previous expectations. These results are a crucial ingredient in the complete next-to-next-to-leading order QED corrections to these processes. A future application will be to reduce theoretical uncertainties associated with luminosity measurements at e^+ e^- colliders. The calculation also tests methods that may be applied to analogous QCD processes.

Two-Loop Correction to Bhabha Scattering

TL;DR

The paper tackles the problem of achieving NNLO precision for Bhabha scattering and related lepton-pair production by computing the full two-loop virtual QED corrections in dimensional regularization. It uses a master-integral reduction framework and expresses results with polylogarithms, while validating the infrared divergence structure against Catani's universal formulas and extracting process-dependent terms. The work provides detailed finite remainders for both e^+e^- → μ^+μ^- and Bhabha scattering, including flavor-decomposed contributions, and it conducts extensive cross-checks, including gauge invariance and independent-code verifications. These results are essential inputs for NNLO QED predictions and luminosity determinations at electron-positron colliders and also serve as a rigorous testing ground for techniques applicable to two-loop QCD calculations.

Abstract

We present the two-loop virtual QED corrections to e^+ e^- to mu^+ mu^- and Bhabha scattering in dimensional regularization. The results are expressed in terms of polylogarithms. The form of the infrared divergences agrees with previous expectations. These results are a crucial ingredient in the complete next-to-next-to-leading order QED corrections to these processes. A future application will be to reduce theoretical uncertainties associated with luminosity measurements at e^+ e^- colliders. The calculation also tests methods that may be applied to analogous QCD processes.

Paper Structure

This paper contains 11 sections, 56 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Two-Loop Amplitudes
  3. General Structure of Divergences
  4. $e^+e^- \to \mu^+\mu^-$ at One Loop to All Orders in $\epsilon$
  5. Modifications for Bhabha Scattering
  6. Bhabha Scattering at One Loop to All Orders in $\epsilon$
  7. Finite Contributions to the Amplitudes
  8. $e^+e^-\to\mu^+\mu^-$
  9. Bhabha Scattering
  10. Checks on the Result
  11. Conclusions

Figures (1)

  • Figure 1: The independent diagrammatic topologies for two-loop four-fermion scattering in QED.