Virtual Hadronic and Heavy-Fermion O(alpha^2) Corrections to Bhabha Scattering

TL;DR

This paper calculates and analyzes the two-loop QED corrections to Bhabha scattering from hadronic and heavy-fermion vacuum polarization effects, providing detailed numerical evaluations relevant for high-energy collider experiments.

Contribution

It provides a detailed calculation and numerical analysis of the previously unknown two-loop hadronic and heavy-fermion corrections to Bhabha scattering cross-sections.

Findings

Corrections are less than 0.5 per mille at 1 GeV

Corrections reach about 2 per mille at 10 GeV

At the Z resonance, corrections are about 2.3 per mille

Abstract

Effects of vacuum polarization by hadronic and heavy-fermion insertions were the last unknown two-loop QED corrections to high-energy Bhabha scattering and have been first announced in \cite{Actis:2007fs}. Here we describe the corrections in detail and explore their numerical influence. The hadronic contributions to the virtual O(alpha^2) QED corrections to the Bhabha-scattering cross-section are evaluated using dispersion relations and computing the convolution of hadronic data with perturbatively calculated kernel functions. The technique of dispersion integrals is also employed to derive the virtual O(alpha^2) corrections generated by muon-, tau- and top-quark loops in the small electron-mass limit for arbitrary values of the internal-fermion masses. At a meson factory with 1 GeV center-of-mass energy the complete effect of hadronic and heavy-fermion corrections amounts to less than 0.5 per mille and reaches, at 10 GeV, up to about 2 per mille. At the Z resonance it amounts to 2.3 per mille at 3 degrees; overall, hadronic corrections are less than 4 per mille. For ILC energies (500 GeV or above), the combined effect of hadrons and heavy-fermions becomes 6 per mille at 3 degrees; hadrons contribute less than 20 per mille in the whole angular region.