Virtual Hadronic and Leptonic Contributions to Bhabha Scattering

TL;DR

This paper calculates the complete virtual QED contributions to Bhabha scattering from vacuum polarization effects, including hadronic and heavy lepton loops, providing precise estimates relevant for high-precision experiments.

Contribution

It presents the first comprehensive estimate of hadronic and heavy lepton loop effects on Bhabha scattering across various energies and angles.

Findings

Hadronic corrections are 2-3 times larger than muon pair contributions.

Effects are generally smaller than electron loop effects but remain significant (~1 per mille).

Results are applicable to precision measurements at meson factories, LEP, and ILC.

Abstract

Using dispersion relations, we derive the complete virtual QED contributions to Bhabha scattering due to vacuum polarization effects in photon propagation. We apply our result to hadronic corrections and to heavy lepton and top quark loop insertions. We give the first complete estimate of their net numerical effects for both small and large angle scattering at typical beam energies of meson factories, LEP, and the ILC. The effects turn out to be smaller, in most cases, than those corresponding to electron loop insertions, but stay, with amounts of typically one per mille, of relevance for precision experiments. Hadronic corrections themselves are typically about 2-3 times larger than those of intermediate muon pairs (the largest heavy leptonic terms).