Virtual Hadronic and Leptonic Contributions to Bhabha Scattering

TL;DR

Using dispersion relations, the complete virtual QED contributions to Bhabha scattering due to vacuum polarization effects are derived and given the first complete estimate of their net numerical effects for both small and large angle scattering at typical beam energies of meson factories, the CERN Large Electron-Positron Collider and the International Linear Collider.

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).

Figures (3)

• Figure 1: Three classes of two-loop virtual hadronic Bhabha diagrams. (a) and (b) represent hadronic irreducible and reducible vertex diagrams, (c) irreducible hadronic box diagrams.
• Figure 2: Two-loop $N_f=2$ vertex and box corrections $d\sigma_2$ to Bhabha scattering in units of $10^{-3}d\sigma_0$ at meson factories, $\sqrt{s}=1$ GeV (a) and $\sqrt{s}=10$ GeV (b).
• Figure 3: Same as Fig. \ref{['fig-1gev']}, but ILC energies of $\sqrt{s}=100$ GeV (GigaZ option) and $\sqrt{s}=500$ GeV.