Hadron Contribution to Vacuum Polarisation

Precision tests of the Standard Theory require theoretical predictions taking into account higher-order quantum corrections. Among these vacuum polarisation plays a predominant role. Vacuum polarisation originates from creation and annihilation of virtual particle–antiparticle states. Leptonic vacuum polarisation can be computed from quantum electrodynamics. Hadronic vacuum polarisation cannot because of the non-perturbative nature of QCD at low energy. The problem is remedied by establishing dispersion relations involving experimental data on the cross section for e+ e− annihilation into hadrons. This chapter sets the theoretical and experimental scene and reviews the progress achieved in the last decades thanks to more precise and complete data sets. Among the various applications of hadronic vacuum polarisation calculations, two are emphasised: the contribution to the anomalous magnetic moment of the muon, and the running of the fine structure constant α to the Z mass scale. They are fundamental ingredients to high precision tests of the Standard Theory.