Low-Energy e⁺e⁻ Hadronic Annihilation Cross Sections

The past decade has seen very significant progress in the measurement of the cross section for the annihilation process e⁺e⁻→hadrons. Different experimental approaches have helped achieve a more complete and fairly consistent picture. I provide a short review of the procedures used to obtain a continuous description of cross sections combining all available results from experiments. These data are necessary input to calculations of hadronic vacuum polarization effects that use dispersion integrals in an energy regime in which perturbative QCD cannot be applied. Applications include the hadronic contribution to the muon magnetic anomaly prediction in the Standard Model and the running of the electromagnetic coupling through the scale dependence of α(s), particularly its value at the Z boson mass, which is necessary for electroweak precision tests. Another application is for QCD studies that aim to accurately determine the strong coupling and its running, αS(s), and the heavy quark masses.