The most precise and specific tests of QED consist of measurements of the electromagnetic fine-structure constant, α, in various physical systems.
Because of this, the comparisons between theory and experiment are usually quoted as independent determinations of α. QED is then confirmed to the extent that these measurements of α from different physical sources agree with each other.
The current state-of-the-art theoretical calculation of the anomalous magnetic dipole moment of the electron includes QED diagrams with up to four loops.
This uncertainty is ten times smaller than the nearest rival method involving atom-recoil measurements.
The muon's anomalous magnetic dipole moment is also sensitive to contributions from new physics beyond the Standard Model, such as supersymmetry.
For this reason, the muon's anomalous magnetic moment is normally used as a probe for new physics beyond the Standard Model rather than as a test of QED.
This leads to the extracted value of α being dominated by theoretical uncertainty: The hyperfine splitting in muonium, an "atom" consisting of an electron and an antimuon, provides a more precise measurement of α because the muon has no internal structure: The Lamb shift is a small difference in the energies of the 2 S1/2 and 2 P1/2 energy levels of hydrogen, which arises from a one-loop effect in quantum electrodynamics.
The Lamb shift is proportional to α5 and its measurement yields the extracted value: Positronium is an "atom" consisting of an electron and a positron.
The decay rate of the singlet ("para-positronium") 1S0 state yields and the decay rate of the triplet ("ortho-positronium") 3S1 state yields This last result is the only serious discrepancy among the numbers given here, but there is some evidence that uncalculated higher-order quantum corrections give a large correction to the value quoted here.
The cross sections of higher-order QED reactions at high-energy electron-positron colliders provide a determination of α.
These experiments typically achieve only percent-level accuracy, but their results are consistent with the precise measurements available at lower energies.