Anomalous magnetic moment

The anomalous magnetic moment of the electron is the small but measurable deviation of the electron's gyromagnetic ratio g from the Dirac value g = 2 predicted by relativistic quantum mechanics with a structureless point electron. The defining quantity is a_e ≡ (g − 2) / 2, the fractional anomalous excess. The Dirac equation alone predicts a_e = 0; QED's one-loop vacuum-polarisation and vertex corrections give Schwinger's 1948 leading-order result a_e = α / (2π) ≈ 0.00115965, the first triumph of perturbative quantum electrodynamics and one of the most-quoted single-line formulas in twentieth-century physics.

Higher-order corrections have been computed to five-loop accuracy: a_e = (α/2π) − 0.328 (α/π)² + 1.182 (α/π)³ − ... The five-loop value of a_e is known theoretically to about 12 significant figures and agrees with the experimental measurement (Penning-trap measurements of trapped electrons, Hanneke-Fogwell-Gabrielse 2008 and refinements through 2023) to about the same precision. The electron magnetic moment is therefore the most-precisely-tested prediction in all of physics. The muon's anomalous magnetic moment a_μ shows a small but persistent ~4σ tension between the Standard Model prediction and the Brookhaven E821 (2001) and Fermilab Run-1 + Run-2 (2021–2023) measurements, of intense interest as a possible signal of physics beyond the Standard Model — though improvements in the QCD hadronic-vacuum-polarisation calculations have somewhat reduced the tension. The clean agreement for the electron and the persistent puzzle for the muon are emblematic of how precisely classical electromagnetism, in its quantum-electrodynamic completion, has been pinned down by experiment.