Abstract
The anomalous magnetic moment of the muon is affected in order by vacuum polarization corrections to the photon propagator which involve strongly interacting particles. The contributions of the two- and three-pion systems to are estimated using the present experimental information on the two-pion and three-pion resonances (the and mesons). The analysis is based on the use of dispersion relations for the muon vertex functions, and of the Lehmann-Källén representation for the photon propagator. If it is assumed that the -meson resonance gives the dominant contribution to the electromagnetic form factor of the pion, the modifications of the photon propagator associated with the two-pion intermediate state lead to a change in , where is the width of the resonance in pion-pion scattering. In the limit of Gell-Mann's unitary symmetry for the meson-baryon interactions, the -meson contributions to are one-third of the -meson contributions. With MeV and the recent Yale value of 60 MeV for , one obtains a combined result which is an order of magnitude larger than (1) would be estimated using perturbation theory and (2) the nominal size of the sixth-order electrodynamic corrections; but which is still negligible in comparison with the quoted limits of error of ±5× in the best measurement of , that of Charpak et al. The possibility of obtaining additional large contributions from and configurations in the three- and four-pion states is discussed briefly.
- Received 21 May 1962
DOI:https://doi.org/10.1103/PhysRev.128.441
©1962 American Physical Society