Hadronic contributions to the anomalous magnetic moment of the muon

We present a new, completely revised calculation of the muon anomalous magnetic moment aμ=(gμ-2)/2 comparing it with the more recent experimental determination of this quantity; this furnishes an important test of theories of strong, weak, and electromagnetic interactions. These theoretical determinations give the very precise numbers, 1011xaμ=116 591 806±50±10(rad)±30(lxl) [Theory,no τ] and 1011xaμ=116 591 889±49±10(rad)±30(lxl) [Theory,τ] to be compared with the experimental number, 1011xaμ=116 592 080±60. In the theoretical evaluations, the first quantity does not, and the second one does, use information from τ decay. The first errors for the theoretical evaluations include statistical plus systematic errors; the other ones are the estimated errors due to incomplete treatment of radiative corrections and the estimated error in the light-by-light scattering contribution. We thus have a significant mismatch between theory and experiment. We also use part of the theoretical calculations to give a precise evaluation of the electromagnetic coupling on the Z, αQED(MZ2), of the masses and widths of the (charged and neutral) rho resonances, of the scattering length and effective range for the P wave in ππ scattering, and of the quadratic radius and second coefficient of the pion form factor