Hadronic contributions to the anomalous magnetic moment of the muon

We present a new, completely revised calculation of the muon anomalous magnetic moment a_μ=(g_μ-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, ${10}¹¹×{}{a}_{{μ}}=116 591 806±{}50±{}10(rad)±{}30({}×{}{}) {{0ex}{0ex}}[Theory,no {τ}]$ and ${10}¹¹×{}{a}_{{μ}}=116 591 889±{}49±{}10(rad)±{}30({}×{}{}) [Theory,{τ}]$ to be compared with the experimental number, ${10}¹¹×{}{a}_{{μ}}=116 592 080±{}60$. 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.