Improved α4 term of the muon anomalous magnetic moment -: art. no. 113001

We have completed the evaluation of all mass-dependent alpha(4) QED contributions to the muon g-2, or a(mu), in two or more different formulations. Their numerical values have been greatly improved by an extensive computer calculation. The new value of the dominant alpha(4) term A(2)((8))(m(mu)/m(e)) is 132.6823 (72), which supersedes the old value 127.50 (41). The new value of the three-mass term A(3)((8))(m(mu)/m(e),m(mu)/m(tau)) is 0.0376 (1). The term A(2)((8))(m(mu)/m(tau)) is crudely estimated to be about 0.005 and may be ignored for now. The total QED contribution to a(mu) is 116 584 719.58(0.02)(1.15)(0.85)x10(-11), where 0.02 and 1.15 are uncertainties in the alpha(4) and alpha(5) terms and 0.85 is from the uncertainty in alpha measured by atom interferometry. This raises the standard model prediction by 13.9x10(-11), or about 1/5 of the measurement uncertainty of a(mu). It is within the noise of current uncertainty (similar to100x10(-11)) in the estimated hadronic contributions to a(mu).