arXiv:hep-ph/0611102v3 20 Apr 2007 KEK–TH–1112 IPPP/06/72 DCPT/06/144 LTH 729 8th November 2006 Revised: 20th April 2007 Improved predictions for g - 2 of the muon and α QED (M 2 Z ) K. Hagiwara a , A.D. Martin b , Daisuke Nomura a and T. Teubner c a Theory Group, KEK, Tsukuba, Ibaraki 305-0801, Japan b Department of Physics and Institute for Particle Physics Phenomenology, University of Durham, Durham DH1 3LE, U.K. c Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, U.K. Abstract We update the Standard Model predictions of the anomalous magnetic moment of the muon, a µ ≡ (g - 2)/2, and the value of the QED coupling at the Z -boson mass, incorpo- rating the new e + e − → ππ data obtained by CMD-2 and KLOE, as well as the corrected SND data, and other improvements. The prediction for a µ = 11659180.4(5.1) × 10 −10 is about 3 × 10 −10 lower than before, and has a smaller uncertainty, which corresponds to a 3.4 σ deviation from the measured value. The prediction for the QED coupling is α(M 2 Z ) −1 = 128.937 ± 0.030. It is important to predict the anomalous magnetic moment of the muon, a µ ≡ (g µ - 2)/2, and the value of the QED coupling on the Z pole as precisely as possible, in order to test the Standard Model and to probe New Physics. For the first quantity, we note that the Brookhaven experiment gives the average of the measurements of the µ + and µ − anomalous magnetic moments to be [1] a exp µ = 11659208.0(6.3) × 10 −10 . (1) If a statistically significant deviation, no matter how tiny, can be definitively established be- tween the measured value a exp µ and the Standard Model prediction, then it will herald the existence of new physics beyond the Standard Model. In particular the comparison offers valu- able constraints on possible contributions from SUSY particles, see, for example, the reviews in [2]. The second quantity, the QED coupling at the Z boson mass, M Z , is equally impor- tant. The uncertainty in its value is one of the major limiting factors for precision electroweak