Predictions for g-2 of the muon and αQED(M2Z)

We update the Standard Model predictions of the anomalous magnetic moment of the muon, aμ ≡ (g − 2)/2, and the value of the QED coupling at the Z-boson mass, incorporating 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 aμ = 11659180.4(5.1) × 10−10 is about 3 × 10−10 lower than before, and has a smaller uncertainty, which corresponds to a 3. 4σ deviation from the measured value. The prediction for the QED coupling is α(M2 Z) −1 = 128.937 ± 0.030. It is important to predict the anomalous magnetic moment of the muon, aμ ≡ (gμ − 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 μ = 11659208.0(6.3)× 10. (1) If a statistically significant deviation, no matter how tiny, can be definitively established between the measured value a μ and the Standard Model prediction, then it will herald the existence of new physics beyond the Standard Model. In particular the comparison offers valuable 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, MZ , is equally important. The uncertainty in its value is one of the major limiting factors for precision electroweak physics. It limits, for example, the accuracy of the indirect estimate of the Higgs mass in the Standard Model. The Standard Model (SM) prediction of the muon anomalous magnetic moment, aμ, may be written as the sum of three terms, a μ = a QED μ + a EW μ + a had μ . (2) The QED contribution, which includes all the photonic and leptonic loops, and the EW contribution, which includes the loops involving the W,Z or Higgs bosons, are known very accurately: a μ = (116584718.09±0.16)×10 [3] and a μ = (154±2)×10 [4]. The main uncertainty lies in the final term, which involves the hadronic loop contributions. This term may, itself, be sub-divided into three parts a μ = a had,LO μ + a had,NLO μ + a had,l b l μ . (3) At present the hadronic vacuum polarisation contributions, a μ , cannot be calculated sufficiently accurately from first principles [5], but instead are evaluated using dispersion integrals over the measured cross sections for ee → γ → hadrons. For our 2003 predictions [6] we found a μ = (692.4 ± 5.9exp ± 2.4rad) × 10 , (4) a μ = (−9.79 ± 0.09exp ± 0.03rad) × 10 , (5) where the last error corresponds to the uncertainty associated with the radiative corrections to the cross section data. The final term in (3), a b l μ , is the hadronic light-by-light contribution. In our previous analysis, we took, in units of 10, either a b l μ = 8.0 ± 4.0 or 13.6 ± 2.5. (6) The major uncertainty in the Standard Model prediction of the anomalous moment, aμ, comes from the contribution of the ee → ππ channel. Indeed, the ee → ππ cross section data, available in 2003, give the dominant contribution to (4) of about (500±5)×10. Since then the situation has improved considerably. In particular, new precise measurements have recently become available from the CMD-2 detector throughout the centre-of-mass energy range 0.37 < √ s < 1.38 GeV [10, 11, 12]. Moreover, the KLOE collaboration have made measurements of the cross section by the radiative return method over the range 0.6 < √ s < 1 GeV [13]. Finally measurements at the SND detector over the interval 0.4 < √ s < 1 GeV have become available [14], and subsequently have been corrected [15]. Clearly all these data will have an impact on the determination of g − 2 of the muon. The first is a representative value of several earlier determinations (see, for example, the review in [7]), whereas the second value (which was used in the note added in proof in [6]) was obtained in [8]. In this paper we take the second value; it is consistent with the upper bound found in [9]. There is the possibility of obtaining indirect information on ee → hadrons in the energy range √ s < mτ , via the conserved vector current (CVC) hypothesis, using the precision data for the hadronic decays of τ leptons. However there is a sizeable discrepancy between the data from the ee → ππ experiments and that extracted from the ππν decay mode of the τ . This suggests that the understanding of the CVC hypothesis may be inadequate at the desired level of precision. We therefore do not include the τ data in the present (or in our previous [6]) analysis.