Updated Estimate of the Muon Magnetic Moment Using Revised Results from e+e- Annihilation

A new evaluation of the hadronic vacuum polarization contribution to the muon magnetic moment is presented. We take into account the reanalysis of the low-energy e+e- annihilation cross section into hadrons by the CMD-2 Collaboration. The agreement between e+e- and tau spectral functions in the pi pi channel is found to be much improved. Nevertheless, significant discrepancies remain in the center-of-mass energy range between 0.85 and 1.0 GeV, so that we refrain from averaging the two data sets. The values found for the lowest-order hadronic vacuum polarization contributions are a_mu[had,LO] = (696.3 +- 6.2[exp] +- 3.6[rad])e-10 (e+e- -based) and a_mu[had,LO] = (711.0 +- 5.0[exp] +- 0.8[rad] +- 2.8[SU2])e-10 (tau-based), where the errors have been separated according to their sources: experimental, missing radiative corrections in e+e- data, and isospin breaking. The corresponding Standard Model predictions for the muon magnetic anomaly read a_mu = (11,659,180.9 +- 7.2[had] +- 3.5[LBL] +- 0.4[QED+EW])e-10 (e+e- -based) and a_mu = (11,659,195.6 +- 5.8[had] +- 3.5[LBL] +- 0.4[QED+EW])e-10 (tau-based), where the errors account for the hadronic, light-by-light (LBL) scattering and electroweak contributions. The deviations from the measurement at BNL are found to be (22.1 +- 7.2 +- 3.5 +- 8.0)e-10 (1.9 sigma) and (7.4 +- 5.8 +- 3.5 +- 8.0)e-10 (0.7 sigma) for the e+e- and tau-based estimates, respectively, where the second error is from the LBL contribution and the third one from the BNL measurement.Comment: 14 pages, 7 figures (to be submitted to Phys Lett B

A theory driven analysis of the effective QED coupling at MZM_Z

An evaluation of the effective QED coupling at the scale M_Z is presented. It employs the predictions of perturbative QCD for the cross section of electron positron annihilation into hadrons up to order \alpha_s^2, including the full quark mass dependence, and of order \alpha_s^3 in the high energy region. This allows to predict the input for the dispersion relations over a large part of the integration region. The perturbative piece is combined with data for the lower energies and the heavy quark thresholds. The result for the hadronic contribution to the running of the coupling \Delta\alpha^{(5)}_{\rm had}(M_Z^2)= (277.5 \pm 1.7)\times 10^{-4} leads to (\alpha(M_Z^2))^{-1}=128.927 \pm 0.023. Compared to previous analyses the uncertainty is thus significantly reduced.Comment: 9 pages (Latex); minor error in result for charm threshold region fixed; final result unchange

A High Statistics Study of the Decay tau- -> pi- pi0 nu

We report a measurement of the branching fraction for tau- -> pi- pi0 nu and the invariant mass spectrum of the resulting pi- pi0 system using 72.2 /fb of data recorded by the Belle detector at the KEKB e+e- collider. The branching fraction obtained is (25.15 +/- 0.04 +/- 0.31)%, where the first error is statistical and the second is systematic. The unfolded pi- pi0 mass spectrum is used to determine resonance parameters for the rho(770), rho'(1450), and rho''(1700) mesons. We also use this spectrum to estimate the hadronic contribution to the anomalous magnetic moment of the muon.Comment: 23 pages, 10 Postscript figures, 7 tables, contributed to the International Europhysics Conference, EPS2005, in Lisbon, Portuga

Recent results from e+ e- --> hadrons

New results on the low energy e+ e- annihilation into hadrons from Novosibirsk and Beijing are described. Implications of the new measurements for the evaluation of the hadronic contribution to the muon anomalous magnetic moment are discussed.Comment: Invited talk at the Seventh International Workshop on Tau Lepton Physics (TAU02), Santa Cruz, Ca, USA, Sept 2002, 7 pages, 4 figure

Study of hyperfine structure in simple atoms and precision tests of the bound state QED

We consider the most accurate tests of bound state QED, precision theory of simple atoms, related to the hyperfine splitting in light hydrogen-like atoms. We discuss the HFS interval of the 1s state in muonium and positronium and of the 2s state in hydrogen, deuterium and helium-3 ion. We summarize their QED theory and pay attention to involved effects of strong interactions. We also consider recent optical measurements of the 2s HFS interval in hydrogen and deuterium.Comment: presented at The International Workshop "e+e- collisions from phi to psi

A new ring structure for muon (g-2) measurements

In a storage ring of discrete magnets with uniform field and edge focusing, the field averaged over the orbit can be independent of orbit radius (particle momentum). This ring is suitable for measuring the anomalous magnetic moment of the muon. The field, averaged over the orbit, can be calibrated by injecting transversely polarized protons of the same momentum and measuring the proton (g-2) precession. A measurement at the level of 0.03 ppm may be feasible.Comment: 4 pages, 2 figures, with more detail of tune calculatio

Evaluation of α(MZ2)\alpha(M_{\rm Z}^2) and (g−2)μ(g-2)_\mu

This talk summarizes the recent developments in the evaluation of the leading order hadronic contributions to the running of the QED fine structure constant $\alpha(s)$, at $s=M_{\rm Z}^2$, and to the anomalous magnetic moment of the muon $(g-2)_\mu$. The accuracy of the theoretical prediction of these observables is limited by the uncertainties on the hadronic contributions. Significant improvement has been achieved in a series of new analyses which is presented historically in three steps: (I), use of $\tau$ spectral functions in addition to $e^+e^-$ cross sections, (II), extended use of perturbative QCD and (III), application of QCD sum rule techniques. The most precise values obtained are: $\Delta\alpha_{\rm had}(M_{\rm Z}^2)$, $=(276.3\pm1.6)\times10^{-4}$, yielding $\alpha^{-1}(M_{\rm Z}^2)=128.933\pm0.021$, and $a_\mu^{\rm had}=(692.4\pm6.2)\times 10^{-10}$ with which one finds for the complete Standard Model prediction $a_\mu^{\rm SM}=(11 659 159.6\pm6.7)\times10^{-10}$. For the electron $(g-2)_e$, the hadronic contribution is $a_e^{\rm had}=(187.5\pm1.8)\times 10^{-14}$.Comment: 13 page

The running of the electromagnetic coupling alpha in small-angle Bhabha scattering

A method to determine the running of alpha from a measurement of small-angle Bhabha scattering is proposed and worked out. The method is suited to high statistics experiments at e+e- colliders, which are equipped with luminometers in the appropriate angular region. A new simulation code predicting small-angle Bhabha scattering is also presentedComment: 15 pages, 3 Postscript figure

Isospin Violation and the Magnetic Moment of the Muon

We calculate the leading isospin-violating and electromagnetic corrections for the decay tau -> pi^0 pi nu_tau at low energies. The corrections are small but relevant for the inclusion of tau decay data in the determination of hadronic vacuum polarization especially for the anomalous magnetic moment of the muon. We show that part of the systematic differences between the measured form factors in tau -> pi^0 pi nu_tau and e^+ e^- -> pi^+ pi^- is due to isospin violation .Comment: 12 pages, 2 figures, minor revisions in the text, references added, version to appear in Physics Letters

Isospin violating effects in e+e- vs. tau measurements of the pion form factor |F_pi|^2 (s)

We study possible so far unaccounted isospin breaking effects in the relation between the pion form factor as determined in e^+e^- experiments and the corresponding quantity obtained after accounting for known isospin breaking effects by an isospin rotation from the tau--decay spectra. In fact the observed 10% discrepancy in the respective pion form factors may be explained by the isospin breaking which is due to the difference between masses and widths of the charged and neutral rho mesons. Since the hadronic contribution to the muon anomalous magnetic moment can be calculated directly in terms of the e^+e^- - data the corresponding evaluation seems to be more reliable. Our estimate is a_mu(had)=694.8(8.6) x 10^{-10}. The tau - data are usefull at the presently aimed level of accuracy only after appropriate input from theory.Comment: 11 pages, Latex, 1 table, 3 figures; update: several points described in more detail, slightly shifted fit parameters (Tab.1), 3 citations adde