New Results on the Hadronic Contributions to alpha(M_Z) and to (g-2)_mu

We reevaluate the dispersion integrals of the leading order hadronic contributions to the running of the QED fine structure constant alpha(s) at s=M_Z^2, and to the anomalous magnetic moments of the muon and the electron. Finite-energy QCD sum rule techniques complete the data from e+e- annihilation and tau decays at low energy and at the cc-bar threshold. Global quark-hadron duality is assumed in order to resolve the integrals using the Operator Product Expansion wherever it is applicable. We obtain delta_alpha_had(M_Z) = (276.3 +/- 1.6)x10^{-4} yielding alpha^{-1}(M_Z) = 128.933 +/- 0.021, and a_mu^had = (692.4 +/- 6.2)x10^{-10} with which we find for the complete Standard Model prediction a_mu^SM = (11659159.6 +/- 6.7)x10^{-10}. For the electron, the hadronic contribution reads a_e^had = (187.5 +/- 1.8)x10^{-14}.Comment: 16 pages, 3 figure

Two-photon exchange model for production of neutral meson pairs in e+e- annihilation

A vector-dominance two-photon exchange model is proposed to explain the recently observed production of $\rho^0\rho^0$ and $\rho^0\phi$ pairs in $e^+e^-$ annihilation at 10.58 GeV with the BaBar detector. All the observed features of the data --angular and decay distributions, rates-- are in agreement with the model. Predictions are made for yet-unobserved final states.Comment: 7 pages, 2 figures, 1 tabl

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

Strange Quark Mass from the Invariant Mass Distribution of Cabibbo-Suppressed Tau Decays

Quark mass corrections to the tau hadronic width play a significant role only for the strange quark, hence providing a method for determining its mass. The experimental input is the vector plus axial-vector strange spectral function derived from a complete study of tau decays into strange hadronic final states performed by ALEPH. New results on strange decay modes from other experiments are also incorporated. The present analysis determines the strange quark mass at the Mtau mass scale using moments of the spectral function. Justified theoretical constraints are applied to the nonperturbative components and careful attention is paid to the treatment of the perturbative expansions of the moments which exhibit convergence problems. The result obtained, m_s(Mtau^2) = (120 +- 11_exp +- 8_Vus +- 19_th) MeV = (120^+21_-26) MeV, is stable over the scale from Mtau down to about 1.4 GeV. Evolving this result to customary scales yields m_s(1 GeV^2) = (160^+28_-35) MeV and m_s(4 GeV^2) = (116^+20_-25) MeV.Comment: LaTex, 8 pages, 4 figures (EPS

Improved Determination of alpha_QED(M_Z^2) and the Anomalous Magnetic Moment of the Muon

We reevaluate the hadronic contribution to the running of the QED fine structure constant alpha(s) at s = M_Z^2. We use data from e+e- annihilation and tau decays at low energy and at the qq-bar thresholds, where resonances occur. Using so-called spectral moments and the Operator Product Expansion (OPE), it is shown that a reliable theoretical prediction of the hadronic production rate R(s) is available at relatively low energies. Its application improves significantly the precision on the hadronic vacuum polarization contribution. We obtain delta_alpha^had = (277.8 +/- 2.6) x 10^-4 yielding alpha^-1(M_Z^2) = 128.923 +/- 0.036$. Inserting this value in a global electroweak fit using current experimental input, we constrain the mass of the Standard Model Higgs boson to be M_Higgs = (129 +103 -62) GeV. Analogously, we improve the precision of the hadronic contribution to the anomalous magnetic moment of the muon for which we obtain a_mu^had = (695.1 +/- 7.5) x 10^-10.Comment: tex, 18 pages and 3 figure

Status of the Fermilab Muon (g-2) Experiment

The New Muon $(g-2)$ Collaboration at Fermilab has proposed to measure the anomalous magnetic moment of the muon, $a_\mu$, a factor of four better than was done in E821 at the Brookhaven AGS, which obtained $a_\mu = [116 592 089 (63)] \times 10^{-11}$ $\pm 0.54$ ppm. The last digit of $a_{\mu}$ is changed from the published value owing to a new value of the ratio of the muon-to-proton magnetic moment that has become available. At present there appears to be a difference between the Standard-Model value and the measured value, at the $\simeq 3$ standard deviation level when electron-positron annihilation data are used to determine the lowest-order hadronic piece of the Standard Model contribution. The improved experiment, along with further advances in the determination of the hadronic contribution, should clarify this difference. Because of its ability to constrain the interpretation of discoveries made at the LHC, the improved measurement will be of significant value, whatever discoveries may come from the LHC.Comment: Proceedings of the PhiPsi09, Oct. 13-16, 2009, Beijing, China, 4 pages 2 figures. Version 2 includes Fermilab report number, minor corrections and one additional referenc

Improved Determination of the Hadronic Contribution to the Muon (g-2) and to alpha(M_Z**2) Using new Data from Hadronic Tau Decays

We have reevaluated the hadronic contribution to the anomalous magnetic moment of the muon (g-2) and to the running of the QED fine structure constant alpha(s) at s=M_Z**2. We incorporated new data from hadronic tau decays, recently published by the ALEPH Collaboration. In addition, compared to previous analyses, we use more extensive e+e- annihilation data sets. The integration over the total hadronic cross section is performed using experimental data up to 40 GeV and results from perturbative QCD above 40 GeV. The improvement from tau data concerns mainly the pion form factor, where the uncertainty in the corresponding integral could be reduced by more than a factor of two. We obtain for the lowest order hadronic vacuum polarization graph a_mu(had) = (695.0 +/- 15.0) x 10^{-10} and delta(alpha(M_Z**2))(had) = (280.9 +/- 6.3) x 10^{-4} using e+e- data only. The corresponding results for combined e+e- and tau data are a_mu(had) = (701.1 +/- 9.4) x 10^{-10} and delta(alpha(M_Z**2))(had) = (281.7 +/- 6.2) x 10^{-4}, where the latter is calculated using the contribution from the five lightest quarks.Comment: 23 pages, LaTex, 6 figures, Paper submitted to Zeitschrift fuer Physik

New results on the hadronic vacuum polarization to the muon g-2

Results on the lowest-order hadronic vacuum polarization contribution to the muon magnetic anomaly are presented. They are based on the latest published experimental data used as input to the dispersion integral. Thus recent results on tau to nutau pi pi0 decays from Belle and on e+ e- annihilation to pi+ pi- from BABAR and KLOE are included. The new data, together with improved isospin-breaking corrections for tau decays, result into a much better consistency among the different results. A discrepancy between the Standard Model prediction and the direct g-2 measurement is found at the level of 3 sigma.Comment: proceedings of the PhiPsi09 conference, Oct. 13-16, 2009, Beijing, Chin

Hadronic light-by-light scattering contribution to the muon g-2

We review recent developments concerning the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon. We first discuss why fully off-shell hadronic form factors should be used for the evaluation of this contribution to the g-2. We then reevaluate the numerically dominant pion-exchange contribution in the framework of large-N_C QCD, using an off-shell pion-photon-photon form factor which fulfills all QCD short-distance constraints, in particular, a new short-distance constraint on the off-shell form factor at the external vertex in g-2, which relates the form factor to the quark condensate magnetic susceptibility in QCD. Combined with available evaluations of the other contributions to hadronic light-by-light scattering this leads to the new result a_{\mu}(LbyL; had) = (116 \pm 40) x 10^{-11}, with a conservative error estimate in view of the many still unsolved problems. Some potential ways for further improvements are briefly discussed as well. For the electron we obtain the new estimate a_{e}(LbyL; had) = (3.9 \pm 1.3) x 10^{-14}.Comment: 6 pages, 1 figure, to be published in the proceedings of the PhiPsi09 workshop, Oct. 13-16, 2009, Beijing, Chin

The Physics of Hadronic Tau Decays

Hadronic tau decays represent a clean laboratory for the precise study of quantum chromodynamics (QCD). Observables (sum rules) based on the spectral functions of hadronic tau decays can be related to QCD quark-level calculations to determine fundamental quantities like the strong coupling constant, parameters of the chiral Lagrangian, |V_us|, the mass of the strange quark, and to simultaneously test the concept of quark-hadron duality. Using the best available measurements and a revisited analysis of the theoretical framework, the value alpha_s(m_tau) = 0.345 +- 0.004[exp] +- 0.009[theo] is obtained. Taken together with the determination of alpha_s(m_Z) from the global electroweak fit, this result leads to the most accurate test of asymptotic freedom: the value of the logarithmic slope of 1/alpha_s(s) is found to agree with QCD at a precision of 4%. In another approach, the tau spectral functions can be used to determine hadronic quantities that, due to the nonperturbative nature of long-distance QCD, cannot be computed from first principles. An example for this is the contribution from hadronic vacuum polarization to loop-dominated processes like the anomalous magnetic moment of the muon. This article reviews the measurements of nonstrange and strange tau spectral functions and their phenomenological applications.Comment: 89 pages, 32 figures; final version accepted for publication by Reviews of Modern Physic