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Register a new userThe hadronic contribution to (g-2) of the muon
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Michel Davier
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The evaluation of the hadronic contribution to the muon magnetic anomaly $a_mu$ is revisited, taking advantage of new experimental data on $e^+e^-$ annihilation into hadrons: SND and CMD-2 for the $pi^+pi^-$ channel, and babar for multihadron final states. Discrepancies are observed between KLOE and CMD-2/SND data, preventing one from averaging all the $e^+e^-$ results. The long-standing disagreement between spectral functions obtained from $tau$ decays and $e^+e^-$ annihilation is still present, and not accounted by isospin-breaking corrections, for which new estimates have been presented. The updated Standard Model value for $a_mu$ based on $e^+e^-$ annihilation data is now reaching a precision better than experiment, and it disagrees with the direct measurement from BNL at the 3.3$sigma$ level, while the $tau$-based estimate is in much better agreement. The $tau$/$e^+e^-$ discrepancy, best revealed when comparing the measured branching fraction for $tau^- to pi^- pi^0 u_tau$ to its prediction from the isospin-breaking-corrected $e^+e^-$ spectral function, remains a serious problem to be understood.
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The leading order hadronic contribution to the muon magnetic moment anomaly, $a^{HAD}_mu$, is determined entirely in the framework of QCD. The result in the light-quark sector, in units of $10^{-10}$, is $a^{HAD}_mu|_{uds} =686 pm 26$, and in the heavy-quark sector $a^{HAD}_mu|_{c} =14.4 pm 0.1$, and $a^{HAD}_mu|_{b} =0.29 pm 0.01$, resulting in $a^{HAD}_mu = 701 pm 26$. The main uncertainty is due to the current lattice QCD value of the first and second derivative of the electromagnetic current correlator at the origin. Expected improvement in the precision of these derivatives may render this approach the most accurate and trustworthy determination of the leading order $a^{HAD}_mu$.
Precise data on e^+e^- to hadrons have recently become available and are used to compute the lowest-order hadronic vacuum polarisation contribution to the muon magnetic anomaly through dispersion relations. This is the case for the dominant pi+ pi- channel, but the most significant progress comes from the near completion of the BABAR program of measuring exclusive processes below 2 GeV with the initial-state radiation method which allows an efficient coverage of a large range of energies.. In this paper we briefly review the data treatment, the achieved improvements, and the result obtained for the full Standard Model prediction of the muon magnetic anomaly. The value obtained, a_mu (had~LO)=(692.6 +- 3.3)x 10^{-10} is 20% more precise than our last estimate in 2010. It deviates from the direct experimental determination by (27.4 +- 7.6)x 10^{-10} (3.6 sigma). Perpectives for further improvement are discussed.
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}.
We reanalyze the two-loop electroweak hadronic contributions to the muon g-2 that may be enhanced by large logarithms. The present evaluation is improved over those already existing in the literature by the implementation of the current algebra Ward identities and the inclusion of the correct short-distance QCD behaviour of the relevant hadronic Greens function.
We present a calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, $a_mu^{mathrm hvp}$, in lattice QCD employing dynamical up and down quarks. We focus on controlling the infrared regime of the vacuum polarization function. To this end we employ several complementary approaches, including Pade fits, time moments and the time-momentum representation. We correct our results for finite-volume effects by combining the Gounaris-Sakurai parameterization of the timelike pion form factor with the Luscher formalism. On a subset of our ensembles we have derived an upper bound on the magnitude of quark-disconnected diagrams and found that they decrease the estimate for $a_mu^{mathrm hvp}$ by at most 2%. Our final result is $a_mu^{mathrm hvp}=(654pm32,{}^{+21}_{-23})cdot 10^{-10}$, where the first error is statistical, and the second denotes the combined systematic uncertainty. Based on our findings we discuss the prospects for determining $a_mu^{mathrm hvp}$ with sub-percent precision.
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