Abstract:
The form factor that yields the light-by-light scattering contribution to the muon anomalous magnetic moment is computed in lattice QCD+QED and QED. A non-perturbative treatment of QED is used and is checked against perturbation theory. The hadronic contribution is calculated for unphysical quark and muon masses, and only the diagram with a single quark loop is computed. Statistically significant signals are obtained. Initial results appear promising, and the prospect for a complete calculation with physical masses and controlled errors is discussed.

Abstract:
We give a short overview of the theory of the muon anomalous magnetic moment with emphasis on the hadronic light-by-light and the pion loop contribution. We explain the difference between the hidden local symmetry and full VMD pion loop and discuss leading logarithms in the anomalous sector of 2-flavour chiral perturbation theory.

Abstract:
We give a short overview of the theory of the muon anomalous magnetic moment with emphasis on the hadronic light-by-light and the pion loop contribution. We explain the difference between the hidden local symmetry and full VMD pion loop and discuss leading logarithms in the anomalous sector of 2-flavour chiral perturbation theory.

Abstract:
We review the status of the hadronic light-by-light contribution to the muon anomalous magnetic moment and critically compare recent calculations. We also study in detail which momentum regions the pi^0 exchange main contribution originates. We also argue that a_\mu^{light-by-light} = (11 \pm 4) \times 10^{-10} encompasses the present understanding of this contribution and comment on some directions to improve on that.

Abstract:
The quark-connected part of the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment is computed using lattice QCD with chiral fermions. We report several significant algorithmic improvements and demonstrate their effectiveness through specific calculations which show a reduction in statistical errors by more than an order of magnitude. The most realistic of these calculations is performed with a near-physical, $171$ MeV pion mass on a $(4.6\;\mathrm{fm})^3$ spatial volume using the $32^3\times 64$ Iwasaki+DSDR gauge ensemble of the RBC/UKQCD Collaboration.

Abstract:
A model for verifying a consistency of the next-to-leading order hadronic contributions to the muon anomalous magnetic moment with those of the leading order is proposed. A part of the next-to-leading order hadronic contributions related to the vacuum polarization is rather accurately reproduced in the model. I find a new numerical value for the light-by-light hadronic contribution that leads to agreement with recent experimental result for the muon anomalous magnetic moment.

Abstract:
We propose a simple parameterization of the two-point correlator of hadronic electromagnetic currents for the evaluation of the hadronic contributions to the muon anomalous magnetic moment. The parameterization is explicitly done in the Euclidean domain. The model function contains a phenomenological parameter which provides an infrared cutoff to guarantee the smooth behavior of the correlator at the origin in accordance with experimental data in e+ e- annihilation. After fixing a numerical value for this parameter from the leading order hadronic contribution to the muon anomalous magnetic moment the next-to-leading order results related to the vacuum polarization function are accurately reproduced. The properties of the four-point correlator of hadronic electromagnetic currents as for instance the so-called light-by-light scattering amplitude relevant for the calculation of the muon anomalous magnetic moment are briefly discussed.

Abstract:
After a brief self-contained introduction to the muon anomalous magnetic moment, (g-2), we review the status of lattice calculations of the hadronic vacuum polarization contribution and present first results from lattice QCD for the hadronic light-by-light scattering contribution. The signal for the latter is consistent with model calculations. While encouraging, the statistical error is large and systematic errors are mostly uncontrolled. The method is applied first to pure QED as a check.

Abstract:
After a brief self-contained introduction to the muon anomalous magnetic moment, (g-2), we review the status of lattice calculations of the hadronic vacuum polarization contribution and present first results from lattice QCD for the hadronic light-by-light scattering contribution. The signal for the latter is consistent with model calculations. While encouraging, the statistical error is large and systematic errors are mostly uncontrolled. The method is applied first to pure QED as a check.

Abstract:
We derive an analytic result for the pion pole contribution to the light-by-light scattering correction to the anomalous magnetic moment of the muon, $a_\mu = (g_\mu-2)/2$. Using the vector meson dominance model (VMD) for the pion transition form factor, we obtain $a_\mu^{{\rm LBL},\pi^0} = +56 \times 10^{-11}$.