The anomalous magnetic moment of the muon: status of lattice QCD calculations

In recent years, the anomalous magnetic moment of the muon has triggered a lot of activity in the lattice QCD community because a persistent tension of about 3.5 σ is observed between the phenomenological estimate and the Brookhaven measurement. The current best phenomenological estimate has an uncertainty comparable to the experimental one and the error is completely dominated by hadronic effects: the leading order hadronic vacuum polarization (HVP) contribution and the hadronic light-by-light (HLbL) scattering contribution. Both are accessible via lattice simulations and a reduction of the error by a factor 4 is required in view of the forthcoming experiments at Fermilab and J-PARC whose results, expected in the next few years, should reduce the experimental precision down to the level of 0.14 ppm. In this article, I review the status of lattice calculations of those quantities, starting with the HVP. This contribution has now reached sub-percent precision and requires a careful understanding of all sources of systematic errors. The HLbL contribution, that is much smaller, still contributes significantly to the error. This contribution is more challenging to compute, but rapid progress has been made on the lattice in the last few years.

Hadronic light-by-light scattering in the muon g − 2

We briefly review the current status of the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon. Based on various model calculations in the literature, we obtain the estimate $ \mathop a\nolimits_\mu ^{HLbL} = (102 \pm 39) \times \mathop {10}\nolimits^{ - 11} $. Recent developments including more model-independent approaches using dispersion relations and lattice QCD, that could lead to a more reliable estimate, are also discussed.

On the Hadronic light-by-light contribution to the muon g – 2

This talk is about the hadronic light-by-light contribution to the muon anomalous magnetic moment, mainly our old work but including some newer results as well. It concentrates on the model calculations. Most attention is paid to pseudo-scalar exchange and the pion loop contribution. Scalar, a1-exchange and other contributions are shortly discussed as well. For the π0-exchange a possible large cancellation between connected and disconnected diagrams is expected.