The anomalous magnetic moment of the muon is one of the most promising observables to identify hints for physics beyond the Standard Model of particle physics. This quantity exhibits a persistent discrepancy of 3.5 standard deviations between the direct measurement by the Brookhaven E821 Collaboration and its theoretical prediction based on the Standard Model. The theory error is now completely dominated by effects of the strong interaction and in particular by the hadronic light-by-light scattering (HLbL) contribution.
I will present two complementary approaches to evaluate this contribution using lattice QCD calculations. In the first approach, lattice QCD can provide valuable inputs to the recently proposed dispersive framework where experimental data are often missing. In this case, the dominant contribution is given by the pion-pole contribution, that can be evaluated on the lattice. Information about other resonances can be obtained from the study of the forward light-by-light scattering amplitudes on the lattice. The second approach corresponds to the direct lattice QCD calculation of the full HLbL contribution where the final result is expressed as a convolution between a QED kernel, computed semi-analytically in position space and in infinite volume, and a four point correlation function computed on the lattice.
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