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.
Recently a few authors pointed out that the positroniums give rise to an extra contribution to the electron $g-2$ with the magnitude comparable to the $O(alpha^5)$ perturbative effect, which is not taken into account in the perturbative calculation u
p to $O(alpha^5)$. Here, we scrutinize how the positronium resonances contribute to the electron $g-2$ through the vacuum polarization function, and conclude that there is no additional sizable $O(alpha^5)$ contribution to the electron $g-2$.
