We report calculations of hadronic light-by-light scattering amplitudes via lattice QCD evaluation of Euclidean four-point functions of vector currents. These initial results include only the fully quark-connected contribution. Particular attention is given to the case of forward scattering, which can be related via dispersion relations to the $gamma^* gamma^* to$ hadrons cross section, and thus allows lattice data to be compared with phenomenology. We also present a strategy for computing the hadronic light-by-light contribution to the muon anomalous magnetic moment.
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