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We compute the hadronic light-by-light scattering contribution to the muon$g-2$ from the up, down, and strange-quark sector directly using lattice QCD.Our calculation features evaluations of all possible Wick-contractions of therelevant hadronic four-point function and incorporates several different pionmasses, volumes, and lattice-spacings. We obtain a value of$a_\mu^{\text{Hlbl}} = 106.8(14.7) \times 10^{-11}$ (adding statistical andsystematic errors in quadrature), which is consistent with currentphenomenological estimates and a previous lattice determination. It now appearsconclusive that the hadronic light-by-light contribution cannot explain thecurrent tension between theory and experiment for the muon $g-2$.

Hadronic light-by-light contribution to $(g-2)_\mu$ from lattice QCD: a complete calculation