Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$

Hadronic light-by-light (HLbL) scattering defines one of the critical contributions in the Standard-Model prediction of the anomalous magnetic moment of the muon. In this Letter, we present a complete evaluation using a dispersive formalism, in which the HLbL tensor is reconstructed from its discontinuities, expressed in terms of simpler hadronic matrix elements that can be extracted from experiment. Profiting from recent developments in the determination of axial-vector transition form factors, short-distance constraints for the HLbL tensor, and the vector-vector-axial-vector correlator, we obtain $a_{\mu }^{\text{HLbL}}=101.9(7.9)\times {10}^{-11}$, which meets the precision requirements set by the final result of the Fermilab experiment.