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

Understand

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 the relevant hadronic four-point function and incorporates several different pion masses, volumes, and lattice-spacings.
• We obtain a value of $a_\mu^{\text{Hlbl}} = 106.8(14.7) \times 10^{-11}$ (adding statistical and systematic errors in quadrature), which is consistent with current phenomenological estimates and a previous lattice determination.
• It now appears conclusive that the hadronic light-by-light contribution cannot explain the current tension between theory and experiment for the muon $g-2$.