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

Abstract

Abstract We compute the hadronic light-by-light scattering contribution to the muon $$g-2$$ 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 $$a_\mu ^{\text {Hlbl}}= 106.8(15.9) \times 10^{-11}$$ a μ Hlbl = 106.8 ( 15.9 ) × 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 $$g-2$$ g - 2 .