AbstractWe 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
.
Hadronic light-by-light scattering contribution to the muon g-2 from lattice QCD: Methodology