Lattice QCD calculation of theπ0-pole contribution to the hadronic light-by-light scattering in the anomalous magnetic moment of the muon.

We develop a method to compute the pion transition form factor directly at arbitrary space-like photon momenta and use it to determine theπ⁰-pole contribution to the hadronic light-by-light scattering in the anomalous magnetic moment of the muon. The calculation is performed using eight gauge ensembles generated with 2+1 flavor domain wall fermions, incorporating multiple pion masses, lattice spacings, and volumes. By introducing a pion structure function and performing a Gegenbauer expansion, we demonstrate that about 98% of theπ⁰-pole contribution can be extracted in a model-independent manner, thereby ensuring that systematic effects are well controlled. After applying finite-volume corrections, as well as performing chiral and continuum extrapolations, we obtain the final result for theπ⁰-pole contribution to the hadronic light-by-light scattering in the muon's anomalous magnetic moment,aμπ0-pole=61.2(1.7)×10-11, and theπ⁰decay width,Γπ0→γγ=7.60(27)eV.