Lattice QCD calculation of the π0-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 the π0-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 the π0-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 the π0-pole contribution to the hadronic light-by-light scattering in the muon’s anomalous magnetic moment, a0 − poleμ π = 61.2 ( 1.7 ) × 10−11, and the π0 decay width, Γπjavax.xml.bind.JAXBElement@5f4774c9 → γ γ = 7.60 ( 27 ) eV.