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arXiv · 2411.06349

Lattice QCD calculation of the $π^0$-pole contribution to the hadronic light-by-light scattering in the anomalous magnetic moment of the muon

Tian Lin·Mattia Bruno·Xu Feng·Lu-Chang Jin·Christoph Lehner·Chuan Liu·Qi-Yuan Luo
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Abstract

We develop a method to compute the pion transition form factor directly at arbitrary space-like photon momenta and use it to determine the $π^0$-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 $π^0$-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 $π^0$-pole contribution to the hadronic light-by-light scattering in the muon's anomalous magnetic moment, $a_μ^{π^0\mathrm{-pole}}=61.2(1.7)\times 10^{-11}$, and the $π^0$ decay width, $Γ_{π^0\to γγ}=7.60(27)$ eV.

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Tian Lin, Mattia Bruno, Xu Feng, Lu-Chang Jin, Christoph Lehner, Chuan Liu, Qi-Yuan Luo. 2025-07-30. Lattice QCD calculation of the $π^0$-pole contribution to the hadronic light-by-light scattering in the anomalous magnetic moment of the muon. https://arxiv.org/abs/2411.06349

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