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arXiv · 2308.12458

Pion Transition Form Factor from Twisted-Mass Lattice QCD and the Hadronic Light-by-Light $\pi^0$-pole Contribution to the Muon $g-2$

C. Alexandrou·S. Bacchio·G. Bergner·S. Burri·J. Finkenrath·A. Gasbarro·K. Hadjiyiannakou·K. Jansen·G. Kanwar·B. Kostrzewa·G. Koutsou·K. Ottnad·M. Petschlies·F. Pittler·F. Steffens·C. Urbach·U. Wenger
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Abstract

The neutral pion generates the leading pole contribution to the hadronic light-by-light tensor, which is given in terms of the nonperturbative transition form factor $\mathcal{F}_{\pi^0\gamma\gamma}(q_1^2,q_2^2)$. Here we present an ab-initio lattice calculation of this quantity in the continuum and at the physical point using twisted-mass lattice QCD. We report our results for the transition form factor parameterized using a model-independent conformal expansion valid for arbitrary space-like kinematics and compare it with experimental measurements of the single-virtual form factor, the two-photon decay width, and the slope parameter. We then use the transition form factors to compute the pion-pole contribution to the hadronic light-by-light scattering in the muon $g-2$, finding $a_\mu^{\pi^0\text{-pole}} = 56.7(3.2) \times 10^{-11}$.

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C. Alexandrou, S. Bacchio, G. Bergner, S. Burri, J. Finkenrath, A. Gasbarro, K. Hadjiyiannakou, K. Jansen, G. Kanwar, B. Kostrzewa, G. Koutsou, K. Ottnad, M. Petschlies, F. Pittler, F. Steffens, C. Urbach, U. Wenger. 2023-08-23. Pion Transition Form Factor from Twisted-Mass Lattice QCD and the Hadronic Light-by-Light $\pi^0$-pole Contribution to the Muon $g-2$. https://doi.org/10.1103/physrevd.108.094514

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