Lattice calculation of the $\pi^0$, $\eta$ and $\eta^{\prime}$ transition form factors and the hadronic light-by-light contribution to the muon $g-2$ - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Lattice calculation of the $\pi^0$, $\eta$ and $\eta^{\prime}$ transition form factors and the hadronic light-by-light contribution to the muon $g-2$

Résumé

In this paper we present a first ab-initio calculation of the $\pi^0$, $\eta$ and $\eta^{\prime}$ transition form factors performed with physical light-quark masses. We provide a complete parametrization of the form factors that includes both single and double-virtual kinematics. Our results are compared with experimental measurements of the form factors in the space-like region and with the measured two-photon decay widths. In a second step, our parametrizations of the transition form factors are used to compute the dominant pseudoscalar-pole contributions to the hadronic light-by-light scattering in the muon $g-2$. Our final result reads $a_{\mu}^{\rm hlbl, ps-pole} = (85.1 \pm 5.2) \times 10^{-11}$. Although the pion-pole is dominant, we confirm that, together, the $\eta$ and $\eta^{\prime}$ provide roughly half of its contribution.

Dates et versions

hal-04103869 , version 1 (23-05-2023)

Identifiants

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Antoine Gérardin, Willem E.A Verplanke, Gen Wang, Zoltan Fodor, Jana N Guenther, et al.. Lattice calculation of the $\pi^0$, $\eta$ and $\eta^{\prime}$ transition form factors and the hadronic light-by-light contribution to the muon $g-2$. 2023. ⟨hal-04103869⟩
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