Lattice calculation of the π0 , η and η′ transition form factors and the hadronic light-by-light contribution to the muon g−2

Abstract

In this paper we present a first calculation of the π0, η and η′ 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 spacelike 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 aμhlbl,ps-pole=(85.1±5.2)×10−11. Although the pion-pole is dominant, we confirm that, together, the η and η′ provide roughly half of its contribution. Published by the American Physical Society 2025