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

Abstract

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 $a_{\mu }^{\mathrm{hlbl},\mathrm{ps}-\mathrm{pole}}=(85.1\pm 5.2)\times 10^{-11}$. Although the pion-pole is dominant, we confirm that, together, the $\eta$ and ${\eta }^{\prime }$ provide roughly half of its contribution.

Comments: 29 pages, 16 figures. Match the published version