Study of transition form factors of the lightest pseudoscalars

In this paper, we study the transition form factors of the lightest pseudoscalar mesons, $\pi^0$, $\eta$, and $\eta'$, within the framework of resonance chiral theory. Our analysis is performed based on the data of time-like and space-like singly-virtual and space-like doubly-virtual form factors, as well as the relevant cross sections and latest invariant mass spectra of $e^+e^-$ pair for the process of $P\to\gamma e^+ e^-$. The transition form factors of these pseudoscalars are obtained. Also, we evaluate their contributions to the light-by-light part of the anomalous magnetic moment of the muon. Our two Fits give similar results, where Fit-A gives $a_\mu^{\pi^0 }=(61.6\pm 1.8)\times10^{-11}$, $a_\mu^{\eta }=(15.2\pm1.7)\times10^{-11}$, $a_\mu^{\eta'}=(16.0\pm 1.2)\times10^{-11}$, and the total contribution of neutral pseudo-scalar meson poles is $a_\mu^{\pi^0+\eta+\eta'}=(92.8\pm2.9)\times10^{-11}$.