Study of transition form factors of the lightest pseudoscalars

Abstract

In this paper, we study the transition form factors of the lightest pseudoscalar mesons, ${\pi }^0$, $\eta$, and ${\eta }^{\prime }$, 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 $a_{\mu }^{{\pi }^0}=(61.6\pm 1.8)\times 10^{-11}$, $a_{\mu }^{\eta }=(15.2\pm 1.7)\times 10^{-11}$, $a_{\mu }^{{\eta }^{\prime }}=(16.0\pm 1.2)\times 10^{-11}$, and the total contribution of neutral pseudo-scalar meson poles is $a_{\mu }^{{\pi }^0+\eta +{\eta }^{\prime }}=(92.8\pm 2.9)\times 10^{-11}$.

23 pages, 9 figures