$\eta$ and $\eta'$ transition form factors from Pad\'e approximants

TL;DR

This paper introduces a systematic, model-independent approach using Padé approximants to precisely determine the transition form factors of eta and eta' mesons from experimental data, impacting our understanding of their properties.

Contribution

It presents a novel, model-independent method employing Padé approximants to extract eta and eta' transition form factors and mixing parameters from experimental data.

Findings

Most precise low-energy parameters for TFFs obtained.

Eta-eta' mixing parameters consistent with previous methods.

Impact of decay width on form factor determination analyzed.

Abstract

We employ a systematic and model-independent method to extract, from space- and time-like data, the $\eta$ and $\eta'$ transition form factors (TFFs) obtaining the most precise determination for their low-energy parameters and discuss the $\Gamma_{\eta\rightarrow\gamma\gamma}$ impact on them. Using TFF data alone, we also extract the $\eta-\eta'$ mixing parameters, which are compatible to those obtained from more sophisticated and input-demanding procedures.