The pi0, eta, eta' -> gamma gamma*(Q^2) Decay Rates and Radii

TL;DR

This paper reviews the measurement of transition form factors and radii of neutral pseudoscalar mesons, comparing experimental results with QCD predictions, and discusses methods to improve the precision of decay rate measurements.

Contribution

It provides a comprehensive overview of the current status of theory and experiment for pseudoscalar meson radii and decay rates, highlighting the similarity of axial transition radii and proposing methods for more precise tests of QCD.

Findings

Axial transition radii of pseudoscalar mesons are similar to each other and to the pion charge radius.

Current experimental accuracy on decay rates is below the theoretical uncertainty of QCD predictions.

Three experimental methods are used to measure the decay rate, with ongoing efforts to improve precision.

Abstract

The low $Q^2$ slopes of the the transition form factors provide a unique method to measure the sizes of the neutral pseudo-scalar mesons, since they do not have electromagnetic form factors. From the slope one obtains the "axial transition RMS radius" $ R_{PS,A} = \sqrt{<r^2>}$ for each PS meson. The present status of theory and experiment for these quantities are presented. A comparison of the $ R_{PS,A}$ is presented along with the electromagnetic and scalar radii of the $\pi^{\pm}$ mesons and the proton. We observe the striking similarity of the values of axial transition radii of all of the pseudoscalar mesons to each other and to the charge radius of the $\pi^{\pm}$. In the $Q^2$ = 0 limit the transition form factor is a measure of the pseudo-scalar meson radiative width (lifetime) and is a possible fourth (unexploited) method to perform such a measurement. The $\pi^{0} \rightarrow \gamma \gamma$ decay rate is a test of QCD at the confinement scale. There is a firm QCD prediction with a theoretical uncertainty of $\simeq $ 1 \% which calls for an experimental test at the same level of accuracy. There are three methods that have been utilized to perform this measurement and the present status of the experimental tests are outlined. The current accuracy is significantly less than the theoretical uncertainty. The efforts to improve this are briefly summarized.