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

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.