Constituent-quark and baryon loops in pseudoscalar-meson transitions

Abstract

Predictions for the $\pi \gamma \gamma$ coupling, the pion charge radius $〈{r_{{\pi }^{+}}}^2〉$, the $q^2$ dependence of the pion decay constant near $q^2=0\mathrm{} \left[f_{\pi }^{\prime }\mathrm{}\right(0\left)\right]$, and the ratio $\gamma$ describing radiative pion decay are obtained in the context of two related models: the constituent-quark model and a baryon-loop model with $n_f=2, 3, or 4$ flavors. All these models lead to two relations among the four above-mentioned parameters, which are satisfied by the data. A sort of equivalence or duality for the two models is observed, particularly for $n_f=4\mathrm{}$.