Quark-photon vertex and the pion charge radius

Abstract

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the dressed quark-photon vertex to study the low-momentum behavior of the pion electromagnetic form factor. With model gluon parameters previously fixed by the pion mass and decay constant, the pion charge radius $r_{\pi }$ is found to be in good agreement with the data. In this work, about half of $r_{\pi }^2$ is seen to be attributable to the presence of the $\rho$ pole in the solution of the ladder Bethe-Salpeter equation.