The 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 $r_π$ is found to be in excellent agreement with the data. When the often-used Ball-Chiu Ansatz is used to construct the quark-photon vertex directly from the quark propagator, less than half of $r_π^2$ is generated. The remainder of $r^2_π$ is seen to be attributable to the presence of the $ρ$-pole in the solution of the ladder Bethe-Salpeter equation.