The Quark-Photon Vertex and the Pion Charge Radius

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 rπ 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 r2 π is generated. The remainder of r2 π is seen to be attributable to the presence of the ρ-pole in the solution of the ladder Bethe–Salpeter equation. Pacs Numbers: 14.40.Aq, 13.40.Gp, 24.85.+p, 11.10.St, 12.38.Lg Typeset using REVTEX