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 $r_{\pi }$ 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 $r_{\pi }^2$ is generated. The remainder 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.

21 pages, 9 figures

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• Bethe-Salpeter Study of Vector Meson Masses and Decay Constants
• Nucleon form factors and a nonpointlike diquark
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