The Quark-Photon Vertex and the Pion Charge Radius

Details The Quark-Photon Vertex and the Pion Charge Radius The Quark-Photon Vertex and the Pion Charge Radius

1999-10-12

arxiv.org/abs/nucl-th/9910033v1

Phys.Rev.C61:045202,2000

Physics

Nuclear Physics

Nuclear Theory

21 pages, 9 figures

Scientific paper

10.1103/PhysRevC.61.045202

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 $r^2_\pi$ is seen to be attributable to the presence of the $\rho$-pole in the solution of the ladder Bethe-Salpeter equation.

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