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The Quark-Photon Vertex and the Pion Charge Radius

P. Maris·P. C. Tandy
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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.

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P. Maris, P. C. Tandy. 1999-10-12. The Quark-Photon Vertex and the Pion Charge Radius. https://doi.org/10.1103/physrevc.61.045202

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