The quark-photon vertex and meson electromagnetic form factors

Abstract

The ladder Bethe-Salpeter solution for the dressed photon-quark vertex is used to study the low-momentum behavior of the pion electromagnetic and the $γ^\star π^0 γ$ transition form factors. With model parameters previously fixed by light meson masses and decay constants, the low-momentum slope of both form factors is in excellent agreement with the data. In comparison, the often-used Ball-Chiu Ansatz for the vertex is found to be deficient; less than half of the obtained $r_π^2$ is generated by that Ansatz while the remainder of the charge radius could be attributed to the tail of the $ρ$ resonance.