Pion form factor in the Kroll-Lee-Zumino model

TL;DR

This paper uses the Kroll-Lee-Zumino model to compute one-loop corrections to the pion form factor, significantly improving agreement with experimental data and confirming the robustness of the VMD model near the rho-meson peak.

Contribution

It provides a detailed one-loop quantum field theory calculation of the pion form factor within the Kroll-Lee-Zumino model, enhancing the theoretical understanding of VMD.

Findings

Improved agreement of the pion form factor with experimental data in the space-like region.

Vertex corrections do not affect the time-like form factor near the rho-meson peak.

The model confirms the validity of the Gounaris-Sakurai formula at the rho resonance.

Abstract

The renormalizable Abelian quantum field theory model of Kroll, Lee, and Zumino is used to compute the one-loop vertex corrections to the tree-level, Vector Meson Dominance (VMD) pion form factor. These corrections, together with the known one-loop vacuum polarization contribution, lead to a substantial improvement over VMD. The resulting pion form factor in the space-like region is in excellent agreement with data in the whole range of accessible momentum transfers. The time-like form factor, known to reproduce the Gounaris-Sakurai formula at and near the rho-meson peak, is unaffected by the vertex correction at order $\cal{O}$$(g_\rpp^2)$.