Electromagnetic and Scalar Pion form factor in the Kroll-Lee-Zumino model

TL;DR

This paper uses the Kroll-Lee-Zumino model at one loop to accurately compute electromagnetic and scalar pion form factors, aligning well with experimental data and providing insights into low-energy constants.

Contribution

It applies the KLZ model at one loop to compute pion form factors and scalar radius, improving theoretical predictions and matching experimental results.

Findings

Electromagnetic pion form factor agrees with data across momentum transfers.

Time-like form factor near rho-meson peak remains unaffected by vertex corrections.

Scalar radius of the pion is calculated as 0.40 fm^2, informing chiral perturbation theory constants.

Abstract

The renormalizable Abelian quantum field theory model of Kroll, Lee, and Zumino is used at the one loop level to compute vertex corrections to the tree-level, Vector Meson Dominance (VMD) electromagnetic pion form factor. These corrections, together with the one-loop vacuum polarization contribution, imply a resulting electromagnetic pion form factor in excellent agreement with data in the whole range of accessible momentum transfers in the space-like region. The time-like form factor, which reproduces the Gounaris-Sakurai formula at and near the rho-meson peak, is unaffected by the vertex correction at order $\cal{O}$$(g^2)$. The KLZ model is also used to compute the scalar radius of the pion at the one loop level, finding $<r^{2}_{\pi}>_{S} = 0.40 fm^{2}$. This value implies for the low energy constant of chiral perturbation theory $\bar{l}_{4} =3.4$.