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

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 $\bar{l}_{4} =3.4$.