Scalar radius of the pion in the Kroll-Lee-Zumino renormalizable theory

The Kroll-Lee-Zumino renormalizable Abelian quantum field theory of pions and a massive ρ-meson is used to calculate the scalar radius of the pion at next-to-leading (one-loop) order in perturbation theory. Because of renormalizability, this determination involves no free parameters. The result is ⟨r_π²⟩ₛ=0.40 fm². This value gives for ₄, the low energy constant of chiral perturbation theory, ₄=3.4, and F_π/F=1.05, where F is the pion decay constant in the chiral limit. Given the level of accuracy in the masses and the ρππ coupling, the only sizable uncertainty in this result is due to the (uncalculated) next-to-next-to-leading order contribution.