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

TL;DR

This paper uses the renormalizable Kroll-Lee-Zumino theory to calculate the pion's scalar radius at one-loop order, providing parameter-free results that connect to chiral perturbation theory constants.

Contribution

It presents a parameter-free calculation of the pion's scalar radius using a renormalizable quantum field theory, linking it to low energy constants in chiral perturbation theory.

Findings

Scalar radius of the pion: 0.40 fm^2

Low energy constant 4 = 3.4

Pion decay constant ratio F_F = 1.05

Abstract

The Kroll-Lee-Zumino renormalizable Abelian quantum field theory of pions and a massive rho-meson is used to calculate the scalar radius of the pion at next to leading (one loop) order in perturbation theory. Due to renormalizability, this determination involves no free parameters. The result is $<r^2_\pi>_s = 0.40 {fm}^2$. This value gives for $\bar{\ell}_4$, the low energy constant of chiral perturbation theory, $\bar{\ell}_4 = 3.4$, and $F_\pi/F = 1.05$, where F is the pion decay constant in the chiral limit. Given the level of accuracy in the masses and the $\rho\pi\pi$ coupling, the only sizable uncertainty in this result is due to the (uncalculated) NNLO contribution.