Determining the axial radius of the nucleon from data on pion electroproduction

Abstract

We discuss a low-energy theorem of threshold pion electroproduction which allows one to determine the axial root-mean-square radius rA of the nucleon. We show that at the same order where the radius appears, pion loops induce a small correction to the momentum dependence of the electric dipole amplitude E0+(−). This correction amounts to a decrease of the axial mean-square radius by 5% from the electroproduction data and allows one to explain the small discrepancy to the values determined from (anti)neutrino-proton scattering data.