Nucleon axial radius

TL;DR

This paper systematically studies the relativistic axial-vector current distributions in nucleons, revealing that the axial form factor slope relates to the spin radius, not the mean-square axial radius, with implications for lattice QCD and experiments.

Contribution

It clarifies the physical interpretation of the axial form factor slope and derives explicit expressions for the spin radius in different frames, highlighting additional contributions.

Findings

The axial form factor slope does not equal the three-dimensional axial radius.

Explicit expressions for the spin radius depend on nucleon mass and form factors.

Provides motivation for lattice QCD and experimental studies of $G_P(Q^2)$.

Abstract

We present the first systematic study of the relativistic axial-vector four-current distributions inside a nucleon. We show in particular that the slope of the axial form factor $G_A(Q^2)$ in the forward limit -- conventionally denoted as $R^2_A$ in the literature -- does not represent the three-dimensional mean-square axial radius in the Breit frame, but corresponds instead to a contribution to the mean-square spin radius. We derive explicit expressions for the latter in different frames and find in general additional contributions that depend on both the nucleon mass and the forward values of the axial-vector form factors $G_A(0)$ and $G_P(0)$. This provides an additional key motivation for ongoing lattice quantum chromodynamics (QCD) calculations and future experimental measurements of the induced pseudoscalar form factor $G_P(Q^2)$.