Axial structure of the nucleon

TL;DR

The paper analyzes the axial structure of the nucleon in the nonperturbative QCD regime, focusing on the axial form factor $G_A(t)$ and the induced pseudoscalar form factor $G_P(t)$ and their experimental probes via (anti)neutrino scattering, charged pion electroproduction, and muon capture. It combines current algebra and chiral perturbation theory to relate observables to fundamental quantities such as the axial radius $\langle r_A^2\rangle$, the pion-nucleon coupling $g_{\pi NN}$, and the axial-pole-dominated behavior of $G_P(t)$, including radiative corrections and resonance effects. The main contributions include a precise dipole description of $G_A(t)$ with $\langle r_A^2\rangle^{1/2}\approx 0.67$ fm, a robust CHPT-based prediction for $g_P$ anchored by the pion pole, and a critical assessment of octet Goldberger–Treiman discrepancies via the Dashen–Weinstein relations. The work highlights tensions in radiative muon capture and underscores the need for improved measurements of kaon-nucleon couplings and threshold electroproduction data to sharpen tests of low-energy QCD and its symmetry structure.

Abstract

We review the current status of experimental and theoretical understanding of the axial nucleon structure at low and moderate energies. Topics considered include (quasi)elastic (anti)neutrino-nucleon scattering, charged pion electroproduction off nucleons and ordinary as well as radiative muon capture on the proton.

Figures (9)

• Figure 1: Axial mass $M_A$ extractions. Left panel: From (quasi)elastic neutrino and antineutrino scattering experiments. The weighted average is $M_A=(1.026\pm 0.021)\,\mathrm{GeV}$. Right panel: From charged pion electroproduction experiments. The weighted average is $M_A=(1.069\pm 0.016)\,\mathrm{GeV}$. Note that value for the MAMI experiment contains both the statistical and systematical uncertainty; for other values the systematical errors were not explicitly given. The labels SP, DR, FPV and BNR refer to different methods evaluating the corrections beyond the soft pion limit as explained in the text.
• Figure 2: Experimental data for the normalized axial form factor extracted from pion electroproduction experiments in the threshold region. Note that for the experiments where various theoretical models were used in the analysis to extract $G_A$, all results are shown. For orientation, the dashed line shows a dipole fit with an axial mass $M_A = 1.1\,$GeV.
• Figure 3: Level scheme for OMC in liquid hydrogen. In the atomic $(p\mu$) state, one has a triplet/singlet state where the sum of the proton and the muon spins is 1/0 (upper two levels). In the ortho ($p\mu p$) state, the two proton spins sum up to one, splitting into two levels with $S=3/2$ and $S=1/2$ as indicated. Weinberg's mixing suggestion WeinO applies to these two levels.
• Figure 4: Determination of the pseudoscalar coupling constant $g_P$ from (electronics) experiments. The numbers have been rescaled to the present value of $g_A = 1.267$. For the measurements on liquid hydrogen, the rate $\lambda_{\rm OP} = (4.1 \pm 1.4) \cdot 10^4\,$s$^{-1}$ is assumed. The weighted average is $g_P = 8.79 \pm 1.92$.
• Figure 5: The "world data" for the induced pseudoscalar form factor $G_P(Q^2)$. The pion electroproduction data (filled circles) are from reference choi. Also shown is the world average for ordinary muon capture at $Q^2 =0.88M_\mu^2$ (diamond). For orientation, we also show the theoretical predictions discussed later. Dashed curve: Pion--pole (current algebra) prediction. Solid curve: Next--to--leading order chiral perturbation theory prediction.