Contribution of the $a_1$ meson to the axial nucleon-to-$\Delta$ transition form factors

TL;DR

This paper investigates the role of the $a_1$ meson in axial form factors relevant to nucleon-to-$ $-transition, using chiral models and quark relations to predict form factors and compare with experimental data.

Contribution

It introduces a chiral effective-Lagrangian model including the $a_1$ meson to analyze axial transition form factors and predicts $G_P(Q^2)$ and $C^A_6(Q^2)$ based on this model.

Findings

Predicted $G_P(Q^2)$ using the $a_1$ meson model.

Determined $C^A_5(Q^2)$ with a quark-model relation.

Predicted $C^A_6(Q^2)$ from $G_P(Q^2)$ and axial radii.

Abstract

We analyze the low-$Q^2$ behavior of the axial form factor $G_A(Q^2)$, the induced pseudoscalar form factor $G_P(Q^2)$, and the axial nucleon-to-$\Delta$ transition form factors $C^A_5(Q^2)$ and $C^A_6(Q^2)$. Building on the results of chiral perturbation theory, we first discuss $G_A(Q^2)$ in a chiral effective-Lagrangian model including the $a_1$ meson and determine the relevant coupling parameters from a fit to experimental data. With this information, the form factor $G_P(Q^2)$ can be predicted. For the determination of the transition form factor $C^A_5(Q^2)$ we make use of an SU(6) spin-flavor quark-model relation to fix two coupling constants such that only one free parameter is left. Finally, the transition form factor $C^A_6(Q^2)$ can be predicted in terms of $G_P(Q^2)$, the mean-square axial radius $\langle r^2_A\rangle$, and the mean-square axial nucleon-to-$\Delta$ transition radius $\langle r^2_{AN\Delta}\rangle$.