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

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 $C_5^A(Q^2)$ and $C_6^A(Q^2)$. 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 $C_5^A(Q^2)$ 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 $C_6^A(Q^2)$ can be predicted in terms of $G_P(Q^2)$, the mean-square axial radius $⟨r_A^2⟩$, and the mean-square axial nucleon-to-$\Delta$ transition radius $⟨r_{AN\Delta }^2⟩$.

Comments: 22 pages, 6 figures, typo in Eq. (55) fixed, matches published version