# Contribution of the ${a}_{1}$ meson to the axial nucleon-to-delta transition form factors

Ünal, Y. (Physics Department, Çanakkale Onsekiz Mart University, 17100 Çanakkale, Turkey) ; Küçükarslan, A. (Physics Department, Çanakkale Onsekiz Mart University, 17100 Çanakkale, Turkey) ; Scherer, S. (PRISMA Cluster of Excellence, Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany)

11 January 2019

Abstract: We analyze the low-${Q}^{2}$ behavior of the axial form factor ${G}_{A}\left({Q}^{2}\right)$, the induced pseudoscalar form factor ${G}_{P}\left({Q}^{2}\right)$, and the axial nucleon-to-delta transition form factors ${C}_{5}^{A}\left({Q}^{2}\right)$ and ${C}_{6}^{A}\left({Q}^{2}\right)$. Building on the results of chiral perturbation theory, we first discuss ${G}_{A}\left({Q}^{2}\right)$ 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 ${G}_{P}\left({Q}^{2}\right)$ can be predicted. For the determination of the transition form factor ${C}_{5}^{A}\left({Q}^{2}\right)$, 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 ${C}_{6}^{A}\left({Q}^{2}\right)$ can be predicted in terms of ${G}_{P}\left({Q}^{2}\right)$, the mean-square axial radius $⟨{r}_{A}^{2}⟩$, and the mean-square axial nucleon-to-delta transition radius $⟨{r}_{AN\Delta }^{2}⟩$.

Published in: Physical Review D 99 (2019)