Pion axioproduction revisited

In this work, we extend the analysis of the pion axioproduction, $aN \to \pi{N}$, to include the impact of the Roper resonance $N^*(1440)$ together the previously studied $\Delta(1232)$ resonance. Our theoretical framework is chiral perturbation theory with explicit resonance fields to account for their respective impacts. We find that the Roper resonance also leads to an enhancement of the cross section within its energy range for various axion models. This enhancement provided by the Roper maintains stability even when the parameter $\sin^2{\beta}$ of the DFSZ model undergoes variations. In contrast, the enhancement given by the $\Delta$ gradually diminishes and finally disappears as $\sin^2{\beta}$ approaches $1$. Furthermore, the resonance peaks given by the $\Delta$ are approximately the same in both the KSVZ model and the DFSZ model with $\sin^2{\beta} = \tfrac{1}{2}$, while the resonance peak given by the Roper in the former model is much more pronounced.