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 with the previously studied $\mathrm{\Delta }(1232)$ resonance. Our theoretical framework is a chiral Lagrangian approach with explicit resonance fields to account for their respective impacts. We find that the $N^{*}(1440)$ also leads to an enhancement of the cross section within its energy range for various axion models. This enhancement given by the $N^{*}(1440)$ maintains stability even when the parameter ${\sin }^2\beta$ of the Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) model undergoes variations. In contrast, the enhancement given by the $\mathrm{\Delta }(1232)$ gradually diminishes and finally disappears as ${\sin }^2\beta$ approaches 1. Furthermore, the resonance peaks given by the $\mathrm{\Delta }(1232)$ are approximately the same in both the Kim-Shifman-Vainstein-Zakharov (KSVZ) model and the DFSZ model with ${\sin }^2\beta =\frac{1}{2}$, while the resonance peak given by the $N^{*}(1440)$ in the former model is much more pronounced.

Figure 1

Tree-level diagrams for $aN\to \pi N$ arising from the lowest order pion-nucleon Lagrangian: (a) contact (Weinberg-Tomozawa) term, (b) $s$-channel $N$ exchange, and (c) $u$-channel $N$ exchange.

Figure 2

Diagrams for $aN\to \pi N$ with the (a) $s$-channel and (b) $u$-channel exchange of the $\mathrm{\Delta }$ resonance.

Figure 3

Diagrams for $aN\to \pi N$ with the (a) $s$-channel and (b) $u$-channel exchange of the $N^{*}$ resonance.

Figure 4

The pion rescattering loop diagram for $aN\to \pi N$.

Figure 5

The total and partial wave cross sections of $an\to {\pi }^{-}p$ versus the c.m. energy $W$ for the DFSZ axion at different values of ${\sin }^2\beta$ (left panel) and the KSVZ axion (right panel). In these plots, the solid lines correspond to the cross sections obtained based on Eq. (46), while the dashed lines correspond to the cross sections obtained considering only the contact and nucleon-mediated diagrams. In the left panel, the red, orange, green, blue and purple lines correspond to the DFSZ model parameter ${\sin }^2\beta =0,1/4,1/2,3/4$ and 1, respectively.

Figure 6

The total cross section of the KSVZ model with two different sets of resonance parameters. The red and blue lines correspond to using the parameters of Fit 2 in Tables 1 and 2, respectively, in Ref. [22]. The dashed line corresponds to the relative deviation from the mean value.

Figure 7

The total and partial wave cross sections of $ap\to {\pi }^{0}p$ for the DFSZ axion at different values of ${\sin }^2\beta$ (left panel) and the KSVZ axion (right panel). See the caption of Fig. 5.

Figure 8

The total and partial wave cross sections of $an\to {\pi }^{0}n$ for the DFSZ axion at different values of ${\sin }^2\beta$ (left panel) and the KSVZ axion (right panel). See the caption of Fig. 5.

Figure 9

The total and partial wave cross sections of $ap\to {\pi }^{+}n$ for the DFSZ axion at different values of ${\sin }^2\beta$ (left panel) and the KSVZ axion (right panel). See the caption of Fig. 5.