$\mathrm{\Delta }(1232)$ production in the $\gamma p\to \phi \pi p$ reaction

In this work, the production of baryon resonances in the $\gamma p\to \phi \pi p$ reaction near threshold is investigated within an effective Lagrangian approach. incorporates intermediate resonances, including $\mathrm{\Delta }(1232)$, $N(1440)$, $N(1520)$, and $N(1535)$, alongside non-resonant background contributions. The results indicate that the reaction is dominated by the $\mathrm{\Delta }(1232)$ excitation near threshold. A key focus of this study is the exploration of the $a_0(980)$ meson exchange in the $\mathrm{\Delta }(1232)$ production, as this reaction offers a unique opportunity to probe the poorly known $\mathrm{\Delta }(1232)N{a}_0$ coupling. We demonstrate that the parity asymmetry ($P_{\sigma }$), accessible through the $\phi$-meson’s spin density matrix elements, serves as a suitable experimental observable to identify the contribution from the $a_0(980)$ exchange.