The $\gamma p \to n a^+_2(1320) \to n \rho^0 \pi^+$ reactions within an effective Lagrangian approach

We investigate the $a_2(1320)$ meson photon production in the $\gamma p \to n a^+_2(1320)$ and $\gamma p \to n \rho^0 \pi^+$ reactions within the effective Lagrangian method. For $\gamma p \to n a^+_2(1320)$ reaction, by considering the contributions only from the $t-$channel $\pi^+$ exchange, we get a fairly good description of the current experimental total cross section data. We also studied the $\gamma p \to n \rho^0 \pi^+$ reaction, which mainly contribute to the $\gamma p \to n \pi^+ \pi^+ \pi^-$ reaction. The latter reaction has measured by the CLAS Collaboration. The total cross sections, invariant mass distribution, and the Dalitz Plot of $\gamma p \to n \rho^0 \pi^+$ reaction are shown, which can be tested by future experiments.