The $γp \to n a^+_2(1320) \to n ρ^0 π^+$ reactions within an effective Lagrangian approach

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