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We investigate the $a_2(1320)$ meson photon production in the $\gamma p \to na^+_2(1320)$ and $\gamma p \to n \rho^0 \pi^+$ reactions within the effectiveLagrangian method. For $\gamma p \to n a^+_2(1320)$ reaction, by consideringthe contributions only from the $t-$channel $\pi^+$ exchange, we get a fairlygood description of the current experimental total cross section data. We alsostudied the $\gamma p \to n \rho^0 \pi^+$ reaction, which mainly contribute tothe $\gamma p \to n \pi^+ \pi^+ \pi^-$ reaction. The latter reaction hasmeasured by the CLAS Collaboration. The total cross sections, invariant massdistribution, and the Dalitz Plot of $\gamma p \to n \rho^0 \pi^+$ reaction areshown, which can be tested by future experiments.

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