Roles of $\Delta(1232)$, $N^*(1520)$, and $N^*(1650)$ resonances in $\gamma p\to \pi^0 \pi^0 p$ reaction within an effective Lagrangian approach

Roles of the $\Delta (1232)$, ${N}^{*}(1520)$, and ${N}^{*}(1650)$ resonances in the $\gamma p\to{\pi }^{0}{\pi }^{0}p $ reaction near threshold is investigated within an effective Lagrangian approach. We have calculated the differential cross sections of the $\gamma p\to{\pi }^{0}{\pi }^{0}p$ reaction by including the contributions from the $\Delta (1232)$, ${N}^{*}(1520)$, and ${N}^{*}(1650)$ intermediate states decaying into $\pi^0 p$ via the $s$-channel nucleon pole and $t$-channel $\rho$ exchange, and found that the current experimental measurements can be well reproduced. The production of $\Delta(1232)$ is mainly from the mechanism of the $s$-channel nucleon pole, while the ${N}^{*}(1520)$ and ${N}^{*}(1650)$ are produced from the mechanism of the $t$-channel $\rho$ exchange. It is expected that more experimental data on the $\gamma p \to \pi^0 \pi^0 p$ reaction can be used to explore the properties of the low-lying excited baryon states and also the scalar $f_0(500)$ and $f_0(980)$ mesons.