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

Abstract

Roles of the $\Delta (1232)$, $N^{\ast }(1520)$, and $N^{\ast }(1650)$ 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 $\Delta (1232)$, $N^{\ast }(1520)$, and $N^{\ast }(1650)$ 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 $N^{\ast }(1520)$ and $N^{\ast }(1650)$ 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.

9 pages, 5 figures