Photoproduction of the scalar mesons $f_0(500)$ and $f_0(980)$ off the nucleon

We investigate photoproduction of the scalar mesona off the nucleon, using the effective Lagrangians and the Regge approach. We first study $f_0(980)$ photoproduction, replacing the Feynman propagator with the Regge ones for the $\rho$-meson exchange in the $t$-channel. The model parameters are fixed by reproducing the experimental data on the differential cross section. We then apply the same method to $f_0(500)$ or $\sigma$ photoproduction with the same parameters for the Regge propagator. Since the threshold energy of the $f_0(500)$ production is rather low, $N^*$ resonances, which can decay into the nucleon and two pions in the isoscalar and scalar state, can come into play in the $s$-channel. To examine the effects of the $N^*$ resonances, we set up two models to look into the respective contribution of the $N^*$ resonances. We find that in particular $N^*(1440)$ and $N^*(1680)$ play important roles in $f_0(500)$ photoproduction. We discuss the physical implications of the present results.