Chiral dynamics in the gamma p --> pi⁰ eta p and gamma p --> pi⁰ K⁰ Sigma^+ reactions

Using a chiral unitary approach for meson-baryon scattering in the strangeness zero sector, where the $N^*(1535)$ resonance is dynamically generated, we study the reactions $\gamma p \to \pi^0 \eta p$ and $\gamma p \to \pi^0 K^0 \Sigma^+$ at photon energies at which the final states are produced close to threshold. Among several reaction mechanisms, we find the most important is the excitation of the $\Delta^*(1700)$ state which subsequently decays into a pseudoscalar meson and a baryon belonging to the $\Delta(1232)$ decuplet. Hence, the reaction provides useful information with which to test current theories of the dynamical generation of the low-lying $3/2^-$ states. The first reaction is shown to lead to sizable cross sections and the $N^*(1535)$ resonance shape is seen clearly in the $\eta p$ invariant mass distribution. The same dynamical model is shown to lead to much smaller cross sections at low energies in the second reaction. Predictions are made for cross sections and invariant mass distributions which can be compared with forthcoming experiments at ELSA.