Structure of $\Lambda$(1405) resonance and $\gamma{p}\rightarrow K^{+}+(\pi\Sigma)^{0}$ reaction

Three-body calculations of $K\bar{K}N$ system with quantum numbers $I=1/2$, $J^{\pi}=(\frac{1}{2})^{+}$ were performed. Using separable potentials for two-body interactions, we calculated the $\pi\Sigma$ mass spectra for the $(\bar{K}N)_{I=0}+K^{+}\rightarrow(\pi\Sigma)^{0}K^{+}$ reaction on the basis of three-body Alt-Grassberger-Sandhas equations in the momentum representation. In this regard, different types of $\bar{K}N-\pi\Sigma$ potentials based on phenomenological and chiral SU(3) approach are used. The possibility to observe the trace of $\Lambda(1405)$ resonance in $(\pi\Sigma)^{0}$ mass spectra was studied. Using the $\chi^{2}$ fitting, it was shown that the mass of $\Lambda$(1405) resonance is about 1417 $\mathrm{MeV}/c^{2}$.