Construction of a local $\bar K N-\pi \Sigma-\pi \Lambda$ potential and composition of the $\Lambda(1405)$

A Kbar N-pi Sigma-pi Lambda coupled-channels potential is constructed on the basis of chiral SU(3) dynamics. Several matching conditions are introduced to formulate an equivalent local potential that reproduces the coupled-channels scattering amplitudes resulting from chiral SU(3)_L times SU(3)_R meson-baryon effective field theory. In contrast to a previously constructed effective single-channel Kbar N potential, the explicit treatment of the pi Sigma channel yields a natural description of the low-mass pole as part of the two-poles structure of the Lambda(1405) resonance. The energy dependence of the potential can now be parametrized with a minimum of polynomial orders. To study the properties of the Lambda(1405) as a quantum-mechanical quasibound state, we derive the normalization condition of its wave function generated by the energy-dependent coupled-channels potential, using the Feshbach projection method. This framework provides an improved understanding of this system from the viewpoint of the compositeness of hadrons. With the properly normalized wave function, we demonstrate and confirm that the high-mass pole of the Lambda(1405) is dominated by the Kbar N component.