Λ(1405) resonance in baryon-meson scattering with a bound state embedded in the continuum

We investigate Lambda(1405) as a resonance in a coupled-channels baryon-meson (Sigma pi-N (K) over bar-Lambda eta) scattering with a 'bound state embedded in the continuum' (BSEC). For this purpose, we solve the Lippmann-Schwinger equation including a BSEC with the semirelativistic kinematics in the momentum space. This BSEC is introduced by hand, as a state not originated from a simple baryon-meson system. We assume it comes from the three-quark state. There appears a resonance in the Sigma pi scattering below the N (K) over bar threshold without introducing a BSEC when the N (K) over bar channel has a strong attraction, just like the chiral unitary approach. Even if the baryon-meson interaction is weakened by using a lower-momentum cut-off parameter, a resonance also appears around 1405 MeV when a BSEC is introduced. The corresponding peak also has a large width, and the N (K) over bar scattering length is well reproduced. The interaction whose channel dependence is the same as the one originated from the color-magnetic interaction, where no N (K) over bar attraction exists, also gives a broad peak with help of a BSEC. In order to reproduce the observed N (K) over bar scattering length, the calculation including a BSEC seems to be preferable. Our calculation gives an appropriate N (K) over bar scattering length when the BSEC contribution to the resonance is roughly half that of the N (K) over bar channel.