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

Abstract

We investigate $\ensuremath{\Lambda}(1405)$ as a resonance in a coupled-channels baryon-meson ($\ensuremath{\Sigma}\ensuremath{\pi}\text{\ensuremath{-}}N\overline{K}\text{\ensuremath{-}}\ensuremath{\Lambda}\ensuremath{\eta}$) 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 $\ensuremath{\Sigma}\ensuremath{\pi}$ scattering below the $N\overline{K}$ threshold without introducing a BSEC when the $N\overline{K}$ 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 $N\overline{K}$ scattering length is well reproduced. The interaction whose channel dependence is the same as the one originated from the color-magnetic interaction, where no $N\overline{K}$ attraction exists, also gives a broad peak with help of a BSEC. In order to reproduce the observed $N\overline{K}$ scattering length, the calculation including a BSEC seems to be preferable. Our calculation gives an appropriate $N\overline{K}$ scattering length when the BSEC contribution to the resonance is roughly half that of the $N\overline{K}$ channel.