We examine how the signature of the strange-dibaryon resonances with $I=1/2$ and $J^{\pi }=0^{-}$ shows up in scattering amplitudes and observables of the three-body $\overline{K}NN$-$\pi YN(Y=\Sigma ,\Lambda )$ system on the physical real energy axis. The so-called point method is applied to handle logarithmic singularities that appear in solving the Alt-Grassberger-Sandhas equations for the real scattering energies. By taking two different kinds of models for the two-body $\overline{K}N$-$\pi \Sigma$ subsystem, both of which reproduce the available data equally well but give quite a different resonance-pole structure for $\Lambda \left(1405\right)$, we also investigate whether the strange-dibaryon production reactions can be used for disentangling the nature of $\Lambda \left(1405\right)$.

• Received 12 February 2013

DOI:https://doi.org/10.1103/PhysRevC.88.025204