Pole trajectories and amplitude lineshapes of a coupled-channel scattering with separable potential

Abstract

Some of the peak structures observed in scattering experiments are not always associated to new hadronic resonance states. If the peak appears close to some two-hadron threshold, the singularity of the scattering amplitude maybe due to the strong coupling of different channels. In this work, we solved the Lippmann-Schwinger equation using a separable potential and investigate the pole trajectories and the resulting shapes of the scattering amplitude. We found that there are cases where increasing the coupling strength of coupled channel interaction can make a weak hadron-hadron interaction strong enough to produce a peak in the scattering region.