Comprehensive application of a coupled-channel complex scaling method to the image system

We have applied the coupled-channel complex scaling method (ccCSM) to image system. One advantage of ccCSM is that resonant states as well as scattering states can be treated in the same framework. For the interactions in the system, we have constructed a meson–baryon potential-matrix by basing on the chiral SU(3) theory and respecting the image scattering length obtained in the Martinʼs analysis. For future purpose to apply it more complicated system such as image, we adopt a local Gaussian form in the r-space. We have investigated both the non-relativistic (NR) and the semi-relativistic (SR) kinematics. In the SR case, two types of the potentials are obtained. To test the constructed potentials, we have calculated scattering amplitudes and searched resonances. One resonance pole, corresponding to image, is found in isospin image system around image (image or image) on complex-energy plane with the NR (SR) kinematics. Mean distance between meson and baryon in the resonant state is image (image) for NR (SR), in which the states are treated as Gamow states. In addition, we have observed a signature of another pole in lower-energy region involving large decay width, although they are unstable against the change of scaling angle θ. This may correspond to the lower pole of the double-pole of image discussed in literature today.