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

TL;DR

This paper applies the coupled-channel complex scaling method to the KbarN-piY system, successfully identifying the \\Lambda(1405) resonance and exploring its properties using chiral SU(3) based potentials in both non-relativistic and semi-relativistic frameworks.

Contribution

It introduces a coupled-channel complex scaling approach to analyze the KbarN-piY system, including resonance and scattering states, with potentials based on chiral SU(3) theory, and investigates the \\Lambda(1405) resonance in detail.

Findings

Identified the \\Lambda(1405) resonance pole around (1419, -20) MeV (NR) and (1425, -25) or (1419, -13) MeV (SR).

Observed a potential lower-energy pole related to the double-pole structure of \\Lambda(1405).

Calculated meson-baryon mean distances in the resonant state (~1.2-1.3 fm).

Abstract

We have applied the coupled-channel complex scaling method (ccCSM) to K^{bar}N-\pi Y 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 K^{bar}N scattering length obtained in the Martin's analysis. For future purpose to apply it more complicated system such as K^{bar}NN, 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 \Lambda(1405), is found in isospin I=0 system around (1419, -20) MeV ((1425, -25) or (1419, -13) MeV) on complex-energy plane with the NR (SR) kinematics. Mean distance between meson and baryon in the resonant state is 1.3 - i0.3 fm (1.2 - i0.5 fm) 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 \theta. This may correspond to the lower pole of the double-pole of \Lambda(1405) discussed in literature to date.