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

Abstract

We have applied the coupled-channel complex scaling method (ccCSM) to K^{bar}N-πY 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 Λ(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 θ. This may correspond to the lower pole of the double-pole of Λ(1405) discussed in literature to date.

51 pages, 17 figures, to appear in Nuclear Physics A

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• Unified description of the $Qs\bar{q}\bar{q}$ molecular bound states, molecular resonances and compact tetraquark states in the quark potential model
• Possible interpretation of the complex expectation values associated with resonances
• Virtual states in the coupled-channel problems with an improved complex scaling method
• Double-pole nature of $\Lambda (1405)$ studied with coupled-channel complex scaling method using complex-range Gaussian basis
• Mirror symmetry breaking in He isotopes and their mirror nuclei
• Soft dipole resonance in neutron-rich ${}^8$He
• Shadow poles in a coupled-channel problem calculated with Berggren basis
• Investigation of $K^{bar}NN$ resonances with a coupled-channel Complex Scaling Method + Feshbach projection