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The excited hyperon $\Lambda(1405)$ is the important building block forkaonic nuclei which are nuclear many-body system with anti-kaons. We have beeninvestigating the $\Lambda(1405)$ resonance with the coupled-channel ComplexScaling Method (ccCSM) in which the $\Lambda(1405)$ is treated as ahadron-molecular state of a $\bar{K}N$-$\pi\Sigma$ coupled system. We use a$\bar{K}N$(-$\pi Y$) potential based on the chiral SU(3) theory. In thisarticle, we report the double-pole nature of the $\Lambda(1405)$, which is acharacteristic property predicted by many studies with chiral SU(3)-basedmodels. With the help of the complex-range Gaussian basis in ccCSM, we havefound successfully another pole besides a pole near the $\bar{K}N$ threshold(called higher pole) which was found in our previous work with the real-rangeGaussian basis. The new pole (called lower pole) is found far below $\bar{K}N$threshold: $(M, -\Gamma/2)=(1395, -138)$ MeV when $f_\pi=110$ MeV. In spite ofso broad width of the lower-pole state, the state is clearly identified withgood separation from continuum states, since the oscillatory behavior of thecontinuum states is improved owing to the complex-range Gaussian basis.Analyzing the ccCSM wave function of the lower pole, we have revealedexplicitly that the lower-pole state is dominated by the $\pi\Sigma$ componentrather than the $\bar{K}N$ component. We have confirmed that the ccCSM wavefunction is correctly connected to the asymptotic form of the resonance wavefunction. We have estimated the meson-baryon mean distance for the lower-polestate as well as for the higher-pole state. In addition, we have investigatedthe origin of the appearance of the lower pole. The lower pole is confirmed tobe generated by the energy dependence attributed to the chiral dynamics, bycomparing the result of an energy-independent potential.

Double-pole nature of $\Lambda(1405)$ studied with coupled-channel complex scaling method using complex-range Gaussian basis