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

Abstract

The excited hyperon $\Lambda(1405)$ is the important building block for kaonic nuclei which are nuclear many-body system with anti-kaons. We have been investigating the $\Lambda(1405)$ resonance with the coupled-channel Complex Scaling Method (ccCSM) in which the $\Lambda(1405)$ is treated as a hadron-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 this article, we report the double-pole nature of the $\Lambda(1405)$, which is a characteristic property predicted by many studies with chiral SU(3)-based models. With the help of the complex-range Gaussian basis in ccCSM, we have found 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-range Gaussian 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 of so broad width of the lower-pole state, the state is clearly identified with good separation from continuum states, since the oscillatory behavior of the continuum states is improved owing to the complex-range Gaussian basis. Analyzing the ccCSM wave function of the lower pole, we have revealed explicitly that the lower-pole state is dominated by the $\pi\Sigma$ component rather than the $\bar{K}N$ component. We have confirmed that the ccCSM wave function is correctly connected to the asymptotic form of the resonance wave function. We have estimated the meson-baryon mean distance for the lower-pole state as well as for the higher-pole state. In addition, we have investigated the origin of the appearance of the lower pole. The lower pole is confirmed to be generated by the energy dependence attributed to the chiral dynamics, by comparing the result of an energy-independent potential.