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.

arXiv comment25 pages, 11 figures, to be published in Nuclear Physics A

References in corpus (33)

• Chiral dynamics in the presence of bound states: kaon-nucleon interactions revisited
• Chiral Dynamics of the Two Λ(1405) States
• Chiral Dynamics and the Low Energy Kaon-Nucleon Interaction
• A New Measurement of Kaonic Hydrogen X rays
• Low lying S=-1 excited baryons and chiral symmetry
• Effective Kbar N interaction based on chiral SU(3) dynamics
• Faddeev calculation of a $K^{-}pp$ quasi-bound state
• K^- p scattering length from scattering experiments
• Strange dibaryon resonance in the anti-KNN--piYN system
• Variational calculation of the ppK^- system based on chiral SU(3) dynamics
• $\bar{K}NN$ quasi-bound state and the $\bar{K}N$ interaction: coupled-channel Faddeev calculations of the $\bar{K}NN-\pi \Sigma N$ system
• Flavor SU(3) breaking effects in the chiral unitary model for meson-baryon scatterings
• Meson-baryon reactions with strangeness -1 within a chiral framework
• $K^{-}pp$ system with chiral SU(3) effective interaction
• Chiral dynamics of kaon-nucleon interactions, revisited
• Realistic calculations of Kbar-N-N, Kbar-N-N-N, and Kbar-Kbar-N-N quasibound states
• New insights into antikaon-nucleon scattering and the structure of the Lambda(1405)
• Kaonic hydrogen X-ray measurement in SIDDHARTA
• Kaonic nuclei studied based on a new framework of Antisymmetric Molecular Dynamics
• Variational calculations for K-few-nucleon systems
• Chirally motivated $\bar{K}N$ amplitudes for in-medium applications
• High-density K nuclear systems with isovector deformation
• Couplings in coupled channels versus wave functions in the case of resonances: application to the two $\Lambda (1405)$ states
• eta-prime nucleus optical potential and possible eta-prime bound states
• Detailed Analysis of the Chiral Unitary Model for Meson-Baryon Scattering with Flavor SU(3) Breaking Effects
• Strangeness nuclear physics - 2010
• Size measurement of dynamically generated resonances with finite boxes
• Level crossing of particle-hole and mesonic modes in eta mesic nuclei
• Structure of Lambda(1405) and threshold behavior of piSigma scattering
• Inclusive spectrum of the $d({\pi }^{+},K^{+})$ reaction at 1.69 GeV/c
• Comprehensive application of a coupled-channel complex scaling method to the KbarN-piY system
• Lambda(1405) in a baryon-meson scattering with a bound state embedded in the continuum
• On the origin and movement of the poles in the coupled channels model for $\bar{K}N$ interactions

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