The $\Lambda (1405)$ resonance as a genuine three-quark or molecular state

Abstract

The mechanism for the formation of the $\Lambda (1405)$ resonance is studied in a chiral quark model that includes quark-meson as well as contact (four point) interactions. The negative-parity $S$-wave scattering amplitudes for strangeness $-1$ and $1$ are calculated within a unified coupled-channel framework that includes the $KN$, $\bar{K}N$, $\pi \Sigma$, $\eta \Lambda$, $K\Xi$, $\pi \Lambda$, and $\eta \Sigma$ channels and possible genuine three-quark bare singlet and octet states corresponding to ${\frac{1}{2}}^{-}$ resonances. We show that in order to reproduce the scattering amplitudes in the $S_{01}$ partial wave it is important to include the pertinent three-quark octet states as well as the singlet state, while the inclusion of the contact term is not mandatory. The Laurent-Pietarinen expansion is used to determine the $S$-matrix poles. Following their evolution as a function of increasing interaction strength, the mass of the singlet state is strongly reduced due to the attractive self-energy in the $\pi \Sigma$ and $\bar{K}N$ channels; when it drops below the $KN$ threshold, the state acquires a dominant $\bar{K}N$ component which can be identified with a molecular state. The attraction between the kaon and the nucleon is generated through the $\bar{K}N{\Lambda }^{\ast }$ interaction rather than by meson-nucleon forces.

13 pages, 9 figures. Updated results and discussion of dynamical generation of resonances

References in corpus (12)

• Effective Kbar N interaction based on chiral SU(3) dynamics
• Lattice QCD Evidence that the Lambda(1405) Resonance is an Antikaon-Nucleon Molecule
• Constraints on the chiral unitary $\bar{K}N$ amplitude from $\pi \Sigma K^{+}$ photoproduction data
• Quark-Model Identification of Baryon Ground and Resonant States
• Dynamical coupled-channels model of $K^{-}p$ reactions (I): Determination of partial-wave amplitudes
• Structure of the $\mathbf{\Lambda }(1405)$ from Hamiltonian effective field theory
• Roper resonances in chiral quark models
• Pole structure from energy-dependent and single-energy fits to $\pi N$ elastic scattering data
• Flavor structure of $\Lambda$ baryons from lattice QCD: From strange to charm quarks
• $\Lambda$ and $\Sigma$ Excitations and the Quark Model
• The negative-parity spin-1/2 $\Lambda$ baryon spectrum from lattice QCD and effective theory
• Structure of $\Lambda$(1405) resonance and $\gamma p\to K^{+}+(\pi \Sigma {)}^0$ reaction