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.

arXiv comment13 pages, 9 figures. Updated results and discussion of dynamical generation of resonances

References in corpus (42)

• Chiral dynamics in the presence of bound states: kaon-nucleon interactions revisited
• Non perturbative chiral approach to s-wave \bar{K}N interactions
• Chiral Dynamics of the Two Λ(1405) States
• Chiral Dynamics and the Low Energy Kaon-Nucleon Interaction
• Relativistic chiral SU(3) symmetry, large N_c sum rules and meson-baryon scattering
• Chiral SU(3) theory of antikaon-nucleon interactions with improved threshold constraints
• Effective Kbar N interaction based on chiral SU(3) dynamics
• $S=-1$ Meson-Baryon Unitarized Coupled Channel Chiral Perturbation Theory and the $S_{01}-$ $\Lambda$(1405) and $-\Lambda$(1670) Resonances
• Lattice QCD Evidence that the Lambda(1405) Resonance is an Antikaon-Nucleon Molecule
• Flavor SU(3) breaking effects in the chiral unitary model for meson-baryon scatterings
• Meson-baryon reactions with strangeness -1 within a chiral framework
• Improved constraints on chiral SU(3) dynamics from kaonic hydrogen
• The light baryon spectrum in a relativistic quark model with instanton-induced quark forces II. The strange baryon spectrum
• Constraints on the chiral unitary $\bar{K}N$ amplitude from $\pi \Sigma K^{+}$ photoproduction data
• Isolating the Λ(1405) in Lattice QCD
• Quark-Model Identification of Baryon Ground and Resonant States
• Dynamical coupled-channels model of $K^{-}p$ reactions (I): Determination of partial-wave amplitudes
• Kaon-nucleon scattering lengths from kaonic deuterium experiments revisited
• Structure of the $\mathbf{\Lambda }(1405)$ from Hamiltonian effective field theory
• Dynamical coupled-channels model of $K^{-}p$ reactions (II): Extraction of ${\Lambda }^{\ast }$ and ${\Sigma }^{\ast }$ hyperon resonances
• Multichannel parametrization of $\bar{K}N$ scattering amplitudes and extraction of resonance parameters
• Hyperon II: Properties of excited hyperons
• Low-lying Lambda Baryons from the Lattice
• Solitons in nonlocal chiral quark models
• Partial-wave analysis of $\bar{K}N$ scattering reactions
• Poles of Karlsruhe-Helsinki KH80 and KA84 solutions extracted by using Laurent+Pietarinen method
• Understanding the Nature of $\Lambda (1405)$ through Regge Physics
• Pion electro-production in the Roper region in chiral quark models
• Hyperon I: Partial wave amplitudes for $K^{-}p$ scattering
• The role of the triangle singularity in $\Lambda (1405)$ production in the ${\pi }^{-}p\to K^0\pi \Sigma$ and $pp\to p{K}^{+}\pi \Sigma$ processes
• A chiral quark model for meson electro-production in the region of D-wave resonances
• 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
• A chiral quark model for meson electro-production in the S11 partial wave
• Theoretical analysis of Lambda(1405) --> (Sigma pi)^0 mass spectra produced in p+p --> p + Lambda(1405) + K^+ reactions
• The Roper resonance: a genuine quark state or a dynamically generated structure?
• $\Lambda$ and $\Sigma$ Excitations and the Quark Model
• The negative-parity spin-1/2 $\Lambda$ baryon spectrum from lattice QCD and effective theory
• Eta and kaon production in a chiral quark model
• Dynamical generation of resonances in the P33 partial wave
• Structure of $\Lambda$(1405) resonance and $\gamma p\to K^{+}+(\pi \Sigma {)}^0$ reaction