Understanding the 1P- and 2S-wave nucleon resonances within the extended Lee-Friedrichs Model

Abstract

We present a unified desciption of the low-lying $1P$- and $2S$-wave nucleon resonance within the framework of an extended Lee-Friedrichs scheme. By incorporating the coupled-channel dynamics between bare quark-model states and the $\pi N$, $\pi \Delta$ and $\eta N$ meson-baryon continua, we examine the mass shifts and structural properties of these excited states. We demonstrate that when the model parameters are calibrated to match the $1P$-wave spectrum and their widths, the pole associated with the bare $2S$ state is naturally shifted downward to the mass region of physical Roper resonance--$N(1440)$, thereby offering a dynamical explanation for the long-standing level-inversion problem. An approximate analysis of compositeness and elementariness reveals that the Roper resonance contains a significant meson-baryon continuum states, consistent with the picture of a bare core heavily dressed by meson-baryon cloud. Simultaneously, the pole positions and properties of five $1P$-wave resonances--$N(1535)$, $N(1650)$, $N(1520)$, $N(1700)$ and $N(1675)$ are successfully reproduced. Our results highlight the essential role of coupled-channel effects in shaping the nucleon spectrum and provide a consistent microscopic insight into the interplay between internal quark degrees of freedom and external hadronic fields.

13 pages, 2 figure

References in corpus (42)

• The Spectrum of the Nucleons and the Strange Hyperons and Chiral Dynamics
• Heavy Baryons in a Quark Model
• Extended Partial-Wave Analysis of piN Scattering Data
• Chiral Dynamics and the $S_{11}(1535)$ Nucleon Resonance
• Properties of baryon resonances from a multichannel partial wave analysis
• What is the structure of the Roper resonance?
• Origin of resonances in the chiral unitary approach
• The $S_{11}-N$(1535) and $-N$(1650) Resonances in Meson-Baryon Unitarized Coupled Channel Chiral Perturbation Theory
• Chiral dynamics of the S11(1535) and S11(1650) resonances revisited
• Disentangling the dynamical origin of P11 Nucleon Resonances
• Comprehensive analysis of the wave function of a hadronic resonance and its compositeness
• Structure and compositeness of hadron resonances
• Probabilistic interpretation of compositeness relation for resonances
• Spectrum of light- and heavy-baryons
• Pion-nucleon scattering in the Roper channel from lattice QCD
• Hamiltonian effective field theory study of the ${\mathbf{N}}^{\ast }(1535)$ resonance in lattice QCD
• Eta-meson production in the resonance energy region
• Strangeness -2 and -3 Baryons in a Constituent Quark Model
• Structure of near-threshold quasi-bound states
• Hamiltonian effective field theory study of the ${\mathbf{N}}^{\ast }(1440)$ resonance in lattice QCD
• Structure of the nucleon's low-lying excitations
• Structure of the Roper Resonance from Lattice QCD Constraints
• $\Omega$ baryon spectrum and their decays in a constituent quark model
• The role of $qqqq\bar{q}$ components in the nucleon and the N(1440) resonance
• Strong decays of baryons and missing resonances
• The phase and pole structure of the N*(1535) in piN-->piN and gammaN-->piN
• $\eta$ photoproduction on the quasi-free nucleons in the chiral quark model
• Light baryon resonances from a coupled-channel study including $\mathbf{K\Sigma }$ photoproduction
• Generalized weak-binding relations of compositeness in effective field theory
• Study of $\eta$ photoproduction on the proton in a chiral constituent quark approach via one-gluon-exchange model
• Updated determination of $N^{\ast }$ resonance parameters using a unitary, multichannel formalism
• Nucleon resonance parameters from Roy-Steiner equations
• The width of the Roper resonance in baryon chiral perturbation theory
• Virtual states and generalized completeness relation in the Friedrichs Model
• The Role of the Roper in Chiral Perturbation Theory
• Neutral pion photoproduction on the nucleon in a chiral quark model
• Partial Wave Decomposition in Friedrichs Model With Self-interacting Continua
• Two-pole structures in a relativistic Friedrichs-Lee-QPC scheme
• Quarks, diquarks and QCD mixing in the $N^{\ast }$ resonance spectrum
• Decays of Roper-like singly heavy baryons in a chiral model
• A case in favor of the $N^{\ast }(1700)(3/2^{-})$
• Compositeness of hadrons, nuclei, and atomic systems