Two-body wave functions and compositeness from scattering amplitudes: II. Application to the physical $N^{\ast }$ and ${\Delta }^{\ast }$ resonances

Abstract

The meson-baryon molecular components for the $N^{\ast }$ and ${\Delta }^{\ast }$ resonances are investigated in terms of the compositeness, which is defined as the norm of the two-body wave function from the meson-baryon scattering amplitudes. The scattering amplitudes are constructed in a $\pi N$-$\eta N$-$\sigma N$-$\rho N$-$\pi \Delta$ coupled-channels problem in a meson exchange model together with several bare $N^{\ast }$ and ${\Delta }^{\ast }$ states, and parameters are fitted so as to reproduce the on-shell $\pi N$ partial wave amplitudes up to the center-of-mass energy 1.9 GeV with the orbital angular momentum $L\le 2$. As a result, the Roper resonance $N(1440)$ is found to be dominated by the $\pi N$ and $\sigma N$ molecular components while the bare-state contribution is small. The squared wave functions in coordinate space imply that both in the $\pi N$ and $\sigma N$ channels the separation between the meson and baryon is about more than 1 fm for the $N(1440)$ resonance. On the other hand, dominant meson-baryon molecular components are not observed in any other $N^{\ast }$ and ${\Delta }^{\ast }$ resonances in the present model, although they have some fractions of the meson-baryon clouds.

20 pages, 5 figures, version accepted for publication in PRC, parameters are updated, description of the discussion part is improved

References in corpus (14)

• Dynamical coupled-channel model of meson production reactions in the nucleon resonance region
• Anatomy of the newly observed hidden-charm pentaquark states: $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$
• Comprehensive analysis of the wave function of a hadronic resonance and its compositeness
• Dynamical Coupled-Channel Model of $\pi N$ Scattering in the W $\le$ 2 GeV Nucleon Resonance Region
• Pion-nucleon scattering in the Roper channel from lattice QCD
• Eta photoproduction in a combined analysis of pion- and photon-induced reactions
• Dynamical coupled-channels model of $K^{-}p$ reactions (I): Determination of partial-wave amplitudes
• Hamiltonian effective field theory study of the ${\mathbf{N}}^{\ast }(1440)$ resonance in lattice QCD
• Dynamical coupled-channels study of pi N --> pi pi N reactions
• Complex scaling : physics of unbound light nuclei and perspective
• Nucleon resonances in πN scattering up to energies \sqrt(s) < 2.0 GeV
• Generalized weak-binding relations of compositeness in effective field theory
• Two-body wave functions and compositeness from scattering amplitudes. I. General properties with schematic models
• Elementarity of composite systems

Cited by in corpus (2)

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