Compositeness of baryonic resonances: Applications to the Delta(1232), N(1535), and N(1650) resonances

Abstract

We present a formulation of the compositeness for baryonic resonances in order to discuss the meson-baryon molecular structure inside the resonances. For this purpose, we derive a relation between the residue of the scattering amplitude at the resonance pole position and the two-body wave function of the resonance in a sophisticated way, and we define the compositeness as the norm of the two-body wave functions. As applications, we investigate the compositeness of the $\Delta (1232)$, $N(1535)$, and $N(1650)$ resonances from precise $\pi N$ scattering amplitudes in a unitarized chiral framework with the interaction up to the next-to-leading order in chiral perturbation theory. The $\pi N$ compositeness for the $\Delta (1232)$ resonance is evaluated in the $\pi N$ single-channel scattering, and we find that the $\pi N$ component inside $\Delta (1232)$ in the present framework is nonnegligible, which supports the previous work. On the other hand, the compositeness for the $N(1535)$ and $N(1650)$ resonances is evaluated in a coupled-channels approach, resulting that the $\pi N$, $\eta N$, $K\Lambda$ and $K\Sigma$ components are negligible for these resonances.

23 pages, 7 eps figures, version accepted for publication in PRC, discussions improved

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• Mixing of pseudoscalar-baryon and vector-baryon in the $J^P=1/2^{-}$ sector and the $N^{\ast }$(1535) and $N^{\ast }$(1650) resonances
• $\Xi (1690)$ as a $\bar{K}\Sigma$ molecular state
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Cited by in corpus (23)

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• Effective range expansion for narrow near-threshold resonances
• QCD and the Strange Baryon Spectrum
• Coupled-channel approach in hadron-hadron scattering
• How much is the compositeness of a bound state constrained by $a$ and $r_0$? The role of the interaction range
• The pole structure of the Lambda(1405) in a recent QCD simulation
• Generalized weak-binding relations of compositeness in effective field theory
• Generalization of Weinberg's Compositeness Relations
• Two-body wave functions and compositeness from scattering amplitudes. I. General properties with schematic models
• Accessing the strong interaction between $\Lambda$ baryons and charged kaons with the femtoscopy technique at the LHC
• Construction of a local barK N-pi Sigma-pi Lambda potential and composition of the Lambda(1405)
• Compositeness of $T_{cc}$ and $X(3872)$ by considering decay and coupled-channels effects
• Structure of hadron resonances with a nearby zero of the amplitude
• Compositeness of hadrons, nuclei, and atomic systems
• Two-body wave functions and compositeness from scattering amplitudes: II. Application to the physical $N^{\ast }$ and ${\Delta }^{\ast }$ resonances
• Compositeness of hadron resonances in finite volume
• Inverse scattering problem with a bare state
• Quark model study of the $\pi N\to \pi N$ reactions up to the $N(1440)$ resonance region
• Double strangeness pentaquarks and other exotic hadrons in the ${\Xi }_b\to \Xi J/\Psi \varphi$ decay
• Theoretical study of photoproduction of ${\eta }^{\prime }N$ bound state on deuteron target with forward proton emission
• The pseudoscalar meson and baryon octet interaction with strangeness zero in the unitary coupled-channel approximation
• Dynamically Generated $\Xi (1690)$
• Structure of exotic hadrons by a weak-binding relation with finite-range correction