Compositeness of dynamically generated states in a chiral unitary approach

Abstract

The structure of dynamically generated states in the chiral unitary approach is studied from a viewpoint of their compositeness. We analyze the properties of bound states, virtual states, and resonances in a single-channel chiral unitary approach, paying attention to the energy dependence of the chiral interaction. We define the compositeness of a bound state using the field renormalization constant which is given by the overlap of the bare state and the physical state in the nonrelativistic quantum mechanics, or by the residue of the bound state propagator in the relativistic field theory. The field renormalization constant enables one to define a normalized quantitative measure of compositeness of the bound state. Applying this scheme to the chiral unitary approach, we find that the bound state generated by the energy-independent interaction is always a purely composite particle, while the energy-dependent chiral interaction introduces the elementary component, depending on the value of the cutoff parameter. This feature agrees with the analysis of the effective interaction by changing the cutoff parameter. A purely composite bound state can be realized by the chiral interaction only when the bound state lies at the threshold or when the strength of the two-body attractive interaction is infinitely large. The natural renormalization scheme, introduced by the property of the loop function and the matching with the chiral low-energy theorem, is shown to generate a bound state which is dominated by the composite structure when the binding energy is small.

18 pages, 5 figures, title changed, published version

References in corpus (11)

• Effective Kbar N interaction based on chiral SU(3) dynamics
• Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory
• Origin of resonances in the chiral unitary approach
• Multi-quark hadrons from Heavy Ion Collisions
• Energy dependence of barKN interactions and resonance pole of strange dibaryons
• Study of exotic hadrons in S-wave scatterings induced by chiral interaction in the flavor symmetric limit
• On the nature of the $\Lambda (1405)$ and $\Lambda (1670)$ from their $N_c$ behavior in chiral dynamics
• Structure of the Lambda(1405) baryon resonance from its large Nc behavior
• Exotic hadrons in s-wave chiral dynamics
• Nature of the sigma meson as revealed by its softening process
• Compositeness of bound states in chiral unitary approach

Cited by in corpus (98)

• Hadronic molecules
• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Coupled-channel approach to $T_{cc}^{+}$ including three-body effects
• Wave functions of composite hadron states and relationship to couplings of scattering amplitudes for general partial waves
• Weak decays of heavy hadrons into dynamically generated resonances
• 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
• Structure and compositeness of hadron resonances
• Probabilistic interpretation of compositeness relation for resonances
• Heavy Hadrons in Nuclear Matter
• $T_{cc}^{+}$ coupled channel analysis and predictions
• On the size of the sigma meson and its nature
• On the nature of near-threshold bound and virtual states
• Different pole structures in line shapes of the $X(3872)$
• Structure of Near-Threshold s-Wave Resonances
• Antikaon-nucleon interaction and Lambda(1405) in chiral SU(3) dynamics
• The $KD$, $\eta D_s$ interaction in finite volume and the nature of the $D_{s^{\ast }0}(2317)$ resonance
• Quarkonium Contribution to Meson Molecules
• Effective range expansion for narrow near-threshold resonances
• QCD and the Strange Baryon Spectrum
• Coupled-channel approach in hadron-hadron scattering
• Structure of near-threshold quasi-bound states
• A meson-baryon molecular interpretation for some ${\Omega }_c$ excited baryons
• General considerations on the nature of $Z_b(10610)$ and $Z_b(10650)$ from their pole positions
• Insights into the inner structures of the fully charmed tetraquark state $X(6900)$
• A chiral covariant approach to $\rho \rho$ scattering
• How much is the compositeness of a bound state constrained by $a$ and $r_0$? The role of the interaction range
• Testing the molecular nature of ${\mathbf{D}}_{\mathbf{s}0}^{\ast }(2317)$ and ${\mathbf{D}}_0^{\ast }(2400)$ in semileptonic ${\mathbf{B}}_{\mathbf{s}}$ and $\mathbf{B}$ decays
• New results from a number operator interpretation of the compositeness of bound and resonant states
• Compositeness of the strange, charm and beauty odd parity $\Lambda$ states
• Compositeness of S-wave weakly-bound states from next-to-leading order Weinberg's relations
• Constraint on K Kbar compositeness of the a0(980) and f0(980) resonances from their mixing intensity
• The pole structure of the Lambda(1405) in a recent QCD simulation
• Generalized weak-binding relations of compositeness in effective field theory
• Hadron mass scaling near the s-wave threshold
• $N\Omega$ interaction: meson exchanges, inelastic channels, and quasibound state
• Compositeness of baryonic resonances: Applications to the Delta(1232), N(1535), and N(1650) resonances
• Size measurement of dynamically generated resonances with finite boxes
• Determination of exotic hadron structure by constituent-counting rule for hard exclusive processes
• $Z_c(3900)$ as a $D{\bar{D}}^{\ast }$ molecule from the pole counting rule
• Generalization of Weinberg's Compositeness Relations
• Two-body wave functions and compositeness from scattering amplitudes. I. General properties with schematic models
• Tetraquarks in large-$N_c$ QCD
• Resonance on top of thresholds: the ${\Lambda }_c(2595{)}^{+}$ as an extremely fine-tuned state
• Study the molecular nature of $\sigma$, $f_0(980)$, and $a_0(980)$ states
• Construction of a local barK N-pi Sigma-pi Lambda potential and composition of the Lambda(1405)
• A unified description of the hidden-charm tetraquark states $Z_{cs}(3985)$, $Z_c(3900)$ and $X(4020)$
• Negative parity $\Lambda$ and $\Sigma$ resonances coupled to pseudoscalar and vector mesons
• $B^0\to D^0{\bar{D}}^0{K}^0$, $B^{+}\to D^0{\bar{D}}^0{K}^{+}$ and the scalar $D\bar{D}$ bound state
• Why $\Xi (1690)$ and $\Xi (2120)$ are so narrow?
• Pseudoscalar and vector open-charm mesons at finite temperature
• $\Xi (1690)$ as a $\bar{K}\Sigma$ molecular state
• Quark scalar, axial, and pseudoscalar charges in the Schwinger-Dyson formalism
• Elementarity of composite systems
• $B_s\pi$--$B\bar{K}$ interactions in finite volume and the $X(5568)$
• The $K\bar{K}\pi$ decay of the $f_1(1285)$ and its nature as a $K^{\ast }\bar{K}-cc$ molecule
• Compositeness of $T_{cc}$ and $X(3872)$ by considering decay and coupled-channels effects
• Constituent-counting rule in photoproduction of hyperon resonances
• Analysis on the composite nature of the light scalar mesons $f_0(980)$ and $a_0(980)$
• The non-ordinary Regge behavior of the K*0(800) or Kappa-meson versus the ordinary K*0(1430)
• Determination of compositeness of the Lambda(1405) resonance from its radiative decay
• The ${\Lambda }_c(2595)$ resonance as a dynamically generated state: the compositeness condition and the large $N_c$ evolution
• Bound states on the lattice with partially twisted boundary conditions
• The interplay between compact and molecular structures in tetraquarks
• A study of the $KN$-$K^{\ast }N$ coupled systems
• Structure of hadron resonances with a nearby zero of the amplitude
• Composite and elementary nature of a resonance in the sigma model
• Determination of the compositeness of resonances from decays: the case of the $B_s^0\to J/\psi f_1(1285)$
• Compositeness of hadrons, nuclei, and atomic systems
• Recent developments in antikaon-nucleon dynamics
• 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
• Line shape and $D^{(\ast )}{\bar{D}}^{(\ast )}$ probabilities of $\psi (3770)$ from the $e^{+}{e}^{-}\to D\bar{D}$ reaction
• Composite nature of $Z_b$ states from data analysis
• Inverse scattering problem with a bare state
• Insights into the nature of the $P_{cs}(4459)$
• What We Know About the Lambda(1405)
• Charge-conjugation asymmetry and molecular content: the $D_{s0}^{\ast }(2317{)}^{\pm }$ in matter
• Singlet baryons in the graded symmetry approach to partially quenched QCD
• Effective-range-expansion study of near threshold heavy-flavor resonances
• $\bar{K}\bar{D}N$ molecular state as a "$uuds\bar{c}$ pentaquark" in a three-body calculation
• Theoretical study of photoproduction of ${\eta }^{\prime }N$ bound state on deuteron target with forward proton emission
• Reanalysis of lattice QCD spectra leading to the $D_{s0}^{\ast }(2317)$ and $D_{s1}^{\ast }(2460)$
• Determining Compositeness of Hadronic Resonances: the $\Lambda (1405)$ Radiative Decay and the $a_0(980)$-$f_0(980)$ Mixing
• Antikaon-nucleon dynamics and its application to few-body systems
• $N_C$ evolution of the light meson resonances
• Compositeness of the Delta(1232) resonance in pi N scattering
• Dynamically Generated $\Xi (1690)$
• Two-body Wave Functions, Compositeness, And The Internal Structure Of Dynamically Generated Resonances
• Compositeness of Near Threshold Quasi-Bound States
• Compositness and wave function of shallow bound states in relation to scattering observables
• Role of the effective range in the weak-binding relation
• Size measurement of dynamically generated hadronic resonances with finite volume effect
• Compositeness of Hadrons and Near-Threshold Dynamics
• Structure of exotic hadrons by a weak-binding relation with finite-range correction
• Hadronic few-body systems in chiral dynamics, -- Few-body systems in hadron physics --
• The Composite Particles Model (CPM), Vacuum Structure and ~ 125 GeV Higgs Mass