Wave functions of composite hadron states and relationship to couplings of scattering amplitudes for general partial waves

Abstract

In this paper we present the connection between scattering amplitudes in momentum space and wave functions in coordinate space, generalizing previous work done for s-waves to any partial wave. The relationship to the wave function of the residues of the scattering amplitudes at the pole of bound states or resonances is investigated in detail. A sum rule obtained for the couplings provides a generalization to coupled channels, any partial wave and bound or resonance states, of Weinberg's compositeness condition, which was only valid for weakly bound states in one channel and s-wave. An example, requiring only experimental data, is shown for the $\rho$ meson indicating that it is not a composite particle of $\pi \pi$ but something else.

References in corpus (11)

• Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts
• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory
• X(2175) as a resonant state of the $\varphi K\bar{K}$ system
• Compositeness of dynamically generated states in a chiral unitary approach
• Three body resonances in two meson-one baryon systems
• Couplings in coupled channels versus wave functions in the case of resonances: application to the two $\Lambda (1405)$ states
• The $N^{\ast }(1710)$ as a resonance in the $\pi \pi N$ system
• Finite volume effects in pion-kaon scattering and reconstruction of the kappa(800) resonance
• Properties of the rho and sigma Mesons from Unitary Chiral Dynamics
• Plausible explanation of the ${\Delta }_{5/2^{+}}(2000)$ puzzle

Cited by in corpus (101)

• Hadronic molecules
• The hidden-charm pentaquark and tetraquark states
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Combining heavy quark spin and local hidden gauge symmetries in the dynamical generation of hidden charm baryons
• Coupled-channel approach to $T_{cc}^{+}$ including three-body effects
• 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
• Probing the long-range structure of the $T_{cc}^{+}$ with the strong and electromagnetic decays
• Interpretation of the LHCb Pc(4312) Signal
• On the nature of near-threshold bound and virtual states
• Different pole structures in line shapes of the $X(3872)$
• Hidden beauty molecules within the local hidden gauge approach and heavy quark spin symmetry
• Molecular ${\Omega }_c$ states generated from coupled meson-baryon channels
• Dynamically generated $J^P=1/2^{-}(3/2^{-})$ singly charmed and bottom heavy baryons
• Antikaon-nucleon interaction and Lambda(1405) in chiral SU(3) dynamics
• Structure of Near-Threshold s-Wave Resonances
• Interplay of quark and meson degrees of freedom in near-threshold states: A practical parametrisation for line shapes
• Decay behaviors of Pc hadronic molecules
• QCD and the Strange Baryon Spectrum
• Structure of near-threshold quasi-bound states
• Hidden beauty baryon states in the local hidden gauge approach with heavy quark spin symmetry
• 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
• Isospin-1/2 $D\pi$ scattering and the lightest $D_0^{\ast }$ resonance from lattice QCD
• 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
• 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
• The pole structure of the Lambda(1405) in a recent QCD simulation
• Constraint on K Kbar compositeness of the a0(980) and f0(980) resonances from their mixing intensity
• Generalized weak-binding relations of compositeness in effective field theory
• Hadron mass scaling near the s-wave threshold
• Compositeness of baryonic resonances: Applications to the Delta(1232), N(1535), and N(1650) resonances
• Size measurement of dynamically generated resonances with finite boxes
• $Z_c(3900)$ 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
• Revisit the isospin violating decays of $X(3872)$
• The small $K\pi$ component in the $K^{\ast }$ wave functions
• Resonance on top of thresholds: the ${\Lambda }_c(2595{)}^{+}$ as an extremely fine-tuned state
• Bound state formation in the $DDK$ system
• 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 $X(4020)$
• The pion-pion Interaction in the rho Channel in Finite Volume
• $B^0$ and $B_s^0$ decays into $J/\psi$ plus a scalar or vector meson
• Study of the $DKK$ and $DK\bar{K}$ systems
• Constraints on a possible dibaryon from combined analysis of the $pn\to d{\pi }^{+}{\pi }^{-}$ and $pn\to pn{\pi }^{+}{\pi }^{-}$ cross sections
• Pseudoscalar and vector open-charm mesons at finite temperature
• Quark scalar, axial, and pseudoscalar charges in the Schwinger-Dyson formalism
• $B_s\pi$--$B\bar{K}$ interactions in finite volume and the $X(5568)$
• Compositeness of $T_{cc}$ and $X(3872)$ by considering decay and coupled-channels effects
• A prediction of $D^{\ast }$-multi-$\rho$ states
• The composite nature of the $\Lambda (1520)$ resonance
• Determination of compositeness of the Lambda(1405) resonance from its radiative decay
• Analysis on the composite nature of the light scalar mesons $f_0(980)$ and $a_0(980)$
• A study of $\eta K\bar{K}$ and ${\eta }^{\prime }K\bar{K}$ with the fixed center approximation to Faddeev equations
• The ${\Lambda }_c(2595)$ resonance as a dynamically generated state: the compositeness condition and the large $N_c$ evolution
• Partial Wave Decomposition in Friedrichs Model With Self-interacting Continua
• $D_{s0}(2590)$ as a dominant $c\bar{s}$ state with a small $D^{\ast }K$ component
• The interplay between compact and molecular structures in tetraquarks
• ${\mathbf{\Omega }}_{\mathbf{b}}^{-}\to ({\mathbf{\Xi }}_{\mathbf{c}}^{+}{\mathbf{K}}^{-}){\mathbf{\pi }}^{-}$ and the ${\mathbf{\Omega }}_{\mathbf{c}}$ states
• ${\bar{B}}^0$ decay into $D^0$ and $f_0(500)$, $f_0(980)$, $a_0(980)$, $\rho$ and ${\bar{B}}_s^0$ decay into $D^0$ and $\kappa (800)$, $K^{\ast 0}$
• Description of $\rho (1700)$ as a $\rho K\bar{K}$ system with the fixed center approximation
• Structure of hadron resonances with a nearby zero of the amplitude
• 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
• Is two-poles' $\Lambda (1405)$ one state or two?
• Meson baryon components in the states of the baryon decuplet
• 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
• Two-body wave functions and compositeness from scattering amplitudes: II. Application to the physical $N^{\ast }$ and ${\Delta }^{\ast }$ resonances
• Composite nature of $Z_b$ states from data analysis
• Inverse scattering problem with a bare state
• Two-pion exchange for coupled-channel scattering of two heavy mesons
• Insights into the nature of the $P_{cs}(4459)$
• Charge-conjugation asymmetry and molecular content: the $D_{s0}^{\ast }(2317{)}^{\pm }$ in matter
• Theoretical study of photoproduction of ${\eta }^{\prime }N$ bound state on deuteron target with forward proton emission
• $\bar{K}\bar{D}N$ molecular state as a "$uuds\bar{c}$ pentaquark" in a three-body calculation
• Possible molecules of triple-heavy pentaquarks within the extended local hidden gauge formalism
• Novel nonperturbative approach for radiative ${\bar{B}}^0({\bar{B}}_s^0)\to J/\psi \gamma$ decays
• States generated in the $K$-multi-$\rho$ interactions
• Determining Compositeness of Hadronic Resonances: the $\Lambda (1405)$ Radiative Decay and the $a_0(980)$-$f_0(980)$ Mixing
• Towards a theory of baryon resonances
• Compositeness of the Delta(1232) resonance in pi N scattering
• Compositeness Of Quasibound States from Effective Field Theory
• $N_C$ evolution of the light meson resonances
• Threshold Effects in Heavy Quarkonium Spectroscopy and Decays
• Hadronic molecules and multiquark states
• Compositeness of Near Threshold Quasi-Bound States
• Role of the effective range in the weak-binding relation
• SU(3) flavor symmetry considerations for the $\bar{K}N$ coupled channels system
• Compositeness of Hadrons and Near-Threshold Dynamics
• Structure of exotic hadrons by a weak-binding relation with finite-range correction