Chiral Symmetry Amplitudes in the S-Wave Isoscalar and Isovector Channels and the σ, f_0(980), a_0(980) Scalar Mesons

Abstract

We use a nonperturbative approach which combines coupled channel Lippmann Schwinger equations with meson-meson potentials provided by the lowest order chiral Lagrangians. By means of one parameter, a cut off in the momentum of the loop integrals, which results of the order of 1 GeV, we obtain singularities in the S-wave amplitudes corresponding to the σ,f_0 and a_0 resonances. The ππ-->ππ, ππ-->K\bar{K} phase shifts and inelasticities in the T=0 scalar channel are well reproduced as well as the π^-ηand K^-K^0 mass distributions in the T=1 channel. Furthermore, the total and partial decay widths of the f_0 and a_0 resonances are properly reproduced including also the decay into the γγchannel. The results seem to indicate that chiral symmetry constraints at low energy and unitarity in coupled channels is the basic information contained in the meson-meson interaction below \sqrt(s)=1.2 GeV.

latex, 22 pages, 9 figures

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• A study of $\eta K\bar{K}$ and ${\eta }^{\prime }K\bar{K}$ with the fixed center approximation to Faddeev equations
• Two-photon decays of pi^0, eta and eta-prime
• Transport coefficients of heavy baryons
• Decays of the vector glueball
• Does nuclear matter bind at large $N_c$?
• Light Scalar Meson sigma(600) in QCD Sum Rule with Continuum
• $X(3872)$, $X(4014)$, and their bottom partners at finite temperature
• Thermal behaviors of light scalar resonances at low temperatures
• Study of the $f_2(1270)$, $f_2^{\prime }(1525)$, ${\bar{K}}_2^{\ast }(1430)$, $f_0(1370)$ and $f_0(1710)$ production from $\psi (nS)$ and ${\rm Y}(nS)$ decays
• Strange Hadron Spectroscopy with Secondary KL Beam in Hall D
• Non-perturbative chiral approach to Kp -->gamma Y reactions
• Chromo-polarizability and pipi final state interaction
• The phi(1020) a0(980) S-wave scattering and hints for a new vector-isovector resonance
• The ${\Lambda }_c(2595)$ resonance as a dynamically generated state: the compositeness condition and the large $N_c$ evolution
• Light scalar mesons in $J/psi->$NN$mesonmeson$ decays in a chiral unitary approach
• The role of the thermal $f_0(500)$ in chiral symmetry restoration
• Preliminary lattice study of $\sigma$ meson decay width
• Further study of $f_0(1710)$ with coupled-channel approach and hadron molecular picture
• Distinguishing cusp effects and near-threshold-pole effects
• Bound states on the lattice with partially twisted boundary conditions
• Nonresonant Contributions in B->rho pi Decay
• Evaluation of the $\pi \pi$ scattering amplitude in the $\sigma$-channel at finite density
• Remarks on non-perturbative three--body dynamics and its application to the $KK\bar{K}$ system
• The $D_s^{+}\to a_0(980)e^{+}{\nu }_e$ reaction and the $a_0(980)-f_0(980)$ mixing
• $D_{s0}^{\ast }(2317{)}^{+}$ in the decay of $B_c$ into $J/\psi DK$
• On the role of meson loops in the $f_0(1710)$ decay into $V\gamma$
• The $DN$, $\pi {\Sigma }_c$ interaction in finite volume and the ${\Lambda }_c(2595)$ resonance
• Combined theoretical study of the $D^{+}\to {\pi }^{+}\eta \eta$ and $D^{+}\to {\pi }^{+}{\pi }^0\eta$ reactions
• Photoproduction of scalar mesons on protons and nuclei
• Predicting the existence of a 2.9 GeV $D{f}_0(980)$ molecular state
• The $\rho (\omega )B^{\ast }(B)$ interaction and states of $J=0,1,2$
• Dispersive calculation of complex Regge trajectories for the lightest $f_2$ resonances
• $P_{cc}^N$ states in a unitarized coupled-channel approach
• Molecular states of $D^{\ast }{D}^{\ast }{\bar{K}}^{\ast }$ nature
• Signatures of the two $K_1(1270)$ poles in $D^{+}\to \nu e^{+}VP$ decay
• Estimating sigma-meson couplings from D \to 3πdecays
• Chiral Symmetry and light resonances in hot and dense matter
• Role of the scalar $f_0(980)$ in the process $D_s^{+}\to {\pi }^{+}{\pi }^0{\pi }^0$
• On the structure of the pi pi invariant mass spectra of the Upsilon(4S)-->Upsilon(1S,2S) pi^+ pi^- decays
• Final state interactions in the decays J/psi->VPP
• Interference effects in the decay ϕ\to π^{0}π^{0}γand the coupling constant g_{ϕσγ}
• Partial decay widths of $\varphi (2170)$ to kaonic resonances
• A new method to study the number of colors in the final-state interactions of hadrons
• S-wave Meson-Meson Scattering from Unitarized U(3) Chiral Lagrangians
• Global parametrizations of $\pi \pi$ scattering with dispersive constraints: Beyond the S0 wave
• Scalar resonances in a unitary $\pi -\pi$ $S$-wave model for $D^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}$
• The $\sigma K$ coupling in the chiral unitary approach and the isoscalar $\bar{K}N$, $\bar{K}A$ interaction
• Scalar resonance in graviton-graviton scattering at high-energies: the graviball
• Pseudotensor mesons as three-body resonances
• A study of the $KN$-$K^{\ast }N$ coupled systems
• Theoretical description of the $\mathbf{J}/\mathbf{\psi }\to \mathbf{\eta }({\mathbf{\eta }}^{\prime }){\mathbf{h}}_1(1380)$, $\mathbf{J}/\mathbf{\psi }\to \mathbf{\eta }({\mathbf{\eta }}^{\prime }){\mathbf{h}}_1(1170)$ and $\mathbf{J}/\mathbf{\psi }\to {\mathbf{\pi }}^0{\mathbf{b}}_1(1235{)}^0$ reactions
• $J/\psi$ decay into $\varphi (\omega )$ and vector-vector molecular states
• Masses of Heavy and Light Scalar Tetraquarks in a Non-Relativistic Quark Model
• Aspects of the ETH model of the pion-nucleon interaction
• Exploring the $D^{\ast }\rho$ system within QCD sum rules
• The three-pion decays of the $a_1(1260)$
• Role of a four-quark and a glueball state in pion-pion and pion-nucleon scattering
• Role of the triangle mechanism in the ${\Lambda }_b\to {\Lambda }_c{\pi }^{-}{f}_0(980)$ reaction
• Properties of light resonances from unitarized Chiral perturbation theory: Nc behavior and quark mass dependence
• Searching for exotic states in the $N\pi K$ system
• The pi N -> pi pi N reaction around the N(1440) energy
• Three-body unitary coupled-channel approach to radiative $J/\psi$ decays and $\eta (1405/1475)$
• Hadronic molecules with four charm or beauty quarks
• Observation of ${\Lambda }_c^{+}\to \Lambda a_0(980{)}^{+}$ and Evidence for $\Sigma (1380{)}^{+}$ in ${\Lambda }_c^{+}\to \Lambda {\pi }^{+}\eta$
• Two photon decay of neutral scalars below 1.5 GeV in a chiral model for bar{q}q and bar{q}bar{q}qq states
• $a_0(980)-f_0(980)$ mixing in ${\chi }_{c1}\to {\pi }^0{f}_0(980)\to {\pi }^0{\pi }^{+}{\pi }^{-}$ and ${\chi }_{c1}\to {\pi }^0{a}_0(980)\to {\pi }^0{\pi }^0\eta$
• To understand the rare decay $B_s\to {\pi }^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$
• The thermal evolution of nuclear matter at zero temperature and definite baryon number density in chiral perturbation theory
• The strong decays of the light scalar mesons $f_0(500)$ and $f_0(980)$
• $\rho \rho$ scattering revisited with coupled-channels of pseudoscalar mesons
• Generalized linear sigma model with two glueballs
• Ordinary and exotic mesons in the extended Linear Sigma Model
• Renormalization of the f0(980) and a0(980) scalar resonances in a nuclear medium
• Remark on pion scattering lengths
• The molecular nature of some exotic hadrons
• Density of States of a Coupled-Channel System
• Chiral Unitary Dynamics of Hadrons and Hadrons in a Nuclear Medium
• Description of $\rho (1700)$ as a $\rho K\bar{K}$ system with the fixed center approximation
• Understanding close-lying exotic charmonia states within QCD sum rules
• Non-Perturbative Study of the Light Pseudoscalar Masses in Chiral Dynamics
• CP Asymmetries in B to f_0 K_S Decays
• Scalar mesons in the chiral theory with quark degrees of freedom
• Preliminary lattice study of the I=1 $K\bar{K}$ scattering length
• An in-medium chiral power counting for nuclear matter and some applications
• Composite and elementary nature of a resonance in the sigma model
• Aspects of Strangeness -1 Meson-Baryon Scattering
• Molecular nature of the $a_1$(1260) axial-vector meson
• Roles of the $N(1535)$ and $a_0(980)$ in the process ${\Lambda }_c^{+}\to {\pi }^{+}\eta n$
• Decay of vector-vector resonances into $\gamma$ and a pseudoscalar meson
• Mixing among lowest-lying scalar mesons and scalar glueball
• Hadronic molecular states with the quark contents $bc\bar{s}\bar{q}$, $b\bar{c}s\bar{q}$, and $b\bar{c}\bar{s}q$
• The $\pi f_0(500)$ decay of the $a_1(1260)$
• Two pion mediated scalar isoscalar NN interaction in the nuclear medium
• Cross sections for inelastic meson-meson scattering via quark-antiquark annihilation
• Compositeness of hadron resonances in finite volume
• ${\chi }_{c1}$ decays into a pseudoscalar meson and a vector-vector molecule
• $J/\psi \to \gamma \pi \pi$, $\gamma {\pi }^0\eta$ reactions and the $f_0(980)$ and $a_0(980)$ resonances
• Unitarized chiral perturbation theory of hadrons
• Line shape and $D^{(\ast )}{\bar{D}}^{(\ast )}$ probabilities of $\psi (3770)$ from the $e^{+}{e}^{-}\to D\bar{D}$ reaction
• Semileptonic $B_s\to K_0^{\ast }(1430)$ transitions with the light-cone sum rules
• Four-body Semileptonic Charm Decays $D\to P_1{P}_2{\ell }^{+}{\nu }_{\ell }$ Based on SU(3) Flavor Analysis
• Scalar sigma meson effects in radiative rho^0-meson decays
• K-pi interaction in finite volume and the K* resonance
• Dynamical study of the light scalar mesons below 1 GeV in a flux-tube model
• Cross sections for inelastic meson-meson scattering
• Scalar resonances: scattering and production amplitudes
• Resonances, Chiral Symmetry, Coupled Channel Unitarity and Effective Lagrangians
• Studying the bound state of the $K^{-}p$ system in the Bethe-Salpeter formalism
• Chiral dynamics and S-wave contributions in ${\bar{B}}^0/D^0\to {\pi }^{\pm }\eta l^{\mp }\nu$ decays
• Degeneracy patterns of chiral companions at finite temperature
• Spinless mesons and glueballs mixing patterns in SU(3) flavor limit
• Insights into the nature of the $P_{cs}(4459)$
• Phenomenology of the pseudoscalar glueball with a mass of 2.6 GeV
• Chromopolarizability of charmonium and $\pi \pi$ final state interaction revisited
• Light quarks at finite temperature: chiral restoration and the fate of the $U(1{)}_A$ symmetry
• The pion-kaon scattering amplitude and the $K^0(700)$ and $K^{\ast }(892)$ resonances at finite temperature
• Roles of the scalar $f_0(500)$ and $f_0(980)$ in the process $D^0\to {\pi }^0{\pi }^0{\bar{K}}^0$
• Reactions gamma gamma -> pi pi and gamma gamma -> K \bar K: the (IJ^{PC}=00^{++})-wave spectra at E_{gamma gamma}^{(c.m.)} = 300- 1900 MeV
• Decay of kaonium in a chiral approach
• Meson-baryon scattering in resummed baryon chiral perturbation theory using time-ordered perturbation theory
• On ambiguities of sign determination of the S-matrix from energy levels in a finite box
• Quark and glue spectroscopy of scalars and pseudoscalars in SU(3) flavor limit
• Is there an isovector companion of the X(2175)?
• The $\rho NN$ coupling with direct coupling and loops
• $J/\psi$ decay to $\varphi ,\omega ,K^{\ast 0}$ plus $f_0(1370)$, $f_0(1710)$, $K_0^{\ast }(1430)$, $f_2(1270)$, $f_2^{\prime }(1525)$ and $K_2^{\ast }(1430)$: role of the $D$-wave for tensor production
• Role of $f_0(980)$ and $a_0(980)$ in the $B^{-}\to {\pi }^{-}{K}^{+}{K}^{-}$ and $B^{-}\to {\pi }^{-}{K}^0{\bar{K}}^0$ reactions
• Study of the resonance contributions in the ${\Xi }_b^{-}\to p{K}^{-}{K}^{-}$ decay
• Cross sections for 2-to-1 meson-meson scattering
• Photoproduction of $f_0(980)$ and $f_0(1500)$ resonances off a proton target
• Low-mass enhancement of kaon pairs in $B^{+}\to {\bar{D}}^{(\ast )0}{K}^{+}{\bar{K}}^0$ and $B^0\to D^{(\ast )-}{K}^{+}{\bar{K}}^0$ decays
• Chiral Symmetry and N*(1440) -> N pi pi Decay
• $\bar{K}$ induced formation of the $f_0(980)$ and $a_0(980)$ resonances on proton targets
• Analysis of the decays ${\psi }^{\prime }\to J/\psi {\pi }^{+}{\pi }^{-}$ and ${\eta }_c^{\prime }\to {\eta }_c{\pi }^{+}{\pi }^{-}$ with the heavy quark symmetry
• Unitarization Technics in Hadron Physics with Historical Remarks
• Inelastic Meson-Meson Scattering in Hadronic Matter
• The Radiative Decay of Vector Mesons
• Two, three, many body systems involving mesons
• Double strangeness pentaquarks and other exotic hadrons in the ${\Xi }_b\to \Xi J/\Psi \varphi$ decay
• Dynamical Generation of Hyperon Resonances
• The role of meson interactions in the $D_s^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}\eta$ decay
• Production of the (predicted) $K^{\ast }(4307)$ in $B$ decays
• Chiral Nonet Mixing in $\pi \eta$ Scattering
• Looking for bound states and resonances in the ${\eta }^{\prime }K\bar{K}$ system
• Investigations of the $D$-multi-$\rho$ interactions
• The pseudoscalar meson and baryon octet interaction with strangeness zero in the unitary coupled-channel approximation
• The Relativistic Cornell-type Mechanism of Exotic Scalar Resonances
• Testing the nature of the $\Lambda$(1520) in the $J/\psi \to \bar{\Lambda }{K}^{-}p$ and $J/\psi \to \bar{\Lambda }{\pi }^{+}{\pi }^{-}\Lambda$ reactions
• Sigma meson mass and width at finite density
• Asymmetry observables in e+ e- --> pi+ pi- gamma in the phi region within a chiral unitary approach
• Charge asymmetries in e+e- -> pi+ pi- gamma at the phi resonance
• Novel nonperturbative approach for radiative ${\bar{B}}^0({\bar{B}}_s^0)\to J/\psi \gamma$ decays
• Quark mass dependence of the low-lying charmed mesons at one loop in HH$\chi$PT
• Resonances f0(1370), f0(1500) and f0(1710) within the extended Linear Sigma Model
• Photoproduction of the $X(3872)$ beyond vector meson dominance: the open-charm coupled-channel mechanism
• On the Determination of Elastic and Inelastic Nuclear Observables from Lattice QCD
• Kaon-antikaon nuclear optical potentials and the kappa meson in the nuclear medium
• Impact of unitarization on the $J/\psi$-light meson cross section
• Strangeness Production in pp and pn Reactions at COSY
• Hadronic decay $D^{+}\to {\pi }^{+}\eta \eta$ and the $a_0(980)$ and $f_0(1370)$ contributions
• The role of triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$
• The $({\pi }^{-},\gamma \gamma )$ reaction in nuclei and the $\sigma$ meson in the medium
• D-meson diffusion in hadronic matter
• Theory overview on amplitude analyses with charm decays
• Unitarization and low-energy scattering data
• Role of scalar dibaryon and $f_0(500)$ in the isovector channel of low-energy neutron-proton scattering
• Study of the $\bar{K}N$ system and coupled channels in a finite volume
• Three-body hadron systems with strangeness
• Photoproduction of meson and baryon resonances in a chiral unitary approach
• States generated in the $K$-multi-$\rho$ interactions
• Exotic Hadrons in the ${\Lambda }_b\to J/\psi \varphi \Lambda$ Decay
• The role of strangeness in chiral and $U(1{)}_A$ restoration
• Theoretical study in the ${\bar{B}}^0\to J/\psi {\bar{K}}^{\ast 0}{K}^0$ and ${\bar{B}}^0\to J/\psi f_1(1285)$ decays
• $D_1$ and $D_2$ resonances in coupled-channel scattering amplitudes from lattice QCD
• Unitarity and Unitarization
• Determining Compositeness of Hadronic Resonances: the $\Lambda (1405)$ Radiative Decay and the $a_0(980)$-$f_0(980)$ Mixing
• The theoretical study of $D_s^{+}\to {\pi }^{+}{\pi }^0{\pi }^0$
• Correction to the energy spectrum of ${}^1{S}_0$ heavy quarkonia due to two-gluon annihilation effect
• Quarkonium interactions with (hot) hadronic matter
• Methods on compositeness and related aspects
• Cross sections for 2-to-3 meson-meson scattering
• The $\eta$ decay into 3$\pi$ in asymmetric nuclear medium
• Transport coefficients of a unitarized pion gas
• Pion scattering in finite volume within the Inverse Amplitude Method
• SU(3) Chiral approach to meson and baryon dynamics
• Revealing dipion correlations for the observed substructure near the ${\pi }^{+}{\pi }^{-}$ mass threshold in $\psi (3686)\to J/\psi {\pi }^{+}{\pi }^{-}$
• $\Lambda (1405)$ and $\bar{\Lambda }(1405)$ in $J/\psi$ four-body decays
• Diquark correlations in baryons: the Interacting Quark Diquark Model
• Strong decays of the isovector-scalar $D^{\ast }{\bar{D}}^{\ast }$ hadronic molecule
• Recent progress on the chiral unitary approach to meson meson and meson baryon interactions
• A note on the tensor and vector exchange contributions to $K\bar{K}\to K\bar{K},D\bar{D}\to D\bar{D}$ and ${\pi }^{+}{\pi }^{-}\to {\pi }^{+}{\pi }^{-}$ reactions
• Study of conventional and non-conventional scalar and vector mesons
• Interactions of the Pseudoscalar Meson Octet and the Baryon Decuplet in the Continuum and a Finite Volume
• Dynamical generation of hadronic resonances in effective models with derivative interactions
• The effect of isospin violation on scalar meson production
• Chiral unitary theory: application to nuclear problems
• Scattering Theory
• Observation of ${\Lambda }_c^{+}\to n{\pi }^{+}\eta$ and search for ${\Lambda }_c^{+}\to n{a}_0(980{)}^{+}$
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$
• Three body systems with strangeness and exotic systems
• Non-conventional mesons at PANDA
• The physics of anomalous glue
• Hadron resonances generated from the dynamics of the lightest scalar ones
• Emergence of kaonium as a sharp resonance in photon-photon to meson-meson cross-sections
• $N^{\ast }(1920)(1/2^{+})$ state in the $NK\bar{K}$ system
• Roles of $a_0(980)$ and $a_0(1710)$ in Cabibbo-suppressed process $D^{+}\to {\pi }^0{\pi }^{+}\eta$
• Precise Measurement of Chromoelectric Dipole Moment of the Charm Quark
• Recent Developments in Chiral Unitary Dynamics of Resonances
• $a_0(980)$ as a companion pole of $a_0(1450)$
• The dynamically generated $h_1$ state by the $K^{\ast }{\bar{K}}^{\ast }$ interaction and its $K_1(1270)\bar{K}$ and $b_1(1235)\pi$ decays