N/D Description of Two Meson Amplitudes and Chiral Symmetry

Abstract

The most general structure of an elastic partial wave amplitude when the unphysical cuts are neglected is deduced in terms of the N/D method. This result is then matched to lowest order, $\mathcal{O}(p^2)$, Chiral Perturbation Theory($\chi$PT) and to the exchange (consistent with chiral symmetry) of resonances in the s-channel. The extension of the method to coupled channels is also given. Making use of the former formalism, the $\pi \pi$ and $K\pi$(I=1/2) P-wave scattering amplitudes are described without free parameters when taking into account relations coming from the 1/$N_c$ expansion and unitarity. Next, the scalar sector is studied and good agreement with experiment up to $\sqrt{s}=1.4$ GeV is found. It is observed that the $a_0(980)$, $\sigma$ and $\kappa (900)$ resonances are meson-meson states originating from the unitarization of the $\mathcal{O}(p^2)$ $\chi$PT amplitudes. On the other hand, the $f_0(980)$ is a combination of a strong S-wave meson-meson unitarity effect and of a preexisting singlet resonance with a mass around 1 GeV. We have also studied the size of the contributions of the unphysical cuts to the $\pi \pi$(I=0) and $K\pi$(I=1/2) elastic S-wave amplitudes from $\chi$PT and the exchange of resonances in crossed channels up to $\sqrt{s}\approx 800$ MeV. The loops are calculated as in $\chi$PT at next to leading order. We find a small correction from the unphysical cuts to our calculated partial waves.

32 pages, LaTeX, 9 Figures. Estimations of the unphysical cuts have been done in a new section. Final version

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• Spinless mesons and glueballs mixing patterns in SU(3) flavor limit
• Insights into the nature of the $P_{cs}(4459)$
• Meson-baryon scattering in resummed baryon chiral perturbation theory using time-ordered perturbation theory
• Poles, the only true resonant-state signals, are extracted from a worldwide collection of partial wave amplitudes using only one, well controlled pole-extraction method
• Nuclear matter from the ladder resummation in terms of the experimental nucleon-nucleon scattering amplitudes
• Further considerations concerning claims for deeply bound kaon atoms and reply to criticisms
• The $\rho NN$ coupling with direct coupling and loops
• Analytical dispersive parameterization for elastic scattering of spinless particles
• Quark and glue spectroscopy of scalars and pseudoscalars in SU(3) flavor limit
• 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
• Photoproduction of $f_0(980)$ and $f_0(1500)$ resonances off a proton target
• Multibody decay analyses -- a new phenomenological model for meson-meson subamplitudes
• Baryon polarization in low-energy unpolarized meson-baryon scattering
• Chiral Partners in a Chirally Broken World
• Two, three, many body systems involving mesons
• $K^{+}$-nucleus elastic scattering revisited from perspective of partial restoration of chiral symmetry
• Chiral dynamics of hadrons in nuclei
• The role of meson interactions in the $D_s^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}\eta$ decay
• Dynamical Generation of Hyperon Resonances
• $\bar{K}$ induced formation of the $f_0(980)$ and $a_0(980)$ resonances on proton targets
• Scalar Mesons and Chiral Dynamics
• The $({\pi }^{-},\gamma \gamma )$ reaction in nuclei and the $\sigma$ meson in the medium
• Chiral dynamics with strange quarks: Mysteries and opportunities
• Asymmetry observables in e+ e- --> pi+ pi- gamma in the phi region within a chiral unitary approach
• Kaon-antikaon nuclear optical potentials and the kappa meson in the nuclear medium
• 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
• Nature of the D_0 meson in the D pi scattering with chiral symmetry
• States generated in the $K$-multi-$\rho$ interactions
• Chiral unitary approach to hadron spectroscopy
• S-wave meson scattering up to 2 GeV and its spectroscopy
• Charge asymmetries in e+e- -> pi+ pi- gamma at the phi resonance
• Unitarization and low-energy scattering data
• Universal scale factors relating mesonic fields and quark operators
• Chiral Partners and their Electromagnetic Radiation -- Ingredients for a systematic in-medium calculation
• The Relativistic Cornell-type Mechanism of Exotic Scalar Resonances
• Unitarizing non-relativistic Coulomb scattering
• Unitarity and Unitarization
• Chiral Meson Masses at Finite Temperature and Density
• Scalar isovector resonance photoproduction through the final state meson-meson interactions
• Dynamically generated resonances
• Polarized $p{K}^{-}$ scattering in Unitary Baryon Chiral Perturbation Theory
• Relativistic chiral representation of the $\pi N$ scattering amplitude I: The Goldberger-Treiman relation
• Determining Compositeness of Hadronic Resonances: the $\Lambda (1405)$ Radiative Decay and the $a_0(980)$-$f_0(980)$ Mixing
• Two-photon production of $f_0$ and $a_0$ resonances as hadronic molecules composed of two vector mesons
• Cross sections for 2-to-3 meson-meson scattering
• Amplitude determination for $MM\to MM$, $M=\pi ,K$ and cross-sections for $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0,{\pi }^0\eta$ in a chiral model
• $\Lambda (1405)$ and $\bar{\Lambda }(1405)$ in $J/\psi$ four-body decays
• Study of conventional and non-conventional scalar and vector mesons
• Pion scattering in finite volume within the Inverse Amplitude Method
• Photo- and Electron-Production of Mesons on Nucleons and Nuclei
• Revealing dipion correlations for the observed substructure near the ${\pi }^{+}{\pi }^{-}$ mass threshold in $\psi (3686)\to J/\psi {\pi }^{+}{\pi }^{-}$
• Investigating the two-pion exchange of the double charm $D{D}^{\ast }$ chiral interactions and $T_{cc}$
• $N_C$ evolution of the light meson resonances
• Recent developments in chiral dynamics of hadrons and hadrons in a nuclear medium
• Towards the (Mexican) discovery of second class currents at Belle-II
• Dynamical generation of hadronic resonances in effective models with derivative interactions
• Towards an effective field theory for vector mesons
• Chiral effective field theory for nuclear matter
• Reaction pp -> pp πππas a background for hadronic decays of the eta-prime meson
• Study $B_{(s)}^0$ decays into $\varphi$ and a scalar or vector meson
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$
• The $e^{+}{e}^{-}\to J/\psi D\bar{D}$, $J/\psi D{\bar{D}}^{\ast }$ reactions with dynamically generated resonances
• Hadron resonances generated from the dynamics of the lightest scalar ones
• Recent Developments in Chiral Unitary Dynamics of Resonances
• Three body systems with strangeness and exotic systems
• A study of the resonances $K_0^{\ast }(800)$ and $K_0^{\ast }(1430)$
• Transition form factors for $D/B$ to $a_0(980)$ from light-cone QCD sum rules
• Production of $\psi (4040)$, $\psi (4160)$, and $\psi (4415)$ mesons in strong interactions
• New c-cbar structure around 3764 MeV at BES and predictions from unquenching the confinement spectrum
• Novel method for determining the light quark mass ratio using ${\eta }^{\prime }\to \eta \pi \pi$ decays
• Wave functions for dynamically generated resonances; the two $\Lambda (1405)$ and $\Lambda (1670)$
• Chiral SU(3) Bethe Salpeter Model: Extension to SU(6) and SU(8) Spin-Flavor Symmetries
• Chiral unitary theory: application to nuclear problems
• $N^{\ast }(1920)(1/2^{+})$ state in the $NK\bar{K}$ system