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Two Meson Scattering Amplitudes and their Resonances from Chiral Symmetry and the N/D Method
High Energy Physics - Phenomenology · Submitted 28 Aug 1999
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Making use of this formalism one observes that the \sigma, \kappa and a_0(980) resonances are meson-meson states originating from the unitarization of the lowest order \chiPT amplitudes.
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We study the vector and scalar meson-meson amplitudes up to \sqrt{s}\lesssim 1.4 GeV and their associated spectroscopy. The study has been done considering jointly the N/D method, Chiral Symmetry and implications from large N_c QCD. The N/D method provides us with the way to unitarize the tree level amplitudes constructed in agreement with Chiral Symmetry and its breaking (explicit and spontaneous). These amplitudes are calculated making use of the lowest order Chiral Perturbation Theory (\chiPT) Lagrangians and the exchanges of resonances compatible with Chiral Symmetry as given in. On the other hand the large N_c considerations allow us to distinguish between elementary (as elementary as the pions, for instance) and compound (meson-meson) states. Making use of this formalism one observes that the \sigma, \kappa and a_0(980) resonances are meson-meson states originating from the unitarization of the lowest order \chiPT 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the vector and scalar meson-meson amplitudes up to \sqrt{s}\lesssim 1.4 GeV and their associated spectroscopy. | contribution 0.99 | 0.92 | 0.06 | asserted 0.93 |
| s1 | The study has been done considering jointly the N/D method, Chiral Symmetry and implications from large N_c QCD. | method 0.92 | 0.87 | 0.04 | asserted 0.97 |
| s2 | The N/D method provides us with the way to unitarize the tree level amplitudes constructed in agreement with Chiral Symmetry and its breaking (explicit and spontaneous). | method 1.00 | 0.41 | 0.06 | asserted 1.00 |
| s3 | These amplitudes are calculated making use of the lowest order Chiral Perturbation Theory (\chiPT) Lagrangians and the exchanges of resonances compatible with Chiral Symmetry as given in. | method 1.00 | 0.80 | 0.04 | asserted 0.99 |
| s4 | On the other hand the large N_c considerations allow us to distinguish between elementary (as elementary as the pions, for instance) and compound (meson-meson) states. | method 0.93 | 0.37 | 0.05 | asserted 0.96 |
| s5 | Making use of this formalism one observes that the \sigma, \kappa and a_0(980) resonances are meson-meson states originating from the unitarization of the lowest order \chiPT amplitudes. | result 0.96 | 0.88 | 0.42 | asserted 0.98 |
| s6 | 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. | result 0.89 | 0.84 | 0.17 | asserted 1.00 |
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Original abstract
We study the vector and scalar meson-meson amplitudes up to \sqrt{s}\lesssim 1.4 GeV and their associated spectroscopy. The study has been done considering jointly the N/D method, Chiral Symmetry and implications from large N_c QCD. The N/D method provides us with the way to unitarize the tree level amplitudes constructed in agreement with Chiral Symmetry and its breaking (explicit and spontaneous). These amplitudes are calculated making use of the lowest order Chiral Perturbation Theory (\chiPT) Lagrangians and the exchanges of resonances compatible with Chiral Symmetry as given in. On the other hand the large N_c considerations allow us to distinguish between elementary (as elementary as the pions, for instance) and compound (meson-meson) states. Making use of this formalism one observes that the \sigma, \kappa and a_0(980) resonances are meson-meson states originating from the unitarization of the lowest order \chiPT 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.
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States the same result 1 paper
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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.
N/D Description of Two Meson Amplitudes and Chiral Symmetry · 1.00
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