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The analytical $\pi\pi$ scattering amplitude and the light scalars
High Energy Physics - Phenomenology · Submitted 19 Nov 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The data agrees with the four-quark nature of the $\sigma (600)$ and $f_0(980)$ mesons.
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
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The abstract, sentence by sentence
In this work we construct the $\pi\pi$ scattering amplitude $T^0_0$ with regular analytical properties in the $s$ complex plane, which describes simultaneously the data on the $\pi\pi$ scattering, $\phi\to\pi^0\pi^0\gamma$ decay, and $\pi\pi\to K\bar K$ reaction. The chiral shielding of the $\sigma (600)$ meson and its mixing with the $f_0(980)$ meson are also taken into account. The data agrees with the four-quark nature of the $\sigma (600)$ and $f_0(980)$ mesons. The amplitude in the range $-5 m_\pi^2 < s < 0.64$ GeV$^2$ also agrees with results, obtained on the base of the chiral expansion, dispersion relations, and the Roy equations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this work we construct the $\pi\pi$ scattering amplitude $T^0_0$ with regular analytical properties in the $s$ complex plane, which describes simultaneously the data on the $\pi\pi$ scattering, $\phi\to\pi^0\pi^0\gamma$ decay, and $\pi\pi\to K\bar K$ reaction. | contribution 0.99 | 0.95 | 0.17 | asserted 1.00 |
| s1 | The chiral shielding of the $\sigma (600)$ meson and its mixing with the $f_0(980)$ meson are also taken into account. | method 0.74 | 0.61 | 0.06 | asserted 0.97 |
| s2 | The data agrees with the four-quark nature of the $\sigma (600)$ and $f_0(980)$ mesons. | interpretation 0.91 | 0.68 | 0.51 | asserted 0.89 |
| s3 | The amplitude in the range $-5 m_\pi^2 < s < 0.64$ GeV$^2$ also agrees with results, obtained on the base of the chiral expansion, dispersion relations, and the Roy equations. | result 0.99 | 0.66 | 0.10 | asserted 0.90 |
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The paper
Original abstract
In this work we construct the $\pi\pi$ scattering amplitude $T^0_0$ with regular analytical properties in the $s$ complex plane, which describes simultaneously the data on the $\pi\pi$ scattering, $\phi\to\pi^0\pi^0\gamma$ decay, and $\pi\pi\to K\bar K$ reaction. The chiral shielding of the $\sigma (600)$ meson and its mixing with the $f_0(980)$ meson are also taken into account. The data agrees with the four-quark nature of the $\sigma (600)$ and $f_0(980)$ mesons. The amplitude in the range $-5 m_\pi^2 < s < 0.64$ GeV$^2$ also agrees with results, obtained on the base of the chiral expansion, dispersion relations, and the Roy equations.
Human review
References
How the literature uses it
11 arXiv papers cite this in 32 sentences
Papers whose main result relates to this one's
States the same result 3 papers
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The data agrees with the four-quark nature of the $\sigma (600)$ and $f_0(980)$ mesons.
Analytical properties of the $\pi\pi$ scattering amplitude and the light scalar mesons · 1.00
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The data agree with the four-quark nature of \sigma (600) and f_0(980).
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It is shown that the data don't contradict the existence of the $\sigma (600)$ meson and yield evidence in favor of the four-quark nature of the $\sigma (600)$ and $f_0(980)$ mesons.
States a conflicting result 1 paper
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A significant gluonium component eventually mixed with \bar qq appears to be necessary for evading the previous difficulties.
The sigma and f_0(980) from Ke4 + pi-pi scatterings data · 0.90
Papers citing it · 20 sentences without a confident label
Uses its method or tool 2 papers
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The background function, suggested in Ref. [ref] to reach the correct analytical properties of the $ππ$ scattering amplitude and used above, is rather complicated and costly in computation.
Analytical $\pi\pi$ scattering amplitude and the light scalars-II · Simple background · 0.86
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The partial wave projection of these gives L_S(C_R^2,M_R,s) = C_R^2(-M_R^2/ρ_1(s) LF(M_R,s)+s) , L_D0(C_R^2,M_R,s) = C_R^2 M_R^2/ρ_1(s)( [1-3 XF^2(M_R,s)] LF(M_R,s)+6 XF(M_R,s) ) , L_D2(C_R^2,M_R,s) = C_R^2 s ρ_1(s)( [1-XF^2(M_R,s)]^2 LF(M_R,s). +2/3 XF(M_R,s).[5-3 XF^2(M_R,s)] ) , where we follow the functional forms given by [ref] : XF(M,s) = 2M^2-2m_π^2+s/s ρ_1(s), LF(M,s) = ln( XF(M,s)+1/XF(M,s)-1 ).
Comprehensive Amplitude Analysis of $\gamma\gamma \rightarrow \pi^+\pi^-, \pi^0\pi^0$ and $\overline{K} K$ below 1.5 GeV · Born terms and amplitudes for exchanges · 0.96
Uses its data or values 1 paper
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The $χ^2_data$ is constructed with the help of the same data, as in Ref. [ref] , except the $δ^0_0$ data in the region $2m_π<m<800$ MeV, where we use the [ref] results.
Analytical $\pi\pi$ scattering amplitude and the light scalars-II · Simple background · 0.99
Compares with it 2 papers
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Aiming the comparison of the results of Refs. [ref] and [ref] , we built up the S-wave $ππ$ scattering amplitude $T^0_0$ with $I=0$ with correct analytical properties in the complex $s$ plane [ref] .
Analytical $\pi\pi$ scattering amplitude and the light scalars-II · Introduction · 0.99
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Our leading-order $χ$PT$_S$ amplitude could also be compared to the results of Refs. [ref] , wherein a phenomenological $ππ$ scattering amplitude with good analyticity properties in the $s$-plane that matches the Roy-equation solution quite well was obtained from the linear $σ$ model and a simple background amplitude.
The reactions $\pi\pi\rightarrow\pi\pi$ and $\gamma\gamma\rightarrow\pi\pi$ in $\chi$PT with an isosinglet scalar resonance · Conclusion · 0.92
Cites it as background 4 papers
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The underlying assignment of the heavier nonet is almost accepted as the quark-antiquark configuration replenished with some possible gluon content [ref] , while the inner nature of scalar mesons in the lighter nonet is still not clear [ref] , even though the compact tetraquark state [ref] and the $KK̅$ bound state [ref] are the most favorite two candidates nowadays.
Probing isovector scalar mesons in the charmless three-body $B$ decays · Introduction · 0.97
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A number of studies have included $a_1$ and $b_1$ contributions [ref] , and more recently those from $f_2$ and $a_2$ exchanges have been added [ref] , in an attempt to make predictions for the $γγ$ reaction up to 1.4 GeV.
Comprehensive Amplitude Analysis of $\gamma\gamma \rightarrow \pi^+\pi^-, \pi^0\pi^0$ and $\overline{K} K$ below 1.5 GeV · $S$-matrix and QED constraints · 0.95
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There are different ways in which these scalar mesons are studied globally viz. conventional quark-antiquark states [ref] and compact multiquark states including diquark-diantiquark [ref] , meson-meson composite molecule [ref] , as well as compact structure of tetra quarks [ref] .
Semileptonic Decays of Charmed Mesons to Light Scalar Mesons · Introduction · 1.00
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