Analytical $\pi\pi$ scattering amplitude and the light scalars-II

A.V. Kiselev; N.N. Achasov

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Analytical $\pi\pi$ scattering amplitude and the light scalars-II

N.N. Achasov, A.V. Kiselev

High Energy Physics - Phenomenology · Submitted 31 Jan 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In particular, we show that the minimization of the $\sigma-f_0$ mixing results in the four-quark scenario for light scalars: the $\sigma$(600) coupling with the $K\bar K$ channel is suppressed relatively to the coupling with the $\pi\pi$ channel, and the $f_0$(980) coupling with the $\pi\pi$ channel is suppressed relatively to the coupling with the $K\bar K$ channel.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.90 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.20 · compares with prior results 0.91 · mentions code or data availability 0.02.

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In the paper Phys. Rev. {\bf D83}, 054008 (2011) we constructed the $\pi\pi$ scattering amplitude $T^0_0$ with regular analytical properties in the $s$ complex plane, describing both experimental data and the results based on chiral expansion and Roy equations. Now the results obtained during development of our work are presented. We dwell on questions dealing with the low $\sigma-f_0$ mixing, inelasticity description and the kaon loop model for $\phi\to \gamma(\sigma+f_0)$ reaction, and show a number of new fits. In particular, we show that the minimization of the $\sigma-f_0$ mixing results in the four-quark scenario for light scalars: the $\sigma$(600) coupling with the $K\bar K$ channel is suppressed relatively to the coupling with the $\pi\pi$ channel, and the $f_0$(980) coupling with the $\pi\pi$ channel is suppressed relatively to the coupling with the $K\bar K$ channel. The correct analytical properties of the $\pi\pi$ scattering amplitude are reached with the help of rather complicated background function. We also suggest much more simple background parameterization, practically preserving the resonance features, which is comfortable for experimental data analysis, but allows to describe the results based on chiral expansion and Roy equations only on the real $s$ axis.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In the paper Phys. Rev. {\bf D83}, 054008 (2011) we constructed the $\pi\pi$ scattering amplitude $T^0_0$ with regular analytical properties in the $s$ complex plane, describing both experimental data and the results based on chiral expansion and Roy equations.	background 0.92	0.85	0.06	asserted 1.00
s1	Now the results obtained during development of our work are presented.	contribution 0.76	0.51	0.02	asserted 0.58
s2	We dwell on questions dealing with the low $\sigma-f_0$ mixing, inelasticity description and the kaon loop model for $\phi\to \gamma(\sigma+f_0)$ reaction, and show a number of new fits.	contribution 1.00	0.83	0.08	asserted 0.95
s3	In particular, we show that the minimization of the $\sigma-f_0$ mixing results in the four-quark scenario for light scalars: the $\sigma$(600) coupling with the $K\bar K$ channel is suppressed relatively to the coupling with the $\pi\pi$ channel, and the $f_0$(980) coupling with the $\pi\pi$ channel is suppressed relatively to the coupling with the $K\bar K$ channel.	result 0.91	0.92	0.70	asserted 1.00
s4	The correct analytical properties of the $\pi\pi$ scattering amplitude are reached with the help of rather complicated background function.	method 0.93	0.80	0.06	asserted 1.00
s5	We also suggest much more simple background parameterization, practically preserving the resonance features, which is comfortable for experimental data analysis, but allows to describe the results based on chiral expansion and Roy equations only on the real $s$ axis.	contribution 0.59	0.88	0.11	hedged possibility 0.60

What kind of paper the classifier reports this is: theoretical result 0.92 · evidence from analysis of existing data 0.46.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

In the paper Phys. Rev. {\bf D83}, 054008 (2011) we constructed the $\pi\pi$ scattering amplitude $T^0_0$ with regular analytical properties in the $s$ complex plane, describing both experimental data and the results based on chiral expansion and Roy equations. Now the results obtained during development of our work are presented. We dwell on questions dealing with the low $\sigma-f_0$ mixing, inelasticity description and the kaon loop model for $\phi\to \gamma(\sigma+f_0)$ reaction, and show a number of new fits. In particular, we show that the minimization of the $\sigma-f_0$ mixing results in the four-quark scenario for light scalars: the $\sigma$(600) coupling with the $K\bar K$ channel is suppressed relatively to the coupling with the $\pi\pi$ channel, and the $f_0$(980) coupling with the $\pi\pi$ channel is suppressed relatively to the coupling with the $K\bar K$ channel. The correct analytical properties of the $\pi\pi$ scattering amplitude are reached with the help of rather complicated background function. We also suggest much more simple background parameterization, practically preserving the resonance features, which is comfortable for experimental data analysis, but allows to describe the results based on chiral expansion and Roy equations only on the real $s$ axis.

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Compares with it 1 paper

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

What it cites · 8 sentences without a confident label

Uses the method or tool of 1 paper

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.

The analytical $\pi\pi$ scattering amplitude and the light scalars · Simple background · 0.86

Uses data or values from 1 paper

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.

The analytical $\pi\pi$ scattering amplitude and the light scalars · Simple background · 0.99

Compares with 1 paper

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] .

The analytical $\pi\pi$ scattering amplitude and the light scalars · Introduction · 0.99

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