Regge-Pole Model for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mi>p</mml:mi></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>pp</mml:mi></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>p</mml:mi></mml:math>Scattering

Rarita, William; Riddell, Robert J.; Chiu, Charles B.; Phillips, R. J.

doi:10.1103/physrev.165.1615

Cited by 231 publications

(67 citation statements)

References 69 publications

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“…Unfortunately, the authors do not offer a critical discussion of their representation, which looks similar to the Regge fit proposed by Rarita et al [13] in 1968, but the parameters are assigned different values and a comparison is not made. For a review of the current knowledge about the structure of the Pomeron, we refer to [14].…”

Section: Asymptoticsmentioning

confidence: 99%

On the precision of the theoretical predictions forππscattering

et al. 2003

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In a recent paper, Peláez and Ynduráin evaluate some of the low energy observables of ππ scattering and obtain flat disagreement with our earlier results. The authors work with unsubtracted dispersion relations, so that their results are very sensitive to the poorly known high energy behaviour of the scattering amplitude. They claim that the asymptotic representation we used is incorrect and propose an alternative one. We repeat their calculations on the basis of the standard, subtracted fixed-t dispersion relations, using their asymptotics. The outcome fully confirms our earlier findings. Moreover, we show that the Regge parametrization proposed by these authors for the region above 1.4 GeV violates crossing symmetry: Their ansatz is not consistent with the behaviour observed at low energies.

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Section: Asymptoticsmentioning

confidence: 99%

On the precision of the theoretical predictions forππscattering

et al. 2003

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“…If we do so, we cover the fits of Rarita et al [10] and of Froggatt and Petersen [11]. Note that we do not give errors for the slopes 0 and 0 …”

Section: Regge Formulasmentioning

confidence: 99%

“…[2] and, for t Þ 0, an uncertainty that covers the extreme fits in Ref. [10] for N scattering, and assume that scattering will vary in a similar manner.…”

Section: Regge Formulasmentioning

confidence: 99%

Pion-pion scattering amplitude. III. Improving the analysis with forward dispersion relations and Roy equations

2008

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We complete and improve the fits to experimental scattering amplitudes, both at low and high energies, that we performed in the previous papers of this series. We then verify that the corresponding amplitudes satisfy analyticity requirements, in the form of partial wave analyticity at low energies, forward dispersion relations (FDR) at all energies, and Roy equations below KK threshold; the first by construction, the last two, inside experimental errors. Then we repeat the fits including as constraints FDR and Roy equations. The ensuing central values of the various scattering amplitudes verify very accurately FDR and, especially, Roy equations, and change very little from what we found by just fitting data, with the exception of the D2 wave phase shift, for which one parameter moves by 1:5 . These improved parametrizations therefore provide a reliable representation of pion-pion amplitudes with which one can test various physical relations. We also present a list of low energy parameters and other observables.

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“…The forward (t ¼ 0) Regge parametrizations were obtained from fits to high energy data [5]. For the t Þ 0 behavior we [3] simply covered the uncertainties between the different fits in [40]. These Regge fits are expected to represent experimental data when 1:42 GeV s 1=2 20 GeV and 4M 2 !…”

Section: P Wavementioning

confidence: 99%

Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV

et al. 2011

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We improve our description of scattering data by imposing additional requirements on our previous fits, in the form of once-subtracted Roy-like equations, while extending our analysis up to 1100 MeV. We provide simple and ready to use parametrizations of the amplitude. In addition, we present a detailed description and derivation of these once-subtracted dispersion relations that, in the 450 to 1100 MeV region, provide an additional constraint which is much stronger than our previous requirements of forward dispersion relations and standard Roy equations. The ensuing constrained amplitudes describe the existing data with rather small uncertainties in the whole region from threshold up to 1100 MeV, while satisfying very stringent dispersive constraints. For the S0 wave, this requires an improved matching of the low and high energy parametrizations. Also for this wave we have considered the latest low energy K '4 decay results, including their isospin violation correction, and we have removed some controversial data points. These changes on the data translate into better determinations of threshold and subthreshold parameters which remove almost all disagreement with previous chiral perturbation theory and Roy equation calculations below 800 MeV. Finally, our results favor the dip structure of the S0 inelasticity around the controversial 1000 MeV region.

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Regge-Pole Model forπp,pp, andp¯pScattering

Cited by 231 publications

References 69 publications

On the precision of the theoretical predictions forππscattering

On the precision of the theoretical predictions forππscattering

Pion-pion scattering amplitude. III. Improving the analysis with forward dispersion relations and Roy equations

Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV

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