On the precision of the theoretical predictions for pi pi scattering

Abstract

In a recent paper, Pelaez and Yndurain evaluate some of the low energy observables of pi pi 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.

arXiv commentAdded more material, mostly in Sects. 7, 8 and 9, in support of the same conclusions. Latex, 28 pages, 3 figures

References in corpus (9)

• ππscattering
• Roy equation analysis of pi pi scattering
• Elastic $\pi \pi$ scattering to two loops
• Hadronic scattering amplitudes: medium-energy constraints on asymptotic behaviour
• Precision Determination of the Pion Form Factor and Calculation of the Muon $g-2$
• Analysis and interpretation of new low-energy Pi-Pi scattering data
• Pion-pion scattering at low energy
• On the precision of chiral-dispersive calculations of $\pi \pi$ scattering
• Pi-pi scattering at low energy: S-wave phase shifts and scattering lengths

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• Direct CP violation in $K^0\to \pi \pi$: Standard Model Status
• Rigorous Bounds on Light-by-Light Scattering
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• Glueball nature of the sigma/f_0(600) from pi-pi and gamma-gamma scatterings
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• Theoretical Aspects of the Pion-Pion Interaction
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• In memory of Paco Yndurain: A precise determination of pion-pion scattering from experiment and dispersion relations
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