New dispersion relations in the description of $\pi \pi$ scattering amplitudes

Abstract

We present a set of once subtracted dispersion relations which implement crossing symmetry conditions for the $\pi \pi$ scattering amplitudes below 1 GeV. We compare and discuss the results obtained for the once and twice subtracted dispersion relations, known as Roy's equations, for three $\pi \pi$ partial JI waves, S0, P and S2. We also show that once subtracted dispersion relations provide a stringent test of crossing and analyticity for $\pi \pi$ partial wave amplitudes, remarkably precise in the 400 to 1.1 GeV region, where the resulting uncertainties are significantly smaller than those coming from standard Roy's equations, given the same input.

8 pages, 2 figures, to appear in the Proceedings of the Meson 2008 conference, June 6-10, 2008, Cracow, Poland

References in corpus (5)

• ππscattering
• A new measurement of K+(e4) decay and the s-wave pi-pi-scattering length a00
• The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations
• Analysis and interpretation of new low-energy Pi-Pi scattering data
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Cited by in corpus (5)

• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
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• Dispersive $\pi K\to \pi K$ and $\pi \pi \to K\bar{K}$ amplitudes from scattering data, threshold parameters and the lightest strange resonance $\kappa$ or $K_0^{\ast }(700)$
• Self-consistent statistical error analysis of $\pi \pi$ scattering
• Dispersive determination of resonances from $\pi \pi$ scattering data