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arXiv · 0809.4766

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

R. Kaminski·R. Garcia-Martin·P. Grynkiewicz·J. R. Pelaez·F. J. Yndurain
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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.

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R. Kaminski, R. Garcia-Martin, P. Grynkiewicz, J. R. Pelaez, F. J. Yndurain. 2008-09-27. New dispersion relations in the description of $\pi\pi$ scattering amplitudes. https://doi.org/10.1142/s0217751x09043730

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