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.

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