Abstract
We derive an exact relation for ππ scattering which yields the real parts of the ππ partial wave amplitudes a l ( I) (s) in the region 4 m 2 π ⩽ s ⩽ 60 m 2 π , is given i) the I = 0 and the I = 2 S wave scattering lengths and ii) the 1m a l ( I) (s) for 4 m 2 π ⩽ s ⩽ ∞, where s denotes the centre-of-mass energy, l the angular momentum and I the isotopic spin. It also provides i) a system of integral equations to determine the a l ( I) (s) for 4 m 2 π ⩽ s ⩽ 16 m 2 π , 16 2 π ⩽ s ⩽ ∞, and ii) necessary and sufficient conditions for crossing symmetry expressed in terms of the physical region partial wave amplitudes only.
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