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Abstract
Using crossing relations on the physical region between the P- and I = 2 S-waves, we estimate the range of ππ scattering lengths allowed by ϱ meson existence. We discuss the difference of our result with some model predictions. We emphasize in particular the role of virtual bound states poles in parametrizations based on current algebra and unitarity constraints. The values of the S-wave scattering lengths can be restricted when some experimental information about the S-waves is added, and improved phenomenological lower bounds may then be obtained.
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