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Simple one-parameter forms for the S and P waves of pion scattering that obey current-algebra constraints and allow for a resonance are constructed. The parameters are completely determined by solving self-consistently three subtracted forward dispersion relations in a region up to 1 GeV. Resonances for the ρ and σ are produced with the mass scale set by the pion decay constant, but the "exotic" $T=2 S$ wave is nonresonant.
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Brown et al. (1971) studied this question.
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