The ππ S-wave scattering-length predictions of Weinberg have been tested by using dispersion sum rules for the infinite-energy cross section. Reasonable agreement is obtained with the infinite-energy cross section (≈15 mb) estimated from the factorization theorem for the Pomeranchon Regge residues. Experimental phase-shift data of Gutay et al., Walker et al., and Baton et al. are used in estimating the dispersion integrals. The analysis seems to rule out an I = 0 S-wave scattering length ⪞0.4μ-1.
D. J. George et al., "Modified Dispersion Relations and π π Scattering," Physical Review, vol. 172, no. 5, pp. 1740-1742, American Physical Society (APS), Aug 1968.
The definitive version is available at http://dx.doi.org/10.1103/PhysRev.172.1740
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