Abstract: The de Alfaro-Fubini-Furlan-Rossetti assumption on the rapid falloff of amplitudes corresponding to pure $I=2$, $t$-channel exchange is applied to pion-pion forward dispersion relations, and a sum rule is obtained for the pion-pion scattering lengths. The sum rule is fairly well satisfied using the $\ensuremath{\rho}$, $f$, and low-energy $s$-wave contributions; but the inclusion of the recently discovered ${g}_{1}$ resonance requires the existence of at least one new $I=0$ resonance to satisfy the sum rule.
Publication Year: 1967
Publication Date: 1967-10-25
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 5
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