Can current algebra determine the low-energy π-π scattering amplitude?
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KeywordsCurrent Algebra Unitarity Correction Legendre Series Amplit Lehmann Ellipse
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- (2).S. Weinberg:Phys. Rev. Lett.,17, 616 (1966);N. N. Khuri:Phys. Rev.,153, 1477 (1967); For previous calculations including unitarity corrections, see:T. Akiba andK. Kang:Phys. Lett.,25 B, 35 (1967); and to be published;J. Sucher andC.-H. Woo:Phys. Rev. Lett.,18, 723 (1967);A. Donnachie: CERN preprint TH. 804 (1967).ADSCrossRefGoogle Scholar
- (3).We thank Dr.A. Martin for having pointed out this point to us.Google Scholar
- (4).The threshold behaviour of the partial-wave amplitudes can be shown if one uses the analyticity domain of the scattering amplitude proved byMartin, with the further assumption that the amplitude is bounded at threshold. For a simple and elegant proof, see:P. Moussa andR. Stora:Lectures given at the International School of Elementary-Particle Physics (Herceg Novi, 1966).Google Scholar
- (5).We have written the constant term in the formA−2E whereA represents the constant term in the expansion of the on-the-mass-shell amplitude. The same holds for the termD+E.Google Scholar
- (8).The parametersB andC are always identical in both the second, and third-order calculations because they are determined by the threshold unitarity equations which are common in both cases.Google Scholar
© Società Italiana di Fisica 1968