Il Nuovo Cimento A (1965-1970)

, Volume 53, Issue 2, pp 552–556 | Cite as

Can current algebra determine the low-energy π-π scattering amplitude?

  • J. Iliopoulos
Lettere alla Redazione


Current Algebra Unitarity Correction Legendre Series Amplit Lehmann Ellipse 
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  1. (1).
    J. Iliopoulos:Nuovo Cimento,52 A, 192 (1967). The unitary equation used in this paper, eq. (22), has the wrong sign. Figure 1 and eqs. (34) and (35) should be changed accordingly.ADSCrossRefGoogle Scholar
  2. (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. (3).
    We thank Dr.A. Martin for having pointed out this point to us.Google Scholar
  4. (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. (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
  6. (6).
    S. L. Adler:Phys. Rev.,137, B 1022 (1965);139, B 1638 (1965).ADSMathSciNetCrossRefGoogle Scholar
  7. (7).
    A. Martin:Nuovo Cimento,47 A, 265 (1967);A. Martin andY. S. Jin:Phys. Rev.,135, B 1369 (1964). The range of validity of (7c) has been extended in the region 1.7≤s≤2 byCommon.ADSCrossRefGoogle Scholar
  8. (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
  9. (9).
    See, for example,T. Akiba andK. Kang:Phys. Lett.,25 B, 35 (1967); and to be published;A. Donnachie: CERN preprint TH. 804 (1967).ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica 1968

Authors and Affiliations

  • J. Iliopoulos
    • 1
  1. 1.CERNGeneva

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