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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

Keywords

Current Algebra Unitarity Correction Legendre Series Amplit Lehmann Ellipse 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  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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