Advertisement

Il Nuovo Cimento (1955-1965)

, Volume 25, Issue 1, pp 104–134 | Cite as

Partial wave dispersion relations for photon-nucleon scattering and nucleon-antinucleon production by photons

  • A. P. Contogouris
Article

Summary

Partial wave dispersion relations for the processes γ
→→γ+
and γ+γ→
+
to the ordere2 are derived with the help of the Mandelstam representation. The angular momentum decomposition for both processes is carried out and the analytic properties of the partial wave amplitudes are determined. The absorptive parts of these amplitudes along part of the physical branch cuts are calculated by means of the unitarity condition. For γ+
→γ+
the resulting expressions involve amplitudes for single pion photoproduction; for γ+γ→
+
they involve theT=0s-wave pion-pion phase shift and the total cross-section for the process γ+π→π+π. The discontinuities along the unphysical branch cuts are calculated by means of crossing symmetry and of analytic continuation through Legendre polynomials. The limits of convergence of the Legendre expansions are discussed and reasons for the importance of the two-pion exchange contribution in photon-nucleon scattering are presented.

Riassunto

In base alla rappresentazione di Mandelstam si deducono le relazioni di dispersione dell’onda parziale per i processi γ+
→γ+
e γ+d→
+
fino all’ordinee2. Si fa la scomposizione del momento angolare per entrambi i processi e si determinano le proprietà analitiche delle ampiezze dell’onda parziale. Per mezzo della condizione di unitarietà si calcolano, lungo una parte dei tagli del ramo fisico, le parti assorbenti di queste ampiezze. Per γ+
→γ+
le espressioni risultanti coinvolgono ampiezze per la fotoproduzione di singoli pioni; per γ+γ→
+
coinvolgono lo spostamento di fase pione-pione in ondas conT=0 e la sezione d’urto totale del processo γ+π→π+π. A mezzo della simmetria incrociata e della continuazione analitica ćon polinomi di Legendre si calcolano le discontinuità lungo i tagli del ramo non fisico. Si discutono i limiti di convergenza degli sviluppi di Legendre e si danno le ragioni dell’importanza del contributo dello scambio di due pioni nello scattering fotone-nucleone.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    M. Gell-Mann, M. Goldberger andW. Thirring:Phys. Rev.,95, 1612 (1954).MathSciNetADSCrossRefMATHGoogle Scholar
  2. (2).
    R. H. Capps:Phys. Rev.,106, 1031 (1957);108, 1032 (1957).ADSCrossRefMATHGoogle Scholar
  3. (3).
    J. Mathews andM. Gell-Mann:Bull. Am. Phys. Soc.,2, 392 (1957);J. Mathews:Ph. D. Thesis, California Institute of Technology (1957), unpublished.Google Scholar
  4. (4).
    T. Akiba andI. Sato:Progr. Theor. Phys.,19, 93 (1958).ADSCrossRefMATHGoogle Scholar
  5. (5).
    L. I. Lapidus andChou Kuang-Chao:Žurn. Ėksp. Teor. Fiz.,37, 1714 (1959) (trans.Sov. Phys. JETP,10, 1213 (1960));38, 201 (1960) (trans.Sov. Phys. JETP,11, 47 (1960)).Google Scholar
  6. (6).
    G. F. Chew:Proc. of the Annual International Conference on High-Energy Physics at CERN (1958), p. 98.Google Scholar
  7. (7).
    M. Jacob andJ. Mathews:Phys. Rev.,117, 854 (1960);L. G. Hyman, R. Ely, D. H. Frisch andM. A. Wahlig:Phys. Rev. Lett.,3, 93 (1959).ADSCrossRefGoogle Scholar
  8. (8).
    G. Bernardini, A. O. Hanson, A. C. Odian, T. Yamagata, L. B. Auerbach andI. Filosofo:Nuovo Cimento,18, 1203 (1960);K. Berkelman;Nuovo Cimento,21, 633 (1961).CrossRefGoogle Scholar
  9. (9).
    L. I. Lapidus andChou Kuang-chao: Dubna preprint D-681.Google Scholar
  10. (10).
    A. P. Contogouris:Nuovo Cimento,21, 674 (1961).CrossRefGoogle Scholar
  11. (11).
    S. Mandelstam:Phys. Rev.,112, 1344 (1958);115, 1741, 1752 (1959).MathSciNetADSCrossRefGoogle Scholar
  12. (13).
    G. F. Chew, M. L. Goldberger, F. E. Low andY. Nambu:Phys. Rev.,106, 1337 (1957).MathSciNetADSCrossRefMATHGoogle Scholar
  13. (14).
    V. I. Ritus:Žurn. Ėksp. Teor. Fiz.,32, 1536 (1957) (transl.Sov. Phys. JETP,5, 1249 (1957)).Google Scholar
  14. (15).
    A. P. Contogouris:Phys. Rev.,124, 912 (1961).ADSCrossRefGoogle Scholar
  15. (16).
    G. F. Chew:S-matrix theory of strong interactions (New York, 1961);C. De-Witt andR. Omnès:Dispersion relations and elementary particles, lecture byChew (New York, 1961);G. F. Chew:Ann. Rev. Nucl. Sci.,9, 29 (1959).Google Scholar
  16. (17).
    M. Sugawara andA. Kanazawa:Phys. Rev.,123, 1895 (1961).MathSciNetADSCrossRefMATHGoogle Scholar
  17. (19).
    W. R. Frazer andJ. R. Fulco:Phys. Rev.,119, 1420 (1960);S. C. Frautschi andJ. D. Walecka:Phys. Rev.,120, 1486 (1960).MathSciNetADSCrossRefMATHGoogle Scholar
  18. (20).
    G. F. Chew, M. L. Goldberger, F. E. Low andY. Nambu:Phys. Rev.,106, 1345 (1957).MathSciNetADSCrossRefMATHGoogle Scholar
  19. (21).
    R. F. Peierls:Phys. Rev. Lett.,1, 174 (1958);J. J. Sakurai:Phys. Rev. Lett.,1, 258 (1958);P. C. Stein:Phys. Rev. Lett.,2, 240 (1958).ADSCrossRefGoogle Scholar
  20. (22).
    R. F. Blackie, A. Engler andJ. H. Mulvey:Phys. Rev. Lett.,5, 384 (1960);V. Glaser andR. A. Ferrell:Phys. Rev.,121, 886 (1961);A. V. Tollestrup, S. Berman, R. Gomez andH. Ruderman:Proc. of the 1960 Annual Intern. Conf. on High-Energy Physics at Rochester (New York) p. 27.ADSCrossRefGoogle Scholar
  21. (23).
    M. L. Goldberger andS. B. Treiman:Nuovo Cimento,9, 451 (1958).CrossRefGoogle Scholar
  22. (25).
    W. R. Frazer andJ. R. Fulco:Phys. Rev.,117, 1609 (1960).MathSciNetADSCrossRefGoogle Scholar
  23. (26).
    M. Jacob andG. C. Wick:Ann. of Phys.,7, 404 (1959).MathSciNetADSCrossRefMATHGoogle Scholar
  24. (28).
    S. Mandelstam:Phys. Rev. Lett.,4, 84 (1960).ADSCrossRefMATHGoogle Scholar
  25. (29).
    M. Gourdin andA. Martin:Nuovo Cimento,17, 224 (1960).CrossRefMATHGoogle Scholar
  26. (30).
    B. R. Desai:Phys. Rev.,124, 1248 (1961).ADSCrossRefGoogle Scholar
  27. (32).
    In defining theS-matrix and the partial helicity amplitudes for γγ→ππ we have followed the notation of ref. (30); as a result, the factor 8πt appears in (9.2).ADSCrossRefGoogle Scholar
  28. (33).
    H. A. Bethe andF. de Hoffman:Mesons and Fields, vol.2, 1st edition (New York, 1900);W. D. Walker, J. Davis andW. D. Shephard:Phys. Rev.,118, 1612 (1960).Google Scholar
  29. (34).
    E. T. Whittaker andG. N. Watson:A Course of Modern Analysis (Cambridge, 4-th ed., 1952), p. 322.Google Scholar
  30. (35).
    R. Oehme andJ. G. Taylor:Phys. Rev.,113, 371 (1959).MathSciNetADSCrossRefMATHGoogle Scholar
  31. (36).
    The spin of η0 is not conclusively known yet. In fact, some recent investigations (Phys. Rev. Lett.,8, 114, 329, 336 (1962)) seem to favorJ=0; in that case the present argument does not apply.Google Scholar
  32. (37).
    The same hypothesis was used byB. R. Desai (ref. (30)) in order to explain the smallness of theT=J=1 pion-pion contribution to the cross-section for Compton scattering on pions.ADSCrossRefGoogle Scholar
  33. (38).
    J. S. Ball:Phys. Rev. Lett.,5, 73 (1960);Phys. Rev.,124, 2014 (1961).ADSCrossRefGoogle Scholar
  34. (39).
    How-sen Wong:Phys. Rev. Lett.,5, 70 (1960); also Lawrence Radiation Laboratory Document UCRL-9251.ADSCrossRefGoogle Scholar
  35. (41).
    D. Hall andA. S. Wightman:Mat. Fys. Medd. Dan. Vid. Selsk.,31, no. 5 (1957).Google Scholar
  36. (42).
    A. C. Hearn:Nuovo Cimento,21, 333 (1961); see also ref. (5).MathSciNetCrossRefMATHGoogle Scholar
  37. (44).
    F. E. Low:Phys. Rev.,96, 1428 (1954);M. Gell-Mann andM. L. Goldberger:Phys. Rev.,96, 1433 (1954).MathSciNetADSCrossRefMATHGoogle Scholar

Copyright information

© Società Italiana di Fisica 1962

Authors and Affiliations

  • A. P. Contogouris
    • 1
  1. 1.Laboratory of Nuclear StudiesCornell UniversityIthaca

Personalised recommendations