Skip to main content
SpringerLink
Log in

Impact-parameter amplitudes

Амплитуды в представлении прицельного параметра

  • Published:
Il Nuovo Cimento A (1965-1970)

Summary

The structure of impact-parameter functions is investigated for several versions of the impact-parameter representation defined for two-particle scattering amplitudes which satisfy Mandelstam analyticity and polynomial bounds.

Riassunto

Si è ricercata la struttura delle funzioni dei parametri d’urto per varie versioni della rappresentazione dei parametri d’urto definita per ampiezza della diffusione di due particelle che soddisfano la condizione di analiticità di Mandelstam e limiti polinomiali.

Реэюме

Исследуется структура функций прицельного параметра для нескольких вариантов представления прицельного параметра, определенного для амплитуд рассеяния двух частиц, которые удовлетворяют аналитичности Манделстама и полиномиальным границам.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. J. Galuber:Lectures in Theoretical Physics, Vol.1 (New York, N. Y., 1959), p. 315.

    Google Scholar 

  2. R. Blankenbecler andM. L. Goldberger:Phys. Rev.,126, 766 (1962).

    Article  MathSciNet  ADS  Google Scholar 

  3. W. N. Cottingham andR. F. Peierls:Phys. Rev.,137, B 147 (1965).

    Google Scholar 

  4. M. M. Islam:Lectures in Theoretical Physics, Vol.10 B (New York, London, Paris, 1968), p. 97.

    Google Scholar 

  5. (seee.g. ref.(5)p. 236)

  6. W. Magnus, F. Oberhettinger andR. P. Soni:Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd ed. (Berlin, Heidelberg, New York, 1966).

  7. A. H. Zemanian:Generalized Integral Transforms (New York, London, Sydney, Toronto, 1968).

  8. R. Henzi:Nuovo Cimento,46 A, 370 (1966).

    Article  ADS  Google Scholar 

  9. J. Kupsch andI. O. Stamatescu:Nuovo Cimento,15 A, 663 (1973).

    Article  ADS  Google Scholar 

  10. T. Adachi andT. Kotani:Suppl. Progr. Theor. Phys., Extra Number, 316 (1965);T. Adachi:Progr. Theor. Phys.,35, 463 (1966);T. Adachi andT. Kotani:Progr. Theor. Phys.,35, 485 (1966);39, 430, 785 (1968).

  11. The existence of such functions is incompatible with the bounds derived byMartin for form factors (10).

  12. A. Martin:Nuovo Cimento,37, 671 (1965).

    Article  Google Scholar 

  13. We use the notations of ref. (11).

  14. I. M. Gelfand andG. E. Shilov:Generalized Functions, Vol.1 (New York and London, 1963).

  15. I. S. Gradshteyn andI. M. Ryzhik:Tables of Integrals, Series and Products (New York and London, 1965).

  16. E. Predazzi:Ann. of Phys.,36, 228 (1966).

    Article  MathSciNet  ADS  Google Scholar 

  17. Unitarity still allows for logarithmic singularities within the physical region (14) and does not lead to a restriction of the singularities in the double-spectral regions.

  18. A. Martin: CERN Report TH 727 (1967).

  19. The domain of holomorphy can be taken smaller than the domain of Mandelstam analyticity, see ref. (7).

    Article  ADS  Google Scholar 

  20. T. Kinoshita, J. J. Loeffel andA. Martin:Phys. Rev.,135, B 1464 (1964).

    Google Scholar 

  21. G. Höhler andH. P. Jakob:Zeits. Phys.,261, 371 (1973);G. Höhler:Strong Interaction Physics, Lecture Notes in Physics, Vol.17 (Berlin, Heidelberg, New York, 1973), p. 21.

    Article  ADS  Google Scholar 

  22. For an explicit calculation of the BG transform of a Veneziano ansatz see ref. (17)

    Article  ADS  Google Scholar 

  23. T. Obara:Progr. Theor. Phys.,49, 586 (1973).

    Article  ADS  Google Scholar 

  24. F. Zachariasen:Phys. Rep.,2 C, 1 (1971).

    Article  ADS  Google Scholar 

  25. B. Schrempp andF. Schrempp: CERN preprint TH 1641 (1973).

  26. M. G. Schmidt andI. O. Stamatescu:Lett. Nuovo Cimento,3, 645 (1972).

    Article  Google Scholar 

  27. H. D. I. Abarbanel:Strong Interaction Physics, Lecture Notes in Physics, Vol.17 (Berlin, Heidelberg, New York, 1973), p. 146.

    Article  ADS  MATH  Google Scholar 

  28. We use the notation of ref. (11).

Download references

Author information

Authors and Affiliations

  1. Fachbereich Physik, Universität Trier-Kaiserslautern, Kaiserslautern

    J. Kupsch

  2. Institut für theoretische Physik, Universität Heidelberg, Heidelberg

    I. O. Stamatescu

Authors
  1. J. Kupsch
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. O. Stamatescu
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kupsch, J., Stamatescu, I.O. Impact-parameter amplitudes. Nuov Cim A 20, 317–353 (1974). https://doi.org/10.1007/BF02821096

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02821096

Search

Navigation