Advertisement

Il Nuovo Cimento A (1965-1970)

, Volume 7, Issue 4, pp 797–823 | Cite as

The asymptotic behaviour of the dual pomeron amplitude

  • V. Alessandrini
  • D. Amati
  • B. Morel
Article

Summary

A rigorous derivation is given of the asymptotic properties of the one-loop nonplanar amplitude. Boths- andt-channel asymptotic behaviours are investigated. They are controlled by the expected Regge singularities and possible exponentials are ruled out. Thes-channel fixed-angle behaviour is again an exponential. The coefficient ofs in the exponential is exactly half of that obtained for the Born approximation and the planar loop.

Асимптотическое поведение дуальной амплитуды Померанчука

Реэюме

Приводится строгий вывод асимптотических свойств неплоской амплитуды с одной петлей. Исследуется асимптотическое поведение вs иt каналах. Асимптотическое поведение проверяется с помошью ожидаемых сингулярностей Редже. Воэможные зкспоненты исключаются. Поведение вs канале при фиксированном угле по-прежнему является зкспоненциальным. Козффициент приs в зкспоненте составляет ровно половину козффициента, полученного в борновском приближении и для плоской петли.

Riassunto

In questo lavoro si ottengono — in modo rigoroso — le proprietà asintotiche del diagramma duale con un cappio non planare, associato comunemente al pomerone. I comportamenti ins et sono controllati dalle corrispondenti singolarità di Regge e si escludono possibili comportamenti esponenziali. Il comportamento asintotico ad angolo fisso è un esponenziale con un coefficiente, all’esponente, metà di quello riscontrato per i diagrammi ad albero (approssimazione di Born).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    C. Lovelace:Phys. Lett.,32 B, 703 (1970);V. Alessandrini:Nuovo Cimento,2 A, 321 (1971).MathSciNetCrossRefADSGoogle Scholar
  2. (2).
    Chang Hong-Mo andJ. Paton:Nucl. Phys.,10 B, 519 (1969).Google Scholar
  3. (3).
    H. Harari:Phys. Rev. Lett.,20, 1395 (1968);P. Freund:Phys. Rev. Lett.,20, 235 (1968).CrossRefADSGoogle Scholar
  4. (4).
    C. Lovelace:Phys. Lett.,34 B, 500 (1971), and unpublished private communication.CrossRefADSGoogle Scholar
  5. (5).
    D. Gross, A. Neveu, J. Scherk andJ. Schwarz:Phys. Rev. D,2, 697 (1970).CrossRefADSGoogle Scholar
  6. (6).
    V. Alessandrini andD. Amati:Nuovo Cimento,4 A, 793 (1971).MathSciNetCrossRefADSGoogle Scholar
  7. (7).
    N. G. Van Kampen:Physica,14, 575 (1949);D. S. Jones andM. Kline:Journ. Math. Phys.,37, 1 (1958).CrossRefADSGoogle Scholar
  8. (8).
    Bateman Manuscript Project, edited byA. Erdelyi, Vol.1 (1953), p. 358.Google Scholar
  9. (9).
    V. Alessandrini andD. Amati:Phys. Lett.,29 B, 193 (1969);F. Drago andS. Matsuda:Phys. Rev.,181, 2095 (1969);D. Fivel andP. K. Mitter:Phys. Rev.,183, 1240 (1969).CrossRefADSGoogle Scholar
  10. (10).
    This result has also been derived byH. B. Nielsen (private communication) using a simple heuristic argument based on the analogue model.Google Scholar
  11. (11).
    G. Sansone andJ. Gerretsen:Lectures on the Theory of Functions of a Complex Variable, Vol.2 (Groningen, 1969).Google Scholar
  12. (12).
    V. Alessandrini andD. Amati: unpublished.Google Scholar

Copyright information

© Societá Italiana di Fisica 1972

Authors and Affiliations

  • V. Alessandrini
    • 1
    • 2
  • D. Amati
    • 3
  • B. Morel
    • 2
  1. 1.CERNGeneva
  2. 2.Institut de Physique ThéoriqueUniversité de GenèveGenève
  3. 3.CERNGeneva

Personalised recommendations