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The Large Coefficient Problem: Can We Make Sense Out of QCD Perturbation Theory?

  • Geoffrey B. West
Part of the NATO ASI Series book series (NSSB, volume 233)

Abstract

There is the possibility of an impending crisis looming on the horizon for QCD. The problem is that in many processes, large coefficients arise in the perturbation series expansion leading to serious uncertainties concerning its predictive power. Until recently most of the examples of such a phenomenon occurred in the calculation of decay rates. These were, by and large, either ignored or dismissed using possible scheme-dependence arguments as a way out. However, more recently a calculation of the 3-loop contribution to the total e + e - annihilation cross-section was performed which gave an enormous coefficient of the order of 50 times that of the 2-loop term(1). If correct, this would imply that the 3-loop contribution actually exceeds that of the 2-loop! Thus, from a conservative viewpoint, the validity of the perturbation series expansion as an estimate for the total e + e - cross-section is called into question. Such a cautionary attitude should even be extended to the lowest order parton-model result, Σ (Q i 2 ); (Q i being the charge of the ith quark species). Since this process has played a key role in the development and understanding of QCD and since, in many ways, it is one of the cleanest methods for extracting α 3 (the conventional QCD fine structure constant) the problem can no longer be avoided. Furthermore, there is no reason to doubt (and, in fact, good reasons to believe) that this problem should occur in all physical processes. Coming to grips with it is, of course, not only important for testing QCD but also for extracting fundamental quantities such as α s . Clearly one needs to understand the nature and origin of such large coefficients before one can confidently continue to use perturbative estimates.

Keywords

Perturbation Theory Saddle Point Large Coefficient Perturbation Series Positive Real Axis 
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References

  1. [1]
    S. G. Gorishny, A. L. Kataev and S. A. Larin, Phys. Lett. 212B, 238 (1988)ADSGoogle Scholar
  2. [2]
    F. Dyson, Phys. Rev. 85, 631 (1952)MathSciNetADSMATHCrossRefGoogle Scholar
  3. [3]
    F. Dyson, Phys. Rev. 83, 608 (1951)MathSciNetADSMATHCrossRefGoogle Scholar
  4. [4]
    R. P. Feynman, Solvay Conference 1959Google Scholar
  5. [5]
    P. M. Stevenson, Phys. Rev. D23, 2916 (1981); C. J. Maxwell,ADSGoogle Scholar
  6. [5a]
    P. M. Stevenson, Phys. Rev. D28, 2037 (1983);Google Scholar
  7. [5b]
    S. J. Brodsky, G. P. Lepage and P. B. Mackenzie, Phys. Rev. D28, 228 (1983)ADSGoogle Scholar
  8. [6]
    W. Celmaster and D. Sievers, Phys Rev. D23, 227 (1981)ADSGoogle Scholar
  9. [7]
    A. Dhar, Phys. Lett. 128B, 407 (1983)ADSGoogle Scholar
  10. [8]
    R. Barbieri et al. Nuc. Phys. B154, 535 (1979)ADSCrossRefGoogle Scholar
  11. [9]
    See, e.g., S. Raby, G. B. West and C. Hoffman, Phys. Rev. 390, 828 (1989)Google Scholar
  12. [10]
    F. Wilczek, Phys. Rev. Lett. 40, 279 (1978)ADSCrossRefGoogle Scholar
  13. [11]
    M. I. Visotsky, Phys. Lett. 97B, 159 (1980);ADSGoogle Scholar
  14. [11a]
    M. I. Visotsky, P. Nason, ibid. 175B, 233 (1986)Google Scholar
  15. [12]
    J. Lee-Franzini, Proc. XXIV Int. Conf. on High Energy Physics (Springer-Verlag, Berlin, 1989) p. 1432Google Scholar
  16. [13]
    J. Fleischer et al., Univ. of Bielefeld preprint BI-TP 05/89Google Scholar
  17. [14]
    See, e.g., G. B. West, Nuc. Phys. B288, 444 (1987)ADSCrossRefGoogle Scholar
  18. [15]
    G. B. West, Phys. Lett. 145B, 103 (1984)ADSGoogle Scholar
  19. [16]
    G. B. West, Nuc. Phys. B (Proc. Suppl.) 1A, 57 (1987ADSMATHCrossRefGoogle Scholar
  20. [17]
    E.T. Whittaker and G. N. Watson, “A Course in Modem Analysis”, Cambridge Univ. Press, 1950)Google Scholar
  21. [18]
    For a review see J. Zinn-Justin, Phys. Rep. 70, 109 (1981)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Geoffrey B. West
    • 1
  1. 1.Theoretical Division, T-8Los Alamos National LaboratoryLos AlamosUSA

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