The Status of ξ-Scaling

  • H. David Politzer
Part of the Studies in the Natural Sciences book series (SNS, volume 12)


The logic of the “ξ-scaling” analysis of inclusive lepton-hadron scattering is reviewed with the emphasis on clarifying what is assumed and what is predicted. The physics content of several recent papers, which purport to criticize this analysis, in fact confirm its validity and utility. For clarity, I concentrate on the orthodox operator product analysis of electroproduction, local duality and precocious scaling. Other physics discussed includes the successes of QCD in the rate of charm production in muon inelastic scattering and in the energy-momentum sum rule. Gluons carry 30 ± 8% of the proton’s energy-momentum at Q2 = 3.5 GeV2. (Several considerations make this considerably smaller than previous estimates; the largest of these is the inclusion of gluon bremsstrahlung effects.)

Can QCD be tested against the available data on inclusive lepton scattering? This question appears absurd given that a major reason for interest in QCD is its explanation of the observed approximate scaling. Yet the question is serious, and its answer is complex. A recent series of papersl,2,3,4 addresses this issue and concludes that the answer is yes. Certainly, much of the evidence is qualitative and, at best, not even good for two significant figures. And since we still don’t know what a proton looks like in QCD, we may yet be barking up the wrong tree.


Structure Function Operator Product Expansion Gluon Distribution Feynman Graph Final State Interaction 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Georgi and H. D. Politzer, Phys. Rev. D14, 1829 (1976)Google Scholar
  2. H. Georgi and H. D. Politzer, Phys. Rev. Lett. 36, 1281 (1976).CrossRefGoogle Scholar
  3. 2.
    A. De Rújula, H. Georgi and H. D. Politzer, Ann. Phys. (to be published) and Phys. Lett. 64B, 428 (1976).CrossRefGoogle Scholar
  4. 3.
    A. De Rújula, H. Georgi and H. D. Politzer, “Trouble with c-Scaling?”, Harvard preprint HUTP-76/A179 (12/76).Google Scholar
  5. 4.
    H. D. Politzer, “u-P Scattering and the Glue Fraction of the Proton”, Harvard preprint HUTP-77/A001 (1/77).Google Scholar
  6. 5.
    V. Baluni and E. Eichten, Institute for Advanced Study Report No. C00–2220–76 (1976).Google Scholar
  7. 6.
    R. K. Ellis, G. Parisi and R. Petronzio, “Mass Dependent Corrections to the Bjorken Scaling Law”, University of Rome preprint (1976).Google Scholar
  8. 7.
    R. Barbieri, J. Ellis, M. K. Gaillard and G. G. Ross, Phys. Lett. 64B, 171 (1976)Google Scholar
  9. R. Barbieri, J. Ellis, M. K. Gaillard and G. G. Ross, CERN preprint TH2223CERN (1976).Google Scholar
  10. 8.
    D. J. Gross, S. B. Treiman and F. A. Wilczek, “Mass Corrections in Deep Inelastic Scattering”, Princeton preprint (1976).Google Scholar
  11. 9.
    E. D. Bloom and F. J. Gilman, Phys. Rev. D4, 2901 (1971).Google Scholar
  12. 10.
    K. Wilson, Phys. Rev. 179, 1499 (1969).CrossRefGoogle Scholar
  13. 11.
    R. Brandt and G. Preparata, Nucl. Phys. B27, 541 (1971).CrossRefGoogle Scholar
  14. 12.
    N. Christ, B. Hasslacher and A. Mueller, Phys. Rev. D6, 3543 (1972).CrossRefGoogle Scholar
  15. 13.
    H. D. Politzer, Phys. Reports 14C, 129 (1974).CrossRefGoogle Scholar
  16. 14.
    O. Nachtmann, Nucl. Phys. B63, 237 (1973).CrossRefGoogle Scholar
  17. 15.
    D. J. Gross and S. B. Treiman, Phys. Rev. D4, 1059 (1971).Google Scholar
  18. 16.
    R. Jaffe, Phys. Rev. D11, 1953 (1975).Google Scholar
  19. 17.
    E. Riordan et al., SLAC-PUB 1634 (8/75).Google Scholar
  20. 18.
    See R. M. Barnett’s and H. Georgi’s contributions to this conference.Google Scholar
  21. 19.
    G. C. Fox, unpublished.Google Scholar
  22. 20.
    E. Witten, Nucl. Phys. B104, 445 (1976).CrossRefGoogle Scholar
  23. 21.
    K. W. Chen in Pnoceed.íngd oli the Intennat.Lona.e Conienence on New Pant c.2ed with New Quantum Numbend ( University of Wisconsin, Madison, 1976 ).Google Scholar
  24. 22.
    H. Anderson et al., “Measurement of the Proton Structure Function”, submitted to the conference proceedings, Tbilisi, 1976.Google Scholar
  25. 23.
    D. H. Perkins, in XVI In,tennat ona. 2 Conbekence on High Enengy Phydicd - Chicago 1972 ( NAL, Batavia, 1972 ).Google Scholar

Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • H. David Politzer
    • 1
  1. 1.Harvard UniversityCambridgeUSA

Personalised recommendations