Advertisement

Renormalization scale-fixing for complex scattering amplitudes

  • S.J. BrodskyEmail author
  • F.J. Llanes-Estrada
Theoretical Physics

Abstract

We show how to fix the renormalization scale for hard-scattering exclusive processes such as deeply virtual meson electroproduction by applying the BLM prescription to the imaginary part of the scattering amplitude and employing a fixed-t dispersion relation to obtain the scale-fixed real part. In this way, we resolve the ambiguity in BLM renormalization scale-setting for complex scattering amplitudes. We illustrate this by computing the H generalized parton distribution at leading twist in an analytic quark-diquark model for the parton-proton scattering amplitude that can incorporate Regge exchange contributions characteristic of the deep inelastic structure functions.

Keywords

Field Theory Quantum Field Theory Imaginary Part Regge Exchange Dispersion Relation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S.J. Brodsky, G.P. Lepage, P.B. Mackenzie, Phys. Rev. D 28, 228 (1983)CrossRefADSGoogle Scholar
  2. 2.
    S.J. Brodsky, C.R. Ji, A. Pang, D.G. Robertson, Phys. Rev. D 57, 245 (1998) [arXiv:hep-ph/9705221]CrossRefADSGoogle Scholar
  3. 3.
    G. Grunberg, A.L. Kataev, Phys. Lett. B 279, 352 (1992)CrossRefADSGoogle Scholar
  4. 4.
    S.J. Brodsky, E. Gardi, G. Grunberg, J. Rathsman, Phys. Rev. D 63, 094017 (2001) [arXiv:hep-ph/0002065]CrossRefADSGoogle Scholar
  5. 5.
    S.J. Brodsky, M.S. Gill, M. Melles, J. Rathsman, Phys. Rev. D 58, 116006 (1998) [arXiv:hep-ph/9801330]CrossRefADSGoogle Scholar
  6. 6.
    E.C.G. Stueckelberg, A. Petermann, Helv. Phys. Acta 26, 499 (1953)zbMATHMathSciNetGoogle Scholar
  7. 7.
    S.J. Brodsky, G.T. Gabadadze, A.L. Kataev, H.J. Lu, Phys. Lett. B 372, 133 (1996) [arXiv:hep-ph/9512367]CrossRefADSGoogle Scholar
  8. 8.
    S.J. Brodsky, H.J. Lu, arXiv:hep-ph/9601301Google Scholar
  9. 9.
    S.J. Brodsky, P. Huet, Phys. Lett. B 417, 145 (1998) [arXiv:hep-ph/9707543]MathSciNetCrossRefADSGoogle Scholar
  10. 10.
    M. Gell-Mann, F.E. Low, Phys. Rev. 95, 1300 (1954)zbMATHMathSciNetCrossRefADSGoogle Scholar
  11. 11.
    J.M. Cornwall, Phys. Rev. D 26, 1453 (1982)CrossRefADSGoogle Scholar
  12. 12.
    T. Appelquist, M. Dine, I.J. Muzinich, Phys. Rev. D 17, 2074 (1978)CrossRefADSGoogle Scholar
  13. 13.
    S.J. Brodsky, M. Melles, J. Rathsman, Phys. Rev. D 60, 096006 (1999) [arXiv:hep-ph/9906324]CrossRefADSGoogle Scholar
  14. 14.
    I.V. Anikin, B. Pire, L. Szymanowski, O.V. Teryaev, S. Wallon, Eur. Phys. J. C 42, 163 (2005) [arXiv:hep-ph/0411408]; I.V. Anikin, B. Pire, L. Szymanowski, O.V. Teryaev, S. Wallon, Phys. Rev. D 70, 011501 (2004) [arXiv:hep-ph/0401130]CrossRefADSGoogle Scholar
  15. 15.
    G.F. Chew, M.L. Goldberger, F.E. Low, Y. Nambu, Phys. Rev. 106, 1345 (1957)zbMATHMathSciNetCrossRefADSGoogle Scholar
  16. 16.
    H.J. Bremermann, R. Oehme, J.G. Taylor, Phys. Rev. 109, 2178 (1958)zbMATHMathSciNetCrossRefADSGoogle Scholar
  17. 17.
    S.J. Brodsky, M. Diehl, D.S. Hwang, Nucl. Phys. B 596, 99 (2001) [arXiv:hep-ph/0009254]CrossRefADSGoogle Scholar
  18. 18.
    S.J. Brodsky, L. Frankfurt, J.F. Gunion, A.H. Mueller, M. Strikman, Phys. Rev. D 50, 3134 (1994) [arXiv:hep-ph/9402283]CrossRefADSGoogle Scholar
  19. 19.
    J.C. Collins, L. Frankfurt, M. Strikman, Phys. Rev. D 56, 2982 (1997) [arXiv:hep-ph/9611433]CrossRefADSGoogle Scholar
  20. 20.
    M. Vanderhaeghen, P.A.M. Guichon, M. Guidal, Phys. Rev. D 60, (1999) [arXiv:hep-ph/9905372]Google Scholar
  21. 21.
    M. Diehl, Phys. Rep. 388, 41 (2003)CrossRefADSGoogle Scholar
  22. 22.
    G.P. Lepage, S.J. Brodsky, Phys. Rev. D 22, 2157 (1980)CrossRefADSGoogle Scholar
  23. 23.
    S.J. Brodsky, F.J. Llanes-Estrada, work in preparationGoogle Scholar
  24. 24.
    A.V. Belitsky, D. Mueller, Phys. Lett. B 513, 349 (2001) [arXiv:hep-ph/0105046]CrossRefADSGoogle Scholar
  25. 25.
    S.J. Brodsky, F.E. Close, J.F. Gunion, Phys. Rev. D 8, 3678 (1973)CrossRefADSGoogle Scholar
  26. 26.
    P.V. Landshoff, J.C. Polkinghorne, R.D. Short, Nucl. Phys. B 28, 225 (1971)CrossRefADSGoogle Scholar
  27. 27.
    D.D. Coon, J.F. Gunion, J. Tran Thanh Van, R. Blankenbecler, Phys. Rev. D 18, 1451 (1978)CrossRefADSGoogle Scholar
  28. 28.
    P. Maris, arXiv:nucl-th/0412059Google Scholar
  29. 29.
    J.C.R. Bloch, C.D. Roberts, S.M. Schmidt, A. Bender, M.R. Frank, Phys. Rev. C 60, 062201 (1999) [arXiv:nucl-th/9907120]CrossRefADSGoogle Scholar
  30. 30.
    M. Oettel, R. Alkofer, L. von Smekal, Eur. Phys. J. A 8, 553 (2000) [arXiv:nucl-th/0006082]CrossRefADSGoogle Scholar
  31. 31.
    R. Alkofer, C.S. Fischer, F.J. Llanes-Estrada, Phys. Lett. B 611, 279 (2005) [arXiv:hep-th/0412330]MathSciNetCrossRefADSGoogle Scholar
  32. 32.
    S.J. Brodsky, T. Huang, G.P. Lepage, SLAC-PUB-2868, Based on lectures given at 9th SLAC Summer Inst. on Particle Physics, Stanford, CA, Jul 27–Aug 7, 1981Google Scholar
  33. 33.
    A. Airapetian et al. [HERMES Collaboration], Eur. Phys. J. C 17, 389 (2000) [arXiv:hep-ex/0004023]; see also the overview in R. Enberg, Nucl. Phys. A 755, 595 (2005)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Stanford Linear Accelerator CenterStanford UniversityStanfordUSA
  2. 2.Depto. Física Teórica I, Fac. Cc. FísicasUniversidad Complutense de MadridMadridSpain

Personalised recommendations