Next-to-leading order evolution of generalized parton distributions for DESY HERA and HERMES

Physical Review D

Volumn 65, Issue 5, 2002, Pages

  Freund, Andreas ^a   McDermott, Martin ^b  

^a UNIVERSITY OF REGENSBURG   (Germany)

^b UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; EVOLUTION; KINEMATICS; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; PARTICLE RADIATION; PARTICLE SIZE; POLARIZATION; QUANTUM CHEMISTRY; RADIATION DOSE DISTRIBUTION;

EID: 0036497320     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.65.056012     Document Type: Article

References (52)

1. D. Müller et al., Fortschr. Phys. 42, 101 (1994).
2. X. Ji, Phys. Rev. D 55, 7114 (1997).
3. A. V. Radyushkin, Phys. Rev. D 56, 5524 (1997).
4. J. C. Collins, L. Frankfurt, and M. Strikman, Phys. Rev. D 56, 2982 (1997).
5. J. C. Collins and A. Freund, Phys. Rev. D 59, 074009 (1999).
6. X. Ji and J. Osborne, Phys. Rev. D 58, 094018 (1998).
7. ZEUS Collaboration, P. R. Saull, "Prompt photon production and observation of deeply virtual Compton scattering," Proc. EPS 1999, 1999, Tampere, Finland, hep-ex/0003030;
8. ZEUS Collaboration, "Measurement of the deeply virtual Compton scattering cross section at HERA," Abstract 564, IECHEP 2001, 2001, Budapest, Hungary.
9. H1 Collaboration, C. Adloff et al., Phys. Lett. B 517, 47 (2001);
10. H1 Collaboration, L. Favart, "Deeply virtual Compton scattering at HERA," Proc. ICHEP 2000, 2000, Osaka, Japan, hep-ex/0101046.
11. Hermes Collaboration, A. Airapetian et al., Phys. Rev. Lett. 87, 182001 (2001).
12. CLAS Collaboration, S. Stepanyan et al., Phys. Rev. Lett. 87, 182002 (2001);
13. J. P. Chen, for Jefferson Lab, http://www.jlab.org/~sabatie/dvcs/index. html
14. A. V. Belitsky, A. Freund, and D. Müller, Nucl. Phys. B574, 347 (2000).
15. A. V. Radyushkin, Phys. Rev. D 59, 014030 (1999).
16. A. V. Radyushkin, Phys. Lett. B 449, 81 (1999);
17. I. V. Musatov and A. V. Radyushkin, Phys. Rev. D 61, 074027 (2000).
18. A. D. Martin, R. G. Roberts, and W. J. Stirling, Phys. Lett. B 354, 155 (1995).
19. T. Gehrmann and W. J. Stirling, Phys. Rev. D 53, 6100 (1996).
20. M. Glück, E. Reya, and A. Vogt, Eur. Phys. J. C 5, 461 (1998).
21. M. Glück et al., Phys. Rev. D 63, 094005 (2001).
22. A solution to the RGBs at NLO has been presented at large x in [19,20], however due to technical problems the methods used could not be applied at smaller x.
23. A. V. Belitsky et al., Phys. Lett. B 437, 160 (1998).
24. A. V. Belitsky et al., Phys. Lett. B 474, 163 (2000).
25. V. Guzey and A. Freund, Phys. Lett. B 462, 178 (1999);
26. "Numerical methods in the LO evolution of non-diagonal parton distributions: the DGLAP case," hep-ph/9801388.
27. K. J. Golec-Biernat and A. D. Martin, Phys. Rev. D 59, 014029 (1999).
28. http://durpdg.dur.ac.uk/hepdata/dvcs.html
29. M. V. Polyakov and C. Weiss, Phys. Rev. D 60, 114017 (1999).
30. N. Kivel, M. V. Polyakov, and M. Vanderhaeghen, Phys. Rev. D 63, 114014 (2001).
31. M. Penttinen, M. V. Polyakov, and K. Goeke, Phys. Rev. D 62, 014024 (2000).
32. V. N. Gribov and L. N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972);
33. V. N. Gribov and L. N. Lipatov, Sov. J. Nucl. Phys. 15, 675 (1972);
34. Yu. L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977);
35. G. Altarelli and G. Parisi, Nucl. Phys. B126, 298 (1977).
36. A. V. Efremov and A. V. Radyushskin, Theor. Math. Phys. 42, 97 (1980);
37. Phys. Lett. 94B, 245 (1980);
38. G. P. Lepage and S. J. Brodsky, Phys. Lett. ibid. 87B, 359 (1979);
39. Phys. Rev. D 22, 2157 (1980).
40. A. V. Belitsky et al., Nucl. Phys. B593, 289 (2001).
41. 0=2 GeV before introducing skewedness into the evolution. For computational reasons, we also found it convenient to use a faithful multiparameter fit to these GRV and GRSV distribution rather than using the codes provided by the authors. For GRSV00 we choose the "standard scenario" option of unbroken polarized sea distributions.
42. The endpoint (z= 1) concentrated terms in Eqs. (22), (25) can be found in [11] and are determined by the requirement that the zeroth order conformal moment of the kernel has to be zero. Note that in the numerical implementation of the evolution the pure singlet component in the qq kernel in both DGLAP and ERBL regions is not regularized (for more details see [11]).
43. http://www.phys.psu.edu/~cteq/#PDFs
44. L. Frankfurt, M. McDermott, and M. Strikman, J. High Energy Phys. 02, 002 (1999).
45. B. Pire, J. Soffer, and O. V. Teryaev/Eur. Phys. J. C 8, 103 (1999).
46. It was not applicable, even at LO, in the polarized case.
47. A slight deviation of the ratio from unity is observed in the plot for X>0.1 because for GRV98, we use an analytic fit to the actual distributions at our input scale. This fit starts to deviate slightly from the results produced by the FORTRAN routines of GRV98 at the input scale. The NLO evolution enhances this difference and thus we do not expect the ratio to approach unity precisely for large X≫ζ. Note however that the deviation is at most 2%. The small wiggles in the curves are artifacts of the fitting procedure since we normalize to the code of GRV98.
48. Small deviations from unity are observed at very large X >0.2 for evolved scales. This results from the fact that in our input GPDs we directly implement Eqs. (9), (10), (13) and Tables I, II of [15] (gluon A) analytically and the resultant numbers deviate slightly from those obtained from the grid-based FORTRAN routine provided by Gehrman-Stirling at such large X. Since we use the latter to normalize this ratio we do not expect to reproduce the forward limit with perfect accuracy.
49. In the quark case, we used only the singlet type combination of the down quark since it does not change sign as the up quark and the strange quark do. A change in sign distorts ratio plots by a large ratio around the point where the distributions changes sign, since this particular point is shifted towards lower X in NLO compared to LO.
50. A. Freund and M. McDermott, hep-ph/0106124, v2.
51. A. Freund and M. McDermott, hep-ph/0106319.
52. A. Freund and M. McDermott, hep-ph/0111472.