Advertisement

The European Physical Journal Special Topics

, Volume 140, Issue 1, pp 169–212 | Cite as

Nucleon structure from lattice QCD

  • J. M. Zanotti
Article

Abstract.

The aim of these lectures will be to provide an introductory overview of the concepts needed to compute hadronic matrix elements on the lattice from which moments of Generalised Parton Distributions (GPDs) are extracted and to highlight the contributions that current lattice calculations are making to this exciting field of research. Interesting related topics that will be covered include recent work on the nucleon electromagnetic form factors and moments of parton distribution functions, including the nucleon's axial coupling constant, gA, and the average fraction of the nucleon's momentum carried by the quarks, 〈 xq〉.

Keywords

Form Factor European Physical Journal Special Topic Chiral Limit Reduce Matrix Element Hadron Structure 
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. D. Muller et al., Fortsch. Phys. 42, 101 (1994) [arXiv:hep-ph/9812448]; A.V. Radyushkin, Phys. Rev. D 56, 5524 (1997) [arXiv:hep-ph/9704207]; M. Diehl et al., Phys. Lett. B 411, 193 (1997) [arXiv:hep-ph/9706344] Google Scholar
  2. M. Diehl, Eur. Phys. J. C 25, 223 (2002) [Erratum-ibid. C 31, 277 (2003)] [arXiv:hep-ph/0205208] ADSGoogle Scholar
  3. M. Burkardt, Int. J. Mod. Phys. A 18, 173 (2003) [arXiv:hep-ph/0207047] zbMATHCrossRefADSGoogle Scholar
  4. X.D. Ji, Phys. Rev. Lett. 78, 610 (1997) [arXiv:hep-ph/9603249]; X.D. Ji, J. Phys. G 24, 1181 (1998) [arXiv:hep-ph/9807358] CrossRefADSGoogle Scholar
  5. M. Göckeler et al., Phys. Rev. Lett. 92, 042002 (2004) [arXiv:hep-ph/0304249]; Nucl. Phys. Proc. Suppl. 128, 203 (2004) [arXiv:hep-ph/0312104] CrossRefADSGoogle Scholar
  6. M. Göckeler et al. [QCDSF Collaboration], Nucl. Phys. Proc. Suppl. 140, 399 (2005) CrossRefADSGoogle Scholar
  7. M. Göckeler et al., Few Body Syst. 36, 111 (2005) [arXiv:hep-lat/0410023] CrossRefADSGoogle Scholar
  8. M. Göckeler et al. [QCDSF Collaboration], Nucl. Phys. A 755, 537 (2005) [arXiv:hep-lat/0501029] CrossRefADSGoogle Scholar
  9. M. Gockeler et al. [QCDSF Collaboration], Phys. Lett. B 627, 113 (2005) [arXiv:hep-lat/0507001] CrossRefADSGoogle Scholar
  10. M. Gockeler et al., Nucl. Phys. Proc. Suppl. 153, 146 (2006) [arXiv:hep-lat/0512011] CrossRefGoogle Scholar
  11. M. Diehl et al. [QCDSF Collaboration], [arXiv:hep-ph/0511032] Google Scholar
  12. P. Hägler et al., [LHPC collaboration], Phys. Rev. D 68, 034505 (2003) [arXiv:hep-lat/0304018] CrossRefGoogle Scholar
  13. Ph. Hägler et al., Phys. Rev. Lett. 93 (2004) 112001 [arXiv:hep-lat/0312014] Google Scholar
  14. J.W. Negele et al., Nucl. Phys. Proc. Suppl. 128, 170 (2004) [arXiv:hep-lat/0404005] CrossRefGoogle Scholar
  15. P. Hägler, J.W. Negele, D.B. Renner, W. Schroers, T. Lippert, K. Schilling, Eur. Phys. J. A 24S1, 29 (2005) [arXiv:hep-ph/0410017] CrossRefGoogle Scholar
  16. D.B. Renner, [arXiv:hep-lat/0501005] Google Scholar
  17. R.G. Edwards et al. [LHPC Collaboration], PoS LAT2005, 056 (2006) [arXiv:hep-lat/0509185] Google Scholar
  18. H.J. Rothe, World Sci. Lect. Notes Phys. 74, 1 (2005); R. Gupta, [arXiv:hep-lat/9807028] MathSciNetGoogle Scholar
  19. G. Curci, P. Menotti, G. Paffuti, Phys. Lett. B 130, 205 (1983) [Erratum-ibid. B 135, 516 (1984)] CrossRefADSGoogle Scholar
  20. M. Luscher, P. Weisz, Commun. Math. Phys. 97, 59 (1985) [Erratum-ibid. 98, 433 (1985)] CrossRefADSMathSciNetGoogle Scholar
  21. K.G. Wilson, Phys. Rev. D 10, 2445 (1974) CrossRefADSGoogle Scholar
  22. K. Symanzik, Nucl. Phys. B 226, 187 (1983) CrossRefADSMathSciNetGoogle Scholar
  23. H.W. Hamber, C.M. Wu, Phys. Lett. B 133, 351 (1983) CrossRefADSGoogle Scholar
  24. F.X. Lee, D.B. Leinweber, Phys. Rev. D 59, 074504 (1999) [arXiv:hep-lat/9711044] CrossRefADSGoogle Scholar
  25. B. Sheikholeslami, R. Wohlert, Nucl. Phys. B 259, 572 (1985) CrossRefADSGoogle Scholar
  26. M. Luscher, S. Sint, R. Sommer, P. Weisz, Nucl. Phys. B 478, 365 (1996) [arXiv:hep-lat/9605038] CrossRefADSMathSciNetGoogle Scholar
  27. S.O. Bilson-Thompson, D.B. Leinweber, A.G. Williams, Ann. Phys. 304, 1 (2003) zbMATHCrossRefADSGoogle Scholar
  28. G. Bhanot, Rept. Prog. Phys. 51, 429 (1988) CrossRefADSMathSciNetGoogle Scholar
  29. N. Cabibbo, E. Marinari, Phys. Lett. B 119, 387 (1982) CrossRefADSGoogle Scholar
  30. N. Mathur, S.J. Dong, Nucl. Phys. Proc. Suppl. 94, 311 (2001) [arXiv:hep-lat/0011015]; S.J. Dong, et al., Phys. Rev. D 58, 074504 (1998) [arXiv:hep-ph/9712483] CrossRefADSMathSciNetGoogle Scholar
  31. R. Lewis, W. Wilcox, R.M. Woloshyn, Phys. Rev. D 67, 013003 (2003) [arXiv:hep-ph/0210064] CrossRefADSGoogle Scholar
  32. M. Gockeler, R. Horsley, D. Pleiter, P.E.L. Rakow, G. Schierholz [QCDSF Collaboration], Phys. Rev. D 71, 114511 (2005) [arXiv:hep-ph/0410187] CrossRefADSGoogle Scholar
  33. G. Martinelli, C. Pittori, C.T. Sachrajda, M. Testa, A. Vladikas, Nucl. Phys. B 445, 81 (1995) [arXiv:hep-lat/9411010] CrossRefADSGoogle Scholar
  34. M. Göckeler et al., Nucl. Phys. B 544, 699 (1999) [arXiv:hep-lat/9807044] CrossRefGoogle Scholar
  35. C. Aubin et al., Phys. Rev. D 70, 094505 (2004) [arXiv:hep-lat/0402030] CrossRefADSGoogle Scholar
  36. M. Gockeler, R. Horsley, H. Perlt, P.E.L. Rakow, A. Schafer, G. Schierholz, A. Schiller, Nucl. Phys. B 717, 304 (2005) [arXiv:hep-lat/0410009] CrossRefADSGoogle Scholar
  37. M.K. Jones et al. [Jefferson Lab Hall A Collaboration], Phys. Rev. Lett. 84, 1398 (2000) [arXiv:nucl-ex/9910005]; O. Gayou et al., Phys. Rev. C 64, 038202 (2001); O. Gayou et al. [Jefferson Lab Hall A Collaboration], Phys. Rev. Lett. 88, 092301 (2002) [arXiv:nucl-ex/0111010] CrossRefGoogle Scholar
  38. M. Gockeler, T.R. Hemmert, R. Horsley, D. Pleiter, P.E.L. Rakow, A. Schafer, G. Schierholz [QCDSF Collaboration], Phys. Rev. D 71, 034508 (2005) [arXiv:hep-lat/0303019] CrossRefADSGoogle Scholar
  39. S.J. Brodsky, G.R. Farrar, Phys. Rev. D 11, 1309 (1975) CrossRefADSGoogle Scholar
  40. G.P. Lepage, S.J. Brodsky, Phys. Rev. D 22, 2157 (1980) CrossRefADSGoogle Scholar
  41. A.V. Belitsky, X.D. Ji, F. Yuan, Phys. Rev. Lett. 91, 092003 (2003) [arXiv:hep-ph/0212351] CrossRefADSGoogle Scholar
  42. R.D. Young, D.B. Leinweber, A.W. Thomas, Phys. Rev. D 71, 014001 (2005) CrossRefADSGoogle Scholar
  43. J.D. Ashley, D.B. Leinweber, A.W. Thomas, R.D. Young, Eur. Phys. J. A 19, 9 (2004) CrossRefADSGoogle Scholar
  44. M. Göckeler et al., Phys. Rev. D 53, 2317 (1996) [arXiv:hep-lat/9508004] CrossRefADSGoogle Scholar
  45. W. Detmold et al., Phys. Rev. Lett. 87, 172001 (2001) [arXiv:hep-lat/0103006]; J.W. Chen, X. Ji, Phys. Rev. Lett. 87, 152002 (2001) [Erratum-ibid. 88, 249901 (2002)] [arXiv:hep-ph/0107158]; D. Arndt, M.J. Savage, Nucl. Phys. A 697, 429 (2002) [arXiv:nucl-th/0105045] CrossRefADSGoogle Scholar
  46. D. Dolgov et al. [LHPC collaboration], Phys. Rev. D 66, 034506 (2002) [arXiv:hep-lat/0201021] CrossRefGoogle Scholar
  47. K. Orginos, T. Blum, S. Ohta, Phys. Rev. D 73, 094503 (2006) [arXiv:hep-lat/0505024] CrossRefADSGoogle Scholar
  48. S. Sint, P. Weisz, Nucl. Phys. B 502, 251 (1997) [arXiv:hep-lat/9704001] CrossRefADSGoogle Scholar
  49. T. Bhattacharya, R. Gupta, W.J. Lee, S.R. Sharpe, Phys. Rev. D 63, 074505 (2001) CrossRefADSGoogle Scholar
  50. S. Sasaki, K. Orginos, S. Ohta, T. Blum, Phys. Rev. D 68, 054509 (2003) [arXiv:hep-lat/0306007] CrossRefADSGoogle Scholar
  51. R.G. Edwards et al. [LHPC Collaboration], Phys. Rev. Lett. 96, 052001 (2006) CrossRefGoogle Scholar
  52. A.A. Khan et al., [arXiv:hep-lat/0603028] Google Scholar
  53. R.L. Jaffe, Comments Nucl. Part. Phys. 19, 239 (1990); R.L. Jaffe, X.D. Ji, Phys. Rev. D 43, 724 (1991); J. Blumlein, N. Kochelev, Nucl. Phys. B 498, 285 (1997) [arXiv:hep-ph/9612318] Google Scholar
  54. M. Gockeler et al., Phys. Rev. D 72, 054507 (2005) [arXiv:hep-lat/0506017] CrossRefADSGoogle Scholar
  55. K. Abe et al. [E143 collaboration], Phys. Rev. D 58, 112003 (1998) [arXiv:hep-ph/9802357] CrossRefGoogle Scholar
  56. P.L. Anthony et al. [E155 Collaboration], Phys. Lett. B 553, 18 (2003) [arXiv:hep-ex/0204028] CrossRefADSGoogle Scholar
  57. M. Göckeler et al., Nucl. Phys. B 472, 309 (1996) [arXiv:hep-lat/9603006] CrossRefGoogle Scholar
  58. M. Göckeler et al., Phys. Rev. D 63, 074506 (2001) [arXiv:hep-lat/0011091] CrossRefADSGoogle Scholar
  59. M. Baake, B. Gemünden, R. Oedingen, J. Math. Phys. 23, 944 (1982) [Erratum-ibid. 23, 2595 (1982)]; J.E. Mandula, G. Zweig, J. Govaerts, Nucl. Phys. B 228, 109 (1983) zbMATHCrossRefADSMathSciNetGoogle Scholar
  60. M. Osipenko et al., Phys. Rev. D 71, 054007 (2005) [arXiv:hep-ph/0503018] CrossRefADSGoogle Scholar
  61. E.B. Zijlstra, W.L. van Neerven, Nucl. Phys. B 417, 61 (1994) [Erratum-ibid. B 426, 245 (1994)] CrossRefADSGoogle Scholar
  62. M. Göckeler et al., [QCDSF Collaboration], Phys. Rev. D 71, 034508 (2005) ; D.B. Leinweber, D.H. Lu, A.W. Thomas, Phys. Rev. D 60, 034014 (1999) ; E.J. Hackett-Jones, D.B. Leinweber, A.W. Thomas, Phys. Lett. B 489, 143 (2000) [arXiv:hep-lat/0004006]; T.R. Hemmert, W. Weise, Eur. Phys. J. A 15, 487 (2002) ; R.D. Young, D.B. Leinweber, A.W. Thomas, Phys. Rev. D 71, 014001 (2005) [arXiv:hep-lat/0406001] CrossRefGoogle Scholar
  63. W. Detmold, W. Melnitchouk, A.W. Thomas, Phys. Rev. D 66, 054501 (2002) CrossRefADSGoogle Scholar
  64. W. Detmold, C.J. Lin, Phys. Rev. D 71, 054510 (2005) [arXiv:hep-lat/0501007] CrossRefADSGoogle Scholar
  65. S. Wandzura, F. Wilczek, Phys. Lett. B 72, 195 (1977) CrossRefADSGoogle Scholar
  66. M. Diehl, Eur. Phys. J. C 19 (2001) 485 [arXiv:hep-ph/0101335] Google Scholar
  67. M. Burkardt, Phys. Rev. D 62 (2000) 071503 [Erratum-ibid. D 66 (2002) 119903], ; M. Burkardt, Phys. Lett. B 595, 245 (2004) [arXiv:hep-ph/0401159] CrossRefADSGoogle Scholar
  68. P. Hägler, Phys. Lett. B 594, 164 (2004) [arXiv:hep-ph/0404138] CrossRefADSGoogle Scholar
  69. Z. Chen, X.D. Ji, Phys. Rev. D 71, 016003 (2005) [arXiv:hep-ph/0404276] CrossRefADSGoogle Scholar
  70. M. Diehl, T. Feldmann, R. Jakob, P. Kroll, [arXiv:hep-ph/0408173] Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • J. M. Zanotti
    • 1
  1. 1.School of Physics, University of EdinburghEdinburghUK

Personalised recommendations