Skip to main content
SpringerLink
Log in

Non-perturbative pion matrix element of a twist-2 operator from the lattice

  • theoretical physics
  • Published:
The European Physical Journal C - Particles and Fields Aims and scope Submit manuscript

Abstract.

We give a continuum limit value of the lowest moment of a twist-2 operator in pion states from non-perturbative lattice calculations. We find that the non-perturbatively obtained renormalization group invariant matrix element is \(\langle x\rangle_{\mathrm{RGI}} = 0.179(11)\), which corresponds to \(\langle x \rangle^{\overline{\mathrm{MS}}}(2\mathrm{ GeV}) = 0.246(15)\). In obtaining the renormalization group invariant matrix element, we have controlled important systematic errors that appear in typical lattice simulations, such as non-perturbative renormalization, finite size effects and effects of a non-vanishing lattice spacing. The crucial limitation of our calculation is the use of the quenched approximation. Another question that remains not fully clarified is the chiral extrapolation of the numerical data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Devenish, A. Cooper-Sarkar, Deep inelastic scattering (Oxford Unversity Press, Oxford 2004)

  2. S. Alekhin, Phys. Rev. D 63, 094022 (2001)

    Google Scholar 

  3. A.D. Martin, R.G. Roberts, W.J. Stirling, R.S. Thorne, hep-ph/0308087

  4. J. Blümlein, H. Böttcher, Nucl. Phys. B 636, 225 (2002)

    Google Scholar 

  5. R. Petronzio, Nucl. Phys. B Proc. 73, 303 (1999); M. Göckeler, R. Horsley, D. Pleiter, P.E.L. Rakow, A. Schäfer, G. Schierholz, Nucl. Phys. B Proc. 119, 32 (2003); S. Capitani, Nucl. Phys. B Proc. 116, 115 (2003); K. Jansen, to be published in Nuclear Physics A, Proceedings of FB17, Durham, USA (2003); A. Shindler, to be published in the Proceedings of DIS04

    Google Scholar 

  6. A. Bucarelli, F. Palombi, R. Petronzio, A. Shindler, Nucl. Phys. B 552, 379 (1999)

    Google Scholar 

  7. M. Guagnelli, K. Jansen, R. Petronzio, Nucl. Phys. B 542, 395 (1999)

    Google Scholar 

  8. M. Guagnelli, K. Jansen, R. Petronzio, Phys. Lett. B 457, 153 (1999)

    Google Scholar 

  9. M. Guagnelli, K. Jansen, R. Petronzio, Phys. Lett. B 459, 594 (1999)

    Google Scholar 

  10. M. Guagnelli, K. Jansen, R. Petronzio, Phys. Lett. B 493, 77 (2000)

    Google Scholar 

  11. ZeRo Collaboration: M. Guagnelli, K. Jansen, F. Palombi, R. Petronzio, A. Shindler, I. Wetzorke, Nucl. Phys. B 664, 276 (2003)

    Google Scholar 

  12. Talk presented by K. Jansen at the XXXth International Conference on High Energy Physics (ICHEP (2000)), July 27-August 2 (2000), hep-lat/0010038

  13. M. Guagnelli, K. Jansen, F. Palombi, R. Petronzio, A. Shindler, I. Wetzorke, plenary talk given by A. Shindler Electron-Nucleus Scattering VII, June 24-28 (2002), Elba; Eur. Phys. J. A 17, 365 (2003)

    Google Scholar 

  14. M. Guagnelli, K. Jansen, F. Palombi, R. Petronzio, A. Shindler, I. Wetzorke (World Scientific, Genoa 2002), Gerasimov-Drell-Hearn sum rule and the spin structure of the nucleon, 69-76

  15. K. Jansen, Nucl. Phys. B Proc. 129-130, 3 (2004)

  16. C. Bernard et al. , Nucl. Phys. B Proc. 106, 199 (2002)

    Google Scholar 

  17. M. L\” uscher, R. Narayanan, P. Weisz, U. Wolff, Nucl. Phys. B 384, 168 (1992); S. Sint, Nucl. Phys. B 421, 135 (1994); B 451, 416 (1995); K. Jansen, C. Liu, M. L\” uscher, H. Simma, S. Sint, R. Sommer, P. Weisz, U. Wolff, Phys. Lett. B 372, 275 (1996); M. L\” uscher, S. Sint, R. Sommer, P. Weisz, Nucl. Phys. B 478, 365 (1996)

    Google Scholar 

  18. R. Sommer, Lectures at Schladming 1997, hep-lat/9711243

  19. M. Lüscher, Lectures given at the Les Houches Summer School, Probing the Standard Model of Particle Interactions, July 28-September 5, 1997, hep-lat/9802029

  20. R. Sommer, Nucl. Phys. B Proc. 119, 185 (2003)

    Google Scholar 

  21. ZeRo Collaboration: M. Guagnelli, K. Jansen, F. Palombi, R. Petronzio, A. Shindler, I. Wetzorke, Phys. Lett. B 597, 216 (2004)

    Google Scholar 

  22. JLQCD Collaboration, S. Aoki et al. , Phys. Rev. D 68, 054502 (2003)

    Google Scholar 

  23. A.W. Thomas, W. Melnitchouk, F.M. Steffens, Phys. Rev. Lett. 85, 2892 (2000)

    Google Scholar 

  24. W. Detmold et al. , Phys. Rev. Lett. 87, 172001 (2001)

    Google Scholar 

  25. D. Arndt, M.J. Savage, Nucl. Phys. A 697, 429 (2002)

    Google Scholar 

  26. J.W. Chen, M.J. Savage, Nucl. Phys. A 707, 452 (2002)

    Google Scholar 

  27. S.R. Beane, M.J. Savage, Phys. Rev. D 68, 114502 (2003)

    Google Scholar 

  28. J.W. Chen, X. Ji Phys. Rev. Lett. 88, 052003 (2002)

    Google Scholar 

  29. P.J. Sutton, A.D. Martin, R.G. Roberts, W.J. Stirling, Phys. Rev. D 45, 2349 (1992); M. Glück, E. Reya, I. Schienbein, Eur. Phys. J. C 10, 313 (1999)

    Google Scholar 

  30. M. Baake, B. Gemünden, R. Oedingen, J. Math. Phys. 23, 944 (1982); J.E. Mandula, G. Zweig, J. Govaerts, Nucl. Phys. B 228, 91 (1983)

    Google Scholar 

  31. ALPHA Collaboration: M. Guagnelli et al. , Nucl. Phys. B 560, 465 (1999)

    Google Scholar 

  32. ALPHA Collaboration: M. Lüscher et al. , Nucl. Phys. B 491, 323 (1997)

    Google Scholar 

  33. B. Sheikholeslami, R. Wohlert, Nucl. Phys. B 259, 572 (1985)

    Google Scholar 

  34. S. Capitani et al. , Nucl. Phys. B Proc. 63, 153 (1998); S. Capitani et al. , Nucl. Phys. B 544, 669 (1999)

    Google Scholar 

  35. R. Sommer, private comunication

  36. S. Necco, R. Sommer, Nucl. Phys. B 622, 328 (2002)

    Article  Google Scholar 

  37. O.V. Tarasov, A.A. Vladimirov, A.Yu. Zharkov, Phys. Lett. B 93, 429 (1980)

    Article  Google Scholar 

  38. E.G. Floratos, D.A. Ross, C.T. Sachrajda, Nucl. Phys. B 129, 66 (1977); Erratum B 139, 545 (1978); A. Gonzalez-Arroyo, C. Lopez, F.J. Yndurain, Nucl. Phys. B 153, 161 (1979); G. Curci, W. Furmanski, R. Petronzio, Nucl. Phys. B 175, 27 (1980)

    Google Scholar 

  39. R. Sommer, Nucl. Phys. B 411, 839 (1994); M. Guagnelli, R. Sommer, H. Wittig, Nucl. Phys. B 535, 389 (1998)

    Google Scholar 

  40. C. Best et al. , Phys. Rev. D 56, 2743 (1997)

    Google Scholar 

  41. ZeRo Collaboration: A. Shindler, M. Guagnelli, K. Jansen, F. Palombi, R. Petronzio, I. Wetzorke, Nucl. Phys. B Proc. 129-130, 278 (2004)

  42. G. Schierholz, private communication

  43. LHPC Collaboration: D. Dolgov et al. , Phys. Rev. D 66, 034506 (2002)

    Google Scholar 

Download references

Author information

Consortia

The Zeuthen-Rome (Zero) Collaboration

Additional information

Received: 28 October 2004, Published online: 4 February 2005

PACS:

11.15.Ha, 12.38.Gc

Rights and permissions

Reprints and permissions

About this article

Cite this article

The Zeuthen-Rome (Zero) Collaboration. Non-perturbative pion matrix element of a twist-2 operator from the lattice. Eur. Phys. J. C 40, 69–80 (2005). https://doi.org/10.1140/epjc/s2005-02121-5

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjc/s2005-02121-5

Keywords

Search

Navigation