Skip to main content
SpringerLink
Log in
Book cover

Strangeness and Charge Symmetry Violation in Nucleon Structure pp 71–97Cite as

Parton Distribution Moments

  • Chapter
  • First Online:

  • 258 Accesses

Part of the book series: Springer Theses ((Springer Theses))

Abstract

The revelation of the late 1960s that the proton has distinct substructure raised a pivotal question: how are hadron observables generated from more fundamental degrees of freedom? Answering this question—where the generic point-like ‘parton’ constituents originally introduced by Feynman [4] are now identified with the asymptotically-free quarks and gluons of QCD—remains one of the most basic challenges of particle and nuclear physics.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    This hinged in particular on a series of deep inelastic scattering (DIS) experiments at MIT and SLAC in late 1967 [1, 2]. Two unexpected features emerged. The first was that the probability of DIS decreased much more slowly with \(Q^2\), the momentum transfer to the proton, than that of elastic scattering, suggesting the existence of some ‘hard core’ within the target protons. The second was scaling [3], i.e., that in the DIS regime the proton structure functions depend only on the ratio \(\omega =\nu / Q^2\) (\(\nu \) being the energy lost by the electron), not \(\nu \) and \(Q^2\) independently—an indication that proton structure always appears the same to an electromagnetic probe, regardless of how hard the proton is struck.

  2. 2.

    The Bjorken variable is \(x=Q^2/2M_B\nu \propto 1/\omega \), where \(M_B\) is the mass of the relevant baryon.

  3. 3.

    For a baryon with valence quark content xxy, the doubly-represented contribution is the total from quarks of flavour x, while the singly-represented contribution is the total from y-flavoured quarks. For example, in the proton the u and d quarks are doubly and singly-represented, respectively.

  4. 4.

    The relatively small values of the gluon spin in the proton, found in both fixed target and collider experiments [60, 61], have eliminated the possibility that the axial anomaly alone might explain the observed suppression, although its effect may still be quantitatively significant.

  5. 5.

    Since the completion of this work, calculations of the quark spin fractions in the \(\Lambda \) baryon have been performed for a subset of the simulation ensembles used here [64]. At this stage, however, the results do not span a sufficient range of meson masses to constrain an extrapolation of the \(\Lambda \) spin fraction to the physical point (when included in our analysis).

  6. 6.

    In Refs. [29, 30] the factor of \(\frac{1}{2}\) appearing at the beginning of the following equations was erroneously omitted. As a result, the values quoted for the CSV terms were too large by a factor of two.

References

  1. E.D. Bloom et al., Phys. Rev. Lett. 23, 930 (1969)

    Article  ADS  Google Scholar 

  2. M. Breidenbach et al., Phys. Rev. Lett. 23, 935 (1969)

    Article  ADS  Google Scholar 

  3. J.D. Bjorken, Phys. Rev. 179, 1547 (1969)

    Article  ADS  Google Scholar 

  4. R.P. Feynman, Phys. Rev. Lett. 23, 1415 (1969)

    Article  ADS  Google Scholar 

  5. J. Ashman et al., European Muon collaboration. Phys. Lett. B 206, 364 (1988)

    Article  ADS  Google Scholar 

  6. V.Y. Alexakhin et al., COMPASS collaboration. Phys. Lett. B 647, 8 (2007)

    Article  ADS  Google Scholar 

  7. H.-L. Lai et al., Phys. Rev. D 82, 074024 (2010)

    Article  ADS  Google Scholar 

  8. C. Adloff et al., H1 collaboration. Eur. Phys. J. C 30, 1 (2003)

    Article  Google Scholar 

  9. R.D. Ball et al., NNPDF collaboration. Nucl. Phys. B 809, 1 (2009)

    Article  ADS  Google Scholar 

  10. A.D. Martin, W.J. Stirling, R.S. Thorne, G. Watt, Phys. Lett. B 652, 292 (2007)

    Article  ADS  Google Scholar 

  11. D. Diakonov, V. Petrov, P. Pobylitsa, M.V. Polyakov, C. Weiss, Nucl. Phys. B 480, 341 (1996)

    Article  ADS  Google Scholar 

  12. A.W. Schreiber, P.J. Mulders, A.I. Signal, A.W. Thomas, Phys. Rev. D 45, 3069 (1992)

    Article  ADS  Google Scholar 

  13. L.P. Gamberg, G.R. Goldstein, K.A. Oganessyan, Phys. Rev. D 67, 071504 (2003)

    Article  ADS  Google Scholar 

  14. I.C. Cloët, W. Bentz, A.W. Thomas, Phys. Lett. B 621, 246 (2005)

    Article  ADS  Google Scholar 

  15. I.C. Cloët, W. Bentz, A.W. Thomas, Phys. Lett. B 659, 214 (2008)

    Article  ADS  Google Scholar 

  16. A. Bacchetta, F. Conti, M. Radici, Phys. Rev. D 78, 074010 (2008)

    Article  ADS  Google Scholar 

  17. C. Lorcé, B. Pasquini, M. Vanderhaeghen, JHEP 1105, 041 (2011)

    Article  ADS  Google Scholar 

  18. J.T. Londergan, A.W. Thomas, Prog. Part. Nucl. Phys. 41, 49 (1998)

    Article  ADS  Google Scholar 

  19. J.T. Londergan, J.C. Peng, A.W. Thomas, Rev. Mod. Phys. 82, 2009 (2010)

    Article  ADS  Google Scholar 

  20. A.D. Martin, R.G. Roberts, W.J. Stirling, R.S. Thorne, Eur. Phys. J. C 35, 325 (2004)

    Article  ADS  Google Scholar 

  21. E.N. Rodionov, A.W. Thomas, J.T. Londergan, Mod. Phys. Lett. A 9, 1799 (1994)

    Article  ADS  Google Scholar 

  22. E. Sather, Phys. Lett. B 274, 433 (1992)

    Article  ADS  Google Scholar 

  23. J.T. Londergan, D.P. Murdock, A.W. Thomas, Phys. Rev. D 72, 036010 (2005)

    Article  ADS  Google Scholar 

  24. J.T. Londergan, A.W. Thomas, Phys. Lett. B 558, 132 (2003)

    Article  ADS  Google Scholar 

  25. J.T. Londergan, Eur. Phys. J. A24S2, 85 (2005)

    Article  Google Scholar 

  26. X. Ji, Phys. Rev. Lett. 110, 262002 (2013)

    Article  ADS  Google Scholar 

  27. W. Detmold, W. Melnitchouk, A.W. Thomas, Phys. Rev. D 66, 054501 (2002)

    Article  ADS  Google Scholar 

  28. G.S. Bali et al., Phys. Rev. D 86, 054504 (2012)

    Article  ADS  Google Scholar 

  29. R. Horsley et al., Phys. Rev. D 83, 051501 (2011)

    Article  ADS  Google Scholar 

  30. I.C. Cloët et al., Phys. Lett. B 714, 97 (2012)

    Article  ADS  Google Scholar 

  31. G.P. Zeller et al., NuTeV collaboration. Phys. Rev. Lett. 88, 091802 (2002)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  33. J.-W. Chen, X. Ji, Phys. Lett. B 523, 107 (2001)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  35. B. Borasoy, B.R. Holstein, R. Lewis, P.P.A. Ouimet, Phys. Rev. D 66, 094020 (2002)

    Article  ADS  Google Scholar 

  36. M. Diehl, A. Manashov, A. Schäfer, Eur. Phys. J. A 31, 335 (2007)

    Article  ADS  Google Scholar 

  37. M. Dorati, T.A. Gail, T.R. Hemmert, Nucl. Phys. A 798, 96 (2008)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  39. M. Burkardt, K.S. Hendricks, C.-R. Ji, W. Melnitchouk, A.W. Thomas, Phys. Rev. D 87, 056009 (2013)

    Article  ADS  Google Scholar 

  40. W. Detmold, C.J.D. Lin, Phys. Rev. D 71, 054510 (2005)

    Article  ADS  Google Scholar 

  41. W. Bietenholz et al., Phys. Rev. D 84, 054509 (2011)

    Article  ADS  Google Scholar 

  42. A.D. Martin, R.G. Roberts, W.J. Stirling, R.S. Thorne, Eur. Phys. J. C 28, 455 (2003)

    Article  ADS  Google Scholar 

  43. C.A. Aidala, S.D. Bass, D. Hasch, G.K. Mallot, Rev. Mod. Phys. 85, 655 (2013)

    Article  ADS  Google Scholar 

  44. M. Anselmino, A. Efremov, E. Leader, Phys. Rept. 261, 1 (1995)

    Article  ADS  Google Scholar 

  45. S.D. Bass, Rev. Mod. Phys. 77, 1257 (2005)

    Article  ADS  Google Scholar 

  46. S.D. Bass, A.W. Thomas, Phys. Lett. B 684, 216 (2010)

    Article  ADS  Google Scholar 

  47. G.S. Bali et al., QCDSF Collaboration. Phys. Rev. Lett. 108, 222001 (2012)

    Article  ADS  Google Scholar 

  48. G. Altarelli, G.G. Ross, Phys. Lett. B 212, 391 (1988)

    Article  ADS  Google Scholar 

  49. R.D. Carlitz, J.C. Collins, A.H. Mueller, Phys. Lett. B 214, 229 (1988)

    Article  ADS  Google Scholar 

  50. G.T. Bodwin, J.-W. Qiu, Phys. Rev. D 41, 2755 (1990)

    Article  ADS  Google Scholar 

  51. S.D. Bass, B.L. Ioffe, N.N. Nikolaev, A.W. Thomas, J. Moscow. Phys. Soc. 1, 317 (1991)

    Google Scholar 

  52. A.V. Efremov, J. Soffer, O.V. Teryaev, Nucl. Phys. B 346, 97 (1990)

    Article  ADS  Google Scholar 

  53. R.L. Jaffe, A. Manohar, Nucl. Phys. B 337, 509 (1990)

    Article  ADS  Google Scholar 

  54. G.M. Shore, G. Veneziano, Nucl. Phys. B 381, 23 (1992)

    Article  ADS  Google Scholar 

  55. F. Myhrer, A.W. Thomas, Phys. Rev. D 38, 1633 (1988)

    Article  ADS  Google Scholar 

  56. K. Tsushima, T. Yamaguchi, Y. Kohyama, K. Kubodera, Nucl. Phys. A 489, 557 (1988)

    Article  ADS  Google Scholar 

  57. H. Høgaasen, F. Myhrer, Phys. Lett. B 214, 123 (1988)

    Article  ADS  Google Scholar 

  58. A.W. Schreiber, A.W. Thomas, Phys. Lett. B 215, 141 (1988)

    Article  ADS  Google Scholar 

  59. M. Wakamatsu, Phys. Lett. B 232, 251 (1989)

    Article  ADS  Google Scholar 

  60. A. Adare et al., PHENIX Collaboration. Phys. Rev. D 76, 051106 (2007)

    Article  ADS  Google Scholar 

  61. B.I. Abelev et al., STAR Collaboration. Phys. Rev. Lett. 100, 232003 (2008)

    Article  ADS  Google Scholar 

  62. F. Myhrer, A.W. Thomas, Phys. Lett. B 663, 302 (2008)

    Article  ADS  Google Scholar 

  63. D. de Florian, G. M. Shore, G. Veneziano, arXiv:hep-ph/9711353

  64. A.J. Chambers et al., CSSM/QCDSF-UKQCD Collaboration. Phys. Rev. D 90, 014510 (2014)

    Article  ADS  Google Scholar 

  65. P.E. Shanahan, A.W. Thomas, K. Tsushima, R.D. Young, F. Myhrer, Phys. Rev. Lett. 110, 202001 (2013)

    Article  ADS  Google Scholar 

  66. A.W. Thomas, Adv. Nucl. Phys. 13, 1 (1984)

    Google Scholar 

  67. A.W. Thomas, S. Theberge, G.A. Miller, Phys. Rev. D 24, 216 (1981)

    Article  ADS  Google Scholar 

  68. S. Theberge, A.W. Thomas, G.A. Miller, Phys. Rev. D 22, 2838 (1980)

    Article  ADS  Google Scholar 

  69. G.A. Miller, Int. Rev. Nucl. Phys. 1, 189 (1984)

    Article  ADS  Google Scholar 

  70. H. Høgaasen, F. Myhrer, Z. Phys. C 68, 625 (1995)

    Article  ADS  Google Scholar 

  71. K. Tsushima, T. Yamaguchi, M. Takizawa, Y. Kohyama, K. Kubodera, Phys. Lett. B 205, 128 (1988)

    Article  ADS  Google Scholar 

  72. J. Beringer et al., Particle Data Group. Phys. Rev. D 86, 010001 (2012)

    Article  ADS  Google Scholar 

  73. J. Blümlein, H. Böttcher, Nucl. Phys. B 841, 205 (2010)

    Article  ADS  Google Scholar 

  74. J.D. Bjorken, Phys. Rev. 148, 1467 (1966)

    Article  ADS  Google Scholar 

  75. J.D. Bjorken, Phys. Rev. D 1, 1376 (1970)

    Article  ADS  Google Scholar 

  76. M.G. Alekseev et al., COMPASS Collaboration. Phys. Lett. B 690, 466 (2010)

    Article  ADS  Google Scholar 

  77. W. Bentz, I.C. Cloët, J.T. Londergan, A.W. Thomas, Phys. Lett. B 693, 462 (2010)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, USA

    Phiala Elisabeth Shanahan

Authors
  1. Phiala Elisabeth Shanahan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Phiala Elisabeth Shanahan .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Shanahan, P.E. (2016). Parton Distribution Moments. In: Strangeness and Charge Symmetry Violation in Nucleon Structure. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-31438-9_6

Download citation

Publish with us

Policies and ethics

Search

Navigation