Few-Body Systems

, Volume 56, Issue 6–9, pp 355–362 | Cite as

\({{\bar{d}} - {\bar{u}}}\) Flavor Asymmetry in the Proton in Chiral Effective Field Theory



The \({\bar d - \bar u}\) flavor asymmetry in the proton arising from pion loops is computed using chiral effective field theory. The calculation includes both nucleon and Δ intermediate states, and uses both the fully relativistic and heavy baryon frameworks. The x dependence of \({\bar d - \bar u}\) extracted from the Fermilab E866 Drell–Yan data can be well reproduced in terms of a single transverse momentum cutoff parameter regulating the ultraviolet behavior of the loop integrals. In addition to the distribution at x > 0, corrections to the integrated asymmetry from zero momentum contributions are computed, which arise from pion rainbow and bubble diagrams at x = 0. These have not been accounted for in previous analyses, and can make important contributions to the lowest moment of \({\bar d-\bar u}\).


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  1. 1.
    Arneodo M. et al.: A reevaluation of the Gottfried sum. Phys. Rev. D 50, 1–3 (1994)CrossRefADSGoogle Scholar
  2. 2.
    Ackerstaff K. et al.: The flavor asymmetry of the light quark sea from semi-inclusive deep-inelastic scattering. Phys. Rev. Lett. 81, 5519–5523 (1998)CrossRefADSGoogle Scholar
  3. 3.
    Baldit A. et al.: Study of the isospin symmetry breaking the in the light quark sea of the nucleon from the Drell–Yan process. Phys. Lett. B 332, 244–250 (1994)CrossRefADSGoogle Scholar
  4. 4.
    Towell R.S. et al.: Improved measurement of the \({\bar d / \bar u}\) asymmetry in the nucleon sea. Phys. Rev. D 64, 052002 (2001)CrossRefADSGoogle Scholar
  5. 5.
    Thomas A.W.: A limit on the pionic component of the nucleon through SU(3) flavor breaking in the sea. Phys. Lett. B 126, 97–100 (1983)CrossRefADSGoogle Scholar
  6. 6.
    Signal A.I., Schreiber A.W., Thomas A.W.: Flavor SU(2) symmetry breaking in deep inelastic scattering. Mod. Phys. Lett. A 6, 271–276 (1991)CrossRefADSGoogle Scholar
  7. 7.
    Melnitchouk W., Thomas A.W., Signal A.I.: Gottfried sum rule and the shape of \({F_2^p - F_2^n}\). Z. Phys. A 340, 85–92 (1991)CrossRefADSGoogle Scholar
  8. 8.
    Kumano S.: Flavor asymmetry of antiquark distributions in the nucleon. Phys. Rep. 303, 183–257 (1998)CrossRefADSGoogle Scholar
  9. 9.
    Speth J., Thomas A.W.: Mesonic contributions to the spin and flavor structure of the nucleon. Adv. Nucl. Phys. 24, 83 (1998)CrossRefGoogle Scholar
  10. 10.
    Chang W.-C., Peng J.-C.: Flavor asymmetry of the nucleon sea and the five-quark components of the nucleons. Phys. Rev. Lett. 106, 252002 (2011)CrossRefADSGoogle Scholar
  11. 11.
    Peng J.-C., Qiu J.-W.: Novel phenomenology of parton distributions from the Drell–Yan process. Prog. Part. Nucl. Phys. 76, 43–75 (2014)CrossRefADSGoogle Scholar
  12. 12.
    Thomas A.W., Melnitchouk W., Steffens F.M.: Dynamical symmetry breaking in the sea of the nucleon. Phys. Rev. Lett. 85, 2892–2894 (2000)CrossRefADSGoogle Scholar
  13. 13.
    Chen J.-W., Ji X.: Constructing parton convolution in effective field theory. Phys. Rev. Lett. 87, 152002 (2001)CrossRefADSGoogle Scholar
  14. 14.
    Chen J.-W., Ji X.: Constructing parton convolution in effective field theory. Phys. Rev. Lett. 88, 249901(E) (2002)CrossRefADSGoogle Scholar
  15. 15.
    Detmold W. et al.: Chiral extrapolation of lattice moments of proton quark distributions. Phys. Rev. Lett. 87, 172001 (2001)CrossRefADSGoogle Scholar
  16. 16.
    Sullivan J.D.: One pion exchange and deep inelastic electron–nucleon scattering. Phys. Rev. D 5, 1732–1737 (1972)CrossRefADSGoogle Scholar
  17. 17.
    Ji C.-R., Melnitchouk W., Thomas A.W.: Comment on ‘taming the pion cloud of the nucleon’. Phys. Rev. Lett. 110, 179101 (2013)CrossRefADSGoogle Scholar
  18. 18.
    Arndt D., Savage M.J.: Chiral corrections to matrix elements of twist-2 operators. Nucl. Phys. A 697, 429–439 (2002)CrossRefADSMATHGoogle Scholar
  19. 19.
    Chen J.W., Ji X.: Is the Sullivan process compatible with QCD chiral dynamics?. Phys. Lett. B 523, 107–110 (2001)CrossRefADSGoogle Scholar
  20. 20.
    Burkardt M. et al.: Pion momentum distributions in the nucleon in chiral effective theory. Phys. Rev. D 87, 056009 (2013)CrossRefADSGoogle Scholar
  21. 21.
    Ji C.-R., Melnitchouk W., Thomas A.W.: Anatomy of relativistic pion loop corrections to the electromagnetic nucleon coupling. Phys. Rev. D 88, 076005 (2013)CrossRefADSGoogle Scholar
  22. 22.
    Moiseeva A.M., Vladimirov A.W.: On chiral corrections to nucleon GPDs. Eur. Phys. J. A 49, 23 (2013)CrossRefADSGoogle Scholar
  23. 23.
    Salamu, Y., et al.: \({\bar d-\bar u}\) Asymmetry in the proton in chiral effective theory. arXiv:1409.1954 [hep-ph]
  24. 24.
    Jenkins E.E., Manohar A.V.: Baryon chiral perturbation theory using a heavy fermion Lagrangian. Phys. Lett. B 255, 558–562 (1991)CrossRefADSGoogle Scholar
  25. 25.
    Bernard V., Kaiser N., Kambor J., Meissner U.-G.: Chiral structure of the nucleon. Nucl. Phys. B 388, 315–345 (1992)CrossRefADSGoogle Scholar
  26. 26.
    Melnitchouk W., Speth J., Thomas A.W.: Dynamics of light anti-quarks in the proton. Phys. Rev. D 59, 014033 (1999)CrossRefADSGoogle Scholar
  27. 27.
    Chen J.-W., Ji X.: Large N c quark distributions in the Δ and chiral logarithms in quark distributions of the nucleon. Phys. Lett. B 523, 73–78 (2001)CrossRefADSGoogle Scholar
  28. 28.
    Wang, P., Thomas, A.W.: The first moments of nucleon generalized parton distributions. Phys. Rev. D 81, 114015 (2010)Google Scholar
  29. 29.
    Dorati M., Gail T.A., Hemmert T.R.: Chiral perturbation theory and the first moments of the generalized parton distributions in a nucleon. Nucl. Phys. A 798, 96–131 (2008)CrossRefADSGoogle Scholar
  30. 30.
    Lin, H.-W., Chen, J.-W., Cohen, S.D., Ji, X.: Flavor structure of the nucleon sea from lattice QCD. arXiv:1402.1462 [hep-ph] (2014)
  31. 31.
    Glück M., Reya E., Schienbein I.: Pionic parton distributions revisited. Eur. Phys. J. C 10, 313–317 (1999)CrossRefADSGoogle Scholar
  32. 32.
    Sutton P.J., Martin A.D., Roberts R.G., Stirling W.J.: Parton distributions for the pion extracted from Drell–Yan and prompt photon experiments. Phys. Rev. D 45, 2349–2359 (1992)CrossRefADSGoogle Scholar
  33. 33.
    Signal A.I., Thomas A.W.: Possible strength of the nonperturbative strange sea of the nucleon. Phys. Lett. B 191, 205–208 (1987)CrossRefADSGoogle Scholar

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© Springer-Verlag Wien 2015

Authors and Affiliations

  1. 1.Institute of High Energy PhysicsCASBeijingChina
  2. 2.North Carolina State UniversityRaleighUSA
  3. 3.Jefferson LabNewport NewsUSA
  4. 4.Theoretical Physics Center for Science FacilitiesCASBeijingChina

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