Skip to main content
SpringerLink
Log in

Pion Loops in Chiral Perturbation Theory and Light-Front Dynamics

  • Published:
Few-Body Systems Aims and scope Submit manuscript

Abstract

From the approximate chiral symmetry of QCD, it is known that the pion loops in chiral perturbation theory play a vital role in understanding the nucleon’s long-range structure. We demonstrate the equivalence of the light-front, equal-time and covariant formulations for the interactions of nucleons with pions in chiral perturbation theory. In particular, we discuss the self-energy Σ of a nucleon dressed by pion loops with the pseudovector πNN coupling. It is shown that the leading nonanalytic behavior of Σ is equivalent whichever formulations are used for the derivation. We also discuss the relation between the mass shift and the wavefunction renormalization as well as the difference between the pseudovector and pseudoscalar theories.

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. Thomas A.W.: Chiral symmetry and the bag model: a new starting point for nuclear physics. Adv. Nucl. Phys. 13, 1–137 (1984)

    Article  Google Scholar 

  2. Ji X.: Generalized parton distributions. Ann. Rev. Nucl. Part. Sci. 54, 413–450 (2004)

    Article  ADS  Google Scholar 

  3. Belitsky A.V., Radyushkin A.V.: Unraveling hadron structure with generalized parton distributions. Phys. Rept. 418, 1–387 (2005)

    Article  ADS  Google Scholar 

  4. Thomas A.W., Melnitchouk W., Steffens F.M.: Dynamical symmetry breaking in the sea of the nucleon. Phys. Rev. Lett. 85, 2892–2894 (2000)

    Article  ADS  Google Scholar 

  5. Detmold W., Melnitchouk W., Negele J.W., Renner D.B., Thomas A.W.: Chiral extrapolation of lattice moments of proton quark distributions. Phys. Rev. Lett. 87, 172001 (2001)

    Article  ADS  Google Scholar 

  6. Chen J.W., Ji X.: Is the Sullivan process compatible with QCD chiral dynamics?. Phys. Lett. B 523, 107–110 (2001)

    Article  ADS  Google Scholar 

  7. Arndt D., Savage M.J.: Chiral corrections to matrix elements of twist-2 operators. Nucl. Phys. A 697, 429–439 (2002)

    Article  ADS  MATH  Google Scholar 

  8. Ji C.-R., Melnitchouk W., Thomas A.W.: Equivalence of pion loops in equal-time and light-front dynamics. Phys. Rev. D 80, 054018 (2009)

    Article  ADS  Google Scholar 

  9. Dirac P.A.M.: Forms of relativistic dynamics. Rev. Mod. Phys. 21, 392–399 (1949)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. Ji, C.-R.: Zero-mode Caveats in transition form factors, pp. 86–89. IPPP/03/71, Durham (2003)

  11. Ji C.-R.: Perspectives of light-front dynamics in few-body systems. Nucl. Phys. A 737, 255–259 (2004)

    Article  ADS  Google Scholar 

  12. Ji C.-R., Bakker B.L.G.: Vector anomaly and practicality of light-front dynamics. Few-Body Syst. 36, 137–144 (2005)

    Article  ADS  Google Scholar 

  13. Ji C.-R., Rey S.-J.: Light front view of the axial anomaly. Phys. Rev. D 53, 5815–5820 (1996)

    Article  ADS  Google Scholar 

  14. Bakker B.L.G., Ji C.-R.: Manifestations of the vector anomaly in covariant and light-front calculations of the anomalous magnetic moment of W+- bosons. Phys. Rev. D 71, 053005 (2005)

    Article  ADS  Google Scholar 

  15. Bakker B.L.G., DeWitt M.A., Ji C.-R., Mishchenko Y.: Restoring the equivalence between the light-front and manifestly covariant formalisms. Phys. Rev. D 72, 076005 (2005)

    Article  ADS  Google Scholar 

  16. Misra A., Warawdekar S.: Equivalence of covariant and light front QED at one loop level. Phys. Rev. D 71, 125011 (2005)

    Article  ADS  Google Scholar 

  17. Bernard V., Kaiser N., Meissner U.G.: Chiral dynamics in nucleons and nuclei. Int. J. Mod. Phys. E 4, 193–346 (1995)

    Article  ADS  Google Scholar 

  18. Ericson T., Weise W.: Pions and Nuclei. Clarendon Press, Oxford (1988)

    Google Scholar 

  19. Leinweber D.B., Thomas A.W., Tsushima K., Wright S.V.: Baryon masses from lattice QCD: beyond the perturbative chiral regime. Phys. Rev. D 61, 074502 (2000)

    Article  ADS  Google Scholar 

  20. Bjorken J.D., Drell S.: Relativistic quantum fields. McGraw Hill, New York (1965)

    MATH  Google Scholar 

  21. Burkardt, M., Ji, C.-R., Melnitchouk, W., Thomas, A.W. (in preparation)

  22. Drell S.D., Levy D.J., Yan T.M.: Theory of deep-inelastic lepton–nucleon scattering and lepton pair annihilation processes. II. Deep-inelastic electron scattering. Phys. Rev. D 1, 1035 (1970)

    Article  ADS  Google Scholar 

  23. Chen, J.W., Ji, X.: Constructing parton convolution in effective field theory. Phys. Rev. Lett. 87, 152002 (2001) [Erratum-ibid. 88, 249901 (2002)]

    Google Scholar 

  24. Chen J.W., Ji X.: Large N(c) quark distributions in the delta and chiral logarithms in quark distributions of the nucleon. Phys. Lett. B 523, 73–78 (2001)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, North Carolina State University, Raleigh, NC, 27695-8202, USA

    Chueng-Ryong Ji

Authors
  1. Chueng-Ryong Ji
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chueng-Ryong Ji.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ji, CR. Pion Loops in Chiral Perturbation Theory and Light-Front Dynamics. Few-Body Syst 52, 421–426 (2012). https://doi.org/10.1007/s00601-011-0270-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00601-011-0270-5

Keywords

Search

Navigation