Advertisement

Limitations of the heavy-baryon expansion as revealed by a pion-mass dispersion relation

  • Jonathan M. M. HallEmail author
  • Vladimir Pascalutsa
Regular Article - Theoretical Physics

Introduction

The dependence of hadron properties on the quark masses—the chiral behaviour—is crucial for interpreting the modern lattice QCD calculations, which usually require an extrapolation in the quark mass. It is also important for determining the quark-mass values, as well as for any quantitative description of chiral symmetry breaking. Chiral perturbation theory (χPT) [1, 2], a low-energy effective field theory (EFT) of QCD, should in principle describe the nonanalytic dependencies on the light-quark masses in a systematic fashion. The analytic (series-like) dependencies are more arbitrary in χPT, and are specified in terms of low-energy constants (LECs). They are to be fixed by matching to the underlying theory, which is usually achieved by fitting to lattice QCD results.

In the baryon sector of χPT one often invokes an additional expansion in the inverse baryon masses called the heavy-baryon expansion, or HBχPT [3, 4]. The baryon χPT without the heavy-baryon expansion will...

Keywords

Anomalous Magnetic Moment Chiral Symmetry Breaking Pion Mass Loop Momentum Nucleon Mass 
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.

Notes

Acknowledgements

V.P. is thankful to Dr. Nikolai Kivel for stimulating discussions of the heavy-quark and heavy-baryon expansions. This work has been supported by the Deutsche Forschungsgemeinschaft through the Collaborative Research Centre SFB1044, and by the Australian Research Council through grant DP110101265.

References

  1. 1.
    S. Weinberg, Physica A 96, 327 (1979) ADSCrossRefGoogle Scholar
  2. 2.
    J. Gasser, H. Leutwyler, Ann. Phys. 158, 142 (1984) ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    E.E. Jenkins, A.V. Manohar, Phys. Lett. B 255, 558 (1991) ADSCrossRefGoogle Scholar
  4. 4.
    V. Bernard, N. Kaiser, U.-G. Meissner, Int. J. Mod. Phys. E 4, 193 (1995). hep-ph/9501384 ADSCrossRefGoogle Scholar
  5. 5.
    H. Georgi, Nucl. Phys. B 361, 339 (1991) ADSCrossRefGoogle Scholar
  6. 6.
    H. Georgi, Annu. Rev. Nucl. Part. Sci. 43, 209 (1993) ADSCrossRefGoogle Scholar
  7. 7.
    T. Becher, H. Leutwyler, Eur. Phys. J. C 9, 643 (1999). hep-ph/9901384 ADSGoogle Scholar
  8. 8.
    T. Fuchs, J. Gegelia, G. Japaridze, S. Scherer, Phys. Rev. D 68, 056005 (2003). hep-ph/0302117 ADSCrossRefGoogle Scholar
  9. 9.
    V. Pascalutsa, B.R. Holstein, M. Vanderhaeghen, Phys. Lett. B 600, 239 (2004). hep-ph/0407313 ADSCrossRefGoogle Scholar
  10. 10.
    B.R. Holstein, V. Pascalutsa, M. Vanderhaeghen, Phys. Rev. D 72, 094014 (2005). hep-ph/0507016 ADSCrossRefGoogle Scholar
  11. 11.
    V. Pascalutsa, M. Vanderhaeghen, Phys. Rev. Lett. 95, 232001 (2005). hep-ph/0508060 ADSCrossRefGoogle Scholar
  12. 12.
    L. Geng, J. Martin Camalich, L. Alvarez-Ruso, M. Vicente Vacas, Phys. Rev. Lett. 101, 222002 (2008). 0805.1419 ADSCrossRefGoogle Scholar
  13. 13.
    T. Ledwig, J. Martin-Camalich, V. Pascalutsa, M. Vanderhaeghen, Phys. Rev. D 85, 034013 (2012). 1108.2523 ADSCrossRefGoogle Scholar
  14. 14.
    J. Alarcon, J. Martin Camalich, J. Oller, 1110.3797 (2011)
  15. 15.
    V. Bernard, N. Kaiser, U.G. Meissner, Phys. Rev. Lett. 67, 1515 (1991) ADSCrossRefGoogle Scholar
  16. 16.
    R.P. Hildebrandt, H.W. Griesshammer, T.R. Hemmert, B. Pasquini, Eur. Phys. J. A 20, 293 (2004). nucl-th/0307070 ADSCrossRefGoogle Scholar
  17. 17.
    V. Pascalutsa, PoS CD09, 095 (2009), 0910.3686
  18. 18.
    T. Ledwig, V. Pascalutsa, M. Vanderhaeghen, Phys. Lett. B 690, 129 (2010). 1004.3449 ADSCrossRefGoogle Scholar
  19. 19.
    J.F. Donoghue, B.R. Holstein, B. Borasoy, Phys. Rev. D 59, 036002 (1999). hep-ph/9804281 ADSGoogle Scholar
  20. 20.
    D.B. Leinweber, D.-H. Lu, A.W. Thomas, Phys. Rev. D 60, 034014 (1999). hep-lat/9810005 ADSCrossRefGoogle Scholar
  21. 21.
    R.D. Young, D.B. Leinweber, A.W. Thomas, S.V. Wright, Phys. Rev. D 66, 094507 (2002). hep-lat/0205017 ADSGoogle Scholar
  22. 22.
    R.D. Young, D.B. Leinweber, A.W. Thomas, Prog. Part. Nucl. Phys. 50, 399 (2003). hep-lat/0212031 ADSCrossRefGoogle Scholar
  23. 23.
    B. Borasoy, B.R. Holstein, R. Lewis, P.P.A. Ouimet, Phys. Rev. D 66, 094020 (2002). hep-ph/0210092 ADSCrossRefGoogle Scholar
  24. 24.
    D.B. Leinweber, A.W. Thomas, R.D. Young, Phys. Rev. Lett. 92, 242002 (2004). hep-lat/0302020 ADSCrossRefGoogle Scholar
  25. 25.
    V. Bernard, T.R. Hemmert, U.-G. Meissner, Nucl. Phys. A 732, 149 (2004). hep-ph/0307115 ADSzbMATHCrossRefGoogle Scholar
  26. 26.
    R.D. Young, D.B. Leinweber, A.W. Thomas, Phys. Rev. D 71, 014001 (2005). hep-lat/0406001 ADSCrossRefGoogle Scholar
  27. 27.
    D.B. Leinweber et al., Phys. Rev. Lett. 94, 212001 (2005). hep-lat/0406002 ADSCrossRefGoogle Scholar
  28. 28.
    D.B. Leinweber, A.W. Thomas, R.D. Young, Nucl. Phys. A 755, 59 (2005). hep-lat/0501028 ADSCrossRefGoogle Scholar
  29. 29.
    S. Aoki et al. (PACS-CS Collaboration), Phys. Rev. D 79, 034503 (2009). 0807.1661 ADSCrossRefGoogle Scholar
  30. 30.
    H. Ohki et al., Phys. Rev. D 78, 054502 (2008). 0806.4744 ADSGoogle Scholar
  31. 31.
    S. Collins, M. Gockeler, P. Hagler, R. Horsley, Y. Nakamura et al., Phys. Rev. D 84, 074507 (2011). 1106.3580 ADSCrossRefGoogle Scholar
  32. 32.
    A. Manohar, H. Georgi, Nucl. Phys. B 234, 189 (1984) ADSCrossRefGoogle Scholar
  33. 33.
    J. Hall, D. Leinweber, R. Young, Phys. Rev. D 82, 034010 (2010). 1002.4924 ADSCrossRefGoogle Scholar
  34. 34.
    J. Hall, F. Lee, D. Leinweber, K. Liu, N. Mathur et al., Phys. Rev. D 84, 114011 (2011). 1101.4411 ADSCrossRefGoogle Scholar
  35. 35.
    V. Lensky, V. Pascalutsa, Eur. Phys. J. C 65, 195 (2010). 0907.0451 ADSCrossRefGoogle Scholar
  36. 36.
    D.B. Kaplan, M.J. Savage, M.B. Wise, Nucl. Phys. B 534, 329 (1998). nucl-th/9802075 ADSCrossRefGoogle Scholar
  37. 37.
    T.D. Cohen, J.M. Hansen, Phys. Rev. C 59, 13 (1999). nucl-th/9808038 ADSCrossRefGoogle Scholar
  38. 38.
    E. Epelbaum, J. Gegelia, Phys. Lett. B 716, 338 (2012). 1207.2420 ADSCrossRefGoogle Scholar
  39. 39.
    M. Gell-Mann, R. Oakes, B. Renner, Phys. Rev. 175, 2195 (1968) ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2012

Authors and Affiliations

  1. 1.Special Research Centre for the Subatomic Structure of Matter (CSSM), Department of PhysicsUniversity of AdelaideAdelaideAustralia
  2. 2.Institut für KernphysikJohannes Gutenberg UniversitätMainzGermany

Personalised recommendations