Advertisement

Physics of Atomic Nuclei

, Volume 71, Issue 8, pp 1461–1469 | Cite as

Study of systematic errors of bound-state parameters in SVZ sum rules

  • W. Lucha
  • D. I. Melikhov
  • S. Simula
Elementary Particles and Fields Theory

Abstract

We study systematic errors of the ground-state parameters obtained from Shifman—Vainshtein—Zakharov sum rules, making use of the harmonic-oscillator potential model as an example. In this case, one knows the exact solution for the polarization operator, which allows one to obtain both the OPE to any order and the parameters (masses and decay constants) of the bound states. We determine the parameters of the ground state making use of the standard procedures of the method of sum rules and compare the obtained results with the known exact values. We show that, in the situation when the continuum contribution to the polarization operator is not known and is modeled by an effective continuum, the method of sum rules does not allow one to control the systematic uncertainties of the extracted ground-state parameters.

PACS numbers

11.55.Hx 12.38.Lg 03.65.Ge 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Shifman, A. Vainshtein, and V. Zakharov, Nucl. Phys. B 147, 385 (1979).CrossRefADSGoogle Scholar
  2. 2.
    V. Novikov, M. Shifman, A. Vainshtein, and V. Zakharov, Nucl. Phys. B 237, 525 (1984).CrossRefADSGoogle Scholar
  3. 3.
    A. I. Vainshtein, V. I. Zakharov, V. A. Novikov, and M. A. Shifman, Sov. J. Nucl. Phys. 32, 840 (1980).MathSciNetGoogle Scholar
  4. 4.
    V. A. Novikov et al., Phys. Rep. 41, 1 (1978); M. B. Voloshin, Nucl. Phys. B 154, 365 (1979); J. S. Bell and R. Bertlmann, Nucl. Phys. B 177, 218 (1981); 187, 285 (1981); V. A. Novikov, M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Nucl. Phys. B 191, 301 (1981).CrossRefADSGoogle Scholar
  5. 5.
    A. Le Yaouanc et al., Phys. Rev. D 62, 074007 (2000); Phys. Lett. B 488, 153 (2000); 517, 135 (2001).Google Scholar
  6. 6.
    D. Melikhov and S. Simula, Phys. Rev. D 62, 074012 (2000).Google Scholar
  7. 7.
    P. Colangelo and A. Khodjamirian, QCD Sum Rules: aModern Perspective, in At the Frontier of Particle Physics, Ed. by M. Shifman (World Sci., Singapore, 2001), Vol. 3, p. 1495; hep-ph/0010175.Google Scholar
  8. 8.
    M. Jamin and B. Lange, Phys. Rev. D 65, 056005 (2002).Google Scholar
  9. 9.
    W. Lucha, D. Melikhov, and S. Simula, Phys. Rev. D 76, 036002 (2007); AIP Conf. Proc. 964, 296 (2007); Phys. Lett. B 657, 148 (2007).Google Scholar
  10. 10.
    V. A. Nesterenko and A. V. Radyushkin, Phys. Lett. B 115, 410 (1982).CrossRefADSGoogle Scholar
  11. 11.
    W. Lucha and D. Melikhov, Phys. Rev. D 73, 054009 (2006); Phys. At. Nucl. 70, 891 (2007); V. Braguta, W. Lucha, and D.Melikhov, hep-ph/0710.5461.Google Scholar
  12. 12.
    W. Lucha, D. Melikhov, and S. Simula, Phys. Rev. D 75, 096002 (2007).Google Scholar
  13. 13.
    D. Melikhov and S. Simula, Eur. Phys. J. C 37, 437 (2004).CrossRefADSGoogle Scholar
  14. 14.
    P. Ball and R. Zwicky, Phys. Rev. D 71, 014015 (2005).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  • W. Lucha
    • 1
  • D. I. Melikhov
    • 1
    • 2
  • S. Simula
    • 3
  1. 1.Institute for High Energy PhysicsAustrian Academy of SciencesViennaAustria
  2. 2.Institute of Nuclear PhysicsMoscow State UniversityMoscowRussia
  3. 3.INFNRomaItaly

Personalised recommendations