The light-by-light contribution to the muon (g-2) from lightest pseudoscalar and scalar mesons within nonlocal chiral quark model

  • A. E. Dorokhov
  • A. E. Radzhabov
  • A. S. Zhevlakov
Regular Article - Theoretical Physics

Abstract

The light-by-light contribution from the lightest neutral pseudoscalar and scalar mesons to the anomalous magnetic moment of muon is calculated in the framework of the nonlocal SU(3)×SU(3) quark model. The model is based on chirally symmetric four-quark interaction of the Nambu–Jona-Lasinio type and Kobayashi–Maskawa–’t Hooft UA(1) breaking six-quark interaction. Full kinematic dependence of vertices with off-shell mesons and photons in intermediate states in the light-by-light scattering amplitude is taken into account. The small positive contributions from the scalar mesons stabilize the total result with respect to change of model parameters and reduces to \(a_{\mu}^{\mathrm{LbL},\mathrm{PS}+\mathrm{S}}=(6.25\pm0.83)\cdot10^{-10}\).

References

  1. 1.
    G.W. Bennett et al., Phys. Rev. D 73, 072003 (2006) ADSGoogle Scholar
  2. 2.
    F. Jegerlehner, A. Nyffeler, Phys. Rep. 477, 1 (2009) ADSCrossRefGoogle Scholar
  3. 3.
    M. Davier, A. Hoecker, B. Malaescu, Z. Zhang, Eur. Phys. J. C 71, 1515 (2011) ADSCrossRefGoogle Scholar
  4. 4.
    F. Jegerlehner, R. Szafron, Eur. Phys. J. C 71, 1632 (2011) ADSCrossRefGoogle Scholar
  5. 5.
    E. de Rafael, Phys. Lett. B 322, 239 (1994) ADSGoogle Scholar
  6. 6.
    M. Hayakawa, T. Kinoshita, A. Sanda, Phys. Rev. Lett. 75, 790 (1995) ADSCrossRefGoogle Scholar
  7. 7.
    J. Bijnens, E. Pallante, J. Prades, Phys. Rev. Lett. 75, 1447 (1995) ADSCrossRefGoogle Scholar
  8. 8.
    M. Hayakawa, T. Kinoshita, Phys. Rev. D 57, 465 (1998) ADSGoogle Scholar
  9. 9.
    A.A. Pivovarov, Phys. At. Nucl. 66, 902 (2003). Yad. Fiz. 66, 934 (2003) CrossRefGoogle Scholar
  10. 10.
    M. Knecht, A. Nyffeler, Phys. Rev. D 65, 073034 (2002) ADSGoogle Scholar
  11. 11.
    K. Melnikov, A. Vainshtein, Phys. Rev. D 70, 113006 (2004) ADSGoogle Scholar
  12. 12.
    A. Nyffeler, Phys. Rev. D 79, 073012 (2009) ADSGoogle Scholar
  13. 13.
    L. Cappiello, O. Cata, G. D’Ambrosio, Phys. Rev. D 83, 093006 (2011) ADSGoogle Scholar
  14. 14.
    J. Bijnens, E. Pallante, J. Prades, Nucl. Phys. B 474, 379 (1996) ADSCrossRefGoogle Scholar
  15. 15.
    E. Bartos, A.Z. Dubnickova, S. Dubnicka, E.A. Kuraev, E. Zemlyanaya, Nucl. Phys. B 632, 330 (2002) ADSCrossRefGoogle Scholar
  16. 16.
    A.E. Dorokhov, W. Broniowski, Phys. Rev. D 78, 073011 (2008) ADSGoogle Scholar
  17. 17.
    A. Dorokhov, A. Radzhabov, A. Zhevlakov, Eur. Phys. J. C 71, 1702 (2011) ADSCrossRefGoogle Scholar
  18. 18.
    C.S. Fischer, T. Goecke, R. Williams, Eur. Phys. J. A 47, 28 (2011) ADSCrossRefGoogle Scholar
  19. 19.
    T. Goecke, C.S. Fischer, R. Williams, Phys. Rev. D 83, 094006 (2011) ADSGoogle Scholar
  20. 20.
    D.K. Hong, D. Kim, Phys. Lett. B 680, 480 (2009) ADSGoogle Scholar
  21. 21.
    I.V. Anikin, A.E. Dorokhov, L. Tomio, Phys. Part. Nucl. 31, 509 (2000). Fiz. Elem. Chast. Atom. Yadra 31, 1023 (2000) Google Scholar
  22. 22.
    A.E. Dorokhov, W. Broniowski, Eur. Phys. J. C 32, 79 (2003) ADSCrossRefGoogle Scholar
  23. 23.
    A.E. Radzhabov, M.K. Volkov, Eur. Phys. J. A 19, 139 (2004) ADSCrossRefGoogle Scholar
  24. 24.
    A.E. Radzhabov, M.K. Volkov, Phys. Part. Nucl. Lett. 1, 1 (2004) Google Scholar
  25. 25.
    A.E. Radzhabov, D. Blaschke, M. Buballa, M.K. Volkov, Phys. Rev. D 83, 116004 (2011) ADSGoogle Scholar
  26. 26.
    M. Kobayashi, T. Maskawa, Prog. Theor. Phys. 44, 1422 (1970) ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    G. ’t Hooft, Phys. Rev. D 14, 3432 (1976). Erratum-ibid. D 18, 2199 (1978) ADSGoogle Scholar
  28. 28.
    N.N. Achasov, A.V. Kiselev, Phys. Rev. D 83, 054008 (2011) ADSGoogle Scholar
  29. 29.
    J. Terning, Phys. Rev. D 44, 887 (1991) ADSGoogle Scholar
  30. 30.
    A. Scarpettini, D. Gomez Dumm, N.N. Scoccola, Phys. Rev. D 69, 114018 (2004) ADSGoogle Scholar
  31. 31.
    K. Nakamura et al., J. Phys. G 37, 075021 (2010) ADSCrossRefGoogle Scholar
  32. 32.
    S.J. Brodsky, E. de Rafael, Phys. Rev. 168, 1620 (1968) ADSCrossRefGoogle Scholar
  33. 33.
    I.R. Blokland, A. Czarnecki, K. Melnikov, Phys. Rev. Lett. 88, 071803 (2002) ADSCrossRefGoogle Scholar
  34. 34.
    M. Oertel, M. Buballa, J. Wambach, Phys. Lett. B 477, 77 (2000) ADSGoogle Scholar
  35. 35.
    M. Knecht, A. Nyffeler, M. Perrottet, E. de Rafael, Phys. Rev. Lett. 88, 071802 (2002) ADSCrossRefGoogle Scholar
  36. 36.
    M. Oertel, M. Buballa, J. Wambach, Phys. At. Nucl. 64, 698 (2001) CrossRefGoogle Scholar
  37. 37.
    D. Blaschke, M. Buballa, A.E. Radzhabov, M.K. Volkov, Phys. At. Nucl. 71, 1981 (2008) CrossRefGoogle Scholar
  38. 38.
    J. Prades, E. de Rafael, A. Vainshtein, Lepton Dipole Moments. Advanced Series on Directions in High Energy Physics, vol. 20 (World Scientific, Singapore, 2009), p. 303. arXiv:0901.0306 [hep-ph] CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • A. E. Dorokhov
    • 1
    • 2
  • A. E. Radzhabov
    • 3
  • A. S. Zhevlakov
    • 3
  1. 1.Bogoliubov Laboratory of Theoretical PhysicsJINRDubnaRussia
  2. 2.N.N. Bogoliubov Institute of Theoretical Problems of MicroworldM.V. Lomonosov Moscow State UniversityMoscowRussia
  3. 3.Institute for System Dynamics and Control Theory SB RASIrkutskRussia

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