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Hadronic contributions to the muon anomaly in the constituent chiral quark model

  • David GreynatEmail author
  • Eduardo de Rafael
Open Access
Article

Abstract

The hadronic contributions to the anomalous magnetic moment of the muon which are relevant for the confrontation between theory and experiment at the present level of accuracy, are evaluated within the same framework: the constituent chiral quark model. This includes the contributions from the dominant hadronic vacuum polarization as well as from the next-to-leading order hadronic vacuum polarization, the contributions from the hadronic light-by-light scattering, and the contributions from the electroweak hadronic Zγγ vertex. They are all evaluated as a function of only one free parameter: the constituent quark mass. We also comment on the comparison between our results and other phenomenological evaluations.

Keywords

Phenomenological Models NLO Computations 

References

  1. [1]
    Muon G-2 collaboration, G. Bennett et al., Final report of the muon E821 anomalous magnetic moment measurement at BNL, Phys. Rev. D 73 (2006) 072003 [hep-ex/0602035] [INSPIRE].ADSGoogle Scholar
  2. [2]
    J.P. Miller, E. de Rafael and B.L. Roberts, Muon (g − 2): experiment and theory, Rept. Prog. Phys. 70 (2007) 795.ADSCrossRefGoogle Scholar
  3. [3]
    F. Jegerlehner and A. Nyffeler, The muon g − 2, Phys. Rept. 477 (2009) 1 [arXiv:0902.3360] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    M. Davier, A. Hoecker, B. Malaescu and Z. Zhang, Reevaluation of the hadronic contributions to the muon g − 2 and to α MZ, Eur. Phys. J. C 71 (2011) 1515 [Erratum ibid. C 72 (2012) 1874] [arXiv:1010.4180] [INSPIRE].
  5. [5]
    J. Prades, E. de Rafael and A. Vainshtein, The hadronic light-by-light contribution to a μ,e, in Lepton dipole moments, Advanced series on directions in high energy physics volume 20, B.L. Roberts and W.J. Marciano eds., World Scientific, Singapore (2009)Google Scholar
  6. [6]
    R. Carey et al., FERMILAB-PROPOSAL-0989.
  7. [7]
    T. Mibe, Measurement of muon g − 2 and EDM with an ultra-cold muon beam at J-PARC, Nucl. Phys. (Proc. Suppl.) B 218 (2011) 242.ADSCrossRefGoogle Scholar
  8. [8]
    A.A. Andrianov and L. Bonora, Finite-mode regularization of the fermion functional integral, Nucl. Phys. B 233 (1984) 232 [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    A. De Rújula, H. Georgi and S. Glashow, Hadron masses in a gauge theory, Phys. Rev. D 12 (1975) 147 [INSPIRE].ADSGoogle Scholar
  10. [10]
    S. Weinberg, Phenomenological lagrangians, Physica 96A (1984) 327.ADSGoogle Scholar
  11. [11]
    E. de Rafael, The constituent chiral quark model revisited, Phys. Lett. B 703 (2011) 60 [arXiv:1107.0226] [INSPIRE].ADSGoogle Scholar
  12. [12]
    S. Weinberg, Pions in large-N quantum chromodynamics, Phys. Rev. Lett. 105 (2010) 261601 [arXiv:1009.1537] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    C. Bouchiat and L. Michel, La résonance dans la diffusion méson π méson π et le moment magnétique anormal du méson μ, J. Phys. Radium 22 (1961) 121.CrossRefGoogle Scholar
  14. [14]
    S.J. Brodsky and E. De Rafael, Suggested boson-lepton pair couplings and the anomalous magnetic moment of the muon, Phys. Rev. 168 (1968) 1620 [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    J. Calmet, S. Narison, M. Perrottet and E. de Rafael, The anomalous magnetic moment of the muon: a review of the theoretical contributions, Rev. Mod. Phys. 49 (1977) 21 [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    A. Pivovarov, Muon anomalous magnetic moment: a consistency check for the next-to-leading order hadronic contributions, Phys. Atom. Nucl. 66 (2003) 902 [hep-ph/0110248] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    J. Erler and G.T. Sanchez, An upper bound on the hadronic light-by-light contribution to the muon g − 2, Phys. Rev. Lett. 97 (2006) 161801 [hep-ph/0605052] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    G. Källen and A. Sabry, Fourth order vacuum polarization, Kgl. Danske Videnskab. Selskab, Mat. Fys. Medd. 29N17 (1955) 17.Google Scholar
  19. [19]
    B. Lautrup and E. De Rafael, Calculation of the sixth-order contribution from the fourth-order vacuum polarization to the difference of the anomalous magnetic moments of muon and electron, Phys. Rev. 174 (1968) 1835 [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    D. Espriu, E. de Rafael and J. Taron, The QCD effective action at long distances, Nucl. Phys. B 345 (1990) 22 [Erratum ibid. B 355 (1991) 278-279] [INSPIRE].
  21. [21]
    ETMC collaboration, X. Feng, K. Jansen, M. Petschlies and D.B. Renner, Two-flavor QCD correction to lepton magnetic moments at leading-order in the electromagnetic coupling, Phys. Rev. Lett. 107 (2011) 081802 [arXiv:1103.4818] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    R. Barbieri and E. Remiddi, Electron and muon 1/2 (g − 2) from vacuum polarization insertions, Nucl. Phys. B 90 (1975) 233.ADSCrossRefGoogle Scholar
  23. [23]
    K. Hagiwara, A. Martin, D. Nomura and T. Teubner, Predictions for g − 2 of the muon and α QED (M 2(Z)), Phys. Rev. D 69 (2004) 093003 [hep-ph/0312250] [INSPIRE].ADSGoogle Scholar
  24. [24]
    B.E. Lautrup, A. Peterman and E. de Rafael, Recent developments in the comparison between theory and experiments in quantum electrodynamics, Phys. Rept. 3C (1972) 193.ADSCrossRefGoogle Scholar
  25. [25]
    E. de Rafael, Hadronic contributions to the muon g − 2 and low-energy QCD, Phys. Lett. B 322 (1994) 239 [hep-ph/9311316] [INSPIRE].ADSGoogle Scholar
  26. [26]
    M. Perrottet and E. de Rafael, unpublished.Google Scholar
  27. [27]
    I. Blokland, A. Czarnecki and K. Melnikov, Pion pole contribution to hadronic light by light scattering and muon anomalous magnetic moment, Phys. Rev. Lett. 88 (2002) 071803 [hep-ph/0112117] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    M. Achasov et al., Experimental study of the processes e + e ϕηγ, π 0 γ at VEPP-2M, Eur. Phys. J. C 12 (2000) 25 [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    K. Hagiwara, R. Liao, A.D. Martin, D. Nomura and T. Teubner, (g − 2)μ and \( \alpha \left( {M_Z^2} \right) \) re-evaluated using new precise data, J. Phys. G 38 (2011) 085003 [arXiv:1105.3149] [INSPIRE].ADSGoogle Scholar
  30. [30]
    F. Jegerlehner, Precision measurements of sigma(hadronic) for α eff(E) at ILC energies and (g − 2)μ, Nucl. Phys. Proc. Suppl. 162 (2006) 22 [hep-ph/0608329] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    J. Aldins, T. Kinoshita, S.J. Brodsky and A. Dufner, Photon-photon scattering contribution to the sixth order magnetic moment of the muon, Phys. Rev. Lett. 23 (1969) 441 [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    S. Laporta and E. Remiddi, The analytical value of the electron light-light graphs contribution to the muon (g − 2) in QED, Phys. Lett. B 301 (1993) 440.ADSGoogle Scholar
  33. [33]
    R. Boughezal and K. Melnikov, Hadronic light-by-light scattering contribution to the muon magnetic anomaly: constituent quark loops and QCD effects, Phys. Lett. B 704 (2011) 193 [arXiv:1104.4510] [INSPIRE].ADSGoogle Scholar
  34. [34]
    M. Knecht and A. Nyffeler, Hadronic light by light corrections to the muon g − 2: the pion pole contribution, Phys. Rev. D 65 (2002) 073034 [hep-ph/0111058] [INSPIRE].ADSGoogle Scholar
  35. [35]
    M. Knecht, A. Nyffeler, M. Perrottet and E. de Rafael, Hadronic light by light scattering contribution to the muon g − 2: an effective field theory approach, Phys. Rev. Lett. 88 (2002) 071802 [hep-ph/0111059] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    J.-P. Aguilar, D. Greynat and E. De Rafael, Muon anomaly from lepton vacuum polarization and the Mellin-Barnes representation, Phys. Rev. D 77 (2008) 093010 [arXiv:0802.2618] [INSPIRE].ADSGoogle Scholar
  37. [37]
    K. Melnikov and A. Vainshtein, Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment revisited, Phys. Rev. D 70 (2004) 113006 [hep-ph/0312226] [INSPIRE].ADSGoogle Scholar
  38. [38]
    D. Babusci, H. Czyz, F. Gonnella, S. Ivashyn, M. Mascolo, et al., On the possibility to measure the π 0 toγγ decay width and the γ γtoπ0 transition form factor with the KLOE-2 experiment, Eur. Phys. J. C 72 (2012) 1917 [arXiv:1109.2461] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    T. Goecke, C.S. Fischer and R. Williams, Hadronic contribution to the muon g − 2: a Dyson-Schwinger perspective, Prog. Part. Nucl. Phys. 67 (2012) 563 [arXiv:1111.0990] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    S. Peris, M. Perrottet and E. de Rafael, Two loop electroweak corrections to the muon g − 2: a new class of hadronic contributions, Phys. Lett. B 355 (1995) 523 [hep-ph/9505405] [INSPIRE].ADSGoogle Scholar
  41. [41]
    A. Czarnecki, B. Krause and W. Marciano, Electroweak fermion loop contributions to the muon anomalous magnetic moment, Phys. Rev. D 52 (1995) 2619 [hep-ph/9506256] [INSPIRE].ADSGoogle Scholar
  42. [42]
    M. Knecht, S. Peris, M. Perrottet and E. De Rafael, Electroweak hadronic contributions to the muon (g − 2), JHEP 11 (2002) 003 [hep-ph/0205102] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    A. Vainshtein, Perturbative and nonperturbative renormalization of anomalous quark triangles, Phys. Lett. B 569 (2003) 187 [hep-ph/0212231] [INSPIRE].ADSGoogle Scholar
  44. [44]
    A. Czarnecki, W.J. Marciano and A. Vainshtein, Refinements in electroweak contributions to the muon anomalous magnetic moment, Phys. Rev. D 67 (2003) 073006 [Erratum ibid. D 73 (2006) 119901] [hep-ph/0212229] [INSPIRE].
  45. [45]
    M. Knecht, S. Peris, M. Perrottet and E. de Rafael, New nonrenormalization theorems for anomalous three point functions, JHEP 03 (2004) 035 [hep-ph/0311100] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA 2012

Authors and Affiliations

  1. 1.Departamento de Física Teórica, Facultad de CienciasUniversidad de ZaragozaZaragozaSpain
  2. 2.Centre de Physique Théorique, CNRS-LuminyMarseille Cedex 9France

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