Advertisement

The European Physical Journal C

, Volume 51, Issue 4, pp 945–952 | Cite as

Fermion family recurrences in the Dyson–Schwinger formalism

  • Felipe J. Llanes-Estrada
  • Tim Van Cauteren
  • Ángel P. Martín
Regular Article - Theoretical Physics

Abstract

We study the multiple solutions of the truncated propagator Dyson–Schwinger equation for a simple fermion theory with Yukawa coupling to a scalar field. Upon increasing the coupling constant g, other parameters being fixed, more than one non-perturbative solution breaking chiral symmetry becomes possible and we find these numerically. These “recurrences” appear as a mechanism to generate different fermion generations as quanta of the same fundamental field in an interacting field theory, without assuming any composite structure. The number of recurrences or flavors is reduced to the question of the value of the Yukawa coupling, and it has no special profound significance in the standard model. The resulting mass function can have one or more nodes and the measurement that potentially detects them can be thought of as a collider-based test of the virtual dispersion relation \(E=\sqrt{p^2+M(p^2)^2}\) for the charged lepton member of each family. This requires the three independent measurements of the charged lepton’s energy, three-momentum and off-shellness. We illustrate how this can be achieved for the (more difficult) case of the tau lepton.

Keywords

Yukawa Coupling Chiral Symmetry Mass Function Charged Lepton Virtual Particle 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. Fritzsch, Nucl. Phys. Proc. Suppl. 40, 121 (1995) [arXiv:hep-ph/9411419]ADSCrossRefGoogle Scholar
  2. 2.
    R. Dermisek, Phys. Rev. D 70, 033007 (2004) [arXiv:hep-ph/0312206]ADSCrossRefGoogle Scholar
  3. 3.
    C.D. Froggatt, H.B. Nielsen, Nucl. Phys. B 147, 277 (1979)ADSCrossRefGoogle Scholar
  4. 4.
    C.D. Froggatt, H.B. Nielsen, D.J. Smith, Phys. Lett. B 385, 150 (1996) [arXiv:hep-ph/9607250]ADSCrossRefGoogle Scholar
  5. 5.
    J.C. Pati, Phys. Rev. D 30, 1144 (1984)ADSCrossRefGoogle Scholar
  6. 6.
    C.D. Roberts, arXiv:nucl-th/0301065Google Scholar
  7. 7.
    P. Maris, C.D. Roberts, Int. J. Mod. Phys. E 12, 297 (2003) [arXiv:nucl-th/0301049]ADSCrossRefGoogle Scholar
  8. 8.
    T. Brauner, J. Hosek, Phys. Rev. D 72, 045007 (2005) [arXiv:hep-ph/0505231]ADSCrossRefGoogle Scholar
  9. 9.
    P.J. de A. Bicudo, J.E.F.T. Ribeiro, Phys. Rev. D 42, 1611 (1990)ADSCrossRefGoogle Scholar
  10. 10.
    A. Le Yaouanc, L. Oliver, S. Ono, O. Pene, J.C. Raynal, Phys. Rev. D 31, 137 (1985)ADSCrossRefGoogle Scholar
  11. 11.
    S.L. Adler, A.C. Davis, Nucl. Phys. B 244, 469 (1984)ADSCrossRefGoogle Scholar
  12. 12.
    A.P. Szczepaniak, E.S. Swanson, Phys. Rev. D 55, 1578 (1997) [arXiv:hep-ph/9609525]ADSCrossRefGoogle Scholar
  13. 13.
    F.J. Llanes-Estrada, S.R. Cotanch, Nucl. Phys. A 697, 303 (2002) [arXiv:hep-ph/0101078]ADSCrossRefGoogle Scholar
  14. 14.
    F.J. Llanes-Estrada, P.J. de A. Bicudo, Phys. Rev. D 68, 094014 (2003) [arXiv:hep-ph/0306146]ADSCrossRefGoogle Scholar
  15. 15.
    P.J. de A. Bicudo, J.E.F.T. Ribeiro, A.V. Nefediev, Phys. Rev. D 65, 085026 (2002) [arXiv:hep-ph/0201173]ADSCrossRefGoogle Scholar
  16. 16.
    A. Kizillersu, private communicationGoogle Scholar
  17. 17.
    A. Kizilersu, T. Sizer, A.G. Williams, Prepared for 5th International Conference on Quark Confinement and the Hadron Spectrum, Gargnano, Brescia, Italy, 10–14 September 2002Google Scholar
  18. 18.
    A.V. Nefediev, J.E.F.T. Ribeiro, Phys. Rev. D 70, 094020 (2004) [arXiv:hep-ph/0409112]ADSCrossRefGoogle Scholar
  19. 19.
    V. Sauli, JHEP 0302, 001 (2003) [arXiv:hep-ph/0209046]ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    D. Mattingly, Living Rev. Relat. 8, 5 (2005) [arXiv:gr-qc/0502097]ADSCrossRefGoogle Scholar
  21. 21.
    O. Igonkina, arXiv:hep-ex/0606009Google Scholar
  22. 22.
    OPERA Collaboration, arXiv:hep-ex/0611023Google Scholar
  23. 23.
    F. Halzen, A.D. Martin, Quarks & Leptons: An Introductory Course in Modern Particle Physics, 1st. edn. (John Wiley & Sons, Inc., New York, 1984)Google Scholar
  24. 24.
    J.A.M. Vermaseren, New features of FORM, math-ph/0010025Google Scholar

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2007

Authors and Affiliations

  • Felipe J. Llanes-Estrada
    • 1
  • Tim Van Cauteren
    • 1
    • 2
  • Ángel P. Martín
    • 1
  1. 1.Depto. Física Teórica IUniversidad Complutense de MadridMadridSpain
  2. 2.Dept. Subatomic and Radiation PhysicsGhent UniversityGhentBelgium

Personalised recommendations