SU(2)×U(1) Yang–Mills theories in 3d with Higgs field and Gribov ambiguity

  • M. A. L. CapriEmail author
  • D. Dudal
  • M. S. Guimaraes
  • I. F. Justo
  • S. P. Sorella
  • D. Vercauteren
Regular Article - Theoretical Physics


We study the structure of the gauge propagators of a 3d version of the electroweak interaction in terms of the Higgs vacuum expectation value ν, of the non-Abelian gauge coupling g, and of the Abelian gauge coupling g′, when nonperturbative effects related to the non-Abelian gauge fixing are introduced by means of an adapted path integral measure. In the perturbative regime of small non-Abelian coupling g and sufficiently large ν, the well-known standard Z and W propagators are recovered, together with a massless photon. In general, depending on the relative magnitudes of g, g′ and ν, we uncover a quite different propagator structure. In a later stage of research, the results here derived can be used to study the associated phase diagram in more depth.


Gauge Boson Gauge Field Higgs Field Landau Gauge Saddle Point Approximation 
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.



The Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq-Brazil), the Faperj, Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro, the Latin American Center for Physics (CLAF), the SR2-UERJ, the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) are gratefully acknowledged. D.D. is supported by the Research-Foundation Flanders.

Work supported by FAPERJ, Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro, under the program Cientista do Nosso Estado, E-26/101.578/2010.


  1. 1.
    E.H. Fradkin, S.H. Shenker, Phys. Rev. D 19, 3682 (1979) ADSCrossRefGoogle Scholar
  2. 2.
    W. Caudy, J. Greensite, Phys. Rev. D 78, 025018 (2008). arXiv:0712.0999 [hep-lat] ADSCrossRefGoogle Scholar
  3. 3.
    J. Greensite, Lect. Notes Phys. 821, 1 (2011) MathSciNetCrossRefGoogle Scholar
  4. 4.
    C. Bonati, G. Cossu, M. D’Elia, A. Di Giacomo, Nucl. Phys. B 828, 390 (2010). arXiv:0911.1721 [hep-lat] ADSCrossRefzbMATHGoogle Scholar
  5. 5.
    M.A.L. Capri, D. Dudal, A.J. Gomez, M.S. Guimaraes, I.F. Justo, S.P. Sorella, Eur. Phys. J. C 73, 2346 (2013). arXiv:1210.4734 [hep-th] ADSCrossRefGoogle Scholar
  6. 6.
    V.N. Gribov, Nucl. Phys. B 139, 1 (1978) MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    R.F. Sobreiro, S.P. Sorella. arXiv:hep-th/0504095
  8. 8.
    N. Vandersickel, D. Zwanziger, Phys. Rep. 520, 175 (2012). arXiv:1202.1491 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    K. Kajantie, M. Laine, K. Rummukainen, M.E. Shaposhnikov, Nucl. Phys. B 458, 90 (1996). hep-ph/9508379 ADSCrossRefGoogle Scholar
  10. 10.
    I.M. Singer, Commun. Math. Phys. 60, 7 (1978) ADSCrossRefzbMATHGoogle Scholar
  11. 11.
    M.A.L. Capri, D. Dudal, M.S. Guimaraes, L.F. Palhares, S.P. Sorella, Phys. Lett. B 719, 448 (2013). arXiv:1212.2419 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    D. Zwanziger, Nucl. Phys. B 323, 513 (1989) MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    L. Baulieu, D. Dudal, M.S. Guimaraes, M.Q. Huber, S.P. Sorella, N. Vandersickel, D. Zwanziger, Phys. Rev. D 82, 025021 (2010). arXiv:0912.5153 [hep-th] ADSCrossRefGoogle Scholar
  14. 14.
    K. Fukushima, K. Kashiwa. arXiv:1206.0685 [hep-ph]
  15. 15.
    K. Fukushima, N. Su. arXiv:1304.8004 [hep-ph]

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  • M. A. L. Capri
    • 1
    Email author
  • D. Dudal
    • 2
  • M. S. Guimaraes
    • 1
  • I. F. Justo
    • 1
  • S. P. Sorella
    • 1
  • D. Vercauteren
    • 1
  1. 1.Departamento de Física Teórica, Instituto de FísicaUERJ—Universidade do Estado do Rio de JaneiroMaracanãBrazil
  2. 2.Department of Physics and AstronomyGhent UniversityKrijgslaan 281-S9Belgium

Personalised recommendations