Skip to main content
SpringerLink
Log in

A non-perturbative study of massive gauge theories

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We consider a non-perturbative formulation of an SU(2) massive gauge theory on a space-time lattice, which is also a discretised gauged non-linear chiral model. The lattice model is shown to have an exactly conserved global SU(2) symmetry. If a scaling region for the lattice model exists and the lightest degrees of freedom are spin one vector particles with the same quantum numbers as the conserved current, we argue that the most general effective theory describing their low-energy dynamics must be a massive gauge theory. We present results of a exploratory numerical simulation of the model and find indications for the presence of a scaling region where both a triplet vector and a scalar remain light.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].

    ADS  Google Scholar 

  2. CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].

    ADS  Google Scholar 

  3. F. Englert and R. Brout, Broken symmetry and the mass of gauge vector mesons, Phys. Rev. Lett. 13 (1964) 321 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. G. Guralnik, C. Hagen and T. Kibble, Global conservation laws and massless particles, Phys. Rev. Lett. 13 (1964) 585 [INSPIRE].

    Article  ADS  Google Scholar 

  5. P.W. Higgs, Broken symmetries and the masses of gauge bosons, Phys. Rev. Lett. 13 (1964) 508 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. S. Weinberg, A model of leptons, Phys. Rev. Lett. 19 (1967) 1264 [INSPIRE].

    Article  ADS  Google Scholar 

  7. K.G. Wilson, Confinement of quarks, Phys. Rev. D 10 (1974) 2445 [INSPIRE].

    ADS  Google Scholar 

  8. S. Elitzur, Impossibility of spontaneously breaking local symmetries, Phys. Rev. D 12 (1975) 3978 [INSPIRE].

    ADS  Google Scholar 

  9. J. Fröhlich, G. Morchio and F. Strocchi, Higgs phenomenon without symmetry breaking order parameter, Nucl. Phys. B 190 (1981) 553 [INSPIRE].

    Article  ADS  Google Scholar 

  10. J. Fröhlich, G. Morchio and F. Strocchi, Higgs phenomenon without a symmetry breaking order parameter, Phys. Lett. B 97 (1980) 249 [INSPIRE].

    Article  ADS  Google Scholar 

  11. W. Caudy and J. Greensite, On the ambiguity of spontaneously broken gauge symmetry, Phys. Rev. D 78 (2008) 025018 [arXiv:0712.0999] [INSPIRE].

    ADS  Google Scholar 

  12. E.H. Fradkin and S.H. Shenker, Phase diagrams of lattice gauge theories with Higgs fields, Phys. Rev. D 19 (1979) 3682 [INSPIRE].

    ADS  Google Scholar 

  13. C. Lang, C. Rebbi and M. Virasoro, The phase structure of a non-Abelian gauge Higgs field system, Phys. Lett. B 104 (1981) 294 [INSPIRE].

    Article  ADS  Google Scholar 

  14. J. Gegelia, Why gauge symmetry?, arXiv:1207.0156 [INSPIRE].

  15. K. Osterwalder and R. Schrader, Axioms for Euclidean Green’s functions, Commun. Math. Phys. 31 (1973) 83 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. K. Osterwalder and R. Schrader, Axioms for Euclidean Green’s functions. 2, Commun. Math. Phys. 42 (1975) 281 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. M. Lüscher and P. Weisz, Scaling laws and triviality bounds in the lattice ϕ 4 theory. 3. N component model, Nucl. Phys. B 318 (1989) 705 [INSPIRE].

    Article  ADS  Google Scholar 

  18. K. Osterwalder and E. Seiler, Gauge field theories on the lattice, Annals Phys. 110 (1978) 440 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. W. Langguth, I. Montvay and P. Weisz, Monte Carlo study of the standard SU(2) Higgs model, Nucl. Phys. B 277 (1986) 11 [INSPIRE].

    Article  ADS  Google Scholar 

  20. I. Campos, On the SU(2) Higgs phase transition, Nucl. Phys. B 514 (1998) 336 [hep-lat/9706020] [INSPIRE].

    Article  ADS  Google Scholar 

  21. C. Bonati, G. Cossu, M. D’Elia and A. Di Giacomo, Phase diagram of the lattice SU(2) Higgs model, Nucl. Phys. B 828 (2010) 390 [arXiv:0911.1721] [INSPIRE].

    Article  ADS  Google Scholar 

  22. R. Ferrari, On the phase diagram of massive Yang-Mills, Acta Phys. Polon. B 43 (2012) 1965 [arXiv:1112.2982] [INSPIRE].

    Article  Google Scholar 

  23. D. Bettinelli and R. Ferrari, On the weak coupling limit for massive Yang-Mills, Acta Phys. Polon. B 44 (2013) 177 [arXiv:1209.4834] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. D. Förster, H.B. Nielsen and M. Ninomiya, Dynamical stability of local gauge symmetry: creation of light from chaos, Phys. Lett. B 94 (1980) 135 [INSPIRE].

    Article  ADS  Google Scholar 

  25. M. Fabbrichesi, R. Percacci, A. Tonero and O. Zanusso, Asymptotic safety and the gauged SU(N) nonlinear σ-model, Phys. Rev. D 83 (2011) 025016 [arXiv:1010.0912] [INSPIRE].

    ADS  Google Scholar 

  26. A. D’Adda, M. Lüscher and P. Di Vecchia, A 1/n expandable series of nonlinear σ-models with instantons, Nucl. Phys. B 146 (1978) 63 [INSPIRE].

    Article  ADS  Google Scholar 

  27. A. D’Adda, P. Di Vecchia and M. Lüscher, Confinement and chiral symmetry breaking in CP n−1 models with quarks, Nucl. Phys. B 152 (1979) 125 [INSPIRE].

    Article  ADS  Google Scholar 

  28. A. Balachandran, A. Stern and C. Trahern, Nonlinear models as gauge theories, Phys. Rev. D 19 (1979) 2416 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  29. M. Bando, T. Kugo, S. Uehara, K. Yamawaki and T. Yanagida, Is ρ meson a dynamical gauge boson of hidden local symmetry?, Phys. Rev. Lett. 54 (1985) 1215 [INSPIRE].

    Article  ADS  Google Scholar 

  30. H. Georgi, New realization of chiral symmetry, Phys. Rev. Lett. 63 (1989) 1917 [INSPIRE].

    Article  ADS  Google Scholar 

  31. R. Casalbuoni, S. De Curtis, D. Dominici and R. Gatto, Physical implications of possible J =1 bound states from strong Higgs, Nucl. Phys. B 282 (1987) 235 [INSPIRE].

    Article  ADS  Google Scholar 

  32. M. Lüscher, Advanced lattice QCD, hep-lat/9802029 [INSPIRE].

  33. APE collaboration, M. Albanese et al., Glueball masses and string tension in lattice QCD, Phys. Lett. B 192 (1987) 163 [INSPIRE].

    Article  ADS  Google Scholar 

  34. M. Della Morte and L. Giusti, Symmetries and exponential error reduction in Yang-Mills theories on the lattice, Comput. Phys. Commun. 180 (2009) 819 [arXiv:0806.2601] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. M. Della Morte and L. Giusti, A novel approach for computing glueball masses and matrix elements in Yang-Mills theories on the lattice, JHEP 05 (2011) 056 [arXiv:1012.2562] [INSPIRE].

    Article  ADS  Google Scholar 

  36. ALPHA collaboration, U. Wolff, Monte Carlo errors with less errors, Comput. Phys. Commun. 156 (2004) 143 [Erratum ibid. 176 (2007) 383] [hep-lat/0306017] [INSPIRE].

  37. M. Lüscher and P. Weisz, Locality and exponential error reduction in numerical lattice gauge theory, JHEP 09 (2001) 010 [hep-lat/0108014] [INSPIRE].

    Article  Google Scholar 

  38. R. Ferrari, On the spectrum of lattice massive SU(2) Yang-Mills, Acta Phys. Polon. B 44 (2013) 1871 [arXiv:1308.1111] [INSPIRE].

    Article  ADS  Google Scholar 

  39. M. Lüscher and P. Weisz, Background field technique and renormalization in lattice gauge theory, Nucl. Phys. B 452 (1995) 213 [hep-lat/9504006] [INSPIRE].

    Article  ADS  Google Scholar 

  40. M. Lüscher and P. Weisz, Computation of the relation between the bare lattice coupling and the MS coupling in SU(N) gauge theories to two loops, Nucl. Phys. B 452 (1995) 234 [hep-lat/9505011] [INSPIRE].

    Article  ADS  Google Scholar 

  41. T. Appelquist and C.W. Bernard, The nonlinear σ model in the loop expansion, Phys. Rev. D 23 (1981) 425 [INSPIRE].

    ADS  Google Scholar 

  42. D. Bettinelli, R. Ferrari and A. Quadri, A massive Yang-Mills theory based on the nonlinearly realized gauge group, Phys. Rev. D 77 (2008) 045021 [arXiv:0705.2339] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  43. D. Bettinelli, R. Ferrari and A. Quadri, One-loop self-energy and counterterms in a massive Yang-Mills theory based on the nonlinearly realized gauge group, Phys. Rev. D 77 (2008) 105012 [Erratum ibid. D 85 (2012) 129901] [arXiv:0709.0644] [INSPIRE].

Download references

Author information

Authors and Affiliations

  1. IFIC (CSIC) and Dpto. Física Teórica, Universidad de Valencia, Edificio Institutos Investigación, Apt. 22085, E-46071, Valencia, Spain

    M. Della Morte & P. Hernández

Authors
  1. M. Della Morte
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Hernández
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Della Morte.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Della Morte, M., Hernández, P. A non-perturbative study of massive gauge theories. J. High Energ. Phys. 2013, 213 (2013). https://doi.org/10.1007/JHEP11(2013)213

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP11(2013)213

Keywords

Search

Navigation