Few-Body Systems

, Volume 56, Issue 6–9, pp 389–394 | Cite as

Confinement and Chiral-Symmetry Breaking in the Covariant Spectator Theory

  • M. T. PeñaEmail author
  • Elmar P. Biernat
  • Alfred Stadler


We show that in the framework of the covariant spectator theory (CST), the equations for the quark anti-quark bound state and for the quark mass function satisfy the requirement of chiral symmetry, incorporating spontaneous chiral symmetry breaking. We then present the results for the pion electromagnetic form factor obtained within a dynamical quark model formulated in Minkowski space and based on the CST.


Form Factor Chiral Limit Quark Propagator Pion Form Factor Spontaneous Chiral Symmetry Breaking 
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  1. 1.
    Edwards R.G., Mathur N., Richards D.G., Wallace S.J.: The flavor structure of the excited baryon spectra from lattice QCD. Phys. Rev. D 87, 054506 (2013)CrossRefADSGoogle Scholar
  2. 2.
    Guo P., Dudek J.J., Edwards R.G., Szczepaniak A.P.: Coupled-channel scattering on a torus. Phys. Rev. D 88, 014501 (2013)CrossRefADSGoogle Scholar
  3. 3.
    Fischer C.S.: Infrared properties of QCD from Dyson–Schwinger equations. J. Phys. G 32, R253–R291 (2006)CrossRefADSGoogle Scholar
  4. 4.
    Maris P., Roberts C.D.: Dyson–Schwinger equations: a tool for hadron physics. Int. J. Mod. Phys. E 12, 297–365 (2003)CrossRefADSGoogle Scholar
  5. 5.
    Alkofer R., von Smekal L.: The infrared behavior of QCD Green’s functions: confinement dynamical symmetry breaking, and hadrons as relativistic bound states. Phys. Rep. 353, 281 (2001)MathSciNetCrossRefADSzbMATHGoogle Scholar
  6. 6.
    de Bicudo P.J.A., Ribeiro J.E.F.T.: Current quark model in p wave triplet condensed vacuum. 3. Generalized r. G.m. equations: the ϕ and ρ resonances. Phys. Rev. D 42, 1635–1650 (1990)CrossRefADSGoogle Scholar
  7. 7.
    Nefediev A.V., Ribeiro J.E.F.T.: Mesonic states and vacuum replicas in potential quark models for QCD. Phys. Rev. D 70, 094020 (2004)CrossRefADSGoogle Scholar
  8. 8.
    Brodsky S.J., Pauli H.C., Pinsky S.S.: Quantum chromodynamics and other field theories on the light cone. Phys. Rep. 301, 299–486 (1998)MathSciNetCrossRefADSGoogle Scholar
  9. 9.
    Sales J., Frederico T., Carlson B., Sauer P.: Light front Bethe–Salpeter equation. Phys. Rev. C 61, 044003 (2000)CrossRefADSGoogle Scholar
  10. 10.
    Allen T.J., Olsson M.G., Veseli S.: From scalar to string confinement. Phys. Rev. D 62, 094021 (2000)CrossRefADSGoogle Scholar
  11. 11.
    Michael C.: The long range spin orbit potential. Phys. Rev. Lett. 56, 1219 (1986)CrossRefADSGoogle Scholar
  12. 12.
    Bali G.S., Schilling K., Wachter A.: Complete O (v**2) corrections to the static interquark potential from SU(3) gauge theory. Phys. Rev. D 56, 2566–2589 (1997)CrossRefADSGoogle Scholar
  13. 13.
    Lucha W., Schoberl F.F., Gromes D.: Bound states of quarks. Phys. Rep. 200, 127–240 (1991)CrossRefADSGoogle Scholar
  14. 14.
    Bhagwat M.S., Pichowsky M.A., Roberts C.D., Tandy P.C.: Analysis of a quenched lattice QCD dressed quark propagator. Phys. Rev. C. 68, 015203 (2003)CrossRefADSGoogle Scholar
  15. 15.
    Ramalho G., Peña M.T.: Covariant model for the \({\gamma\,{\rm N} \rightarrow{\rm N}}\) (1535) transition at high momentum transfer. Phys. Rev. D 84, 033007 (2011)CrossRefADSGoogle Scholar
  16. 16.
    Gross F., Milana J.: Covariant, chirally symmetric, confining model of mesons. Phys. Rev. D 43, 2401–2417 (1991)CrossRefADSGoogle Scholar
  17. 17.
    Gross F., Milana J.: Goldstone pion and other mesons using a scalar confining interaction. Phys. Rev. D 50, 3332–3349 (1994)CrossRefADSGoogle Scholar
  18. 18.
    Savkli C., Gross F.: Quark–antiquark bound states in the relativistic spectator formalism. Phys. Rev. C 63, 035208 (2001)CrossRefADSGoogle Scholar
  19. 19.
    Biernat E.P., Gross F., Peña M.T., Stadler A.: Confinement, quark mass functions, and spontaneous chiral symmetry breaking in Minkowski space. Phys. Rev. D 89, 016005 (2014)CrossRefADSGoogle Scholar
  20. 20.
    Biernat E.P., Gross F., Peña M.T., Stadler A.: Pion electromagnetic form factor in the covariant spectator theory. Phys. Rev. D 89, 016006 (2014)CrossRefADSGoogle Scholar
  21. 21.
    Surya Y., Gross F.: Unitary, gauge invariant, relativistic resonance model for pion photoproduction. Phys. Rev. C 53, 2422–2448 (1996)CrossRefADSGoogle Scholar
  22. 22.
    Leitão S., Stadler A., Peña M.T., Biernat E.P.: Linear confinement in momentum space: singularity-free bound-state equations. Phys. Rev. D 90, 096003 (2014)CrossRefADSGoogle Scholar
  23. 23.
    Bowman P.O., Heller U.M., Leinweber D.B., Parappilly M.B., Williams A.G. et al.: Unquenched quark propagator in Landau gauge. Phys. Rev. D 71, 054507 (2005)CrossRefADSGoogle Scholar
  24. 24.
    Gross F.: Relativistic treatment of loosely bound systems in scattering theory. Phys. Rev. 140, B410–B421 (1965)CrossRefADSGoogle Scholar
  25. 25.
    Huber G.M., Al E.: Charged pion form factor between Q 2 = 0.60 and 2.45 GeV2. ii. Determination of, and results for, the pion form factor. Phys. Rev. C. 78, 045203 (2008)CrossRefADSGoogle Scholar
  26. 26.
    Biernat E.P., Peña M.T., Ribeiro J.E., Stadler A., Gross F.: Chiral symmetry and π-π scattering in the covariant spectator theory. Phys. Rev. D. 90, 096008 (2014)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Wien 2015

Authors and Affiliations

  • M. T. Peña
    • 1
    Email author
  • Elmar P. Biernat
    • 1
  • Alfred Stadler
    • 1
    • 2
  1. 1.Centro de Física Teórica de Partículas (CFTP), Instituto Superior Técnico (IST)Universidade de LisboaLisbonPortugal
  2. 2.Departamento de FísicaUniversidade de ÉvoraÉvoraPortugal

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