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Few-Body Systems

, Volume 54, Issue 12, pp 2283–2301 | Cite as

Scalar-Particle Self-Energy Amplitudes and Confinement in Minkowski Space

  • Elmar P. Biernat
  • Franz Gross
  • Teresa Peña
  • Alfred StadlerEmail author
Article

Abstract

We analyze the analytic structure of the Covariant Spectator Theory (CST) contribution to the self-energy amplitude for a scalar particle in a \({\phi^2\chi}\) theory. To this end we derive dispersion relations in 1+1 and in 3+1 dimensional Minkowski space. The divergent loop integrals in 3+1 dimensions are regularized using dimensional regularization. We find that the CST dispersion relations exhibit, in addition to the usual right-hand branch cut, also a left-hand cut. The origin of this “spectator” left-hand cut can be understood in the context of scattering for a scalar \({\phi^2\chi^2}\) -type theory. If the interaction kernel contains a linear confining component, its contribution to the self-energy vanishes exactly.

Keywords

Dispersion Relation Scalar Particle Dimensional Regularization Chiral Limit Compress Baryonic Matter 
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.

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References

  1. 1.
    Jegerlehner F., Nyffeler A.: The muon g-2. Phys. Rep. 477, 1–110 (2009). doi: 10.1016/j.physrep.2009.04.003 ADSCrossRefGoogle Scholar
  2. 2.
    Friman, B., Höhne, C., Knoll, J., Leupold, S., Randrup, J., Rapp, R.: The CBM Physics Book: Compressed Baryonic Matter in Laboratory Experiments. Lecture Notes in Physics, Springer, Berlin (2011)Google Scholar
  3. 3.
    Maris P., Roberts C.D.: Dyson–Schwinger equations: a tool for hadron physics. Int. J. Mod. Phys. E12, 297–365 (2003). doi: 10.1142/S0218301303001326 ADSCrossRefGoogle Scholar
  4. 4.
    Wick G.: Properties of Bethe–Salpeter wave functions. Phys. Rev. 96, 1124–1134 (1954). doi: 10.1103/PhysRev.96.1124 MathSciNetCrossRefADSzbMATHGoogle Scholar
  5. 5.
    Zuilhof M., Tjon J.: Electromagnetic properties of the deuteron and the Bethe–Salpeter equation with one boson exchange. Phys. Rev. C22, 2369–2382 (1980). doi: 10.1103/PhysRevC.22.2369 ADSGoogle Scholar
  6. 6.
    Carbonell J., Karmanov V.: Solutions of the Bethe–Salpeter equation in Minkowski space and applications to electromagnetic form factors. Few Body Syst. 49, 205–222 (2011). doi: 10.1007/s00601-010-0133-5 CrossRefADSGoogle Scholar
  7. 7.
    Carbonell J., Karmanov V., Mangin-Brinet M.: Electromagnetic form factor via Bethe–Salpeter amplitude in Minkowski space. Eur. Phys. J. A 39, 53–60 (2009). doi: 10.1140/epja/i2008-10690-6 CrossRefADSGoogle Scholar
  8. 8.
    Gross F.: Three-dimensional covariant integral equations for low-energy systems. Phys. Rev. 186, 1448 (1969)CrossRefADSGoogle Scholar
  9. 9.
    Gross F.: Relativistic few-body problem. I. Two-body equations. Phys. Rev. C 26, 2203 (1982)CrossRefADSGoogle Scholar
  10. 10.
    Gross F.: Relativistic few-body problem. II. Three-body equations and three-body forces. Phys. Rev. C 26, 2226 (1982)CrossRefADSGoogle Scholar
  11. 11.
    Stadler A., Gross F.: Covariant spectator theory: foundations and applications. Few Body Syst. 49, 91–110 (2011)CrossRefADSGoogle Scholar
  12. 12.
    Nieuwenhuis T., Tjon J.: Nonperturbative study of generalized ladder graphs in a \({\varphi^2 \chi}\) theory. Phys. Rev. Lett. 77, 814–817 (1996). doi: 10.1103/PhysRevLett.77.814 CrossRefADSGoogle Scholar
  13. 13.
    Gross F., Milana J.: Covariant, chirally symmetric, confining model of mesons. Phys. Rev. D 43, 2401–2417 (1991). doi: 10.1103/PhysRevD.43.2401 CrossRefADSGoogle Scholar
  14. 14.
    Gross F., Milana J.: Decoupling confinement and chiral symmetry breaking: an explicit model. Phys. Rev. D 45, 969–974 (1992). doi: 10.1103/PhysRevD.45.969 CrossRefADSGoogle Scholar
  15. 15.
    Gross F., Milana J.: Goldstone pion and other mesons using a scalar confining interaction. Phys. Rev. D 50, 3332–3349 (1994). doi: 10.1103/PhysRevD.50.3332 CrossRefADSGoogle Scholar
  16. 16.
    Savkli C., Gross F.: Quark-antiquark bound states in the relativistic spectator formalism. Phys. Rev. C 63, 035–208 (2001). doi: 10.1103/PhysRevC.63.035208 CrossRefGoogle Scholar
  17. 17.
    Nambu Y., Jona-Lasinio G.: Dynamical model of elementary particles based on an analogy with superconductivity. I. Phys. Rev. 122, 345–358 (1961). doi: 10.1103/PhysRev.122.345 CrossRefADSGoogle Scholar
  18. 18.
    Becher T., Leutwyler H.: Baryon chiral perturbation theory in manifestly Lorentz invariant form. Eur. Phys. J. C 9, 643–671 (1999)ADSGoogle Scholar
  19. 19.
    Gross, F.: Construction of covariant effective field theories. Unpublished (2004)Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Elmar P. Biernat
    • 1
  • Franz Gross
    • 2
    • 3
  • Teresa Peña
    • 1
  • Alfred Stadler
    • 4
    • 5
    Email author
  1. 1.CFTP (Centro de Física Teórica de Partículas), Instituto Superior TécnicoUniversidade Técnica de LisboaLisboaPortugal
  2. 2.Thomas Jefferson National Accelerator FacilityNewport NewsUSA
  3. 3.College of William and MaryWilliamsburgUSA
  4. 4.Departamento de Física daUniversidade deÉvoraÉvoraPortugal
  5. 5.Centro de Física Nuclear da Universidade de LisboaLisboaPortugal

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