Advertisement

Beyond rainbow-ladder in bound state equations

  • Walter Heupel
  • Tobias Goecke
  • Christian S. FischerEmail author
Regular Article - Theoretical Physics

Abstract

In this work we devise a new method to study quark-anti-quark interactions beyond simple ladder-exchange that yield massless pions in the chiral limit. The method is based on the requirement to have a representation of the quark-gluon vertex that is explicitly given in terms of quark dressings functions. We outline a general procedure to generate the Bethe-Salpeter kernel for a given vertex representation. Our method allows not only the identification of the mesons' masses but also the extraction of their Bethe-Salpeter wave functions exposing their internal structure. We exemplify our method with vertex models that are of phenomenological interest.

Keywords

Chiral Limit Gluon Propagator Quark Propagator Vertex Model Interaction Kernel 
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.

References

  1. 1.
    D.W. McKay, H.J. Munczek, Phys. Rev. D 40, 4151 (1989).ADSCrossRefGoogle Scholar
  2. 2.
    H.J. Munczek, Phys. Rev. D 52, 4736 (1995) hep-th/9411239.ADSCrossRefGoogle Scholar
  3. 3.
    P. Maris, C.D. Roberts, P.C. Tandy, Phys. Lett. B 420, 267 (1998) nucl-th/9707003.ADSCrossRefGoogle Scholar
  4. 4.
    P. Maris, C.D. Roberts, Int. J. Mod. Phys. E 12, 297 (2003) nucl-th/0301049.ADSCrossRefGoogle Scholar
  5. 5.
    P. Maris, P.C. Tandy, Nucl. Phys. Proc. Suppl. 161, 136 (2006) nucl-th/0511017.ADSCrossRefGoogle Scholar
  6. 6.
    T. Goecke, C.S. Fischer, R. Williams, Phys. Lett. B 704, 211 (2011) arXiv:1107.2588 [hep-ph].ADSCrossRefGoogle Scholar
  7. 7.
    Phys. Rev. D870340132013 arXiv:1210.1759 [hep-ph].
  8. 8.
    G. Eichmann, R. Alkofer, A. Krassnigg, D. Nicmorus, Phys. Rev. Lett. 104, 201601 (2010) arXiv:0912.2246 [hep-ph].ADSCrossRefGoogle Scholar
  9. 9.
    G. Eichmann, R. Alkofer, I.C. Cloet, A. Krassnigg, C.D. Roberts, Phys. Rev. C 77, 042202 (2008) arXiv:0802.1948 [nucl-th].ADSCrossRefGoogle Scholar
  10. 10.
    S.-x. Qin, L. Chang, Y.-x. Liu, C.D. Roberts, D.J. Wilson, Phys. Rev. C 85, 035202 (2012) arXiv:1109.3459 [nucl-th].ADSCrossRefGoogle Scholar
  11. 11.
    C.S. Fischer, R. Alkofer, Phys. Rev. D 67, 094020 (2003) hep-ph/0301094.ADSCrossRefGoogle Scholar
  12. 12.
    A. Bender, C.D. Roberts, L. Von Smekal, Phys. Lett. B 380, 7 (1996) nucl-th/9602012.ADSCrossRefGoogle Scholar
  13. 13.
    P. Watson, W. Cassing, P.C. Tandy, Few-Body Syst. 35, 129 (2004) hep-ph/0406340.ADSGoogle Scholar
  14. 14.
    M.S. Bhagwat, A. Holl, A. Krassnigg, C.D. Roberts, P.C. Tandy, Phys. Rev. C 70, 035205 (2004) nucl-th/0403012.ADSCrossRefGoogle Scholar
  15. 15.
    H.H. Matevosyan, A.W. Thomas, P.C. Tandy, Phys. Rev. C 75, 045201 (2007) nucl-th/0605057.ADSCrossRefGoogle Scholar
  16. 16.
    R. Alkofer, C.S. Fischer, F.J. Llanes-Estrada, K. Schwenzer, Ann. Phys. 324, 106 (2009) arXiv:0804.3042 [hep-ph].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    C.S. Fischer, D. Nickel, J. Wambach, Phys. Rev. D 76, 094009 (2007) arXiv:0705.4407 [hep-ph].ADSCrossRefGoogle Scholar
  18. 18.
    C.S. Fischer, R. Williams, Phys. Rev. Lett. 103, 122001 (2009) arXiv:0905.2291 [hep-ph].ADSCrossRefGoogle Scholar
  19. 19.
    C.S. Fischer, R. Williams, Phys. Rev. D 78, 074006 (2008) arXiv:0808.3372 [hep-ph].ADSCrossRefGoogle Scholar
  20. 20.
    C.S. Fischer, P. Watson, W. Cassing, Phys. Rev. D 72, 094025 (2005) hep-ph/0509213.ADSCrossRefGoogle Scholar
  21. 21.
    L. Chang, C.D. Roberts, Phys. Rev. Lett. 103, 081601 (2009) arXiv:0903.5461 [nucl-th].ADSCrossRefMathSciNetGoogle Scholar
  22. 22.
    L. Chang, Y.-X. Liu, C.D. Roberts, Phys. Rev. Lett. 106, 072001 (2011) arXiv:1009.3458 [nucl-th].ADSCrossRefGoogle Scholar
  23. 23.
    L. Chang, C.D. Roberts, Phys. Rev. C 85, 052201 (2012) arXiv:1104.4821 [nucl-th].ADSCrossRefGoogle Scholar
  24. 24.
    J.M. Cornwall, R. Jackiw, E. Tomboulis, Phys. Rev. D 10, 2428 (1974).ADSCrossRefzbMATHGoogle Scholar
  25. 25.
    J. Berges, Phys. Rev. D 70, 105010 (2004) hep-ph/0401172.ADSCrossRefMathSciNetGoogle Scholar
  26. 26.
    J.S. Ball, T.-W. Chiu, Phys. Rev. D 22, 2542 (1980).ADSCrossRefGoogle Scholar
  27. 27.
    Y.-B. Dai, C.-S. Huang, H.-Y. Jin, Phys. Rev. D 51, 2347 (1995).ADSGoogle Scholar
  28. 28.
    M. Gell-Mann, R.J. Oakes, B. Renner, Phys. Rev. 175, 2195 (1968).ADSCrossRefGoogle Scholar
  29. 29.
    E. Eichten, F. Feinberg, Phys. Rev. D 10, 3254 (1974).ADSCrossRefGoogle Scholar
  30. 30.
    A. Krassnigg, PoS CONFINEMENT 8, 075 (2008) arXiv:0812.3073 [nucl-th].Google Scholar
  31. 31.
    A. Krassnigg, Phys. Rev. D 80, 114010 (2009) arXiv:0909.4016 [hep-ph].ADSCrossRefGoogle Scholar
  32. 32.
    W. Heupel, G. Eichmann, C.S. Fischer, Phys. Lett. B 718, 545 (2012) arXiv:1206.5129 [hep-ph].ADSCrossRefGoogle Scholar
  33. 33.
    P. Maris, P.C. Tandy, Phys. Rev. C 60, 055214 (1999) nucl-th/9905056.ADSCrossRefGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Walter Heupel
    • 1
  • Tobias Goecke
    • 1
  • Christian S. Fischer
    • 1
    Email author
  1. 1.Institute for Theoretical PhysicsJustus-Liebig-University GießenGießenGermany

Personalised recommendations