Linearly Confining Force from Quark and Gluon Condensates

  • J. M. Namysłowski
Conference paper
Part of the Few-Body Systems book series (FEWBODY, volume 2)


Quark and gluon condensates of QCD sum rules \(\left| {\surd {\alpha _s}\bar \psi \psi } \right|\rangle = - {\rm{ \{ }}{\left( {240MeV} \right)^3}\) and \(< |\frac{{{}^{\alpha }s}}{\pi }{{G}_{{\mu \nu }}}{{G}^{{\mu \nu }}}| > = {{(360 \pm 20 MeV)}^{4}}\) generate quark and gluon self-energies, as well as an extra term, which in light front dynamics gives linearly confining force. Transversality of the gluon self-energy, following from Ward identity, sellects this extra term. It is proportional to product of null vectors, and in hadron bound state equation it gives linear quark-antiquark potential
$${V_{q\bar q}}\left( r \right) = \lambda r,\lambda = \left( {0.13 \pm 0.03} \right)Ge{V^2}$$
, in any light meson. In baryons the linear quark-quark potential is (8/9)2/2 ≈ 0.4 weaker. The above λ corresponds to string tension equal to (0.17 ± 0.03) GeV2, and to the slope α’ of Regge trajectories within experimental errors α’= (1.0 ± 0.2) GeV-2.


Ward Identity Tensorial Structure Regge Trajectory Gluon Propagator Gluon Condensate 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M.Shifman, A.Vainshtein and V.Zakharov, Nucl.Phys.B147, 385, 448(1979); L.J.Reinders, H.R.Rubinstein and S.Yazaki, Phys.Rep. 127, 1 (1985).ADSCrossRefGoogle Scholar
  2. 2.
    J.M.Namyslowski in “Quarks and Nuclear Structure” ed. K.Bleuler, Lecture Notes in Physics 197, 65(1984), Spring-Verlag, Berlin, Heidelberg, New York, Tokyo 1984.Google Scholar
  3. 3.
    B.L.Ioffe, Nucl.Phys. B188, 317 (1981); Erratum Nucl.Phys. B191,591 (1981).ADSCrossRefGoogle Scholar
  4. 4.
    J.M.Namyslowski, Phys.Lett. B192, 170 (1987).ADSGoogle Scholar
  5. 5.
    J.M.Namyslowski, Progress in Part, and Nucl.Phys. 14, 49 (1984), ed. A. Faessler, Pergamon Press.Google Scholar
  6. 6.
    A.S.Wightman, in “Lectures on Invariance in Relativistic Quantum Mecha-nics, in Dispersion Relations and Elementary Particles”, eds. C. De Witt and R. Omnes, p.198, Herman, Paris; A.J.Macfariane, Rev. Mod.Phys. 34, 41 (1962).Google Scholar
  7. 7.
    J.M.Namyslowski, Phys.Rev. D18, 3676 (1978).ADSGoogle Scholar
  8. 8.
    S.Mandelstam, Phys.Rev. D20, 3223 (1979).ADSGoogle Scholar
  9. 9.
    Y.Nambu, Phys.Rev. D10, 4262 (1974).ADSGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • J. M. Namysłowski
    • 1
  1. 1.Institute of Theoretical PhysicsWarsaw UniversityWarsawPoland

Personalised recommendations