What the Infrared Behaviour of QCD Vertex Functions in Landau gauge can tell us about Confinement
arXiv:0705.4402 · doi:10.1142/S0218301307008367
Abstract
The infrared behaviour of Landau gauge QCD vertex functions is investigated employing a skeleton expansion of the Dyson-Schwinger and Renormalization Group equations. Results for the ghost-gluon, three-gluon, four-gluon and quark-gluon vertex functions are presented. Positivity violation of the gluon propagator, and thus gluon confinement, is demonstrated. Results of the Dyson-Schwinger equations for a finite volume are compared to corresponding lattice data. It is analytically demonstrated that a linear rising potential between heavy quarks can be generated by infrared singularities in the dressed quark-gluon vertex. The selfconsistent mechanism that generates these singularities necessarily entails the scalar Dirac amplitudes of the full vertex and the quark propagator. These can only be present when chiral symmetry is broken, either explicitly or dynamically.
arXiv comment13 pages, 13 figures; to appear in the Proceedings of ``X Hadron Physics 2007'', Florianopolis, Brazil, March 26 - 31, 2007
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