Elusiveness of infrared critical exponents in Landau gauge YangMills theories
Abstract
We solve a truncated system of coupled DysonSchwinger equations for the gluon and ghost propagators in SU(N_{c}) YangMills theories in FaddeevPopov quantization on a fourtorus. This compact spacetime manifold provides an efficient mean to solve the gluon and ghost DysonSchwinger equations without any angular approximations. We verify that analytically two powerlike solutions in the very far infrared seem possible. However, only one of these solutions can be matched to a numerical solution for nonvanishing momenta. For a bare ghostgluon vertex this implies that the gluon propagator is only weakly infrared vanishing, D_{gl}(k^{2})~(k^{2})^{2κ1}, κ~0.595, and the ghost propagator is infrared singular, D_{gh}(k^{2})~(k^{2})^{κ1}. For nonvanishing momenta our solutions are in agreement with the results of recent SU(2) Monte Carlo lattice calculations. The running coupling possesses an infrared fixed point. We obtain α(0)=8.92/N_{c} for all gauge groups SU(N_{c}). Above one GeV the running coupling rapidly approaches its perturbative form.
 Publication:

Physical Review D
 Pub Date:
 May 2002
 DOI:
 10.1103/PhysRevD.65.094008
 arXiv:
 arXiv:hepph/0202195
 Bibcode:
 2002PhRvD..65i4008F
 Keywords:

 12.38.Aw;
 11.15.Tk;
 12.38.Lg;
 14.70.Dj;
 General properties of QCD;
 Other nonperturbative techniques;
 Other nonperturbative calculations;
 Gluons;
 High Energy Physics  Phenomenology;
 High Energy Physics  Lattice;
 High Energy Physics  Theory;
 Nuclear Theory
 EPrint:
 30 pages, REVTEX4 style, 11 figures