Loop calculations in the three dimensional Gribov-Zwanziger Lagrangian

Abstract

The three dimensional Gribov-Zwanziger Lagrangian is analysed at one and two loops. Specifically, the two loop gap equation is evaluated and the Gribov mass is expressed in terms of the coupling constant. The one loop corrections to the propagators of all the fields are determined. It is shown that when the gap equation is satisfied the Faddeev-Popov ghost and both Bose and Grassmann localizing ghosts all enhance in the infrared limit at one loop. This verifies that the Kugo-Ojima confinement criterion holds to this order and we also show that both Grassmann ghosts are enhanced at two loops. For the Bose ghost we determine the full form of the propagator in the zero momentum limit for both the transverse and longitudinal pieces and confirm Zwanziger's recent general analysis for the low energy behaviour. We provide an alternative but equivalent version of the horizon condition expressing it as the vacuum expectation value of an operator involving only the localizing Bose ghost field. The one loop static potential is also determined.

39latex pages, 1 figure

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• The QCD Running Coupling
• Gauge bosons at zero and finite temperature
• BRST-Symmetry Breaking and Bose-Ghost Propagator in Lattice Minimal Landau Gauge
• BRST Cohomology and Physical Space of the GZ Model
• The No-Pole Condition in Landau gauge: Properties of the Gribov Ghost Form-Factor and a Constraint on the 2d Gluon Propagator
• Infrared Saturation and Phases of Gauge Theories with BRST Symmetry
• Low momentum propagators at two loops in gluon mass model
• Confinement, the gluon propagator and the interquark potential for heavy mesons
• Numerical Evaluation of the Bose-Ghost Propagator in Minimal Landau Gauge on the Lattice