The one loop MSbar static potential in the Gribov-Zwanziger Lagrangian

Abstract

We compute the static potential in the Gribov-Zwanziger Lagrangian as a function of the Gribov mass, gamma, in the MSbar scheme in the Landau gauge at one loop. The usual gauge independent one loop perturbative static potential is recovered in the limit as gamma -> 0. By contrast the Gribov-Zwanziger static potential contains the term gamma^2/(p^2)^2. However, the linearly rising potential in coordinate space as a function of the radial variable r does not emerge due to a compensating behaviour as r -> infty. Though in the short distance limit a dipole behaviour is present. We also demonstrate enhancement in the propagator of the bosonic localizing Zwanziger ghost field when the one loop Gribov gap equation is satisfied. The explicit form of the one loop gap equation for the Gribov mass parameter is also computed in the MOM scheme and the zero momentum value of the renormalization group invariant effective coupling constant is shown to be the same value as that in the MSbar scheme.

54 latex pages, 6 figures, flaw in original Feynman rules corrected with updated two loop gap equation; new details added on derivation of propagators and their one loop corrections as well as bosonic ghost enhancement

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• BRST Cohomology and Physical Space of the GZ Model
• Infrared analysis of Dyson-Schwinger equations taking into account the Gribov horizon in Landau gauge
• On the reanimation of a local BRST invariance in the (Refined) Gribov-Zwanziger formalism
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• Loop calculations in the three dimensional Gribov-Zwanziger Lagrangian
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• Numerical Evaluation of the Bose-Ghost Propagator in Minimal Landau Gauge on the Lattice
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