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

Understand

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.