Gribov-Zwanziger Lagrangian Research Articles

Natural solution in the refined Gribov-Zwanziger theory

We analyse the one loop effective action of the Gribov-Zwanziger Lagrangian and use the local composite operator formalism to include the most general Becchi-Rouet-Stora-Tyutin (BRST) dimension two mass operator for the localizing ghost fields. We show that the energetically favourable colour channel corresponds to what is known as the R direction.

Power corrections to symmetric point vertices in Gribov-Zwanziger theory

The 3-point vertices of QCD are examined at the symmetric subtraction point at one loop in the Landau gauge in the presence of the Gribov mass, gamma. They are expanded in powers of gamma^2 up to dimension four in order to determine the order of the leading correction. As well as analysing the pure Gribov-Zwanziger Lagrangian, its extensions to include localizing ghost masses are also examined. For comparison a pure gluon mass term is also considered.

Alternative refined Gribov-Zwanziger Lagrangian

We consider the implications of the condensation of a general local BRST invariant dimension two operator built out of the localizing ghost fields of the Gribov-Zwanziger Lagrangian which is a localized Lagrangian incorporating the Gribov problem in the Landau gauge. For different colour tensor projections of the general operator, the properties of a frozen gluon propagator and unenhanced Faddeev-Popov ghost propagator, which are observed in lattice computations, can be reproduced. The alternative possibilities are distinguished by the infrared structure of the propagators of the spin-1 fields, other than those of the gluon and Faddeev-Popov ghost, for which there is no numerical simulation data to compare with yet.

Loop calculations in the three dimensional Gribov–Zwanziger Lagrangian

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.

Erratum: one loop gluon form factor and freezing of α s in the Gribov-Zwanziger QCD Lagrangian

We use the Gribov-Zwanziger Lagrangian in QCD to evaluate the one loop correction to the gluon propagator as a function of the Gribov volume and verify that the propagator vanishes in the infrared limit. Using the corresponding correction to the Faddeev-Popov ghost propagator we construct the renormalization group invariant coupling constant, alpha^eff_S(p^2), from the gluon and ghost form factors and verify, using the Gribov mass gap condition, that it freezes out at zero momentum to a non-zero value. This is qualitatively consistent with other approaches. We also show that there is an enhancement of the propagator of one of the Zwanziger ghosts at two loops similar to that which occurs for the Faddeev-Popov ghosts. From the exact evaluation of the form factors we examine power corrections for the gluon propagator and the effective coupling. We find that both have the same qualitative behaviour in that the leading power correction is O(1/p^2) and not O(1/(p^2)^2).

The one loop $$ \overline {\text{MS}} $$ static potential in the Gribov-Zwanziger lagrangian

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.

Two-loop Gribov mass gap equation with massive quarks

We compute the two-loop correction to the Gribov mass gap equation in the Landau gauge using the Gribov–Zwanziger Lagrangian with massive quarks included. The computation involves dilogarithms of complex arguments and reproduces the known gap equation when the quark mass tends to zero.

Exploring the infrared structure of QCD with the Gribov-Zwanziger Lagrangian

We review recent one and two loop ${\overline{\mbox{MS}}}$ Landau gauge calculations using the Gribov-Zwanziger Lagrangian. The behaviour of the gluon and Faddeev-Popov ghost propagators as well as the renormalization group invariant effective coupling constant is examined in the infrared limit.

Loop calculations with the Gribov-Zwanziger Lagrangian

We review recent loop computations with the Gribov-Zwanziger Lagrangian including the two loop correction to the Gribov gap equation. The one loop corrections to the propagators are computed and an estimate given for the freeze-out value of an effective strong coupling constant.