J. A. Gracey

Refinement of the Gribov-Zwanziger approach in the Landau gauge: Infrared propagators in harmony with the lattice results

Recent lattice data have reported an infrared suppressed, positivity violating gluon propagator which is nonvanishing at zero momentum and a ghost propagator which is no longer enhanced. This paper discusses how to obtain analytical results which are in qualitative agreement with these lattice data within the Gribov-Zwanziger framework. This framework allows one to take into account effects related to the existence of gauge copies, by restricting the domain of integration in the path integral to the Gribov region. We elaborate to great extent on a previous short paper by presenting additional results, also confirmed by the numerical simulations. A detailed discussion on the soft breaking of the Becchi-Rouet-Stora-Tyutin symmetry arising in the Gribov-Zwanziger approach is provided.

Remarks on a class of renormalizable interpolating gauges

A class of covariant gauges allowing one to interpolate between the Landau, the maximal abelian, the linear covariant and the Curci-Ferrari gauges is discussed. Multiplicative renormalizability is proven to all orders by means of algebraic renormalization. All one-loop anomalous dimensions of the fields and gauge parameters are explicitly evaluated in the scheme.

Three loop MS renormalization of the Curci–Ferrari model and the dimension two BRST invariant composite operator in QCD

Abstract The massless Curci–Ferrari model with Nf flavours of quarks is renormalized to three loops in the MS scheme in an arbitrary covariant gauge with parameter α. The renormalization of the BRST invariant dimension two composite operator, 1 2 A a 2 μ −α c a c a , which corresponds to the mass operator in the massive Curci–Ferrari model, is determined by renormalizing the Greens function where the operator is inserted in a ghost two-point function. Consequently the anomalous dimension of the QCD Landau gauge operator, 1 2 A a 2 μ , and the (gauge independent) photon mass anomalous dimension in QED are both deduced at three loops.

Landau gauge gluon and ghost propagators in the refined Gribov-Zwanziger framework in 3 dimensions

In previous works, we have constructed a refined version of the Gribov-Zwanziger action in 4 dimensions, by taking into account a novel dynamical effect. In this paper, we explore the 3-dimensional case. Analogously to 4 dimensions, we obtain a ghost propagator behaving like 1/p{sup 2} in the infrared, while the gluon propagator reaches a finite nonvanishing value at zero momentum. Simultaneously, a clear violation of positivity by the gluon propagator is also found. This behavior of the propagators turns out to be in agreement with the recent numerical simulations.

Dynamical gluon mass generation from in linear covariant gauges

We construct the multiplicatively renormalizable effective potential for the mass dimension two local composite operator AμaAμa in linear covariant gauges. We show that the formation of AμaAμa is energetically favoured and that the gluons acquire a dynamical mass due to this gluon condensate. We also discuss the gauge parameter independence of the resultant vacuum energy.

Determination of the anomalous dimension of gluonic operators in deep inelastic scattering at O(1/Nf)

Using large Nf methods we compute the anomalous dimension of the predominantly gluonic flavour singlet twist-2 composite operator which arises in the operator product expansion used in deep inelastic scattering. We obtain a d-dimensional expression for it which depends on the operator moment n. Its expansion in powers of e = (4 − d)/2 agrees with the explicit exact three-loop MS results available for n ⩽ 8 and allows us to determine some new information on the explicit n-dependence of the three and higher order coefficients. In particular the n-dependence of the three-loop anomalous dimension γgg(a) is determined in the C2(G) sector at O(1/Nf).

Erratum: one loop gluon form factor and freezing of αs 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, αeffS(p2), 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/p2) and not O(1/(p2)2).

Two loop effective potential for in the Landau gauge in quantum chromodynamics

We construct the effective potential for the dimension two composite operator ½Aa 2μ in QCD with massless quarks in the Landau gauge for an arbitrary colour group at two loops. For SU(3) we show that an estimate for the effective gluon mass decreases as Nf increases.

The anomalous dimension of the gluon-ghost mass operator in Yang-Mills theory

Abstract The local composite gluon-ghost operator ( 1 2 A aμ A μ a +α c a c a ) is analysed in the framework of the algebraic renormalization in SU(N) Yang–Mills theories in the Landau, Curci–Ferrari and maximal abelian gauges. We show, to all orders of perturbation theory, that this operator is multiplicatively renormalizable. Furthermore, its anomalous dimension is not an independent parameter of the theory, being given by a general expression valid in all these gauges. We also verify the relations we obtain for the operator anomalous dimensions by explicit 3-loop calculations in the MS scheme for the Curci–Ferrari gauge.

Computation of critical exponent η at O(1/Nf2) in quantum electrodynamics in arbitrary dimensions

Abstract We present a detailed evaluation of η, the critical exponent corresponding to the electron anomalous dimension, at O(1/ N f 2 ) in a large flavour expansion of QED in arbitrary dimensions in the Landau gauge. The method involves solving the skeleton Dyson equations with dressed propagators in the critical region of the theory. Various techniques to compute massless two-loop Feynman diagrams, which are of independent interest, are also given.