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D. Dudal

Publications and source records attributed to D. Dudal.

At least 55 records · Page 3Linked to original sources
arXiv2013

An all-order proof of the equivalence between Gribov's no-pole and Zwanziger's horizon conditions

The quantization of non-Abelian gauge theories is known to be plagued by Gribov copies. Typical examples are the copies related to zero modes of the Faddeev-Popov operator, which give rise to singularities in the ghost propagator. In this work we present an exact and compact expression for the ghost propagator as a function of external gauge fields, in SU(N) Yang-Mills theory in the Landau gauge. It is shown, to all orders, that the condition for the ghost propagator not to have a pole, the so-called Gribov's no-pole condition, can be implemented by demanding a nonvanishing expectation value for a functional of the gauge fields that turns out to be Zwanziger's horizon function. The action allowing to implement this condition is the Gribov-Zwanziger action. This establishes in a precise way the equivalence between Gribov's no-pole condition and Zwanziger's horizon condition.

hep-th↗
arXiv2013

(Lattice) Propagators and Extraction of Spectral Densities

In this proceeding, we explain a few steps for an alternative extraction of the spectral density of a two-point function (propagator) based on a discrete set of data points. We present a so-called Tikhonov regularization of this particular inverse problem. We test it on 2 cases: lattice 0++} glueball data and mock gluon data.

hep-lat↗
arXiv2012

Glueball spectral densities from the lattice

The propagator of a physical degree of freedom ought to obey a Källén-Lehmann spectral representation, with positive spectral density. The latter quantity is directly related to a cross section based on the optical theorem. The spectral density is a crucial ingredient of a quantum field theory with elementary and bound states, with a direct experimental connection as the masses of the excitations reflect themselves into (continuum) $δ$-singularities. In usual lattice simulational approaches to the QCD spectrum the spectral density itself is not accessed. The (bound state) masses are extracted from the asymptotic exponential decay of the two-point function. Given the importance of the spectral density, each nonperturbative continuum approach to QCD should be able to adequately describe it or to take into proper account. In this work, we wish to present a first trial in extracting an estimate for the scalar glueball spectral density in SU(3) gluodynamics using lattice gauge theory.

hep-lat↗
arXiv2012

Nontrivial ghost-gluon vertex and the match of RGZ, DSE and lattice Yang-Mills propagators

Either by solving the ghost propagator DSE or through a one-loop computation in the RGZ (Refined Gribov-Zwanziger) formalism, we show that a non-trivial ghost-gluon vertex is anyhow required to obtain a ghost propagator prediction compatible with the available corresponding lattice data in the SU(3) case. For the necessary gluon propagator input, we present RGZ tree level fits which account well for the gluon lattice data. Interestingly, this propagator can be rewritten in terms of a running gluon mass. A comparison of both DSE and RGZ results for the ghost propagator is furthermore provided. We also briefly discuss the connection between the RGZ and the OPE $d=2$ gluon condensate.

hep-ph↗
arXiv2012

On the leading OPE corrections to the ghost-gluon vertex and the Taylor theorem

This brief note is devoted to a study of genuine non-perturbative corrections to the Landau gauge ghost-gluon vertex in terms of the non-vanishing dimension-two gluon condensate. We pay special attention to the kinematical limit which the bare vertex takes for its tree-level expression at any perturbative order, according to the well-known Taylor theorem. Based on our OPE analysis, we also present a simple model for the vertex, in acceptable agreement with lattice data.

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arXiv2011

From Running Gluon Mass to Chiral Symmetry Breaking

The gluon propagator is one of the fundamental Green's functions of QCD. It is an essential ingredient in, for example, the modeling of the Schwinger-Dyson equation used to describe hadronic phenomenology. From the Landau gauge gluon propagator, computed with lattice QCD methods, we discuss its interpretation as a massive propagator and measure the gluon mass as a function of the momenta. Special attention is given to the mass at infrared scales. In the last part of the talk, the gluon mass and chiral symmetry breaking are related via an effective model for QCD.

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arXiv2011

On the reanimation of a local BRST invariance in the (Refined) Gribov-Zwanziger formalism

We localize a previously established nonlocal BRST invariance of the Gribov-Zwanziger (GZ) action by the introduction of additional fields. We obtain a modified GZ action with a corresponding local BRST invariance. We show that correlation functions of the original elementary GZ fields do not change upon evaluation with the modified partition function. We discuss that for vanishing Gribov mass, we are brought back to the original Yang-Mills theory with standard BRST invariance.

hep-th↗
arXiv2011

The dynamical origin of the refinement of the Gribov-Zwanziger theory

In recent years, the Gribov-Zwanziger action was refined by taking into account certain dimension 2 condensates. In this fashion, one succeeded in bringing the gluon and the ghost propagator obtained from the GZ model in qualitative and quantitative agreement with the lattice data. In this paper, we shall elaborate further on this aspect. First, we shall show that more dimension 2 condensates can be taken into account than considered so far and, in addition, we shall give firm evidence that these condensates are in fact present by discussing the effective potential. It follows thus that the Gribov-Zwanziger action dynamically transforms itself into the refined version, thereby showing that the continuum nonperturbative Landau gauge fixing, as implemented by the Gribov-Zwanziger approach, is consistent with lattice simulations.

hep-th↗
arXiv2011

Glueball masses from an infrared moment problem and nonperturbative Landau gauge

We set up an infrared-based moment problem to obtain estimates of the masses of the scalar, pseudoscalar and tensor glueballs in Euclidean Yang-Mills theories using the Refined Gribov-Zwanziger (RGZ) version of the Landau gauge, which takes into account nonperturbative physics related to gauge copies. Employing lattice input for the mass scales of the RGZ gluon propagator, the lowest order moment problem approximation gives the values m_{0++}\approx 1.96 GeV, m_{2++} \approx 2.04 GeV and m_{0-+}\approx 2.19 GeV in the SU(3) case, all within a 20% range of the corresponding lattice values. We also recover the mass hierarchy m_{0++}<m_{2++}<m_{0-+}.

hep-th↗
arXiv2010

From propagators to glueballs in the Gribov-Zwanziger framework

Over the last years, lattice calculations in pure Yang-Mills gauge theory seem to have come more or less to a consensus. The ghost propagator is not enhanced and the gluon propagator is positivity violating, infrared suppressed and non-vanishing at zero momentum. From an analytical point of view, several groups are agreeing with these results. Among them, the refined Gribov-Zwanziger (RGZ) framework also accommodates for these results. The question which rises next is, if our models hold the right form for the propagators, how to extract information on the real physical observables, i.e. the glueballs? How do the operators which represent glueballs look like? We review the current status of this matter within the RGZ framework.

hep-th↗
arXiv2010

From unphysical gluon and ghost propagators to physical glueball propagators (in the Gribov-Zwanziger picture): a not so trivial task?

During recent years, a good agreement was found between the analytical derivation and the numerical simulation of the Landau gauge gluon and ghost propagators. We mention the Schwinger-Dyson and Gribov-Zwanziger formalism for the analytical work. Although the agreement between several approaches is nice, these propagators do not correspond to the relevant physical degrees of freedom. In the case of pure gauge theories, one should start to study the glueball correlators. We shall try to explain why it looks like a hard challenge to go from the unphysical to the physical propagators in the case of the Gribov-Zwanziger theory (but similar conclusions might hold for other approaches giving similar propagators).

hep-th↗
arXiv2010

Gribov horizon and i-particles: about a toy model and the construction of physical operators

Restricting the functional integral to the Gribov region $Ω$ leads to a deep modification of the behavior of Euclidean Yang-Mills theories in the infrared region. For example, a gluon propagator of the Gribov type, $\frac{k^2}{k^4+{\hat γ}^4}$, can be viewed as a propagating pair of unphysical modes, called here $i$-particles, with complex masses $\pm i{\hat γ}^2$. From this viewpoint, gluons are unphysical and one can see them as being confined. We introduce a simple toy model describing how a suitable set of composite operators can be constructed out of $i$-particles whose correlation functions exhibit only real branch cuts, with associated positive spectral density. These composite operators can thus be called physical and are the toy analogy of glueballs in the Gribov-Zwanziger theory.

hep-th↗
arXiv2010

Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate $\braket{A^2}$ in the Landau gauge

We consider the gluon propagator $D(p^2)$ at various lattice sizes and spacings in the case of pure SU(3) Yang-Mills gauge theories using the Landau gauge fixing. We discuss a class of fits in the infrared region in order to (in)validate the tree level analytical prediction in terms of the (Refined) Gribov-Zwanziger framework. It turns out that an important role is played by the presence of the widely studied dimension two gluon condensate $\braket{A^2}$. Including this effect allows to obtain an acceptable fit up to 1 á 1.5 GeV, while corroborating the Refined Gribov-Zwanziger prediction for the gluon propagator. We also discuss the infinite volume extrapolation, leading to the estimate $D(0)=8.3\pm0.5\text{GeV}^{-2}$. As a byproduct, we can also provide the prediction $\braket{g^2 A^2}\approx 3\text{GeV}^2$ obtained at the renormalization scale $μ=10\text{GeV}$.

hep-lat↗
arXiv2010

More on the renormalization of the horizon function of the Gribov-Zwanziger action and the Kugo-Ojima Green function(s)

In this paper we provide strong evidence that there is no ambiguity in the choice of the horizon function underlying the Gribov-Zwanziger action. We show that there is only one correct possibility which is determined by the requirement of multiplicative renormalizability. As a consequence, this means that relations derived from other horizon functions cannot be given a consistent interpretation in terms of a local and renormalizable quantum field theory. In addition, we also discuss that the Kugo-Ojima functions $u(p^2)$ and $w(p^2)$ can only be defined after renormalization of the underlying Green function(s).

hep-th↗
arXiv2010

Gribov horizon and BRST symmetry: a pathway to confinement

We summarize the construction of the Gribov-Zwanziger action and how it leads to a scenario which explains the confinement of gluons, in the sense that the elementary gluon excitations violate positivity. Then we address the question of how one can construct operators within this picture whose one-loop correlation functions have the correct analytic properties in order to correspond to physical excitations. For this we introduce the concept of i-particles.

hep-th↗
arXiv2009

Aspects of the Gribov-Zwanziger framework

The existence of gauge (Gribov) copies disturbs the usual Faddeev-Popov quantization procedure in the Landau gauge. It is a very hard job to treat these in the continuum, even in a partial manner. A decent way to do so was worked out by Gribov, and later on by Zwanziger. The final point was a renormalizable action (the Gribov-Zwanziger action), implementing the restriction of the path integration to the so-called Gribov region, which is free of a subset of gauge copies, but not of all copies. Till recently, everybody agreed upon the fact that the restriction to the Gribov region implied a infrared enhanced ghost, and vanishing zero momentum gluon propagator. We discuss how the Gribov-Zwanziger action naturally leads to the existence of vacuum condensates of dimension two. As it is very common, such condensates can seriously alter the dynamics. In particular, the Gribov-Zwanziger condensates give rise to a gluon propagator with a finite but nonvanishing zero momentum limit, and reconstitute a nonenhanced ghost. We call this the refined Gribov-Zwanziger framework. The predictions are in qualitative agreement with most recent lattice simulations, and certain solutions of the Schwinger-Dyson equations. A crucial feature of the Gribov-Zwanziger framework is the soft (controllable) breaking of the BRST symmetry. We also point out that imposing the Kugo-Ojima confinement criterion on the Faddeev-Popov theory as a boundary condition from the beginning leads to the same partition function as of Gribov-Zwanziger, with associated BRST symmetry breaking. This clouds the interpretation of the Kugo-Ojima criterion in se.

hep-th↗
arXiv2009

A candidate for the scalar glueball operator within the Gribov-Zwanziger framework

This proceeding gives an overview of the renormalization of $F^2_{μν}$ using the Faddeev-Popov action and the more complicate Gribov-Zwanziger action, which deals with Gribov copies. We show that using the Faddeev-Popov action, $F^2_{μν}$ mixes with other $d=4$ operators. However, due to the BRST invariance of the action, this mixing is not relevant at the level of the correlator, $\Braket {F^2_{μν}(x) F^2_{αβ}(y)}$. In contrast, when turning to the Gribov-Zwanziger action, the mixing of $F^2_{μν}$ with other $d=4$ operator does have consequences at the level of the correlator. This is due to the breaking of the BRST. We then present a possible candidate for a physical operator in the Gribov-Zwanziger framework.

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