Dynamical Gluon Mass Generation Research Articles

QCD fixed points: Banks–Zaks scenario or dynamical gluon mass generation?

Fixed points in QCD can appear when the number of quark flavors [Formula: see text] is increased above a certain critical value as proposed by Banks and Zaks (BZ). There is also the possibility that QCD possess an effective charge indicating an infrared frozen coupling constant. In particular, an infrared frozen coupling associated to dynamical gluon mass (DGM) generation does lead to a fixed point even for a small number of quarks. We compare the BZ and DGM mechanisms, their [Formula: see text] functions and fixed points, and within the approximations of this work, which rely basically on extrapolations of the dynamical gluon masses at large [Formula: see text], we verify that between [Formula: see text] and [Formula: see text] both cases exhibit fixed points at similar coupling constant values [Formula: see text]. We argue that the states of minimum vacuum energy, as a function of the coupling constant up to [Formula: see text] and for several [Formula: see text] values, are related to the dynamical gluon mass generation mechanism.

Mass generation and the problem of seagull divergences

The gluon mass generation is a purely non-perturbative effect, and the natural framework to study it in the continuum are the Schwinger-Dyson equations (SDEs) of the theory. At the level of the SDEs the generation of such a mass is associated with the existence of infrared finite solutions for the gluon propagator. From the theoretical point of view, the dynamical gluon mass generation has been traditionally plagued with seagull divergences. In this work, we will review how such divergences can be eliminated completely by virtue of a characteristic identity, valid in dimensional regularization. As a pedagogical example, we will first discuss in the context of scalar QED how it is possible to eliminate all seagull divergences, by triggering the aforementioned special identity, which enforces the masslessness of the photon. Then, we will discuss what happens in QCD and present an Ansatz for the three gluon vertex, which completely eliminates all seagull divergences and at same time allows for the possibility of a dynamical gluon mass generation.

Exploring dynamical gluon mass generation in three dimensions

In the d=3 gluon mass problem in pure-glue non-Abelian $SU(N)$ gauge theory we pay particular attention to the observed (in Landau gauge) violation of positivity for the spectral function of the gluon propagator. This causes a large bulge in the propagator at small momentum. Mass is defined through $m^{-2}=\Delta (p=0)$, where $\Delta(p)$ is the scalar function for the gluon propagator in some chosen gauge, it is not a pole mass and is generally gauge-dependent, except in the gauge-invariant Pinch Technique (PT). We truncate the PT equations with a new method called the vertex paradigm that automatically satisfies the QED-like Ward identity relating the 3-gluon PT vertex function with the PT propagator. The mass is determined by a homogeneous Bethe-Salpeter equation involving this vertex and propagator. This gap equation also encapsulates the Bethe-Salpeter equation for the massless scalar excitations, essentially Nambu-Goldstone fields, that necessarily accompany gauge-invariant gluon mass. The problem is to find a good approximate value for $m$ and at the same time explain the bulge, which by itself leads, in the gap equation for the gluon mass, to excessively large values for the mass. Our point is not to give a high-accuracy determination of $m$ but to clarify the way in which the propagator bulge and a fairly accurate estimate of $m$ can co-exist, and we use various approximations that illustrate the underlying mechanisms. The most critical point is to satisfy the Ward identity. In the PT we estimate a gauge-invariant dynamical gluon mass of $m \approx Ng^2/(2.48 \pi)$. We translate these results to the Landau gauge using a background-quantum identity involving a dynamical quantity $\kappa$ such that $m=\kappa m_L$, where $m_L^{-2}\equiv \Delta_L(p=0)$. Given our estimates for $m,\kappa$ the relation is fortuitously well-satisfied for $SU(2)$ lattice data.

Stability of chromomagnetic condensation and mass generation for confinement in SU(2) Yang-Mills theory

We show that the Nielsen-Olesen instability of the Savvidy vacuum with a homogeneous chromomagnetic condensation disappears in the framework of the functional renormalization group. This result follows from our observations: (i) the vanishing imaginary part of the effective average action is realized for arbitrary infrared cutoff as a novel fixed point solution of the flow equation for the complex-valued effective average action and (ii) an approximate analytical solution for the effective average action is obtained without the pure imaginary part for large infrared cutoff. This result suggests that there exists a physical mechanism for maintaining the stability or staying on the fixed point even for sufficiently small infrared cutoff. We argue that dynamical gluon mass generation (related to two-gluon bound states identified with glueballs) occurs due to the Becchi-Rouet-Stora-Tyutin-invariant vacuum condensate of mass dimension two without causing instability.

Confined gluon from Minkowski space continuation of the PT-BFM SDE solution

Recent lattice studies exhibit infrared finite effective QCD charges. The corresponding gluon propagator in the Landau gauge is finite and nonzero, suggesting that the mechanism of dynamical gluon mass generation is in the operation. In this paper, the analytical continuation of the Euclidean (spacelike) pinch technique–background field method solution of the Schwinger–Dyson equation for the gluon propagator to the timelike region of q2 is found. We found the continuation numerically showing good agreement with a generalized Lehman representation for small Schwinger coupling. The associated non-positive spectral function has an unexpected behavior. Albeit the infrared Euclidean space solution naively suggests a like single-scale ‘massive’ propagator, the obtained spectrum of the gluon propagator does not correspond to the delta function at single scale q = m; instead more possible singularities are generated. The pattern depends on the details of the assumed Schwinger mechanism: for stronger coupling there are a few maxima and minima which appear at the scale Λ, while for perturbatively small Schwinger coupling, the spectral function shows two narrow peaks: particle and ghost excitation, which have mutually opposite signs.

Gluon mass generation without seagull divergences

Dynamical gluon mass generation has been traditionally plagued with seagull divergences, and all regularization procedures proposed over the years yield finite but scheme-dependent gluon masses. In this work we show how such divergences can be eliminated completely by virtue of a characteristic identity, valid in dimensional regularization. The ability to trigger the aforementioned identity hinges crucially on the particular Ansatz employed for the three-gluon vertex entering into the Schwinger-Dyson equation governing the gluon propagator. The use of the appropriate three-gluon vertex brings about an additional advantage: one obtains two separate (but coupled) integral equations, one for the effective charge and one for the gluon mass. This system of integral equations has a unique solution, which unambiguously determines these two quantities. Most notably, the effective charge freezes in the infrared, and the gluon mass displays power-law running in the ultraviolet, in agreement with earlier considerations.

Scrutinizing the Green's functions of QCD: Lattice meets Schwinger-Dyson

The Green's functions of QCD encode important information about the infrared dynamics of the theory. The main non-perturbative tools used to study them are their own equations of motion, known as Schwinger-Dyson equations, and large-volume lattice simulations. We have now reached a point where the interplay between these two methods can be most fruitful. Indeed, the quality of the lattice data is steadily improving, while a recently introduced truncation scheme for the Schwinger-Dyson equations makes their predictions far more reliable. In this talk several of the above points will be reviewed, with particular emphasis on how to enforce the crucial requirement of gauge invariance at the level of the Schwinger-Dyson equations, the detailed mechanism of dynamical gluon mass generation and its implications for the ghost sector, the non-perturbative effective charge of QCD, and the indirect extraction of the Kugo-Ojima function from existing lattice data.

Quantum properties of a non-Abelian gauge invariant action with a mass parameter

We continue the study of a local, gauge invariant Yang-Mills action containing a mass parameter, which we constructed in a previous paper starting from the nonlocal gauge invariant mass dimension two operator ${F}_{\ensuremath{\mu}\ensuremath{\nu}}({D}^{2}{)}^{\ensuremath{-}1}{F}_{\ensuremath{\mu}\ensuremath{\nu}}$. We return briefly to the renormalizability of the model, which can be proven to all orders of perturbation theory by embedding it in a more general model with a larger symmetry content. We point out the existence of a nilpotent Becchi-Rouet-Stora-Tyutin (BRST) symmetry. Although our action contains extra (anti)commuting tensor fields and coupling constants, we prove that our model in the limit of vanishing mass is equivalent with ordinary massless Yang-Mills theories. The full theory is renormalized explicitly at two loops in the $\overline{\mathrm{MS}}$ scheme and all the renormalization group functions are presented. We end with some comments on the potential relevance of this gauge model for the issue of a dynamical gluon mass generation.

On the dynamical mass generation in confining Yang–Mills theories

The dynamical mass generation for gluons is discussed in Euclidean Yang–Mills theories supplemented with a renormalizable mass term. The mass parameter is not free, being determined in a self-consistent way through a gap equation which obeys the renormalization group. The example of the Landau gauge is worked out explicitly at one-loop order. The issues of the unitarity and of the gauge invariance are also addressed.

Remarks on the dynamical mass generation in confining Yang-Mills theories

The dynamical mass generation for gluons is discussed in Euclidean Yang-Mills theories supplemented with a renormalizable mass term. The mass parameter is not free, being determined in a self-consistent way through a gap equation which obeys the renormalization group. The example of the Landau gauge is worked out explicitly at one loop order. A few remarks on the issue of the unitarity are provided.

Dynamical gluon mass generation from in linear covariant gauges

We construct the multiplicatively renormalizable effective potential for the mass dimension two local composite operator A^2 in linear covariant gauges. We show that the formation of <A^2> 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.