The color matrix elements of the ghost triangle diagram that appears in the triple gluon vertex and the ghost-ghost-gluon triangle diagram that appears in the ghost-gluon-ghost vertex are calculated. The ghost-ghost-gluon triangle contains a loop consisting of two color diagonal ghosts and one gluon and a loop consisting of two color antisymmetric ghosts and one gluon. Consequently, the pQCD argument in the infrared region based on the one particle irreducible diagram should be modified. Implications for the Kugo-Ojima color confinement and the QCD running coupling are discussed.
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 study the dominant non-perturbative power corrections to the ghost and gluon propagators in Landau gauge pure Yang-Mills theory using OPE and lattice simulations. The leading order Wilson coefficients are proven to be the same for both propagators. The ratio of the ghost and gluon propagators is thus free from this dominant power correction. Indeed, a purely perturbative fit of this ratio gives smaller value ($\simeq 270$MeV) of $Λ_{\ms}$ than the one obtained from the propagators separately($\simeq 320$MeV). This argues in favour of significant non-perturbative $\sim 1/q^2$ power correctio…
We study a manifestly gauge invariant set of Schwinger-Dyson equations to determine the nonperturbative dynamics of the gluon and ghost propagators in $d=3$ Yang-Mills. The use of the well-known Schwinger mechanism, in the Landau gauge, leads to the dynamical generation of a mass for the gauge boson (gluon in $d=3$), which, in turn, gives rise to an infrared finite gluon propagator and ghost dressing function. The propagators obtained from the numerical solution of these nonperturbative equations are in very good agreement with the results of $SU(2)$ lattice simulations.
The quenched gluon and ghost propagator data published in [1] is reanalysed following the suggestion of [2] to resolve the differences between the infrared data of the simulations. Our results confirms that the procedure works well either for the gluon or for the ghost propagator but not for both propagators simultaneously as the observed deviations in the data follow opposite patterns. Definitive conclusions require improving the determination of the (ratios) of lattice spacings. A simple procedure for the relative calibration of the lattice spacing in lattice simulations is suggested.
We investigate the temperature dependence of the Landau gauge gluon and ghost propagators in lattice QCD with two flavors of maximally twisted mass fermions. For these propagators we provide and analyze data which corresponds to pion mass values between 300 and 500 MeV. For the gluon propagator we find that both the longitudinal and transversal component change smoothly in the crossover region, while the ghost propagator exhibits only a very weak temperature dependence. For momenta between 0.4 and 3.0 GeV we give a parametrization for our lattice data. It may serve as input to studies which em…
The compatibility of the pure power law infrared solution of QCD and lattice data for the gluon and ghost propagators in Landau gauge is discussed. For the gluon propagator, the lattice data is well described by a pure power law with an infrared exponent $κ\sim 0.53$, in the Dyson-Schwinger notation. $κ$ is measured using a technique that suppresses finite volume effects. This value implies a vanishing zero momentum gluon propagator, in agreement with the Gribov-Zwanziger confinement scenario. For the ghost propagator, the lattice data seem not to follow a pure power law, at least for the rang…
We study the gluon and ghost propagators of SU(2) lattice Landau gauge theory and find their low-momentum behavior being sensitive to the lowest non-trivial eigenvalue (λ_1) of the Faddeev-Popov operator. If the gauge-fixing favors Gribov copies with small (large) values for λ_1 both the ghost dressing function and the gluon propagator get enhanced (suppressed) at low momentum. For larger momenta no dependence on Gribov copies is seen. We compare our lattice data to the corresponding (decoupling) solutions from the DSE/FRGE study of Fischer, Maas and Pawlowski [Annals Phys. 324 (2009) 2408] an…
We reinvestigate the problem of Gribov ambiguities within the Landau (or Lorentz) gauge for the ghost and gluon propagators in pure SU(2) lattice gauge theory. We make use of the full symmetry group of the action taking into account {\it large}, i.e. non-periodic $\mathbb{Z}(2)$ gauge transformations leaving lattice plaquettes invariant. Enlarging in this way the gauge orbits for any given gauge field configuration the Landau gauge can be fixed at higher local extrema of the gauge functional in comparison with standard (overrelaxation) techniques. This has a clearly visible effect not only for…
The authors of ref. Phys.Rev. D94 (2016) no.1, 014502 reported about a careful analysis of the impact of lattice artifacts on the $SU(3)$ gauge-field propagators. In particular, they found that the low-momentum behavior of the renormalized propagators depends on the lattice bare coupling and interpreted this fact as the result of it being affected by finite lattice spacing artifacts. We do not share this interpretation and present here a different and more suitable explanation for these results.
We study the nonperturbative gluon and ghost propagators in d=3 Yang-Mills, using the Schwinger-Dyson equations of the pinch technique. The use of the Schwinger mechanism leads to the dynamical generation of a gluon mass, which, in turn, gives rise to an infrared finite gluon propagator and ghost dressing function. The propagators obtained are in very good agreement with the results of SU(2) lattice simulations.
So far, the infrared behavior of the gluon and ghost propagator based on the Gribov-Zwanziger approach predicted a positivity violating gluon propagator vanishing at zero momentum, and an infrared enhanced ghost propagator. However, recent data based on huge lattices have revealed a positivity violating gluon propagator which turns out to attain a finite nonvanishing value very close to zero momentum. At the same time the ghost propagator does not seem to be infrared enhanced anymore. We point out that these new features can be accounted for by yet unexploited dynamical effects within the Grib…
We show that the application of a novel gauge invariant truncation scheme to the Schwinger-Dyson equations of QCD leads, in the Landau gauge, to an infrared finite gluon propagator and a divergent ghost propagator, in qualitative agreement with recent lattice data.
We derive some exact relations in Landau gauge that follow from a cut-off at the Gribov horizon which is then implemented by a local, renormalizable action involving auxiliary bose and fermi ghosts. The fermi ghost propagator is more singular than $1/k^2$ at $k = 0$, and the relation $α_D + 2 α_G = (D - 4)/2$ holds between the infrared critical exponents of the gluon and ghost propagators $D(k)$ and $G(k)$ in $D$ Euclidean dimensions. Finally, in $D$ Euclidean dimensions, there is a long-range force, transmitted by the propagator of the auxiliary bose ghost that corresponds to a linearly risin…
The behavior of the Landau gauge gluon and ghost propagators is studied in pure SU(3) gauge theory at non-zero temperature on the lattice. We concentrate on the momentum range [0.6, 2.0] GeV. For the longitudinal as well as for the transverse component of the gluon propagator we extract the continuum limit. We demonstrate the smallness of finite-size and Gribov-copy effects at temperatures close to the deconfinement phase transition at T=T_c and within the restricted range of momenta. Since the longitudinal component D_L(q) turns out to be most sensitive with respect to the phase transition we…
We compute the full non-perturbative ghost and gluon two-point Green functions by using gauge field configurations with $\nf=2$ and $\nf=2+1+1$ twisted-mass quark flavours. We use simulations with several different light quark masses, heavy quark masses close to that of the strange and charm quarks, and lightest pseudoscalar masses ranging from 270 to 510 [MeV]. Quark flavour effects on both the gluon and the ghost propagators are then investigated in a wide range of momenta, bridging the deep infrared and intermediate momenta domain of QCD interactions in the presence of dynamical quarks. The…
The effects of the Gribov copies on the gluon and ghost propagators are investigated in SU(2) Euclidean Yang-Mills theory quantized in the maximal Abelian gauge. The diagonal component of the gluon propagator displays the characteristic Gribov type behavior. The off-diagonal component of the gluon propagator is found to be of the Yukawa type, with a dynamical mass originating from the dimension two condensate <A^2>, which is also taken into account. Finally, the off-diagonal ghost propagator exhibits infrared enhancement.
The Dyson-Schwinger equations of Landau-gauge Yang-Mills theory for the gluon and ghost propagators are investigated. Numerical results are obtained within a truncation scheme which has proven to be successful at vanishing temperature. For temperatures up to 250 MeV we find only minor quantitative changes in the infrared behaviour of the gluon and ghost propagators. The effective action calculated from these propagators is temperature-independent within the numerical uncertainty.
We present an analytic description of numerical results for the ghost propagator G(p^2) in minimal Landau gauge on the lattice. The data were produced in the SU(2) case using the largest lattice volumes to date, for d = 2, 3 and 4 space-time dimensions. Our proposed form for G(p^2) is derived from the one-loop relation between ghost and gluon propagators, considering a tree-level ghost-gluon vertex and our previously obtained gluon-propagator results \cite{Cucchieri:2011ig}. Although this one-loop expression is not a good description of the data, it leads to a one-parameter fit of our ghost-pr…
We study the asymptotic behavior of the ghost propagator in the quenched SU(3) lattice gauge theory with Wilson action. The study is performed on lattices with a physical volume fixed around 1.6 fm and different lattice spacings: 0.100 fm, 0.070 fm and 0.055 fm. We implement an efficient algorithm for computing the Faddeev-Popov operator on the lattice. We are able to extrapolate the lattice data for the ghost propagator towards the continuum and to show that the extrapolated data on each lattice can be described up to four-loop perturbation theory from 2.0 GeV to 6.0 GeV. The three-loop value…
From first principles, using a screened expansion, a simple one-loop analytical expression is provided for the ghost propagator of pure SU(3) Yang-Mills theory in a generic linear covariant gauge. At variance with the Landau gauge, the ghost dressing function is suppressed in the infrared and vanishes at $p=0$, as predicted by other approaches in the continuum. However, in the very limited range where lattice data are available no detectable deviation is found from the Landau gauge, thus reconciling some recent lattice data and previous continuum predictions.
A universal behavior is predicted for ghost and gluon propagators in the infrared. The universal behavior is shown to be a signature of a one-loop approximation and emerges naturally by the massive expansion that predicts universal analytical functions for the inverse dressing functions that do not depend on any parameter or color number. By a scaling of units and by adding an integration constant, all lattice data, for different color numbers (and even quark content for the ghosts), collapse on the same universal curves predicted by the massive expansion.
We discuss the renormalization of the $1^{--}$ vector meson propagator within Resonance chiral theory at one loop. Using the particular form of the interaction Lagrangian we show that additional poles of the renormalized propagator corresponding to $1^{+-}$ degrees of freedom can be generated. We give a concrete example of such an effect.
This brief note is devoted to reconcile the conclusions from a recent analysis of the IR solutions for the ghost propagator Dyson-Schwinger equations in Coulomb gauge with previous studies in Landau gauge.
We present a review of our numerical studies of the running coupling constant, gluon and ghost propagators, ghost-gluon vertex and ghost condensate for the case of pure SU(2) lattice gauge theory in the minimal Landau gauge. Emphasis is given to the infrared regime, in order to investigate the confinement mechanisms of QCD. We compare our results to other theoretical and phenomenological studies.
In this work we compute, at the "one-loop-dressed" level, the nonperturbative contribution of the ghost loops to the self-energy of the gluon propagator, in the Landau gauge. This is accomplished within the PT-BFM formalism, which guarantees the gauge-invariance of the emerging answer. In particular, the contribution of the ghost-loops is automatically transverse, by virtue of the QED-like Ward identities satisfied in this framework. Using as nonperturbative input the available lattice data for the ghost dressing function, we show that the ghost contributions have a rather sizable effect on th…
We consider the constraints of the Slavnov-Taylor identity of the IR behaviour of gluon and ghost propagators and their compatibility with solutions of the ghost Dyson-Schwinger equation and with the lattice picture.
Starting from the lattice Landau gauge gluon and ghost propagator data we use a sequence of Padé approximants, identify the poles and zeros for each approximant and map them into the analytic structure of the propagators. For the Landau gauge gluon propagator the Padé analysis identifies a pair of complex conjugate poles and a branch cut along the negative real axis of the Euclidean $p^2$ momenta. For the Landau gauge ghost propagator the Padé analysis shows a single pole at $p^2 = 0$ and a branch cut also along the negative real axis of the Euclidean $p^2$ momenta. The method gives precise es…
We examine the possibility that there may exist a logarithmic correction to the infrared asymptotic solution with power behavior which has recently been found for the gluon and Faddeev-Popov ghost propagators in the Landau gauge. We propose a new Ansatz to find a pair of solutions for the gluon and ghost form factors by solving the coupled Schwinger-Dyson equation under a simple truncation. This Ansatz enables us to derive the infrared and ultraviolet asymptotic solutions simultaneously and to understand why the power solution and the logarithmic solution is possible only in the infrared and u…
The dependence of the Landau gauge two point gluon and ghost correlation functions on the lattice spacing and on the physical volume are investigated for pure SU(3) Yang-Mills theory in four dimensions using lattice simulations. We present data from very large lattices up to $128^4$ and for two lattice spacings $0.10$ fm and $0.06$ fm corresponding to volumes of $\sim$ (13 fm)$^4$ and $\sim$ (8 fm)$^4$, respectively. Our results show that, for sufficiently large physical volumes, both propagators have a mild dependence on the lattice volume. On the other hand, the gluon and ghost propagators c…
We give an update on our lattice determination of r_0 LambdaMS for different Nf. Our calculations employ the strong coupling constant in the minimal MOM scheme for QCD in Landau gauge, and we report here on our progress towards a quantitative understanding of the intrinsic lattice discretization artifacts at large momenta. This is important for a high-precision analysis, in particular for the unquenched calculations for which the access to small lattice spacings is restricted by the available gauge configurations.
We discuss a non-perturbative lattice calculation of the ghost and gluon propagators in the pure Yang-Mills theory in Landau gauge. The ultraviolet behaviour is checked up to NNNLO yielding the value $Λ^{n_f=0}_{\ms}=269(5)^{+12}_{-9}\text{MeV}$, and we show that lattice Green functions satisfy the complete Schwinger-Dyson equation for the ghost propagator for all considered momenta. The study of the above propagators at small momenta showed that the infrared divergence of the ghost propagator is enhanced, whereas the gluon propagator seem to remain finite and non-zero. The result for the ghos…
Non-Abelian gauge theories with fermions transforming in the adjoint representation of the gauge group (AdjQCD) are a fundamental ingredient of many models that describe the physics beyond the Standard Model. Two relevant examples are N=1 Supersymmetric Yang-Mills (SYM) theory and Minimal Walking Technicolor, which are gauge theories coupled to one adjoint Majorana and two adjoint Dirac fermions, respectively. While confinement is a property of N=1 SYM, Minimal Walking Technicolor is expected to be infrared conformal. We study the propagators of ghost and gluon fields in the Landau gauge to co…
We compute the gluon and ghost propagators of Yang-Mills theory in linear covariant gauges from the coupled system of Dyson-Schwinger equations. For small values of the gauge fixing parameter $ξ\sim 0.1$, the deviations to the Landau gauge already become clearly visible. For the ghost dressing function, this is reflected in a logarithmic infrared suppression. Also, the gluon dressing function changes - but only quantitatively - and the gluon propagator remains finite at zero momentum. From the results, a running coupling is extracted.
We consider the analytic continuation of Euclidean propagator data obtained from 4D simulations to Minkowski space. In order to perform this continuation, the common approach is to first extract the Källén-Lehmann spectral density of the field. Once this is known, it can be extended to Minkowski space to yield the Minkowski propagator. However, obtaining the Källén-Lehmann spectral density from propagator data is a well known ill-posed numerical problem. To regularize this problem we implement an appropriate version of Tikhonov regularization supplemented with the Morozov discrepancy principle…
An introduction is given into current lattice investigations of the non-perturbative gluon and ghost propagators, in the light of the Gribov-Zwanziger and Kugo-Ojima scenarios of confinement, in the context of results obtained from the non-perturbative Dyson-Schwinger approach in the continuum and in connection with the vortex mechanism of confinement.
The infrared behavior of the gluon and ghost propagators is studied in SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge within the Gribov-Zwanziger framework. The nonperturbative effects associated with the Gribov copies and with the dimension two condensates are simultaneously encoded into a local and renormalizable Lagrangian. The resulting behavior turns out to be in good agreement with the lattice data.
We examine analytically the ghost propagator Dyson-Schwinger Equation (DSE) in the deep IR regime and prove that a finite ghost dressing function at vanishing momentum is an alternative solution (solution II) to the usually assumed divergent one (solution I). We furthermore find that the Slavnov-Taylor identities discriminate between these two classes of solutions and strongly support the solution II. The latter turns out to be also preferred by lattice simulations within numerical uncertainties.
We study an approximate version of the Schwinger-Dyson equation that controls the nonperturbative behavior of the ghost-gluon vertex, in the Landau gauge. In particular, we focus on the form factor that enters in the dynamical equation for the ghost dressing function, in the same gauge, and derive its integral equation, in the "one-loop dressed" approximation. We consider two special kinematic configurations, which simplify the momentum dependence of the unknown quantity; in particular, we study the soft gluon case, and the well-known Taylor limit. When coupled with the Schwinger-Dyson equatio…
We employ Padé approximants in the study of the analytic structure of the four-dimensional $SU(2)$ Landau-gauge gluon and ghost propagators in the infrared regime. The approximants, which are model independent, serve as fitting functions for the lattice data. We carefully propagate the uncertainties due to the fitting procedure, taking into account all possible correlations. For the gluon-propagator data, we confirm the presence of a pair of complex poles at $p_{\rm pole}^2 = \left[(-0.37 \,\pm\, 0.05_{\rm stat}\,\pm\, 0.08_{\rm sys}) \pm i\,(0.66\, \pm\, 0.03_{\rm stat}\, \pm\, 0.02_{\rm sys}…
We demonstrate how to obtain from the Schwinger-Dyson equations of QCD an infrared finite ghost propagator in the Feynman gauge. The key ingredient in this construction is the longitudinal form factor of the non-perturbative gluon-ghost vertex, which, contrary to what happens in the Landau gauge, contributes non-trivially to the gap equation of the ghost. The detailed study of the corresponding vertex equation reveals that in the presence of a dynamical infrared cutoff this form factor remains finite in the limit of vanishing ghost momentum. This, in turn, allows the ghost self-energy to reach…
We prove that the Faddeev-Popov ghost dressing function in the Yang-Mills theory is non-zero and finite in the limit of vanishing momenta and hence the ghost propagator behaves like free in the deep infrared regime, within the Gribov-Zwanziger framework of the $D$-dimensional SU(N) Yang-Mills theory in the Landau gauge for any $D>2$. This result implies that the Kugo-Ojima color confinement criterion is not satisfied in its original form. We point out that the result crucially depends on the explicit form of the non-local horizon term adopted. The original Gribov prediction in the Landau gauge…
A solvable systematic truncation scheme for the Dyson-Schwinger equations of Euclidean QCD in Landau gauge is presented. It implements the Slavnov-Taylor identities for the three-gluon and ghost-gluon vertices, whereas irreducible four-gluon couplings as well as the gluon-ghost and ghost-ghost scattering kernels are neglected. The infrared behavior of gluon and ghost propagators is obtained analytically: The gluon propagator vanishes for small spacelike momenta whereas the ghost propagator diverges stronger than a massless particle pole. The numerical solutions are compared with recent lattice…
A truncation scheme for the Dyson-Schwinger equations of QCD in Landau gauge is presented which implements the Slavnov-Taylor identities for the 3-point vertex functions. Neglecting contributions from 4-point correlations such as the 4-gluon vertex function and irreducible scattering kernels, a closed system of equations for the propagators is obtained. For the pure gauge theory without quarks this system of equations for the propagators of gluons and ghosts is solved in an approximation which allows for an analytic discussion of its solutions in the infrared: The gluon propagator is shown to …
In QCD both the quark and ghost propagators are important for governing the non-perturbative dynamics of the theory. It turns out that the dynamical properties of the quark and ghost fields impose non-perturbative constraints on the analytic structure of these propagators. In this work we explicitly derive these constraints. In doing so we establish that the corresponding spectral densities include components which are multiples of discrete mass terms, and that the propagators are permitted to contain singular contributions involving derivatives of $δ(p)$, both of which are particularly releva…
In a Quantum Field Theory, the analytic structure of the 2-points correlation functions, ie the propagators, encloses information about the properties of the corresponding quanta, particularly if they are or not confined. However, in Quantum Chromodynamics (QCD), we can only have an analytic solution in a perturbative picture of the theory. For the non-perturbative propagators, one resorts on numerical solutions of QCD that accesses specific regions of the Euclidean momentum space, as, for example, those computed via Monte Carlo simulations on the lattice. In the present work, we rely on Padé …
We study the low-momentum ghost propagator Dyson-Schwinger equation (DSE) in Landau gauge, assuming for the truncation a constant ghost-gluon vertex, as it is extensively done, and a simple model for a massive gluon propagator. Then, regular DSE solutions (the zero-momentum ghost dressing function not diverging) appear to emerge and we show the ghost propagator to be described by an asymptotic expression reliable up to the order ${\cal O}(q^2)$. That expression, depending on the gluon mass and the zero-momentum Taylor-scheme effective charge, is proven to fit pretty well the low-momentum ghost…
With proposing a unified description of the fields variation at the level of generating functional, we obtain a new identity for the quark-gluon interaction vertex based on gauge symmetry, which is similar to the Slavnov-Taylor Identities(STIs) based on the Becchi-Rouet-Stora-Tyutin transformation. With these identities, we find that in Landau gauge, the dressing function of the ghost propagator approaches to a constant as its momentum goes to zero, which provides a strong constraint on the infrared behaviour of ghost propagator.
Exploiting the gauge-invariant properties of the PT-BFM truncation scheme for the gluon Schwinger-Dyson equation, we estimate the individual non-perturbative contribution of the "one-loop dressed" ghost loop to the gluon propagator. Using the available quenched lattice data for the gluon and the ghost propagators in d=4 and d=3, we determine how the overall shape of the gluon propagator is affected by the removal of the ghost loop, and what are the consequences on the phenomenon of gluon mass generation.
In BRST-quantised Yang-Mills theory the existence of BRST symmetry imposes significant constraints on the analytic structure of the continuum theory. In particular, the presence of this symmetry in the non-perturbative regime implies that any on-shell state with vanishing norm must have an associated partner state with identical mass, but negative inner product. In this work we demonstrate that for quantum chromodynamics (QCD) this constraint gives rise to an interconnection between the ghost and gluon spectra, and in doing so provides a non-trivial test of whether BRST symmetry is realised no…
The Gluon and Ghost propagators in Landau gauge QCD are investigated using the Schwinger-Dyson equation approach. Working in Euclidean spacetime, we solve for these propagators using a selection of vertex inputs, initially for the ghost equation alone and then for both propagators simultaneously. The results are shown to be highly sensitive to the choices of vertices. We favor the infrared finite ghost solution from studying the ghost equation alone where we argue for a specific unique solution. In order to solve this simultaneously with the gluon using a dressed-one-loop truncation, we find t…
We study both regular (the zero-momentum ghost dressing function not diverging), also named decoupling, and critical (diverging), also named scaling, Yang-Mills propagators solutions by analyzing the low-momentum behaviour of the ghost propagator Dyson-Schwinger equation (DSE) in Landau gauge, assuming for the truncation a constant ghost-gluon vertex, as it is extensively done, and a simple model for a massive gluon propagator. The asymptotic expression obtained for the regular or decoupling ghost dressing function up to the order ${\cal O}(q^2)$ fits pretty well the low-momentum ghost propaga…
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 enhanc…
We present approximate non-perturbative solutions for the propagators as well as the running coupling of QCD from a coupled system of renormalised, truncated Dyson--Schwinger equations. We employ ansaetze for the dressed vertices such that the running coupling and the quark mass function are independent of the renormalisation point. Our solutions are in good agreement with the results of recent lattice calculations. We find a weakly vanishing gluon propagator at small momenta and an infrared singular ghost propagator in agreement with Zwanziger's horizon condition and the Kugo-Ojima confinemen…
The coupled Dyson-Schwinger equations for the gluon and ghost propagators are investigated in the Landau gauge using a two-loop improved truncation that preserves the multiplicative renormalizability of the propagators. In this truncation all diagrams contribute to the leading order infrared analysis. The infrared contributions of the nonperturbative two-loop diagrams to the gluon vacuum polarization are computed analytically, and this reveals that infrared power behaved propagator solutions only exist when the squint diagram contribution is taken into account. For small momenta the gluon and …
We present results for a numerical study of the ghost propagator in Coulomb gauge whereby lattice results for the spatial gluon propagator are used as input to solving the ghost Dyson-Schwinger equation. We show that in order to solve completely, the ghost equation must be supplemented by a boundary condition (the value of the inverse ghost propagator dressing function at zero momentum) which determines if the solution is critical (zero value for the boundary condition) or subcritical (finite value). The various solutions exhibit a characteristic behavior where all curves follow the same (crit…
We study the low-momentum behaviour of Yang-Mills propagators obtained from Landau-gauge Dyson-Schwinger equations (DSE) in the PT-BFM scheme. We compare the ghost propagator numerical results with the analytical ones obtained by analyzing the low-momentum behaviour of the ghost propagator DSE in Landau gauge, assuming for the truncation a constant ghost-gluon vertex and a simple model for a massive gluon propagator. The asymptotic expression obtained for the regular or decoupling ghost dressing function up to the order ${\cal O}(q^2)$ is proven to fit pretty well the numerical PT-BFM results.…
We calculate gluon and ghost propagators in Yang-Mills theory in linear covariant gauges. To that end, we utilize Nielsen identities with Landau gauge propagators and vertices as the starting point. We present and discuss numerical results for the gluon and ghost propagators for values of the gauge parameter $0<ξ\le 5$. Extrapolating the propagators to $ξ\to \infty $ we find the expected qualitative behavior. We provide arguments that our results are quantitatively reliable at least for values $ξ\lesssim 1/2$ of the gauge fixing parameter. It is shown that the correlation functions, and in par…
We derive the form of the infrared gluon propagator by proving a mapping in the infrared of the quantum Yang-Mills and $λϕ^4$ theories. The equivalence is complete at a classical level. But while at a quantum level, the correspondence is spoiled by quantum fluctuations in the ultraviolet limit, we prove that it holds in the infrared where the coupling constant happens to be very large. The infrared propagator is then obtained from the quantum field theory of the scalar field producing a full spectrum. The results are in fully agreement with recent lattice computations. We get a finite propagat…
Implications stemming from the inclusion of non-perturbative, confinining effects, as contained in the Stochastic Vacuum Model of Dosch and Simonov, are considered in the context of a, hypothetical, quark-quark `scattering process' in the Regge kinematical region. In a computation wherein the non-perturbative input enters as a correction to established perturbative results, a careful treatment of infrared divergencies is shown to imply the presence of an effective propagator associated with the existence of a linear term in the static potential. An equivalent statement is to say that the modif…
