We present recent results of the Landau gauge gluon and ghost propagators in SU(3) pure gauge theory at Wilson β=5.7 for lattice sizes up to 80^4 corresponding to physical volumes up to (13.2 fm)^4. In particular, we focus on finite-volume and Gribov copy effects. We employ a gauge fixing method that combines a simulated annealing algorithm with finalizing overrelaxation. We find the gluon propagator for the largest volumes and at q^2 ~ 0.01 GeV^2 to become flat. Although not excluded by our data, there is still no clear indication of a gluon propagator tending towards zero in the zero-momentum limit. New data for the ghost propagator are reported, too.
We study numerically the chromoelectric-chromomagnetic asymmetry of the dimension two gluon condensate as well as the longitudinal gluon propagator at $T\simeq T_c$ in the Landau-gauge $SU(2)$ lattice gauge theory. We show that substantial correlation between the asymmetry and the Polyakov loop as well as the correlation between the longitudinal propagator and the Polyakov loop pave the way to studies of the critical behavior of the asymmetry and the longitudinal propagator. The respective values of critical exponents and amplitudes are evaluated.
We continue the systematic computation of Landau gauge gluon and ghost propagators of SU(2) gluodynamics using a sequence of increasing lattice sizes L^4 up to L=112 with corresponding β-values chosen to keep the linear physical size a(β)L ~ 9.6 fm fixed. To extremize the Landau gauge functional we employ simulated annealing combined with subsequent overrelaxation. Renormalizing the propagators at momentum μ= 2.2 GeV we observe quite strong lattice artifacts for the gluon propagator as well as for the ghost dressing function within the momentum region q < 1.0 GeV. The dependence on the lattice…
We study numerically the chromoelectric-chromomagnetic asymmetry of the dimension two $A^2$ gluon condensate as well as the infrared behavior of the gluon propagators at $T\simeq T_c$ in the Landau-gauge $SU(3)$ lattice gauge theory. We find that a very significant correlation of the real part of the Polyakov loop with the asymmetry as well as with the longitudinal propagator makes it possible to determine the critical behavior of these quantities. We obtain the screening masses in different Polyakov-loop sectors and discuss the dependence of chromoelectric and chromomagnetic interactions of s…
Recently we reported on the infrared behavior of the Landau gauge gluon and ghost dressing functions in SU(3) Wilson lattice gluodynamics with special emphasis on the Gribov problem. Here we add an investigation of the spectral properties of the Faddeev-Popov operator at $β$=5.8 and 6.2 for lattice sizes 12^4, 16^4 and 24^4. The larger the volume the more of its eigenvalues are found accumulated close to zero. Using the eigenmodes for the spectral representation it turns out that for our smallest lattice O(200) eigenmodes are sufficient to saturate the ghost propagator at lowest momentum. We a…
In the Landau-gauge lattice gluodynamics we find that, both in the SU(2) and SU(3) theory, a correlation of the Polyakov loop with the asymmetry of the $A^2$ gluon condensate as well as with the longitudinal propagator makes it possible to determine the critical behavior of these quantities. We discuss finite-volume corrections and reveal that they can be reduced by the use of regression analysis. We also analyze the temperature dependence of low-momenta propagators in different Polyakov-loop sectors.
Landau gauge gluon propagators are studied numerically in the SU(3) gluodynamics as well as in the full QCD with the number of flavors $n_F=2$ using efficient gauge fixing technique. We compare these propagators at temperatures very close to the transition point in two phases : confinement and deconfinement. The electric mass $m_E$ has been determined from the momentum space longitudinal gluon propagator. Gribov copy effects are found to be rather strong in the gluodynamics, while in the full QCD case they are weak ("Gribov noise"). Also we analyse finite volume dependence of the transverse an…
We derive the Schwinger-Dyson equations for the SU(2) Yang-Mills theory in the maximal Abelian gauge and solve them in the infrared asymptotic region. We find that the infrared asymptotic solutions for the gluon and ghost propagators are consistent with the hypothesis of Abelian dominance.
We study the SU(2) gluon and ghost propagators in Landau gauge on lattices up to a size of 112^4. A comparison with the SU(3) case is made and finite-volume effects are then investigated. We find that for a large range of momenta the SU(2) and SU(3) propagators are remarkably alike. In the low-momentum region we compare with recent results obtained in DSE studies on a 4-torus.
We study the behavior of the gluon and ghost dressing functions in SU(3) Landau gauge at low momenta available on lattice sizes 12^4-32^4 at $β$=5.8, 6.0 and 6.2. We demonstrate the ghost dressing function to be systematically dependent on the choice of Gribov copies, while the influence on the gluon dressing function is not resolvable. The running coupling given in terms of these functions is found to be decreasing for momenta q<0.6 GeV. We study also effects of the finite volume and of the lattice discretization.
We study numerically the chromoelectric-chromomagnetic asymmetry of the dimension two $A^2$ gluon condensate as well as the transverse and longitudinal gluon propagators at $T>T_c$ in the Landau-gauge $SU(2)$ lattice gauge theory with a particular emphasis on finite-volume effects. We show that previously found so called symmetric point at which asymmetry changes sign is an artifact of the finite volume effects. We find that with increasing temperature the asymmetry decreases approaching zero value from above in agreement with perturbative result. Instead of the asymmetry we suggest the ratio …
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…
We show that off-diagonal gluons and off-diagonal ghosts acquire their masses dynamically in QCD if the maximal Abelian gauge is adopted. This result strongly supports the Abelian dominance in low-energy region of QCD. The mass generation is shown to occur due to ghost-anti-ghost condensation caused by attractive quartic ghost interactions within the Abelian projected effective gauge theory (derived by one of the authors). In fact, the quartic ghost interaction is indispensable for the renormalizability due to nonlinearity of the maximal Abelian gauge. The ghost-anti-ghost condensation is asso…
Infrared features of the ghost propagator of color diagonal and color antisymmetric ghost propagator of quenched SU(2) and quenched SU(3) are compared with those of unquenched Kogut-Susskind fermion SU(3) lattice Landau gauge. We compare 1) the fluctuation of the ghost propagator, 2) the ghost condensate parameter $v$ of the local composite operator (LCO) approach and 3) the Binder cumulant of color anti-symmetric ghost propagator between quenched and unquenched configurations.
The ghost propagator in Landau gauge is studied at finite temperature below and above $T_c$ using lattice QCD simulations. For high temperatures, we find that the ghost propagator is enhanced, compared to the confined phase. The results suggest that the ghost propagator can be used to identify the phase transition, similarly to the gluon propagator case.
We discuss the subtleties concerning the lattice computation of the ghost propagator in linear covariant gauges, and present preliminary numerical results.
We discuss the possible form of gluon and ghost propagators in the infrared region of Yang-Mills theory in the covariant gauge from the viewpoint of general principles of quantized gauge field theories.
The dependence of the Landau gauge gluon and ghost propagators on the choice of Gribov copies is studied in pure SU(3) lattice gauge theory. Whereas the influence on the gluon propagator is small, the ghost propagator becomes clearly affected by the copies in the infrared region. We compare our data with the infrared exponents predicted by the Dyson-Schwinger equation approach
We present a numerical study of the ghost propagators in Landau gauge for SU(2) and SU(3) gauge theories at $β$=2.7 and $β$=6.0, respectively. Analyzing different lattice sizes up to $32^4$, we find small finite size effects. Down to the smallest available momenta, we observe no evidence for dipole behaviour of the ghost propagators.
We report on the infrared limit of the quenched lattice Landau gauge gluon and ghost propagators as well as the strong coupling constant computed from large asymmetric lattices. The infrared lattice propagators are compared with the pure power law solutions from Dyson-Schwinger equations (DSE). For the gluon propagator, the lattice data is compatible with the DSE solution. The preferred measured gluon exponent being $\sim 0.52$, favouring a null zero momentum propagator. The lattice ghost propagator shows finite volume effects and, for the volumes considered, the propagator does not follow a p…
The compatibility of the pure power law infrared solution of QCD Dyson-Schwinger equations (DSE) and lattice data for the gluon and ghost propagators in Landau gauge is discussed. For the gluon propagator, the lattice data is compatible with the DSE infrared solution with an exponent $κ\sim0.53$, measured using a technique that suppresses finite volume effects and allows to model these corrections to the lattice data. For the ghost propagator, the lattice data does not seem to follow the infrared DSE power law solution.
We complete our high-accuracy studies of the lattice ghost propagator in Landau gauge in Numerical Stochastic Perturbation Theory up to three loops. We present a systematic strategy which allows to extract with sufficient precision the non-logarithmic parts of logarithmically divergent quantities as a function of the propagator momentum squared in the infinite-volume and $a\to 0$ limits. We find accurate coincidence with the one-loop result for the ghost self-energy known from standard Lattice Perturbation Theory and improve our previous estimate for the two-loop constant contribution to the g…
The dependence of the gluon and ghost propagator in pure SU(3) gauge theory on the choice of Gribov copies in Landau gauge is studied. Simulations were performed on several lattice sizes at $β$=5.8, 6.0 and 6.2. In the infrared region the ghost propagator turns out to depend on the choice, while the impact on the gluon propagator is not resolvable. Also the eigenvalue distribution of the Faddeev-Popov operator is sensitive to Gribov copies.
The results of Coulomb gauge and Landau gauge lattice QCD simulation do not agree completely with continuum theory. There are indications that the ghost propagator in the infrared region is not purely color diagonal as in high energy region. After presenting lattice simulation of configurations produced with Kogut-Susskind fermion (MILC collaboration) and those with domain wall fermion (RBC/UKQCD collaboration), I investigate in triple gluon vertex and the ghost-gluon-ghost vertex how the square of the color antisymmetric ghost contributes. Then the effect of the vertex correction to the gluon…
We report on the infrared limit of the quenched lattice Landau gauge gluon propagator computed from large asymmetric lattices. In particular, the compatibility of the pure power law infrared solution $(q^2)^{2κ}$ of the Dyson-Schwinger equations is investigated and the exponent $κ$ is measured. Some results for the ghost propagator and for the running coupling constant will also be shown.
In SU(2) lattice pure gauge theory we study numerically the dependence of the ghost propagator G(p) on the choice of Gribov copies in Lorentz (or Landau) gauge. We find that the effect of Gribov copies is essential in the scaling window region, however, it tends to decrease with increasing beta. On the other hand, we find that at larger beta-values very strong fluctuations appear which can make problematic the calculation of the ghost propagator.
This is the first of a series of two papers on the perturbative computation of the ghost and gluon propagators in SU(3) Lattice Gauge Theory. Our final aim is to eventually compare with results from lattice simulations in order to enlight the genuinely non-perturbative content of the latter. By means of Numerical Stochastic Perturbation Theory we compute the ghost propagator in Landau gauge up to three loops. We present results in the infinite volume and $a \to 0$ limits, based on a general strategy that we discuss in detail.
We present clear evidence of strong effects of Gribov copies in Landau gauge gluon and ghost propagators computed on the lattice at small momenta by employing a new approach to Landau gauge fixing and a more effective numerical algorithm. It is further shown that the new approach substantially decreases notorious finite-volume effects.
We study the influence of Gribov copies on gluon and ghost propagators in lattice Landau gauge. For the gluon propagator, Gribov noise seems to be of the order of magnitude of the numerical accuracy. On the contrary, for the ghost propagator, Gribov noise is clearly observable, at least in the strong- coupling regime. We also observe, in the limit of large lattice volume, a gluon propagator decreasing as the momentum goes to zero. Finally, we introduce an implementation of the method of Fourier Acceleration which avoids the use of the fast Fourier transform, being well suited for parallel and …
We present a numerical study of the lattice Landau gluon and ghost propagators in three-dimensional pure SU(2) gauge theory. Data have been obtained using asymmetric lattices (V = 20^2 X 40, 20^2 X 60, 8^2 X 64, 8^2 X 140, 12^2 X 140 and 16^2 X 140) for the lattice coupling beta = 3.4, in the scaling region. We find that the gluon (respectively ghost) propagator is suppressed (respec. enhanced) at small momenta in the limit of large lattice volume V. By comparing these results with data obtained using symmetric lattices (V = 60^3 and 140^3), we find that both propagators suffer from systematic…
We present higher loop results for the gluon and ghost propagator in Landau gauge on the lattice calculated in numerical stochastic perturbation theory. We make predictions for the perturbative content of those propagators as function of the lattice momenta for finite lattices. To find out their nonperturbative contributions, the logarithmic definition of the gauge fields and the corresponding Faddeev-Popov operator have to be implemented in the Monte Carlo simulations.
Lattice studies of the infrared behavior of gluon and ghost propagators are a key probe of confinement scenarios in Yang-Mills theories. However, finite-volume effects become an important issue as the infrared limit is approached. By considering general quantities -- namely an associated susceptibility in the gluon case and properties of the lowest-lying eigenmode of the Faddeev-Popov matrix in the ghost case -- one can derive rigorous upper and lower bounds for the propagators. The bounds allow a better control over the extrapolation of lattice results to the infinite-volume limit. In the cas…
We study the Landau gauge gluon and ghost propagators of SU(3) gauge theory, employing the logarithmic definition for the lattice gluon fields and implementing the corresponding form of the Faddeev-Popov matrix. This is necessary in order to consistently compare lattice data for the bare propagators with that of higher-loop numerical stochastic perturbation theory (NSPT). In this paper we provide such a comparison, and introduce what is needed for an efficient lattice study. When comparing our data for the logarithmic definition to that of the standard lattice Landau gauge we clearly see the p…
We study the ultraviolet behaviour of the ghost and gluon propagators in quenched QCD using lattice simulations. Extrapolation of the lattice data towards the continuum allows to use perturbation theory to extract $Λ_{\text{QCD}}$ - the fundamental parameter of the pure gauge theory. The values obtained from the ghost and gluon propagators are coherent. The result for pure gauge SU(3) at three loops is $Λ_{\ms}\approx 320\text{MeV}$. However this value does depend strongly upon the order of perturbation theory and upon the renormalisation description of the continuum propagators. Moreover, thi…
We report on the infrared limit of the quenched lattice Landau gauge gluon propagator computed from large asymmetric lattices. In particular, the compatibility of the pure power law infrared solution $(q^2)^{2κ}$ of the Dyson-Schwinger equations is investigated and the exponent $κ$ is measured. The lattice data favours $κ\sim 0.52$, which would imply a vanishing zero momentum gluon propagator as predicted by the Kugo-Ojima confinement mechanism and the Zwanziger horizon condition. Results for the ghost propagator and for the running coupling constant are shown.
In this talk we report on a recent lattice investigation of the Landau gauge gluon and ghost propagators in pure SU(3) lattice gauge theory with a special emphasis on the Gribov copy problem. In the (infrared) region of momenta $q^2 \le 0.3 \mathrm{GeV}^2$ we find the corresponding MOM scheme running coupling $α_s(q^2)$ to rise in $q$. We also report on a first SU(3) computation of the ghost-gluon vertex function showing that it deviates only weakly from being constant. In addition we study the spectrum of low-lying eigenvalues and eigenfunctions of the Faddeev-Popov operator as well as the sp…
We present one- and two-loop results for the ghost propagator in Landau gauge calculated in Numerical Stochastic Perturbation Theory (NSPT). The one-loop results are compared with available standard Lattice Perturbation Theory in the infinite-volume limit. We discuss in detail how to perform the different necessary limits in the NSPT approach and discuss a recipe to treat logarithmic terms by introducing ``finite-lattice logs''. We find agreement with the one-loop result from standard Lattice Perturbation Theory and estimate, from the non-logarithmic part of the ghost propagator in two-loop or…
We study the momentum dependence of the ghost propagator and of the space and time components of the gluon propagator at equal time in pure SU(3) lattice Coulomb gauge theory carrying out a joint analysis of data collected independently at RCNP Osaka and Humboldt University Berlin. We focus on the scaling behavior of these propagators at beta=5.8,...,6.2 and apply a matching technique to relate the data for the different lattice cutoffs. Thereby, lattice artifacts are found to be rather strong for both instantaneous gluon propagators at large momentum. As a byproduct we obtain the respective l…
A comparative study of the lattice Landau gauge gluon and ghost propagators for SU(2) and SU(3) pure Yang-Mills theories is carried out. The data were specially produced with equivalent lattice parameters to allow for a careful comparison of the two cases. We find very good agreement between the two theories. Our results seem to confirm the predicton of Schwinger-Dyson equations that the infrared exponents are independent of the gauge group SU(N).
In this contribution we extend our unquenched computation of the Landau gauge gluon and ghost propagators in lattice QCD at non-zero temperature. The study was aimed at providing input for investigations employing continuum functional methods. We show data which correspond to pion mass values between 300 and 500 MeV and are obtained for a lattice size 32**3 x 12. The longitudinal and transversal components of the gluon propagator turn out to change smoothly through the crossover region, while the ghost propagator exhibits only a very weak temperature dependence. For a pion mass of around 400 M…
Several analytic approaches predict for SU(N_c) Yang-Mills theories in Landau gauge an enhanced ghost propagator G(p^2) and a suppressed gluon propagator D(p^2) at small momenta. This prediction applies to two, three and four space-time dimensions. Moreover, the gluon propagator is predicted to be null at p = 0. Numerical studies by several groups indeed support an enhanced ghost propagator when compared to the tree-level behavior $1/p^2$ and a finite infrared gluon propagator. However, the agreement between analytic and numerical studies is only at the qualitative level in three and in four d…
We study the influence of Gribov copies on gluon and ghost propagators, evaluated numerically in pure SU(2) lattice gauge theory in the minimal Landau gauge. Simulations are done at four different values of $β$ (namely $β$ = 0, 0.8, 1.6 and 2.7) and for volumes up to $16^4$ (up to $24^4$ at $β$ = 1.6). For the gluon propagator, Gribov noise seems to be of the order of magnitude of the numerical accuracy, even at very small values of the coupling $β$. On the contrary, for the ghost propagator, Gribov noise is clearly observable for the three values of $β$ in the strong-coupling regime. In parti…
We report on recent numerical computations of the Landau gauge gluon and ghost propagators as well as of the ghost-gluon vertex function in pure SU(3) Yang-Mills theory and in full QCD on the lattice. Special emphasis is paid to the low momentum region. In particular, we present new data for the gluon propagator at momenta below 300 MeV. We also discuss different systematic effects as there are finite-size, lattice discretization and Gribov copy but also unquenching effects. A MOM-scheme running coupling α_s(q^2) based on the ghost-gluon vertex is calculated and found to decrease for momenta b…
Effects of the quark field on the ghost propagator of the lattice Landau gauge are investigated by using the quenched gauge configuration of SU(2) first copy and the parallel tempering (PT) gauge fixed samples, quenched SU(3) $56^4$ configuration and unquenched SU(3) configurations produced by the MILC collaboration. We measure color symmetric and color antisymmetric ghost propagator and the Binder cumulant of $l^1$ norm and $l^2$ norm of color antisymmetric ghost propagator and investigate deviation from that of Gaussian distribution. The dynamical quarks make color antisymmetric ghost propag…
We present numerical details of the evaluation of the so-called Bose-ghost propagator in lattice minimal Landau gauge, for the SU(2) case in four Euclidean dimensions. This quantity has been proposed as a carrier of the confining force in the Gribov-Zwanziger approach and, as such, its infrared behavior could be relevant for the understanding of color confinement in Yang-Mills theories. Also, its nonzero value can be interpreted as direct evidence of BRST-symmetry breaking, which is induced when restricting the functional measure to the first Gribov region Omega. Our simulations are done for l…
The scalar, isovector meson propagator is analyzed in quenched QCD, using the MQA pole-shifting ansatz to study the chiral limit. In addition to the expected short-range exponential falloff characteristic of a heavy scalar meson, the propagator also exhibits a longer-range, negative metric contribution which becomes pronounced for smaller quark masses. We show that this is a quenched chiral loop effect associated with the anomalous structure of the $η'$ propagator in quenched QCD. Both the time dependence and the quark mass dependence of this effect are well-described by a chiral loop diagram …
We present recent results for the Landau-gauge gluon and ghost propagators in SU(3) lattice gluodynamics obtained on a sequence of lattices with linear extension ranging from L=64 to L=96 at $β= 5.70$, thus reaching "deep infrared" momenta down to 75 MeV. Our gauge-fixing procedure essentially uses a simulated annealing technique which allows us to reach gauge-functional values closer to the global maxima than standard approaches do. Our results are consistent with the so-called decoupling solutions found for Dyson-Schwinger and functional renormalization group equations.
We perform numerical studies of the running coupling constant alpha_R(p^2) and of the gluon and ghost propagators for pure SU(2) lattice gauge theory in the minimal Landau gauge. Different definitions of the gauge fields and different gauge-fixing procedures are used respectively for gaining better control over the approach to the continuum limit and for a better understanding of Gribov-copy effects. We find that the ghost-ghost-gluon-vertex renormalization constant is finite in the continuum limit, confirming earlier results by all-order perturbation theory. In the low momentum regime, the gl…
Fundamental quantities of QCD, such as the strong coupling and $Λ_{QCD}$, are studied in the framework of lattice QCD with $N_f=2$ twisted mass fermions. In particular, the contact between lattice and continuous calculations is made by comparing the renormalized ghost-gluon vertex in MOM scheme with 4-loop perturbative results. A power correction is needed in order to have agreement between the two descriptions. This suggests the presence of a dimension-two $\VEV{A^2}$ gluon condensate whose value is found to be higher than in the quanched case.
The color diagonal and color antisymmetric ghost propagators slightly above $T_c$ of $N_f=2$ MILC $24^3\times 12$ lattices are measured and compared with zero temperature unquenched $N_f=2+1$ MILC$_c$ $20^3\times 64$ and MILC$_f$ $28^3\times 96$ lattices and zero temperature quenched $56^4$ $β=6.4$ and 6.45 lattices. The expectation value of the color antisymmetric ghost propagator $ϕ^c(q)$ is zero but its Binder cumulant, which is consistent with that of $N_c^2-1$ dimensional Gaussian distribution below $T_c$, decreases above $T_c$. Although the color diagonal ghost propagator is temperature …
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. …
The Bose-ghost propagator has been proposed as a carrier of the confining force in Yang-Mills theories in minimal Landau gauge. We present the first numerical evaluation of this propagator, using lattice simulations for the SU(2) gauge group in the scaling region. Our data are well described by a simple fitting function, which is compatible with an infrared-enhanced Bose-ghost propagator. This function can also be related to a massive gluon propagator in combination with an infrared-free (Faddeev-Popov) ghost propagator. Since the Bose-ghost propagator can be written as the vacuum expectation …
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…
The subtraction of hypercubic lattice corrections, calculated at 1-loop order in lattice perturbation theory (LPT), is common practice, e.g., for determinations of renormalization constants in lattice hadron physics. Providing such corrections beyond 1-loop order is however very demanding in LPT, and numerical stochastic perturbation theory (NSPT) might be the better candidate for this. Here we report on a first feasibility check of this method and provide (in a parametrization valid for arbitrary lattice couplings) the lattice corrections up to 3-loop order for the SU(3) gluon and ghost propa…
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.
We study finite (physical) volume and scaling violation effects of the Landau gauge ghost propagator as well as of the running coupling $α_s(p)$ in the $SU(2)$ lattice gauge theory. We consider lattices with physical linear sizes between $aL \simeq 3$ fm and $7$ fm and values of lattice spacing between $a=0.2$ fm and $0.07$ fm. To fix the gauge we apply an efficient gauge fixing method aimed at finding extrema as close as possible to the global maximum of the gauge functional. We find finite volume effects to be small for the lattice size $aL \simeq 3$ fm at momenta $|p|\, \ge \, 0.6$ GeV. For…
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.
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…
We investigate different aspects of lattice QCD in Landau gauge using Monte Carlo simulations. In particular, we focus on the low momentum behavior of gluon and ghost propagators. The gauge group is SU(3). Different systematic effects on the gluon and ghost propagators are studied, e.g. the dependence on the choice of Gribov copies or the influence of dynamical Wilson fermions. We compare our data with results from studies of Dyson-Schwinger equations for the gluon and ghost propagators. We demonstrate that the infrared behavior of both propagators, as found in this thesis, is consistent with …
