Two loop QCD vertices at the symmetric point

We compute the triple gluon, quark-gluon and ghost-gluon vertices of QCD at the symmetric subtraction point at two loops in the MSbar scheme. In addition we renormalize each of the three vertices in their respective momentum subtraction schemes, MOMggg, MOMq and MOMh. The conversion functions of all the wave functions, coupling constant and gauge parameter renormalization constants of each of the schemes relative to MSbar are determined analytically. These are then used to derive the three loop anomalous dimensions of the gluon, quark, Faddeev-Popov ghost and gauge parameter as well as the beta-function in an arbitrary linear covariant gauge for each MOM scheme. There is good agreement of the latter with earlier Landau gauge numerical estimates of Chetyrkin and Seidensticker.Comment: 36 latex pages, anc directory contains txt file with anomalous dimensions, beta-functions, coupling constant mappings, conversion functions and amplitudes in analytic for

A brief comment on the similarities of the IR solutions for the ghost propagator DSE in Landau and Coulomb gauges

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.Comment: 4 pages, 1 figur

More on Gribov copies and propagators in Landau-gauge Yang-Mills theory

Fixing a gauge in the non-perturbative domain of Yang-Mills theory is a non-trivial problem due to the presence of Gribov copies. In particular, there are different gauges in the non-perturbative regime which all correspond to the same definition of a gauge in the perturbative domain. Gauge-dependent correlation functions may differ in these gauges. Two such gauges are the minimal and absolute Landau gauge, both corresponding to the perturbative Landau gauge. These, and their numerical implementation, are described and presented in detail. Other choices will also be discussed. This investigation is performed, using numerical lattice gauge theory calculations, by comparing the propagators of gluons and ghosts for the minimal Landau gauge and the absolute Landau gauge in SU(2) Yang-Mills theory. It is found that the propagators are different in the far infrared and even at energy scales of the order of half a GeV. In particular, also the finite-volume effects are modified. This is observed in two and three dimensions. Some remarks on the four-dimensional case are provided as well.Comment: 23 pages, 16 figures, 6 tables; various changes throughout most of the paper; extended discussion on different possibilities to define the Landau gauge and connection to existing scenarios; in v3: Minor changes, error in eq. (3) & (4) corrected, version to appear in PR

The gluon propagator from large asymmetric lattices

The Landau-gauge gluon propagator is computed for the SU(3) gauge theory on lattices up to a size of $32^3 \times 200$. We use the standard Wilson action at $\beta = 6.0$ and compare our results with previous computations using large asymmetric and symmetric lattices. In particular, we focus on the impact of the lattice geometry and momentum cuts to achieve compatibility between data from symmetric and asymmetric lattices for a large range of momenta.Comment: Poster presented at Lattice2007, Regensburg, July 30 - August 4, 200

Constraints on the IR behavior of the gluon propagator in Yang-Mills theories

We present rigorous upper and lower bounds for the zero-momentum gluon propagator D(0) of Yang-Mills theories in terms of the average value of the gluon field. This allows us to perform a controlled extrapolation of lattice data to infinite volume, showing that the infrared limit of the Landau-gauge gluon propagator in SU(2) gauge theory is finite and nonzero in three and in four space-time dimensions. In the two-dimensional case we find D(0) = 0, in agreement with Ref. [1]. We suggest an explanation for these results. We note that our discussion is general, although we only apply our analysis to pure gauge theory in Landau gauge. Simulations have been performed on the IBM supercomputer at the University of Sao Paulo.Comment: 4 pages, 3 figures, 1 tabl

Ghost-gluon coupling, power corrections and ΛMS‾\Lambda_{\overline {\rm MS}} from twisted-mass lattice QCD at Nf=2

We present results concerning the non-perturbative evaluation of the ghost-gluon running QCD coupling constant from $N_f=2$ twisted-mass lattice calculations. A novel method for calibrating the lattice spacing, independent of the string tension and hadron spectrum is presented with results in agreement with previous estimates. The value of $\Lambda_{\overline{MS}}$ is computed from the running of the QCD coupling only after extrapolating to zero dynamical quark mass and after removing a non-perturbative OPE contribution that is assumed to be dominated by the dimension-two \VEV{A^2} gluon condensate. The effect due to the dynamical quark mass in the determination of \Lams is discussed.Comment: 33 pages, 6 fig

Infrared Gluon and Ghost Propagators from Lattice QCD. Results from large asymmetric lattices

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 pure power law. Furthermore, the strong coupling constant is computed and its infrared behaviour investigated.Comment: Talk given at QNP06; final version with improved english, accepted for publication at EPJ

Infrared exponents and the strong-coupling limit in lattice Landau gauge

We study the gluon and ghost propagators of lattice Landau gauge in the strong-coupling limit beta=0 in pure SU(2) lattice gauge theory to find evidence of the conformal infrared behavior of these propagators as predicted by a variety of functional continuum methods for asymptotically small momenta $q^2 \ll \Lambda_\mathrm{QCD}^2$. In the strong-coupling limit, this same behavior is obtained for the larger values of a^2q^2 (in units of the lattice spacing a), where it is otherwise swamped by the gauge field dynamics. Deviations for a^2q^2 < 1 are well parameterized by a transverse gluon mass $\propto 1/a$. Perhaps unexpectedly, these deviations are thus no finite-volume effect but persist in the infinite-volume limit. They furthermore depend on the definition of gauge fields on the lattice, while the asymptotic conformal behavior does not. We also comment on a misinterpretation of our results by Cucchieri and Mendes in Phys. Rev. D81 (2010) 016005.Comment: 17 pages, 12 figures. Revised version (mainly sections I and II); references and comments on subsequent work on the subject added

Scaling behavior and positivity violation of the gluon propagator in full QCD

The Landau-gauge gluon propagator is studied using the coarse and fine dynamical MILC configurations. The effects of dynamical quarks are clearly visible and lead to a reduction of the nonperturbative infrared enhancement relative to the quenched case. Lattice spacing effects are studied and found to be small. The gluon spectral function is shown to clearly violate positivity in both quenched and full QCD.Comment: 7 pages, 9 figures. References and 1 figure added, minor text modifications, version to be published in PR