We report on new results on the infrared behavior of the three-gluon vertex in quenched Quantum Chromodynamics, obtained from large-volume lattice simulations. The main focus of our study is the appearance of the characteristic infrared feature known as ‘zero crossing’, the origin of which is intimately connected with the nonperturbative masslessness of the Faddeev–Popov ghost. The appearance of this effect is clearly visible in one of the two kinematic configurations analyzed, and its theoretical origin is discussed in the framework of Schwinger–Dyson equations. The effective coupling in the momentum subtraction scheme that corresponds to the three-gluon vertex is constructed, revealing the vanishing of the effective interaction at the exact location of the zero crossing.The research of J.P. and J.R-Q is supported by the Spanish MINECO under grant FPA2014-53631-C2-1-P and FPA2014-53631-C2-2-P and SEV-2014-0398, and Generalitat Valenciana under grant Prometeo II/2014/066. S. Z. acknowledges support by the Alexander von Humboldt Foundation. We thank K. Cichy, M. Creutz, O. Pene, O. Philipsen, M. Teper, J. Verbaarschot for fruitful discussions. Numerical computations have used resources of CINES and GENCI-IDRIS as well as resources at the IN2P3 computing facility in Lyon

Using lattice configurations for quantum ​​​​​chromodynamics (QCD) generated with three domain-wall fermions at a physical pion mass, we obtain a parameter-free prediction of QCD’s renormalisation-group-invariant process-independent effective charge, . Owing to the dynamical breaking of scale invariance, evident in the emergence of a gluon mass-scale, GeV, this coupling saturates at infrared momenta: . Amongst other things: is almost identical to the process-dependent (PD) effective charge defined via the Bjorken sum rule; and also that PD charge which, employed in the one-loop evolution equations, delivers agreement between pion parton distribution functions computed at the hadronic scale and experiment. The diversity of unifying roles played by suggests that it is a strong candidate for that object which represents the interaction strength in QCD at any given momentum scale; and its properties support a conclusion that QCD is a mathematically well-defined quantum field theory in four dimensions.

We compute a formula including operator-product expansion power corrections to describe the running of a QCD coupling nonperturbatively defined through the ghost and gluon dressing functions. This turns out to be rather accurate. We propose the ''plateau'' procedure to compute à MS from the lattice computation of the running coupling constant. We show a good agreement between the different methods which have been used to estimate à N f ¼0 MS . We argue that à MS or the strong coupling constant computed with different lattice spacings may be used to estimate the lattice spacing ratio.

We argue that the ͗A OPE 2 ͘ condensate found in the Landau gauge on lattices, when an operator product expansion of Green's functions is performed, might be explained by instantons. We use cooling to estimate the instanton contribution and extrapolate back the result to the thermalized configuration. The resulting ͗A inst 2 ͘ is similar to ͗A OPE 2 ͘.

This letter reports on the first computation, from data obtained in lattice QCD with u, d, s and c quarks in the sea, of the running strong coupling via the ghost-gluon coupling renormalized in the MOM Taylor scheme. We provide with estimates of α MS (m 2 τ ) and α MS (m 2 Z ) in very good agreement with experimental results. Including a dynamical c quark makes safer the needed running of α MS .

The SU (3) gauge-field propagators computed from the lattice have been exhaustively used in the investigation of the low-momentum dynamics of QCD, in a judicious interplay with results from other nonperturbative approaches, and for the extraction of fundamental parameters of QCD like Λ MS as well. The impact of the discretization artifacts and their role in the extrapolation of the results to the continuum limit have not been fully understood so far. We report here about a very careful analysis of the physical scaling violation of the Landau-gauge propagators renormalized in MOM scheme and the Taylor coupling, steering us towards an insightful understanding of the effects from discretization artifacts which makes therefore possible a reliable continuum-limit extrapolation. PACS numbers: 12.38.Aw, 12.38.Lg I.

This article reports on the detailed study of the three-gluon vertex in four-dimensional SU (3) Yang-Mills theory employing lattice simulations with large physical volumes and high statistics. A meticulous scrutiny of the so-called symmetric and asymmetric kinematical configurations is performed and it is shown that the associated form-factor changes sign at a given range of momenta. The lattice results are compared to the model independent predictions of Schwinger-Dyson equations and a very good agreement among the two is found.

This note presents a comparative study of various options to reduce the errors coming from the discretization of a Quantum Field Theory in a lattice with hypercubic symmetry. We show that it is possible to perform an extrapolation towards the continuum which is able to eliminate systematically the artifacts which break the O(4) symmetry.