We investigate the generation of a gluon screening mass in Yang-Mills theory in the Landau gauge. We propose a gauge-fixing procedure where the Gribov ambiguity is overcome by summing over all Gribov copies with some weight function. This can be formulated in terms of a local field theory involving constrained, nonlinear sigma model fields. We show that a phenomenon of radiative symmetry restoration occurs in this theory, similar to what happens in the standard nonlinear sigma model in two dimensions. This results in a nonzero gluon screening mass, as seen in lattice simulations.
Correlation functions of Landau gauge Yang-Mills theory are calculated from their equations of motion. Solutions for the three- and four-gluon vertices and the role of two-loop diagrams in the gluon propagator equation are discussed.
The compatibility of the results from the Gribov-Zwanziger tree level prediction and lattice simulations, using large statistical ensembles, for the Landau gauge gluon propagator are investigated, thereby complementing earlier work using small-scale statistics. Our results show that the data is well described by the tree level estimate only up to momenta $p \lesssim 1$ GeV while clearly favoring the so-called Refined Gribov-Zwanziger scenario, implying particular relations between certain possible $d=2$ condensates. We also provide a global fit of the lattice data which interpolates between th…
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…
In lattice QCD the computation of one-particle irreducible (1PI) Green's functions with a large number (> 2) of legs is a challenging task. Besides tuning the lattice spacing and volume to reduce finite size effects, the problems associated with the estimation of higher order moments via Monte Carlo methods and the extraction of 1PI from complete Green's functions are limitations of the method. Herein, we address these problems revisiting the calculation of the three gluon 1PI Green's function.
We investigate Landau gauge $SU(3)$ Yang-Mills theory in a systematic vertex expansion scheme for the effective action with the functional renormalisation group. Particular focus is put on the dynamical creation of the gluon mass gap at non-perturbative momenta and the consistent treatment of quadratic divergences. The non-perturbative ghost and transverse gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices are calculated self-consistently with the classical action as only input. The apparent convergence of the expansion scheme is discussed and …
We reconstruct the gluon spectral function in Landau gauge QCD from numerical data for the gluon propagator. The reconstruction relies on two novel ingredients: Firstly we derive analytically the low frequency asymptotics of the spectral function. Secondly we construct a functional basis from a careful consideration of the analytic properties of the gluon propagator in Landau gauge. This allows us to reliably capture the non-perturbative regime of the gluon spectrum. We also compare different reconstruction methods and discuss the respective systematic errors.
We present an analytic method to compute the one-loop magnetic correction to the gluon polarization tensor starting from the Landau-level representation of the quark propagator in the presence of an external magnetic field. We show that the general expression contains the vacuum contribution that can be isolated from the zero-field limit for finite gluon momentum. The general tensor structure for the gluon polarization also contains two spurious terms that do not satisfy the transversality properties. However, we also show that the coefficients of this structures vanish and thus do not contrib…
We investigate the quark-gluon three-point correlation function within a one-loop computation performed in the Curci-Ferrari massive extension of the Faddeev-Popov gauge-fixed action. The mass term is used as a minimal way for taking into account the influence of the Gribov ambiguity. Our results, with renormalization-group improvement, are compared with lattice data. We show that the comparison is in general very satisfactory for the functions which are compatible with chiral symmetry, except for one. We argue that this may be due to large systematic errors {when extracting this function from…
We investigate the gluon, ghost and quark propagators in the Landau gauge with dynamic quarks. We perform a one-loop calculation in a model where the standard Faddeev-Popov Lagrangian is complemented by a mass term for the gluons which is seen as a minimal way of taking into account the effect of the Gribov copies. The analytic results are compared with lattice data obtained in four dimension and for two, three and four quark flavors. The gluon and ghost propagators are reproduced with a few percent accuracy in the whole range of accessible momenta. The scalar part of the quark propagator is f…
We study analytic structures of the gluon, quark, and ghost propagators in the Landau-gauge QCD and general properties from the existence of unusual singularities. First, we investigate analytic structures of the QCD propagators using the massive Yang-Mills model, in which the one-loop gluon and ghost propagators are in good agreement with the numerical lattice results in the Landau gauge. We find that both gluon and quark propagators in this model have complex poles that invalidate the usual spectral representation. Second, we discuss general properties of propagators in the presence of such …
In view of the expectation that the existence of complex poles is a signal of confinement, we investigate the analytic structure of the gluon, quark, and ghost propagators in the Landau gauge QCD and QCD-like theories by employing an effective model with a gluon mass term of the Yang-Mills theory, which we call the massive Yang-Mills model. In this model, we particularly investigate the number of complex poles in the parameter space of the model consisting of gauge coupling constant, gluon mass, and quark mass for the gauge group $SU(3)$ and various numbers of quark flavors $N_F$ within the as…
