High precision statistical Landau gauge lattice gluon propagator computation vs. the Gribov–Zwanziger approach

Abstract

In this article we report on lattice results for the Landau gauge gluon propagator using large statistical ensembles. In particular, the compatibility of the lattice data with the tree level predictions of the Refined Gribov-Zwanziger and the Very Refined Gribov-Zwanziger actions is analysed, 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 1 GeV and clearly favors the so-called Refined Gribov-Zwanziger scenario propagator. For the Very Refined Gribov-Zwanziger action, this results implies a particular relation between d = 2 condensates. Furthermore, we also provide a global fit of the lattice data that interpolates between the above scenario at low momenta and the usual continuum one-loop renormalization improved perturbation theory after introducing an infrared log-regularizing term.

Gluon Propagators in QC2D at High Baryon Density

“…We consider both masses in our study. Similar approach was considered in [31]. to compare its dependence on µ q with that ofm E , we show 1.6m E for the chromoelectric mass and 2.1m M for the chromomagnetic mass.…”

“…The first definition is as follows: chromoelectric(magnetic) screening mass is the parameterm that appears in the Taylor expansion of the respective (longitudinal or transverse) propagator at zero momentum (see Refs. [30,31])…”

The generalised infrared structure of the gluon propagator

“…Although many different parametrisations of the gluon propagator have been considered over the years, the potential appearance of generalised poles has not yet been fully investigated. In the remainder of this section we will outline infrared fits to the lattice data of [26] testing for the existence of these terms. Since lattice calculations are inherently Euclidean, one must first consider the Euclidean generalisation of Eq.…”

“…This fitting approach is particuraly well-suited to cases where the data is heavily influenced by energydependent effects, for example in assigning a shape error to a nuclear reactor flux for neutrino experiments [33]. Since the purpose of f is to simulate the sort of shape changes that can occur due to systematic effects, such as the appearance of Gribov copies [26], we used the propagator data from [32] in order to establish a reasonable functional form. In particular, f was established such that the shape of the data sets for the different lattice spacings in [32] could be transformed into one another after multiplication by this function.…”

“…The major goal of this work will be to fully elaborate the connection between the infrared structure of this representation, and the spectrum of the theory. Focussing on the specific case of Landau gauge, we will then use the Euclidean generalisation of this representation in order to test the feasibility of different infrared ansätze using the high precision pure Yang-Mills lattice data from [26], and ultimately help to shed new light on the non-perturbative gluon spectrum.…”