Gluon correlation functions from lattice quantum chromodynamics

TL;DR

This paper uses lattice QCD to compute gluon correlation functions, analyze their deviations from continuum theory, verify gauge identities, and explore infrared properties like the zero crossing and ghost mass, advancing understanding of non-perturbative QCD.

Contribution

It provides the first lattice tensor representations for gluon propagators in four dimensions and investigates the infrared behavior of three and four gluon vertices with detailed modeling.

Findings

Lattice tensor representations improve continuum deviation understanding.

Verification of Slavnov-Taylor identities on the lattice.

Evidence for zero crossing and potential ghost mass in infrared gluon behavior.

Abstract

We study the gluon sector in pure Yang-Mills theories via the computation of two, three and four point Landau gauge gluon correlation functions via LQCD using the Wilson action for Monte-Carlo simulations. The first goal was to use lattice tensor representations for the propagator in four dimensions to understand/quantify deviations of the lattice propagator from its continuum form. We also identified classes of kinematic configurations where these deviations are minimal and the continuum description of lattice tensors is improved. These tensor structures also allow to verify that the continuum Slavnov-Taylor identity for the propagator is is fulfilled, with good accuracy, on the lattice. The computation of the three gluon vertex served to explore the so-called zero crossing, a property related to the ghost dominance at the infrared scales that restricts the behaviour of the three gluon vertex. We also explore the possible existence of a ghost mass preventing the IR divergence. Functional forms were used to model the lattice data and explore the two different possibilities for the IR behaviour. In the first case we estimate the mass scale associated with the crossing and search for a possible sign of the divergence. Secondly, we study the possibility of a sign change and a finite zero momentum value of the vertex. A last topic is the calculation of the four gluon vertex. A suitable choice of kinematics allows to eliminate the unwanted contributions from lower order functions while large statistical fluctuations hinder the precise computation of this object. Our investigation is a proof of concept, we show that the lattice computation of the four gluon correlation function is feasible with reasonable computational resources. An increase in statistics is necessary to provide a clearer signal on the complete correlation function and to compute the one particle irreducible function.