Non-perturbative singularity structure of gluon and quark propagators

TL;DR

This paper constructs a gauge-invariant observable in lattice gauge theory that reveals the non-perturbative singularity structure of gluon and quark propagators, enabling a definition of parton mass beyond perturbation theory.

Contribution

It introduces a gauge-invariant, non-local observable equivalent to the gluon propagator, providing a non-perturbative framework to analyze propagator singularities and parton masses.

Findings

Correlator decays exponentially with Hamiltonian eigenvalues

Reveals gauge-invariant singularity structure of propagators

Enables non-perturbative definition of parton mass

Abstract

A gauge invariant, non-local observable is constructed in lattice pure gauge theory, which is identical to the gluon propagator in a particular gauge. The transfer matrix formalism is used to show that this correlator decays exponentially with eigenvalues of the Hamiltonian. This implies a gauge invariant singularity structure of the propagator in momentum space, permitting a non-perturbative definition of a parton mass. The relation to gauge fixing and the extension to matter fields are discussed.