Looking at the analytic structure of Landau gauge propagators

TL;DR

This study analyzes the analytic structure of Landau gauge propagators from lattice QCD simulations, identifying poles and branch cuts to understand their infrared behavior and complex features.

Contribution

It introduces the use of Padé approximants to identify poles and branch cuts in gluon, ghost, and quark propagators from lattice data, revealing their complex analytic structures.

Findings

Gluon propagator has complex conjugate poles and a branch point.

Ghost propagator shows a pole at zero momentum and a branch point.

Quark propagator has a Minkowski-like pole correlated with pion mass.

Abstract

We report on a study of the analytical structure of the Landau gauge gluon, ghost and quark propagators taken from lattice simulations using large physical volumes, to better access the IR region, and large gauge ensembles to reduce the statistical uncertainties. The investigation uses Pad\'e approximants to look at poles and branch cuts for each of the propagators. For the gluon propagator we identify complex conjugate poles and a branch point. For the ghost propagator the procedure identifies a pole at zero momentum and a branch point for Minkowski-like momenta. The quark propagator appears to have a pole for Minkowski-like momenta that is correlated with the pion mass as expected from PCAC.