The analytic structure of the lattice Landau gauge gluon and ghost propagators

TL;DR

This paper uses Padé approximants to analyze lattice Landau gauge gluon and ghost propagators, revealing their complex poles and branch cuts, and providing insights into their analytic structure consistent with existing literature.

Contribution

It introduces a systematic Padé-based method to determine the analytic structure of propagators from lattice data, identifying poles and branch cuts.

Findings

Gluon propagator has a pair of complex conjugate poles and a branch cut.

Ghost propagator has a single pole at zero and a branch cut.

The method provides estimates consistent with previous literature.

Abstract

Starting from the lattice Landau gauge gluon and ghost propagator data we use a sequence of Pad\'e 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 Pad\'e 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 Pad\'e 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 estimates for the gluon complex poles, that agree well with other estimates found in the literature. For the branch cut the Pad\'e analysis gives, at least, a rough estimate of the corresponding branch point.