# Spectral functions of confined particles

## TL;DR

This paper reconstructs the spectral functions of gluons and ghosts from numerical gauge correlator data, revealing a branch cut and complex conjugate poles, which have implications for understanding confined particles.

## Contribution

It introduces a novel reconstruction technique to analyze spectral functions, uncovering complex poles in gluon propagators not previously well-characterized.

## Key findings

- Gluon spectral function exhibits a branch cut and complex conjugate poles.
- Ghost spectral function shows a branch cut consistent with theoretical expectations.
- Implications for confinement and particle spectrum are discussed.

## Abstract

We determine the gluon and ghost spectral functions along with the analytic structure of the associated propagators from numerical data describing gauge correlators at space-like momenta obtained by either solving the Dyson-Schwinger equations or through lattice simulations. Our novel reconstruction technique shows the expected branch cut for the gluon and the ghost propagator, which, in the gluon case, is supplemented with a pair of complex conjugate poles. Possible implications of the existence of these poles are briefly addressed.