Ghost spectral function from the spectral Dyson-Schwinger equation

TL;DR

This paper calculates the ghost spectral function in Yang-Mills theory by solving Dyson-Schwinger equations, revealing key spectral features and the ghost dressing function across the complex plane.

Contribution

It introduces a method to compute the ghost spectral function from a given gluon spectral input, covering both scaling and decoupling solutions.

Findings

Ghost spectral function has a particle peak at zero momentum

Spectral function exhibits a negative scattering spectrum

Infrared and ultraviolet tails are analytically derived

Abstract

We compute the ghost spectral function in Yang-Mills theory by solving the corresponding Dyson-Schwinger equation for a given input gluon spectral function. The results encompass both scaling and decoupling solutions for the gluon propagator input. The resulting ghost spectral function displays a particle peak at vanishing momentum and a negative scattering spectrum, whose infrared and ultraviolet tails are obtained analytically. The ghost dressing function is computed in the entire complex plane, and its salient features are identified and discussed.