Effects of a quark chemical potential on the analytic structure of the gluon propagator

TL;DR

This study analyzes how a nonzero quark chemical potential affects the analytic structure of the gluon propagator using an effective Landau-gauge Yang-Mills model, revealing new complex pole behaviors relevant to confinement.

Contribution

It introduces a detailed complex analysis of the gluon propagator at finite chemical potential within an effective model, highlighting the emergence of new complex poles.

Findings

Gluon propagator exhibits one or two pairs of complex conjugate poles depending on chemical potential.

A new pole pair appears near the real axis when chemical potential is between the effective quark and gluon masses.

Proves the uniqueness of analytic continuation of the Matsubara propagator under specified conditions.

Abstract

We perform complex analyses of the gluon propagator at nonzero quark chemical potential in the long-wavelength limit, using an effective model with a gluon mass term of the Landau-gauge Yang-Mills theory, which is a Landau-gauge limit of the Curci-Ferrari model with quantum corrections being included within the one-loop level. We mainly investigate complex poles of the gluon propagator, which could be relevant to confinement. Around typical values of the model parameters, we show that the gluon propagator has one or two pairs of complex conjugate poles depending on the value of the chemical potential. In addition to a pair similar to that in the case of zero chemical potential, a new pair appears near the real axis when the chemical potential is roughly between the effective quark mass and the effective gluon mass of the model. We discuss possible interpretations of these poles. Additionally, we prove the uniqueness of analytic continuation of the Matsubara propagator to a class of functions that vanish at infinity and are holomorphic except for a finite number of complex poles and singularities on the real axis.