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

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