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.
Highlights
For a long time, it has been expected that quark degrees of freedom would dominate in a highly dense matter of quantum chromodynamics (QCD) rather than hadrons, details of the phase structure are still unclear mainly due to the sign-problem [1]
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
I.e., vanishing chemical potential μq 1⁄4 0, we have investigated the analytic structures of the gluon, quark, and ghost propagators and revealed that the gluon and quark propagators have one pair of complex conjugate poles while the ghost propagator has no complex poles [29,30,31]
Summary
It has been expected that quark degrees of freedom would dominate in a highly dense matter of quantum chromodynamics (QCD) rather than hadrons, details of the phase structure are still unclear mainly due to the sign-problem [1]. If one enables the gluon mass parameter M to depend on the chemical potential, one can obtain a fair agreement between the massive Yang-Mills model and the numerical lattice results. This model may lack some important aspects, it is still worthwhile studying the analytic structure of the gluon propagator at a finite chemical potential by utilizing the massive Yang-Mills model with various model parameters. We investigate the analytic structure of the in-medium gluon propagator at finite quark chemical potential μq by employing the massive Yang-Mills model with quantum corrections being included within the oneloop level. VI, a summary of these findings and future prospects are given
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