Abstract
We study the phase structure and phase transition of cold dense QCD matter via the Dyson–Schwinger equation approach. We take the rainbow approximation and the Gaussian-type gluon model. In order to guarantee that the quark number density begins to appear at the nuclear liquid-gas phase transition chemical potential, we propose a chemical potential dependent modification factor for the gluon model. We find that for the iso-symmetric quark matter, the modification reduces the chemical potential of the phase coexistence region of the first-order phase transition. We also implement the relativistic mean field theory to describe the hadron matter, and make use of the Maxwell and Gibbs construction method to study the phase transition of beta -equilibrium and charge neutral matter in compact stars. The results show that the phase transition will not happen in case of the Gaussian-type gluon model without any modification. The results also indicate that the upper boundary of the coexistence region should be larger than the current Nambu solution existing region. We also calculate the mass-radius relation of the compact stars, and find that the hadron-quark phase transition happens at too high chemical potential so that the maximum mass of the compact star is hardly affected by the hadron-quark phase transition.
Highlights
At sufficiently high temperature or/and large chemical potential, since the interaction is weak, the perturbative QCD approach can provide reliable results on the property of QCD matter [52,53]
The Nambu solution corresponds to dynamical chiral symmetry breaking (DCSB) phase, since the mass function M( p) = B( p)/A( p) acquires a non-zero value
There are hints that there might exist a quarkyonic phase where the quark is confined but the chiral symmetry is preserving, it is usually believed that the DCSB (Nambu) solution corresponds to the confined hadron phase, and the DCS (Wigner) solution corresponds to the deconfined quark phase
Summary
At sufficiently high temperature or/and large chemical potential, since the interaction is weak, the perturbative QCD approach can provide reliable results on the property of QCD matter [52,53]. In this paper, we propose that a chemical potential dependent modification should be applied on the coupling strength of the model in DSE approach. Even if we correctly recover the liquid–gas phase transition chemical potential, the DSE results is not as accurate as the hadron model in describing the properties of hadron matter. In this paper, we will use the hadron model for the hadron sector, and take different construction schemes to describe the phase transition in the cold dense matter. 2, we reiterate briefly the DS equation approach at zero temperature and finite chemical potential, and propose the chemical potential dependent modification on the model.
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