The calculation of the equation of state of QCD at finite chemical potential and zero temperature

TL;DR

This paper presents a direct method to calculate the QCD equation of state at finite chemical potential and zero temperature, using Dyson-Schwinger equations and a meromorphic quark propagator, with potential applications to neutron star studies.

Contribution

The paper introduces an analytic expression for the QCD EOS at finite chemical potential and zero temperature based on Dyson-Schwinger equations and a meromorphic quark propagator, advancing previous approaches.

Findings

Derived full analytic EOS of QCD at finite μ and T=0.

Compared EOS with perturbative QCD results.

Provided a new approach for neutron star research.

Abstract

In this paper, we give a direct method for calculating the partition function, and hence the equation of state (EOS) of Quantum Chromodynamics (QCD) at finite chemical potential and zero temperature. In the EOS derived in this paper the pressure density is the sum of two terms: the first term ${\cal P}(\mu)|_{\mu=0}$ (the pressure density at $\mu=0$) is a $\mu$-independent constant; the second term, which is totally determined by $G_R[\mu](p)$ (the renormalized dressed quark propagator at finite $\mu$), contains all the nontrivial $\mu$-dependence. By applying a general result in the rainbow-ladder approximation of the Dyson-Schwinger approach obtained in our previous study [Phys. Rev. {\bf C 71}, 015205 (2005)], $G_R[\mu](p)$ is calculated from the meromorphic quark propagator proposed in [Phys. Rev. {\bf D 70}, 014014 (2004)]. From this the full analytic expression of the EOS of QCD at finite $\mu$ and zero $T$ is obtained (apart from the constant term ${\cal P}(\mu)|_{\mu=0}$ which can in principle be calculated from the CJT effective action). A comparison between our EOS and the cold, perturbative EOS of QCD of Fraga, Pisarski and Schaffner-Bielich is made. It is expected that our EOS can provide a possible new approach for the study of neutron stars.