Calculation of the equation of state of QCD at finite chemical and zero temperature

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 P(µ)| µ=0 (the pressure density at µ = 0) is a µ-independent constant; the second term, which is totally determined by G R [µ](p) (the renormalized dressed quark propagator at finite µ), contains all the nontrivial µ-dependence. By applying a general result in the rainbow-ladder approximation of the Dyson-Schwinger approach obtained in our previous study [Phys. Rev. C 71, (2005)], G R [µ](p) is calculated from the meromorphic quark propagator proposed in [Phys.Rev. D 70, 014014 (2004)]. From this the full analytic expression of the EOS of QCD at finite µ and zero T is obtained (apart from the constant term P(µ)| µ=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.

Nonstrange quark stars from an NJL model with proper-time regularization

“…The model-independent equations of state of strong interaction matter at finite µ and zero T are [36,37]:…”

Nonlinear susceptibilities under the framework of Dyson-Schwinger equations

“…From the first principle of QCD theory at zero temperature and finite chemical potential, the quark-number density is determined by the dressed quark propagator at finite chemical potential only [22],…”

“…The baryon-number fluctuations, especially the variance, the skewness, and the kurtosis, are experimental observables (in this paper, the experimental data come from the STAR experiment at RHIC [21]). When studying the quark numbers at finite chemical potential by the fundamental theories of QCD, it is found that the quark-number density is determined by the corresponding dressed quark propagator only [22]. Then by generalizing this conclusion to the most universal situation of finite temperature and chemical potential [23], we can calculate the nth order susceptibilities at finite temperature and chemical potential, and compare them with the experimental data from RHIC.…”

Recent progress in theoretical nuclear physics related to large-scale scientific facilities

“…Based on the method proposed in [24], the EOS of QCD at zero temperature and finite quark chemical potential is calculated under the hard-dense-loop (HDL) approximation [25]. A comparison between the EOS under HDL approximation and the cold, perturbative EOS of QCD proposed in [26,27] is made.…”