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

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(mu)vertical bar(mu=0) (the pressure density at mu = 0) is a mu-independent constant; the second term, which is totally determined by GR[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. C 71, 015205 (2005)], G(R)[mu](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 mu and zero T is obtained (apart from the constant term P(mu)vertical bar(mu=0) which can in principle be calculated from the Cornwall-Jackiw-Tomboulis 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.