The calculation of the equation of state of QCD at finite chemical potential 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 ${\cal P}(\mu)|_{\mu=0}$ (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.