Color superconductivity and speed of sound in the two-flavor quark-meson diquark model

We discuss the properties of the two-flavor quark-meson diquark (QMD) model as a renormalizable low-energy model for QCD in the 2SC phase of QCD. The effective degrees of freedom are the mesons (sigma and pions), quarks, and diquarks. Some of the parameters of the model can be determined by expressing them in terms of the vacuum meson masses and the pion decay constant using the on-shell renormalization scheme. The remaining parameters are considered free, although they in principle can be calculated from QCD. The thermodynamic potential is calculated in a mean-field approximation taking only quark loops into account. In this approximation, we derive a set of renormalization group equations for the running masses and couplings. The solutions to these equations are used to improve the thermodynamic potential $\Omega$ and thereby thermodynamic quantities. Four parameter sets are chosen and the phase diagram in the $\bar{\mu}$--$T$ plane is obtained (with $\bar{\mu}={1\over3}\mu_B$). We also calculate the speed of sound $c_s$ as a function of $\bar{\mu}$ at vanishing temperature. For large values of $\bar{\mu}$, the speed of sound approaches the conformal limit $c_s={1\over\sqrt{3}}$ from above, in disagreement with perturbative calculations, but agreement with hard-dense-loop resummed perturbation theory.