Instanton effects in dense quark matter

Abstract

The equilibrium statistical mechanics of color neutral quark matter in the gas phase is discussed in QCD. The approach is framed in the grand canonical ensemble starting from the path integral representation of the thermodynamic potential Ω based on the θ-vacuum. The description of instantons is limited to the weak coupling, dilute-gas approximation. We develop the general formalism for the perturbation theory expansion of Ω in the instanton background. An approximate evaluation of the finite-density contribution of the quark determinant is attempted in order to reach a quantitative understanding of the instanton correction to the ideal gas term. We also synthesize the current understanding of the perturbative contributions to Ω, up to fourth order inclusive, drawing a distinction between renormalization schemes based on on-shell and off-shell parametrizations of quark masses. All this information on perturbative as well as instanton corrections is assembled to achieve a realistic discussion of the equilibrium properties of cold quark matter with u, d, s flavors from the nuclear saturation density out to densities an order of magnitude larger. Particular attention is devoted to the sensitivity of predictions on the basic QCD parameters, Λ and quark masses. The phase metastability of quark matter and the implications for a quark-hadron first-order phase transition are addressed from a non-dynamical point of view. A small instanton suppression correction is found with a very weak dependence on baryonic density. We also consider the sensitivity of this correction to some of the known uncertainties in the description of the instanton density.