Renormalization group invariant mean-field model for QCD at finite isospin density

QCD at nonzero isospin chemical potentials has phenomenological relevance for a series of physical systems and provides an ideal test ground for the modeling of dense, strongly interacting matter. The two-flavor quark-meson model is known to effectively describe the condensation of charged pions in QCD that occurs in this setting. In this paper, we derive a renormalization group invariant mean-field formulation of the model and demonstrate that the resulting phase diagram and equation of state are in quantitative agreement with data from lattice QCD simulations at small and intermediate isospin chemical potentials. In particular, the speed of sound from the model shows an excess over the conformal bound, as previously seen in lattice computations, in agreement with chiral perturbation theory. We then consider the speed of sound in the limit of large isospin chemical potentials and see that it approaches the conformal limit from above, in qualitative agreement with recent lattice results and in quantitative agreement with perturbation theory in the presence of a Bardeen-Cooper-Schrieffer gap. Finally, we consider the phase diagram in the approach to the chiral limit. We find that within the model, the chiral phase transition connects to the pion condensation phase boundary in the chiral limit and we discuss the implications for the properties of the chiral transition point.