Phases of QCD with nonvanishing isospin density

The propagation of low-momentum baryons through QCD matter at low isospin density is studied using chiral perturbation theory. When the isospin chemical potential exceeds a critical value, the dispersion relation for the lowest nucleon mode becomes anomalous near zero momentum — increasing momentum yields decreasing energy — so that the momentum for the lowest energy state, pmin, becomes nonzero. This can be interpreted as a new phase of QCD, with pmin serving as the order parameter and the kinetic mass (defined as the inverse of the second derivative of the energy with respect to the momentum at pmin) serving as the susceptibility. A lowest-order chiral-perturbation-theory calculation yields a critical isospin chemical potential of ∼285 MeV. Since this is small compared to the chiral-symmetry-breaking scale, corrections to it are likely to be modest.