Phases of QCD with nonvanishing isopin 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, p_min, becomes nonzero. This can be interpreted as a new phase of QCD, with p_min 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 p_min) 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.