Chiral density wave versus pion condensation at finite density and zero temperature

The quark-meson model is often used as a low-energy effective model for QCD to study the chiral transition at finite temperature T, baryon chemical potential μB, and isospin chemical potential μI. We determine the parameters of the model by matching the meson and quark masses, as well as the pion decay constant to their physical values using the on shell (OS) and modified minimal subtraction (MS) schemes. In this paper, the existence of different phases at zero temperature is studied. In particular, we investigate the competition between an inhomogeneous chiral condensate and a homogeneous pion condensate. For the inhomogeneity, we use a chiral-density wave ansatz. For a sigma mass of 600 MeV, we find that an inhomogeneous chiral condensate exists only for pion masses below approximately 37 MeV. We also show that due to our parameter fixing, the onset of pion condensation takes place exactly at μc I ¼ 1 2mπ in accordance with exact results.publishedVersio