Chiral density wave versus pion condensation at finite density

TL;DR

This paper explores the competition between inhomogeneous chiral condensates and pion condensation at zero temperature within the quark-meson model, revealing conditions under which each phase occurs and confirming theoretical expectations for pion condensation onset.

Contribution

It introduces a detailed analysis of phase competition at zero temperature using a chiral-density wave ansatz and confirms the pion condensation threshold within the model.

Findings

Inhomogeneous chiral condensate exists only for pion masses below ~37 MeV.

Pion condensation onset occurs at half the pion mass, consistent with theoretical predictions.

The model parameters are fixed to physical meson and quark masses, ensuring realistic results.

Abstract

The quark-meson model is often used as an effective low-energy model for QCD to study the chiral transition at finite temperature $T$, baryon chemical potential $\mu_B$, and isospin chemical potential $\mu_I$. The parameters of the model are determined by matching the meson and quark masses, as well as the pion decay constant to their physical values using the on-shell and modified minimal subtraction schemes. In this paper, we study the possibility of different phases at zero temperature. In particular, we investigate the competition between an inhomogeneous chiral condensate and a 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 exist 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 $\mu_I={1\over2}m_{\pi}$ in accordance with exact results.