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

Jens O Andersen,Patrick Kneschke

doi:10.1103/physrevd.97.076005

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.

Highlights

The phases of dense QCD as functions of the baryon chemical potential μB or the quark chemical potential μ 1⁄4μB have been studied in detail since the first phase diagram was suggested in the 1970s [1,2,3]
Schemes, we have determined the parameters of the model, whose values are consistent with the approximation that we used for the effective potential
In contrast to other model calculations, where the parameters are fixed at tree level, our method guarantees that the critical isospin chemical potential at is exactly at μI

Summary

INTRODUCTION

The phases of dense QCD as functions of the baryon chemical potential μB or the quark chemical potential μ 1⁄4. In addition to chiral perturbation theory [16,17,18,19,20], there have been a number of other approaches and model calculations studying various aspects of the QCD phase diagram at finite isospin density These include the resonance gas model [21], random matrix models [22], the NJL model [23,24,25,26,27,28,29,30,31,32,33,34], the quark-meson model [35,36,37], perturbative QCD [38], and hard-thermal-loop perturbation theory [39]. Appendix C, we show that the critical isospin chemical potential is exactly in our approximation

QUARK-MESON MODEL

EFFECTIVE POTENTIAL

Homogeneous chiral condensate

Inhomogeneous chiral condensate versus homogeneous pion condensate

SUMMARY