Dyson–Schwinger equation and quantum phase transitions in massless QCD

Wei Yuan,Huan Chen,Yu-Xin Liu

doi:10.1016/j.physletb.2006.03.076

Abstract

We study the stability of the highest symmetric solution (Wigner-solution) of Dyson–Schwinger equations in chiral limit and at zero temperature. Our results confirm that if the chemical potential is not very large, the QCD vacuum is in the chiral symmetry breaking phase and the quantum phase-transition of the chiral symmetry restoration is in first order. Meanwhile, it seems that there is not competition between chiral breaking phase and color superconductivity phase since the color superconductivity phase appears only if the chemical potential is very large. Moreover, we propose that chiral symmetry breaking arises from the positive feedback with respect to the mass perturbation.

Highlights

Within Feynman’s framework, one can derive a series of dynamical integralequations (Dyson-Schwinger equations)[5] and a series of identities which come from the symmetries
As we will see at below, the fact that chiral susceptibility of Wigner mass function in the chiral limit is negative indicates the chiral-symmetry breaking of the QCD vacuum in a natural sense, and the restoration of chiral symmetry is closely related to the presence of positive chiral susceptibility beyond some critical chemical potential
Flavor has nothing to do with dynamics, the gapped flavor channel should be chosen to leave the maximal unbroken symmetries [1], such as Ψiαǫ1αβǫijγ5CΨjβ in case of two flavors and ΨiαǫA αβǫAijγ5CΨjβ in case of three flavors(α, β are color indexes and i, j are flavor indexes), which are the well known two-flavor color superconductivity (2CS) and color flavor locking (CFL) channels, respectively. All these considerations, which do not change the equations of the susceptibilities in chiral limit, are nontrivial in case of real mass spectrum of {u, d, s} quarks because it has strongly indicated a transition from the 2CS phase to the CFL phase at some relatively high chemical potential

Summary

Introduction

Within Feynman’s framework, one can derive a series of dynamical integralequations (Dyson-Schwinger equations)[5] and a series of identities which come from the symmetries. As we will see at below, the fact that chiral susceptibility of Wigner mass function in the chiral limit is negative indicates the chiral-symmetry breaking of the QCD vacuum in a natural sense, and the restoration of chiral symmetry is closely related to the presence of positive chiral susceptibility beyond some critical chemical potential.

Results

Conclusion