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QCD at Finite Baryon Density: Nucleon Droplets and Color Superconductivity

M. Alford, K. Rajagopal, F. Wilczek

TL;DR

This paper studies QCD at finite baryon density using a variational approach with an instanton-inspired four-fermion interaction. It finds that the uniform phase with chiral symmetry breaking is mechanically unstable at any nonzero density, implying nucleon-like droplets of chirally restored matter and a percolation-driven chiral transition. At high density, color superconductivity arises via a diquark condensate in the color-antitriplet channel, producing a sizable Lorentz-scalar gap for two colors (and a smaller axial-vector gap for the third color), with an equation of state close to deconfined quark matter. The work outlines a coherent picture linking chiral restoration, nucleon structure, and color superconductivity, and points to extensions including strange quarks and RG analyses.

Abstract

We use a variational procedure to study finite density QCD in an approximation in which the interaction between quarks is modelled by that induced by instantons. We find that uniform states with conventional chiral symmetry breaking have negative pressure with respect to empty space at all but the lowest densities, and are therefore unstable. This is a precisely defined phenomenon which motivates the basic picture of hadrons assumed in the MIT bag model, with nucleons as droplets of chiral symmetry restored phase. At all densities high enough that the chirally symmetric phase fills space, we find that color symmetry is broken by the formation of a <qq> condensate of quark Cooper pairs. A plausible ordering scheme leads to a substantial gap in a Lorentz scalar channel involving quarks of two colors, and a much smaller gap in an axial vector channel involving quarks of the third color.

QCD at Finite Baryon Density: Nucleon Droplets and Color Superconductivity

TL;DR

This paper studies QCD at finite baryon density using a variational approach with an instanton-inspired four-fermion interaction. It finds that the uniform phase with chiral symmetry breaking is mechanically unstable at any nonzero density, implying nucleon-like droplets of chirally restored matter and a percolation-driven chiral transition. At high density, color superconductivity arises via a diquark condensate in the color-antitriplet channel, producing a sizable Lorentz-scalar gap for two colors (and a smaller axial-vector gap for the third color), with an equation of state close to deconfined quark matter. The work outlines a coherent picture linking chiral restoration, nucleon structure, and color superconductivity, and points to extensions including strange quarks and RG analyses.

Abstract

We use a variational procedure to study finite density QCD in an approximation in which the interaction between quarks is modelled by that induced by instantons. We find that uniform states with conventional chiral symmetry breaking have negative pressure with respect to empty space at all but the lowest densities, and are therefore unstable. This is a precisely defined phenomenon which motivates the basic picture of hadrons assumed in the MIT bag model, with nucleons as droplets of chiral symmetry restored phase. At all densities high enough that the chirally symmetric phase fills space, we find that color symmetry is broken by the formation of a <qq> condensate of quark Cooper pairs. A plausible ordering scheme leads to a substantial gap in a Lorentz scalar channel involving quarks of two colors, and a much smaller gap in an axial vector channel involving quarks of the third color.

Paper Structure

This paper contains 5 sections, 15 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Model
  3. Chiral Symmetry Breaking and Restoration
  4. Color Superconductivity
  5. Discussion

Figures (2)

  • Figure 1: Chiral gap (in GeV) and the pressure (in GeV$^4$) as a function of $p_F = (n \pi^2/2)^{1/3}$ in GeV. The pressure is positive at very small $p_F$; it becomes negative at a $p_F$ which is less than 0.001. At $n=n_c$, the gap vanishes and the pressure, which is still negative, has a cusp. At $n=n_0>n_c$, the pressure crosses zero and becomes positive.
  • Figure 2: Gap created by the Lorentz scalar color superconductor condensate, as a function of $\mu=p_F$ for $\nu=1$ and (from left to right) $\Lambda=0.4,0.8$ GeV. Each curve begins where $n$ is given by the appropriate $n_0$.