Patterns of Symmetry Breaking in QCD at High Baryon Density

TL;DR

This paper investigates the symmetry breaking patterns in high-density QCD for various numbers of flavors, revealing that chiral symmetry remains broken at large chemical potential and identifying different breaking patterns depending on the flavor number.

Contribution

It provides a detailed analysis of symmetry breaking in high-density QCD for arbitrary flavor numbers, including calculations of order parameters and novel symmetry patterns for more than three flavors.

Findings

Chiral symmetry remains broken at high density for all flavors greater than two.

Standard symmetry breaking pattern for three flavors is confirmed, with deviations for more flavors.

Quantitative estimates of chiral order parameters show a hierarchy in their magnitudes.

Abstract

We study the structure of QCD at very large baryon density for an arbitrary number of flavors $N_f$. We provide evidence that for any number of flavors larger than $N_f=2$ chiral symmetry remains broken at asymptotically large chemical potential. For $N_c=N_f=3$, chiral symmetry breaking follows the standard pattern $SU(3)_L\times SU(3)_R\to SU(3)$, but for $N_f>3$ unusual patterns emerge. We study the case $N_f=3$ in more detail and calculate the magnitude of the chiral order parameters $<\bar\psi\psi>$ and $<(\bar\psi\psi)^2>$ in perturbative QCD. We show that, asymptotically, $<\bar\psi\psi>^{1/3}$ is much smaller than $<(\bar\psi\psi)^2>^{1/6}$. The result can be understood in terms of an approximate discrete symmetry.