Vacuum quark condensate, chiral Lagrangian, and Bose-Einstein statistics

TL;DR

This paper argues that the quark condensate is an intrinsic property of the QCD vacuum, countering recent claims that it is confined within hadrons, by analyzing the implications of the chiral Lagrangian and Bose-Einstein statistics.

Contribution

It demonstrates that the quark condensate's nature aligns with the vacuum properties, challenging recent alternative interpretations.

Findings

The quark condensate is essential for the QCD vacuum structure.

Chiral Lagrangian analysis supports the vacuum property of the condensate.

Bose-Einstein statistics of pions reinforce the vacuum interpretation.

Abstract

In a series of articles it was recently claimed that the quantum chromodynamic (QCD) condensates are not the properties of the vacuum but of the hadrons and are confined inside them. We point out that this claim is incompatible with the chiral Lagrangian and Bose-Einstein statistics of the Goldstone bosons (pions) in chiral limit and conclude that the quark condensate must be the property of the QCD vacuum.